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