ELEC 105 Laboratory Exercise #5 Spring 2010ELEC 105 Laboratory Exercise #5 Spring 2010Strain GaugesWhy is this important? The resistance of a strain gauge varies when it is stretched or compressed. Thus, a strain gauge acts as a transducer that converts a mechanical quantity, strain, to an electrical quantity, resistance. Strain gauges can be used in circuits to monitor the strain experienced by structures such as bridges, robotic arms, or human bones. These simple transducers are commonly used in mechanical, civil, and biomedical engineering. In this lab, you will design a circuit to monitor the bending strain experienced by a metal bar. GradingThis lab is a “familiarization exercise” and therefore will be weighted 50 points. To receive full credit, submit the plot and comments requested in Step 11 below to your instructor by 5 pm on the day following thelab. Only one submission per lab group is required; however, each member of the group should contribute to its production. BackgroundThe size and shape of the conductive pathways through a material determine the resistance of that material. For example, the resistance of a slab of material with resistivity ρ, length L, and cross-sectional area A placedbetween two conducting electrodes (see Figure 1) is given by R = ρL/A. The resistance is proportional to the length of the material and inversely proportional to its cross-sectional area.Figure 1: Material between parallel-plate electrodes.Figure 2 shows a top view of a typical strain gauge. A thin metal foil (shown in black) is printed with a serpentine pattern on an insulating substrate (light gray). Two large electrical contacts are provided on the right side of the sensor. Note that the serpentine pattern has long thin lines running horizontally and short thick vertical connecting lines. This makes the gauge much more sensitive to stress that is parallel to the long lines and relatively insensitive to orthogonal stresses. In a typical application, the strain gauge is cemented to a structure to measure the strain it experiences. Strain gauges can be mounted in various ways so that they respond to tension, compression, bending, torsion, or shear (see examples and further applications information from National Instruments at zone.ni.com/devzone/cda/tut/p/id/3092#toc3).To visualize what happens when a strain gauge is in tension, consider a rubber band. When the rubber band is stretched, its length increases, and its cross-sectional area decreases. The thin metal lines in a strain gauge respond to tension in the same way. Both actions increase the electrical resistance. (R is proportional to electrodeALL/A.) Conversely, compressing the device decreases its length and increases its cross-sectional area, thus decreasing the electrical resistance. In practice, the achievable change in resistance is less than 1%, so cleverarrangements called bridge circuits are used to enhance the measured changes and compensate for temperature effects.Figure 2. Metal foil strain gauge.Procedure1. You will be given a metal bar with two strain gauges attached to it. Note the placement of the gauges. With the end nearest the gauges clamped to the lab bench, predict how the resistance of each gauge will change when you press down on the opposite (free) end of the bar and when you pull up on the free end.2. Measure the resistance of each gauge when no external force is applied to the free end of the bar.3. Measure the resistance of each gauge when you flex the free end of the bar downward by 2 cm.4. Assemble the circuit shown in Figure 3, where the strain gauge on the top side of the bar is represented by the resistance R + R, and the strain gauge on the bottom side is R – R. Based on your resistance measurements, predict and then measure the voltage Vab between points a and b when:a. no external force is applied to the bar.b. you press down on the free end of the bar to produce a deflection of −2 cm.c. you press up on the free end of the bar to produce a deflection of +2 cm.How well did your predictions and measurements agree?Figure 3. Strain gauge voltage divider.12 V+−R + R+Vab−R − Rab25. You probably found that the change in voltage between the strained and unstrained cases was very small. The circuit in Figure 4, called a bridge circuit, produces a larger percentage change in the voltage measured between points a and b when the bar is deflected. The resistors marked R + ΔR and R − ΔR arethe two strain gauge resistances. The values of R1 and R2 are often chosen so that with no stress on the strain gauge R1 = R2 = R + ΔR = R − ΔR, where ΔR = 0. That is, resistors R1 and R2 have the same (or almost the same) resistances as the unstrained gauges.Figure 4. Bridge circuit with two strain gauges.6. Assemble the circuit shown in Figure 4, and apply 12 V using the bench-top power supply. Verify that the voltage across R2 is as expected. (What should it be?) Measure the voltage Vab between points a andb when no external force is applied to the bar. Why isn’t the measured voltage exactly zero? (If the measured voltage is larger than 0.2 V or so, then you should check your connections and verify that R1 and R2 have the desired values.)7. The offset voltage that exists with no stress applied to the bar can make it difficult to observe and measure the true voltage response of the bridge. To remove this offset from your voltage measurements, press the button marked “Null” on the multimeter. You should see the voltage scale change to millivolts and the word “Math” will appear under the units on the multimeter display. The voltage value that was being displayed when you pressed the “Null” button will be subtracted from subsequent measurements. The voltage displayed now should be very close to zero (within about 10 V). Pressing the “Null” button again disables this feature.8. Now measure the voltage Vab between points a and b when:a. no external force is applied to the bar.b. you press down on the free end of the bar to produce a deflection of −2 cm.c. you press up on the free end of the bar to produce a deflection of +2 cm.9. Measure the bridge voltage Vab when the end of the bar is deflected the following distances (in cm) from the unstrained position: −2.5, −2.0, −1.5, −1.0, −0.5, 0, 0.5, 1.0, 1.5, 2.0, and 2.5. Assume that positive values of deflection are up and negative values are down.10. Plot Vab as a