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  • Overview Displacement Force Experimentation Summary Pre-Lab/LE References

    Sensors and Instrumentation:Force and Displacement Measurement

    Prof. R.G. Longoria

    Department of Mechanical EngineeringThe University of Texas at Austin

    July 10, 2014

    ME 144L Dynamic Systems and Controls Lab (Longoria)

  • Overview Displacement Force Experimentation Summary Pre-Lab/LE References

    Overview

    Force and displacement measurement methods are part of essentialengineering knowledge, especially for mechanical engineers. Thislaboratory is meant to provide familiarity with some of the most commonapproaches used to sense these quantities.

    1 This lecture first reviews displacement sensing devices and systems

    a strain gauges, classified as a resistive sensorb LVDTs, inductive sensorsc optical sensors

    2 Sensing displacement is key to force sensing as well

    3 The application of strain-gauges to force sensing in particular isdescribed in detail, especially using beam-type configurations

    4 Laboratory study provides experience with both displacement andforce sensor systems and their usage

    ME 144L Dynamic Systems and Controls Lab (Longoria)

  • Overview Displacement Force Experimentation Summary Pre-Lab/LE References

    Sensing displacement, motion, or distance

    Mechanical (gage blocks, rulers, etc.)

    Strain gauges measure deflection

    Contact sensors: LVDT, Inertialsensors (accelerometers, seismometers)

    Non-contact sensors: Optical,magnetic, capacitive

    ME 144L Dynamic Systems and Controls Lab (Longoria)

  • Overview Displacement Force Experimentation Summary Pre-Lab/LE References

    Strain gauges are resistive type sensors

    Strain gauges take advantage of change in resistance due to straining ofmaterial (see Appendix A).

    Strain gauges exhibit piezoresistivebehavior, and are one of the mostcommon ways to measure strain, ,the change in length per unitlength.

    Strain gauges can be made in thefollowing forms:

    unbonded wire - basically awire under strain (c. 1940s)

    foil - type shown to left (c.1950s) are most common

    semiconductor (c. 1960s)

    ME 144L Dynamic Systems and Controls Lab (Longoria)

  • Overview Displacement Force Experimentation Summary Pre-Lab/LE References

    Strain gauge sensitivity: gauge factor, G

    A measure of the sensitivity of a strain gauge is given by the gauge factor,which is defined as,

    G =fractional change in resistance

    fractional change in strain

    From the derivation detailed in Appendix A,

    G =1

    dR

    R= (1 + 2) +

    1

    d

    The first term on the right-hand side includes Poissons ratio, and thesecond term is a piezoresistive effect (temperature dependent).

    Typical types/values: 1) 80% Ni, 20% Cr, G = 2, 2) 45% Ni, 55% Cu, G = 2, 3)Platinum, G = 4.8, 4) 95% Pt, 5% Ir, G = 5.1, 5) Semiconductor, G = 70 to 135

    ME 144L Dynamic Systems and Controls Lab (Longoria)

  • Overview Displacement Force Experimentation Summary Pre-Lab/LE References

    Strain gauge type selection

    Strain gauges come in many specialized forms for detecting different typesof strain behaviors and should be matched to a material type (aluminum,steels, etc.)

    All types have a calibrated gauge factor, G.

    Semiconductor strain gauges have the highest values of G, from 70 to 135,and are typically very small. However, there are some disadvantages thatinclude: a) output not linear with strain, b) very temperature

    ME 144L Dynamic Systems and Controls Lab (Longoria)

  • Overview Displacement Force Experimentation Summary Pre-Lab/LE References

    Strain is measured by monitoring resistance change in astrain-gauge

    Consider a situation where the strain is on the order of 1 microstrain.

    For a metallic foil strain gauge with G = 2, R = 120 ohm,

    R = G R = 2 1 106 120 = 0.0024

    That represents a fractional change in resistance of 0.0024/120, or a 0.002%change in R.

    Detecting this small a change in resistance is very difficult.

    To use strain gauges practically, it is necessary to configure them within a circuit

    and a structure so the change in resistance is detectable and has physical

    meaning. This requires understanding concepts from signal conditioning and

    structural design.

    ME 144L Dynamic Systems and Controls Lab (Longoria)

  • Overview Displacement Force Experimentation Summary Pre-Lab/LE References

    Signal conditioning circuits: monitor current or voltage

    Strain gauges can be monitored by a simple voltage divider, as used tomonitor potentiometric sensors. Alternatively, small resistance changesmay require balancing potentiometric circuits, null bridges, or impedancebridges (next slide).

    ME 144L Dynamic Systems and Controls Lab (Longoria)

  • Overview Displacement Force Experimentation Summary Pre-Lab/LE References

    When all arms on a bridge are resistive, this is aWheatstone bridge

    Typically, an input DC voltage is applied, say, across terminals A and B and theoutput voltage is measured across C and D.

    The Wheatstone bridge is balancedwhen the ratio of resistances of anytwo adjacent arms is equal to the ratioof resistances of the remaining twoarms (taken in the same sense), i.e.,

    R1R2

    =R3R4

    R1R3

    =R2R4

    In this case, the output voltage wouldbe zero.

    ME 144L Dynamic Systems and Controls Lab (Longoria)

  • Overview Displacement Force Experimentation Summary Pre-Lab/LE References

    Impedance bridges

    Impedance bridges are used to detect changes in resistive, capacitive, or inductivesensors. There are many types of impedance bridges.

    Most inductive and capacitive sensors rely on impedance bridges for signal

    conditioning. AC type signals are used in these circuits.ME 144L Dynamic Systems and Controls Lab (Longoria)

  • Overview Displacement Force Experimentation Summary Pre-Lab/LE References

    Sensors based on changes in inductance (or reluctance)

    Recall that electrical resistors can be used as sensors, taking advantage ofchanges in resistance due to changes in geometry and/or material properties. Anexample is how a potentiometer can be used as a motion/displacement sensor.

    In the same way, some electrical inductors, which store magnetic energy, can alsobe used as sensors. These sensors take advantage of how changes in geometry ormaterial properties influence inductance (or reluctance).

    Inductive or variable-reluctance sensorsrequire a magnetic flux to be set up sothat changes in electrical inductancecan be detected.

    Examples are shown to the right thatshow how distances can be inferred bythis type of sensing mechanism.

    Can you conceive a variable-reluctance pressure sensor?

    ME 144L Dynamic Systems and Controls Lab (Longoria)

  • Overview Displacement Force Experimentation Summary Pre-Lab/LE References

    LVDT sensors rely on detecting change in inductance

    A linear variable differential transformer (LVDTs) senses displacement of acore that modulates the mutual inductance between two coils.

    LVDTs are inductive (or variable-reluctance) sensors.

    ME 144L Dynamic Systems and Controls Lab (Longoria)

  • Overview Displacement Force Experimentation Summary Pre-Lab/LE References

    Typical LVDT wiring and calibration

    ME 144L Dynamic Systems and Controls Lab (Longoria)

  • Overview Displacement Force Experimentation Summary Pre-Lab/LE References

    Displacement sensors can be made using position sensitivedetectors

    Position sensitive detectors (or PSDs) operate on the principle of photoeffect,relying on surface resistance of a silicon photodiode, with the output signalproportional to the continuous position of a beam incident on the sensitivesurface.

    Digital PSDs have been made using CMOS and CCD sensors and these have adiscrete number of photodiodes in an array (not considered optimal but suitablefor some applications) [2]

    ME 144L Dynamic Systems and Controls Lab (Longoria)

  • Overview Displacement Force Experimentation Summary Pre-Lab/LE References

    Displacement measurement using (optical) triangularmethod [2]

    From similar triangles: Lo/LB = f/x, where x = D/(P + 1) andP = IA/IB. Then, Lo = k(P + 1).

    ME 144L Dynamic Systems and Controls Lab (Longoria)

  • Overview Displacement Force Experimentation Summary Pre-Lab/LE References

    Commercially available sensors, systems

    1 and 2D PSD sensor components(Hammamatsu photonics, Japan)

    Industrial optical displacement sensor(CMOS-based. Keyence Corp.)

    ME 144L Dynamic Systems and Controls Lab (Longoria)

  • Overview Displacement Force Experimentation Summary Pre-Lab/LE References

    Simple force and weight measurement

    Spring-based force sensors Classical weighing by balancing

    Calibration weights are required.

    Can you think of a force sensing devicethat does not infer force fromdisplacement?

    ME 144L Dynamic Systems and Controls Lab (Longoria)

  • Overview Displacement Force Experimentation Summary Pre-Lab/LE References

    Electromechanical force and torque sensors

    Force and torque sensors provide an output in the form of an electrical signal(voltage, current).

    Examples:Off-the-shelf strain-gauge sensors: Optical in-line torque sensor:

    ME 144L Dynamic Systems and Controls Lab (Longoria)

  • Overview Displacement Force Experimentation Summary Pre-Lab/LE References

    Force sensing in commercial products

    ME 144L Dynamic Systems and Controls Lab (Longoria)

  • Overview Displacement Force Experimentation Summary Pre-Lab/LE References

    Force is typically inferred from displacement sensing, whichrequires understanding the structural design

    To measure force (or torque), it is usually necessary to design a compliantmechanical structure. This structure may itself be a sensing material.

    Force will induce stress, leading to strain which can be detected in variousways, for example:

    using strain gauges (piezoresistive effect)

    using crystals or ceramics (piezoelectric effect)

    displacement using contact or non-contact sensing

    ME 144L Dynamic Systems and Controls Lab (Longoria)

  • Overview Displacement Force Experimentation Summary Pre-Lab/LE References

    Example: keyboard force measurement

    problem: measure low-level forcesrequired to trigger key-switch on acomputer keyboard

    Here is a home-made solution:

    This design requires means for measuring the displacementsindicated.

    ME 144L Dynamic Systems and Controls Lab (Longoria)

  • Overview Displacement Force Experimentation Summary Pre-Lab/LE References

    Using beam configurations for strain-gauge-based forcesensors

    The beam structure/geometry is used extensively in designing manytypes of force and torque sensors.

    A beam offers certain advantages:I easy geometry for basic analysis and designI strain gauges can be mounted easily and configured in several different

    ways to achieve different objectives

    Example: a tip loaded cantilever is a common design element. The tip deflectioncan be related to applied tip force by a linear spring-like relation, where thestiffness is related to beam geometry and material.

    ME 144L Dynamic Systems and Controls Lab (Longoria)

  • Overview Displacement Force Experimentation Summary Pre-Lab/LE References

    Beams for bending, shearing, and axial and torsional loads

    ME 144L Dynamic Systems and Controls Lab (Longoria)

  • Overview Displacement Force Experimentation Summary Pre-Lab/LE References

    Beam configurations used for strain gauge sensors

    The strain gauges are typically monitored as part of a Wheatstone bridge. Sometimes you may have a bridge with all activestrain-gauges (full-bridge), meaning they are all under strain. There may be cases where only 2 of 4 (half-bridge) or 1 of 4(quarter-bridge) are active. You typically have the same nominal resistance on all arms. Why?

    ME 144L Dynamic Systems and Controls Lab (Longoria)

  • Overview Displacement Force Experimentation Summary Pre-Lab/LE References

    The full-bridge beam sensor configuration

    A very common force sensing design uses a cantilever beam with a full-bridge.

    If all the gauges have the same resistance, it can be shown that:

    dvoVs

    =dR1 dR2 dR3 + dR4

    R=G

    4[1 2 3 + 4]

    This equation can be used to guide placement of gauges on a specimen.

    ME 144L Dynamic Systems and Controls Lab (Longoria)

  • Overview Displacement Force Experimentation Summary Pre-Lab/LE References

    A strain gauge measurement system

    The strain gauge is part of a multi-stage process that generates a voltagesignal proportional to the strain.

    The amplifier is required because the changes in the bridge circuit output voltageare usually in the millivolt range.

    ME 144L Dynamic Systems and Controls Lab (Longoria)

  • Overview Displacement Force Experimentation Summary Pre-Lab/LE References

    Laboratory set up and equipment

    An aluminum cantilevered beam thathas been instrumented with straingauges in a full-bridge configurationwill be used in the laboratory.

    1 Beam support and cantileverbeam

    2 OMEGA DMD-465WB (straingauge amplifier)

    3 LVDT support and LVDT sensor

    4 Laser displacement sensor

    5 Calibration weights/masses

    ME 144L Dynamic Systems and Controls Lab (Longoria)

  • Overview Displacement Force Experimentation Summary Pre-Lab/LE References

    Strain gauge amplifier

    The amplifier used in lab provides the input voltage and then amplifies thebridge output. Adjustments are available to balance the bridge, to set theamplifier gain, and to set the input voltage level.

    ME 144L Dynamic Systems and Controls Lab (Longoria)

  • Overview Displacement Force Experimentation Summary Pre-Lab/LE References

    Laboratory objectives

    1 Learn how to set up and use a strain-gauge beam, run calibrations and testfor force measurement

    2 Learn about a laser displacement sensor and its proper and safe usage;assess calibration

    3 Learn about and use a LVDT for displacement measurement; assesscalibration

    4 Continue use of LabVIEW and myDAQ for data acquisition; create a VI forstatic calibration and for force and displacement sensing

    5 Use the LabVIEW VI to conduct experiments and collect data to estimatethe beam stiffness and to estimate the Youngs modulus for the aluminumbeam

    ME 144L Dynamic Systems and Controls Lab (Longoria)

  • Overview Displacement Force Experimentation Summary Pre-Lab/LE References

    Summary

    Force measurement takes advantage of the relationship between force,displacement and stiffness.

    Strain gauges are a common basis for sensors that can measure forceor torque

    We wrap the sensor with signal conditioning to get a measurablesignal (voltage or current)

    Strain gauges are core knowledge for mechanical engineers

    ME 144L Dynamic Systems and Controls Lab (Longoria)

  • Overview Displacement Force Experimentation Summary Pre-Lab/LE References

    Pre-Lab: Problem 1 strain-gauge concepts

    Review the derivation of the relationship between strain and strain gaugeelectrical resistance found in Appendix A, in order to understand the keyparameters that play a role in this sensing mechanism.

    What is the term used to refer to sensitivity of a strain-gauge?

    Say you mounted strain gauges with R = 120 ohm and G = 2 as shown below onan axially loaded, aluminum beam. If thickness, b = 5 mm, and width h = 7 mm,what would you expect to see at the output of the bridge circuit if F = 5 N?

    ME 144L Dynamic Systems and Controls Lab (Longoria)

  • Overview Displacement Force Experimentation Summary Pre-Lab/LE References

    Pre-Lab: Problem 2 beam mechanics

    In a lecture example, the stiffness of a beam was given in terms of Youngsmodulus, E, area moment of inertia, I, and beam length, L (or distance tolocation of force application). Conduct some research to justify this relation.

    In completing this pre-lab, you should gain an understanding for how to relate thestrain at the strain gauge position on the beam (e.g., as shown on the lab setup)to the force applied at the end (tip) of the beam and to the deflection at the tipof the beam.

    ME 144L Dynamic Systems and Controls Lab (Longoria)

  • Overview Displacement Force Experimentation Summary Pre-Lab/LE References

    Pre-Lab: Problem 3 full-bridge configuration

    Sketch a three-dimensional drawing of a cantilevered beam and illustrate thelocation of the strain gauges for a full-bridge configuration.

    Identify each gauge with its location within a circuit schematic of the Wheatstonebridge (use 1, 2, 3, and 4). Indicate on your sketch the input voltage terminalsand the output voltage terminals.

    For the case where a force is applied at the tip of the beam in a downwarddirection, indicate the stress state of each strain gauge with T for tension and Cfor compression both on the sketch of the beam and gauges as well as on thecircuit schematic.

    ME 144L Dynamic Systems and Controls Lab (Longoria)

  • Overview Displacement Force Experimentation Summary Pre-Lab/LE References

    Pre-Lab: Problem 4 estimating bridge outputs

    Consider a beam with strain gauges in a full-bridge (as in Pre-Lab Problem 3)that has a balanced output when there is no applied force (unstrained). Under acertain load, the strain gauges on the top of the beam are strained by +5microstrain and those on the bottom side of the beam are strained by 5microstrain. Calculate the output voltage from the bridge assuming that eachgauge has a resistance of 350 ohms and the gauge factor is 2.0. Also assume thatthe input voltage is 8 volts.

    Re-consider the case above, but now assume that after the bridge was balancedthe temperature changed and caused the resistance of each strain gauge todecrease by a factor of 10% (from the unstrained value). Show how this willaffect the output voltage (from zero volts in a balanced state).

    ME 144L Dynamic Systems and Controls Lab (Longoria)

  • Overview Displacement Force Experimentation Summary Pre-Lab/LE References

    Lab Evaluation

    1 Develop a calibration relation for the beam sensor based on at least fivemeasured data points (force vs. deflection). The data should be recorded forthis LE in both tabular and graph form. Derive a measurement sensitivity(N/Volts) based on your force-voltage measurements.

    2 Use your calibrated beam sensor to measure two unknown weights providedby the TA. You will be asked to compute the error in measuring each weight.

    3 Using the measured force and displacement data, estimate the beamstiffness, kb, relating a vertically applied load to the beam tip displacement.Show how you can use this value to estimate the Youngs modulus for thebeam material (aluminum).

    ME 144L Dynamic Systems and Controls Lab (Longoria)

  • Overview Displacement Force Experimentation Summary Pre-Lab/LE References

    References

    [1] Beckwith, Buck, and Marangoni, Mechanical Measurements,Addison-Wesley, 3rd ed, 1982.

    [2] Fraden, Handbook of Modern Sensors: Physics, Design andApplications, 1996)

    ME 144L Dynamic Systems and Controls Lab (Longoria)

  • Appendix A: Piezoresistivity (1)

    We know that for a conductor of uniform area, the resistance is given by,R = L/A, where is the resistivity (cm ohm)., L is the length, and A isthe cross-sectional area. Under strain, the change in R is,

    dR =R

    ldL+

    R

    AdA+

    R

    d

    which for uniform A is,

    dR =

    AdL L

    A2dA+

    L

    Ad

    The fractional change of R is of more interest, so we find,

    dR

    R=dL

    L dA

    A+d

    where the fractional changes in length, area, and resistivity are given bydL/L, dA/A, and d/, respectively.

    For typical conductors, the resistivity values in units of ohm mm2/m are: Aluminum 0.0278, Pure Iron 0.1, Constantan 0.48,Copper 0.0172, Gold 0.0222, Tungsten 0.059, Manganese 0.423, Nickel 0.087.

    ME 144L Dynamic Systems and Controls Lab (Longoria)

  • Appendix A: Piezoresistivity (2)

    For a linearly elastic body,

    xx = F/A = E x = E dL

    L

    where E is the Youngs modulus. Recall,

    x =dL

    L, y =

    dL

    L, z =

    dL

    L

    and for an area A = wt, the fractional change is,

    dA

    A=dw

    w+dt

    t= 2x

    Recall that is Poissons ratio. Now the fractional change in R is,

    dR

    R= (1 + 2) x +

    d

    ME 144L Dynamic Systems and Controls Lab (Longoria)

  • Appendix B: Belt testing machine

    Marshek and Kim (UT-Austin, c. 1985), Flat belt test machine, US Patent4841783 A

    ME 144L Dynamic Systems and Controls Lab (Longoria)

  • Appendix B: Custom XY force sensors for flow-inducedforces on cylinders

    Longoria (UT-Austin, c. 1989)

    ME 144L Dynamic Systems and Controls Lab (Longoria)

  • Appendix B: Four bar XY force sensor

    This force sensor resolves a total forceapplied on the shaft into an X and a Ycomponent.

    There are two full-bridge circuits, soeight total strain gauges.

    There is some cross-talk (e.g., the Ycomponent is sensitive to forcesapplied in X) in the measurement, butthis can be almost completelyeliminated with a good calibration.

    ME 144L Dynamic Systems and Controls Lab (Longoria)

    OverviewDisplacementForceExperimentationSummaryPre-Lab/LEReferencesAppendix