6. strain gages and strain...
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6. Strain Gages and Strain Measurement
DEU-MEE 5070 Actuator and Sensors in Mechanical Systems Assoc.Prof.Dr.Levent Malgaca, Spring 2016
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.
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 = 0.0024 ohm
The fractional change in resistance 0.0024/120 = 0.002 %
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.
6.2 Equations for Strain Measurements:
L/L
R/RGF
A
LR
R: resistance, : density,
L: length of conductor, A: Area of cross-section
GF:Gage factor
6.3 Wheatstone Bridge
+ -
V1
R1 R2
R3
R4 V2
V1: Supply voltage
V2: Measured voltage 1
43
3
21
12 V
RR
R
RR
RV
R1=R2=R3=R4, V2=0
R2=R3=R4=R, R1=R+δR
12 VR2R4
RV
δR<<R 12 VR
R
4
1V
Amplification:
Amplifier V2 V2A
Linear:
Decibel: 2
A2
V
Vlog20K dB
2
A2
V
VK
6.4 Bridge Types and Strain Equations
Quarter Bridge (Type-1)
QB-1 measures either axial or bending
strain
Half Bridge (Type-1)
HB-1 measures either axial or bending
strain
R4: Strain gage R3: Strain gage (Compression,- )
R4: Strain gage (Tensile, +)
(NI, SCC-SG Series Strain Gage Modules User Guide)
Rs: Shunt calibration resistor
Rg: Nominal gage resistance
RL: Lead resistance (long length)
(simulated strain)
VR: Voltage ratio
Full Bridge (Type-1)
FB-1 measures only bending strain.
Full Bridge (Type-3)
FB-3 measures only axial strain.
Example-6.1:
+ -
V1
R
R
R V2
F F
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 0.005 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.
Example-6.2:
Calculate the bending strains of a cantilever beam at the selected points as shown in
the figure. E=69 GPa.
L
Strain gage-1
Strain gage-2 F
Lf
Ls2
Ls1
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
)LL(FM1sf
z
I
My
12
bhI
3
z E
Matlab program: Calculate strain values in Example 6.2
clc,clear,close all;
m=116e-3; % tip mass
L=158e-3; % length of beam
h=1.5e-3; % height of beam
b=20e-3; % width of beam
Lf=153e-3; % load distance
Ls1=15e-3; % straingage-1 distance
Ls2=75e-3; % straingage-2 distance
E=69e9;
ct=h/2;
I=b*h^3/12;
g=9.81;
sigma1=m*g*(Lf-Ls1)*ct/I;sigma2=m*g*(Lf-Ls2)*ct/I;
eps1=sigma1/E,eps2=sigma2/E,
Results: eps1 = 3.0346e-004
eps2 = 1.7152e-004
Example-6.3:
Calculate the bending strains of the cantilever beam in Example 6.2 using commercial
engineering programs (ANSYS, SOLIDWORKS).
Strain Measurement
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
Measure the bending strains of the cantilever beam considered in
Example 6.2.
Example-6.4:
Load is considered as a tip mass:
m=116 g (7 pieces nut)
20-pin board
Scc-Sg01
Power
supply
Nı 6008
Tip mass
Cantilever beam
NI SCC-SG01
NI USB-6008
GND
AI0+
AI0-
GND
AI1+
AI1-
GND
Connections on DAQ
• Channel-1 : AI0 Pin4, GND Pin 6
• Channel-2 : AI1Pin 1, GND Pin 6
Connections on SCC-SG01
• Strain gage-1 : 4 AI(x), 2 Vex+
• Strain gage-2 : 6 AI(x+8), 2 Vex+
Connections on 20-pin Board
(from a power supply)
• +5V Pin9
• GND Pin 10
• +15V Pin 13
• -15V Pin 14
Labview program: Voltage measurement
Sampling rate: 1000 Hz
AI channel: ai0 (Strain gage-1)
AI channel: ai1 (Strain gage-2)
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)
Matlab program: Experiment: voltage-strain equations
Results:
v2a =0.0420
eps_e =3.3644e-004
Recorded data
Filtered data
Strained data
Unstrained data
Shifted data
strain1.lvm
Recorded data
Shifted data
Filtered data
Strained data
Unstrained data
strain2.lvm
Results:
v2a = -0.0225 V
eps_e = -1.7992e-004