Strain Gages

1
Strain Gages

• Electrical resistance in material changes when
  the material is deformed

R Resistance ? Resistivity l Length A
Cross-sectional area
Taking the differential
Change in resistance is from change in shape as
well as change in resistivity
For linear deformations
strain Ss sensitivity or gage factor (2-6
for metals and 40 200 for semiconductor)
2

• The change in resistance is measured using an
  electrical circuit
• Many variables can be measured displacement,
  acceleration, pressure, temperature, liquid
  level, stress, force and torque
• Some variables (stress, force, torque) can be
  determined by measuring the strain directly
• Other variables can be measured by converting the
  measurand into stress using a front-end device

Strain gage accelerometer
3
Strain gages are manufactured as metallic foil
(copper-nickel alloy constantan)
Direction of Sensitivity
Foil Grid
Single Element
Two-Element Rosette
Backing Film
Solder Tabs (For Leads)
Three-Element Rosettes
Semiconductor (silicon with impurity)
Doped Silicon Crystal (P or N Type)
Welded Gold Leads
Nickle-Plated Copper Ribbons
Phenolic Glass Backing Plate
4
Potentiometer or Ballast Circuit


v

o

Strain Gage
Output


R
v
ref

-
(Supply)
Rc

• Ambient temperature changes will introduce error
• Variations in supply voltage will affect the
  output
• Electrical loading effect will be significant
• Change in voltage due to strain is a very small
  percentage of the output

Question Show that errors due to ambient
temperature changes will cancel if the
temperature coefficients of R and Rc are the same
5
Wheatstone Bridge Circuit
A
Small i

R1
vo
R2
RL
Load (High)
R4
-
R3
B
-

vref (Constant Voltage)
When the bridge is balanced
True for any RL
6
Null Balance Method

• When the stain gage in the bridge deforms, the
  balance is upset.
• Balance is restored by changing a variable
  resistor
• The amount of change corresponds to the change in
  stain
• Time consuming servo balancing can be used

Direct Measurement of Output Voltage

• Measure the output voltage resulting from the
  imbalance
• Determine the calibration constant
• Bridge sensitivity

To compensate for temperature changes,
temperature coefficients of adjacent pairs should
be the same
7
The Bridge Constant

• More than one resistor in the bridge can be
  active
• If all four resistors are active, best
  sensitivity can be obtained
• R1 and R4 in tension and R2 and R3 in compression
  gives the largest sensitivity
• The bridge sensitivity can be expressed as

Bridge Constant
8
Example 4.4
A strain gage load cell (force sensor) consists
of four identical strain gages, forming
a Wheatstone bridge, that are mounted on a rod
that has square cross-section.  One opposite pair
of strain gages is mounted axially and the other
pair is mounted in the transverse direction, as
shown below.  To maximize the bridge
sensitivity, the strain gages are connected to
the bridge as shown.  Determine the bridge
constant k in terms of Poissons ratio v of the
rod material.
Axial Gage
2
1
1

vo
Transverse Gage
2
3
-
Cross Section Of Sensing Member
3
4
4

-
vref
Transverse strain (-v) x longitudinal strain
9
Calibration Constant
k Bridge Constant Ss Sensitivity or gage
factor
10
Example 4.5
A schematic diagram of a strain gage
accelerometer is shown below.  A point mass of
weight W is used as the acceleration sensing
element, and a light cantilever with rectangular
cross-section, mounted inside the accelerometer
casing, converts the inertia force of the mass
into a strain.  The maximum bending strain at the
root of the cantilever is measured using four
identical active semiconductor strain gages. Two
of the strain gages (A and B) are mounted axially
on the top surface of the cantilever, and the
remaining two (C and D) are mounted on the bottom
surface. In order to maximize the sensitivity of
the accelerometer, indicate the manner in which
the four strain gages A, B, C, and D should be
connected to a Wheatstone bridge circuit.  What
is the bridge constant of the resulting circuit?
A
C
Strain Gages A, B

dvo
W
-
C, D
D
B
l
A
b
B

-
C
vref
h
D
11

• Obtain an expression relating applied
  acceleration a (in units of g) to bridge output
  (bridge balanced at zero acceleration) in terms
  of the following parameters
• W Mg weight of the seismic mass at the free
  end of the cantilever element
• E Youngs modulus of the cantilever
• l length of the cantilever
• b cross-section width of the cantilever
• h cross-section height of the cantilever
• Ss gage factor (sensitivity) of each strain
  gage
• vref supply voltage to the bridge.
• If M 5 gm, E 5x1010 N/m2, l 1 cm, b 1 mm,
  h 0.5 mm, Ss 200, and vref 20 V, determine
  the sensitivity of the accelerometer in mV/g.
• If the yield strength of the cantilever element
  is 5xl07 N/m2, what is the maximum acceleration
  that could be measured using the accelerometer?
• If the ADC which reads the strain signal into a
  process computer has the range 0 to 10 V, how
  much amplification (bridge amplifier gain) would
  be needed at the bridge output so that this
  maximum acceleration corresponds to the upper
  limit of the ADC (10 V)?
• Is the cross-sensitivity (i.e., the sensitivity
  in the two directions orthogonal to the direction
  of sensitivity small with this arrangement?
  Explain.
• Hint For a cantilever subjected to force F at
  the free end, the maximum stress at the root is
  given by

12
MEMS Accelerometer
Signal Conditioning
Mechanical Structure
Applications Airbag Deployment
13
Data Acquisition

• Supply frequency 1kHz
• Output Voltage few micro volts 1 mV
• Advantages Stability (less drift), low power
  consumption

• Foil gages - 50O kO
• Power consumption decreases with resistance
• Resolutions on the order of 1 ?m/m

14
Semiconductor Strain Gages
Conductor Ribbons
Single Crystal of Semiconductor
Gold Leads
Phenolic Glass Backing Plate

• Gage factor 40 200
• Resitivity is higher reduced power consumption
• Resistance 5kO
• Smaller and lighter

15
Properties of common strain gage material
16
Disadvantages of Semiconductor Strain Gages

• The strain-resistance relationship is nonlinear
• They are brittle and difficult to mount on curved
  surfaces.
• The maximum strain that can be measured is an
  order of magnitude smaller 0.003 m/m (typically,
  less than 0.01 m/m)
• They are more costly
• They have a much larger temperature sensitivity.

Resistance Change
Resistance Change
P-type
N-type
0.4
0.4
0.3
?? 1 Microstrain Strain of 110-6
0.3
0.2
0.2
0.1
0.1
-3
-2
-1
1
2
3
-3
-2
-1
1
2
3
103 ??
103 ??
Strain
-0.1
-0.1
Strain
-0.2
-0.2
-0.3
-0.3
17
For semiconductor strain gages

• S1 linear sensitivity
• Positive for p-type gages
• Negative for n-type gages
• Magnitude is larger for p-type
• S2 nonlinearity
• Positive for both types
• Magnitude is smaller for p-type

18
Linear Approximation
Quadratic Curve
Change in Resistance
Linear Approximation
Error
-?max
?max
?
0
Strain
Quadratic Error
Minimize Error
0
Maximum Error
19
Range change in resistance
Percentage nonlinearity error
20
Temperature Compensation
a Temperature Coefficient of Resistance ß
Temperature Coefficient of Gage Factor
3
a
Compensation Feasible
Temperature coefficients (per F)
2
(-ß)
Compensation Not Feasible
Compensation Feasible
1
0
Concentration of Trace Material (Atoms/cc)
Resistance change due to temperature
Sensitivity change due to temperature
21
Self Compensation with a Resistor
R1
R
R
R2

R
R
dvo
-

-
vi
Rc
R4

-
R3
Compensating Resistor Rc

-
vref
vi
For self compensation the output after the
temperature change must be the same
vref
Possible only for certain ranges