chapter – 5 modeling and simulation of...

5.1

Chapter – 5 Modeling and Simulation of Mechanism

In the present study, KED analysis of four bar planar mechanism using

MATLAB program and ANSYS software has been carried out. The analysis has also

been carried out by considering rigid links in the same mechanism. In the analysis of

rigid links all pin joint forces, angular velocities and angular accelerations of links has

been computed. The coupled solution of governing equations of motion has been

obtained using MATLAB. In this MATLAB analysis each link has been considered as

an element. The simulated results have been validated with the experimental results

available in literature [13]. The modeling and simulations of four bar planar

mechanism has been executed in ANSYS by considering rigid link and flexible links

with more elements. The effect of moment of inertia of coupler and its length, flexibly

of crank and rocker, and rocker length on the strain developed in coupler has been

studied. After the dynamic analysis of four bar planar mechanism this methodology is

extended to six bar mechanism.

Multibody simulation deals with deals with study and analysis of dynamic

behavior of system of flexible and/or rigid interconnected bodies. These bodies are

subjected to constrain with respect to one another through a kinematic constraints

modeled as joints. These systems can represent a space structure with antenna

deployment capabilities, an automobile, a robot with manipulator arms, an aircraft as

an assemblage of rigid and flexible parts, and so on. The components may be

subjected to large displacement, large rotation, and also effects of finite strain.

Multibody systems have conventionally been modeled as rigid body systems

with superimposed elastic effects of one or more components. A major limitation of

these methods is that non-linear large-deformation, finite strain effects or non-linear

material cannot be incorporated completely into model.

The FE method used in ANSYS offers an attractive approach to modeling a

multibody system. The ANSYS multibody analysis method may require more

5.2

computational resources and modeling time compared to standard analysis; it has the

following advantages [75]:

• The finite element mesh automatically represents the geometry while the large

deformation/rotation effects are built into the finite element formulation.

• Inertial effects are greatly simplified by the consistent mass formulation or

even point mass representations.

• Interconnection of parts via joints is greatly simplified by considering the

finite motions at the two nodes forming the joint element.

A general steps for FEM for non-linear analysis is as follows:

(i) Build the model: A flexible mechanism usually comprises of flexible and/or rigid

body parts connected via joint elements. The modeling the flexible parts with any

of the 3-D solid, shell, or beam elements. The flexible and/or rigid parts are

connected using joint elements. In one scenario, two parts may be simply

connected to ensure that the displacements at the joints are identical. In other

scenario, the two connected parts may involve joint such as the universal joint or a

planar joint. While modeling these joints, a suitable kinematic constraint is

implemented on the relative motion (displacement and rotation) between the two

nodes that form the joint.

(ii) Define element types: Simulation of a flexible multibody involving flexible and

rigid components joined together subjected to some form of kinematic

constraints, using appropriate joint and contact element types.

(iii) Define materials: Defining the linear and non-linear material properties for each

components of multibody system.

(iv) Mesh the model: Mesh the all flexible components of multibody system. Two

nodes define joint elements and no special meshing is required to define them.

(v) Solve the model: Multibody analyses generally involve large rotations in static or

transient dynamics analysis, so non-linear geometric effects must be accounted

for.

5.3

(vi) Review the results of model: Results from a flexible multibody analysis consist

mainly of displacements, velocities, accelerations, stresses, strains, and reaction

forces in structural components. Constraint forces, current relative positions,

relative velocities, and relative accelerations in joint elements are also available.

5.1 Analysis of mechanism in ANSYS

The procedure for rigid and dynamic analysis of mechanism in ANSYS

Workbench software is as follows [75]:

5.1.1 Selection of types of analysis

In its most basic use, the ANSYS Workbench process is straight forward to

select the type of analysis that is to be performed from the analysis systems group of

the Toolbox and add that system to the project schematic. When the system is in

place, than work through the cells in the system, generally from top-to-bottom, until

completed all the required steps for analysis are completed. In most cases, data flows

from top to bottom through the system as well. For example, in a mechanical system,

the geometry must be defined before one defines the model; the model cell uses the

geometry defined in the geometry cell as its input.

5.1.2 Renaming Systems

In general, it is good practice to give each system a name which is most

meaningful for analysis as shown in Fig. 5.1. When new systems are added to the

project schematic, the system name initially has focus to encourage the user to enter a

meaningful name. To rename a system that already exists on the project schematic,

one can either double-click on the system name (shown below the system) or right-

click and select rename from the system context menu (right click on the system

header, row 1 in the system, to access the system context menu). The system name

will be highlighted as shown in Fig. 5.1.

5.4

Fig. 5.1 Step for renaming the system

5.1.3 Define engineering data

Engineering data serves as a resource related to material properties that is used

in system analysis. Engineering data can be used as a repository for company or

department data, such as material data libraries. While designing the engineering data

workspace care is taken to allow user to create, save, and retrieve material models,

and also to create libraries of data that can be saved and subsequently used in projects

and by different users or in other analysis. User interface for engineering data is

shown in Fig. 5.2.

Engineering data can be shown as a component system or as a cell in any

mechanical analysis system. As a standalone component system, the workspace

accesses all material models and properties by default. Properties and material models

related to system physics are shown in workspace when viewed as a cell in

mechanical analysis system. The engineering data can be access by inserting an

engineering data component system or a mechanical system into the project

5.5

schematic. The analyst can select edit from the engineering data cell's menu, or opt to

double-click the cell. Subsequently, the engineering data workspace appears. From

here, the user can navigate through the database required for analysis system, access

external data sources, create new data, as well as store data for subsequent use.

Fig. 5.2 Step for defining the engineering data

5.1.4 Attach geometry

There are no geometry creation tools in the mechanical application so

geometry must be attached to the mechanical application. The geometry can be

created from either of the following sources: (i) from within Workbench using design

modeler or (ii) From a CAD system supported by workbench.

To import the geometry following step can be performed. From the analysis

system subroutine, select the geometry cell. Browse to the CAD file from the

following access points: Right-click on the geometry cell in the project schematic and

choose import geometry. The model cell in the project schematic can be selected via

5.6

double click. Subsequently the mechanical application displays the geometry. The

dialogue box related to geometry import as shown in Fig. 5.3.

Fig. 5.3 Step for attaching the geometry

5.1.5 Define the part behavior

After attaching geometry it is possible to access settings related to part

behavior by right-clicking on the model cell in the analysis system schematic and

choosing edit. The mechanical application opens with the environment representing

the analysis system displayed under the model object in the tree, as mention in Fig.

5.4. Under this tree first branch is geometry and second is coordinate systems. In

geometry list of parts or bodies with following options:

(i) Stiffness behavior: In addition to making changes to the material properties of a

part, it is also possible to designate a part's stiffness behavior as being flexible or

rigid. The solution time is reduced significantly by setting a part behavior as rigid

which in turn reduces the representation of part to single point mass. Mass of rigid

part will be calculated from density of the material. In case of density being

5.7

function of temperature, it is evaluated at the reference temperature. For contact

conditions, specify Young’s modulus. Flexible is the default stiffness behavior. To

change, simply select rigid from the stiffness behavior drop-down menu.

Fig. 5.4 Step for defining the parts behaviour

(ii) Coordinate systems: The coordinate systems object and its child object, global

coordinate system is automatically placed in the tree with a default location of 0,

0, 0, when a model is imported. For solid parts and bodies by default, a part and

any associated bodies, use the global coordinate system. If desired, it is also

possible to apply a local coordinate system to the part or body. When a local

coordinate system is assigned to a part, by default, the bodies also assume this

coordinate system but one may modify the system on the bodies individually as

desired. For surface bodies, solid shell bodies, and line bodies by default, these

types of geometries generate coordinates systems on a per element type basis. It is

necessary for the user to create a local coordinate system and associated it with the

5.8

parts and/or bodies using the coordinate system setting in the details view for the

part/body if one wishes to orient those elements in a specific direction.

(iii) Reference temperature: The default reference temperature is taken from the

environment (by environment), which occurs when solving. This necessarily

means that the reference temperature can change for different solutions. The

reference temperature can also be specified for a body and will be constant for

each solution (by body). Selecting by body will cause the reference temperature

value field to specify the reference temperature for the body. It is important to

recognize that any value set by body will only set the reference temperature of the

body and not actually causes the body to exist at that temperature.

(iv) Material property assignment: Once the geometry has been attached, the next step

is to choose a material for the simulation. Upon selecting a part in the tree outline,

the assignment entry under Material in the details view lists a default material for

the part. This can be edited using material properties in the engineering data

workspace.

(v) Non-linear material effects: It is possible to ignore any nonlinear effects from the

material properties. As default setting, all pertinent material properties are used,

including non-linear properties such as stress-strain curve data. Setting non-linear

effects to no will ignore any non-linear properties only for that part. This option

will allow the analyst to assign same material to two different parts and also treat

one of the parts as linear.

(vi) Thermal strain effects: For structural analyses, it is possible to have workbench to

calculate a thermal strain result by setting thermal strain effects to yes. Choosing

this option enables the coefficient of thermal expansion to be sent to the solver.

5.1.6 Define connections

Connections include contact regions, joints, springs, or beams. Explicit

analysis connections include body interactions.

Contact conditions arise where bodies meet. On importing an assembly from a

CAD system, contact between various parts is automatically detected. In addition to

this contact regions can also be set up manually. It is possible to transfer heat flows

5.9

across the contact boundaries and structural loads and connects the various bodies.

The analysis can be linear or nonlinear, depending on the type of contact.

A joint is an idealized kinematic linkage that controls the relative movement

between two bodies. Joint types are characterized by their translational and rotational

DOF as being fixed or free, as shown in Fig. 5.5

Fig. 5.5 Step for defining the connections

5.1.7 Apply mesh control and preview mesh

Meshing is the process in which the mechanism geometry is spatially

discretized into elements and nodes. This mesh along with material properties is used

to mathematically represent the stiffness and mass distribution of the structure.

The model is automatically meshed for further process. The element size by

default is determined based on various factors including body curvature, the overall

model size, the complexity of the feature and the proximity of other topologies. When

required, the mesh size is adjusted up to four times (eight times for an assembly) till a

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successful mesh is achieved. The dialogue box for meshing the model is shown in Fig.

5.6.

If desired, it is possible to preview the mesh before solving. Mesh controls are

available to assist you in fine tuning the mesh.

There are some options available to modify the mesh: (i) default group, (ii)

sizing group, (iv) inflation group, (v) advanced group, (vi) pinch group and (vii)

statistics group.

Fig. 5.6 Step of meshing the model

5.1.8 Establish the analysis setting

For transient structural (ANSYS) analysis the basic controls are:

Slender structures typically require large deflection. The user can use large

deflection in case a slender structure has transverse displacements that are more than

10% of the thickness. Small strain and small deflection analysis assume that

5.11

displacements are small enough so that the resulting stiffness changes are

insignificant. Switching ON large deflection will account for stiffness changes

resulting from change in orientation and element shape due to large deflection, large

strain, and large rotation. This ensures that the results will be more accurate. But this

effect demands an iterative solution. In addition it may also need the load to be

applied in small increments. Hence the solution may take longer time. Use of hyper

elastic materials also requires large deflection to be turned on as shown in Fig. 5.7.

Fig. 5.7 Step for setting the analysis steps

Step controls permits to control the time step size in a transient analysis. In

addition this control also makes it possible to create multiple steps. In case new loads

are to be introduced or removed at different times in the load history, or if the analyst

wants to change the analysis settings such as the time step size at some points in the

time history, multiple steps are to be used. In case nonlinearities are present or if the

applied load has high frequency content, one might be required to use a small time

5.12

step size (that is, small load increments) and compute solutions at these intermediate

time steps to subsequently arrive at more accurate results. This group can be modified

on a per step basis.

Output controls option is useful to specify the time points at which results

should be available for post processing. In a transient nonlinear analysis it may be

necessary to perform many solutions at intermediate time values. However, (i) one

may not be interested in all the intermediate results, and (ii) writing all the results can

make the results file size unwieldy. This group can be modified on a per step basis

except for calculating stress and strain.

Non-linear controls feature allow the user to modify convergence criteria and

other specialized solution controls. Typically one will not need to change the default

values for this control. This group can be modified on a per step basis.

Damping controls are used to specify damping for the structure in a transient

analysis. The following forms of damping are available for a transient analysis: beta

damping and numerical damping. In addition, element based damping from spring

elements as well as material based damping factors are also available for the transient

structural (ANSYS) analysis.

Analysis data management settings make it possible to save specific solution

files from the transient structural (ANSYS) analysis for other analyses. The default

behavior is to only keep the files required for post processing. These controls can be

used to keep all files created during solution or to create and save the mechanical

APDL application database (db file).

5.1.9 Define the initial conditions

For transient structural (ANSYS) analysis the initial conditions are:

A transient analysis involves loads that are functions of time. The first step in

applying transient loads is to establish initial conditions (that is, the condition at initial

time = 0).

5.13

The default initial condition for a transient structural (ANSYS) analysis is that

the structure is “at rest”, that is, both initial displacement and initial velocity are zero.

A transient structural (ANSYS) analysis is at rest, by default. The initial conditions

object allows to specified velocity.

In many analyses one or more parts will have an initial known velocity such as

in a drop test, metal forming analysis or kinematic analysis. A constant velocity initial

condition can be specified if required. The constant velocity could be aimed at one or

more parts of the structure. The remaining parts of the structure which are not part of

the horizon will be subjected to the “at rest” initial condition.

Initial condition can also be specified using step controls, that is, by specifying

multiple steps in a transient analysis and controlling the time integration effects along

with activation/deactivation of loads. This is extremely useful when there are different

parts of a model that have different initial velocities or more complex initial

conditions. Some commonly encountered initial condition is tackled as explained

below:

Initial displacement = 0, Initial velocity ≠ 0 for some parts: The non zero

velocity is established by applying small displacements over a small time interval on

the part of the structure where velocity is to be specified.

Specify second steps in the analysis. The first step is used to establish initial

velocity on one or more parts. A small end time (compared to the total span of the

transient analysis) is choosen for the first step. The second step will cover the total

time span.

Specify displacement(s) on one or more faces of the part(s) that will give the

required initial velocity. This requires that one does not have any other boundary

condition on the part that will interfere with rigid body motion of that part. Make sure

that these displacements are ramped from a value of zero.

Deactivate or release the specified displacement load in the second step so that

the part is free to move with the specified initial velocity.

5.14

Initial displacement ≠ 0, Initial velocity ≠ 0: This is similar to previous case

except that the imposed displacements are the actual values instead of “small” values.

Specify second steps in the analysis. The first step is used to establish initial

displacement and velocity on one or more parts. A small end time (compared to the

total span of the transient analysis) is choosen for the first step. The second step will

cover the total time span.

The initial displacement(s) on one or more faces of the part(s) is specified, as

needed. This requires that the user does not have any other boundary condition on the

part that will interfere with rigid body motion of that part. Make sure that these

displacements are ramped from a value of zero. Further release the specified

displacement load as explained previously.

Initial Displacement ≠ 0, Initial Velocity = 0: This requires the use of two

steps also. The main difference between the above and this scenario is that the

displacement load in the first step is not ramped from zero. Instead it is step applied as

shown below with two or more sub steps to ensure that the velocity is zero at the end

of step 1.

Specify second steps in the analysis. The first step will be used to establish

initial displacement on one or more parts. An end time for the first step is choosen

that together with the initial displacement values will create the necessary initial

velocity.

The initial displacement(s) on one or more faces of the part(s) is specified as

needed. This requires that user does not have any other boundary condition on the part

that will interfere with rigid body motion of that part. Make sure that this load is step

applied, that is, apply the full value of displacements at time = 0 itself and maintain it

throughout the first step.

Deactivate or release the specified displacement load in the second step so that

the part is free to move with the initial displacement values.

5.15

5.1.10 Apply loads and supports

For a transient structural (ANSYS) analysis applicable loads/supports are all

inertial and structural loads, and all structural supports. Joint loads are used to

kinematically drive joints.

For joints in a transient structural (ANSYS) or transient structural (MBD)

analysis, one has to use a joint load object to apply a kinematic driving condition to a

single DOF on a joint object. Joint load objects are applicable to all joint types except

fixed, general, universal, and spherical joints. For translation DOF, the joint load can

apply a displacement, velocity, acceleration, or force. For rotation DOF, the joint load

can apply a rotation, angular velocity, angular acceleration, or moment. The directions

of the DOF are based on the reference coordinate system of the joint and not on the

mobile coordinate system.

A positive joint load will tend to cause the mobile body to move in the

positive DOF direction with respect to the reference body, assuming the mobile body

is free to move. If the mobile body is not free to move then the reference body will

tend to move in the negative DOF direction for the joint load. One way to learn how

the mechanism will behave is to use the configure feature. For the joint with the

applied joint load, dragging the mouse will indicate the nature of the reference/mobile

definition in terms of positive and negative motion.

To apply a joint load: Highlight the transient environment object and insert a

joint load from the right mouse button context menu or from the loads drop down

menu in the environment tool bar as shown Fig. 5.8.

From the joint drop down list in the details view of the joint load, select the

particular joint object that has to be applied to the joint load. Apply a joint load to the

mobile bodies of the joint. It is therefore important to carefully select the reference

and mobile bodies while defining the joint.

5.16

Fig. 5.8 Step for applying the load

The unconstrained DOF has to be selected for applying the joint load, based

on the type of joint. This selection can be made from the DOF drop down list. For

joint types that allow multiple unconstrained DOF, a separate joint load is necessary

to drive each one. Joint load objects that include velocity, acceleration, rotational

velocity or rotational acceleration are not applicable to static structural analyses.

Type of joint load has to be selected from the type drop down list. The list is

filtered with choices of displacement, velocity, acceleration, and force if case of

selection of a translational DOF in step 3. The choices are rotation, rotational velocity,

rotational acceleration, and moment if you selected a rotational DOF.

The magnitude of the joint load type is specified in step 4 as a constant, in

tabular format, or as a function of time using the same procedure as is done for most

loads in the mechanical application.

5.17

5.1.11 Description of solve tool

When performing a nonlinear analysis, one may encounter convergence

difficulties due to a number of reasons. Some examples may be initially open contact

surfaces causing rigid body motion, large load increments causing non-convergence,

material instabilities, or large deformations causing mesh distortion that result in

element shape errors. Dialogue box for setting solve method and result tracker is

shown in Fig. 5.9.

Solution output continuously updates any listing output from the solver and

also specifies useful information related to behavior of the structure during the

analysis.

Fig. 5.9 Step for setting solve method and result tracker

It is possible to view contour plots of Newton-Raphson residuals in a non-

linear static analysis. Such a capability can be useful when user experience

convergence issues in the middle of a step, where the model has non-linearties and a

5.18

large number of contact surfaces. When the solution diverges, identifying regions of

high Newton-Raphson residual forces can provide insight into possible problems.

Result tracker is also a useful tool that permits monitoring of displacement and

energy results as the solution moves ahead. This is typically useful when structures

that go through convergence difficulties owing to buckling instability.

5.1.12 Post processing of analysis results

The analysis type determines the results available for user to examine after

solution. For example, in a structural analysis, one may be interested in maximum

shear results or equivalent stress results, while in a thermal analysis, the user may be

interested in total heat flux or temperature. The result in the mechanical application

section lists various results available for post processing.

In order to add result objects in the mechanical application:

• Highlight a solution object in the tree structure.

• Select the pertinent result from the solution context toolbar or opt for

the right-mouse click option.

• To review results in the mechanical application:

• Click on a result object in the tree structure.

After the solution has been obtained, it is possible to review and interpret the

output as explained below:

• Contour plots - Displays a contour plot of a result such as stress over

geometry.

• Vector Plots - Displays some results in the form of vectors (arrows).

• Probes - Displays a result at a single time point, or as a variation over

time, using a table as well as a graph. It is also possible to set up

various probes to review results as shown in Fig. 5.10.

• Charts – Shows various results over period of time, or displays one

result versus another, for example, force versus displacement.

5.19

• Animation - Animates the change of results over geometry along with

deformation of structure.

• Stress Tool - to access a design using different failure theories.

• Fatigue Tool - to carry out advanced life prediction calculations.

• Contact Tool - to review contact zone behavior in complex assemblies.

• Beam Tool - to study stresses in line body representations.

Fig. 5.10 Step to set the different probe to review results

5.2 Modeling of four bar planar mechanism

The kinematic and dynamic analysis using MATLAB and ANSYS software

have been carried with different considerations and also tabulated in Table 5.1.

5.20

Table: 5.1 Detail of cases simulated in present study

Sr. No.

Cases considered for simulation ANSYS MATLAB Importance of study

1 Position analysis No Yes Necessary for dynamic analysis 2 Velocity analysis Yes Yes

3 Acceleration analysis Yes Yes 4. To study effect of

transmission angle No Yes Necessary for joint

force and torque calculation which is useful for selection of drives

5. Determination of joint force Yes Yes

6. Flexible dynamic analysis of coupler

Yes Yes Important for light weight links, which affect the mechanism performance due to deflection of links

7. To study effect of link orientation and cross section

Yes No Useful for proper selection of link cross section

8. To study the effect of rocker arm length

Yes No Useful for proper selection of link length and transmission angle9. To study the effect of coupler

length Yes No

10. To study the effect of links flexibility on coupler strain

Yes No Important for light weight links, which affect the mechanism performance due to deflection of links

11. Flexible dynamic analysis of six bar Watt’s mechanism

Yes No Important for light weight links, which affect the mechanism performance due to deflection of links

Two type of analysis have been carried out in ANSYS software, (i) Rigid

analysis and (ii) Flexible analysis. The links are connected to each other through

revolute joints. The effect of gravity is taken into consideration. The crank, follower

and coupler are modeled using beam elements. A constant time step was chosen for

the simulation. The strain of coupler at various time intervals is calculated.

Flexible analysis is carried out by considering the coupler as flexible and

remaining links are to be rigid. Geometry has been prepared in Pro-E as per the

specification mention in Table 5.2 and exported to ANSYS of analysis. Meshed

5.21

model of four bar planar mechanism has been presented in Fig. 5. 11. Detail related to

modeling and parameters to be selected for analysis have been mention in Table 5.3.

Table 5.2 Specification of four bar planar mechanism [12, 13]

Parameters Fixed link (1) Crank (2) Coupler (3) Follower (4)

Length (mm) 250 110 280 260

C/S Area (mm2) - 108 40 40

Area moment of

Inertia (mm4) - 160 9 9

Modulus of Elasticity, E = 7.10 × 104 MPa

Density = 2770 kg/m3 Crank speed = 32.3 rad/sec

Fig. 5.11 Meshed model of four bar planar mechanism

5.22

Table 5.3 Detail of finite element model of four bar planar mechanism

Object Name LINK1 (Fix)

LINK2 (Crank)

LINK3 (Coupler)

LINK4 (Rocker)

Definition

Stiffness Behavior

Rigid Flexible Rigid

Reference Temperature

By Environment

Material

Assignment Aluminum Alloy

Nonlinear Effects

Yes

Thermal Strain Effects

Yes

Properties

Volume(mm3) 51571 22451 21903 21103

Mass (kg) 0.14285 0.06219 0.06067 0.058455

Moment of Inertia Ip1

kg·mm² 5.9932 4.4632 3.9738 3.8673

Moment of Inertia

Ip2kg·mm² 799.36 124.38 784.46 665.22

Moment of Inertia

Ip3kg·mm² 802.97 122.08 782.45 663.31

Statistics

Nodes 1 924 1

Elements 1 102 1

Modeling of four bar mechanism has been done for varying different

parameter i.e. cross section and orientation of cross section of coupler, length of the

rocker and coupler, and flexibility of other links to study the effect on the strain

produce in flexible coupler. Therefore, different models have been prepared in Pro-E

5.23

and exported ANSYS for analysis as presented in Figs 5.12-5.18 and detail of model

i.e. number of nodes and element are presented in Tables 5.4-5.8.

Fig. 5.12 Coupler link having rectangular cross section with orientation 1

Fig. 5.13 Coupler link having rectangular cross section with orientation 2

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Figures 5.15 to 5.18 show the rectangular, circular and elliptical cross section

with different orientation of coupler link with cross section area of 40 mm2. Due to

the change in orientation of coupler has changed its moment of inertia from Ixx to Iyy

(rectangular cross section). It is worth to mention here, that in case of Ixx, the width of

coupler is parallel axis of rotation while, it is perpendicular to axis of rotation in case

of Iyy.

Fig. 5.14Coupler link having circular cross section

Fig. 5.15Coupler link having elliptical cross section

5.25

Table 5.4 Detail of FE model for different cross section and orientation of coupler

Object Name For Fig. 5.12

For Fig. 5.13

For Fig. 5.14

For Fig. 5.15

Definition

Stiffness Behavior Flexible

Reference Temperature

By Environment

Material


Nonlinear Effects Yes

Thermal Strain Effects

Yes

Properties

Volume(mm³) 21903 22386 22014 14102

Mass (kg) 0.060672 0.06201 0.060979 0.039063

Moment of Inertia Ip1 (kg·mm²)

3.9738 4.1438 2.7188 2.5527


784.46 800.83 785.77 660.59


782.45 799.84 786.37 661.19

Statistics

Nodes 924 1595 1858 1151

Elements 102 723 958 504

Table 5.5 Detail of FE model for different length of coupler

Coupler length

(mm) 260 270 280 290 300

Statistics

Nodes 883 883 924 921 921

Elements 96 96 102 100 100

5.26

Fig. 5.16 Meshed model of mechanism with flexible coupler and rocker

Table 5.6 Detail of finite element model with flexible coupler and rocker

Object Name LINK1 LINK2 LINK3 LINK4

Stiffness Behavior Rigid Flexible

Reference Temperature By Environment

Material



Thermal Strain Effects Yes

Statistics

Nodes 1 886 845

Elements 1 98 92

5.27

Fig. 5.17 Meshed model of mechanism with flexible crank and coupler

Table 5.7 Detail of finite element model with flexible crank and coupler


Stiffness Behavior Rigid Flexible Rigid


Material




Statistics

Nodes 1 904 924 1

Elements 1 114 102 1

5.28

Fig. 5.18 Meshed model of mechanism with flexible crank, coupler and rocker

Table 5.8 Detail of finite element model with flexible crank, coupler and rocker


Stiffness Behavior Rigid Flexible


Material




Statistics

Nodes 1 904 886 845

Elements 1 114 98 92

5.29

5.3 Modeling of Watt’s mechanism

The strain developed in links of Watt’s mechanism (six bar planar mechanism)

has been investigated using the ANYSYS. In this analysis two links are to be

considered as flexible with numbers of beam elements.

Specifications of six bar mechanism for analysis are mentioned in Table 5.9

and mesh model of six bar mechanism is shown in Fig. 5.19.

Table 5.9 Specification of six bar mechanism

Parameters Link1 Link 2 Link 3 Link 4 Link 5 Link 6

Length (mm) 250 110 280 260 270 200

C/S Area (mm2) - 108 40 40 45 40

Area moment of Inertia (mm4)

- 160 9 9 10 9

Modulus of Elasticity, E = 7.1 × 104 MPa

Density = 2770 kg/m3 Crank speed = 32.3 rad/sec

Fig. 5.19 Meshed model of six bar mechanism

5.30

Table 5.10 Detail of finite model of six bar mechanism

Object Name LINK 1 LINK2 LINK3 LINK4 LINK5 LINK6

Stiffness Behavior Rigid Flexible Rigid Flexible Rigid


Material


Nonlinear Effects Yes Yes

Thermal Strain Effects Yes Yes

Properties

Volume (mm³) 1.0015e+005 22451 37872 3.9238e+005 26751 28067

Mass (kg) 0.27742 0.06219 0.1049 1.0869 0.074101 0.077746


(kg·mm²) 227.69 4.4632 6.2678 5411.9 4.6573 5.2736


(kg·mm²) 5129.4 124.38 1036.6 2914.7 799.88 839.61


(kg·mm²) 5352.4 122.08 1032.5 8308.5 797.21 836.42

5.31

Object Name LINK 1 LINK2 LINK3 LINK4 LINK5 LINK6

Statistics

Nodes 1 152 1 240 1

Elements 1 42 1 88 1

Mesh Metric None

chapter – 5 modeling and simulation of...

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