6. Strain Gages and Strain Measurement

Transcription

1 6. Strain Gages and Strain Measurement 6.1 Strain gages: (Silva p.273) Strain gage measures strain and the measurements can be directly related to stress and force. Hence, strain gages can be utilized as to produce force, torque displacement, acceleration, pressure and temperature sensors. Typical foil strain gage with single-element and three-element (rosettes) are shown below. DEU-MEE 5070 Actuator and Sensors in Mechanical Systems Assoc.Prof.Dr.Levent Malgaca, Spring 2016

2 6.2 Equations for Strain Measurements: R L A R / R GF L / L R: resistance, : density, L: length of conductor, A: Area of cross-section GF:Gage factor Consider a case where the strain value is 1. For a metallic foil strain gage with GF= 2, R=120 ohm, R=GF..R =2 x 1x10^-6 x 120 = ohm The fractional change in resistance /120 = % There is a small change in the resistance of strain gage. It is difficult to measure this type of small changes. Wheatstone bridges are used for strain measurements to convert small changes in resistance to a voltage value.

3 6.3 Wheatstone Bridge R 1 R 2 R 4 V 2 V R R V1 R1R2 R3R4 V 1 : Supply voltage V 2 : Measured voltage R V 1 R 1 =R 2 =R 3 =R 4, V 2 =0 R 2 =R 3 =R 4 =R, R 1 =R+δR V R 4R 2R 2 V 1 1 R δr<<r V2 V1 4 R Amplification: Linear: K V V 2A 2 V 2 Amplifier V 2A Decibel: K 20log V V 2A 2 db

4 6.4 Bridge Types and Strain Equations (NI, SCC-SG Series Strain Gage Modules User Guide) (simulated strain) V R : Voltage ratio Quarter Bridge (Type-1) QB-1 measures either axial or bending strain R 4 : Strain gage R s : Shunt calibration resistor R g : Nominal gage resistance R L : Lead resistance (long length) Half Bridge (Type-1) HB-1 measures either axial or bending strain R 3 : Strain gage (Compression,- ) R 4 : Strain gage (Tensile, +)

5 Full Bridge (Type-1) FB-1 measures only bending strain. Full Bridge (Type-3) FB-3 measures only axial strain.

6 Example-6.1: Strain measurement system is shown in the figure. The bridge output voltage is amplified with a linear gain of 100 and the amplified voltage is measured as 0.24 V. The plate material is steel and the modules of elasticity is 200 GPa. The are of cross-section is 0.03 m x m. The bridge resistance is 120 Ω and gage factor is 2. The excitation voltage is 5 V. a) Calculate the strain value from the measured voltage. b) Calculate the axial stress of the plate. c) Calculate the tensile force. F F R R R + - V 2 V 1

7 Example-6.2: Calculate the bending strains of a cantilever beam at the selected points as shown in the figure. E=69 GPa. Ls1 Strain gage-1 Ls2 Lf Strain gage-2 L F F=0.116 kg x 9.81 E=69 GPa L=158 mm Lm=153 mm Ls1= 15 mm Ls2= 75 mm b=20 mm h=1.5 mm M F(L f Ls1) My Iz I z bh 12 3 E

8 Matlab program: Calculate strain values in Example 6.2 clc,clear,close all; m=116e-3; L=158e-3; h=1.5e-3; b=20e-3; Lf=153e-3; Ls1=15e-3; Ls2=75e-3; E=69e9; ct=h/2; I=b*h^3/12; g=9.81; % tip mass % length of beam % height of beam % width of beam % load distance % straingage-1 distance % straingage-2 distance sigma1=m*g*(lf-ls1)*ct/i;sigma2=m*g*(lf-ls2)*ct/i; eps1=sigma1/e,eps2=sigma2/e, Results: eps1 = e-004 eps2 = e-004

9 Example-6.3: Calculate the bending strains of the cantilever beam in Example 6.2 using commercial engineering programs (ANSYS, SOLIDWORKS).

10 Example-6.4: Instruments Cantilever beam with strain gage NI SCC-SG01 strain gage module 20-pin external board Power supply (+12 V, -12 V, +5V) NI 6008 DAQ system Strain Measurement Measure the bending strains of the cantilever beam considered in Example 6.2. Scc-Sg01 20-pin board Nı 6008 Power supply Load is considered as a tip mass: m=116 g (7 pieces nut) Cantilever beam Tip mass

11 NI SCC-SG01

12 GND AI0+ AI0- GND AI1+ AI1- GND NI USB-6008 Connections on DAQ Channel-1 : AI0 Pin4, GND Pin 6 Channel-2 : AI1Pin 1, GND Pin 6 Connections on 20-pin Board (from a power supply) +5V Pin9 GND Pin V Pin 13-15V Pin 14 Connections on SCC-SG01 Strain gage-1 : 4 AI(x), 2 Vex+ Strain gage-2 : 6 AI(x+8), 2 Vex+

13 Labview program: Voltage measurement Sampling rate: 1000 Hz AI channel: ai0 (Strain gage-1) AI channel: ai1 (Strain gage-2)

14 Matlab program: Experiment: voltage-strain equations fl='strain1.lvm'; nc=floor(tc/dt)+1; data=load(fl);t=data(:,1);v=data(:,2); tu=t(1:nc);vu=v(1:nc);vu0=abs(mean(vu)); v=v-vu0; fn=fs/2;[b,a]=butter(2,fc/fn);vf=filter(b,a,v); tfc=t(nc:end);,vfc=vf(nc:end); vs=mean(vfc); v2a=vs v2=v2a/k; u=v2/v1; dr=4*r*u/(1-2*u); eps_e=dr/(r*gf) subplot(4,1,1);plot(t,v) subplot(4,1,2);plot(t,v) subplot(4,1,3);plot(t,vf) subplot(4,1,4);plot(tfc-tc,vfc)

15 strain1.lvm Recorded data Shifted data Filtered data Unstrained data Strained data Results: v2a = eps_e =3.3644e-004

16 strain2.lvm Recorded data Shifted data Unstrained data Filtered data Strained data Results: v2a = V eps_e = e-004