ME 22.302 Mechnicl Lb I Strin Gge Mesurements Note: Some mteril ws obtined from unidentified web sources nd origin cnnot be determined t this time Dr. Peter Avitbile University of Msschusetts Lowell Strin Gges - 122601-1 Copyright 2001
A trnsducer is device tht converts some mechnicl quntity into some mesurble electricl quntity. Through clibrtion procedure, the sensitivity of the trnsducer cn be obtined INPUT Physicl Phenomenon Pressure, Temperture, Strin, Displcement, Velocity, Accelertion, etc trnsducer Volts per Engineering Unit V/EU OUTPUT Electricl Signl relted to Physicl Phenomenon DC voltge, AC voltge, current, resistnce, etc Dr. Peter Avitbile University of Msschusetts Lowell Strin Gges - 122601-2 Copyright 2001
There re wide vriety of methods to mesure stress & strin Moire Fringe Techniques Hologrphic Interferometry Brittle Cot Methods Photoelsticity Strin Gges Only strin gges will be considered here. Strin gges re used for vriety of trnsducer designs for the mesurement of force, ccelertion, torque nd others Dr. Peter Avitbile University of Msschusetts Lowell Strin Gges - 122601-3 Copyright 2001
Strin Gge Construction - Cn be mde with stright wires - More common to etch them from thin metl foil sheets bonded to plstic bcking which is then glued to the structure - Size cn be s smll s 0.2 mm which is reltively smll Points to Note - emember tht stress is verge stress over gge re SIZE IS IMPOTANT!!! - Orienttion is eqully importnt for single direction gges - osettes combine 3 gges to form one integrl gge - Accurte to 1% typiclly but mounting (bond & orienttion) nd environmentl effect my introduce 1% to 3% dditionl error O WOSE!!! Dr. Peter Avitbile University of Msschusetts Lowell Strin Gges - 122601-4 Copyright 2001
eview of Stress-Strin eltionships D F L stress σ strin ε strin ε t F A dl L dd D (xil stress) (xil strin) (trverse or lterl strin) Poisson' s rtio ν ε ε t dd dl / / D L (typiclly 0.3) σ E σ ε (Young Modulus or Modulus of elsticity) Elstic Limit ε Dr. Peter Avitbile University of Msschusetts Lowell Strin Gges - 122601-5 Copyright 2001
Electricl esistnce Strin Gge A reltionship exists between the strin nd chnge in resistnce in mny mterils (Lord Kelvin). Using this reltionship, the resistnce, the cross sectionl re A, the length of the wire L nd the resistivity re relted s ρl A The strin gge fctor is defined s S S G gge fctor d / ε The strin gge fctor is the slope of the curves shown in the plot Note: Some mteril ws obtined from unidentified web sources nd origin cnnot be determined t this time s is the cse for the plot Dr. Peter Avitbile University of Msschusetts Lowell Strin Gges - 122601-6 Copyright 2001
Electricl esistnce Strin Gge Assuming smll chnges in resistnce to chnges in the resistivity, length, nd re, reltionship referred to s the Gge Fctor cn be developed s S G d / d / dρ/ ρ gge fctor + 1+ 2υ dl / L ε ε The gge fctor nd resistnce of the gge re typiclly specified by the mnufcturer Gge fctors re typiclly between 1.5 nd 4.0 but cn be s high s 6.0 (other specil mterils hve higher vlues) Dr. Peter Avitbile University of Msschusetts Lowell Strin Gges - 122601-7 Copyright 2001
Strin Gge Fctor - elted Informtion If the resistivity does not chnge significntly with strin, then S G dρ/ ρ + 1+ 2υ ε The electricl resistnce is generlly 120 or 350 Ohm Cross sensitivity generlly refers to the distortion of the strin due to the gge deformtion itself nd is generlly smll However, the gge is generlly very sensitive to lods nd stress perpendiculr to the min sensing xis of the strin gge Dr. Peter Avitbile University of Msschusetts Lowell Strin Gges - 122601-8 Copyright 2001
Strin Gge Fctor for Different Mterils S G d / d / dρ / ρ gge fctor + 1+ 2υ dl / L ε ε Note: Some mteril ws obtined from unidentified web sources nd origin cnnot be determined t this time s is the cse for this tble Dr. Peter Avitbile University of Msschusetts Lowell Strin Gges - 122601-9 Copyright 2001
The strin gge resistnce chnge is very smll Therefore, the signl is mplified in the signl conditioner Dr. Peter Avitbile University of Msschusetts Lowell Strin Gges - 122601-10 Copyright 2001
Dr. Peter Avitbile University of Msschusetts Lowell Strin Gges - 122601-11 Copyright 2001 Mechnicl Engineering - 22.302 ME Lb I Whetstone Bridge - Qurter Bridge Circuit ( )( ) 4 1 3 2 2 4 1 3 V V s o + + Using Ohm s Lw, the current is Combining terms nd rewriting, the following is obtined ( ) 4 1 s ABC V I + ( ) 3 2 s ADC V I + 3 4 2 1 2 4 1 3 or The bridge is sid to be blnced if
Whetstone Bridge - Qurter Bridge Circuit When the strin gge is strined, there is chnge in resistnce in the strin gge. Noting this s 3 nd substituting, using the gge fctor reltionship nd neglecting reltively smll terms in this eqution, then AFTE MUCH ALGEBA!!! 2 V o ( 2 + 3) ε VS SG 23 nd if equl resistors re used for 1, 2, 3, 4, then ε V 4 V o S 1 S G Dr. Peter Avitbile University of Msschusetts Lowell Strin Gges - 122601-12 Copyright 2001
Whetstone Bridge - Hlf Bridge Circuit Temperture cn hve n effect on the mesured strin. This cn be delt with using hlf bridge to blnce the effects. If 1 is the ctive gge, then 2 cn be used for temperture compenstion (in n unstrined environment) Dr. Peter Avitbile University of Msschusetts Lowell Strin Gges - 122601-13 Copyright 2001
Whetstone Bridge - Hlf Bridge Circuit Using two gges on either side on bem in bending (nd mesuring the sme but opposite stress/strin) yields strin mesurement which is twice s lrge s single gge Dr. Peter Avitbile University of Msschusetts Lowell Strin Gges - 122601-14 Copyright 2001
Strin Gge Wiring Considertions Dr. Peter Avitbile University of Msschusetts Lowell Strin Gges - 122601-15 Copyright 2001
Whetstone Bridge - Some Compenstion Considertions Dr. Peter Avitbile University of Msschusetts Lowell Strin Gges - 122601-16 Copyright 2001
Whetstone Bridge - Some Compenstion Considertions Dr. Peter Avitbile University of Msschusetts Lowell Strin Gges - 122601-17 Copyright 2001
Whetstone Bridge - 2311 Signl Conditioner Trim Low Pss Filter Excittion Voltge Gin Power Dr. Peter Avitbile University of Msschusetts Lowell Strin Gges - 122601-18 Copyright 2001