Strain Gauge Measurements - Math Problem Example

Experiment 1: Strain gauge measurements 1. Summary: This report aims at describing the strain gauge measurement using Quarter, half and Full Wheatstone bridge configurations. Their respective response for same load conditions and respective sensitivity of the circuits compared. 2. Table of contents: Sl no Contents Page no 1 Introduction 1 2 Theory 1 3 Experimental Apparatus and Procedure 3 4 Results and Discussion 6 5 Conclusions 9 3. Introduction: The objective of this experiment is to measure strain and output voltage of quarter, half and full bridge circuit configurations for varying loads and prove that the measured output voltage is more linear and approximately double for the same applied load in half bridge compared to quarter bridge and full bridge compared to half bridge configurations. Sensitivities of the respective circuits to external load are also compared. 4. Theory: An external force applied on a body causes deformation, specifically along its length resulting in change in length. The ratio of change in length (L) to the actual length (L) of the body is called Strain () [1]. This change in length can be positive (tensile) or negative (compressive). Strain is dimensionless, often expressed as micro strain (). L/L Strain gauge is a device used to measure strain. This gauge works on the principle that due to applied load, the amount of strain developed in the body is proportional to change in its resistance[1]. Strain gauge materials are thermally sensitive. To compensate thermal sensitivity strain gauges are used in a bridge configuration. Characteristics or behavior of a circuit depends of its components. Characteristics of a components change with time and no two identical components exhibit exactly the same characteristics. The actual value of component may be slightly different from its specified value due to tolerances in manufacturing. All these factors affect the behavior of a circuit. Sensitivity is the measure of change in the characteristic of a circuit for a given change in the value of a particular component [9]. A Wheatstone bridge consists of four resistive arms with an excitation voltage applied across the bridge. Output voltage is zero in the balanced condition where (R2/R1) = (R3/R4) [1]. Bridge enters an unbalanced condition when a resistance change happens in any arm of the bridge resulting in a non zero output voltage. If resistance in one arm is replaced with a strain gauge in compression (Rg - R) to the applied load, output voltage will be non zero due to the change in the ratio of resistances (R3/(Rg - R)) when external strain is applied. The following figure shows the schematic of a Quarter bridge circuit [2]. Half bridge circuit contains two strain gauges in one leg one gauge mounted in tension and another in compression. Full bridge circuit contains all strain gauges instead of resistances two gauges in tension and two in compression Figure (1). Wheatstone bridge configuration In a Half bridge, resistances in two arms can be replaced with strain gauges, one gauge mounted in tension (Rg + R) and the other one in compression (Rg - R) where R is the change in resistance. Hence for the same applied load the ratio (Rg + R)/ (Rg - R) in Half bridge configuration is more compared to the ratio (R3/(Rg - R)) in Quarter bridge configuration. Unbalance is more in half bridge configuration compared to Quarter bridge configuration. Hence, half bridge configuration yields an output voltage that is linear and approximately double the output of the Quarter bridge configuration. Similarly Full bridge configuration output voltage will be more linear and approximately double the output of the Half bridge configuration. Cantilever is a beam supported on only one end as shown in figure 2. The beam carries the load to the support [5]. It can be loaded in different conditions like End Load, Uniform distribution etc [4]. Strain gauge can be connected to a cantilever to apply external force by loading the cantilever. Figure (2). Cantilever beam with an end load condition [3] 5. Experimental Apparatus and Procedure: Experimental Apparatus: 1. Two resistances R1 and R3 2. One rheostat 3. Strain gauge reader 4. Hanger for applying load at the end of cantilever beam 5. Cantilever beam with built-in strain gauges 6. Voltmeter 7. Standard weights Procedure: a) Quarter bridge configuration 1. Two known resistances R1 and R3, rheostat R2 and a strain gauge Rg are connected in a Wheatstone bridge configuration as shown in figure 1. R1 connected across B and C terminals, R2 across A and B terminals, R3 across A and D terminals, Rg across C and D terminals. 2. Excitation voltage Vin is given across A and C. 3. Output voltage VOUT is measured across B and D. 4. Strain gauge Rg is attached to the cantilever beam. A hanger is available at the unsupported end to apply load as shown in figure 2. 5. Initially balance bridge. Observing output voltage on voltmeter adjust the rheostat R2 such that the output voltage becomes zero, while no load is applied on cantilever beam. 6. Now increase the load on cantilever to 100grams. 7. Measure the output voltage and strain developed in the gauge Rg. 8. Linearly increase the load in steps of 100g to a maximum load of1000g. Measure the output voltage and strain developed in the gauge Rg for each load. 9. Tabulate the reading. b) Half bridge configuration 1. One known resistance R1, one rheostat R2 and two identical strain gauges Rg1 and Rg2 are connected in a Wheatstone bridge configuration as shown in figure 1. R1 connected across B and C terminals, R2 across A and B terminals, Rg2 across A and D terminals, Rg1 across C and D terminals. 2. Excitation voltage Vin is given across A and C. 3. Output voltage VOUT is measured across B and D. 4. Strain gauges Rg1 and Rg2 are attached to the cantilever beam such that Rg1 is in compression and Rg2 is in tension. A hanger is available at the unsupported end to apply load as shown in figure 2. 5. Initially balance bridge. Observing output voltage on voltmeter adjust the rheostat R2 such that the output voltage becomes zero, while no load is applied on cantilever beam. 6. Now increase the load on cantilever to 100grams. 7. Measure the output voltage and strain developed in the gauge Rg1. 8. Linearly increase the load in steps of 100g to a maximum load of1000g. Measure the output voltage and strain developed in the gauge Rg1 for each load. 9. Tabulate the reading. c) Full bridge configuration 1. Four identical strain gauges Rg1, Rg2, Rg3, and Rg4 are connected in a Wheatstone bridge configuration. Rg1 connected across B and C terminals, Rg2 across A and B terminals, Rg3 across A and D terminals, Rg4 across C and D terminals. 2. Excitation voltage Vin is given across A and C. 3. Output voltage V is measured across B and D. 4. Strain gauges are attached to cantilever beam such that Rg1 and Rg4 are in tension and Rg2, Rg4 are in compression. A hanger is available at the unsupported end to apply load. 5. Ideally the bridge should be in balanced condition, while no load is applied on beam. However, due to resistance tolerances initial offset voltage is generated which we consider as negligible. 6. Now increase the load on cantilever to 100grams. 7. Measure the output voltage and strain developed in the gauge Rg1. 8. Linearly increase the load in steps of 100g to a maximum load of1000g. Measure the output voltage and strain developed in the gauge Rg1 for each load. 9. Tabulate the readings. 6. Results and discussion: Readings obtained from experiment on Quarter bridge circuit are tabulated in table 6(a). Table 6(a). Strain & Voltage measurements for varying loads in Quarter bridge configuration Load(g) Voltage(V) Microstrain () 0 0 0 100 0.11 0.13 200 0.21 0.23 300 0.31 0.32 400 0.41 0.44 500 0.51 0.53 600 0.61 0.63 700 0.72 0.74 800 0.82 0.85 900 0.93 93 1000 0.103 103 Figure (3). Voltage Vs Load curve for Quarter Bridge configuration Readings obtained from experiment on Half bridge circuit are tabulated in table 6(b). Table 6(b). Strain & Voltage measurements for varying loads in Half bridge configuration Load(g) Voltage(V) Microstrain () 0 0 0 100 0.2 0.22 200 0.4 0.43 300 0.61 0.63 400 0.82 0.83 500 1.02 1.03 600 1.23 1.25 700 1.42 1.44 800 1.63 1.66 900     1000     Figure (4). Voltage Vs Load curve for Half Bridge configuration Readings obtained from experiment on Full bridge circuit are tabulated in table 6(c). Table 6(c). Strain & Voltage measurements for varying loads in full bridge configuration Load(g) Voltage(V) Microstrain () 0 0 0 100 0.4 0.47 200 0.8 0.89 300 1.22 1.27 400 1.64 1.69 500 2.04 2.09 600 2.46 2.5 700 2.84 2.91 800 3.26 3.31 900     1000     Figure (5). Voltage Vs Load curve for Full Bridge configuration From the results we can observe that for a given load, output voltage and strain developed in the half bridge circuit are almost double to the output voltage and strain developed in the quarter bridge circuit. Similarly, output voltage and strain developed in the full bridge circuit are almost double to the output voltage and strain developed in the half bridge circuit. From the Voltage Vs Load curves of the three bridge configurations we can obtain the sensitivity of the circuits by calculating the slope of the linear portion of the curves respectively. We can observe that the slope of the Half bridge circuit is 0.00197V/gm, is 93% more than the slope of 0.00102V/gm in Quarter bridge circuit. Similarly the slope of Full bridge circuit is 0.00343V/gm, is 74% more that the slope of Half bridge circuit. 7. Conclusions: The output voltage and strain at different loads is measured for Quarter, Half and Full bridge configurations. From the experiment results we can conclude that the strain developed in the gauge is dependent on applied load and is directly proportional to output voltage. For a given load, the sensitivity of the circuit is directly proportional to the order of bridge configuration. Sensitivity is almost double in half bridge configuration compared to Quarter bridge configuration. Similarly, full bridge configuration sensitivity is approximately twice that of half bridge configuration, confirmed by the obtained slopes. Experiment 2: Calibration of a Linear Potentiometer 1. Summary: This report aims at describing the calibration of a linear potentiometer at no load and loaded conditions. Sensitivity of the potentiometer is compared in both conditions. 2. Table of contents: Sl no Contents Page no 1 Introduction 10 2 Theory 10 3 Experimental Apparatus and Procedure 12 4 Results and Discussion 14 5 Conclusions 15 3. Introduction: The objective of this experiment is to calibrate linear potentiometer for no load and loaded conditions and to prove that its sensitivity to displacement of slider is more in no load condition compared to loaded condition. 4. Theory: Potentiometer is a three-terminal resistor with a sliding contact providing a fixed electrical resistance between the two ends. By varying the slider position output resistance can be changed to a desired value within the range of the potentiometer [7]. It is used to vary the resistance in electrical circuits [7]. It is basically used in voltage divider circuits to obtain a smooth variation in the output voltage. Linear potentiometer is a variable resistor whose output resistance changes linearly with the displacement of the slider. Different types of linear potentiometers are available like wire-wound, conductive plastic and also in two different shapes rectangular and cylindrical [6]. As the output voltage is taken across the output resistance, it changes linearly with the input displacement. In ideal conditions change in the resistance and hence voltage is a linear function of the slider displacement. But when connected in a circuit, potentiometer gets loaded with the resistance offered by the circuit. This affects the linear characteristic of the potentiometer i.e. the change in the resistance may not be a linear function of the displacement. This is called loading effect [8]. Figure (6). Potentiometer with external load [11] Effective output resistance changes when an external load resistance is connected across potentiometer output terminals. The output voltage is given by below equation [11]. If the external resistance is large compared to potentiometer output resistances R1 & R2, then the output voltage can be approximated by below equation [11]. Characteristics or behavior of a circuit depends of its components. Characteristics of a components change with time and no two identical components exhibit exactly the same characteristics. The actual value of component may be slightly different from its specified value due to tolerances in manufacturing. All these factors affect the behavior of a circuit. Sensitivity is the measure of change in the characteristic of a circuit for a given change in the value of a particular component [9]. To calibrate a linear potentiometer its output voltage is measured at equal intervals of slider displacement. As the output voltage is proportional to the displacement of the slider, for a given output voltage the position of the slider can be determined by calibrating the potentiometer [10]. 5. Experimental Apparatus and Procedure: Experimental apparatus: 1. DC Power Supply 2. Variable-resistance linear potentiometer 3. Resistances 5.6 kΩ and 1 kΩ 4. 1 cm calibration blocks 5. Voltmeter 6. Micrometer Procedure: 1. Connect the supply voltage Vin across the two fixed terminals A and B of the potentiometer such that the supply positive is connected to A and negative to B. 2. Slider rod C is moved completely towards B and no external load is applied on potentiometer. 3. Turn on the power supply. 4. Measure the output voltage across C and B using a voltmeter. 5. Now insert 1cm calibration block to move the slider rod C by 1cm. 6. Measure the output voltage Vout. 7. Linearly increase the displacement in steps of 1cm by inserting calibration blocks to a maximum displacement of 10cm. 8. Measure the output voltage for each displacement. 9. Turn off the power supply. 10. Now place a 5.6 kΩ resistor across the output terminals of the potentiometer i.e. across C and B. 11. Move slider rod C completely towards B. 12. Turn on the power supply. 13. Measure the output voltage across C and B using a voltmeter. 14. Now insert 1cm calibration block to move the slider rod C by 1cm. 15. Measure the output voltage. 16. Linearly increase the displacement in steps of 1cm by inserting calibration blocks to a maximum displacement of 10cm and measure the output voltage for each displacement. 17. Turn off the power supply. 18. Now remove the 5.6 kΩ resistor and place a 1 kΩ resistor across the output terminals of the potentiometer i.e. across C and B. 19. Move slider rod C completely towards B. 20. Turn on the power supply. 21. Measure the output voltage across C and B using a voltmeter. 22. Now insert 1cm calibration block to move the slider rod C by 1cm and measure the output voltage. 23. Linearly increase the displacement in steps of 1cm by inserting calibration blocks to a maximum displacement of 10cm and measure the output voltage for each displacement. 24. Turn off the power supply. 25. Tabulate the readings. 6. Results and discussion: Readings obtained from the experiment are tabulated in the following table. Table 6(d). No-Load & Load calibration results of Linear Potentiometer Distance (cm) Voltage (v) No external load 5.6 kΩ 1 kΩ 0 0.42 0.42 0.42 1 1.62 1.54 1.21 2 2.9 2.64 1.85 3 4.16 3.68 2.4 4 5.43 4.71 2.92 5 6.69 5.73 3.45 6 7.94 6.78 4.04 7 9.2 7.87 4.7 8 10.42 9.01 5.5 9 11.68 10.25 6.51 10 12.89 11.59 7.84 Figure (6): Voltage Vs Displacement curves for no load, 5.6 kΩ and 1 kΩ loads From the experimental results we observe that under no external load conditions, change in voltage is linearly proportional to the displacement. The sensitivity of potentiometer at different loads is calculated by the slope of the curve for the respective condition. The slope of the graph for no external load condition is 1.25 volt/cm, indicating maximum linearity. No external load is an open circuit condition and the maximum output resistance across the output terminals is equal to R2. As the load resistance decreases, the effective output resistance decreases and hence the induced output voltage decreases. This loading affects the linearity of the response and it can be observed from the decreasing slope values with decreasing load resistances. For 5.6 kΩ load the response is nearly linear with a slope of 1.09V/cm but for 1 kΩ it is non linear with 0.68V/cm. Sensitivity of potentiometer is more in no load condition. 7. Conclusions: Linear potentiometer calibration procedure is discussed and the output voltage at different loads is measured as a function of slider displacement. From the experiment results we can conclude that the sensitivity of the potentiometer is more in no load condition and it decreases with increase in load or decrease in load resistance. As the load increases, the response of the potentiometer becomes more non-linear with decreasing load resistance due to reduction in effective output resistance seen by the voltage source. References: 1. Measuring Strain with Strain Gages, National Instruments, [Internet]. Available from: < http://zone.ni.com/devzone/cda/tut/p/id/3642> [Accessed 23 July 2009]. 2. The Strain Gauge, [Internet]. Available from: [Accessed 23 July 2009]. 3. Cantilever Beam Analysis, [Internet]. Available from: [Accessed 23 July 2009]. 4. Loading options, Cantilever beams, [Internet]. Available from: [Accessed 23 July 2009]. 5. Cantilever, wikipedia, [Internet]. Available from: < http://en.wikipedia.org/wiki/Cantilever> [Accessed 23 July 2009]. 6. GLOBALSPEC, [Internet]. Available from: [Accessed 24 July 2009]. 7. US Patent 5565785 - Potentiometer calibration method, [Internet]. Available from :< http://www.patentstorm.us/patents/5565785/description.html> [Accessed 24 July 2009]. 8. Experiment No. 5, [Internet]. Available from: [Accessed 24 July 2009]. 9. Analyzing circuit sensitivity for analog circuit design, [Internet]. Available from: [Accessed 25 July 2009]. 10. Lab 5 -2DOF Pendulum-Slider System Free Vibration Analysis and Measurements, [Internet]. Available from: [Accessed 24 July 2009]. 11. Potentiometer, Wikipedia, [Internet]. Available from: [Accessed 25 July 2009] Read More