ABE425 Engineering Measurement
Systems
Strain Gages, Bridges
and Load Cells
Dr. Tony E. Grift
Dept. of Agricultural & Biological Engineering
University of Illinois
This presentation covers measuring force (1-3),
displacement (4), velocity (5) and acceleration (6)
1. Strain gage
(Force)
4. Linear Variable
Differential Transformer
2. Wheatstone
bridge
5. Pro-laser Doppler
velocity sensor
3. S-type load cell
6. Accelerometer
Force measurement
The elongation of a thin wire due to strain changes
its electrical resistance which can be measured
Strain and stress in metals are linearly related in
the elastic range (Hooke’s law)
Elastic range
Videos (notice ‘necking’)
Steel tensile test
HDPE tensile test
Strain gages are composed of thin wires that
change their resistance by being stretched
The resistance of a thin wire is a function of
resistivity, length and cross sectional area
Resistance is proportional to
Resistivity 
Length
L
A
And inversely proportional to
L
Cross sectional area A
R  
  m * L  m
2

A  m 
Manipulate equation to get a resistance change
expression
Original equation
R
*L
A
Change in resistance is a function
of partial derivatives
R
R
R
R 
 
L 
A

L
A
Stick in the partial derivatives
L

R    L   LA2 A
A
A
Divide by original resistance
equation
R

L A



R

L
A
Express the change in area in a change in diameter
D
A
A
D

 D  D 
A  A 4

 2
A
D
4
2
D


2
 2 DD  D 2
D2
A 2D

A
D
  1  2D
D
Use Poisson ratio (material property) to simplify the
strain gage equation
R  L A



R

L
A
A 2D

A
D
R  L
D


2
R

L
D
Axial strain  a
Transverse strain  t
 t   a
Poisson ratio
When you stretch a metal it becomes thinner. The negative
ratio between transverse and axial strain is the Poisson ratio
D
D+D
L
L+L
 t   a
Transverse strain
Axial strain
Poisson ratio
Change in resistance is a function of the Poisson
ratio and the change in resistivity (temperature)
R 


  a  2 t  R 
R


  a 1  2 

R


 t   a

  
 R 
  


R
  1  2  

S
a
Strain gage factor
a
f(temperature)
To measure strain in different directions, strain
gages come in rosettes
Rectangular
Equiangular
Here is an example of a rectangular strain gage
rosette
Strain measurement using Wheatstone bridge
In a quarter bridge circuit the strain gage takes up
one branch, there is no temperature compensation
Having four gages in the bridge gives inherent
temperature compensation and increased output
+e
-e
F
Switching within the bridge is a bad idea since the contact
resistances are part of the bridge and the strain gages need
to maintain a constant temperature
It is better to switch outside the bridge since 1) there is no
current where the contacts are and hence no voltage drops
and 2) the temperature of the strain gages is constant
Load cells
Load cells are structures fitted with strain gage
sets, and built-in temperature compensation
Cantilever type
Hollow cylinder type. When the cylinder
is compressed it becomes shorter
which is measured by compressive
gages and the diameter increases
which is measured by the tensile gages
Proving rings are simple devices to calibrate load
cells for larger load (up to 250kN)
Dynamometers are power measurement devices
based on measuring torque and RPM
 Nm 
 rad 
P

T  Nm   Watt


 s 
 s 
Eddy current dynamometers dissipate energy by generating
magnetic fields through eddy currents. The dissipated energy
is carried away using a water flow
 Nm 
 rad 
P

T  Nm   Watt


 s 
 s 
Torque can be measured using a shaft torque
meter that can be read with a stroboscope
Torque can be measured using angled strain gages
and slip rings (watch out for their resistance)
To avoid slip rings, an microcontroller chip can be
used with built-in wireless data communication
RFpic 12c509
Dual Inline Package
(DIP)
RFpic 12c509
Surface Mounted Device
(SMD)
Displacement measurement
The slider of a potentiometer can be used as a relatively
inaccurate displacement sensor
Rotary potentiometers can be used for inaccurate angle
measurement
A Linear Variable Differential Transformer (LVDT) is an
accurate sensor for small displacements
LVDT’s are linear in the rated range, outside the range edge
effects render them non-linear
In an LVDT the electrical coupling between magnets is
provided by a movable core
LVDT’s also come in a rotary version, which allows angle
measurements. Notice the complicated core shape
Measuring the phase difference between primary and
secondary voltages yields direction
Signal conditioning is used to create a DC signal proportional
to displacement with the correct sign for direction
The capacitance of a capacitor is a function of the overlap
between its plates. These devices are used to measure
extremely small displacements
Non-linear
Linear
The change in capacitance can be measured
accurately using an AC Wheatstone bridge
Angular encoders can measure a shaft position.
They suffer from simultaneous state changes
0000
0001
0010
0011
0100
0101
0110
0111
1000
1001
1010
1011
1100
1101
1110
1111
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Gray code is a much more reliable encoding since
no simultaneous state changes occur
0000
0001
0011
0010
0110
0111
0101
0100
1100
1101
1111
1110
1010
1011
1001
1000
0
1
3
2
6
7
5
4
12
13
15
14
10
11
9
8
Velocity measurement
The voltage output of a winding is proportional to
the velocity of a magnetic core passing it
Permanent
magnet
Winding
Voltage is function of speed AND position
The voltage output of a winding is proportional to a
magnetic core passing it
Voltage is function of speed NOT position
Doppler shift is the simplest way to measure the
speed of an object non-intrusively and linearly
Magnetic pickups (proximity sensors) give pulses
from which the shaft RPM can be derived
A stroboscopic tachometer can be used to measure
shaft RPM: This method is primitive and obsolete
Contactless tachometers can count the number of times a
reflective strip passes per second and give RPM
Accelerometers
Piezoelectric sensors can be used to measure
either force or (very small) displacement
A charge amplifier is needed to obtain signals from
the Piezoelectric sensor as an accelerometer
Piezoelectric accelerometers have a seismic mass
and can measure vibrations up to 25 kHz
Semiconductor type strain gage accelerometers
can measure vibrations up to 100 Hz
A servo accelerometer is an accurate automatic
compensation method that can measure 50 g
A vibrometer has a relatively large and measures
earth quakes vibrations
This is what we covered today. Questions?
1. Strain gage
(Force)
4. Linear Variable
Differential Transformer
2. Wheatstone
bridge
5. Pro-laser Doppler
velocity sensor
3. S-type load cell
6. Accelerometer