Force sensor A force sensor is made of a strip of steel with

Force sensor. A force sensor is made of a strip of steel with cross-sectional area of a = 40 mm by b = 10 mm with a platinum. 350 Ohm strain gauge (nominal, unstressed resistance) bonded to one surface, as shown in Figure 6.46. The sensor is intended for use as a compression force sensor. Given the modulus of elasticity of 200 GPa, calculate the range of resistance of the sensor if it cannot exceed a strain of 3%. What is the range of forces that can be applied? Calculate the sensitivity of the sensor assuming it is prestressed to 3%.

Solution

Given Force sensor

Sensor was made of Platinum whose cross-section area is a*b=40*10 *10^-6 m²

Resistance of unstressed gauge is 350 ohm

a ) To find range of resistance and range of force can be applied is

Modulus of Elasticity = 200 GPa

Maximum strain is = 3%

We know Modulus of Elasticity = Stress/Strain

Now can find Stress using above relation

Stress = Modulus of Elasticity * Strain = 200*10⁹ * 0.03 = 6*10⁹ N/m²

Stress = Force / Area ;

Area = (a+0.03a)(b+0.03b) = 41.2*10.3 = 424.36*10^-6 m²

Force = Stress * Area = 6*10⁹ * 424.36*10^-6 = 2546160 N

Range of Force is between 0 < F < 2546160 N

Range of Resistance will be between

400 mm²   ----- 350 ohm

424.36 mm²  -----   

R_max  = (424.36*350)/400 = 371.315 ohm

350 ohm < R < 371.315 ohm

b) Sensitivity of sensor is

Sensitivity = Change in resistance / change in Area = (371.315-350)/(424.36 - 400) = 0.875 ;