Flexible Strain Gage Array Calculations

Strain gages:

Platinum:
resistivity, rho=1.042 x 10-7 ohm-m
thermal coeffiecient of resistance, TCR = 3.7 x10-3 per degree K
poisson's ratio, nu=0.39
coefficient of thermal expansion, CTE = 9 x10-6 per degree C

Gold:
resistivity, rho=2.24 x 10-8 ohm-m
thermal coeffiecient of resistance, TCR = 3.4 x10-3 per degree K
poisson's ratio, nu=0.42
coefficient of thermal expansion, CTE = 1.42 x10-5 per degree C

Predicted and Actual Values:

predicted dimensions(m)

actual dimensions(m) --average

platinum

gold

platinum

gold

rho(ohm-m)

1.04E-07

2.24E-08

1.04E-07

2.24E-08

TCR(per degK)

3.70E-03

3.40E-03

3.70E-03

3.40E-03

Poissons ratio

0.39

0.42

0.39

0.42

CTE(per deg C)

9.00E-06

1.42E-05

9.00E-06

1.42E-05

width(m)=

7.50E-05

1.50E-04

6.00E-05

1.28E-04

thickness(m)=

1.00E-07

5.00E-07

1.00E-07

4.50E-07

length of turn(m)=

2.50E-03

varies

2.50E-03

varies

spacing of turns(m)=

7.50E-05

7.50E-05

number of turns(m)=

11

11

largest

largest

total length (L) =

2.75E-02

7.62E-02

2.75E-02

7.62E-02

area (A)=

7.50E-12

7.50E-11

6.00E-12

5.76E-11

Resistance (R) =rho*L/A=

382.07

22.76

477.58

29.63

gage factor=(dR/R)/(dL/L)=

1.78

1.84

1.78

1.84

=1 + 2*nu + (drho/rho)/(dL/L)


pruitt@cdr.stanford.edu
allisono@cdr.stanford.edu