Experiment 4 - Resistive Sensors II

Tasks:

There is three bending beams, each of them is equipped with a different setup of strain gauges. All strain gauges have a nominal resistance of 120 Ohms and a k-factor of 2.

Fig. 1: amplifier                             Fig. 2: mounted bending beam

Fig. 3: single strain gauge for quarter-bridge on bending beam one, half-bridge on bending beam two, full-bridge on torsional wave (left to right)

1. On bending beam 1 just one strain gauge is fixed.
   1. Use a multimeter to measure the resistivity change when bending the beam.
   2. If you had a 10mA current source like in fig. 4, what voltage change would you expect across the strain gauge for a 1‰ strain of the beam? What voltage change would you need to measure, if you want to resolve the maximum strain of 1‰ to 100 steps?
2. Use an additional resistor to build the setup from circuit 2 (fig. 5), a voltage divider. Measure the voltage with the multimeter across the strain gauge if you connect a 5V source as V_s for both the unloaded and loaded beam.
3. Now imagine the strain gauge in circuit 3 (fig. 6) as a quarterbridge with the strain gauge as R₁. What do you expect?
   1. For this setup, give the equation for the voltage V_d. What happens if R₁ changes?
   2. What voltage change would you measure for a 1‰ strain and 5V supply voltage?
   3. Would it be possible to compensate a temperature difference here?
4. Use bending beam 2 which has 2 strain gauges to set up a halfbridge as shown in circuit 3 (fig. 6). The two straing gauges on the beam need to be connected to the amplifier by using the screw terminal. Then set the amplifier to half-bridge and use a supply voltage of 10V. The top turning knob should be set to 0.5mV/V at U_B=10V. The lower switch should be set to 1mV/V.
   
   1. Give the equation for V_d in this setup.
   2. Try to balance the voltage to as close as possible to zero without any load on the beam by using the "zero balance".
   3. Use the amplifier manual/the settings to find the corresponding real value of V_d for 1V amplifier output voltage.
   4. Now put load on the beam and compare the outputs of the amplifier with and without load on the beam. Calculate the stress you applied.
   5. Could a temperature change cause a strain, would this setup be able to compensate it?
   6. What would happen if one strain gauge were on top and the other one on the bottom of the beam?
5. Beam 3 is not a usual bending beam, but a torsional wave. The strain gauges are fixed in a 45° angle, as the strain is largest in this angle. Connect the strain gauges to the amplifier by using the screw terminal. Set the amplifier to full-bridge, use a supply voltage of 10V and set the zero balance. Keep all other settings.
   
   1. Measure the amplified voltage of V_d while applying a torque to the wave/shaft!
   2. Calculate the torque you have applied by using these equations:

Fig. 4: Circuit 1 - current source

Fig. 5: Circuit 2 - voltage divider

Fig. 6: Circuit 3 - Wheatstone-Bridge

Sources:

[1]     S. Keil, Dehnungsmessstreifen. Wiesbaden: Springer Fachmedien Wiesbaden, 2017.

[2]     P. P. L. Regtien, Hg., Sensors for Mechatronics // Sensors for mechatronics. Amsterdam: Elsevier, 2012.