Technological Science 1 Strain Gauge Laboratory Report By Akash Sherchan Student I. D. #: 1124433 University of Warwick Summary The strain gauge laboratory session had a lot of aims and one of the main aims was to provide us with experience in using circuits based on operational amplifiers and examine the characteristics of these circuits when they amplify DC signals. Another aim was to also investigate the use and characteristics of resistive strain gauges. The overall objective was to understand the how these widely used transducers are used and how they behave.

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This will be done through custom pre-built electronic circuits which will then be used to amplify signals from a resistive strain gauge when weighed down with washers. Table of Contents Introduction Method Results Graphical Representation Analysis and Discussion of Results Conclusion Bibliography Appendix Introduction: The aim of the laboratory was to gain experience in the use of Operational-Amplifiers and the study of their characteristics. This report will cover the method used to study Op-Amps and analyse the results thus explaining and showing the behaviour and Op-Amps.

This laboratory had 3 sections looking at a non-inverting amplifier, inverting amplifier and a strain gauge bridge (differential op-amp) respectively. Where: • V+ : non-inverting input • V? : inverting input • Vout: output • VS+: positive power supply • VS? : negative power supply Where: • V+ : non-inverting input • V? : inverting input • Vout: output • VS+: positive power supply • VS? : negative power supply Operational-Amplifiers are key components in many electronic circuits and were first used in analogue computers to carry out mathematical functions such as addition, multiplication, and integration.

Ideally the op-amp only amplifies the difference in voltage between the two inputs. Vout (Output) = [V+ (+ Input) – V- (- input)] X Gain There are 3 main op-amps available and these 3 will also be used in this laboratory. They are: * Non-inverting * Inverting * Differential Circuits also rely on op-amps to be almost ideal. To be an ideal op-amp they must have the following characteristics: * Infinite Bandwidth (ability to amplify AC signals) * Infinite Gain * Infinite input impedance * Zero Noise (no effect of electrical and environmental noise) Method:

This laboratory was split into 3 separate parts, looking at a non-inverting amplifier, inverting amplifier and a strain gauge bridge (differential op-amp) respectively. When setting up the operational amplifiers we had to use resistors between the values of 1k? to 1M?. This is because the OP177 is not an ideal op-amp and has internal resistances. Using the values within this range the equations we use are still accurate. The apparatus used were circuits based on op-amps, specifically the OP177 op-amp. The pin connection of this device and other apparatus used are shown below : Figure 1: Basic op-amp connections

Figure 1: Basic op-amp connections Sockets for resistors Sockets for resistors Figure 2: Actual test board used in the laboratory Figure 2: Actual test board used in the laboratory Figure 3: Laboratory test set-up with equipment Figure 3: Laboratory test set-up with equipment 1) Non-inverting Amplifier 1. 1 The first step was to set up a non-inverting amplifier using figure 4. However, we had to set up the circuit so we would have a gain of about 15, using ‘preferred value’ resistors. So with a certain amount of resistors with their own specific values we had to calculate and pick two resistors to use for this circuit.

We did this with the equation to calculate the gain of a non-inverting amplifier: Gain = V0/Vi = R1 + R2 / R2 Figure 4 Figure 4 I used the resistors of values 33 k? and 470 k? to make a real gain of 15. 24 for this circuit. 1. 2 We then physically set up the circuits as shown in figure 3 and placed the resistors as labelled in the resistor sockets on the test board. We connected the variable potentiometer to the V+, V- and 0V lines to CON2 on the board. This supplies power to the PCB. Then, with wires, connected the output of the potentiometer to IN1, making sure that PIN 1 of the potentiometer goes to PIN 1 of IN1. The variable potentiometer ets us set a specific input voltage to the non-inverting amplifier. 1. 3 After assembling the circuit we switched the power on. We then joined the Digital Volt Meter (DVM) so that it will measure the input voltage Vi and adjust the input to about 0. 5V. Using a second DVM as shown in figure 3 we could measure the output voltage V0. We repeated the procedure to find the maximum negative output voltage and the minimum input voltage needed to achieve this. 1. 4 We took a total of 10 readings within the range of input voltages and plotted a graph. 2) Inverting Amplifier Gain = V0 / Vi = -R4 / R3 Gain = V0 / Vi = -R4 / R3 2. Again we had to set up an Operational-amplifier, this time an inverting op-amp using figure 6. We were again told to use resistors to make a gain of about 15, but R3 had to be higher than 150 k?. I used 330 k? for R3 and 4. 7 M? for R4. The predicted gain was 14. 24 using the equation: 2. 2 Next we constructed the circuit putting the resistors inFigure 5 Figure 5 to place in the Inverting amplifier part of the test board. Similar to before we connected the variable potentiometer to the inverting amplifier inputs (IN2). 2. 3 Like before we measured the range of the output and input voltages and took 10 readings within the range.

We also calculated the gain and compared it to the predicted gain. Another graph was plotted for this. 3) Strain gauge bridge In this exercise we examined the use of strain gauges with an operational amplifier. The ‘Analogue Experimental Transducer’ (figure 6) was used for this experiment. Strain gauges were bonded to the top and bottom of the beam to measure its deflection. Also, it is used to gain a measure of the load applied to the end of the beam. Figure 6: The ‘Analogue Experimental Transducer’. Equipment and layout for third section (strain gauge) Figure 6: The ‘Analogue Experimental Transducer’.

Equipment and layout for third section (strain gauge) Figure 6 Figure 6 Figure 5 Figure 5 Stretching a strain gauge increases its resistance while compressing it makes the resistance fall. Therefore, a load applied to the end of the beam will cause it to deflect downwards, increasing the resistance of the strain gauge on top of the cantilever while at the same time decreasing the resistance of the gauge on the bottom part of it. The circuit for the differential omp-amp had already been set up for us and the configuration is given below in figure 7. For a differential op-amp the following equation applies: VO = (V1 – V2) x R6/R5

Figure 7 Figure 7 3. 1 As stated earlier the circuit was already constructed with the values of R5= 12 k? and R6= 1. 2M?. With this we could calculate and expect Vo (output voltage) to be 1V. (V1 = 1. 01V AND V2 = 1. 00V). We then had to wire the analogue experimental transducer to CON3 on the test board to supply power to out strain gauge. The entire set up for this exercise should look like figure 8. The deflecting cantilever beam affects the output of the circuit. The DVM was then used to balance the bridge by adjusting the potentiometer to give 0 volts at the output of the amplifier when the beam has no load.

Figure 8 Figure 8 3. 2 Next we had to add M4 washers to the nylon screw at the end of the beam to add weight and bend the beam. We added 2 washers at a time and recorded the Vin and Vout for each time. Results: 1) Results from the non-inverting op-amp exercise: Figure9: Results for exercise 1. The uncertainties were +- 0. 02 as we read from the DVB which is digital. It went up to two decimal places and I also noticed a variation when reading the voltages before being balanced out. Figure9: Results for exercise 1. The uncertainties were +- 0. 02 as we read from the DVB which is digital.

It went up to two decimal places and I also noticed a variation when reading the voltages before being balanced out. Figure10: Free hand graph for exercise 1 plotting V out (Y-axis) against V in (X-axis). From this I calculated the gradient: 11. 4- -7. 5/0. 75- -0. 5= 15. 12 The gradient of the graph represents the Gain of the circuit. Figure10: Free hand graph for exercise 1 plotting V out (Y-axis) against V in (X-axis). From this I calculated the gradient: 11. 4- -7. 5/0. 75- -0. 5= 15. 12 The gradient of the graph represents the Gain of the circuit. 2) Results from the inverting op-amp exercise:

Figure 11: Results from exercise 2 Figure 11: Results from exercise 2 Figure12: Free hand graph for exercise 2 plotting V out (Y-axis) against V in (X-axis). From this I calculated the gradient: -(11. 4- -6/0. 75- -0. 4)= -15. 13 Again, the gradient of the graph represents the Gain of the circuit. Figure12: Free hand graph for exercise 2 plotting V out (Y-axis) against V in (X-axis). From this I calculated the gradient: -(11. 4- -6/0. 75- -0. 4)= -15. 13 Again, the gradient of the graph represents the Gain of the circuit. 3) Results from the Strain gauge (differential op-amp) exercise: Figure 13: Results from exercise 3

Figure 13: Results from exercise 3 Figure 14: Free hand graph for exercise 3 plotting Voltage Output (Y-axis) against the number of washers put on the cantilever beam to increase the load (X-axis). From this I calculated the gradient as: 48-20 x10^-3 / 17. 6-7. 6 = 2. 8 x 10^-3 With the reciprocal being the Gain of the differential amplifier giving a gain of: 1/ 2. 8 x 10^-3= 357. 1 Figure 14: Free hand graph for exercise 3 plotting Voltage Output (Y-axis) against the number of washers put on the cantilever beam to increase the load (X-axis). From this I calculated the gradient as: 48-20 x10^-3 / 17. 6-7. = 2. 8 x 10^-3 With the reciprocal being the Gain of the differential amplifier giving a gain of: 1/ 2. 8 x 10^-3= 357. 1 Analysis and Discussion of Results: The uncertainties were +- 0. 02 as we read from the DVB which is digital. It went up to two decimal places and I also noticed a variation when reading the voltages before being balanced out. The equation to calculate the gain from a non-inverting amplifier was given below. Using the graph I plotted I could figure out actual value of the gain from the gradient and compare it to the ‘theoretical’ value I calculated with the values of the resistors I used.

The theoretical value of the circuit was 15. 24 and the ‘real’ value calculated from the graph was 15. 12. Overall, this was quite an accurate experiment proving the equation given below for non-inverting op-amps: Gain = V0/Vi = R1 + R2 / R2 The percentage difference between the real and theoretical gains was only 0. 8 % which could have been from the internal resistance of the circuit and resistors (which we did not account for) and human error. There are two anomalies on the graph which are the first and last values for V in.

This is because these are the maximum and minimum values for the input and output voltages. Past a certain point when you increase or decrease the values of Vin Vout doesn’t follow the linear behaviour. This is because part a certain point the op-amp will reach saturation and is not able to amplify the signal anymore as the op-amp does not actually possess infinite bandwidth. Therefore, the output voltage will be limited by the input voltage. This can also be seen in exercise 2 with the inverting operational amplifier. The theoretical gain for the inverting amplifier was 14. 4 (from the equation) and the real value being 15. 13. The percentage error was considerably higher than the last exercise with a percentage error of 6. 25 % this time. This may have been because we were asked to use resistors of much higher resistance than the last exercise. Resistors with higher resistance are going to have higher internal resistance as well which will add to the error. As we used much higher value resistors the internal resistance and therefore error will also greatly increase. The range of values we received for the voltage outputs were slightly different but not by much.

The inverting amplifier had a higher range of voltage outputs but only by 0. 1V. The difference could’ve been higher or even lower but the overall errors including the internal resistances, the varying voltmeters and human error I think there is an overall error of +-0. 2V for this reading. For exercise three I plotted a graph of the voltage output by the number of washers added to the cantilever beam (thus changing the resistances of the strain gauges) and showing their relationship. So the more weight is added to a strain gauge the higher the voltage output.

The reciprocal of the gradient gives the gain and was quite high for this circuit with a real value of approximately 357. 1. Conclusions: The operational-amplifier is one of the most useful pieces of electronics used in analogue circuits. It only has a handful of components and can be made to perform a wide variety of analogue signal processing tasks. These modern ones have also been designed to sustain direct short-circuits on their outputs without any damage. Overall, all the equations and theories given were proven correct with only small uncertainties to each result.

The gains calculated from the theories were very similar to the ‘real’ approximate values we found and calculated. A lot of insight on the use of op-amp circuits was also gained which was another goal of this laboratory. Refs: 1) http://www2. warwick. ac. uk/fac/sci/eng/eso/modules/year1/es180/studentresources/labs/lab_strain. pdf 2) http://www2. warwick. ac. uk/fac/sci/eng/staff/yc/strain_gauge_briefing_lecture2011_2012. pdf 3) http://www. allaboutcircuits. com/vol_3/chpt_8/1. html 4) http://www. philbrickarchive. org/ 5) Introduction to Materials Science for Engineers, 7th Edition, James F. Shackelford