60983300 2 sim hydraulics reference

SimHydraulics® 1Reference

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Revision HistoryMarch 2006 Online only New for Version 1.0 (Release 2006a+)September 2006 Online only Revised for Version 1.1 (Release 2006b)March 2007 Online only Revised for Version 1.2 (Release 2007a)September 2007 Online only Revised for Version 1.2.1 (Release 2007b)March 2008 Online only Revised for Version 1.3 (Release 2008a)October 2008 Online only Revised for Version 1.4 (Release 2008b)March 2009 Online only Revised for Version 1.5 (Release 2009a)

Contents

Block Reference1

Accumulators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-2

Hydraulic Cylinders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-3

Hydraulic Utilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-4

Local Hydraulic Resistances . . . . . . . . . . . . . . . . . . . . . . . . 1-5

Low-Pressure Blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-6

Orifices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-7

Pipelines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-8

Pumps and Motors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-9

Valves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-10Directional Valves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-10Flow Control Valves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-10Pressure Control Valves . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-11Valve Actuators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-11Valve Forces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1-12

v

Blocks — Alphabetical List

2

Glossary

Index

vi Contents

1

Block Reference

Accumulators (p. 1-2) Hydraulic accumulatorsHydraulic Cylinders (p. 1-3) Hydraulic cylindersHydraulic Utilities (p. 1-4) Environment blocks, such as

hydraulic fluidLocal Hydraulic Resistances (p. 1-5) Various local hydraulic resistancesLow-Pressure Blocks (p. 1-6) Low-pressure blocksOrifices (p. 1-7) Hydraulic orifices, to be used as

valve building blocksPipelines (p. 1-8) Hydraulic pipelinesPumps and Motors (p. 1-9) Hydraulic pumps and motorsValves (p. 1-10) Hydraulic valves

1 Block Reference

Accumulators

Gas-Charged Accumulator Simulate hydraulic accumulatorwith gas as compressible medium

Spring-Loaded Accumulator Simulate hydraulic accumulatorwith spring used for energy storage

1-2

Hydraulic Cylinders

Hydraulic Cylinders

Cylinder Friction Simulate friction in hydrauliccylinders

Double-Acting Hydraulic Cylinder Simulate hydraulic actuator exertingforce in both directions

Double-Acting Rotary Actuator Simulate double-acting hydraulicrotary actuator

Single-Acting Hydraulic Cylinder Simulate hydraulic actuator exertingforce in one direction

Single-Acting Rotary Actuator Simulate single-acting hydraulicrotary actuator

1-3

1 Block Reference

Hydraulic UtilitiesHydraulic Fluid Set working fluid properties by

selecting from list of predefinedfluids

Reservoir Simulate pressurized hydraulicreservoir

1-4

Local Hydraulic Resistances

Local Hydraulic ResistancesElbow Simulate hydraulic resistance in

elbowGradual Area Change Simulate gradual enlargement or

contractionLocal Resistance Simulate all kinds of hydraulic

resistances specified by losscoefficient

Pipe Bend Simulate hydraulic resistance inpipe bend

Sudden Area Change Simulate sudden enlargement orcontraction

T-junction Simulate hydraulic resistance ofT-junction in pipe

1-5

1 Block Reference

Low-Pressure Blocks

Constant Head Tank Simulate tank where pressurizationand fluid level remain constantregardless of volume change

Hydraulic Pipe LP Simulate hydraulic pipeline withresistive, fluid compressibility, andelevation properties

Resistive Pipe LP Simulate hydraulic pipeline whichaccounts for friction losses and portelevations

Segmented Pipe LP Simulate hydraulic pipelinewith resistive, fluid inertia, fluidcompressibility, and elevationproperties

Variable Head Tank Simulate tank withconstant pressurization andvolume-dependent fluid level

1-6

Orifices

Orifices

Annular Orifice Simulate hydraulic variable orificecreated by circular tube and roundinsert

Fixed Orifice Simulate hydraulic orifice withconstant cross-sectional area

Orifice with Variable Area RoundHoles

Simulate hydraulic variable orificeshaped as set of round holes drilledin sleeve

Orifice with Variable Area Slot Simulate hydraulic variable orificeshaped as rectangular slot

Variable Orifice Simulate generic hydraulic variableorifice

1-7

1 Block Reference

PipelinesHydraulic Pipeline Simulate hydraulic pipeline with

resistive and fluid compressibilityproperties

Segmented Pipeline Simulate hydraulic pipeline withresistive, fluid inertia, and fluidcompressibility properties

1-8

Pumps and Motors

Pumps and Motors

Centrifugal Pump Simulate centrifugal pumpFixed-Displacement Pump Simulate fixed-displacement

hydraulic pumpHydraulic Motor Simulate fixed-displacement

hydraulic motorVariable-Displacement HydraulicMachine

Simulate variable-displacementreversible hydraulic machine withregime-dependable efficiency

Variable-Displacement Motor Simulate variable-displacementreversible hydraulic motor

Variable-DisplacementPressure-Compensated Pump

Simulate hydraulic pumpmaintaining preset pressure atoutlet by regulating its flow delivery

Variable-Displacement Pump Simulate variable-displacementreversible hydraulic pump

1-9

1 Block Reference

Valves

Directional Valves (p. 1-10) Hydraulic directional valvesFlow Control Valves (p. 1-10) Hydraulic flow control valvesPressure Control Valves (p. 1-11) Hydraulic pressure control valvesValve Actuators (p. 1-11) Actuators for driving directional

valvesValve Forces (p. 1-12) Blocks that simulate hydraulic

forces exerted on valves

Directional Valves

2-Way Directional Valve Simulate hydraulic continuous2-way directional valve



Cartridge Valve Insert Simulate hydraulic cartridge valveinsert

Check Valve Simulate hydraulic valve that allowsflow in one direction only

Pilot-Operated Check Valve Simulate hydraulic check valve thatallows flow in one direction, but canbe disabled by pilot pressure

Shuttle Valve Simulate hydraulic valve that allowsflow in one direction only

Flow Control Valves

Ball Valve Simulate hydraulic ball valveNeedle Valve Simulate hydraulic needle valve

1-10

Valves

Poppet Valve Simulate hydraulic poppet valvePressure-Compensated Flow ControlValve

Simulate hydraulic pressurecompensating valve

Pressure Control Valves

Pressure Compensator Simulate hydraulic pressurecompensating valve

Pressure Reducing Valve Simulate pressure control valvemaintaining reduced pressure inportion of system

Pressure Relief Valve Simulate pressure control valvemaintaining preset pressure insystem

Valve Actuators

2-Position Valve Actuator Simulate actuator for two-positionvalves

3-Position Valve Actuator Simulate actuator for three-positionvalves

Hydraulic Cartridge Valve Actuator Simulate double-acting hydraulicactuator for cartridge valves

Hydraulic Double-Acting ValveActuator

Simulate double-acting hydraulicvalve actuator

Hydraulic Single-Acting ValveActuator

Simulate single-acting hydraulicvalve actuator

Proportional and Servo-ValveActuator

Simulate continuous valve driverwith output proportional to inputsignal

1-11

1 Block Reference

Valve Forces

Spool Orifice Hydraulic Force Simulate axial hydraulic forceexerted on spool

Valve Hydraulic Force Simulate axial hydraulic static forceexerted on valve

1-12

2

Blocks — Alphabetical List

2-Position Valve Actuator

Purpose Simulate actuator for two-position valves

Library Valve Actuators

Description The 2-Position Valve Actuator block represents an actuator that you canuse with directional valves to control their position. This actuator candrive a two-position valve. The block is developed as a data-sheet-basedmodel and all its parameters are generally provided in catalogs or datasheets. The key parameters are the stroke, switch-on, and switch-offtimes.

The block accepts a physical input signal and produces a physicaloutput signal that can be associated with a mechanical translational orrotational push-pin motion. Connect the block output to the directionalvalve control port.

The actuator is represented as an ideal transducer, where outputdoes not depend on the load exerted on the push-pin and the push-pinmotion profile remains the same under any loading conditions. Themotion profile represents a typical transition curve for electromagneticactuators and is shown in the following figure:

2-2


The push-pin is actuated when the input signal value crosses thethreshold of 50% of the nominal input signal, where Nominal signalvalue is a block parameter. The motion is divided into three phases,equal in time: delay (t1), motion at constant acceleration (t2), andmotion at constant velocity (t3). The motion stops when the switch-ontime (ton) elapses. At this moment, the push-pin reaches the specifiedstroke value (xstr). To return the push-pin into initial position, thecontrol signal must be removed, which causes the push-pin to retract.The retract motion follows exactly the same profile but “stretches” over

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the switch-off time. Switching-on time and Switching-off time arethe block parameters.

The transition in any direction can be interrupted at any time bychanging the input signal. If motion is interrupted, the switch-onor switch-off times are proportionally decreased depending on theinstantaneous push-pin position.

The push-pin is actuated only by positive signal, similar to the AC or DCelectromagnets. The direction of push-pin motion is controlled by theActuator orientation parameter, which can have one of two values:Acts in positive direction or Acts in negative direction.

BasicAssumptionsandLimitations

The model is based on the following assumption:

• Push-pin loading, such as inertia, spring, hydraulic forces, and so on,is not taken into account.

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DialogBox andParameters

Push-pin strokeThe push-pin stroke. The default value is 0.01 m.

Switching-on timeTime necessary to fully extend the push-pin after the controlsignal is applied. The default value is 0.1 s.

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Switching-off timeTime necessary to retract push-pin from fully extended positionafter the input signal is removed. The default value is 0.1 s.

Nominal signal valueSets the value of the nominal input signal. The output motion isinitiated as the input signal crosses 50% value of the nominalsignal. Other than that, the input signal has no effect on themotion profile. This parameter is meant to reproduce the ratedvoltage feature of an electromagnet. The default value is 24.

Initial positionSpecifies the initial position of the push-pin. The parameter canhave one of two values: Extended or Retracted. The defaultvalue is Retracted.

Actuator orientationParameter controls the direction of the push-pin motion and canhave one of two values: Acts in positive direction or Actsin negative direction. The first value causes the push-pin tomove in positive direction, similarly to the action of electromagnetA attached to a directional valve. If the parameter is set to Actsin negative direction, the control signal causes the push-pinto move in negative direction from the initial position. The defaultvalue is Acts in positive direction.

Restricted Parameters

When your model is in Restricted editing mode, you cannot modify thefollowing parameters:

• Initial position

• Actuator orientation

All other block parameters are available for modification.

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Ports The block has one physical signal input port, associated with the inputsignal, and one physical signal output port, associated with the outputsignal (push-pin displacement).

Examples In the 2-Position Valve Actuator demo (sh_2_pos_valve_actuator),the hydraulic circuit contains two actuators. The first one is set tostart from the retracted position, while the second one starts from theextended position. Both actuators are driven with a Pulse Generator.The actuators start extending at 1 s, but the second actuator firstretracts from 0.01 m to zero, since it was initially extended and therewas no signal keeping it there.

In the Hydraulic Circuit with Single-Acting Cylinder demo(sh_circuit_sa_cylinder), the 2-Position Valve Actuator block is usedalong with a 3-Way Directional Valve block to simulate an electricallyoperated 3-way directional valve.

See Also 3-Position Valve Actuator

Hydraulic Double-Acting Valve Actuator

Hydraulic Single-Acting Valve Actuator

Proportional and Servo-Valve Actuator

2-7

2-Way Directional Valve

Purpose Simulate hydraulic continuous 2-way directional valve

Library Directional Valves

Description The 2-Way Directional Valve block represents a continuous, 2-waydirectional valve, also referred to as a shut-off valve. It is the devicethat controls the connection between two lines. The block has twohydraulic connections, corresponding to inlet port (P) and outlet port(A), and one physical signal port connection (S), which controls thespool position. The block is built based on a Variable Orifice block,where the Orifice orientation parameter is set to Opens in positivedirection. This means that positive signal x at port S opens the orifice,and its instantaneous opening h is computed as follows:

h x x= +0

where

h Orifice openingx0 Initial openingx Control member displacement from initial position

Because the block is based on a variable orifice, you can choose one ofthe following model parameterization options:

• By maximum area and opening— Use this option if the data sheetprovides only the orifice maximum area and the control membermaximum stroke.

• By area vs. opening table — Use this option if the catalog ordata sheet provides a table of the orifice passage area based on thecontrol member displacement A=A(h).

• By pressure-flow characteristic— Use this option if the catalogor data sheet provides a two-dimensional table of the pressure-flowcharacteristics q=q(p,h).

2-8


In the first case, the passage area is assumed to be linearly dependenton the control member displacement, that is, the orifice is assumed to beclosed at the initial position of the control member (zero displacement),and the maximum opening takes place at the maximum displacement.In the second case, the passage area is determined by one-dimensionalinterpolation from the table A=A(h). Flow rate is determinedanalytically, which additionally requires data such as flow dischargecoefficient, critical Reynolds number, and fluid density and viscosity.The computation accounts for the laminar and turbulent flow regimesby monitoring the Reynolds number and comparing its value with thecritical Reynolds number. See the Variable Orifice block reference pagefor details. In both cases, a small leakage area is assumed to exist evenafter the orifice is completely closed. Physically, it represents a possibleclearance in the closed valve, but the main purpose of the parameter isto maintain numerical integrity of the circuit by preventing a portion ofthe system from getting isolated after the valve is completely closed.An isolated or “hanging” part of the system could affect computationalefficiency and even cause failure of computation.

In the third case, when an orifice is defined by its pressure-flowcharacteristics, the flow rate is determined by two-dimensionalinterpolation. In this case, neither flow regime nor leakage flowrate is taken into account, because these features are assumed to beintroduced through the tabulated data. Pressure-flow characteristicsare specified with three data sets: array of orifice openings, array ofpressure differentials across the orifice, and matrix of flow rate values.Each value of a flow rate corresponds to a specific combination of anopening and pressure differential. In other words, characteristics mustbe presented as the Cartesian mesh, i.e., the function values mustbe specified at vertices of a rectangular array. The argument arrays(openings and pressure differentials) must be strictly monotonicallyincreasing. The vertices can be nonuniformly spaced. You have a choiceof three interpolation methods and two extrapolation methods.

The block positive direction is from port A to port B. This means that theflow rate is positive if it flows from A to B and the pressure differential

2-9


is determined as p p pA B= − . Positive signal at the physical signalport S opens the valve.


The model is based on the following assumptions:

• Fluid inertia is not taken into account.

• Spool loading, such as inertia, spring, hydraulic forces, and so on,is not taken into account.


2-10


2-11


Model parameterizationSelect one of the following methods for specifying the valve:

• By maximum area and opening — Provide values for themaximum valve passage area and the maximum valve opening.The passage area is linearly dependent on the control memberdisplacement, that is, the valve is closed at the initial positionof the control member (zero displacement), and the maximumopening takes place at the maximum displacement. This isthe default method.

2-12


• By area vs. opening table — Provide tabulated data ofvalve openings and corresponding valve passage areas. Thepassage area is determined by one-dimensional table lookup.You have a choice of three interpolation methods and twoextrapolation methods.

• By pressure-flow characteristic— Provide tabulated dataof valve openings, pressure differentials, and correspondingflow rates. The flow rate is determined by two-dimensionaltable lookup. You have a choice of three interpolation methodsand two extrapolation methods.

Valve passage maximum areaSpecify the area of a fully opened valve. The parameter valuemust be greater than zero. The default value is 5e-5 m^2. Thisparameter is used if Model parameterization is set to Bymaximum area and opening.

Valve maximum openingSpecify the maximum displacement of the control member. Theparameter value must be greater than zero. The default value is5e-3 m. This parameter is used if Model parameterization isset to By maximum area and opening.

Tabulated valve openingsSpecify the vector of input values for valve openings as atabulated 1-by-m array. The input values vector must be strictlymonotonically increasing. The values can be nonuniformlyspaced. You must provide at least three values. The defaultvalues, in meters, are [-0.002 0 0.002 0.005 0.015]. IfModelparameterization is set to By area vs. opening table, theTabulated valve openings values will be used together withTabulated valve passage area values for one-dimensional tablelookup. IfModel parameterization is set to By pressure-flowcharacteristic, the Tabulated valve openings values willbe used together with Tabulated pressure differentials andTabulated flow rates for two-dimensional table lookup.

2-13


Tabulated valve passage areaSpecify the vector of output values for valve passage area as atabulated 1-by-m array. The valve passage area vector must bethe same size as the valve openings vector. All the values mustbe positive. The default values, in m^2, are [1e-09 2.0352e-074.0736e-05 0.00011438 0.00034356]. This parameter is usedif Model parameterization is set to By area vs. openingtable.

Tabulated pressure differentialsSpecify the vector of input values for pressure differentials as atabulated 1-by-n array. The input values vector must be strictlymonotonically increasing. The values can be nonuniformly spaced.You must provide at least three values. The default values, inPa, are [-1e+07 -5e+06 -2e+06 2e+06 5e+06 1e+07]. Thisparameter is used if Model parameterization is set to Bypressure-flow characteristic.

Tabulated flow ratesSpecify the output values for flow rates as a tabulated m-by-nmatrix, defining the function values at the input grid vertices.Each value in the matrix specifies flow rate taking place at aspecific combination of valve opening and pressure differential.The matrix size must match the dimensions defined by the inputvectors. The default values, in m^3/s, are:

[-1e-07 -7.0711e-08 -4.4721e-08 4.4721e-08 7.0711e-08 1e-07;

-2.0352e-05 -1.4391e-05 -9.1017e-06 9.1017e-06 1.4391e-05 2.0352e-05;

-0.0040736 -0.0028805 -0.0018218 0.0018218 0.0028805 0.0040736;

-0.011438 -0.0080879 -0.0051152 0.0051152 0.0080879 0.011438;

-0.034356 -0.024293 -0.015364 0.015364 0.024293 0.034356;]

This parameter is used if Model parameterization is set to Bypressure-flow characteristic.

Interpolation methodSelect one of the following interpolation methods forapproximating the output value when the input value is betweentwo consecutive grid points:

2-14


• Linear — For one-dimensional table lookup (By areavs. opening table), uses a linear interpolation function.For two-dimensional table lookup (By pressure-flowcharacteristic), uses a bilinear interpolation algorithm,which is an extension of linear interpolation for functions intwo variables.

• Cubic — For one-dimensional table lookup (By areavs. opening table), uses the Piecewise Cubic HermiteInterpolation Polinomial (PCHIP). For two-dimensional tablelookup (By pressure-flow characteristic), uses the bicubicinterpolation algorithm.

• Spline — For one-dimensional table lookup (By area vs.opening table), uses the cubic spline interpolation algorithm.For two-dimensional table lookup (By pressure-flowcharacteristic), uses the bicubic spline interpolationalgorithm.

For more information on interpolation algorithms, see the PSLookup Table (1D) and PS Lookup Table (2D) block referencepages.

Extrapolation methodSelect one of the following extrapolation methods for determiningthe output value when the input value is outside the rangespecified in the argument list:

• From last 2 points— Extrapolates using the linear method(regardless of the interpolation method specified), based onthe last two output values at the appropriate end of the range.That is, the block uses the first and second specified outputvalues if the input value is below the specified range, and thetwo last specified output values if the input value is above thespecified range.

• From last point— Uses the last specified output value at theappropriate end of the range. That is, the block uses the lastspecified output value for all input values greater than the last

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specified input argument, and the first specified output valuefor all input values less than the first specified input argument.

For more information on extrapolation algorithms, see the PSLookup Table (1D) and PS Lookup Table (2D) block referencepages.

Flow discharge coefficientSemi-empirical parameter for valve capacity characterization. Itsvalue depends on the geometrical properties of the valve, andusually is provided in textbooks or manufacturer data sheets.The default value is 0.7.

Initial openingOrifice initial opening. The parameter can be positive(underlapped orifice), negative (overlapped orifice), or equal tozero for zero lap configuration. The default value is 0.

Critical Reynolds numberThe maximum Reynolds number for laminar flow. The transitionfrom laminar to turbulent regime is supposed to take placewhen the Reynolds number reaches this value. The valueof the parameter depends on orifice geometrical profile, andthe recommendations on the parameter value can be found inhydraulic textbooks. The default value is 12.

Leakage areaThe total area of possible leaks in the completely closed valve.The main purpose of the parameter is to maintain numericalintegrity of the circuit by preventing a portion of the system fromgetting isolated after the valve is completely closed. An isolated or“hanging” part of the system could affect computational efficiencyand even cause failure of computation. Extreme caution shouldbe exercised if the parameter is set to 0. The default value is1e-12 m^2.

2-16




• Model parameterization

• Interpolation method

• Extrapolation method

All other block parameters are available for modification. The actualset of modifiable block parameters depends on the value of the Modelparameterization parameter at the time the model entered Restrictedmode.

GlobalParameters

Fluid densityThe parameter is determined by the type of working fluid selectedfor the system under design. Use the Hydraulic Fluid block or theCustom Hydraulic Fluid block to specify the fluid properties.

Fluid kinematic viscosityThe parameter is determined by the type of working fluid selectedfor the system under design. Use the Hydraulic Fluid block or theCustom Hydraulic Fluid block to specify the fluid properties.

Ports The block has the following ports:

AHydraulic conserving port associated with the valve inlet.

BHydraulic conserving port associated with the valve outlet.

SPhysical signal port to control spool displacement.

Examples In the Hydraulic Closed-Loop Circuit with 2-Way Valve demo(sh_closed_loop_circuit_2_way_valve), the 2-Way Directional Valve

2-17


block is used to control the position of a double-acting cylinder. At thestart of simulation, the valve is open by 0.42 mm to make the circuitinitial position as close as possible to its neutral position.

See Also 3-Way Directional Valve


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Purpose Simulate actuator for three-position valves


Description The 3-Position Valve Actuator block represents an actuator thatyou can use with directional valves to control their position. Thisactuator can drive a three-position valve. The block is developed as adata-sheet-based model and all its parameters are generally provided incatalogs or data sheets. The key parameters are the stroke, switch-on,and switch-off times.

The block has two signal inputs associated with the activation signalsfor electromagnets A or B. It produces a physical output signal that canbe associated with a mechanical translational or rotational push-pinmotion. Connect the block output to the directional valve control port.

The actuator is represented as an ideal transducer, where outputdoes not depend on the load exerted on the push-pin and the push-pinmotion profile remains the same under any loading conditions. Themotion profile represents a typical transition curve for electromagneticactuators. The following figure shows the motion profile for a case whenthe input signal is applied long enough for the push-pin to reach the endof the stroke (xstr), and then the input signal is removed, causing thepush-pin to return to initial position:

2-19


The push-pin is actuated when the input signal value crosses thethreshold of 50% of the nominal input signal, where Nominal signalvalue is a block parameter. The motion is divided into three phases,equal in time: delay (tde), motion at constant acceleration (tae), andmotion at constant velocity (tve). The motion stops when the switch-ontime (ton) elapses. At this moment, the push-pin reaches the specifiedstroke value (xstr). To return the push-pin into initial position, thecontrol signal must be removed, which causes the push-pin to retract.The retract motion also consists of three phases, equal in time: delay(tdr), motion at constant acceleration (tar), and motion at constantvelocity (tvr). It follows exactly the same profile but “stretches” overthe switch-off time. Switching-on time and Switching-off time arethe block parameters.

The signal applied to port A causes the output to move in positivedirection. To shift the push-pin in negative direction, you must applythe signal to port B. Only one control signal can be applied at a time.This means that if the actuator is being controlled by the signal at portA, the push-pin must be allowed to return to initial position before thecontrol signal at port B can be processed. The transition in any directioncan be interrupted at any time by changing the input signal. If motion

2-20


is interrupted, the switch-on or switch-off times are proportionallydecreased depending on the instantaneous push-pin position.

Only positive signals activate the actuator. In other words, negativesignals at ports A and B have no effect on the actuator, which is similarto the behavior of electromagnetically controlled 3-position directionalvalves.



• Push-pin loading, such as inertia, spring, hydraulic forces, and so on,is not taken into account.

2-21



Push-pin strokeThe push-pin stroke. The default value is 0.01 m.

Switching-on timeTime necessary to fully extend the push-pin after the controlsignal is applied. The default value is 0.1 s.

Switching-off timeTime necessary to retract push-pin from fully extended positionafter the input signal is removed. The default value is 0.1 s.

2-22


Nominal signal valueSets the value of the nominal input signal. The output motion isinitiated as the input signal crosses 50% value of the nominalsignal. Other than that, the input signal has no effect on themotion profile. This parameter is meant to reproduce the ratedvoltage feature of an electromagnet. The default value is 24.

Initial positionSpecifies the initial position of the push-pin. The parametercan have one of three values: Extended positive, Extendednegative, or Neutral. The default value is Neutral.


When your model is in Restricted editing mode, you cannot modify thefollowing parameter:

• Initial position



APhysical signal input port associated with the port A input signal.

BPhysical signal input port associated with the port B input signal.

The block also has one physical signal output port, which is associatedwith the output signal (push-pin displacement).

Examples In the 3-Position Valve Actuator demo (sh_3_pos_valve_actuator),all three actuators are set to different strokes, switch-on and switch-offtimes, and initial positions. If the initial position is not Neutral and thecontrol signal at the beginning of simulation equals zero, the push-pinstarts moving towards neutral position, as the actuators A and C showin the demo.

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2-24




Description The 3-Way Directional Valve block represents a continuous,symmetrical, 3-way directional valve. The fluid flow is pumped in thevalve through the inlet line and is distributed between an outsidepressure line (usually connected to a single-acting actuator) and thereturn line. The block has three hydraulic connections, correspondingto inlet port (P), actuator port (A), and return port (T), and one physicalsignal port connection (S), which controls the spool position. The blockis built of two Variable Orifice blocks, connected as shown in thefollowing diagram.

One Variable Orifice block, called orifice_PA, is installed in the P-Apath. The second Variable Orifice block, called orifice_AT, is installedin the A-T path. Both blocks are controlled by the same positionsignal, provided through the physical signal port S, but the Orificeorientation parameter in the block instances is set in such a way thatpositive signal at port S opens orifice_PA and closes orifice_AT. As aresult, the openings of the orifices are computed as follows:

2-25


h h xPA PA= +0

h h xAT AT= −0

where

hPA Orifice opening for the orifice_PA blockhAT Orifice opening for the orifice_AT blockhPA0 Initial opening for the orifice_PA blockhAT0 Initial opening for the orifice_AT blockx Control member displacement from initial position

The valve simulated by the 3-Way Directional Valve block is assumed tobe symmetrical. This means that both orifices are of the same shapeand size and are parameterized with the same method. You can chooseone of the following block parameterization options:




In the first case, the passage area is assumed to be linearly dependenton the control member displacement, that is, the orifice is assumed to beclosed at the initial position of the control member (zero displacement),and the maximum opening takes place at the maximum displacement.In the second case, the passage area is determined by one-dimensionalinterpolation from the table A=A(h). Flow rate is determinedanalytically, which additionally requires data such as flow discharge

2-26


coefficient, critical Reynolds number, and fluid density and viscosity.The computation accounts for the laminar and turbulent flow regimesby monitoring the Reynolds number and comparing its value with thecritical Reynolds number. See the Variable Orifice block reference pagefor details. In both cases, a small leakage area is assumed to exist evenafter the orifice is completely closed. Physically, it represents a possibleclearance in the closed valve, but the main purpose of the parameter isto maintain numerical integrity of the circuit by preventing a portion ofthe system from getting isolated after the valve is completely closed.An isolated or “hanging” part of the system could affect computationalefficiency and even cause failure of computation.


If you need to simulate a nonsymmetrical 3-way valve (i.e., withdifferent orifices), use any of the variable orifice blocks from theBuilding Blocks library (such as Orifice with Variable Area RoundHoles, Orifice with Variable Area Slot, or Variable Orifice) and connectthem the same way as the Variable Orifice blocks in the schematicdiagram of this 3-Way Directional Valve block.

Positive signal at the physical signal port S opens the orifice in the P-Apath and closes the orifice in the A-T path. The directionality of nestedblocks is clear from the schematic diagram.

2-27






• Only symmetrical configuration of the valve is considered. In otherwords, both orifices are assumed to have the same shape and size.


2-28


2-29



• By maximum area and opening — Provide values for themaximum valve passage area and the maximum valve opening.The passage area is linearly dependent on the control memberdisplacement, that is, the valve is closed at the initial positionof the control member (zero displacement), and the maximum

2-30


opening takes place at the maximum displacement. This isthe default method.





Tabulated valve openingsSpecify the vector of input values for valve openings as atabulated 1-by-m array. The input values vector must be strictlymonotonically increasing. The values can be nonuniformlyspaced. You must provide at least three values. The defaultvalues, in meters, are [-0.002 0 0.002 0.005 0.015]. IfModelparameterization is set to By area vs. opening table, theTabulated valve openings values will be used together withTabulated valve passage area values for one-dimensional tablelookup. IfModel parameterization is set to By pressure-flowcharacteristic, the Tabulated valve openings values will

2-31


be used together with Tabulated pressure differentials andTabulated flow rates for two-dimensional table lookup.




[-1e-07 -7.0711e-08 -4.4721e-08 4.4721e-08 7.0711e-08 1e-07;

-2.0352e-05 -1.4391e-05 -9.1017e-06 9.1017e-06 1.4391e-05 2.0352e-05;

-0.0040736 -0.0028805 -0.0018218 0.0018218 0.0028805 0.0040736;

-0.011438 -0.0080879 -0.0051152 0.0051152 0.0080879 0.011438;

-0.034356 -0.024293 -0.015364 0.015364 0.024293 0.034356;]


2-32








• From last 2 points—Extrapolates using the linear method(regardless of the interpolation method specified), based onthe last two output values at the appropriate end of the range.That is, the block uses the first and second specified outputvalues if the input value is below the specified range, and the

2-33


two last specified output values if the input value is above thespecified range.

• From last point—Uses the last specified output value at theappropriate end of the range. That is, the block uses the lastspecified output value for all input values greater than the lastspecified input argument, and the first specified output valuefor all input values less than the first specified input argument.



Orifice P-A initial openingInitial opening for the orifice in the P-A path. The parameter canbe positive (underlapped orifice), negative (overlapped orifice), orequal to zero for zero lap configuration. The default value is 0.

Orifice A-T initial openingInitial opening for the orifice in the A-T path. The parameter canbe positive (underlapped orifice), negative (overlapped orifice), orequal to zero for zero lap configuration. The default value is 0.


Leakage areaThe total area of possible leaks in the completely closed valve.The main purpose of the parameter is to maintain numerical

2-34


integrity of the circuit by preventing a portion of the system fromgetting isolated after the valve is completely closed. An isolated or“hanging” part of the system could affect computational efficiencyand even cause failure of computation. Extreme caution shouldbe exercised if the parameter is set to 0. The default value is1e-12 m^2.







GlobalParameters




PHydraulic conserving port associated with the pressure supplyline inlet.

2-35


THydraulic conserving port associated with the return lineconnection.

AHydraulic conserving port associated with the actuator connectionport.


Examples The 3-Way Directional Valve block is demonstrated in theHydraulic Circuit with 3-Way Valve and Differential Cylinder demo(sh_circuit_3_way_valve_diff_cylinder), where it is used to switchbetween a conventional and differential connection of the cylinder.



2-36




Description The 4-Way Directional Valve block represents a continuous,symmetrical, 4-way directional valve. The fluid flow is pumped in thevalve through the inlet line and is distributed between two outsidepressure lines (usually connected to a double-acting actuator) and thereturn line. The block has four hydraulic connections, correspondingto inlet port (P), actuator ports (A and B), and return port (T), and onephysical signal port connection (S), which controls the spool position.The block is built of four Variable Orifice blocks, connected as shownin the following diagram.

The Variable Orifice blocks are installed as follows: orifice_PA is inthe P-A path, orifice_PB is in the P-B path, orifice_AT is in the A-Tpath, and orifice_BT is in the B-T path. All blocks are controlled bythe same position signal, provided through the physical signal portS, but the Orifice orientation parameter in the block instances isset in such a way that positive signal at port S opens orifice_PA and

2-37


orifice_BT and closes orifice_PB and orifice_AT. As a result, theopenings of the orifices are computed as follows:

h h xPA PA= +0

h h xPB PB= −0

h h xAT AT= −0

h h xBT BT= +0

where

hPA Orifice opening for the orifice_PA blockhPB Orifice opening for the orifice_PB blockhAT Orifice opening for the orifice_AT blockhBT Orifice opening for the orifice_BT blockhPA0 Initial opening for the orifice_PA blockhPB0 Initial opening for the orifice_PB blockhAT0 Initial opening for the orifice_AT blockhBT0 Initial opening for the orifice_BT blockx Control member displacement from initial position

The valve simulated by the 4-Way Directional Valve block is assumed tobe symmetrical. In other words, all four orifices are of the same shapeand size and are parameterized with the same method. You can chooseone of the following block parameterization options:


2-38




In the first case, the passage area is assumed to be linearly dependenton the control member displacement, that is, the orifice is assumed to beclosed at the initial position of the control member (zero displacement),and the maximum opening takes place at the maximum displacement.In the second case, the passage area is determined by one-dimensionalinterpolation from the table A=A(h). Flow rate is determinedanalytically, which additionally requires data such as flow dischargecoefficient, critical Reynolds number, and fluid density and viscosity.The computation accounts for the laminar and turbulent flow regimesby monitoring the Reynolds number and comparing its value with thecritical Reynolds number. See the Variable Orifice block reference pagefor details. In both cases, a small leakage area is assumed to exist evenafter the orifice is completely closed. Physically, it represents a possibleclearance in the closed valve, but the main purpose of the parameter isto maintain numerical integrity of the circuit by preventing a portion ofthe system from getting isolated after the valve is completely closed.An isolated or “hanging” part of the system could affect computationalefficiency and even cause failure of computation.

In the third case, when an orifice is defined by its pressure-flowcharacteristics, the flow rate is determined by two-dimensionalinterpolation. In this case, neither flow regime nor leakage flowrate is taken into account, because these features are assumed to beintroduced through the tabulated data. Pressure-flow characteristicsare specified with three data sets: array of orifice openings, array ofpressure differentials across the orifice, and matrix of flow rate values.Each value of a flow rate corresponds to a specific combination of anopening and pressure differential. In other words, characteristics mustbe presented as the Cartesian mesh, i.e., the function values mustbe specified at vertices of a rectangular array. The argument arrays

2-39


(openings and pressure differentials) must be strictly monotonicallyincreasing. The vertices can be nonuniformly spaced. You have a choiceof three interpolation methods and two extrapolation methods.

If you need to simulate a nonsymmetrical 4-way valve (i.e., withdifferent orifices), use any of the variable orifice blocks from theBuilding Blocks library (such as Orifice with Variable Area RoundHoles, Orifice with Variable Area Slot, or Variable Orifice) and connectthem the same way as the Variable Orifice blocks in the schematicdiagram of this 4-Way Directional Valve block.

Positive signal at the physical signal port S opens the orifices in the P-Aand B-T paths and closes the orifices in the P-B and A-T paths. Thedirectionality of nested blocks is clear from the schematic diagram.





• Only symmetrical configuration of the valve is considered. In otherwords, all four orifices are assumed to have the same shape and size.


The block dialog box contains two tabs:

• “Basic Parameters” on page 2-41

• “Initial Openings” on page 2-48

2-40


Basic Parameters

2-41


2-42



• By maximum area and opening — Provide values for themaximum valve passage area and the maximum valve opening.The passage area is linearly dependent on the control memberdisplacement, that is, the valve is closed at the initial positionof the control member (zero displacement), and the maximum

2-43







Tabulated valve openingsSpecify the vector of input values for valve openings as atabulated 1-by-m array. The input values vector must be strictlymonotonically increasing. The values can be nonuniformlyspaced. You must provide at least three values. The defaultvalues, in meters, are [-0.002 0 0.002 0.005 0.015]. IfModelparameterization is set to By area vs. opening table, theTabulated valve openings values will be used together withTabulated valve passage area values for one-dimensional tablelookup. IfModel parameterization is set to By pressure-flowcharacteristic, the Tabulated valve openings values will

2-44






[-1e-07 -7.0711e-08 -4.4721e-08 4.4721e-08 7.0711e-08 1e-07;

-2.0352e-05 -1.4391e-05 -9.1017e-06 9.1017e-06 1.4391e-05 2.0352e-05;

-0.0040736 -0.0028805 -0.0018218 0.0018218 0.0028805 0.0040736;

-0.011438 -0.0080879 -0.0051152 0.0051152 0.0080879 0.011438;

-0.034356 -0.024293 -0.015364 0.015364 0.024293 0.034356;]


2-45








• From last 2 points— Extrapolates using the linear method(regardless of the interpolation method specified), based onthe last two output values at the appropriate end of the range.That is, the block uses the first and second specified outputvalues if the input value is below the specified range, and the

2-46



• From last point— Uses the last specified output value at theappropriate end of the range. That is, the block uses the lastspecified output value for all input values greater than the lastspecified input argument, and the first specified output valuefor all input values less than the first specified input argument.





2-47


Initial Openings

Orifice P-A initial openingInitial opening for the orifice in the P-A path. The parameter canbe positive (underlapped orifice), negative (overlapped orifice), orequal to zero for zero lap configuration. The default value is 0.

2-48


Orifice P-B initial openingInitial opening for the orifice in the P-B path. The parameter canbe positive (underlapped orifice), negative (overlapped orifice), orequal to zero for zero lap configuration. The default value is 0.

Orifice A-T initial openingInitial opening for the orifice in the A-T path. The parameter canbe positive (underlapped orifice), negative (overlapped orifice), orequal to zero for zero lap configuration. The default value is 0.

Orifice B-T initial openingInitial opening for the orifice in the B-T path. The parameter canbe positive (underlapped orifice), negative (overlapped orifice), orequal to zero for zero lap configuration. The default value is 0.







GlobalParameters



2-49



PHydraulic conserving port associated with the pressure supplyline inlet.

THydraulic conserving port associated with the return lineconnection.

AHydraulic conserving port associated with the actuator connectionport.

BHydraulic conserving port associated with the actuator connectionport.


Examples The 4-Way Directional Valve block in the Closed-LoopCircuit with 4-Way Valve and Custom Cylinder demo(sh_closed_loop_circuit_4_way_valve_cust_cyl) is an open-center,symmetrical valve controlling a double-acting cylinder.



2-50

Annular Orifice

Purpose Simulate hydraulic variable orifice created by circular tube and roundinsert

Library Orifices

Description The Annular Orifice block models a variable orifice created by a circulartube and a round insert, which may be eccentrically located withrespect to the tube. The radial gap between the tube and the insertand its axial length are assumed to be essentially smaller than theinsert diameter, causing the flow regime to be laminar all the time. Aschematic representation of the annular orifice is shown in the followingillustration.

The flow rate is computed using the Hagen-Poiseuille equation (see [1]):

qR R r

Lp= − +⎛

⎝⎜⎞⎠⎟

πνρ

ε( )32

61

32

i i

ε =−e

R r

where

2-51

Annular Orifice

q Flow ratep Pressure differentialR Orifice radiusr Insert radiusL Overlap lengthε Eccentricity ratioe Eccentricityρ Fluid densityν Fluid kinematic viscosity

Use this block to simulate leakage path in plungers, valves, andcylinders.

The block positive direction is from port A to port B. This means that theflow rate is positive if it flows from A to B and the pressure differentialis determined as p p pA B= − . Positive signal at the physical signalport S increases or decreases the overlap, depending on the value of theparameter Orifice orientation.




2-52

Annular Orifice


Orifice radiusThe radius of the tube. The default value is 0.01 m.

Insert radiusThe radius of the insert. The default value is 0.0098 m.

EccentricityThe distance between the central axes of the insert and the tube.The parameter can be a positive value, smaller than the differencebetween the radius of the tube and the radius of the insert, orequal to zero for coaxial configuration. The default value is 0.

Initial lengthInitial overlap between the tube and the insert. The parametermust be positive. The value of initial length does not depend onthe orifice orientation. The default value is 0.003 m.

2-53

Annular Orifice

Orifice orientationThe parameter is introduced to specify the effect of the controlsignal on the orifice overlap. The parameter can be set to one oftwo options: Positive signal increases overlap or Negativesignal increases overlap. The default value is Positivesignal increases overlap.



• Orifice orientation


GlobalParameters




AHydraulic conserving port associated with the orifice inlet.

BHydraulic conserving port associated with the orifice outlet.

SPhysical signal port that controls the insert displacement.

2-54

Annular Orifice

References [1] Noah D. Manring, Hydraulic Control Systems, John Wiley & Sons,2005

See Also Constant Area Orifice

Fixed Orifice

Orifice with Variable Area Round Holes

Orifice with Variable Area Slot

Variable Area Orifice

Variable Orifice

2-55

Ball Valve

Purpose Simulate hydraulic ball valve

Library Flow Control Valves

Description The Ball Valve block models a variable orifice created by a spherical balland a round sharp-edged orifice.

The flow rate through the valve is proportional to the valve openingand to the pressure differential across the valve. The model accountsfor the laminar and turbulent flow regimes by monitoring the Reynoldsnumber (Re) and comparing its value with the critical Reynolds number(Recr). The flow rate is determined according to the following equations:

2-56

Ball Valve

qC A p sign p Re Re

C AD

p Re Re

D

DLH

=( )i i

ii

2

2

ρ

ν ρ

| | for >=

for <

cr

cr

⎧

⎨⎪⎪

⎩⎪⎪

h x x= +0

A h

A h

rr

DD h h

A A

leak

OB

leak

( ) max

max

=

<=

−⎛⎝⎜

⎞⎠⎟ < <

+

for

for

0

1 02

πi i

ffor h h>=

⎧

⎨⎪⎪

⎩⎪⎪ max

D r r h rB O O= − +( ) +2 2 22

2

p p pA B= −

Re( )

= q DA h

Hiiν

CC

DLD

cr=

⎛

⎝⎜⎜

⎞

⎠⎟⎟Re

2

DA h

H = 4 ( )π

AdO

max =π 2

4

where

2-57

Ball Valve

q Flow ratep Pressure differentialpA,pB Gauge pressures at the block terminalsCD Flow discharge coefficientA(h) Instantaneous orifice passage areax0 Initial opening

x Ball displacement from initial positionh Valve openingdO Orifice diameterrO Orifice radiusdB Ball diameterrB Ball radiusρ Fluid densityDH Valve instantaneous hydraulic diameterν Fluid kinematic viscosityAleak Closed valve leakage areaAmax Maximum valve open area

The block positive direction is from port A to port B. This means that theflow rate is positive if it flows from A to B and the pressure differentialis determined as p p pA B= − . Positive signal at the physical signalport S opens the valve.




• The transition between laminar and turbulent regimes is assumed tobe sharp and taking place exactly at Re=Recr.

2-58

Ball Valve

• The flow passage area is assumed to be equal to the side surfaceof the frustum of the cone located between the ball center and theorifice edge.


Valve ball diameterThe diameter of the valve ball. It must be greater than the orificediameter. The default value is 0.01 m.

Orifice diameterThe diameter of the orifice of the valve. The default value is0.005 m.

2-59

Ball Valve

Initial openingThe initial opening of the valve. Its value must be nonnegative.The default value is 0.

Flow discharge coefficientSemi-empirical parameter for valve capacity characterization. Itsvalue depends on the geometrical properties of the orifice, andusually is provided in textbooks or manufacturer data sheets.The default value is 0.65.



GlobalParameters




2-60

Ball Valve




See Also Needle Valve

Poppet Valve

Pressure-Compensated Flow Control Valve

2-61

Cartridge Valve Insert

Purpose Simulate hydraulic cartridge valve insert


Description The Cartridge Valve Insert block represents an insert of a hydrauliccartridge valve consisting of a poppet interacting with the seat. Thepoppet position is determined by pressures at ports A, B, and X andforce of the spring. A schematic diagram of the cartridge valve insert isshown in the following illustration.

The Cartridge Valve Insert block is a structural model consisting of aHydraulic Cartridge Valve Actuator block and a Variable Orifice block,as shown in the next illustration.

2-62


Pressures at port A and port B tend to open the valve, while pressureat the control port X, together with the spring, acts to close it. Themodel does not account for flow rates caused by poppet displacementand any loading on the poppet, such as inertia and friction. The valveremains closed as long as the aggregate pressure force is lower than thespring preload force. The poppet is forced off its seat as the preloadforce is reached and moves up proportionally to pressure increase untilit passes the full stroke. Hydraulic properties of the gap between thepoppet and the seat are simulated with the Variable Orifice block.

Connections A, B, and X are hydraulic conserving ports associated withthe valve inlet, valve outlet, and valve control terminal, respectively.

2-63


The block positive direction is from port A to port B. Pressure at portX acts to close the valve, while pressures at port A and port B act toopen the orifice.



• Valve opening is linearly proportional to the pressure differential.

• No loading on the poppet, such as inertia or friction, is considered.

• The model does not account for flow rates caused by poppetdisplacement.

• For orifices specified by the passage area (the first twoparameterization options), the transition between laminar andturbulent regimes is assumed to be sharp and taking place exactlyat Re=Recr.

• For orifices specified by pressure-flow characteristics (the thirdparameterization option), the model does not explicitly account forthe flow regime or leakage flow rate because the tabulated data isassumed to account for these characteristics.

2-64



2-65


2-66


2-67


Port A poppet areaEffective poppet area at port A. The parameter value must begreater than zero. The default value is 2e-4 m^2.

Port A to port X area ratioRatio between poppet areas at port A and port X. The parametervalue must be greater than zero. The default value is 0.66.

Preload forceSpring preload force. The default value is 26 N.

Spring rateSpring rate. The default value is 1.4e4 N/m.

Poppet strokeMaximum poppet stroke. The parameter value must be greaterthan or equal to zero. The default value is 5e-3m. This parameteris used if Orifice specification is set to By maximum area andopening.

Orifice specificationSelect one of the following methods for specifying the hydraulicproperties of the gap between the poppet and the seat:

• By maximum area and opening — Provide values for themaximum orifice area and the maximum orifice opening. Thepassage area is linearly dependent on the control memberdisplacement, that is, the orifice is closed at the initial positionof the control member (zero displacement), and the maximumopening takes place at the maximum displacement. This isthe default method.

• By area vs. opening table — Provide tabulated data oforifice openings and corresponding orifice areas. The passagearea is determined by one-dimensional table lookup. You havea choice of three interpolation methods and two extrapolationmethods.

• By pressure-flow characteristic— Provide tabulated dataof orifice openings, pressure differentials, and correspondingflow rates. The flow rate is determined by two-dimensional

2-68


table lookup. You have a choice of three interpolation methodsand two extrapolation methods.

For more information on these options, see the Variable Orificeblock reference page.

Orifice maximum areaSpecify the area of a fully opened orifice. The parameter valuemust be greater than zero. The default value is 5e-5 m^2. Thisparameter is used if Orifice specification is set to By maximumarea and opening.

Tabulated orifice openingsSpecify the vector of input values for orifice openings as atabulated 1-by-m array. The input values vector must be strictlymonotonically increasing. The values can be nonuniformlyspaced. You must provide at least three values. The defaultvalues, in meters, are [-0.002 0 0.002 0.005 0.015]. IfOrifice specification is set to By area vs. opening table,the Tabulated orifice openings values will be used togetherwith Tabulated orifice area values for one-dimensional tablelookup. If Orifice specification is set to By pressure-flowcharacteristic, the Tabulated orifice openings values willbe used together with Tabulated pressure differentials andTabulated flow rates for two-dimensional table lookup.

Tabulated orifice areaSpecify the vector of output values for orifice area as a tabulated1-by-m array. The orifice area vector must be the same size asthe orifice openings vector. All the values must be positive. Thedefault values, in m^2, are [1e-09 2.0352e-07 4.0736e-050.00011438 0.00034356]. This parameter is used if Orificespecification is set to By area vs. opening table.

Tabulated pressure differentialsSpecify the vector of input values for pressure differentials as atabulated 1-by-n array. The input values vector must be strictlymonotonically increasing. The values can be nonuniformly spaced.You must provide at least three values. The default values,

2-69


in Pa, are [-1e+07 -5e+06 -2e+06 2e+06 5e+06 1e+07].This parameter is used if Orifice specification is set to Bypressure-flow characteristic.

Tabulated flow ratesSpecify the output values for flow rates as a tabulated m-by-nmatrix, defining the function values at the input grid vertices.Each value in the matrix specifies flow rate taking place at aspecific combination of orifice opening and pressure differential.The matrix size must match the dimensions defined by the inputvectors. The default values, in m^3/s, are:

[-1e-07 -7.0711e-08 -4.4721e-08 4.4721e-08 7.0711e-08 1e-07;

-2.0352e-05 -1.4391e-05 -9.1017e-06 9.1017e-06 1.4391e-05 2.0352e-05;

-0.0040736 -0.0028805 -0.0018218 0.0018218 0.0028805 0.0040736;

-0.011438 -0.0080879 -0.0051152 0.0051152 0.0080879 0.011438;

-0.034356 -0.024293 -0.015364 0.015364 0.024293 0.034356;]

This parameter is used if Orifice specification is set to Bypressure-flow characteristic.




2-70









2-71






• Orifice specification



All other block parameters are available for modification. The actualset of modifiable block parameters depends on the value of the Orificespecification parameter at the time the model entered Restrictedmode.

GlobalParameters


2-72






XHydraulic conserving port associated with the valve controlterminal.

See Also Check Valve

Hydraulic Cartridge Valve Actuator

Pilot-Operated Check Valve

2-73

Centrifugal Pump

Purpose Simulate centrifugal pump

Library Pumps and Motors

Description The Centrifugal Pump block represents a centrifugal pump of anytype as a data-sheet-based model. Depending on data listed in themanufacturer’s catalogs or data sheets for your particular pump, youcan choose one of the following model parameterization options:

• By approximating polynomial— Provide values for the polynomialcoefficients. These values can be determined analytically orexperimentally, depending on the data available. This is the defaultmethod.

• By two 1D characteristics: P-Q and N-Q— Provide tabulateddata of pressure differential and brake power versus pump deliverycharacteristics. The pressure differential and brake power aredetermined by one-dimensional table lookup. You have a choice ofthree interpolation methods and two extrapolation methods.

• By two 2D characteristics: P-Q-W and N-Q-W — Providetabulated data of pressure differential and brake power versus pumpdelivery characteristics at different angular velocities. The pressuredifferential and brake power are determined by two-dimensionaltable lookup. You have a choice of three interpolation methods andtwo extrapolation methods.

These parameterization options are further described in greater detail:

• “Parameterizing the Pump by Approximating Polynomial” on page2-75

• “Parameterizing the Pump by Pressure Differential and Brake PowerVersus Pump Delivery” on page 2-79

• “Parameterizing the Pump by Pressure Differential and Brake PowerVersus Pump Delivery at Different Angular Velocities ” on page 2-80

2-74

Centrifugal Pump

Connections P and T are hydraulic conserving ports associated withthe pump outlet and inlet, respectively. Connection S is a mechanicalrotational conserving port associated with the pump driving shaft. Theblock positive direction is from port T to port P. This means that thepump transfers fluid from T to P as its driving shaft S rotates in theglobally assigned positive direction.

Note The model is developed only for positive, nonzero shaft speeds. Inother words, the pump driving shaft must rotate in positive directiononly, without stopping.

Parameterizing the Pump by Approximating Polynomial

If you set the Model parameterization parameter to Byapproximating polynomial, the pump is parameterized withthe polynomial whose coefficients are determined, analytically orexperimentally, for a specific angular velocity depending on the dataavailable. The pump characteristics at other angular velocities aredetermined from the affinity laws.

The approximating polynomial is derived from the Euler pulse momentequation [1, 2], which for a known pump can be represented as thefollowing:

p k p p pE HL D= − −i

where

p Pressure differential across the pumpk Correction factor. The factor is introduced to account for

dimensional fluctuations, blade incongruity, blade volumes,fluid internal friction, and so on. The factor should beset to 1 if the approximating coefficients are determinedexperimentally.

pE Euler pressure

2-75

Centrifugal Pump

pHL Pressure loss due to hydraulic losses in the pump passagespD Pressure loss caused by deviations of the pump delivery from

its nominal value

The Euler pressure, pE, is determined with the Euler equation forcentrifugal machines [1, 2] based on known pump dimensions. For anexisting pump, operating at constant angular velocity and specific fluid,the Euler pressure can be approximated with the equation

p c c qE ref P= −( )ρ 0 1 i

where

ρref Fluid densityc0,c1 Approximating coefficients. They can be determined either

analytically from the Euler equation [1, 2] or experimentally.qP Pump volumetric delivery

The pressure loss due to hydraulic losses in the pump passages, pHL, isapproximated with the equation

p c qHL ref P= ρ i i22

where

ρref Fluid densityc2 Approximating coefficientqP Pump volumetric delivery

The blade profile is determined for a specific fluid velocity, and deviationfrom this velocity results in pressure loss due to inconsistency betweenthe fluid velocity and blade profile velocity. This pressure loss, pD, isestimated with the equation

2-76

Centrifugal Pump

p c q qD ref D P= −( )ρ i 32

where

ρref Fluid densityc3 Approximating coefficientqP Pump volumetric deliveryqD Pump design delivery (nominal delivery)

The resulting approximating polynomial takes the form:

p k c c q c q c q qref D P= − − − −( )( )ρ ( )0 1 22

32

(2-1)

The pump characteristics, approximated with four coefficientsc0, c1, c2, and c3, are determined for a specific fluid and a specificangular velocity of the pump’s driving shaft. These two parameterscorrespond, respectively, to the Reference density and Referenceangular velocity parameters in the block dialog box. To apply thecharacteristics for another velocity ω or density ρ, the affinity laws areused. First, the new reference delivery is computed with the expression

q qrefref=

ωω (2-2)

where q and ω are the instantaneous values of the pump delivery andangular velocity. Then the pressure differential across the pump at adifferent angular velocity and density is determined with the formula

p prefref ref

=⎛

⎝⎜⎜

⎞

⎠⎟⎟i i

ωω

ρρ

2

where pref is the pressure differential computed with Equation 2-1 atpump delivery determined according to Equation 2-2.

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Centrifugal Pump

The pump efficiency is assumed to be the same as it is at the referenceparameters. It is computed with the following equations:

η =N

Nref hyd

ref br

.

.

N p qref hyd ref ref. = i

N p q Nref br Eref ref mech loss. .= +i

where

η Pump efficiencyNref.hyd Power of the flow at the pump’s outletpref Pressure differential across the pump at delivery q = qrefqref Pump reference deliverypEref Euler pressure at reference parametersNref.br Mechanical brake power at the pump’s driving shaftNmech.lossPower of mechanical losses in the pump drive train

Assuming that the efficiency remains the same at similar regimes, thetorque at the driving shaft is determined from the following equation:

TNref br

ref ref ref=

⎛

⎝⎜⎜

⎞

⎠⎟⎟

.

ωω

ωρ

ρi i

2

The hydraulic power at the pump outlet is computed with the equation

N p qhyd = i

where p and q are the current values of the pump pressure differentialand delivery, respectively.

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Centrifugal Pump

Parameterizing the Pump by Pressure Differential and BrakePower Versus Pump Delivery

If you set the Model parameterization parameter to By two 1Dcharacteristics: P-Q and N-Q, the pump characteristics arecomputed by using two one-dimensional table lookups: for the pressuredifferential based on the pump delivery and for the pump brake powerbased on the pump delivery. Both characteristics are specified at thesame angular velocity ωref (Reference angular velocity) and the samefluid density ρref (Reference density).

To compute pressure differential at another angular velocity, affinitylaws are used, similar to the first parameterization option. First, thenew reference delivery qref is computed with the expression

q qrefref=

ωω

where q is the current pump delivery. Then the pressure differentialacross the pump at current angular velocity ω and density ρ is computedas

p prefref ref

=⎛

⎝⎜⎜

⎞

⎠⎟⎟i i

ωω

ρρ

2

where pref is the pressure differential determined from the P-Qcharacteristic at pump delivery qref.

Brake power is determined with the equation

N Nrefref ref

=⎛

⎝⎜⎜

⎞

⎠⎟⎟i i

ωω

ρρ

3

where Nref is the reference brake power obtained from the N-Qcharacteristic at pump delivery qref.

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Centrifugal Pump

The torque at the pump driving shaft is computed with the equationT = N / ω .

Parameterizing the Pump by Pressure Differential and BrakePower Versus Pump Delivery at Different Angular Velocities

If you set the Model parameterization parameter to By two 2Dcharacteristics: P-Q-W and N-Q-W, the pump characteristics areread out from two two-dimensional table lookups: for the pressuredifferential based on the pump delivery and angular velocity and for thepump brake power based on the pump delivery and angular velocity.

Both the pressure differential and brake power are scaled if fluid densityρ is different from the reference density ρref, at which characteristicshave been obtained

p prefref

= iρ

ρ

N Nrefref

= iρ

ρ

where pref and Nref are the pressure differential and brake powerobtained from the plots.



• Fluid compressibility is neglected.

• The pump rotates in positive direction only, with nonzero speed.

• No reverse flow through the pump is allowed.

• The pump efficiency remains the same at similar regimes.

2-80

Centrifugal Pump


2-81

Centrifugal Pump

2-82

Centrifugal Pump

Model parameterizationSelect one of the following methods for specifying the pumpparameters:

2-83

Centrifugal Pump

• By approximating polynomial — Provide values for thepolynomial coefficients. These values can be determinedanalytically or experimentally, depending on the data available.The relationship between pump characteristics and angularvelocity is determined from the affinity laws. This is the defaultmethod.

• By two 1D characteristics: P-Q and N-Q — Providetabulated data of pressure differential and brake power versuspump delivery characteristics. The pressure differentialand brake power are determined by one-dimensional tablelookup. You have a choice of three interpolation methods andtwo extrapolation methods. The relationship between pumpcharacteristics and angular velocity is determined from theaffinity laws.

• By two 2D characteristics: P-Q-W and N-Q-W— Providetabulated data of pressure differential and brake power versuspump delivery characteristics at different angular velocities.The pressure differential and brake power are determinedby two-dimensional table lookup. You have a choice of threeinterpolation methods and two extrapolation methods.

First approximating coefficientApproximating coefficient c0 in the block description preceding.The default value is 326.8 Pa/(kg/m^3). This parameter isused if Model parameterization is set to By approximatingpolynomial.

Second approximating coefficientApproximating coefficient c1 in the block description preceding.The default value is 3.104e4 Pa*s/kg. This parameter is usedif Model parameterization is set to By approximatingpolynomial.

Third approximating coefficientApproximating coefficient c2 in the block description preceding.This coefficient accounts for hydraulic losses in the pump. Thedefault value is 1.097e7 Pa*s^2/(kg*m^3). This parameter is

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Centrifugal Pump

used if Model parameterization is set to By approximatingpolynomial.

Fourth approximating coefficientApproximating coefficient c3 in the block description preceding.This coefficient accounts for additional hydraulic losses causedby deviation from the nominal delivery. The default value is2.136e5 Pa*s^2/(kg*m^3). This parameter is used if Modelparameterization is set to By approximating polynomial.

Correction factorThe factor, denoted as k in the block description preceding,accounts for dimensional fluctuations, blade incongruity, bladevolumes, fluid internal friction, and other factors that decreaseEuler theoretical pressure. The default value is 0.8. Thisparameter is used if Model parameterization is set to Byapproximating polynomial.

Pump design deliveryThe pump nominal delivery. The blades profile, pump inlet, andpump outlet are shaped for this particular delivery. Deviationfrom this delivery causes an increase in hydraulic losses. Thedefault value is 130 lpm. This parameter is used if Modelparameterization is set to By approximating polynomial.

Reference angular velocityAngular velocity of the driving shaft, at which the pumpcharacteristics are determined. The default value is 1.77e3 rpm.This parameter is used if Model parameterization is set to Byapproximating polynomial or By two 1D characteristics:P-Q and N-Q.

Reference densityFluid density at which the pump characteristics are determined.The default value is 920 kg/m^3.

Mechanical loss powerPower of mechanical loss in the pump drive train at referenceparameters. The default value is 350 W. This parameter is

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Centrifugal Pump

used if Model parameterization is set to By approximatingpolynomial.

Pump delivery vector for P-Q tableSpecify the vector of pump deliveries, as a tabulated 1-by-n array,to be used together with the vector of pressure differentialsto specify the P-Q pump characteristic. The vector valuesmust be strictly monotonically increasing. The values can benonuniformly spaced. You must provide at least three values.The default values, in lpm, are [0 28 90 130 154 182]. Thisparameter is used if Model parameterization is set to By two1D characteristics: P-Q and N-Q.

Pressure differential across pump vectorSpecify the vector of pressure differentials across the pump as atabulated 1-by-n array. The vector will be used together with thepump deliveries vector to specify the P-Q pump characteristic.The vector must be of the same size as the pump deliveries vectorfor the P-Q table. The default values, in bar, are [2.6 2.4 2 1.61.2 0.8]. This parameter is used ifModel parameterization isset to By two 1D characteristics: P-Q and N-Q.

Pump delivery vector for N-Q tableSpecify the vector of pump deliveries, as a tabulated 1-by-n array,to be used together with the vector of the pump brake power tospecify the N-Q pump characteristic. The vector values must bestrictly monotonically increasing. The values can be nonuniformlyspaced. You must provide at least three values. The defaultvalues, in lpm, are [0 20 40 60 80 100 120 140 160]. Thisparameter is used if Model parameterization is set to By two1D characteristics: P-Q and N-Q.

Brake power vector for N-Q tableSpecify the vector of pump brake power as a tabulated 1-by-narray. The vector will be used together with the pump deliveriesvector to specify the N-Q pump characteristic. The vector must beof the same size as the pump deliveries vector for the N-Q table.The default values, in W, are [220 280 310 360 390 420 480

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Centrifugal Pump

500 550]. This parameter is used ifModel parameterization isset to By two 1D characteristics: P-Q and N-Q.

Pump delivery vector for P-Q and W tableSpecify the vector of pump deliveries, as a tabulated 1-by-marray, to be used together with the vector of angular velocitiesand the pressure differential matrix to specify the pump P-Q-Wcharacteristic. The vector values must be strictly monotonicallyincreasing. The values can be nonuniformly spaced. You mustprovide at least three values. The default values, in lpm, are [050 100 150 200 250 300 350]. This parameter is used ifModelparameterization is set to By two 2D characteristics:P-Q-W and N-Q-W.

Angular velocity vector for P-Q and W tableSpecify the vector of angular velocities, as a tabulated 1-by-narray, to be used for calculating both the pump P-Q-W andN-Q-W characteristics. The vector values must be strictlymonotonically increasing. The values can be nonuniformlyspaced. You must provide at least three values. The defaultvalues, in rpm, are [3.2e+03 3.3e+03 3.4e+03 3.5e+03]. Thisparameter is used if Model parameterization is set to By two2D characteristics: P-Q-W and N-Q-W.

Pressure differential matrix for P-Q and W tableSpecify the matrix of pressure differentials across pump, as atabulated m-by-n matrix, defining the pump P-Q-W characteristictogether with the pump delivery and angular velocity vectors.Each value in the matrix specifies pressure differential for aspecific combination of pump delivery and angular velocity. Thematrix size must match the dimensions defined by the pumpdelivery and angular velocity vectors. The default values, in bar,are:

[ 8.3 8.8 9.3 9.9 ;7.8 8.3 8.8 9.4 ;7.2 7.6 8.2 8.7 ;6.5 7 7.5 8 ;

2-87

Centrifugal Pump

5.6 6.1 6.6 7.1 ;4.7 5.2 5.7 6.2 ;3.4 4 4.4 4.9 ;2.3 2.7 3.4 3.6 ; ]

This parameter is used if Model parameterization is set to Bytwo 2D characteristics: P-Q-W and N-Q-W.

Pump delivery vector for N-Q and W tableSpecify the vector of pump deliveries, as a tabulated 1-by-m array,to be used together with the vector of angular velocities and thebrake power matrix to specify the pump N-Q-W characteristic.The vector values must be strictly monotonically increasing.The values can be nonuniformly spaced. You must provide atleast three values. The default values, in lpm, are [0 50 100150 200 250 300 350]. This parameter is used if Modelparameterization is set to By two 2D characteristics:P-Q-W and N-Q-W.

Brake power matrix for N-Q and W tableSpecify the matrix of pump brake power, as a tabulated m-by-nmatrix, defining the pump N-Q-W characteristic together with thepump delivery and angular velocity vectors. Each value in thematrix specifies brake power for a specific combination of pumpdelivery and angular velocity. The matrix size must match thedimensions defined by the pump delivery and angular velocityvectors. The default values, in W, are:

[ 1.223e+03 1.341e+03 1.467e+03 1.6e+03 ;1.414e+03 1.551e+03 1.696e+03 1.85e+03 ;1.636e+03 1.794e+03 1.962e+03 2.14e+03 ;1.941e+03 2.129e+03 2.326e+03 2.54e+03 ;2.224e+03 2.439e+03 2.66e+03 2.91e+03 ;2.453e+03 2.691e+03 2.947e+03 3.21e+03 ;2.757e+03 3.024e+03 3.307e+03 3.608e+03 ;2.945e+03 3.23e+03 3.533e+03 3.854e+03 ; ]

2-88

Centrifugal Pump

This parameter is used if Model parameterization is set to Bytwo 2D characteristics: P-Q-W and N-Q-W.


• Linear — For one-dimensional table lookup (By two 1Dcharacteristics: P-Q and N-Q), uses a linear interpolationfunction. For two-dimensional table lookup (By two 2Dcharacteristics: P-Q-W and N-Q-W), uses a bilinearinterpolation algorithm, which is an extension of linearinterpolation for functions in two variables.

• Cubic — For one-dimensional table lookup (By two 1Dcharacteristics: P-Q and N-Q), uses the PiecewiseCubic Hermite Interpolation Polinomial (PCHIP). Fortwo-dimensional table lookup (By two 2D characteristics:P-Q-W and N-Q-W), uses the bicubic interpolation algorithm.

• Spline — For one-dimensional table lookup (By two 1Dcharacteristics: P-Q and N-Q), uses the cubic splineinterpolation algorithm. For two-dimensional table lookup(By two 2D characteristics: P-Q-W and N-Q-W), uses thebicubic spline interpolation algorithm.

This parameter is used if Model parameterization is set to ByBy two 1D characteristics: P-Q and N-Q or By two By two2D characteristics: P-Q-W and N-Q-W. For more informationon interpolation algorithms, see the PS Lookup Table (1D) and PSLookup Table (2D) block reference pages.


• From last 2 points— Extrapolates using the linear method(regardless of the interpolation method specified), based on

2-89

Centrifugal Pump

the last two output values at the appropriate end of the range.That is, the block uses the first and second specified outputvalues if the input value is below the specified range, and thetwo last specified output values if the input value is above thespecified range.


This parameter is used if Model parameterization is set to ByBy two 1D characteristics: P-Q and N-Q or By two By two2D characteristics: P-Q-W and N-Q-W. For more informationon extrapolation algorithms, see the PS Lookup Table (1D) andPS Lookup Table (2D) block reference pages.







GlobalParameters


2-90

Centrifugal Pump


THydraulic conserving port associated with the pump suction, orinlet.

PHydraulic conserving port associated with the pump outlet.

SMechanical rotational conserving port associated with the pumpdriving shaft.

References [1] T.G. Hicks, T.W. Edwards, Pump Application Engineering,McGraw-Hill, NY, 1971

[2] I.J. Karassic, J.P. Messina, P. Cooper, C.C. Heald, Pump Handbook,Third edition, McGraw-Hill, NY, 2001

See Also Fixed-Displacement Pump

Variable-Displacement Pressure-Compensated Pump

Variable-Displacement Pump

2-91

Check Valve

Purpose Simulate hydraulic valve that allows flow in one direction only


Description The Check Valve block represents a hydraulic check valve as adata-sheet-based model. The purpose of the check valve is to permitflow in one direction and block it in the opposite direction. The followingfigure shows the typical dependency between the valve passage area Aand the pressure differential across the valve p p pA B= − .

The valve remains closed while pressure differential across the valveis lower than the valve cracking pressure. When cracking pressure isreached, the value control member (spool, ball, poppet, etc.) is forcedoff its seat, thus creating a passage between the inlet and outlet. If theflow rate is high enough and pressure continues to rise, the area isfurther increased until the control member reaches its maximum. Atthis moment, the valve passage area is at its maximum. The valve

2-92

Check Valve

maximum area and the cracking and maximum pressures are generallyprovided in the catalogs and are the three key parameters of the block.

In addition to the maximum area, the leakage area is also required tocharacterize the valve. The main purpose of the parameter is not toaccount for possible leakage, even though this is also important, but tomaintain numerical integrity of the circuit by preventing a portion ofthe system from getting isolated after the valve is completely closed.An isolated or “hanging” part of the system could affect computationalefficiency and even cause failure of computation. Theoretically, theparameter can be set to zero, but it is not recommended.

The model accounts for the laminar and turbulent flow regimes bymonitoring the Reynolds number (Re) and comparing its value with thecritical Reynolds number (Recr). The flow rate is determined accordingto the following equations:

qC A p sign p Re Re

C AD

p Re Re

D

DLH

=( )i i

ii

2

2

ρ

ν ρ

| | for >=

for <

cr

cr

⎧

⎨⎪⎪

⎩⎪⎪

A pA p pA k p p p p p

leak crack

leak crack crack( ) max=<=

+ −( ) < <for for i

AA p pmax maxfor >=

⎧⎨⎪

⎩⎪

kA Ap p

leak

crack=

−−

max

max

p p pA B= −

Re( )

= q DA p

Hiiν

2-93

Check Valve

CC

DLD

cr=

⎛

⎝⎜⎜

⎞

⎠⎟⎟Re

2

DA p

H = 4 ( )π

where

q Flow rate through the valvep Pressure differential across the valvepA,pB Gauge pressures at the block terminalsCD Flow discharge coefficientA(p) Instantaneous orifice passage areaAmax Fully open valve passage areaAleak Closed valve leakage area

pcrack Valve cracking pressurepmax Pressure needed to fully open the valveDH Instantaneous orifice hydraulic diameterρ Fluid densityν Fluid kinematic viscosity

The block positive direction is from port A to port B. This meansthat the flow rate is positive if it flows from A to B, and the pressuredifferential is determined as p p pA B= − .

2-94

Check Valve




• No loading on the valve, such as inertia, friction, spring, and so on,is considered.



2-95

Check Valve

Maximum passage areaValve passage maximum cross-sectional area. The default valueis 1e-4 m^2.

Cracking pressurePressure level at which the orifice of the valve starts to open. Thedefault value is 3e4 Pa.

Maximum opening pressurePressure differential across the valve needed to fully open thevalve. Its value must be higher than the cracking pressure. Thedefault value is 1.2e5 Pa.




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Check Valve

GlobalParameters






Examples The Graetz Flow Control Circuit demo (sh_Graetz_circuit) illustratesthe use of check valves to build a rectifier that keeps the flow passingthrough a flow control valve always in the same direction, and to selectan appropriate orifice depending on the flow direction.

See Also Pilot-Operated Check Valve

2-97

Constant Head Tank

Purpose Simulate tank where pressurization and fluid level remain constantregardless of volume change

Library Low-Pressure Blocks

Description The Constant Head Tank block represents a pressurized hydraulicreservoir, in which fluid is stored under a specified pressure. The size ofthe tank is assumed to be large enough to neglect the pressurizationand fluid level change due to fluid volume. The block accounts for thefluid level elevation with respect to the tank bottom, as well as forpressure loss in the connecting pipe that can be caused by a filter,fittings, or some other local resistance. The loss is specified with thepressure loss coefficient. The block computes the volume of fluid in thetank and exports it outside through the physical signal port V.

The fluid volume value does not affect the results of simulation. It isintroduced merely for information purposes. It is possible for the fluidvolume to become negative during simulation, which signals that thefluid volume is not enough for the proper operation of the system. Byviewing the results of the simulation, you can determine the extentof the fluid shortage.

The pressure at the tank inlet is computed with the following equations:

p p p pelev loss pr= − +

p g Helev = ρi i

p KA

q qlossp

= ρ2 2

| |

Ad

p = πi 2

4

where

2-98

Constant Head Tank

p Pressure at the tank inletpelev Pressure due to fluid levelploss Pressure loss in the connecting pipeppr Pressurizationρ Fluid densityg Acceleration of gravityH Fluid level with respect to the bottom of the tankK Pressure loss coefficientAp Connecting pipe aread Connecting pipe diameterq Flow rate

Connection T is a hydraulic conserving port associated with the tankinlet. Connection V is a physical signal port. The flow rate is consideredpositive if it flows into the tank.

2-99

Constant Head Tank


PressurizationGage pressure acting on the in the tank. It can be created by a gascushion, membrane, bladder, or piston, as in bootstrap reservoirs.This parameter must be greater than or equal to zero. The defaultvalue is 0, which corresponds to a tank connected to atmosphere.

Fluid levelThe fluid level with respect to the tank bottom. This parametermust be greater than zero. The default value is 1 m.

Initial fluid volumeThe initial volume of fluid in the tank. This parameter must begreater than zero. The default value is 0.2 m^3.

Inlet pipeline diameterThe diameter of the connecting pipe. This parameter must begreater than zero. The default value is 0.02 m.

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Constant Head Tank

Pipeline pressure loss coefficientThe value of the pressure loss coefficient, to account for pressureloss in the connecting pipe. This parameter must be greater thanzero. The default value is 1.2.

The loss is computed with the equation similar to that used inthe Fixed Orifice block:

qK

A pp= 1 2ρ

The Critical Reynolds number is set to 15.


THydraulic conserving port associated with the tank inlet.

VPhysical signal port that outputs the volume of fluid in the tank.

See Also Reservoir

Variable Head Tank

2-101

Cylinder Friction

Purpose Simulate friction in hydraulic cylinders

Library Hydraulic Cylinders

Description The Cylinder Friction block simulates friction in the contact betweenmoving bodies in hydraulic cylinders and is intended to be usedprimarily as a building block in combination with both the double- andsingle-acting cylinders to develop a cylinder model with friction. Thefriction force is simulated as a function of relative velocity and pressure,and is assumed to be the sum of Stribeck, Coulomb, and viscouscomponents. The Coulomb friction force consists of the preload force,caused by the seal squeeze during assembly, and the force proportionalto pressure. The sum of the Coulomb and Stribeck friction forces at zerovelocity is often referred to as the breakaway friction force. For moreinformation, see the Translational Friction block reference page.

The friction force is approximated with the following equations:

F F K c v sign v f vC brk v vfr= + −( ) −( )( ) ( ) +i i i1 1 exp | |

F F f p pC pr cfr A B= + +( )

where

F Friction forceFC Coulomb frictionFpr Preload forcefcfr Coulomb friction coefficientpA,pB Pressures in cylinder chambersKbrk Breakaway friction force increase coefficientcv Transition coefficient

2-102

Cylinder Friction

v Relative velocity in the contactfvfr Viscous friction coefficient

To avoid discontinuity at v = 0, a small region |v| ≤ vth is introducedaround zero velocity, where friction force is assumed to be linearlyproportional to velocity:

F K v= i

KF K c v f v

vC brk v th vfr th

th=

+ −( ) −( )( ) +1 1 i iexp

where

K Proportionality coefficientvth Velocity threshold

Connections R and C are mechanical translational conserving portsassociated with the rod and case, respectively. Connections A and Bare hydraulic conserving ports to be connected to ports A and B ofthe cylinder model, as shown in the following illustration. The forcegenerated by the block always opposes relative motion between therod and the case.

2-103

Cylinder Friction

2-104

Cylinder Friction


Preload forceThe preload force, caused by the seal squeeze during assembly.The default value is 10 N.

Coulomb friction force coefficientCoulomb friction coefficient, which defines the proportionalitybetween the Coulomb friction force and the pressure in cylinderchambers. The default value is 1e-6 N/Pa.

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Cylinder Friction

Breakaway friction increase coefficientThe friction force increase over the Coulomb friction. TheCoulomb friction force, multiplied by this coefficient, is referred toas breakaway friction force. The default value is 1.

Viscous friction coefficientProportionality coefficient between the viscous friction force andthe relative velocity. The parameter value must be greater thanor equal to zero. The default value is 100 N/(m/s).

Transition approximation coefficientThe parameter sets the value of coefficient cv, which is used forthe approximation of the transition between the breakawayand the Coulomb frictions. Its value is assigned based on thefollowing considerations: the Stribeck friction component reachesapproximately 5% of its steady-state value at velocity 3/cv, and 2%at velocity 4/cv, which makes it possible to develop an approximaterelationship cv ~= 4/vmin,where vmin is the relative velocity atwhich friction force has its minimum value. By default, cv is setto 10 s/m, which corresponds to a minimum friction at velocityof about 0.4 m/s.

Linear region velocity thresholdThe parameter sets the small vicinity near zero velocity, withinwhich friction force is considered to be linearly proportional tothe relative velocity. The MathWorks recommends that you usevalues in the range between 1e-6 and 1e-4 m/s. The defaultvalue is 1e-4 m/s.


AHydraulic conserving port connected to the cylinder inlet.

BHydraulic conserving port connected to the cylinder outlet.

2-106

Cylinder Friction

RMechanical translational conserving port associated with thecylinder rod.

CMechanical translational conserving port associated with thecylinder clamping structure.

See Also Double-Acting Hydraulic Cylinder

Single-Acting Hydraulic Cylinder

2-107

Double-Acting Hydraulic Cylinder

Purpose Simulate hydraulic actuator exerting force in both directions


Description The Double-Acting Hydraulic Cylinder block models a device thatconverts hydraulic energy into mechanical energy in the form oftranslational motion. Hydraulic fluid pumped under pressure into oneof the two cylinder chambers forces the piston to move and exert forceon the cylinder rod. Double-acting cylinders transfer force and motionin both directions.

The model of the cylinder is built of Simscape™ Foundation libraryblocks. The schematic diagram of the model is shown below.

Connections R and C are mechanical translational conserving portscorresponding to the cylinder rod and cylinder clamping structure,respectively. Connections A and B are hydraulic conserving ports. PortA is connected to chamber A and port B is connected to chamber B.

The energy through hydraulic port A or B is directed to the appropriateTranslational Hydro-Mechanical Converter block and Piston Chamberblock. The converter transforms hydraulic energy into mechanicalenergy, while the chamber accounts for the fluid compressibility in

2-108


the cylinder chamber. The rod motion is limited with the mechanicalTranslational Hard Stop block in such a way that the rod can travelonly between cylinder caps. The Ideal Translational Motion Sensorblock in the schematic is introduced to determine an instantaneouspiston position, which is necessary for the Piston Chamber blocks.

The block directionality is adjustable and can be controlled with theCylinder orientation parameter.



• No leakage, internal or external, is taken into account.

• No loading on piston rod, such as inertia, friction, spring, and soon, is taken into account. If necessary, you can easily add them byconnecting an appropriate building block to cylinder port R.

2-109



Piston area AChamber A effective piston area. The default value is 0.001 m^2.

Piston area BChamber B effective piston area. The default value is 5e-5 m^2.

Piston strokePiston maximum travel between caps. The default value is 0.1 m.

2-110


Piston initial distance from cap AThe distance that the piston is extended at the beginning ofsimulation. You can set the piston position to any point withinits stroke. The default value is 0, which corresponds to the fullyretracted position.

Dead volume AFluid volume in chamber A that remains in the chamber after therod is fully retracted. The default value is 1e-4 m^3.

Dead volume BFluid volume in chamber B that remains in the chamber after therod is fully extended. The default value is 1e-4 m^3.

Specific heat ratioGas-specific heat ratio for the Piston Chamber blocks. The defaultvalue is 1.4.

Contact stiffnessSpecifies the elastic property of colliding bodies for theTranslational Hard Stop block. The greater the value of theparameter, the less the bodies penetrate into each other, themore rigid the impact becomes. Lesser value of the parametermakes contact softer, but generally improves convergence andcomputational efficiency. The default value is 1e6 N/m.

Contact dampingSpecifies dissipating property of colliding bodies for theTranslational Hard Stop block. At zero damping, the impact isclose to an absolutely elastic one. The greater the value of theparameter, the more energy dissipates during an interaction.Keep in mind that damping affects slider motion as long as theslider is in contact with the stop, including the period when slideris pulled back from the contact. For computational efficiencyand convergence reasons, The MathWorks recommends that youassign a nonzero value to this parameter. The default value is150 N*s/m.

2-111


Cylinder orientationSpecifies cylinder orientation with respect to the globally assignedpositive direction. The cylinder can be installed in two differentways, depending upon whether it exerts force in the positive orin the negative direction when pressure is applied at its inlet. Ifpressure applied at port A exerts force in negative direction, setthe parameter to Acts in negative direction. The defaultvalue is Acts in positive direction.



• Cylinder orientation


GlobalParameters

Fluid bulk modulusThe parameter is determined by the type of working fluid selectedfor the system under design. Use the Hydraulic Fluid block or theCustom Hydraulic Fluid block to specify the fluid properties.


AHydraulic conserving port associated with the cylinder chamber A.

BHydraulic conserving port associated with the cylinder chamber B.



2-112


Examples The Double-Acting Hydraulic Cylinder with Flexible Clamping demo(sh_cylinder_da_flexible_clamping) illustrates simulation of acylinder whose clamping is too flexible to be neglected. The structurecompliance is represented with a spring and a damper, installedbetween the cylinder case and reference point. The cylinder performsforward and return strokes, and is loaded with inertia, viscous friction,and constant opposing load of 400 N.

The Closed-Loop Circuit with 4-Way Valve and Custom Cylinder demo(sh_closed_loop_circuit_4_way_valve_cust_cyl) demonstrates theuse of a 4-way valve in combination with a double-acting cylinder in asimple closed-loop actuator. The demo shows how to connect the blocksand set the initial orifice openings for the 4-way valve to model theforward and return strokes of the cylinder under load.

See Also Single-Acting Hydraulic Cylinder

Ideal Translational Motion Sensor

Translational Hard Stop

Translational Hydro-Mechanical Converter

Piston Chamber

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Double-Acting Rotary Actuator

Purpose Simulate double-acting hydraulic rotary actuator


Description The Double-Acting Rotary Actuator block models a double-actinghydraulic rotary actuator, which directly converts hydraulic energyinto mechanical rotational energy without employing intermediarytransmissions such as rack-and-pinion, sliding spline, chain, and so on.Hydraulic fluid pumped under pressure into one of the two actuatorchambers forces the shaft to rotate and generate torque. Double-actingactuators generate torque and motion in both directions.

The model of the actuator is built of Simscape Foundation libraryblocks. The schematic diagram of the model is shown below.

2-114


The blocks in the diagram perform the following functions:

RotationalHydro-MechanicalConverter A

Converts hydraulics energy intomechanical rotational energy when fluidis pumped into actuator chamber A.

RotationalHydro-MechanicalConverter B

Converts hydraulics energy intomechanical rotational energy when fluidis pumped into actuator chamber B.

Rotational Hard Stop Imposes limits on shaft rotation.Linear HydraulicResistance

Accounts for leakages.

Piston Chamber A Accounts for fluid compressibility inactuator chamber A.

Piston Chamber B Accounts for fluid compressibility inactuator chamber B.

Ideal TranslationalMotion Sensor

Determines an instantaneous shaftposition, which is necessary for the PistonChamber block.

Wheel and Axle Converts shaft rotation into translationalmotion to provide input to the IdealTranslational Motion Sensor block

Connections A and B are hydraulic conserving ports. Port A is connectedto chamber A and port B is connected to chamber B. Connection S isa mechanical rotational conserving port associated with the actuatorshaft.

The block directionality is adjustable and can be controlled with theActuator orientation parameter.

2-115




• No loading, such as inertia, friction, spring, and so on, is taken intoaccount. If necessary, you can easily add them by connecting anappropriate building block to port S.


2-116


Actuator displacementEffective displacement of the actuator. The default value is4.5e-5 m^3/rad.

Shaft strokeShaft maximum travel between stops. The default value is 5.1rad.

Shaft initial angleThe position of the shaft at the beginning of simulation. You canset the shaft position to any angle within its stroke. The defaultvalue is 0, which corresponds to the shaft position at the verybeginning of the stroke.

Dead volume AFluid volume in chamber A that remains in the chamber whenthe shaft is positioned at the very beginning of the stroke. Thedefault value is 1e-4 m^3.

Dead volume BFluid volume in chamber B that remains in the chamber when theshaft is positioned at the end of the stroke. The default value is1e-4 m^3.

Leak coefficientLeak coefficient for the Linear Hydraulic Resistance block. Thedefault value is 1e-14 (m^3/s)/Pa.

Specific heat ratioGas-specific heat ratio for the Piston Chamber block. The defaultvalue is 1.4.

Contact stiffnessSpecifies the elastic property of colliding bodies for the RotationalHard Stop block. The greater the value of the parameter, the lessthe bodies penetrate into each other, the more rigid the impactbecomes. Lesser value of the parameter makes contact softer, butgenerally improves convergence and computational efficiency.The default value is 1e6 N*m/rad.

2-117


Contact dampingSpecifies dissipating property of colliding bodies for the RotationalHard Stop block. At zero damping, the impact is close to anabsolutely elastic one. The greater the value of the parameter, themore energy dissipates during an interaction. Keep in mind thatdamping affects slider motion as long as the slider is in contactwith the stop, including the period when slider is pulled backfrom the contact. For computational efficiency and convergencereasons, The MathWorks recommends that you assign a nonzerovalue to this parameter. The default value is 150 N*m/(rad/s).

Actuator orientationSpecifies actuator orientation with respect to the globally assignedpositive direction. The actuator can be installed in two differentways, depending upon whether it generates torque in the positiveor in the negative direction when pressure is applied at its inlet.If pressure applied at port A generates torque in the negativedirection, set the parameter to Acts in negative direction.The default value is Acts in positive direction.





GlobalParameters



2-118


AHydraulic conserving port associated with the actuator chamberA.

BHydraulic conserving port associated with the actuator chamberB.

SMechanical rotational conserving port associated with theactuator shaft.

See Also Ideal Translational Motion Sensor

Linear Hydraulic Resistance

Rotational Hard Stop

Rotational Hydro-Mechanical Converter

Piston Chamber

Wheel and Axle

2-119

Elbow

Purpose Simulate hydraulic resistance in elbow

Library Local Hydraulic Resistances

Description The Elbow block represents an elbow as a local hydraulic resistance.The pressure loss is computed with the semi-empirical formula basedon pressure loss coefficient, which is determined in accordance with theCrane Co. recommendations (see [1], p. A-29). Two types of elbow areconsidered: smoothly curved (standard) and sharp-edged (miter). Theblock covers elbows in the 5–100 mm and 0–90 degrees range.

The block is based on the Local Resistance block. It computes thepressure loss coefficient and passes its value, as well as the criticalReynolds number value, to the Local Resistance block, which computesthe pressure loss according to the formulas explained in the referencedocumentation for that block.

The pressure loss for turbulent flow regime is determined accordingto the following formula:

p KA

q q= ρ2 2

| |

where

q Flow ratep Pressure lossK Pressure loss coefficientA Elbow cross-sectional areaρ Fluid density

The flow regime is checked in the underlying Local Resistance blockby comparing the Reynolds number to the specified critical Reynoldsnumber value. For laminar flow regime, the formula for pressure losscomputation is modified, as described in the reference documentationfor the Local Resistance block.

2-120

Elbow

The core data for the pressure loss coefficient computation is thetable-specified relationship between the friction factor fT and theinternal diameter for clean commercial steel pipes, with flow in the zoneof complete turbulence (see [1], p. A-26). For smoothly curved, standard90o elbows, the pressure loss coefficient is determined with the formula

K fT= 30

For elbows with different angles, the coefficient is corrected with therelationship presented in [2], Fig.4.6:

Kcorr = − −α α( . . )0 0142 3 703 10 5i

where α is the elbow angle in degrees (0 ≤ α ≤ 90).

Therefore, the pressure loss coefficient for smoothly curved, standardelbows is determined with the formula

K fSCE T= − −30 0 0142 3 703 10 5i iα α( . . )

For sharp-edged, miter bends the pressure loss coefficient is determinedaccording to the table provided in [1], p. A-29, as a function of the elbowdiameter and angle

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Elbow

K f dME = ( , )α

where 5 ≤ d ≤ 100 mm and 0 ≤ α ≤ 90 degrees.

Connections A and B are conserving hydraulic ports associated with theblock inlet and outlet, respectively.

The block positive direction is from port A to port B. This means thatthe flow rate is positive if fluid flows from A to B, and the pressuredifferential is determined as p p pA B= − .

Warning

The formulas used in the Elbow block are very approximate,especially in the laminar and transient flow regions. Formore accurate results, use the Local Resistance block with atable-specified K=f(Re) relationship.





• The elbow is assumed to be made of a clean commercial steel pipe.

2-122

Elbow


Elbow internal diameterThe internal diameter of the pipe. The value must be in the rangebetween 5 and 100 mm. The default value is 0.01 m.

Elbow angleThe angle of the bend. The value must be in the range between 0and 90 degrees. The default value is 90 deg.

Elbow typeThe parameter can have one of two values: Smoothly curvedelbow or Miter bend. The default value is Smoothly curvedelbow.

Critical Reynolds numberThe maximum Reynolds number for laminar flow. The transitionfrom laminar to turbulent regime is supposed to take place

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Elbow

when the Reynolds number reaches this value. The valueof the parameter depends on geometrical profile, and therecommendations on the parameter value can be found inhydraulic textbooks. The default value is 80.



• Elbow type


GlobalParameters




AHydraulic conserving port associated with the elbow inlet.

BHydraulic conserving port associated with the elbow outlet.

References [1] Flow of Fluids Through Valves, Fittings, and Pipe, Crane ValvesNorth America, Technical Paper No. 410M

[2] George R. Keller, Hydraulic System Analysis, Published by theEditors of Hydraulics & Pneumatics Magazine, 1970

2-124

Elbow

See Also Gradual Area Change

Local Resistance

Pipe Bend

Sudden Area Change

T-junction

2-125

Fixed Orifice

Purpose Simulate hydraulic orifice with constant cross-sectional area

Library Orifices

Description The Fixed Orifice block models a sharp-edged constant-area orifice,flow rate through which is proportional to the pressure differentialacross the orifice. The model accounts for the laminar and turbulentflow regimes by monitoring the Reynolds number (Re) and comparingits value with the critical Reynolds number (Recr). The flow rate isdetermined according to the following equations:

qC A p sign p Re Re

C AD

p Re Re

D

DLH

=( )i i

ii

2

2

ρ

ν ρ

| | for >=

for <

cr

cr

⎧

⎨⎪⎪

⎩⎪⎪

p p pA B= −

Re = q DA

Hiiν

CC

DLD

cr=

⎛

⎝⎜⎜

⎞

⎠⎟⎟Re

2

DA

H = 4π

where

q Flow ratep Pressure differentialpA,pB Gauge pressures at the block terminals

2-126

Fixed Orifice

CD Flow discharge coefficientA Orifice passage areaDH Orifice hydraulic diameterρ Fluid densityν Fluid kinematic viscosity






2-127

Fixed Orifice


Orifice areaOrifice passage area. The default value is 1e-4 m^2.

Flow discharge coefficientSemi-empirical parameter for orifice capacity characterization.Its value depends on the geometrical properties of the orifice, andusually is provided in textbooks or manufacturer data sheets.The default value is 0.7.

Critical Reynolds numberThe maximum Reynolds number for laminar flow. The transitionfrom laminar to turbulent regime is supposed to take placewhen the Reynolds number reaches this value. The valueof the parameter depends on orifice geometrical profile, andthe recommendations on the parameter value can be found inhydraulic textbooks. The default value is 12, which corresponds toa round orifice in thin material with sharp edges.

2-128

Fixed Orifice

GlobalParameters






See Also Annular Orifice

Constant Area Orifice




Variable Orifice

2-129

Fixed-Displacement Pump

Purpose Simulate fixed-displacement hydraulic pump


Description The Fixed-Displacement Pump block represents a positive,fixed-displacement pump of any type as a data-sheet-based model.The key parameters required for this block are pump displacement,volumetric and total efficiencies, nominal pressure, and angularvelocity. All these parameters are generally provided in the data sheetsor catalogs. The fixed-displacement pump is represented with thefollowing equations:

q D k pleak= −i iω

T D p mech= i / η

k kleak HP= / ν ρi

kD

pHPnom V nom

nom=

−( )i i iω η ν ρ1

p p pP T= −

where

q Pump deliveryp Pressure differential across the pumppP,pT Gauge pressures at the block terminalsT Torque at the pump driving shaftD Pump displacementω Pump angular velocitykleak Leakage coefficient

2-130


kHP Hagen-Poiseuille coefficientηV Pump volumetric efficiencyηmech Pump mechanical efficiencyν Fluid kinematic viscosityρ Fluid densitypnom Pump nominal pressureωnom Pump nominal angular velocityνnom Nominal fluid kinematic viscosity

The leakage flow is determined based on the assumption that it islinearly proportional to the pressure differential across the pump andcan be computed by using the Hagen-Poiseuille formula

pl

dq

kqleak

HPleak= =128

4μ

πμ

where

qleak Leakage flowd, l Geometric parameters of the leakage pathμ Fluid dynamic viscosity, μ = ν.ρ

The leakage flow at p = pnom and ν = νnom can be determined from thecatalog data

q Dleak nom V= −( )ω η1

which provides the formula to determine the Hagen-Poiseuillecoefficient

kD

pHPnom V nom

nom=

−( )ω η ν ρ1 i i

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The pump mechanical efficiency is not usually available in data sheets,therefore it is determined from the total and volumetric efficiencies byassuming that the hydraulic efficiency is negligibly small

η η ηmech total V= /

The block positive direction is from port T to port P. This means thatthe pump transfers fluid from T to P provided that the shaft S rotatesin the positive direction. The pressure differential across the pump isdetermined as p p pP T= − .




• No loading on the pump shaft, such as inertia, friction, spring, andso on, is considered.

• Leakage inside the pump is assumed to be linearly proportional toits pressure differential.

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Pump displacementPump displacement. The default value is 5e-6 m^3/rad.

Volumetric efficiencyPump volumetric efficiency specified at nominal pressure, angularvelocity, and fluid viscosity. The default value is 0.92.

Total efficiencyPump total efficiency, which is determined as a ratio betweenthe hydraulic power at the pump outlet and mechanical power atthe driving shaft at nominal pressure, angular velocity, and fluidviscosity. The default value is 0.8.

2-133


Nominal pressurePressure differential across the pump, at which both thevolumetric and total efficiencies are specified. The default valueis 1e7 Pa.

Nominal angular velocityAngular velocity of the driving shaft, at which both the volumetricand total efficiencies are specified. The default value is 188 rad/s.

Nominal kinematic viscosityWorking fluid kinematic viscosity, at which both the volumetricand total efficiencies are specified. The default value is 18 cSt.

GlobalParameters






Examples The Power Unit with Fixed-Displacement Pump demo(sh_power_unit_fxd_dspl_pump) contains a fixed-displacement pump,which is driven by a motor through a compliant transmission, apressure-relief valve, and a variable orifice, which simulates systemfluid consumption. The motor model is represented as an Ideal AngularVelocity Source block, which rotates the shaft at 188 rad/s at zero torque.The load on the shaft decreases the velocity with a slip coefficient of 1.2

2-134


(rad/s)/Nm. The load on the driving shaft is measured with the torquesensor. The shaft between the motor and the pump is assumed to becompliant and simulated with rotational spring and damper.

The simulation starts with the variable orifice open, which results in alow system pressure and the maximum flow rate going to the system.The orifice starts closing at 0.5 s, and is closed completely at 3 s. Theoutput pressure builds up until it reaches the pressure setting of therelief valve (75e5 Pa), and is maintained at this level by the valve. At3 s, the variable orifice starts opening, thus returning the system toits initial state.

See Also Centrifugal Pump



2-135

Gas-Charged Accumulator

Purpose Simulate hydraulic accumulator with gas as compressible medium

Library Accumulators

Description This block models a gas-charged accumulator. The accumulatorconsists of a precharged gas chamber and a fluid chamber connected toa hydraulic system. The chambers are separated by a bladder, piston,or any kind of elastic diaphragm.

If the fluid pressure at the accumulator inlet becomes higher thanthe precharge pressure, fluid enters the accumulator chamber andcompresses the gas, thus storing hydraulic energy. A drop in the fluidpressure at the inlet forces the stored fluid back into the system.

Normally, pressure in the gas chamber is equal to that of the fluidchamber. But if pressure at the accumulator inlet (p) drops below theaccumulator’s precharge value (ppr), the gas chamber gets isolatedfrom the system with the inlet valve. In this case, pressure in the gaschamber remains constant and equal to the precharge value, whilepressure at the inlet depends on pressure in the system to which theaccumulator is connected. If pressure at the inlet builds up to theprecharge value or higher, the chambers start interacting again. Theaccumulator is described with the following equations:

qdVdt

F=

VV

p

pF

Apr k=

−⎛

⎝⎜

⎞

⎠⎟

⎛

⎝

⎜⎜⎜

⎞

⎠

⎟⎟⎟

0

1

1

for p <= p

for p > p

inl pr

inli ppr

⎧

⎨

⎪⎪

⎩

⎪⎪

where

2-136


VF Fluid volumeVA Accumulator capacityp Inlet gauge pressureppr Precharge pressurek Specific heat ratioq Volumetric flow ratet Time



• The gas compression is determined on the basis of thethermodynamics of ideal gases.

• The process is assumed to be polytropic.

• No loading on the separator, such as inertia, friction, and so on, isconsidered.

• Fluid compressibility is not taken into account.

2-137



CapacityAccumulator capacity. The default value is 0.008 m^3.

Preload pressure (gauge)Precharge gauge pressure. The default value is 1e6 Pa.

Specific heat ratioSpecific heat ratio (adiabatic index). No units. The default valueis 1.4. To account for heat exchange, you can set it within a rangebetween 1 (isothermal process) and 1.4 (adiabatic process).

Initial volumeInitial volume of fluid in the accumulator. This parameterspecifies the initial condition for use in computing the block’sinitial state at the beginning of a simulation run. For moreinformation, see “Computing Initial Conditions”. The defaultvalue is 0.

2-138


GlobalParameters

Atmospheric pressureAbsolute pressure of the environment. The default value is101325 Pa.

Ports The block has one hydraulic conserving port associated with theaccumulator inlet.

The flow rate is positive if fluid flows into the accumulator.

See Also Spring-Loaded Accumulator

2-139

Gradual Area Change

Purpose Simulate gradual enlargement or contraction


Description The Gradual Area Change block represents a local hydraulic resistance,such as a gradual cross-sectional area change. The resistancerepresents a gradual enlargement (diffuser) if fluid flows from inlet tooutlet, or a gradual contraction if fluid flows from outlet to inlet. Theblock is based on the Local Resistance block. It determines the pressureloss coefficient and passes its value to the underlying Local Resistanceblock. The block offers two methods of parameterization: by applyingsemi-empirical formulas (with a constant value of the pressure losscoefficient) or by table lookup for the pressure loss coefficient basedon the Reynolds number.

If you choose to apply the semi-empirical formulas, you providegeometric parameters of the resistance, and the pressure loss coefficientis determined according to the A.H. Gibson equations (see [1] and [2]):

K

KAA

KAA

GE

cors

L

o

cors

L

=−

⎛

⎝⎜

⎞

⎠⎟

−⎛

⎝

1 2 62

45

1

2

i . sinα αfor 0 < <=

⎜⎜⎞

⎠⎟

⎧

⎨

⎪⎪⎪

⎩

⎪⎪⎪

2

45 180for < < o oα

K

KAA

K

GC

cors

L

o

cor

=−

⎛

⎝⎜

⎞

⎠⎟i i

i

0 5 1 1 62

450 75

. . sin.

α αfor 0 < <=

00 5 12

45 1800 75

. sin.

−⎛

⎝⎜

⎞

⎠⎟

⎧

⎨

⎪⎪⎪

⎩

⎪⎪⎪

AA

s

L

o oiα αfor < <

where

2-140

Gradual Area Change

KGE Pressure loss coefficient for the gradual enlargement, whichtakes place if fluid flows from inlet to outlet

KGC Pressure loss coefficient for the gradual contraction, whichtakes place if fluid flows from outlet to inlet

Kcor Correction factor

AS Small areaAL Large areaα Enclosed angle

If you choose to specify the pressure loss coefficient by a table, you haveto provide a tabulated relationship between the loss coefficient and theReynolds number. In this case, the loss coefficient is determined byone-dimensional table lookup. You have a choice of three interpolationmethods and two extrapolation methods.

The pressure loss coefficient, determined by either of the two methods,is then passed to the underlying Local Resistance block, which computesthe pressure loss according to the formulas explained in the referencedocumentation for that block. The flow regime is checked in theunderlying Local Resistance block by comparing the Reynolds number

2-141

Gradual Area Change

to the specified critical Reynolds number value, and depending on theresult, the appropriate formula for pressure loss computation is used.

The Gradual Area Change block is bidirectional and computes pressureloss for both the direct flow (gradual enlargement) and return flow(gradual contraction). If the loss coefficient is specified by a table, thetable must cover both the positive and the negative flow regions.


The block positive direction is from port A to port B. This means thatthe flow rate is positive if fluid flows from A to B, and the pressureloss is determined as p p pA B= − .




• If you select parameterization by semi-empirical formulas, thetransition between laminar and turbulent regimes is assumed to besharp and taking place exactly at Re=Recr.

• If you select parameterization by the table-specified relationshipK=f(Re), the flow is assumed to be turbulent.

2-142

Gradual Area Change


2-143

Gradual Area Change

Small diameterResistance small diameter. The default value is 0.01 m.

Large diameterResistance large diameter. The default value is 0.02 m. Thisparameter is used if Model parameterization is set to Bysemi-empirical formulas.

2-144

Gradual Area Change

Cone angleThe enclosed angle. The default value is 30 deg. This parameteris used ifModel parameterization is set to By semi-empiricalformulas.

Model parameterizationSelect one of the following methods for block parameterization:

• By semi-empirical formulas — Provide geometricalparameters of the resistance. This is the default method.

• By loss coefficient vs. Re table — Provide tabulatedrelationship between the loss coefficient and the Reynoldsnumber. The loss coefficient is determined by one-dimensionaltable lookup. You have a choice of three interpolation methodsand two extrapolation methods. The table must cover both thepositive and the negative flow regions.

Correction coefficientCorrection factor used in the formula for computation of the losscoefficient. The default value is 1. This parameter is used ifModelparameterization is set to By semi-empirical formulas.

Critical Reynolds numberThe maximum Reynolds number for laminar flow. The transitionfrom laminar to turbulent regime is supposed to take placewhen the Reynolds number reaches this value. The valueof the parameter depends on geometrical profile, and therecommendations on the parameter value can be found inhydraulic textbooks. The default value is 350. This parameter isused if Model parameterization is set to By semi-empiricalformulas.

Reynolds number vectorSpecify the vector of input values for Reynolds numbers as atabulated 1-by-m array. The input values vector must be strictlymonotonically increasing. The values can be nonuniformly spaced.You must provide at least three values. The default values are[-4000, -3000, -2000, -1000, -500, -200, -100, -50,-40, -30, -20, -15, -10, 10, 20, 30, 40, 50, 100, 200,

2-145

Gradual Area Change

500, 1000, 2000, 4000, 5000, 10000]. This parameter isused ifModel parameterization is set to By loss coefficientvs. Re table.

Loss coefficient vectorSpecify the vector of output values for the loss coefficient as atabulated 1-by-m array. The loss coefficient vector must be thesame size as the Reynolds numbers vector. The default valuesare [0.25, 0.3, 0.65, 0.9, 0.65, 0.75, 0.90, 1.15,1.35, 1.65, 2.3, 2.8, 3.10, 5, 2.7, 1.8, 1.46, 1.3,0.9, 0.65, 0.42, 0.3, 0.20, 0.40, 0.42, 0.25]. Thisparameter is used ifModel parameterization is set to By losscoefficient vs. Re table.


• Linear— Uses a linear interpolation function.

• Cubic — Uses the Piecewise Cubic Hermite InterpolationPolinomial (PCHIP).

• Spline— Uses the cubic spline interpolation algorithm.

For more information on interpolation algorithms, see the PSLookup Table (1D) block reference page. This parameter is used ifModel parameterization is set to By loss coefficient vs.Re table.


• From last 2 points— Extrapolates using the linear method(regardless of the interpolation method specified), based onthe last two output values at the appropriate end of the range.That is, the block uses the first and second specified output

2-146

Gradual Area Change

values if the input value is below the specified range, and thetwo last specified output values if the input value is above thespecified range.


For more information on extrapolation algorithms, see the PSLookup Table (1D) block reference page. This parameter is used ifModel parameterization is set to By loss coefficient vs.Re table.







GlobalParameters


2-147

Gradual Area Change



AHydraulic conserving port associated with the resistance inlet.

BHydraulic conserving port associated with the resistance outlet.


[2] Idelchik, I.E., Handbook of Hydraulic Resistance, CRC Begell House,1994

See Also Elbow

Local Resistance

Pipe Bend

Sudden Area Change

T-junction

2-148


Purpose Simulate double-acting hydraulic actuator for cartridge valves


Description Use the Hydraulic Cartridge Valve Actuator block as a pilot actuatorfor cartridge valves, as well as pilot-operated pressure and controlvalves in applications where all the forces, except spring and pressureforces, and flow consumption can be neglected. This block represents adouble-acting hydraulic valve actuator driven by three pressures. Theactuator drives a valve (spool, poppet, etc.) whose position depends onpressures at ports A, B, and X and the force of the spring. Pressures atports A and B tend to open the valve, while pressure at control port Xtogether with the spring force act to close it.

The valve remains closed as long as the aggregate pressure force islower than the spring preload force. The poppet is forced off its seat asthe preload force is reached and moves up proportionally to pressureincrease until it passes the full stroke.

Connections A, B, and X are hydraulic conserving ports associated withthe actuator ports. Connection P is a physical signal port whose outputcorresponds to piston displacement. Pressures applied at ports A and Bmove the piston in the positive or negative direction, depending on thevalue of the Actuator orientation parameter, with pressure at port Xacting in the opposite direction.



• The flow consumption associated with the valve motion is assumedto be negligible.

• The inertia, friction, and hydraulic axial forces are assumed to besmall and are not taken into account.

• The clearances between the valve and the washers are not takeninto account.

2-149



Port A poppet areaEffective poppet area at port A. The parameter value must begreater than zero. The default value is 3.3e-4 m^2.

Port A to port X area ratioRatio between poppet areas at port A and port X. The parametervalue must be greater than zero. The default value is 0.66.

2-150



Spring rateSpring rate. The default value is 1.4e4 N/m.

Poppet strokeMaximum poppet stroke. The parameter value must be greaterthan or equal to zero. The default value is 5e-3 m.

Actuator orientationSpecifies actuator orientation with respect to the globally assignedpositive direction. The actuator can be installed in two differentways, depending upon whether it moves the piston in the positiveor in the negative direction when pressure is applied at itsinlet. If pressures applied at ports A and B move the poppet inthe negative direction, set the parameter to Acts in negativedirection. The default value is Acts in positive direction.








XHydraulic conserving port associated with the valve controlterminal.

2-151


PPhysical signal port that outputs poppet displacement.







2-152


Purpose Simulate double-acting hydraulic valve actuator


Description Use the Hydraulic Double-Acting Valve Actuator block as a pilotactuator for directional, pressure, or flow control valves in applicationswhere all the forces, except spring force, and flow consumption can beneglected. The actuator consists of two single-acting actuators actingagainst each other. Each single-acting actuator consists of a piston,centering spring, and centering washer. When control pressure isapplied to either hydraulic port, only one centering spring is compressedby its washer while the other butts against the valve body and exertsno force on the spool. When both control pressures are released, thesprings force the washers against the valve body, and the spool centersbetween them. This design allows each actuator to have a differentspring, preload force, and piston area.

As pressure applied to the piston develops enough force to overcome thespring preload, the piston moves to the opposite position until it reachesits maximum stroke. Pressure applied at port X shifts the valve in thex-direction, overcoming the spring located in the Y chamber. Pressure

2-153


applied at port Y shifts the valve in the y-direction, overcoming thespring located in the X chamber.

The actuator is simulated according to the following equations:

F p A p Ax x y y= −i i

Lstr

F Fxx

x prx=

−max

Lstr

F Fyy

y pry=

−max

If F >= 0,

s

F F

L F F or F F F

str or F

pry

y pry pry y

y

=

<=

−( ) < <

>=

0 for

for

for

i i

imax

FF ymax

⎧

⎨⎪⎪

⎩⎪⎪

If F < 0,

s

F F

L F F or F F F

str o

prx

x prx prx x

x

=

<=

− −( ) < <

−

0 for |

for |

|

| | | maxi i

i rr F F xfor | | max>=

⎧

⎨⎪

⎩⎪

where

F Force acting on the valves Piston displacementpx Pressure in the actuator X chamberpy Pressure in the actuator Y chamberAx Valve face area in the X chamber

2-154


Ay Valve face area in the Y chamberstrx Valve stroke in x-directionstry Valve stroke in y-directionFprx Chamber X spring preload forceFmaxx Chamber X spring maximum forceFpry Chamber Y spring preload forceFmaxy Chamber Y spring maximum forceor Actuator orientation with respect to the globally assigned

positive direction. If pressure applied at port X moves thepiston in positive direction, or equals 1. If pressure applied atport X moves the piston in negative direction, or equals –1.

Connections X and Y are hydraulic conserving ports associated with thevalve chambers. Connection P is a physical signal port whose outputcorresponds to piston displacement. Pressure applied at port X movesthe piston in the positive or negative direction depending on the valueof the Actuator orientation parameter.



• The flow consumption associated with the valve motion is assumedto be negligible.

• The inertia, friction, and hydraulic axial forces are assumed to besmall and are not taken into account.

• The clearances between the valve and the washers are not takeninto account.

2-155



2-156


Piston area at port XEffective piston area at port X. The parameter value must begreater than zero. The default value is 2e-4 m^2.

Piston area at port YEffective piston area at port Y. The parameter value must begreater than zero. The default value is 2e-4 m^2.

Preload force at port XSpring preload force at port X. The default value is 0.

Preload force at port YSpring preload force at port Y. The default value is 0.

Spring maximum force at port XChamber X spring maximum force. The parameter value must begreater than the spring preload force. The default value is 50 N.

Spring maximum force at port YChamber Y spring maximum force. The parameter value must begreater than the spring preload force. The default value is 50 N.

Piston stroke at port XPiston stroke in chamber X. The parameter value must be greaterthan or equal to zero. The default value is 5e-3 m.

Piston stroke at port YPiston stroke in chamber Y. The parameter value must be greaterthan or equal to zero. The default value is 5e-3 m.

Actuator orientationSpecifies actuator orientation with respect to the globally assignedpositive direction. The actuator can be installed in two differentways, depending upon whether it moves the piston in the positiveor in the negative direction when pressure is applied at its inlet.If pressure applied at port X moves the piston in the negativedirection, set the parameter to Acts in negative direction.The default value is Acts in positive direction.

2-157







XHydraulic conserving port associated with the valve X chamber.

YHydraulic conserving port associated with the valve Y chamber.

PPhysical signal port that outputs piston displacement.

Examples The following illustration shows a typical control unit of avariable-displacement pump that provides load sensing and pressurelimiting (see [1]). In the unit, the load-sensing compensator varies thepump displacement to maintain a preset pressure differential acrossthe variable orifice, while the pressure-limiting compensator does notallow the pump pressure to exceed the pressure limit.

2-158


The Hydraulic Actuator with Load-Sensing Variable-DisplacementPump demo (sh_hydraulic_actuator_load_sensing_pump)implements this type of control. The next illustration shows theschematic of the Load-Sensing and Pressure-Limiting Control blockin the demo.

2-159


There are three hydraulic valve actuators in the model:

• SA1— A single-acting actuator that controls the Pressure-LimitingValve.

• SA — A single-acting valve actuator that acts on the pumpdisplacement control device (yoke control).

• DAA— A double-acting valve actuator that controls the Load-SensingValve. Its output is proportional to the difference between the pumppressure (port P) and the load pressure (port A).

Open the demo model to see the parameter settings for the blocks.

References [1] F. Yeapple, Fluid Power Design Handbook, Marcel Dekker, Inc., 1995

2-160






2-161

Hydraulic Fluid

Purpose Set working fluid properties by selecting from list of predefined fluids

Library Hydraulic Utilities

Description The Hydraulic Fluid block lets you specify the type of hydraulic fluidused in a loop of hydraulic blocks. It provides the hydraulic fluidproperties, such as kinematic viscosity, density, and bulk modulus, forall the hydraulic blocks in the loop. These fluid properties are assumedto be constant during simulation time. The density is determined by thetype of fluid, while kinematic viscosity additionally requires that thetemperature is specified.

The bulk modulus value shown in the block dialog box is the bulkmodulus of pure liquid, and is determined by the type of fluid and by thetemperature. When the fluid properties are used in hydraulic blocks,such as Constant Volume Chamber or Variable Volume Chamber,the fluid is represented as a mixture of liquid and a small amount ofentrained, nondissolved gas, which is specified in the Hydraulic Fluidblock as Relative amount of trapped air. The mixture bulk modulusin these blocks is determined as:

E E

pp p

p

n p p

El

a

a

n

an

a

nn

l

=+

+⎛

⎝⎜

⎞

⎠⎟

++( )

+

1

1

1

1

1

α

α

/

/

i

where

El Pure liquid bulk moduluspα Atmospheric pressureα Relative gas content at atmospheric pressure, α = VG/VLVG Gas volume at atmospheric pressure

2-162

Hydraulic Fluid

VL Volume of liquidn Gas-specific heat ratio

The main objective of representing fluid as a mixture of liquid and gasis to introduce an approximate model of cavitation, which takes placein a chamber if pressure drops below fluid vapor saturation level. Asit is seen in the graph below, the bulk modulus of a mixture decreasesat p pa→ , thus considerably slowing down further pressure change.At high pressure, p pa>> , a small amount of nondissolved gas haspractically no effect on the system behavior.

Cavitation is an inherently thermodynamic process, requiringconsideration of multiple-phase fluids, heat transfers, etc., and as suchcannot be accurately simulated with SimHydraulics® software. But the

2-163

Hydraulic Fluid

simplified version implemented in the block is good enough to signalif pressure falls below dangerous level, and to prevent computationfailure that normally occurs at negative pressures.

If it is known that cavitation is unlikely in the system under design, youcan set the relative gas content in the fluid properties to zero, thusincreasing the speed of computations.

The Hydraulic Fluid block offers a selection of predefined fluids. See“Examples” on page 2-167 for how you can get information on the fluidproperties used in the block. Once you select a fluid name, you canalso specify the temperature of the fluid and the relative amount ofentrained, nondissolved gas.

The Hydraulic Fluid block has one port. You can connect it to ahydraulic diagram by branching a connection line off the main line andconnecting it to the port. When you connect the Hydraulic Fluid blockto a hydraulic line, the software automatically identifies the hydraulicblocks connected to the particular loop and propagates the hydraulicfluid properties to all the hydraulic blocks in the loop.

Each topologically distinct hydraulic loop in a diagram requires aHydraulic Fluid block or Custom Hydraulic Fluid block to be connectedto it. Therefore, there must be as many Hydraulic Fluid blocks (orCustom Hydraulic Fluid blocks) as there are loops in the system.

Note If no Hydraulic Fluid block or Custom Hydraulic Fluid block isattached to a loop, the hydraulic blocks in this loop use the default fluid,which is Skydrol LD-4 at 60°C and with a 0.005 ratio of entrapped air.

2-164

Hydraulic Fluid


Hydraulic fluidHydraulic fluid type. Select one of the predefined fluids:

• Skydrol LD-4 (default)

• Skydrol 500B-4

• Skydrol-5

• HyJet-4A

• Fluid MIL-F-83282

2-165

Hydraulic Fluid



• Oil-10W

• Oil-30W

• Oil-50W

• Oil SAE-30

• Oil SAE-50

• Transmission fluid ATF (Dexron III)

• ISO VG 22 (ESSO UNIVIS N 22)



• Brake fluid DOT3



• Gasoline

• Diesel fuel

• Jet fuel

• Water-Glycol 60/40

• Water

Relative amount of trapped airAmount of entrained, nondissolved gas in the fluid. The amountis specified as the ratio of gas volume at normal conditions to thefluid volume in the chamber. The default value is 0.005.

System temperatureFluid temperature (C). The default value is 60.

2-166

Hydraulic Fluid

Viscosity derating factorProportionality coefficient that you can use to adjust fluidviscosity, if needed. Specify a value between 0.5 and 1.5. Thedefault value is 1.



• Hydraulic fluid


Ports The block has one hydraulic conserving port.

Examples You can get information on the fluids and their properties through theMATLAB® command line. In the following example, the first commandbrings you the list of available fluids, and the second command plots theproperties of a selected fluid from the list, in this case, Skydrol LD-4.

1 In the MATLAB Command Window, type:

props = sh_stockfluidproperties

The system responds with a list of available fluids:

props =

skydrol_ld_4: [1x1 struct]skydrol_500_4: [1x1 struct]

skydrol_5: [1x1 struct]hy_jet: [1x1 struct]

f_83282: [1x1 struct]f_5606: [1x1 struct]

f_87257: [1x1 struct]oil_10w: [1x1 struct]

2-167

Hydraulic Fluid

oil_30w: [1x1 struct]oil_50w: [1x1 struct]

oil_sae_30: [1x1 struct]oil_sae_50: [1x1 struct]atf_dexron: [1x1 struct]iso_vg_32: [1x1 struct]gasoline: [1x1 struct]

diesel_fuel: [1x1 struct]jet_fuel: [1x1 struct]

water_glycol: [1x1 struct]

2 To plot the properties of the first fluid in the list, Skydrol LD-4, type:

props.skydrol_ld_4.plot()

The plot window opens:

2-168

Hydraulic Fluid

Fluid properties for the Skydrol family of hydraulic fluids were obtainedfrom literature provided by the manufacturer, Solutia, Inc. Moreinformation is available on their website at: http://www.skydrol.com.

See Also Custom Hydraulic Fluid

2-169

http://www.skydrol.com

Hydraulic Motor

Purpose Simulate fixed-displacement hydraulic motor


Description The Hydraulic Motor block represents a positive, fixed-displacementhydraulic motor of any type as a data-sheet-based model. The keyparameters required to parameterize the block are motor displacement,volumetric and total efficiencies, nominal pressure, and angularvelocity. All these parameters are generally provided in the data sheetsor catalogs. The motor is represented with the following equations:

q D k pleak= +i iω

T D p mech= i iη


kD

pHPnom V nom

nom=


p p pA B= −

where

q Flow rate through the motorp Pressure differential across the motorpA,pB Gauge pressures at the block terminalsT Torque at the motor output shaft

D Motor displacementω Output shaft angular velocitykleak Leakage coefficient

2-170

Hydraulic Motor

kHP Hagen-Poiseuille coefficientηV Motor volumetric efficiencyηmech Motor mechanical efficiencyν Fluid kinematic viscosityρ Fluid densitypnom Motor nominal pressureωnom Motor nominal angular velocityνnom Nominal fluid kinematic viscosity

The leakage flow is determined based on the assumption that it islinearly proportional to the pressure differential across the motor andcan be computed by using the Hagen-Poiseuille formula

pl

dq

kqleak

HPleak= =128

4μ

πμ

where





kD

pHPnom V nom

nom=

−( )ω η ν ρ1 i i

2-171

Hydraulic Motor

The motor mechanical efficiency is not usually available in data sheets,therefore it is determined from the total and volumetric efficiency byassuming that the hydraulic efficiency is negligibly small


The block hydraulic positive direction is from port A to port B. Thismeans that the flow rate is positive if it flows from A to B and rotates theoutput shaft in the globally assigned positive direction. The pressuredifferential across the motor is determined as p p pA B= − , and positivepressure differential accelerates the shaft in the positive direction.




• No loading on the motor shaft, such as inertia, friction, spring, andso on, is considered.

• Leakage inside the motor is assumed to be linearly proportional toits pressure differential.

2-172

Hydraulic Motor


Motor displacementMotor displacement. The default value is 5e-6 m^3/rad.

Volumetric efficiencyMotor volumetric efficiency specified at nominal pressure, angularvelocity, and fluid viscosity. The default value is 0.92.

Total efficiencyMotor total efficiency, which is determined as a ratio between themechanical power at the output shaft and hydraulic power atthe motor inlet at nominal pressure, angular velocity, and fluidviscosity. The default value is 0.8.

2-173

Hydraulic Motor

Nominal pressurePressure differential across the motor, at which both thevolumetric and total efficiencies are specified. The default valueis 1e7 Pa.

Nominal angular velocityAngular velocity of the output shaft, at which both the volumetricand total efficiencies are specified. The default value is 188 rad/s.


GlobalParameters



AHydraulic conserving port associated with the motor inlet.

BHydraulic conserving port associated with the motor outlet.

SMechanical rotational conserving port associated with the motoroutput shaft.

See Also Variable-Displacement Motor

2-174

Hydraulic Pipeline

Purpose Simulate hydraulic pipeline with resistive and fluid compressibilityproperties

Library Pipelines

Description The Hydraulic Pipeline block models hydraulic pipelines with circularand noncircular cross sections. The block accounts for friction loss alongthe pipe length and for fluid compressibility. The block does not accountfor fluid inertia and cannot be used for predicting effects like waterhammer or changes in pressure caused by fluid acceleration.

The model is built of Simscape Foundation library building blocks andits schematic diagram is shown below.

The Resistive Tube blocks account for friction losses, while the ConstantVolume Chamber block accounts for fluid compressibility. By usingthe block parameters, you can set the model to simulate pipeline withrigid or compliant walls, including simulation of hydraulic hoses withelastic and viscoelastic properties.

The block positive direction is from port A to port B. This means thatthe flow rate is positive if it flows from A to B, and the pressure loss isdetermined as p p pA B= − .

2-175

Hydraulic Pipeline



• Flow is assumed to be fully developed along the pipe length.



2-176

Hydraulic Pipeline

2-177

Hydraulic Pipeline

Pipe cross section typeThe parameter can have one of two values: Circular orNoncircular. For a circular pipe, you need to specify its internaldiameter. For a noncircular pipe, you need to specify its hydraulicdiameter and pipe cross-sectional area. The default value of theparameter is Circular.

2-178

Hydraulic Pipeline

Pipe internal diameterPipe internal diameter. The parameter is used if Pipe crosssection type is set to Circular. The default value is 0.01 m.

Noncircular pipe cross-sectional areaPipe cross-sectional area. The parameter is used if Pipe crosssection type is set to Noncircular. The default value is 1e-4m^2.

Noncircular pipe hydraulic diameterHydraulic diameter of the pipe cross section. The parameter isused if Pipe cross section type is set to Noncircular. Thedefault value is 0.0112 m.

Geometrical shape factorThe parameter is used for computing friction factor at laminarflow and depends of the shape of the pipe cross section. For apipe with noncircular cross section, you must set the factor to anappropriate value, for example, 56 for a square, 96 for concentricannulus, 62 for rectangle (2:1), and so on (see [1]). The defaultvalue is 64, which corresponds to a pipe with a circular crosssection.

Pipe lengthPipe geometrical length. The default value is 5 m.

Aggregate equivalent length of local resistancesThis parameter represents total equivalent length of all localresistances associated with the pipe. You can account for thepressure loss caused by local resistances, such as bends, fittings,armature, inlet/outlet losses, and so on, by adding to the pipegeometrical length an aggregate equivalent length of all the localresistances. This length is added to the geometrical pipe lengthonly for hydraulic resistance computation. The fluid volumedepends on pipe geometrical length only. The default value is 1 m.

Internal surface roughness heightRoughness height on the pipe internal surface. The parameter istypically provided in data sheets or manufacturer’s catalogs. Thedefault value is 1.5e-5 m, which corresponds to drawn tubing.

2-179

Hydraulic Pipeline

Laminar flow upper marginSpecifies the Reynolds number at which the laminar flow regimeis assumed to start converting into turbulent. Mathematically,this is the maximum Reynolds number at fully developed laminarflow. The default value is 2000.

Turbulent flow lower marginSpecifies the Reynolds number at which the turbulent flow regimeis assumed to be fully developed. Mathematically, this is theminimum Reynolds number at turbulent flow. The default valueis 4000.

Pipe wall typeThe parameter is available only for circular pipes and can haveone of two values: Rigid or Flexible. If the parameter is setto Rigid, wall compliance is not taken into account, whichcan improve computational efficiency. The value Flexible isrecommended for hoses and metal pipes where wall compliancecan affect the system behavior. The default value is Rigid.

Static pressure-diameter coefficientCoefficient that establishes relationship between the pressure andthe internal diameter at steady-state conditions. This coefficientcan be determined analytically for cylindrical metal pipes orexperimentally for hoses. The parameter is used if the Pipe walltype parameter is set to Flexible. The default value is 2e-10m/Pa.

Viscoelastic process time constantTime constant in the transfer function that relates pipe internaldiameter to pressure variations. By using this parameter, thesimulated elastic or viscoelastic process is approximated withthe first-order lag. The value is determined experimentally orprovided by the manufacturer. The parameter is used if the Pipewall type parameter is set to Flexible. The default value is0.008 s.

2-180

Hydraulic Pipeline

Specific heat ratioGas-specific heat ratio for the Constant Volume Chamber block.The default value is 1.4.



• Pipe cross section type

• Pipe wall type

All other block parameters are available for modification. The actualset of modifiable block parameters depends on the values of the Pipecross section type and Pipe wall type parameters at the time themodel entered Restricted mode.

GlobalParameters




AHydraulic conserving port associated with the pipe inlet.

BHydraulic conserving port associated with the pipe outlet.

References [1] White, F.M., Viscous Fluid Flow, McGraw-Hill, 1991

2-181

Hydraulic Pipeline

See Also Linear Hydraulic Resistance

Resistive Tube

Segmented Pipeline

2-182

Hydraulic Pipe LP

Purpose Simulate hydraulic pipeline with resistive, fluid compressibility, andelevation properties


Description The Hydraulic Pipe LP block models hydraulic pipelines with circularand noncircular cross sections. The block accounts for friction loss alongthe pipe length and for fluid compressibility. The block does not accountfor fluid inertia and cannot be used for predicting effects like waterhammer or changes in pressure caused by fluid acceleration.

The model is built of Simscape Foundation library building blocks andits schematic diagram is shown below.

The Resistive Pipe LP blocks account for friction losses, while theConstant Volume Chamber block accounts for fluid compressibility. Byusing the block parameters, you can set the model to simulate pipelinewith rigid or compliant walls, including simulation of hydraulic hoseswith elastic and viscoelastic properties.

The difference in elevation between ports A and B is distributed evenlybetween pipe segments.


2-183

Hydraulic Pipe LP






The block dialog box contains three tabs:


• “Wall Compliance” on page 2-187

• “Vertical Position” on page 2-190

Basic Parameters

2-184

Hydraulic Pipe LP


Pipe internal diameterPipe internal diameter. The parameter is used if Pipe crosssection type is set to Circular. The default value is 0.01 m.

2-185

Hydraulic Pipe LP





Aggregate equivalent length of local resistancesThis parameter represents total equivalent length of all localresistances associated with the pipe. You can account for thepressure loss caused by local resistances, such as bends, fittings,armature, inlet/outlet losses, and so on, by adding to the pipegeometrical length an aggregate equivalent length of all the localresistances. This length is added to the geometrical pipe lengthonly for hydraulic resistance computation. The fluid volumedepends on pipe geometrical length only. The default value is 1 m.


Laminar flow upper marginSpecifies the Reynolds number at which the laminar flow regimeis assumed to start converting into turbulent. Mathematically,

2-186

Hydraulic Pipe LP

this is the maximum Reynolds number at fully developed laminarflow. The default value is 2000.


Wall Compliance

2-187

Hydraulic Pipe LP

Pipe wall typeThe parameter is available only for circular pipes and can haveone of two values: Rigid or Flexible. If the parameter is setto Rigid, wall compliance is not taken into account, whichcan improve computational efficiency. The value Flexible isrecommended for hoses and metal pipes where wall compliancecan affect the system behavior. The default value is Rigid.

Static pressure-diameter coefficientCoefficient that establishes relationship between the pressure andthe internal diameter at steady-state conditions. This coefficientcan be determined analytically for cylindrical metal pipes orexperimentally for hoses. The parameter is used if the Pipe wall

2-188

Hydraulic Pipe LP

type parameter is set to Flexible. The default value is 2e-12m/Pa.


Specific heat ratioGas-specific heat ratio for the Constant Volume Chamber block.The default value is 1.4. If Pipe cross section type is setto Noncircular, then this is the only parameter on the WallCompliance tab.

2-189

Hydraulic Pipe LP

Vertical Position

Port A elevation wrt reference planeThe parameter specifies vertical position of the pipe port A withrespect to the reference plane. The default value is 0.

Port B elevation wrt reference planeThe parameter specifies vertical position of the pipe port B withrespect to the reference plane. The default value is 0.



2-190

Hydraulic Pipe LP


• Pipe wall type

All other block parameters are available for modification. The actualset of modifiable block parameters depends on the values of the Pipecross section type and Pipe wall type parameters at the time themodel entered Restricted mode.

GlobalParameters







See Also Hydraulic Pipeline


Resistive Pipe LP

Resistive Tube

Segmented Pipeline

Segmented Pipe LP

2-191


Purpose Simulate single-acting hydraulic valve actuator


Description Use the Hydraulic Single-Acting Valve Actuator block as a pilot actuatorfor directional, pressure, or flow control valves in applications where allthe forces, except spring force, and flow consumption can be neglected.

The actuator consists of a piston and a spring. The spring, which can bepreloaded, tends to keep the piston at the initial position. As pressureapplied to the piston develops enough force to overcome the springpreload, the piston moves to the opposite position until it reaches itsmaximum stroke.

The actuator is simulated according to the following equations:

F p A= i

Lstroke

F Fpr=

−max

s

F F

L F F or F F F

stroke or F F

pr

pr pr=

<=

−( ) < <

>=

0 for

for

for

i i

imax

maxx

⎧

⎨⎪

⎩⎪

2-192


where

p Pressure applied to the pistons Piston displacementA Piston areaF Instantaneous spring forceFpr Spring preload forceFmax Spring force at maximum piston displacementstroke Piston strokeor Actuator orientation with respect to the globally assigned

positive direction. If pressure applied at port X moves thepiston in positive direction, or equals 1. If pressure applied atport X moves the piston in negative direction, or equals –1.

Connection X is a hydraulic conserving port associated with thevalve chamber. Connection P is a physical signal port whose outputcorresponds to piston displacement. Pressure applied at port X movesthe piston in the positive or negative direction, depending on the valueof the Actuator orientation parameter.



• No loading, such as inertia, friction, hydraulic force, and so on, istaken into account. The only force considered is a spring force.

• No flow consumption associated with the piston motion, leakage, orfluid compressibility is taken into account.

2-193



Piston areaEffective piston area. The default value is 2e-4 m^2.


Full stroke forceForce necessary to move the piston to maximum stroke. Thedefault value is 70 N.

Piston strokePiston stroke. The default value is 5e-3 m.

Actuator orientationSpecifies actuator orientation with respect to the globally assignedpositive direction. The actuator can be installed in two different

2-194


ways, depending upon whether it moves the piston in the positiveor in the negative direction when pressure is applied at its inlet.If pressure applied at port X moves the piston in the negativedirection, set the parameter to Acts in negative direction.The default value is Acts in positive direction.






XHydraulic conserving port associated with the valve chamber.

PPhysical signal port that outputs piston displacement.

Examples The following example shows a model of a pressure-relief valve builtusing the Hydraulic Single-Acting Valve Actuator and Orifice withVariable Area Round Holes blocks.

2-195






2-196

Local Resistance

Purpose Simulate all kinds of hydraulic resistances specified by loss coefficient


Description The Local Resistance block represents a generic local hydraulicresistance, such as a bend, elbow, fitting, filter, local change in theflow cross section, and so on. The pressure loss caused by resistanceis computed based on the pressure loss coefficient, which is usuallyprovided in catalogs, data sheets, or hydraulic textbooks. The pressureloss coefficient can be specified either as a constant, or by a table, inwhich it is tabulated versus Reynolds number.

The pressure loss is determined according to the following equations:

pK

Aq q Re Re

KD A

q Re RecrH

=

⎧

⎨⎪⎪

ρ

ν ρ2

2

2| |

Re

for >

for <=

cr

crii

i⎩⎩⎪⎪

p p pA B= −

KK

=⎧⎨⎩

const (Re)

Re = q DA

Hiiν

DA

H = 4π

where

q Flow ratep Pressure loss

2-197

Local Resistance

pA,pB Gauge pressures at the block terminalsK Pressure loss coefficient, which can be specified either as a

constant, or as a table-specified function of the Reynoldsnumber

Re Reynolds numberRecr Reynolds number of the transition from laminar to turbulent

flowDH Orifice hydraulic diameterA Passage area

ρ Fluid densityν Fluid kinematic viscosity

Two block parameterization options are available:

• By semi-empirical formulas — The pressure loss coefficient isassumed to be constant for a specific flow direction. The flow regimecan be either laminar or turbulent, depending on the Reynoldsnumber.

• By table-specified K=f(Re) relationship — The pressure losscoefficient is specified as function of the Reynolds number. Theflow regime is assumed to be turbulent all the time. It is yourresponsibility to provide the appropriate values in the K=f(Re) tableto ensure turbulent flow.

The resistance can be symmetrical or asymmetrical. In symmetricalresistances, the pressure loss practically does not depend on flowdirection and one value of the coefficient is used for both the direct andreverse flow. For asymmetrical resistances, the separate coefficientsare provided for each flow direction. If the loss coefficient is specifiedby a table, the table must cover both the positive and the negative flowregions.

2-198

Local Resistance







• If you select parameterization by the table-specified relationshipK=f(Re), the flow is assumed to be completely turbulent.

2-199

Local Resistance


2-200

Local Resistance

Resistance areaThe smallest passage area. The default value is 1e-4 m^2.

Model parameterizationSelect one of the following methods for specifying the pressureloss coefficient:

• By semi-empirical formulas — Provide a scalar value forthe pressure loss coefficient. For asymmetrical resistances,you have to provide separate coefficients for direct and reverseflow. This is the default method.

2-201

Local Resistance

• By loss coefficient vs. Re table — Provide tabulateddata of loss coefficients and corresponding Reynolds numbers.The loss coefficient is determined by one-dimensional tablelookup. You have a choice of three interpolation methods andtwo extrapolation methods. For asymmetrical resistances, thetable must cover both the positive and the negative flow regions.

Pressure loss coefficient for direct flowLoss coefficient for the direct flow (flowing from A to B). For simpleideal configurations, the value of the coefficient can be determinedanalytically, but in most cases its value is determined empiricallyand provided in textbooks and data sheets (for example, see[1]). The default value is 2. This parameter is used if Modelparameterization is set to By semi-empirical formulas.

Pressure loss coefficient for reverse flowLoss coefficient for the reverse flow (flowing from B to A). Theparameter is similar to the loss coefficient for the direct flow andmust be set to the same value if the resistance is symmetrical.The default value is 2. This parameter is used if Modelparameterization is set to By semi-empirical formulas.


Reynolds number vectorSpecify the vector of input values for Reynolds numbers as atabulated 1-by-m array. The input values vector must be strictlymonotonically increasing. The values can be nonuniformly spaced.You must provide at least three values. The default values are[-4000, -3000, -2000, -1000, -500, -200, -100, -50,-40, -30, -20, -15, -10, 10, 20, 30, 40, 50, 100, 200,

2-202

Local Resistance

500, 1000, 2000, 4000, 5000, 10000]. This parameter isused ifModel parameterization is set to By loss coefficientvs. Re table.

Loss coefficient vectorSpecify the vector of output values for the loss coefficient as atabulated 1-by-m array. The loss coefficient vector must be thesame size as the Reynolds numbers vector. The default valuesare [0.25, 0.3, 0.65, 0.9, 0.65, 0.75, 0.90, 1.15,1.35, 1.65, 2.3, 2.8, 3.10, 5, 2.7, 1.8, 1.46, 1.3,0.9, 0.65, 0.42, 0.3, 0.20, 0.40, 0.42, 0.25]. Thisparameter is used ifModel parameterization is set to By losscoefficient vs. Re table.







• From last 2 points— Extrapolates using the linear method(regardless of the interpolation method specified), based onthe last two output values at the appropriate end of the range.That is, the block uses the first and second specified output

2-203

Local Resistance

values if the input value is below the specified range, and thetwo last specified output values if the input value is above thespecified range.



GlobalParameters






References [1] Idelchik, I.E., Handbook of Hydraulic Resistance, CRC Begell House,1994

2-204

Local Resistance

See Also Elbow

Gradual Area Change

Pipe Bend

Sudden Area Change

T-junction

2-205

Needle Valve

Purpose Simulate hydraulic needle valve


Description The Needle Valve block models a variable orifice created by a conicalneedle and a round sharp-edged orifice in thin material.


2-206

Needle Valve

qC A p sign p Re Re

C AD

p Re Re

D

DLH

=( )i i

ii

2

2

ρ

ν ρ

| | for >=

for <

cr

cr

⎧

⎨⎪⎪

⎩⎪⎪

h x x= +0

hds

maxtan

= ( )α2

A hA hd h h A h h

A

leak

s leak( ) cos sin sin max=<=

−( ) + < <for for

00α α αi i

mmax max+ >=

⎧⎨⎪

⎩⎪ A h hleak for

p p pA B= −

Re( )

= q DA h

Hiiν

CC

DLD

cr=

⎛

⎝⎜⎜

⎞

⎠⎟⎟Re

2

DA h

H = 4 ( )π

Ads

max =π 2

4

where

2-207

Needle Valve

q Flow ratep Pressure differentialpA,pB Gauge pressures at the block terminalsCD Flow discharge coefficientA(h) Instantaneous orifice passage areax0 Initial opening

x Needle displacement from initial positionh Valve openinghmax Maximum needle strokeds Orifice diameterα Needle angleρ Fluid densityDH Valve instantaneous hydraulic diameterν Fluid kinematic viscosityAleak Closed valve leakage areaAmax Maximum valve open area






2-208

Needle Valve

• The flow passage area is assumed to be equal to the frustum sidesurface area.


Valve orifice diameterThe diameter of the orifice of the valve. The default value is0.005 m.

Needle cone angleThe angle of the valve conical needle. The parameter value mustbe in the range between 0 and 180 degrees. The default valueis 90 degrees.

2-209

Needle Valve

Initial openingThe initial opening of the valve. You can specify both positive andnegative values. The default value is 0.




GlobalParameters




2-210

Needle Valve




See Also Ball Valve

Poppet Valve


2-211


Purpose Simulate hydraulic variable orifice shaped as set of round holes drilledin sleeve

Library Orifices

Description The block models a variable orifice created by a cylindrical spool anda set of round holes drilled in the sleeve. All the holes are of the samediameter, evenly spread along the sleeve perimeter, and their centerlines are located in the same plane. The flow rate through the orificeis proportional to the orifice opening and to the pressure differentialacross the orifice. The following schematic shows the cross section of anorifice with variable round holes, where

q Flow rateh Orifice openingx Spool displacement from initial positiond0 Orifice hole diameter

2-212



qC A p sign p Re Re

C AD

p Re Re

D

DLH

=( )i i

ii

2

2

ρ

ν ρ

| | for >=

for <

cr

cr

⎧

⎨⎪⎪

⎩⎪⎪

h x x or= +0 i

2-213


A h

A h

z dh

d

leak

( ) arccos sin arccos=

<=

−⎛

⎝⎜

⎞

⎠⎟ − −

for 0

18

2 12

2 12

02

0i

hhd

A h d

A A

leak

le

000

⎛

⎝⎜

⎞

⎠⎟

⎛

⎝⎜⎜

⎞

⎠⎟⎟

⎛

⎝⎜⎜

⎞

⎠⎟⎟

⎛

⎝⎜⎜

⎞

⎠⎟⎟

+ < <

+

for

max aak h dfor >=

⎧

⎨

⎪⎪

⎩

⎪⎪

0

p p pA B= −

Re( )

= q DA h

Hiiν

CC

DLD

cr=

⎛

⎝⎜⎜

⎞

⎠⎟⎟Re

2

DA h

H = 4 ( )π

Ad

max =π 0

2

4

where

q Flow ratep Pressure differentialpA,pB Gauge pressures at the block terminalsCD Flow discharge coefficientA(h) Instantaneous orifice passage aread0 Hole diameterz Number of holesx0 Initial opening

2-214


x Spool displacement from initial positionh Orifice openingor Orifice orientation indicator. The variable assumes +1 value

if a spool displacement in the globally assigned positivedirection opens the orifice, and –1 if positive motion decreasesthe opening.

ρ Fluid densityDH Instantaneous orifice hydraulic diameterν Fluid kinematic viscosityAleak Closed orifice leakage areaAmax Fully open orifice passage area

The block positive direction is from port A to port B. This means that theflow rate is positive if it flows from A to B and the pressure differentialis determined as p p pA B= − . Positive signal at the physical signal portS opens or closes the orifice depending on the value of the parameterOrifice orientation.





2-215



Diameter of round holesDiameter of the orifice holes. The default value is 5e-3 m.

Number of round holesNumber of holes. The default value is 6.


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Initial openingOrifice initial opening. The parameter can be positive(underlapped orifice), negative (overlapped orifice), or equal tozero for zero lap configuration. The value of initial opening doesnot depend on the orifice orientation. The default value is 0.

Orifice orientationThe parameter is introduced to specify the effect of the orificecontrol member motion on the valve opening. The parameter canbe set to one of two options: Opens in positive direction orOpens in negative direction. The value Opens in positivedirection specifies an orifice whose control member opens thevalve when it is shifted in the globally assigned positive direction.The parameter is extremely useful for building a multi-orificevalve with all the orifices being controlled by the same spool. Thedefault value is Opens in positive direction.





2-217




GlobalParameters







The flow rate is positive if fluid flows from port A to port B. Positivesignal at the physical signal port S opens or closes the orifice dependingon the value of the parameter Orifice orientation.



Fixed Orifice



Variable Orifice

2-218


Purpose Simulate hydraulic variable orifice shaped as rectangular slot

Library Orifices

Description The block models a variable orifice created by a cylindrical sharp-edgedspool and a rectangular slot in a sleeve. The flow rate through the orificeis proportional to the orifice opening and to the pressure differentialacross the orifice. The model accounts for the laminar and turbulentflow regimes by monitoring the Reynolds number (Re) and comparingits value with the critical Reynolds number (Recr). The flow rate isdetermined according to the following equations:

qC A p sign p Re Re

C AD

p Re Re

D

DLH

=( )i i

ii

2

2

ρ

ν ρ

| | for >=

for <

cr

cr

⎧

⎨⎪⎪

⎩⎪⎪

h x x or= +0 i

A hb h A hA h

leak

leak( ) =

+ ><=

⎧⎨⎩

i for for

00

p p pA B= −

Re( )

= q DA h

Hiiν

CC

DLD

cr=

⎛

⎝⎜⎜

⎞

⎠⎟⎟Re

2

DA h

H = 4 ( )π

2-219


where

q Flow ratep Pressure differentialpA,pB Gauge pressures at the block terminalsCD Flow discharge coefficientA(h) Instantaneous orifice passage areab Width of the orifice slotx0 Initial openingx Spool displacement from initial positionh Orifice openingor Orifice orientation indicator. The variable assumes +1 value

if a spool displacement in the globally assigned positivedirection opens the orifice, and –1 if positive motion decreasesthe opening.

ρ Fluid densityDH Instantaneous orifice hydraulic diameterν Fluid kinematic viscosityAleak Closed orifice leakage area

The block positive direction is from port A to port B. This means that theflow rate is positive if it flows from A to B and the pressure differentialis determined as p p pA B= − . Positive signal at the physical signal portS opens or closes the orifice depending on the value of the parameterOrifice orientation.

2-220







Orifice widthThe width of the rectangular slot. The default value is 1e-2 m.

Flow discharge coefficientSemi-empirical parameter for orifice capacity characterization.Its value depends on the geometrical properties of the orifice, and

2-221


usually is provided in textbooks or manufacturer data sheets.The default value is 0.7.





2-222






GlobalParameters










Fixed Orifice

2-223




Variable Orifice

2-224


Purpose Simulate hydraulic check valve that allows flow in one direction, butcan be disabled by pilot pressure


Description The Pilot-Operated Check Valve block represents a hydraulicpilot-operated check valve as a data-sheet-based model. The purposeof the check valve is to permit flow in one direction and block it in theopposite direction, as shown in the following figure.

Unlike a conventional check valve, the pilot-operated check valve canbe opened by inlet pressure pA, pilot pressure pX, or both. The forceacting on the poppet is determined as

F p A p A p AA A X X B B= + −i i i

where

pA,pB Gauge pressures at the valve terminalspX Gauge pressure at the pilot terminalAA Area of the spool in the A chamber

2-225


AB Area of the spool in the B chamberAX Area of the pilot chamber

This equation is commonly used in a slightly modified form

p p p k pe A X p B= + −i

where kp = AX/AA is usually referred to as pilot ratio and pe is theequivalent pressure differential across the poppet. The valve remainsclosed while this pressure differential across the valve is lower thanthe valve cracking pressure. When cracking pressure is reached, thevalue control member (spool, ball, poppet, etc.) is forced off its seat, thuscreating a passage between the inlet and outlet. If the flow rate is highenough and pressure continues to rise, the area is further increaseduntil the control member reaches its maximum. At this moment, thevalve passage area is at its maximum. The valve maximum area andthe cracking and maximum pressures are generally provided in thecatalogs and are the three key parameters of the block.



2-226


qC A p sign p Re Re

C AD

p Re Re

D

DLH

=( )i i

ii

2

2

ρ

ν ρ

| | for >=

for <

cr

cr

⎧

⎨⎪⎪

⎩⎪⎪

p p p k pe A X p B= + −i

A pA p pA k p p p p p

leak e crack

leak e crack crack e( ) =<=

+ −( ) < <for for i mmax

max maxA p pefor >=

⎧⎨⎪

⎩⎪

kA Ap p

leak

crack=

−−

max

max

p p pA B= −

Re( )

= q DA p

Hiiν

CC

DLD

cr=

⎛

⎝⎜⎜

⎞

⎠⎟⎟Re

2

DA p

H = 4 ( )π

where

q Flow rate through the valvep Pressure differential across the valvepe Equivalent pressure differential across the control member

2-227


pA,pB Gauge pressures at the valve terminalspX Gauge pressure at the pilot terminalkp Pilot ratio, kp = pX/pA

k Valve gain coefficientCD Flow discharge coefficientA(p) Instantaneous orifice passage areaAmax Fully open valve passage areaAleak Closed valve leakage area

pcrack Valve cracking pressurepmax Pressure needed to fully open the valveDH Instantaneous orifice hydraulic diameterρ Fluid densityν Fluid kinematic viscosity






• No flow consumption is associated with the pilot chamber.


2-228




Cracking pressurePressure level at which the orifice of the valve starts to open. Thedefault value is 3e4 Pa.

Maximum opening pressurePressure differential across the valve needed to fully open thevalve. Its value must be higher than the cracking pressure. Thedefault value is 1.2e5 Pa.

2-229


Pilot ratioRatio between effective area in the pilot chamber to the effectivearea in the inlet chamber. The default value is 5.




GlobalParameters




2-230




XHydraulic conserving port associated with the valve pilot terminal.


2-231

Pipe Bend

Purpose Simulate hydraulic resistance in pipe bend


Description The Pipe Bend block represents a pipe bend as a local hydraulicresistance. The pressure loss in the bend is assumed to consist of

• Loss in the straight pipe

• Loss due to curvature

The loss in a straight pipe is simulated with the Resistive Tube block.The loss due to curvature is simulated with the Local Resistance block,and the pressure loss coefficient is determined in accordance with theCrane Co. recommendations (see [1], p. A-29). The flow regime ischecked in the underlying Local Resistance block by comparing theReynolds number to the specified critical Reynolds number value.

The pressure loss due to curvature for turbulent flow regime isdetermined according to the following formula:

p KA

q q= ρ2 2

| |

where

q Flow ratep Pressure lossK Pressure loss coefficientA Bend cross-sectional areaρ Fluid density

For laminar flow regime, the formula for pressure loss computation ismodified, as described in the reference documentation for the LocalResistance block.

2-232

Pipe Bend

The pressure loss coefficient is determined according to the tableprovided in [1], p. A-29:

K f r d= ( , , )α

where

d Pipe internal diameterr Curvature radius (d ≤ r ≤ 20d)α Bend angle in degrees (0 ≤ α ≤ 180)

Correction for non-90o bends is performed with the empirical formula(see [2], Fig. 4.6):

Kcorr = − −α α( . . )0 0142 3 703 10 5i


The block positive direction is from port A to port B. This means thatthe flow rate is positive if fluid flows from A to B, and the pressuredifferential is determined as p p pA B= − .

2-233

Pipe Bend

Warning

The formulas used in the Pipe Bend block are very approximate,especially in the laminar and transient flow regions. For moreaccurate results, use a combination of the Local Resistanceblock with a table-specified K=f(Re) relationship and theResistive Tube block.



• Fluid inertia, fluid compressibility, and wall compliance are nottaken into account.


• The bend is assumed to be made of a clean commercial steel pipe.

2-234

Pipe Bend


Pipe diameterThe internal diameter of the pipe. The default value is 0.01 m.

Bend radiusThe radius of the bend. The default value is 0.04 m.

Bend angleThe angle of the bend. The value must be in the range between 0and 180 degrees. The default value is 90 deg.

2-235

Pipe Bend


Critical Reynolds numberThe maximum Reynolds number for laminar flow. The transitionfrom laminar to turbulent regime is supposed to take placewhen the Reynolds number reaches this value. The valueof the parameter depends on geometrical profile, and therecommendations on the parameter value can be found inhydraulic textbooks. The default value is 350.

GlobalParameters




AHydraulic conserving port associated with the bend inlet.

BHydraulic conserving port associated with the bend outlet.


[2] George R. Keller, Hydraulic System Analysis, Published by theEditors of Hydraulics & Pneumatics Magazine, 1970

2-236

Pipe Bend

See Also Elbow

Gradual Area Change

Local Resistance

Resistive Tube

Sudden Area Change

T-junction

2-237

Poppet Valve

Purpose Simulate hydraulic poppet valve


Description The Poppet Valve block models a variable orifice created by a cylindricalsharp-edged stem and a conical seat.


2-238

Poppet Valve

qC A p sign p Re Re

C AD

p Re Re

D

DLH

=( )i i

ii

2

2

ρ

ν ρ

| | for >=

for <

cr

cr

⎧

⎨⎪⎪

⎩⎪⎪

h x x= +0

A hA hd h h A h h

A

leak

s leak( ) cos sin sin max=<=

+( ) + < <for for

00α α αi i

mmax max+ >=

⎧⎨⎪

⎩⎪ A h hleak for

p p pA B= −

Re( )

= q DA h

Hiiν

CC

DLD

cr=

⎛

⎝⎜⎜

⎞

⎠⎟⎟Re

2

DA h

H = 4 ( )π

Ads

max =π 2

4

where

q Flow ratep Pressure differentialpA,pB Gauge pressures at the block terminals

2-239

Poppet Valve

CD Flow discharge coefficientA(h) Instantaneous orifice passage areax0 Initial opening

x Stem displacement from initial positionh Valve openinghmax Maximum valve opening. The passage area remains constant

and equal to Amax after this.ds Stem diameterα Cone angleρ Fluid densityDH Valve instantaneous hydraulic diameterν Fluid kinematic viscosityAleak Closed valve leakage areaAmax Maximum valve open area






• The flow passage area is assumed to be equal to the frustum sidesurface area.

2-240

Poppet Valve


Valve stem diameterThe diameter of the valve stem. The default value is 0.01 m.

Seat cone angleThe angle of the valve conical seat. The parameter value mustbe in the range between 0 and 180 degrees. The default valueis 120 degrees.

Initial openingThe initial opening of the valve. The parameter value must benonnegative. The default value is 0.

Flow discharge coefficientSemi-empirical parameter for valve capacity characterization. Itsvalue depends on the geometrical properties of the orifice, and

2-241

Poppet Valve




GlobalParameters






2-242

Poppet Valve


See Also Ball Valve

Needle Valve


2-243


Purpose Simulate hydraulic pressure compensating valve


Description The Pressure-Compensated Flow Control Valve block represents apressure-compensated flow control valve as a data-sheet-based model.The valve is based on a Pressure Compensator block installed upstreamfrom a Variable Orifice block, as shown in the following illustration.

Depending on data listed in the manufacturer’s catalogs or data sheetsfor your particular valve, you can choose one of the following modelparameterization options:



2-244


In the first case, the passage area is assumed to be linearly dependenton the control member displacement, that is, the orifice is assumed to beclosed at the initial position of the control member (zero displacement),and the maximum opening takes place at the maximum displacement.In the second case, the passage area is determined by one-dimensionalinterpolation from the table A=A(h). In both cases, a small leakagearea is assumed to exist even after the orifice is completely closed.Physically, it represents a possible clearance in the closed valve, but themain purpose of the parameter is to maintain numerical integrity ofthe circuit by preventing a portion of the system from getting isolatedafter the valve is completely closed. An isolated or “hanging” part of thesystem could affect computational efficiency and even cause failureof computation.

The block positive direction is from port A to port B. This means that theflow rate is positive if it flows from A to B, and the pressure differentialis determined as p p pA B= − . Positive signal at port C opens the valve.

AssumptionsandLimitations



2-245



2-246


Model parameterizationSelect one of the following methods for specifying the orifice:

• By maximum area and opening — Provide values for themaximum orifice area and the maximum orifice opening. Thepassage area is linearly dependent on the control memberdisplacement, that is, the orifice is closed at the initial position

2-247


of the control member (zero displacement), and the maximumopening takes place at the maximum displacement. This isthe default method.


Orifice maximum areaSpecify the area of a fully opened orifice. The parameter valuemust be greater than zero. The default value is 5e-5 m^2. Thisparameter is used if Model parameterization is set to Bymaximum area and opening.

Orifice maximum openingSpecify the maximum displacement of the control member. Theparameter value must be greater than zero. The default value is5e-4 m. This parameter is used if Model parameterization isset to By maximum area and opening.

Tabulated orifice openingsSpecify the vector of input values for orifice openings as atabulated 1-by-m array. The input values vector must be strictlymonotonically increasing. The values can be nonuniformly spaced.You must provide at least three values. The default values, inmeters, are [-2e-3,0,5e-3,15e-3]. This parameter is usedif Model parameterization is set to By area vs. openingtable. Tabulated orifice openings values will be used togetherwith Tabulated orifice area values for one-dimensional tablelookup.

Tabulated orifice areaSpecify the vector of output values for orifice area as a tabulated1-by-m array. The orifice area vector must be the same size asthe orifice openings vector. All the values must be positive. Thedefault values, in m^2, are [1e-12,4e-12,1.e-5,1.02e-5]. This

2-248


parameter is used ifModel parameterization is set to By areavs. opening table.

Interpolation methodThis parameter is used if Model parameterization is set toBy area vs. opening table. Select one of the followinginterpolation methods for approximating the output value whenthe input value is between two consecutive grid points:




For more information on interpolation algorithms, see the PSLookup Table (1D) block reference page.

Extrapolation methodThis parameter is used if Model parameterization is set toBy area vs. opening table. Select one of the followingextrapolation methods for determining the output value when theinput value is outside the range specified in the argument list:



2-249


For more information on extrapolation algorithms, see the PSLookup Table (1D) block reference page.

Pressure differential across the orificePressure difference that must be maintained across the elementby the pressure compensator. The default value is 6e5 Pa.

Pressure reducing valve regulation rangePressure increase over the preset level needed to fully close thevalve. Must be less than 0.2 of the Pressure differential acrossthe orifice parameter value. The default value is 5e4 Pa.




Leakage areaThe total area of possible leaks in the completely closed valve.The main purpose of the parameter is to maintain numericalintegrity of the circuit by preventing a portion of the system fromgetting isolated after the valve is completely closed. An isolated or“hanging” part of the system could affect computational efficiencyand even cause failure of computation. Extreme caution should

2-250


be exercised if the parameter is set to 0. The default value is1e-12 m^2.







GlobalParameters






CPhysical signal control port.

2-251


See Also Ball Valve

Needle Valve

Poppet Valve

2-252

Pressure Compensator

Purpose Simulate hydraulic pressure compensating valve

Library Pressure Control Valves

Description The Pressure Compensator block represents a hydraulic pressurecompensating valve, or pressure compensator. Pressure compensatorsare used to maintain preset pressure differential across a hydrauliccomponent to minimize the influence of pressure variation on a flow ratepassing through the component. The following illustration shows typicalapplications of a pressure compensator, where it is used in combinationwith the orifice installed downstream (left figure) or upstream (rightfigure). The compensator can be also used in combination with meteringpumps, flow dividers, and so on.

The block is implemented as a data-sheet-based model, based onparameters usually provided in the manufacturer’s catalogs or datasheets.

Pressure compensator is a normally open valve. Its opening isproportional to pressure difference between ports X and Y and thespring force. The following illustration shows typical relationshipbetween the valve passage area A and the pressure difference pxy.

2-253


The orifice remains fully open until the pressure difference is lowerthan valve preset pressure determined by the spring preload. Whenthe preset pressure is reached, the valve control member is forced offits stop and starts closing the orifice, thus trying to maintain pressuredifferential at preset level. Any further increase in the pressuredifference causes the control member to close the orifice even more,until the point when the orifice if fully closed. The pressure increasethat is necessary to close the valve is referred to as regulation range,or pressure compensator static error, and usually is provided inmanufacturer’s catalog or data sheets.

The main parameters of the block are the valve maximum area andregulation range. In addition, you need to specify the leakage area ofthe valve. Physically, it represents a possible clearance in the closedvalve, but the main purpose of the parameter is to maintain numerical

2-254


integrity of the circuit by preventing a portion of the system fromgetting isolated after the valve is completely closed. An isolated or“hanging” part of the system could affect computational efficiency andeven cause failure of computation.

The model accounts for the laminar and turbulent flow regimes bymonitoring the Reynolds number (Re) and comparing its value with thecritical Reynolds number (Recr). The flow rate is computed accordingto the following equations:

qC A p sign p Re Re

C AD

p Re Re

D

DLH

=( )i i

ii

2

2

ρ

ν ρ

| | for >=

for <

cr

cr

⎧

⎨⎪⎪

⎩⎪⎪

h x x or= +0 i

A hA p pA k p p p p pA

xy set

set set xy

lea

( )max

max max=<=

− −( ) < <for for i

kk xyp pfor >=

⎧

⎨⎪

⎩⎪

max

kA A

pleak

reg=

−max

p p pA B= −

p p pxy x y= −

Re( )

= q DA h

Hiiν

2-255


CC

DLD

cr=

⎛

⎝⎜⎜

⎞

⎠⎟⎟Re

2

DA h

H = 4 ( )π

where

q Flow ratep Pressure differential across the valvepxy Pressure differential across valve control terminalspA,pB Gauge pressures at the valve main terminalspx,py Gauge pressures at the valve control terminalspset Valve preset pressurepmax Pressure needed to fully close the orificepreg Regulation rangeA(h) Instantaneous orifice passage areaAmax Orifice maximum areaCD Flow discharge coefficientρ Fluid densityDH Instantaneous orifice hydraulic diameterν Fluid kinematic viscosityAleak Closed orifice leakage area

The block positive direction is from port A to port B. This means that theflow rate is positive if it flows from A to B, and the pressure differentialis determined as p p pA B= − . The control pressure differential is

2-256


measured as p p pxy x y= − , and it creates a force acting against thespring preload.

AssumptionsandLimitations




• Flow consumption associated with the spool motion is neglected.



2-257


Valve pressure settingPressure difference that must be maintained across an elementconnected to ports X and Y. At this pressure the valve orificestarts to close. The default value is 3e6 Pa.

Valve regulation rangePressure increase over the preset level needed to fully close thevalve. Must be less than 0.2 of the Valve pressure settingparameter value. The default value is 1.5e5 Pa.




GlobalParameters


2-258






XHydraulic conserving port associated with the pressure controlterminal that opens the orifice.

YHydraulic conserving port associated with the pressure controlterminal that closes the orifice.

See Also Pressure Reducing Valve

Pressure Relief Valve

2-259

Pressure Reducing Valve

Purpose Simulate pressure control valve maintaining reduced pressure inportion of system


Description The Pressure Reducing Valve block represents a hydraulicpressure-reducing valve as a data-sheet-based model.Pressure-reducing valves are used to maintain reduced pressure in aportion of a system. The following figure shows the typical dependencybetween the valve passage area A and the pressure pB downstreamfrom the valve.

The pressure-reducing valve is a normally open valve and it remainsfully open while outlet pressure is lower than the valve preset pressure.When the preset pressure is reached, the value control member (spool,ball, poppet, etc.) is forced off its stop and starts closing the orifice, thus

2-260


trying to maintain outlet pressure at preset level. Any further increasein the outlet pressure causes the control member to close the orificeeven more until the point when the orifice if fully closed. The pressureincrease that is necessary to close the valve is referred to as regulationrange, and is generally provided in the catalogs, along with the valvemaximum area. The valve maximum area and regulation range arethe key parameters of the block.


The block is built as a structural model based on the PressureCompensator block, as shown in the following schematic.


2-261




Valve pressure settingPreset pressure level, at which the orifice of the valve starts toclose. The default value is 5e6 Pa.

Valve regulation rangePressure increase over the preset level needed to fully close thevalve. Must be less than 0.2 of the Valve pressure settingparameter value. The default value is 5e5 Pa.

Flow discharge coefficientSemi-empirical parameter for valve capacity characterization. Itsvalue depends on the geometrical properties of the orifice, and

2-262




Leakage areaThe total area of possible leaks in the completely closed valve.The main purpose of the parameter is to maintain numericalintegrity of the circuit by preventing a portion of the system fromgetting isolated after the valve is completely closed. An isolated or“hanging” part of the system could affect computational efficiencyand even cause failure of computation. Extreme caution shouldbe exercised if the parameter is set to 0. The default value is1e-12m^2.

GlobalParameters






2-263


Examples The Power Unit with Pressure Reducing Valve demo(sh_power_unit_pressure_red_valve) illustrates the use of thePressure Reducing Valve block in hydraulic systems. The pressurereducing valve is set to 20e5 Pa and maintains this pressuredownstream, as long as the upstream pressure is higher than thissetting.

See Also Pressure Compensator


2-264


Purpose Simulate pressure control valve maintaining preset pressure in system


Description The Pressure Relief Valve block represents a hydraulic pressure reliefvalve as a data-sheet-based model. The following figure shows thetypical dependency between the valve passage area A and the pressuredifferential p across the valve.

The valve remains closed while pressure at the valve inlet is lower thanthe valve preset pressure. When the preset pressure is reached, thevalue control member (spool, ball, poppet, etc.) is forced off its seat, thuscreating a passage between the inlet and outlet. Some fluid is divertedto a tank through this orifice, thus reducing the pressure at the inlet. If

2-265


this flow rate is not enough and pressure continues to rise, the area isfurther increased until the control member reaches its maximum. Atthis moment, the maximum flow rate is passing through the valve. Thevalue of a maximum flow rate and the pressure increase over the presetlevel to pass this flow rate are generally provided in the catalogs. Thepressure increase over the preset level is frequently referred to as valvesteady state error, or regulation range. The valve maximum area andregulation range are the key parameters of the block.



qC A p sign p Re Re

C AD

p Re Re

D

DLH

=( )i i

ii

2

2

ρ

ν ρ

| | for >=

for <

cr

cr

⎧

⎨⎪⎪

⎩⎪⎪

A pA p pA k p p p p pA

leak set

leak set set( ) max

max

=<=

+ −( ) < <for for fo

irr p p>=

⎧⎨⎪

⎩⎪ max

kApreg

= max

2-266


p p pA B= −

Re( )

= q DA p

Hiiν

CC

DLD

cr=

⎛

⎝⎜⎜

⎞

⎠⎟⎟Re

2

DA p

H = 4 ( )π

where

q Flow rate through the valvep Pressure differential across the valvepA,pB Gauge pressures at the block terminalsCD Flow discharge coefficientA(p) Instantaneous orifice passage areaAmax Fully open valve passage areaAleak Closed valve leakage areapreg Regulation rangepset Valve preset pressurepmax Valve pressure at maximum openingDH Instantaneous orifice hydraulic diameterρ Fluid densityν Fluid kinematic viscosity

2-267


The block positive direction is from port A to port B. This meansthat the flow rate is positive if it flows from A to B and the pressuredifferential is determined as p p pA B= − .







2-268



Valve pressure settingPreset pressure level, at which the orifice of the valve starts toopen. The default value is 50e5 Pa.

Valve regulation rangePressure increase over the preset level needed to fully open thevalve. Must be less than 0.2 of the Valve pressure settingparameter value. The default value is 5e5 Pa.



Leakage areaThe total area of possible leaks in the completely closed valve.The main purpose of the parameter is to maintain numericalintegrity of the circuit by preventing a portion of the system fromgetting isolated after the valve is completely closed. An isolated or“hanging” part of the system could affect computational efficiencyand even cause failure of computation. Extreme caution shouldbe exercised if the parameter is set to 0. The default value is1e-12m^2.

2-269


GlobalParameters






Examples The Power Unit with Fixed-Displacement Pump demo(sh_power_unit_fxd_dspl_pump) illustrates the use of the PressureRelief Valve block in hydraulic systems. The valve is set to 75e5 Paand starts diverting fluid to tank as soon as the pressure at its inletreaches this value.

See Also Pressure Compensator


2-270


Purpose Simulate continuous valve driver with output proportional to inputsignal


Description The Proportional and Servo-Valve Actuator block represents anelectromagnetic actuator that is used in proportional and servo-valvesto drive a spool or other working member. The block is intended towork with one of the directional valve models to form a desirableconfiguration of a proportional or servo-valve. The block is implementedas a data-sheet-based model and reproduces only the input/outputrelationship, or the actuator’s transient response, as presented in thecatalog or data sheet.

The Proportional and Servo-Valve Actuator block is built using theblocks from the Physical Signals library. Both the input and the outputof the block are physical signals. The block diagram of the model isshown in the following figure.

The model consists of the first-order lag, PS Integrator, PS Saturationblock, and the PS Subtract block that closes the feedback. Theconfiguration is found to be suitable to simulate behavior of servo-valvesand high-quality proportional valves.

The typical transient responses of a servo-valve or a high-qualityproportional valve are shown in the following figure. The onlydifference between the two responses in the figure is the value of thesaturation. The response that corresponds to 100% of the input signal isconsiderable slower than that with the 20% saturation.

2-271


You can adjust the block parameters, such as saturation, gain, andtime constant, to make the transient responses close enough to thoseprovided in the data sheet. The most effective way to adjust theparameters is to use the Optimization Toolbox™ software.

2-272

http://www.mathworks.com/products/simresponse/



GainGain of the first-order lag. The default value is 377.

Time constantTime constant of the first-order lag. The default value is 0.002 s.

SaturationSaturation level of the Saturation block in the actuator model.The default value is 0.3.

Ports The block has one physical signal input port and one physical signaloutput port.

2-273


Examples The Closed-Loop Electrohydraulic Actuator with ProportionalValve demo (sh_closed_loop_actuator) illustrates the use of theProportional and Servo-Valve Actuator block in hydraulic systems.





2-274

Reservoir

Purpose Simulate pressurized hydraulic reservoir

Library Hydraulic Utilities

Description The Reservoir block represents a pressurized hydraulic reservoir, inwhich fluid is stored under a specified pressure. The pressure remainsconstant regardless of volume change. The block accounts for pressureloss in the return line that can be caused by a filter, fittings, or someother local resistance. The loss is specified with the pressure losscoefficient. The block computes the volume of fluid in the tank andexports it outside through the physical signal port V.

The fluid volume value does not affect the results of simulation. It isintroduced merely for information purposes. It is possible for the fluidvolume to become negative during simulation, which signals that thefluid volume is not enough for the proper operation of the system. Byviewing the results of the simulation, you can determine the extentof the fluid shortage.

2-275

Reservoir


Pressurization levelThe pressure inside the reservoir. The default value is 0.

Initial fluid volumeThe initial volume of fluid in the tank. The default value is 0.02m^3.

Return line diameterThe diameter of the return line. The default value is 0.02 m.

Pressure loss coefficient in return lineThe value of the pressure loss coefficient, to account for pressureloss in the return line. The default value is 1.


PHydraulic conserving port associated with the pump line.

2-276

Reservoir

RHydraulic conserving port associated with the return line.


See Also Constant Head Tank

Hydraulic Reference

Variable Head Tank

2-277

Resistive Pipe LP

Purpose Simulate hydraulic pipeline which accounts for friction losses and portelevations


Description The Resistive Pipe LP block models hydraulic pipelines with circularand noncircular cross sections and accounts for resistive property only.In other words, the block is developed with the basic assumption of thesteady state fluid momentum conditions. Neither fluid compressibilitynor fluid inertia is considered in the model, meaning that features suchas water hammer cannot be investigated. If necessary, you can addfluid compressibility, fluid inertia, and other effects to your model usingother blocks, thus producing a more comprehensive model.

The end effects are also not considered, assuming that the flow is fullydeveloped along the entire pipe length. To account for local resistances,such as bends, fittings, inlet and outlet losses, and so on, all theresistances are converted into their equivalent lengths, and then thetotal length of all the resistances is added to the pipe geometrical length.

Pressure loss due to friction is computed with the Darcy equation, inwhich losses are proportional to the flow regime-dependable frictionfactor and the square of the flow rate. The friction factor in turbulentregime is determined with the Haaland approximation (see [1]). Thefriction factor during transition from laminar to turbulent regimes isdetermined with the linear interpolation between extreme points ofthe regimes. As a result of these assumptions, the tube is simulatedaccording to the following equations:

p fL L

D Aq q g z z

eq

HB A=

+( )+ −( )ρ ρ

2 2i i| |

2-278

Resistive Pipe LP

f

K Re Re Re

ff f

Re ReRe Re Re Re Re

s L

LT L

T LL L T=

<=

+ −−

−( ) < <

−

/ for

for

1

1.. log. /

.

.8

6 93 710

1 11 2

Rer D

Re Re

H+ ⎛⎝⎜

⎞⎠⎟

⎛

⎝⎜⎜

⎞

⎠⎟⎟

⎛

⎝⎜⎜

⎞

⎠⎟⎟

>=for TT

⎧

⎨

⎪⎪⎪⎪⎪⎪

⎩

⎪⎪⎪⎪⎪⎪

Re = q DA

Hiiν

where

p Pressure loss along the pipe due to frictionq Flow rate through the pipeRe Reynolds numberReL Maximum Reynolds number at laminar flowReT Minimum Reynolds number at turbulent flowKs Shape factor that characterizes the pipe cross sectionfL Friction factor at laminar borderfT Friction factor at turbulent borderA Pipe cross-sectional areaDH Pipe hydraulic diameterL Pipe geometrical lengthLeq Aggregate equivalent length of local resistancesr Height of the roughness on the pipe internal surface

2-279

Resistive Pipe LP

ν Fluid kinematic viscosityzA, zB Elevations of the pipe port A and port B, respectivelyg Gravity acceleration





• Fluid inertia, fluid compressibility, and wall compliance are nottaken into account.


The block dialog box contains two tabs:



2-280

Resistive Pipe LP

Basic Parameters

2-281

Resistive Pipe LP


Internal diameterPipe internal diameter. The parameter is used if Pipe crosssection type is set to Circular. The default value is 0.01 m.

2-282

Resistive Pipe LP





Aggregate equivalent length of local resistancesThis parameter represents total equivalent length of all localresistances associated with the pipe. You can account for thepressure loss caused by local resistances, such as bends, fittings,armature, inlet/outlet losses, and so on, by adding to the pipegeometrical length an aggregate equivalent length of all the localresistances. The default value is 1 m.



2-283

Resistive Pipe LP


Vertical Position


2-284

Resistive Pipe LP





All other block parameters are available for modification. The actual setof modifiable block parameters depends on the value of the Pipe crosssection type parameter at the time the model entered Restricted mode.

GlobalParameters








Hydraulic Pipe LP

2-285

Resistive Pipe LP


Resistive Tube

Segmented Pipeline

Segmented Pipe LP

2-286

Segmented Pipeline

Purpose Simulate hydraulic pipeline with resistive, fluid inertia, and fluidcompressibility properties

Library Pipelines

Description The Segmented Pipeline block models hydraulic pipelines with circularcross sections. Hydraulic pipelines, which are inherently distributedparameter elements, are represented with sets of identical, connected inseries, lumped parameter segments. It is assumed that the larger thenumber of segments, the closer the lumped parameter model becomesto its distributed parameter counterpart. The equivalent circuit of apipeline adopted in the block is shown below, along with the segmentconfiguration.

Pipeline Equivalent Circuit

Segment Configuration

The model contains as many Constant Chamber blocks as there aresegments. The chamber lumps fluid volume equal to

2-287

Segmented Pipeline

Vd L

N= πi 2

4

where

V Fluid volumed Pipe diameterL Pipe lengthN Number of segments

The Constant Chamber block is placed between two branches, eachconsisting of a Resistive Tube block and a Fluid Inertia block. EveryResistive Tube block lumps (L+L_ad)/(N+1)-th portion of the pipelength, while Fluid Inertia block has L/(N+1) length (L_ad denotesadditional pipe length equal to aggregate equivalent length of pipe localresistances, such as fitting, elbows, bends, and so on).

The nodes to which Constant Chamber blocks are connected areassigned names N_1, N_2, …, N_n (n is the number of segments).Pressures at these nodes are assumed to be equal to average pressureof the segment. Intermediate nodes between Resistive Tube and FluidInertia blocks are assigned names nn_0, nn_1, nn_2, …, nn_n. TheConstant Chamber blocks are named ch_1, ch_2, …, ch_n, ResistiveTube blocks are named tb_0, tb_1, tb_2, …, tb_n, and Fluid Inertiablocks are named fl_in_0, fl_in_1, fl_in_2, …, fl_in_n.

The number of segments is the block parameter. In determining thenumber of segments needed, you have to find a compromise betweenthe accuracy and computational burden for a particular application. Itis practically impossible to determine analytically how many elementsare necessary to get the results with a specified accuracy. The goldenrule is to use as many elements as possible based on computationalconsiderations, and an experimental assessment is perhaps the onlyreliable way to make any conclusions. As an approximate estimate,you can use the following formula:

2-288

Segmented Pipeline

NLc

> 4π

ωi

where

N Number of segmentsL Pipe lengthc Speed of sound in the fluidω Maximum frequency to be observed in the pipe response

The table below contains an example of simulation of a pipeline wherethe first four true eigenfrequencies are 89.1 Hz, 267 Hz, 446 Hz, and624 Hz.

Number ofSegments

1st Mode 2nd Mode 3rd Mode 4th Mode

1 112.3 – – –2 107.2 271.8 – –4 97.7 284.4 432.9 6898 93.2 271.9 435.5 628

As you can see, the error is less than 5% if an eight-segmented versionis used.





2-289

Segmented Pipeline


Pipe internal diameterInternal diameter of the pipe. The default value is 0.01 m.


Number of segmentsNumber of lumped parameter segments in the pipeline model.The default value is 1.

2-290

Segmented Pipeline

Aggregate equivalent length of local resistancesThis parameter represents total equivalent length of all localresistances associated with the pipe. You can account for thepressure loss caused by local resistances, such as bends, fittings,armature, inlet/outlet losses, and so on, by adding to the pipegeometrical length an aggregate equivalent length of all the localresistances. This length is added to the geometrical pipe lengthonly for hydraulic resistance computation. Both the fluid volumeand fluid inertia are determined based on pipe geometrical lengthonly. The default value is 1 m.




Pipe wall typeThe parameter can have one of two values: Rigid or Compliant.If the parameter is set to Rigid, wall compliance is not taken intoaccount, which can improve computational efficiency. The valueCompliant is recommended for hoses and metal pipes where wallcompliance can affect the system behavior. The default value isRigid.

Static pressure-diameter coefficientCoefficient that establishes relationship between the pressure andthe internal diameter at steady-state conditions. This coefficient

2-291

Segmented Pipeline

can be determined analytically for cylindrical metal pipes orexperimentally for hoses. The parameter is used if the Pipewall type parameter is set to Compliant, and the default valueis 2e-10 m/Pa.

Viscoelastic process time constantTime constant in the transfer function that relates pipe internaldiameter to pressure variations. By using this parameter, thesimulated elastic or viscoelastic process is approximated withthe first-order lag. The value is determined experimentally orprovided by the manufacturer. The default value is 0.008 s.




• Pipe wall type


GlobalParameters





2-292

Segmented Pipeline




Resistive Tube

2-293

Segmented Pipe LP

Purpose Simulate hydraulic pipeline with resistive, fluid inertia, fluidcompressibility, and elevation properties


Description The Segmented Pipe LP block models hydraulic pipelines with circularcross sections. Hydraulic pipelines, which are inherently distributedparameter elements, are represented with sets of identical, connected inseries, lumped parameter segments. It is assumed that the larger thenumber of segments, the closer the lumped parameter model becomesto its distributed parameter counterpart. The equivalent circuit of apipeline adopted in the block is shown below, along with the segmentconfiguration.

Pipeline Equivalent Circuit

Segment Configuration

The model contains as many Constant Chamber blocks as there aresegments. The chamber lumps fluid volume equal to

2-294

Segmented Pipe LP

Vd L

N= πi 2

4

where

V Fluid volumed Pipe diameterL Pipe lengthN Number of segments

The Constant Chamber block is placed between two branches, eachconsisting of a Resistive Tube block and a Fluid Inertia block. EveryResistive Tube block lumps (L+L_ad)/(N+1)-th portion of the pipelength, while Fluid Inertia block has L/(N+1) length (L_ad denotesadditional pipe length equal to aggregate equivalent length of pipe localresistances, such as fitting, elbows, bends, and so on).

The nodes to which Constant Chamber blocks are connected areassigned names N_1, N_2, …, N_n (n is the number of segments).Pressures at these nodes are assumed to be equal to average pressureof the segment. Intermediate nodes between Resistive Tube and FluidInertia blocks are assigned names nn_0, nn_1, nn_2, …, nn_n. TheConstant Chamber blocks are named ch_1, ch_2, …, ch_n, ResistiveTube blocks are named tb_0, tb_1, tb_2, …, tb_n, and Fluid Inertiablocks are named fl_in_0, fl_in_1, fl_in_2, …, fl_in_n.

The number of segments is the block parameter. In determining thenumber of segments needed, you have to find a compromise betweenthe accuracy and computational burden for a particular application. Itis practically impossible to determine analytically how many elementsare necessary to get the results with a specified accuracy. The goldenrule is to use as many elements as possible based on computationalconsiderations, and an experimental assessment is perhaps the onlyreliable way to make any conclusions. As an approximate estimate,you can use the following formula:

2-295

Segmented Pipe LP

NLc

> 4π

ωi

where

N Number of segmentsL Pipe lengthc Speed of sound in the fluidω Maximum frequency to be observed in the pipe response

The table below contains an example of simulation of a pipeline wherethe first four true eigenfrequencies are 89.1 Hz, 267 Hz, 446 Hz, and624 Hz.

Number ofSegments

1st Mode 2nd Mode 3rd Mode 4th Mode

1 112.3 – – –2 107.2 271.8 – –4 97.7 284.4 432.9 6898 93.2 271.9 435.5 628

As you can see, the error is less than 5% if an eight-segmented versionis used.

The difference in elevation between ports A and B is distributed evenlybetween pipe segments.


2-296

Segmented Pipe LP







• “Wall Compliance” on page 2-299


Basic Parameters

2-297

Segmented Pipe LP

Pipe internal diameterInternal diameter of the pipe. The default value is 0.01 m.


Number of segmentsNumber of lumped parameter segments in the pipeline model.The default value is 1.

Aggregate equivalent length of local resistancesThis parameter represents total equivalent length of all localresistances associated with the pipe. You can account for thepressure loss caused by local resistances, such as bends, fittings,armature, inlet/outlet losses, and so on, by adding to the pipegeometrical length an aggregate equivalent length of all the localresistances. This length is added to the geometrical pipe lengthonly for hydraulic resistance computation. Both the fluid volumeand fluid inertia are determined based on pipe geometrical lengthonly. The default value is 1 m.




2-298

Segmented Pipe LP

Wall Compliance

2-299

Segmented Pipe LP

Pipe wall typeThe parameter can have one of two values: Rigid or Flexible. Ifthe parameter is set to Rigid, wall compliance is not taken intoaccount, which can improve computational efficiency. The valueFlexible is recommended for hoses and metal pipes where wallcompliance can affect the system behavior. The default value isRigid.

Static pressure-diameter coefficientCoefficient that establishes relationship between the pressure andthe internal diameter at steady-state conditions. This coefficientcan be determined analytically for cylindrical metal pipes orexperimentally for hoses. The parameter is used if the Pipe wall

2-300

Segmented Pipe LP

type parameter is set to Flexible. The default value is 2e-12m/Pa.



2-301

Segmented Pipe LP

Vertical Position





2-302

Segmented Pipe LP

• Pipe wall type

All other block parameters are available for modification. The actual setof modifiable block parameters depends on the value of the Pipe walltype parameter at the time the model entered Restricted mode.

GlobalParameters








Hydraulic Pipe LP


Resistive Pipe LP

Resistive Tube

Segmented Pipeline

2-303

Shuttle Valve

Purpose Simulate hydraulic valve that allows flow in one direction only


Description The Shuttle Valve block represents a hydraulic shuttle valve as adata-sheet-based model. The valve has two inlet ports (A and A1) andone outlet port (B). The valve is controlled by pressure differentialp p pc A A= − 1 . The valve permits flow either between ports A and Bor between ports A1 and B, depending on the pressure differential pc.Initially, path A-B is assumed to be opened. To open path A1-B (andclose A-B at the same time), pressure differential must be less than thevalve cracking pressure (pcr <=0).

When cracking pressure is reached, the value control member (spool,ball, poppet, etc.) is forced off its seat and moves to the opposite seat,thus opening one passage and closing the other. If the flow rate is highenough and pressure continues to change, the control member continuesto move until it reaches its extreme position. At this moment, one ofthe valve passage areas is at its maximum. The valve maximum areaand the cracking and maximum pressures are generally provided in thecatalogs and are the three key parameters of the block.

The relationship between the A-B, A1–B path openings and controlpressure pc is shown in the following illustration.

2-304

Shuttle Valve


The model accounts for the laminar and turbulent flow regimes bymonitoring the Reynolds number for each orifice (ReAB,ReA1B) andcomparing its value with the critical Reynolds number (Recr). Theflow rate through each of the orifices is determined according to thefollowing equations:

qC A p sign p Re Re

C AD

AB

D AB AB AB AB

DL ABHAB

=( )i i

ii

2

2

ρ

ν ρ

| | for >= cr

pp Re ReAB ABfor < cr

⎧

⎨⎪⎪

⎩⎪⎪

2-305

Shuttle Valve

qC A p sign p Re Re

C AD

A B

D A B A B A B A B

DL A B

1

1 1 1 1

1

2

2

=( )i i

i

ρ| | for >= cr

HHA BA B A Bp Re Re1

1 1ν ρifor < cr

⎧

⎨⎪⎪

⎩⎪⎪

AA p pA k p p p p p pA

AB

leak AB cr

leak AB cr cr AB cr op=<=

+ −( ) < < +for for i

mmax for p p pAB cr op>= +

⎧

⎨⎪

⎩⎪

AA p p pA k p p p p pA B

leak A B cr op

A B cr cr A B1

1

1 1=>= +

− −( ) < <for for max i ccr op

A B cr

pA p p

+<=

⎧⎨⎪

⎩⎪ max for 1

kA A

pleak

op=

−max

p p pAB A B= −

p p pA B A B1 1= −

ReABAB HAB

AB

q DA

= iiν

ReA BA B HA B

A B

q DA11 1

1= i

iν

CC

DLD

cr=

⎛

⎝⎜⎜

⎞

⎠⎟⎟Re

2

2-306

Shuttle Valve

DA

HABAB= 4

π

DA

HA BA B

114=

π

where

qAB,qA1B Flow rates through the AB and A1B orificespAB,pA1B Pressure differentials across the AB and A1B

orificespA,pA1,pB Gauge pressures at the block terminalsCD Flow discharge coefficientAAB,AA1B Instantaneous orifice AB and A1B passage areasAmax Fully open orifice passage areaAleak Closed valve leakage area

pcr Valve cracking pressure differentialpopx Pressure differential needed to fully shift the valveDHAB,DHA1B Instantaneous orifice hydraulic diametersρ Fluid densityν Fluid kinematic viscosity

The block positive direction is from port A to port B and from port A1 toport B. Control pressure is determined as p p pc A A= − 1 .





2-307

Shuttle Valve




Cracking pressurePressure differential level at which the orifice of the valve startsto open. The default value is -1e4 Pa.

Opening pressurePressure differential across the valve needed to shift the valvefrom one extreme position to another. The default value is 1e4 Pa.

2-308

Shuttle Valve




GlobalParameters





2-309

Shuttle Valve

A1Hydraulic conserving port associated with the valve inlet.




2-310


Purpose Simulate hydraulic actuator exerting force in one direction


Description The Single-Acting Hydraulic Cylinder block models a device thatconverts hydraulic energy into mechanical energy in the form oftranslational motion. Hydraulic fluid pumped under pressure intothe cylinder chamber forces the piston to move and exert force onthe cylinder rod. Single-acting cylinders transfer force and motion inone direction only. Use an external device, such as a spring, weight,or another opposite installed cylinder, to move the rod in oppositedirection.

The model of the cylinder is built of Simscape Foundation library blocks.The schematic diagram of the model is shown below.

Connections R and C are mechanical translational conserving portscorresponding to the cylinder rod and cylinder clamping structure,

2-311


respectively. Connection A is a hydraulic conserving port associatedwith the cylinder inlet. The physical signal output port provides roddisplacement.

The energy through port A is directed to the TranslationalHydro-Mechanical Converter block and the Piston Chamber block.The converter transforms hydraulic energy into mechanical energy,while the chamber accounts for the fluid compressibility in the cylinderchamber. The rod motion is limited with the mechanical TranslationalHard Stop block in such a way that the rod can travel only betweencylinder caps. The Ideal Translational Motion Sensor block in theschematic is introduced to determine an instantaneous piston position,which is necessary for the Piston Chamber block.

The block directionality is adjustable and can be controlled with theCylinder orientation parameter.



• No leakage, internal or external, is taken into account.

• No loading on piston rod, such as inertia, friction, spring, and soon, is taken into account. If necessary, you can easily add them byconnecting an appropriate building block to cylinder port R.

2-312



Piston areaEffective piston area. The default value is 0.001 m^2.

Piston strokePiston maximum travel between caps. The default value is 0.1 m.

Piston initial positionThe distance that the piston is extended at the beginning ofsimulation. You can set the piston position to any point withinits stroke. The default value is 0, which corresponds to the fullyretracted position.

2-313


Dead volumeFluid volume that remains in the chamber after the rod is fullyretracted. The default value is 1e-4 m^3.


Contact stiffnessSpecifies the elastic property of colliding bodies for theTranslational Hard Stop block. The greater the value of theparameter, the less the bodies penetrate into each other, themore rigid the impact becomes. Lesser value of the parametermakes contact softer, but generally improves convergence andcomputational efficiency. The default value is 1e6 N/m.

Contact dampingSpecifies dissipating property of colliding bodies for theTranslational Hard Stop block. At zero damping, the impact isclose to an absolutely elastic one. The greater the value of theparameter, the more energy dissipates during an interaction.Keep in mind that damping affects slider motion as long as theslider is in contact with the stop, including the period when slideris pulled back from the contact. For computational efficiencyand convergence reasons, The MathWorks recommends that youassign a nonzero value to this parameter. The default value is150 N*s/m.

Cylinder orientationSpecifies cylinder orientation with respect to the globally assignedpositive direction. The cylinder can be installed in two differentways, depending upon whether it exerts force in the positive orin the negative direction when pressure is applied at its inlet. Ifpressure applied at port A exerts force in negative direction, setthe parameter to Acts in negative direction. The defaultvalue is Acts in positive direction.

2-314




• Cylinder orientation


GlobalParameters



AHydraulic conserving port associated with the cylinder inlet.



The block also has a physical signal output port, which outputs roddisplacement.

See Also Double-Acting Hydraulic Cylinder

Ideal Translational Motion Sensor

Translational Hard Stop

Translational Hydro-Mechanical Converter

Piston Chamber

2-315

Single-Acting Rotary Actuator

Purpose Simulate single-acting hydraulic rotary actuator


Description The Single-Acting Rotary Actuator block models a single-actinghydraulic rotary actuator, which directly converts hydraulic energyinto mechanical rotational energy without employing intermediarytransmissions such as rack-and-pinion, sliding spline, chain, and so on.Single-acting actuators generate torque and motion in a single directiononly. Use an external device, such as a spring or another oppositeinstalled actuator, to move the shaft in opposite direction.

The model of the actuator is built of Simscape Foundation libraryblocks. The schematic diagram of the model is shown below.

2-316


The blocks in the diagram perform the following functions:

RotationalHydro-MechanicalConverter

Converts hydraulics energy intomechanical rotational energy and viceversa.

Rotational Hard Stop Imposes limits on shaft rotation.Linear HydraulicResistance

Accounts for leakages.

Piston Chamber Accounts for fluid compressibility.Ideal TranslationalMotion Sensor

Determines an instantaneous shaftposition, which is necessary for the PistonChamber block.

Wheel and Axle Converts shaft rotation into translationalmotion to provide input to the IdealTranslational Motion Sensor block

Connection A is a hydraulic conserving port corresponding to theactuator chamber. Connection S is a mechanical rotational conservingport associated with the actuator shaft.

The block directionality is adjustable and can be controlled with theActuator orientation parameter.



• No loading, such as inertia, friction, spring, and so on, is taken intoaccount. If necessary, you can easily add them by connecting anappropriate building block to port S.

2-317



Actuator displacementEffective displacement of the actuator. The default value is4.5e-5 m^3/rad.

Shaft strokeShaft maximum travel between stops. The default value is 5.1rad.

Shaft initial angleThe position of the shaft at the beginning of simulation. You canset the shaft position to any angle within its stroke. The default

2-318


value is 0, which corresponds to the shaft position at the verybeginning of the stroke.

Dead volumeFluid volume that remains in the chamber when the shaft ispositioned at the very beginning of the stroke. The default valueis 1e-4 m^3.

Leak coefficientLeak coefficient for the Linear Hydraulic Resistance block. Thedefault value is 1e-14 (m^3/s)/Pa.


Contact stiffnessSpecifies the elastic property of colliding bodies for the RotationalHard Stop block. The greater the value of the parameter, the lessthe bodies penetrate into each other, the more rigid the impactbecomes. Lesser value of the parameter makes contact softer, butgenerally improves convergence and computational efficiency.The default value is 1e6 N*m/rad.

Contact dampingSpecifies dissipating property of colliding bodies for the RotationalHard Stop block. At zero damping, the impact is close to anabsolutely elastic one. The greater the value of the parameter, themore energy dissipates during an interaction. Keep in mind thatdamping affects slider motion as long as the slider is in contactwith the stop, including the period when slider is pulled backfrom the contact. For computational efficiency and convergencereasons, The MathWorks recommends that you assign a nonzerovalue to this parameter. The default value is 150 N*m/(rad/s).

Actuator orientationSpecifies actuator orientation with respect to the globally assignedpositive direction. The actuator can be installed in two differentways, depending upon whether it generates torque in the positiveor in the negative direction when pressure is applied at its inlet.

2-319


If pressure applied at port A generates torque in the negativedirection, set the parameter to Acts in negative direction.The default value is Acts in positive direction.





GlobalParameters



AHydraulic conserving port associated with the actuator inlet.

SMechanical rotational conserving port associated with theactuator shaft.

See Also Ideal Translational Motion Sensor


Rotational Hard Stop

Rotational Hydro-Mechanical Converter

Piston Chamber

Wheel and Axle

2-320

Spool Orifice Hydraulic Force

Purpose Simulate axial hydraulic force exerted on spool

Library Valve Forces

Description The Spool Orifice Hydraulic Force block simulates the steady-state axialhydraulic force exerted on the spool by fluid flowing through the orifice.The orifice is supposed to be rectangular with the width considerablylarger than the radial clearance between the spool and the sleeve.

The force is simulated according to the following equations:

F pqA

or=2

cosθi

θ = + − −0 3663 0 8373 1 1 848. . ( exp( / . ))x

x x s or= +0 i

A b x xb x

= +⎧⎨⎪

⎩⎪ii

2 2 00

δδ

for > for <=

where

F Axial hydraulic forceq Flow rate through the orificeρ Fluid densityA Orifice areaΘ Jet angle (rad)x0 Orifice initial openings Spool displacementb Orifice width

2-321


δ Radial clearanceor Orientation parameter with respect to the globally assigned

positive direction. If the orifice is opened while the spoolis shifted in positive direction, or equals 1. If the orifice isopened while the spool is shifted in negative direction, orequals –1.

Connections A and B are hydraulic conserving ports that shouldbe connected in series with the orifice block to monitor the flowrate. Connection S is a physical signal port that provides the spooldisplacement. Connection F is a physical signal port that outputs thehydraulic axial force value. This port should be connected to the controlport of an Ideal Force Source block. The force computed in the blockalways acts to close the orifice.



• The transient effects are assumed to be negligible.

• The jet angle approximation is based on the Richard von Misesequation.

• The block can be used with rectangular orifices whose width isconsiderably larger than the axial opening.

2-322



Orifice widthOrifice width. The parameter must be greater than zero. Thedefault value is 0.01 m.

Radial clearanceThe radial clearance between the spool and the sleeve. Thedefault value is 1e-5 m.


Orifice orientationThe parameter is introduced to specify the effect of the forceon the orifice opening. The parameter can be set to one of twooptions: Opens in positive direction or Opens in negativedirection. The value Opens in positive direction specifies

2-323


an orifice that opens when the spool moves in the globally assignedpositive direction. The default value is Opens in positivedirection.






AHydraulic conserving port associated with an orifice inlet.

BHydraulic conserving port associated with an orifice outlet.

SPhysical signal port that provides the spool displacement.

FPhysical signal port that outputs hydraulic axial force.

Examples The following example shows a model of a 4-way, 3-position,hydraulically-operated directional valve where the hydraulic axialforces acting on the spool are being taken into consideration.

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The spool (mass M1, viscous friction TD1) is shifted by the servo-actuatorsimulated by two Translational Hydro-Mechanical Converter blocks.Connections A_S and B_S are hydraulic ports for applying pilot controlpressure.

Four variable orifices are represented by subsystems:

• Orifice with Hydraulic Force PA

• Orifice with Hydraulic Force PB

• Orifice with Hydraulic Force AT

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• Orifice with Hydraulic Force BT

The structure of a subsystem is shown in the following illustration.

It consists of an Orifice with Variable Area Slot block, which simulateshydraulic properties of the orifice, connected in series with a SpoolOrifice Hydraulic Force block. The force value computed in the block isexported through its port F and passed to the Force block.

The forces on all four orifices (F_PA, F_PB, F_AT, F_BT) are applied to thevalve spool as it is shown in the first schematic.

For more details and for parameter settings, see the Hydraulic Systemwith Servo-Valve demo (sh_hydraulic_system_with_servo_valve).

See Also Valve Hydraulic Force

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Spring-Loaded Accumulator

Purpose Simulate hydraulic accumulator with spring used for energy storage

Library Accumulators

Description This block represents a spring-loaded accumulator, where fluid enteringthe accumulator compresses the spring, thus storing hydraulic energy.Since the spring compression increases as fluid enters the chamberand decreases as the accumulator is discharged, the pressure is notconstant. The spring is preloaded. Therefore, fluid starts entering thechamber only after the inlet pressure crosses over this threshold. Theaccumulator is described with the following equations:

qdVdt

F=

V

p p

k p p p p p

V p pF

pr

pr pr=

<=

−( ) < <

>=

⎧

⎨⎪

⎩⎪

0 for

for

for max

max max

kV

p ppr=

−max

max

where

p Pressure at the accumulator inletq Flow rate into accumulatorVmax Accumulator capacity (maximum volume)VF Instantaneous volume of fluid in the accumulatorppr Preload pressurepmax Pressure needed to fully fill the accumulator

The block positive direction is from port A into the accumulator. Thismeans that the flow rate is positive if it flows into the accumulator.

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• The spring has linear characteristics.

• No loading on the separator, such as inertia, friction, and so on, isconsidered.

• Fluid compressibility is not taken into account.


CapacityAccumulator volumetric capacity. The default value is 0.008m^3.

Preload pressurePressure at which fluid starts entering the chamber. The defaultvalue is 1e6 Pa.

Maximum pressurePressure at which the accumulator is fully charged. The defaultvalue is 3e6 Pa.

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Initial fluid volumeInitial volume of fluid in the accumulator. This parameterspecifies the initial condition for use in computing the block’sinitial state at the beginning of a simulation run. For moreinformation, see “Computing Initial Conditions”. The defaultvalue is 0.

Ports The block has one hydraulic conserving port associated with theaccumulator inlet.

The flow rate is positive if fluid flows into the accumulator.

See Also Gas-Charged Accumulator

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Sudden Area Change

Purpose Simulate sudden enlargement or contraction


Description The Sudden Area Change block represents a local hydraulic resistance,such as a sudden cross-sectional area change. The resistance representsa sudden enlargement if fluid flows from inlet to outlet, or a suddencontraction if fluid flows from outlet to inlet. The block is based on theLocal Resistance block. It determines the pressure loss coefficient andpasses its value to the underlying Local Resistance block. The blockoffers two methods of parameterization: by applying semi-empiricalformulas (with a constant value of the pressure loss coefficient) or bytable lookup for the pressure loss coefficient based on the Reynoldsnumber.

If you choose to apply the semi-empirical formulas, you providegeometric parameters of the resistance, and the pressure loss coefficientis determined automatically according to the following equations (see[1]):

K KAASE cor

S

L= −

⎛

⎝⎜

⎞

⎠⎟12

K KAASC cor

S

L= −

⎛

⎝⎜

⎞

⎠⎟i0 5 10 75

..

where

KSE Pressure loss coefficient for the sudden enlargement, whichtakes place if fluid flows from inlet to outlet

KSC Pressure loss coefficient for the sudden contraction, whichtakes place if fluid flows from outlet to inlet

Kcor Correction factor

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Sudden Area Change

AS Small areaAL Large area

If you choose to specify the pressure loss coefficient by a table, you haveto provide a tabulated relationship between the loss coefficient and theReynolds number. In this case, the loss coefficient is determined byone-dimensional table lookup. You have a choice of three interpolationmethods and two extrapolation methods.

The pressure loss coefficient, determined by either of the two methods,is then passed to the underlying Local Resistance block, which computesthe pressure loss according to the formulas explained in the referencedocumentation for that block. The flow regime is checked in theunderlying Local Resistance block by comparing the Reynolds numberto the specified critical Reynolds number value, and depending on theresult, the appropriate formula for pressure loss computation is used.

The Sudden Area Change block is bidirectional and computes pressureloss for both the direct flow (sudden enlargement) and return flow(sudden contraction). If the loss coefficient is specified by a table, thetable must cover both the positive and the negative flow regions.







• If you select parameterization by the table-specified relationshipK=f(Re), the flow is assumed to be turbulent.

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Sudden Area Change


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Sudden Area Change

Small diameterResistance small diameter. The default value is 0.01 m.

Large diameterResistance large diameter. The default value is 0.02 m. Thisparameter is used if Model parameterization is set to Bysemi-empirical formulas.

Model parameterizationSelect one of the following methods for block parameterization:

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Sudden Area Change

• By semi-empirical formulas — Provide geometricalparameters of the resistance. This is the default method.

• By loss coefficient vs. Re table — Provide tabulatedrelationship between the loss coefficient and the Reynoldsnumber. The loss coefficient is determined by one-dimensionaltable lookup. You have a choice of three interpolation methodsand two extrapolation methods. The table must cover both thepositive and the negative flow regions.

Correction coefficientCorrection factor used in the formula for computation of the losscoefficient. The default value is 1. This parameter is used ifModelparameterization is set to By semi-empirical formulas.


Reynolds number vectorSpecify the vector of input values for Reynolds numbers as atabulated 1-by-m array. The input values vector must be strictlymonotonically increasing. The values can be nonuniformly spaced.You must provide at least three values. The default values are[-4000, -3000, -2000, -1000, -500, -200, -100, -50,-40, -30, -20, -15, -10, 10, 20, 30, 40, 50, 100, 200,500, 1000, 2000, 4000, 5000, 10000]. This parameter isused ifModel parameterization is set to By loss coefficientvs. Re table.

Loss coefficient vectorSpecify the vector of output values for the loss coefficient as atabulated 1-by-m array. The loss coefficient vector must be the

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Sudden Area Change

same size as the Reynolds numbers vector. The default valuesare [0.25, 0.3, 0.65, 0.9, 0.65, 0.75, 0.90, 1.15,1.35, 1.65, 2.3, 2.8, 3.10, 5, 2.7, 1.8, 1.46, 1.3,0.9, 0.65, 0.42, 0.3, 0.20, 0.40, 0.42, 0.25]. Thisparameter is used ifModel parameterization is set to By losscoefficient vs. Re table.








• From last point— Uses the last specified output value at theappropriate end of the range. That is, the block uses the lastspecified output value for all input values greater than the last

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Sudden Area Change

specified input argument, and the first specified output valuefor all input values less than the first specified input argument.








GlobalParameters





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Sudden Area Change


References [1] Idelchik, I.E., Handbook of Hydraulic Resistance, CRC Begell House,1994

See Also Elbow

Gradual Area Change

Local Resistance

Pipe Bend

T-junction

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T-junction

Purpose Simulate hydraulic resistance of T-junction in pipe


Description The T-junction block represents a T-junction (wye connection)consisting, in general, of a main run and a branch merging to the mainrun. The junction as a hydraulic resistance is built of three LocalResistance blocks, as shown in the following diagram.

To specify pressure loss for all possible flow directions, you have toprovide six pressure loss coefficients. The flow regime is checked in theunderlying Local Resistance blocks by comparing the Reynolds numberto the specified critical Reynolds number value, and depending on theresult, the appropriate formula for pressure loss computation is used.For more information, see the reference documentation for the LocalResistance block.

The block positive direction is from port A to port B, from port A to portA1, and from port A1 to port B.

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T-junction





2-339

T-junction


Main pipe diameterThe internal pipe diameter of the main run. The default valueis 0.01 m.

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T-junction

Branch pipe diameterThe internal pipe diameter of the branch. The default value is0.01 m.

A-B pressure loss coefficientThe pressure loss coefficient between ports A and B when fluidflows in the direction from A to B. The default value is 1.12.

B-A pressure loss coefficientThe pressure loss coefficient between ports A and B when fluidflows in the direction from B to A. The default value is 1.12.

A-A1 pressure loss coefficientThe pressure loss coefficient between ports A and A1 when fluidflows in the direction from A to A1. The default value is 1.36.

A1-A pressure loss coefficientThe pressure loss coefficient between ports A and A1 when fluidflows in the direction from A1 to A. The default value is 1.65.

A1-B pressure loss coefficientThe pressure loss coefficient between ports A1 and B when fluidflows in the direction from A1 to B. The default value is 1.6.

B-A1 pressure loss coefficientThe pressure loss coefficient between ports A1 and B when fluidflows in the direction from B to A1. The default value is 1.8.

Critical Reynolds numberThe maximum Reynolds number for laminar flow. The transitionfrom laminar to turbulent regime is supposed to take placewhen the Reynolds number reaches this value. The valueof the parameter depends on geometrical profile, and therecommendations on the parameter value can be found inhydraulic textbooks. The default value is 120.

GlobalParameters


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T-junction



AHydraulic conserving port associated with the main run inlet.

BHydraulic conserving port associated with the main run outlet.

A1Hydraulic conserving port associated with the branch inlet.

See Also Elbow

Gradual Area Change

Local Resistance

Pipe Bend

Sudden Area Change

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Valve Hydraulic Force

Purpose Simulate axial hydraulic static force exerted on valve

Library Valve Forces

Description The Valve Hydraulic Force block simulates axial hydraulic static forceexerted on a valve by fluid flowing through the orifice. The relationshipbetween the valve opening, the pressure drop, and the force is providedas a two-dimensional table, which is processed by the PS Lookup Table(2D) block. The table can be obtained experimentally or analytically andcan represent both the hydraulic static axial force and pressure forces.The force matrix must be rectangular and contain as many rows asthere are pressure differential measurements and as many columns asthere are valve openings. The pressure differential and opening vectorsmust be arranged in strictly ascending order and cover the whole rangeof valve operation. Connect the block in parallel with the orifice whoseflow induces the force.

Connections A and B are hydraulic conserving ports that should beconnected to the valve block ports in such a way as to monitor thepressure differential across the valve. Connection S is a physical signalport that provides the valve control member displacement. ConnectionF is a physical signal port that outputs the hydraulic axial force value.This port should be connected to the control port of an Ideal ForceSource block. The pressure differential inside the block is determinedas p p pA B= − . The force orientation is specified by the table valuesand can be positive or negative with respect to the globally assignedpositive direction, depending on the value of the Orifice orientationparameter.



• No transient effects can be simulated.

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2-344


Orifice orientationThe parameter is introduced to specify the effect of the valveopening on the valve force. The parameter can be set to oneof two options: Opens in positive direction or Opens innegative direction. The value Opens in positive directionspecifies an orifice that opens when the valve is shifted in theglobally assigned positive direction. The default value is Opensin positive direction.

Tabulated valve openingsSpecify the vector of input values for valve openings as atabulated 1-by-n array. The input values vector must be strictlymonotonically increasing. The values can be nonuniformly spaced.You must provide at least three values. The default values, inmeters, are [0,1e-3,2e-3,3e-3,4e-3]. The Tabulated valveopenings values will be used together with Tabulated pressuredifferentials for two-dimensional table lookup in the Hydraulicaxial force table.

Tabulated pressure differentialsSpecify the vector of input values for pressure differentials as atabulated 1-by-m array. The input values vector must be strictlymonotonically increasing. The values can be nonuniformly spaced.You must provide at least three values. The default values, in Pa,are [-100e5,-75e5,-50e5,-25e5,0,25e5,50e5,75e5,100e5].

Hydraulic axial force tableSpecify the output values for the hydraulic axial force as atabulated m-by-n matrix, defining the function values at the inputgrid vertices. Each value in the matrix specifies an axial forcecorresponding to a specific combination of valve opening andpressure differential. The matrix size must match the dimensionsdefined by the input vectors. The default values, in N, are:

[0, -127.3576, -27.8944, 227.2513, 575.3104; ...0, -95.5182, -20.9208, 170.4385, 431.4828; ...0, -63.6788, -13.9472, 113.6256, 287.6552; ...0, -31.8394, -6.9736, 56.8128, 143.8276; ...

2-345


0, 0, 0, 0, 0; ...196.3495, 120.7506, 97.5709, 111.9898, 150.9306; ...392.6991, 241.5013, 195.1418, 223.9797, 301.8613; ...589.0486, 362.2519, 292.7126, 335.9695, 452.7919; ...785.3982, 483.0025, 390.2835, 447.9594, 603.7225]


• Linear— Uses a bilinear interpolation algorithm, which is anextension of linear interpolation for functions in two variables.

• Cubic— Uses the bicubic interpolation algorithm.

• Spline— Uses the bicubic spline interpolation algorithm.

For more information on interpolation algorithms, see the PSLookup Table (2D) block reference page.




2-346


For more information on extrapolation algorithms, see the PSLookup Table (2D) block reference page.








AHydraulic conserving port associated with a valve port.

BHydraulic conserving port associated with another valve port tomonitor the pressure differential.

SPhysical signal port that provides the valve control memberdisplacement.

FPhysical signal port that outputs hydraulic axial force.

Examples The following example shows a model of a poppet valve built of a PoppetValve block and a Valve Hydraulic Force block. The Valve HydraulicForce block is connected in parallel and provides tabulated data tocompute hydraulic force acting on the valve. The force value is exportedthrough the F port.

2-347


See Also Spool Orifice Hydraulic Force

2-348

Variable Head Tank

Purpose Simulate tank with constant pressurization and volume-dependentfluid level


Description The Variable Head Tank block represents a pressurized hydraulicreservoir, in which fluid is stored under a specified pressure. Thepressurization remains constant regardless of volume change. Theblock accounts for the fluid level change caused by the volume variation,as well as for pressure loss in the connecting pipe that can be caused bya filter, fittings, or some other local resistance. The loss is specified withthe pressure loss coefficient. The block computes the volume of fluid inthe tank and exports it outside through the physical signal port V.

The pressure at the tank inlet is computed with the following equations:

p p p pelev loss pr= − +

p g Helev = ρi i

p KA

q qlossp

= ρ2 2

| |

Ad

p = πi 2

4

HVAf V

=⎧ for constant-area tank

for table-specified tank ( )⎨⎨⎪

⎩⎪

V V q t= +0 i

where

2-349

Variable Head Tank

p Pressure at the tank inletpelev Pressure due to fluid levelploss Pressure loss in the connecting pipeppr Pressurizationρ Fluid densityg Acceleration of gravityH Fluid level with respect to the bottom of the tankK Pressure loss coefficientAp Connecting pipe aread Connecting pipe diameterq Flow rateV Instantaneous fluid volumeV0 Initial fluid volumeA Tank cross-sectional areat Simulation time

For a tank with a variable cross-sectional area, the relationship betweenfluid level and volume is specified with the table lookup

H f V= ( )

You have a choice of three interpolation methods and two extrapolationmethods.

Connection T is a hydraulic conserving port associated with the tankinlet. Connection V is a physical signal port. The flow rate is consideredpositive if it flows into the tank.

2-350

Variable Head Tank


2-351

Variable Head Tank

Initial fluid volumeThe initial volume of fluid in the tank. This parameter must begreater than zero. The default value is 20 l.

PressurizationGage pressure acting on the in the tank. It can be created by a gascushion, membrane, bladder, or piston, as in bootstrap reservoirs.This parameter must be greater than or equal to zero. The defaultvalue is 0, which corresponds to a tank connected to atmosphere.

Level/Volume relationshipSelect one of the following block parameterization options:

• Linear — Provide a value for the tank cross-sectional area.The level is assumed to be linearly dependent on the fluidvolume. This is the default method.

2-352

Variable Head Tank

• Table-specified — Provide tabulated data of fluid volumesand fluid levels. The level is determined by one-dimensionaltable lookup. You have a choice of three interpolation methodsand two extrapolation methods.

Tank cross-section areaThe cross-sectional area of the tank. This parameter must begreater than zero. The default value is 0.8 m^2. This parameteris used if Level/Volume relationship is set to Linear.

Tabulated fluid volumesSpecify the vector of input values for fluid volume as atabulated 1-by-m array. The input values vector must be strictlymonotonically increasing. The values can be nonuniformly spaced.You must provide at least three values. The default values, inm^3, are [0 0.0028 0.0065 0.0114 0.0176 0.0252 0.03440.0436 0.0512 0.0574 0.0623 0.066 0.0688 0.0707 0.0720.0727]. This parameter is used if Level/Volume relationshipis set to Table-specified.

Tabulated fluid levelsSpecify the vector of output values for the fluid level as a tabulated1-by-m array. The pump displacements vector must be the samesize as the control member positions vector. The default values,in meters, are [0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.160.18 0.2 0.22 0.24 0.26 0.28 0.3]. This parameter is used ifLevel/Volume relationship is set to Table-specified.

Inlet pipeline diameterThe diameter of the connecting pipe. This parameter must begreater than zero. The default value is 0.02 m.

Pipeline pressure loss coefficientThe value of the pressure loss coefficient, to account for pressureloss in the connecting pipe. This parameter must be greater thanzero. The default value is 1.2.

The loss is computed with the equation similar to that used inthe Fixed Orifice block:

2-353

Variable Head Tank

qK

A pp= 1 2ρ

The Critical Reynolds number is set to 15.





For more information on interpolation algorithms, see the PSLookup Table (1D) block reference page. This parameter is used ifLevel/Volume relationship is set to Table-specified.




2-354

Variable Head Tank

For more information on extrapolation algorithms, see the PSLookup Table (1D) block reference page. This parameter is used ifLevel/Volume relationship is set to Table-specified.


THydraulic conserving port associated with the tank inlet.


See Also Constant Head Tank

Reservoir

2-355

Variable Orifice

Purpose Simulate generic hydraulic variable orifice

Library Orifices

Description The block represents a variable orifice of any type as a data-sheet-basedmodel. Depending on data listed in the manufacturer’s catalogs or datasheets for your particular orifice, you can choose one of the followingmodel parameterization options:




In the first case, the passage area is assumed to be linearly dependenton the control member displacement, that is, the orifice is assumed to beclosed at the initial position of the control member (zero displacement),and the maximum opening takes place at the maximum displacement.In the second case, the passage area is determined by one-dimensionalinterpolation from the table A=A(h). In both cases, a small leakagearea is assumed to exist even after the orifice is completely closed.Physically, it represents a possible clearance in the closed valve, but themain purpose of the parameter is to maintain numerical integrity ofthe circuit by preventing a portion of the system from getting isolatedafter the valve is completely closed. An isolated or “hanging” part of thesystem could affect computational efficiency and even cause failureof computation.

In the first and second cases, the model accounts for the laminar andturbulent flow regimes by monitoring the Reynolds number (Re) andcomparing its value with the critical Reynolds number (Recr). After the

2-356

Variable Orifice

area has been determined, the flow rate is computed according to thefollowing equations:

qC A p sign p Re Re

C AD

p Re Re

D

DLH

=( )i i

ii

2

2

ρ

ν ρ

| | for >=

for <

cr

cr

⎧

⎨⎪⎪

⎩⎪⎪

h x x or= +0 i

A hh A h A hA h

leak

leak( )

/max max=+ >

<=⎧⎨⎩

i for for

00

p p pA B= −

Re( )

= q DA h

Hiiν

CC

DLD

cr=

⎛

⎝⎜⎜

⎞

⎠⎟⎟Re

2

DA h

H = 4 ( )π

where

q Flow ratep Pressure differentialpA,pB Gauge pressures at the block terminalsCD Flow discharge coefficientA(h) Instantaneous orifice passage area

2-357

Variable Orifice

Amax Orifice maximum areahmax Control member maximum displacementx0 Initial openingx Control member displacement from initial positionh Orifice openingor Orifice orientation indicator. The variable assumes +1 value

if the control member displacement in the globally assignedpositive direction opens the orifice, and –1 if positive motiondecreases the opening.

ρ Fluid densityDH Instantaneous orifice hydraulic diameterν Fluid kinematic viscosityAleak Closed orifice leakage area


The block positive direction is from port A to port B. This means that theflow rate is positive if it flows from A to B and the pressure differentialis determined as p p pA B= − . Positive signal at the physical signal

2-358

Variable Orifice

port S opens or closes the orifice depending on the value of the orificeorientation indicator.




• For orifices specified by the passage area (the first twoparameterization options), the transition between laminar andturbulent regimes is assumed to be sharp and taking place exactlyat Re=Recr.

• For orifices specified by pressure-flow characteristics (the thirdparameterization option), the model does not explicitly account forthe flow regime or leakage flow rate, because the tabulated data isassumed to account for these characteristics.

2-359

Variable Orifice


2-360

Variable Orifice

2-361

Variable Orifice

Model parameterizationSelect one of the following methods for specifying the orifice:

• By maximum area and opening — Provide values for themaximum orifice area and the maximum orifice opening. Thepassage area is linearly dependent on the control memberdisplacement, that is, the orifice is closed at the initial positionof the control member (zero displacement), and the maximum

2-362

Variable Orifice



• By pressure-flow characteristic— Provide tabulated dataof orifice openings, pressure differentials, and correspondingflow rates. The flow rate is determined by two-dimensionaltable lookup. You have a choice of three interpolation methodsand two extrapolation methods.

Orifice maximum areaSpecify the area of a fully opened orifice. The parameter valuemust be greater than zero. The default value is 5e-5 m^2. Thisparameter is used if Model parameterization is set to Bymaximum area and opening.

Orifice maximum openingSpecify the maximum displacement of the control member. Theparameter value must be greater than zero. The default value is5e-4 m. This parameter is used if Model parameterization isset to By maximum area and opening.

Tabulated orifice openingsSpecify the vector of input values for orifice openings as atabulated 1-by-m array. The input values vector must be strictlymonotonically increasing. The values can be nonuniformlyspaced. You must provide at least three values. The defaultvalues, in meters, are [-0.002 0 0.002 0.005 0.015]. IfModelparameterization is set to By area vs. opening table,the Tabulated orifice openings values will be used togetherwith Tabulated orifice area values for one-dimensional tablelookup. IfModel parameterization is set to By pressure-flowcharacteristic, the Tabulated orifice openings values will

2-363

Variable Orifice


Tabulated orifice areaSpecify the vector of output values for orifice area as a tabulated1-by-m array. The orifice area vector must be the same size asthe orifice openings vector. All the values must be positive. Thedefault values, in m^2, are [1e-09 2.0352e-07 4.0736e-050.00011438 0.00034356]. This parameter is used if Modelparameterization is set to By area vs. opening table.


Tabulated flow ratesSpecify the output values for flow rates as a tabulated m-by-nmatrix, defining the function values at the input grid vertices.Each value in the matrix specifies flow rate taking place at aspecific combination of orifice opening and pressure differential.The matrix size must match the dimensions defined by the inputvectors. The default values, in m^3/s, are:

[-1e-07 -7.0711e-08 -4.4721e-08 4.4721e-08 7.0711e-08 1e-07;

-2.0352e-05 -1.4391e-05 -9.1017e-06 9.1017e-06 1.4391e-05 2.0352e-05;

-0.0040736 -0.0028805 -0.0018218 0.0018218 0.0028805 0.0040736;

-0.011438 -0.0080879 -0.0051152 0.0051152 0.0080879 0.011438;

-0.034356 -0.024293 -0.015364 0.015364 0.024293 0.034356;]


2-364

Variable Orifice







• From last 2 points— Extrapolates using the linear method(regardless of the interpolation method specified), based onthe last two output values at the appropriate end of the range.That is, the block uses the first and second specified outputvalues if the input value is below the specified range, and the

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Variable Orifice







Critical Reynolds numberThe maximum Reynolds number for laminar flow. The transitionfrom laminar to turbulent regime is supposed to take place

2-366

Variable Orifice

when the Reynolds number reaches this value. The valueof the parameter depends on orifice geometrical profile, andthe recommendations on the parameter value can be found inhydraulic textbooks. The default value is 12.









GlobalParameters


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Variable Orifice







Examples The Hydraulic Flapper-Nozzle Amplifier demo(sh_hydraulic_flapper_nozzle_amplifier) illustrates the use of theVariable Orifice block in hydraulic systems.



Fixed Orifice



PS Lookup Table (1D)

PS Lookup Table (2D)


2-368

Variable-Displacement Hydraulic Machine

Purpose Simulate variable-displacement reversible hydraulic machine withregime-dependable efficiency


Description The Variable-Displacement Hydraulic Machine block representsa variable-displacement hydraulic machine of any type as adata-sheet-based model. The model accounts for the power flowdirection and simulates the machine in both the motor and pumpmode. The efficiency of the machine is variable, and you can set it inaccordance with experimental data provided in the catalog or data sheet.

The machine displacement is controlled by the signal provided throughthe physical signal port C. The machine efficiency is simulated byimplementing regime-dependable leakage and friction torque basedon the experimentally established correlations between the machineefficiencies and pressure, angular velocity, and displacement.

With respect to the relationship between the control signal and thedisplacement, two block parameterization options are available:

• By the maximum displacement and stroke — The displacement isassumed to be linearly dependent on the control member position.

• By table-specified relationship between the control member positionand the machine displacement — The displacement is determinedby one-dimensional table lookup based on the control memberposition. You have a choice of three interpolation methods and twoextrapolation methods.

The variable-displacement machine is represented with the followingequations:

q D k qm L= −i iω

T D p k Tm fr= +i i

2-369


DDx

x

D x=

⎧⎨⎪

⎩⎪

max

max

( )

i

p p pA B= −

where

q Machine flow ratep Pressure differential across the machinepA,pB Gauge pressures at the block terminalsD Machine instantaneous displacementDmax Machine maximum displacementx Control member displacementxmax Control member maximum strokeT Torque at the machine shaftω Machine shaft angular velocityqL Leakage flowTfr Friction torquekm Machine type coefficient. km = 1 for the pump, km = –1 for the

motor.

The key parameters that determine machine efficiency are its leakageand friction on the shaft. In the block, these parameters are specifiedwith experimentally-based correlations similar to [1]

q D kp

pD

DL Lnom

k k

nom

kLP LD L

=⎛

⎝⎜

⎞

⎠⎟

⎛

⎝⎜

⎞

⎠⎟

⎛

⎝⎜

⎞

⎠⎟i iω ω

ω

ω

1max

2-370


T D p kp

pD

Dfr Fnom

k k

nom

kFP FD F

=⎛

⎝⎜

⎞

⎠⎟

⎛

⎝⎜

⎞

⎠⎟

⎛

⎝⎜

⎞

⎠⎟i i 1

max

ωω

ω

where

pnom Nominal pressureωnom Nominal angular velocitykL1 Leakage proportionality coefficientkF1 Friction proportionality coefficientkLP,kLD,kLω,kFP,kFD,kFω

Approximating coefficients

The approximating coefficients are determined from the efficiency plots,usually provided by the machine manufacturer. With the leakageknown, the pump volumetric efficiency can be expressed as

η ωω

ω

ωvp

LL

nom

k k

nom

kD q

Dk

pp

DD

LP LD L

=−

= −⎛

⎝⎜

⎞

⎠⎟

⎛

⎝⎜

⎞

⎠⎟

⎛

⎝⎜

⎞

⎠⎟1 1

max

ωω

For a motor, the expression looks like the following

ηω

ω

ω

ωvm

LL

nom

k k

nom

kD

D qk

pp

DD

LP LD=

+=

+⎛

⎝⎜

⎞

⎠⎟

⎛

⎝⎜

⎞

⎠⎟

⎛

⎝⎜

⎞

⎠⎟

1

1 1max

LLω

The mechanical efficiency is based on the known friction torque

2-371


ηω

ω

mpp

p frF

nom

k k

nom

D

D Tk

pp

DD

FP FD=

+=

+⎛

⎝⎜

⎞

⎠⎟

⎛

⎝⎜

⎞

⎠⎟

⎛

⎝⎜

⎞

⎠⎟

1

1 1max

kkFω

η ωωmm

p fr

pF

nom

k k

nom

kD T

Dk

pp

DD

FP FD

=−

= −⎛

⎝⎜

⎞

⎠⎟

⎛

⎝⎜

⎞

⎠⎟

⎛

⎝⎜

⎞

⎠⎟1 1

max

FFω

The curve-fitting procedure is based on the comparison of the efficiency,determined with one of the above expressions, and the experimental

data η ωexp ( , , )= f p D , an example of which is shown in the followingplot.

2-372


The procedure can be performed with the Optimization Toolboxsoftware. For instance, the pump volumetric efficiency approximatingcoefficients can be found by solving the following problem:

min ( )x

F x

x k k k kL LP LD L= [ ]1, , , ω

F x p D kp

p

D

Di j k Li

nom

kj

kk

LP LD

( ) , ,expmax

= ( ) − −⎛

⎝⎜

⎞

⎠⎟

⎛

⎝⎜

⎞

⎠⎟η ω

ωω

1 1nnom

k

kji

L⎛

⎝⎜

⎞

⎠⎟

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟

⎛

⎝

⎜⎜

⎞

⎠

⎟⎟∑∑∑

ω2

where

i Number of experimental pressure points, from 1 to nj Number of experimental displacement points, from 1 to mk Number of experimental angular velocity points, from 1 to l

Connections A and B are hydraulic conserving ports associatedwith the machine inlet and outlet, respectively. Connection S is amechanical rotational conserving port associated with the machineshaft. Connection C is a physical signal port that controls machinedisplacement. The flow rate from port A to port B causes the shaft torotate in positive direction, provided positive signal is applied to port C.




• No inertia on the machine shaft is considered.

• The model is applicable only for fluid and fluid temperature at whichthe approximating coefficients have been determined.

2-373


• Extreme caution must be exercised to not exceed the limits withinwhich the approximating coefficients have been determined. Theextrapolation could result in large errors.



• “Displacement” on page 2-375

• “Nominal Parameters” on page 2-379

• “Efficiencies” on page 2-380

2-374


Displacement

2-375


Displacement is specifiedSelect one of the following block parameterization options:

• By maximum displacement and control member stroke— Provide values for maximum machine displacement andmaximum stroke. The displacement is assumed to be linearlydependent on the control member position. This is the defaultmethod.

• By displacement vs. control member position table— Provide tabulated data of machine displacements and

2-376


control member positions. The displacement is determinedby one-dimensional table lookup. You have a choice of threeinterpolation methods and two extrapolation methods.

Maximum displacementMachine maximum displacement. The default value is 5e-6m^3/rad. This parameter is used if displacement is specified as Bymaximum displacement and control member stroke.

Maximum strokeMaximum control member stroke. The default value is 0.005 m.This parameter is used if displacement is specified as By maximumdisplacement and control member stroke.

Control member positions tableSpecify the vector of input values for control member positionas a tabulated 1-by-m array. The input values vector must bestrictly monotonically increasing. The values can be nonuniformlyspaced. You must provide at least three values. The defaultvalues, in meters, are [-0.0075 -0.0025 0 0.0025 0.0075].This parameter is used if displacement is specified as Bydisplacement vs. control member position table.

Pump displacements tableSpecify the vector of output values for the machine displacementas a tabulated 1-by-m array. The machine displacements vectormust be the same size as the control member positions vector.The default values, in m^3/rad, are [-5e-06 -3e-06 0 3e-065e-06]. This parameter is used if displacement is specified as Bydisplacement vs. control member position table.




2-377



For more information on interpolation algorithms, see the PSLookup Table (1D) block reference page. This parameter is usedif displacement is specified as By displacement vs. controlmember position table.




For more information on extrapolation algorithms, see the PSLookup Table (1D) block reference page. This parameter is usedif displacement is specified as By displacement vs. controlmember position table.

2-378


Nominal Parameters

Nominal pressureNominal pressure differential across the machine. The defaultvalue is 1e7 Pa.

Nominal angular velocityNominal angular velocity of the output shaft. The default value is188 rad/s.

2-379


Shaft velocity at peak frictionThe friction torque on the machine shaft ideally should beintroduced as Tfrsign(ω). To avoid discontinuity at ω –> 0, thefriction is defined as Tfrtanh(4ω /ωmax ), where ωmax is a smallvelocity, representing the shaft velocity at peak friction, at whichtanh(4ω /ωmax ) is equal to 0.999. The default value of ωmax is0.01 rad/s.

Efficiencies

2-380


Volumetric efficiency proportionality coefficientApproximating coefficient kL1 in the block description preceding.The default value is 0.05.

Volumetric efficiency pressure coefficientApproximating coefficient kLP in the block description preceding.The default value is 0.65.

Volumetric efficiency angular velocity coefficientApproximating coefficient kLω in the block description preceding.The default value is -0.2.

Volumetric efficiency displacement coefficientApproximating coefficient kLD in the block description preceding.The default value is -0.8.

Mechanical efficiency proportionality coefficientApproximating coefficient kF1 in the block description preceding.The default value is 0.06.

Mechanical efficiency pressure coefficientApproximating coefficient kFP in the block description preceding.The default value is -0.65.

Mechanical efficiency angular velocity coefficientApproximating coefficient kFω in the block description preceding.The default value is 0.2.

Mechanical efficiency displacement coefficientApproximating coefficient kFD in the block description preceding.The default value is -0.75.



• Displacement is specified



2-381


All other block parameters are available for modification. The actualset of modifiable block parameters depends on the value of theDisplacement is specified parameter at the time the model enteredRestricted mode.


AHydraulic conserving port associated with the machine inlet.

BHydraulic conserving port associated with the machine outlet.

CPhysical signal port that controls machine displacement.

SMechanical rotational conserving port associated with themachine shaft.

References [1] C.R. Cornell, Dynamic Simulation of a Hydrostatically PropelledVehicle, SAE paper 811253, 1981, p. 22

See Also Variable-Displacement Motor


2-382

Variable-Displacement Motor

Purpose Simulate variable-displacement reversible hydraulic motor


Description The Variable-Displacement Motor block represents avariable-displacement reversible motor of any type as adata-sheet-based model. The motor displacement is controlled by thesignal provided through the physical signal port C. The motor efficiencyis determined based on volumetric and total efficiencies, nominalpressure, and nominal angular velocity. All these parameters aregenerally provided in the data sheets or catalogs.


• By the motor maximum displacement and stroke — The displacementis assumed to be linearly dependent on the control member position.

• By table-specified relationship between the control member positionand the motor displacement — The displacement is determinedby one-dimensional table lookup based on the control memberposition. You have a choice of three interpolation methods and twoextrapolation methods.

The variable-displacement motor is represented with the followingequations:


T D p mech= i iη

DDx

x

D x=

⎧⎨⎪

⎩⎪

max

max

( )

i


2-383


kD

pHPnom V nom

nom=


p p pA B= −

where

q Motor flow ratep Pressure differential across the motorpA,pB Gauge pressures at the block terminalsD Motor instantaneous displacementDmax Motor maximum displacementx Control member displacementxmax Control member maximum strokeT Torque at the motor output shaftω Output shaft angular velocitykleak Leakage coefficientkHP Hagen-Poiseuille coefficientηV Motor volumetric efficiencyηmech Motor mechanical efficiencyν Fluid kinematic viscosityρ Fluid densitypnom Motor nominal pressureωnom Motor nominal angular velocityνnom Nominal fluid kinematic viscosity


2-384


pl

dq

kqleak

HPleak= =128

4μ

πμ

where





kD

pHPnom V nom

nom=

−( )ω η ν ρ1 i i

The motor mechanical efficiency is not usually available in data sheets,therefore it is determined from the total and volumetric efficiencies byassuming that the hydraulic efficiency is negligibly small


The block positive direction is from port A to port B. This means thatthe motor rotates its shaft in the globally assigned positive direction ifthe fluid flows from port A to port B and a positive signal is applied toport C.

2-385





• No loading on the motor shaft, such as inertia, friction, spring, andso on, is considered.

• Leakage inside the motor is assumed to be linearly proportional toits pressure differential.

2-386



2-387


Model parameterizationSelect one of the following block parameterization options:

• By maximum displacement and control member stroke— Provide values for maximum motor displacement and

2-388


maximum stroke. The displacement is assumed to be linearlydependent on the control member position. This is the defaultmethod.

• By displacement vs. control member position table— Provide tabulated data of motor displacements and controlmember positions. The displacement is determined byone-dimensional table lookup. You have a choice of threeinterpolation methods and two extrapolation methods.

Maximum displacementMotor maximum displacement. The default value is 5e-6m^3/rad. This parameter is used ifModel parameterization isset to By maximum displacement and control member stroke.

Maximum strokeMaximum control member stroke. The default value is 0.005 m.This parameter is used if Model parameterization is set to Bymaximum displacement and control member stroke.

Control member positions tableSpecify the vector of input values for control member positionas a tabulated 1-by-m array. The input values vector must bestrictly monotonically increasing. The values can be nonuniformlyspaced. You must provide at least three values. The defaultvalues, in meters, are [-0.0075 -0.0025 0 0.0025 0.0075].This parameter is used if Model parameterization is set to Bydisplacement vs. control member position table.

Pump displacements tableSpecify the vector of output values for the motor displacement asa tabulated 1-by-m array. The motor displacements vector must bethe same size as the control member positions vector. The defaultvalues, in m^3/rad, are [-5e-06 -3e-06 0 3e-06 5e-06]. Thisparameter is used if Model parameterization is set to Bydisplacement vs. control member position table.

2-389






For more information on interpolation algorithms, see the PSLookup Table (1D) block reference page. This parameter is usedif Model parameterization is set to By displacement vs.control member position table.




For more information on extrapolation algorithms, see the PSLookup Table (1D) block reference page. This parameter is usedif Model parameterization is set to By displacement vs.control member position table.

2-390


Volumetric efficiencyMotor volumetric efficiency specified at nominal pressure, angularvelocity, and fluid viscosity. The default value is 0.85.

Total efficiencyMotor total efficiency, which is determined as a ratio betweenthe hydraulic power at the motor inlet and mechanical power atthe output shaft at nominal pressure, angular velocity, and fluidviscosity. The default value is 0.75.

Nominal pressurePressure differential across the motor, at which both thevolumetric and total efficiencies are specified. The default valueis 1e7 Pa.

Nominal angular velocityAngular velocity of the output shaft, at which both the volumetricand total efficiencies are specified. The default value is 188 rad/s.








2-391


GlobalParameters



AHydraulic conserving port associated with the motor inlet.

BHydraulic conserving port associated with the motor outlet.

CPhysical signal port that controls motor displacement.

SMechanical rotational conserving port associated with the motoroutput shaft.

See Also Hydraulic Motor

2-392


Purpose Simulate hydraulic pump maintaining preset pressure at outlet byregulating its flow delivery


Description The Variable-Displacement Pressure-Compensated Pump blockrepresents a positive, variable-displacement, pressure-compensatedpump of any type as a data-sheet-based model. The key parametersrequired to parameterize the block are the pump maximumdisplacement, regulation range, volumetric and total efficiencies,nominal pressure, and angular velocity. All these parameters aregenerally provided in the data sheets or catalogs.

The following figure shows the delivery-pressure characteristic of thepump.

The pump tries to maintain preset pressure at its outlet by adjusting itsdelivery flow in accordance with the system requirements. If pressuredifferential across the pump is less than the setting pressure, the pumpoutputs its maximum delivery corrected for internal leakage. After

2-393


the pressure setting has been reached, the output flow is regulatedto maintain preset pressure by changing the pump’s displacement.The displacement can be changed from its maximum value down tozero, depending upon system flow requirements. The pressure rangebetween the preset pressure and the maximum pressure, at which thedisplacement is zero, is referred to as regulation range. The smaller therange, the higher the accuracy at which preset pressure is maintained.The range size also affects the pump stability, and decreasing the rangegenerally causes stability to decrease.

The variable-displacement, pressure-compensated pump is representedwith the following equations:


T D p mech= i / η

DD p pD K p p p p p

p p

set

set set=<=

− −( ) < <>=

max

max max

max

for for for 0

⎧⎧⎨⎪

⎩⎪

p p pset regmax = +

K D p pset= −( )max max/


kD

pHPnom V nom

nom=


p p pP T= −

where

2-394


q Pump deliveryp Pressure differential across the pumppP,pT Gauge pressures at the block terminalsD Pump instantaneous displacementDmax Pump maximum displacementpset Pump setting pressurepmax Maximum pressure, at which the pump displacement is zeroT Torque at the pump driving shaftω Pump angular velocitykleak Leakage coefficientkHP Hagen-Poiseuille coefficientηV Pump volumetric efficiencyηmech Pump mechanical efficiencyν Fluid kinematic viscosityρ Fluid densitypnom Pump nominal pressureωnom Pump nominal angular velocityνnom Nominal fluid kinematic viscosity


pl

dq

kqleak

HPleak= =128

4μ

πμ

where

2-395






kD

pHPnom V nom

nom=

−( )ω η ν ρ1 i i



The block positive direction is from port T to port P. This means thatthe pump transfers fluid from T to P provided that the shaft S rotatesin the positive direction. The pressure differential across the pump isdetermined as p p pP T= − .






2-396



Maximum displacementPump displacement. The default value is 5e-6 m^3/rad.

Setting pressurePump pressure setting. The default value is 1e7 Pa.

Pressure regulation rangePressure range required to change the pump displacement fromits maximum to zero. The default value is 6e5 Pa.

2-397







GlobalParameters






2-398


Examples The Closed-Loop Electrohydraulic Actuator with ProportionalValve demo (sh_closed_loop_actuator) illustrates the use of theVariable-Displacement Pressure-Compensated Pump block in hydraulicsystems.




2-399


Purpose Simulate variable-displacement reversible hydraulic pump


Description The Variable-Displacement Pump block represents avariable-displacement reversible pump of any type as adata-sheet-based model. The pump delivery is proportional to thecontrol signal provided through the physical signal port C. The pumpefficiency is determined based on volumetric and total efficiencies,nominal pressure, and angular velocity. All these parameters aregenerally provided in the data sheets or catalogs.


• By the pump maximum displacement and stroke — The displacementis assumed to be linearly dependent on the control member position.

• By table-specified relationship between the control memberposition and pump displacement — The displacement is determinedby one-dimensional table lookup based on the control memberposition. You have a choice of three interpolation methods and twoextrapolation methods.

The variable-displacement pump is represented with the followingequations:


T D p mech= i / η

DDx

x

D x=

⎧⎨⎪

⎩⎪

max

max

( )

i


2-400


kD

pHPnom V nom

nom=


p p pP T= −

where

q Pump deliveryp Pressure differential across the pumppP,pT Gauge pressures at the block terminalsD Pump instantaneous displacementDmax Pump maximum displacementx Control member displacementxmax Control member maximum strokeT Torque at the pump driving shaft

ω Pump angular velocitykleak Leakage coefficientkHP Hagen-Poiseuille coefficientηV Pump volumetric efficiencyηmech Pump mechanical efficiencyν Fluid kinematic viscosityρ Fluid densitypnom Pump nominal pressureωnom Pump nominal angular velocityνnom Nominal fluid kinematic viscosity

2-401



pl

dq

kqleak

HPleak= =128

4μ

πμ

where





kD

pHPnom V nom

nom=

−( )ω η ν ρ1 i i



The block positive direction is from port T to port P. This means thatthe pump transfers fluid from T to P as its driving shaft S rotates in theglobally assigned positive direction and a positive signal is applied toport C.

2-402








2-403


Model parameterizationSelect one of the following block parameterization options:

• By maximum displacement and control member stroke —Provide values for maximum pump displacement and maximum

2-404


control member stroke. The displacement is assumed to belinearly dependent on the control member position. This is thedefault method.

• By displacement vs. control member position table— Provide tabulated data of pump displacements and controlmember positions. The displacement is determined byone-dimensional table lookup. You have a choice of threeinterpolation methods and two extrapolation methods.

Maximum displacementPump maximum displacement. The default value is 5e-6m^3/rad. This parameter is used ifModel parameterization isset to By maximum displacement and control member stroke.

Maximum strokeMaximum control member stroke. The default value is 0.005 m.This parameter is used if Model parameterization is set to Bymaximum displacement and control member stroke.

Control member positions tableSpecify the vector of input values for control member positionas a tabulated 1-by-m array. The input values vector must bestrictly monotonically increasing. The values can be nonuniformlyspaced. You must provide at least three values. The defaultvalues, in meters, are [-0.0075 -0.0025 0 0.0025 0.0075].This parameter is used if Model parameterization is set to Bydisplacement vs. control member position table.

Pump displacements tableSpecify the vector of output values for the pump displacement asa tabulated 1-by-m array. The pump displacements vector must bethe same size as the control member positions vector. The defaultvalues, in m^3/rad, are [-5e-06 -3e-06 0 3e-06 5e-06]. Thisparameter is used if Model parameterization is set to Bydisplacement vs. control member position table.

2-405






For more information on interpolation algorithms, see the PSLookup Table (1D) block reference page. This parameter is usedif Model parameterization is set to By displacement vs.control member position table.




For more information on extrapolation algorithms, see the PSLookup Table (1D) block reference page. This parameter is usedif Model parameterization is set to By displacement vs.control member position table.

2-406













2-407


GlobalParameters





CPhysical signal port that controls pump displacement.





2-408

Glossary

Glossary

across variablesVariables that are measured with a gauge connected in parallel to anelement.

behavioral block implementation modelA block that is implemented based on its physical behavior, described bya system of mathematical equations. An example of a behavioral blockimplementation is the Variable Orifice block.

conserving portsBidirectional hydraulic or mechanical ports that represent physicalconnections and relate physical variables based on the Physical Networkapproach.

constructional block implementation modelA block that is constructed out of other blocks, connected in a certainway. An example of a constructional block implementation is the 4-WayDirectional Valve block, which is constructed based on four VariableOrifice blocks.

data-sheet-based modelA block with a set of parameters determined by data that is usuallylisted in the manufacturer’s catalogs or data sheets.

globally assigned positive directionDirection considered positive for a model diagram.

nonrestricted parametersParameters that are available for modification when you open a modelin Restricted mode. Usually, these are the block parameters with plainnumerical values, such as Pipe internal diameter or Resistancearea. Information on restricted and nonrestricted parameters is listedin block reference pages.

physical signal portsUnidirectional ports (inports and outports) transferring signals that usean internal physical modeling engine for computations.

Glossary-1

Glossary

restricted parametersParameters that are not available for modification when you open amodel in Restricted mode. You have to be in Full mode to modifythem. Usually, these are the block parameterization options, such asPipe cross section type or Interpolation method. Information onrestricted and nonrestricted parameters is listed in block referencepages.

through variablesVariables that are measured with a gauge connected in series to anelement.

vertical productsProducts in the Physical Modeling family that use Simscape platformand, as a result, share common functionality such as physical unitsmanagement, editing modes, and so on. SimHydraulics software is oneof the Simscape vertical products.

Glossary-2

Index

IndexSymbols and Numerics2-Position Valve Actuator block 2-22-Way Directional Valve block 2-83-Position Valve Actuator block 2-193-Way Directional Valve block 2-254-Way Directional Valve block 2-37

Aaccumulators

gas-charged 2-136spring-loaded 2-327

Annular Orifice block 2-51

BBall Valve block 2-56

CCartridge Valve Insert block 2-62Centrifugal Pump block 2-74Check Valve block 2-92Constant Head Tank block 2-98Cylinder Friction block 2-102

DDouble-Acting Hydraulic Cylinder block 2-108Double-Acting Rotary Actuator block 2-114

EElbow block 2-120

FFixed Orifice block 2-126Fixed-Displacement Pump block 2-130

GGas-Charged Accumulator block 2-136Gradual Area Change block 2-140

HHydraulic Cartridge Valve Actuator block 2-149Hydraulic Double-Acting Valve Actuator

block 2-153Hydraulic Fluid block 2-162Hydraulic Motor block 2-170Hydraulic Pipe LP block 2-183Hydraulic Pipeline block 2-175Hydraulic Single-Acting Valve Actuator

block 2-192

LLocal Resistance block 2-197

NNeedle Valve block 2-206

OOrifice with Variable Area Round Holes

block 2-212Orifice with Variable Area Slot block 2-219

PPilot-Operated Check Valve block 2-225Pipe Bend block 2-232Poppet Valve block 2-238Pressure Compensator block 2-253Pressure Reducing Valve block 2-260Pressure Relief Valve block 2-265Pressure-Compensated Flow Control Valve

block 2-244

Index-1

Index

Proportional and Servo-Valve Actuatorblock 2-271

RReservoir block 2-275Resistive Pipe LP block 2-278

SSegmented Pipe LP block 2-294Segmented Pipeline block 2-287Shuttle Valve block 2-304Single-Acting Hydraulic Cylinder block 2-311Single-Acting Rotary Actuator block 2-316Spool Orifice Hydraulic Force block 2-321Spring-Loaded Accumulator block 2-327Sudden Area Change block 2-330

TT-junction block 2-338terminology Glossary-1

VValve Hydraulic Force block 2-343Variable Head Tank block 2-349Variable Orifice block 2-356Variable-Displacement Hydraulic Machine

block 2-369Variable-Displacement Motor block 2-383Variable-Displacement Pressure-Compensated

Pump block 2-393Variable-Displacement Pump block 2-400

Index-2

60983300 2 sim hydraulics reference

Documents

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