Strain Gauge Experiments - Lab Report Example

www.academia-research.com Sumanta Sanyal d: 20/05/2006 Laboratory Report: Strain Gauge Experiments Summary This report is on a set of four experiments on two methods of measuring microstrains on strain gauges. The first method is a simple current and voltage one while the second one is a balanced Wheatstone bridge one. The primary objective of the experiments is to determine how accurate measurements can be made of microstrains in strain gauges. After analysis of the results it is found that the second method - the balanced Wheatstone bridge one - is more accurate. Explanations are furnished in the conclusion as to why this is so. It is also recommended that a balanced Wheatstone bridge with an amplifier be tried out as a measuring entity. It is envisaged that this would be the most efficient method of all. Contents Page Introduction.5 Theory & Apparatus.6-7 Basic current and voltage measurement method Wheatstone bridge measurement method Wheatstone bridge and amplifier method Procedure.8-12 1st Method 2nd method 3rd Method Results.13-16 1st Method 2nd method Discussion..17 Conclusion.18 References List of Symbols (Greek small letter delta) - Deflection at the end of the strain gauge beam (max of 45 mm) (Greek omega) - Ohm - Unit of resistance Introduction This report includes the proceedings of a set of practical laboratory experiments that encompasses three electrical measurement techniques for measuring strain using strain gauges. The objectives of the experiments are as follows: to demonstrate various strain measurement techniques, to reveal and discuss the limitations of each such technique and how such limitations can be overcome, to investigate the problems that may arise out of the occurrence of electrical noise and fluctuations in instrument resolutions, and to analyze the errors inherent in the measurements. The three experimental methods employed are as follows: Basic current and voltage measurement method Wheatstone bridge measurement method Wheatstone bridge and amplifier method It must be noted at first that the 3rd method is a recommended on and no actual experiments have been done on it. It has nevertheless been included here because a combination of the Wheatstone bridge and an amplifier is a very efficient method for measuring voltages as the amplifier maximizes it and makes measurement easier. Also occurrence of electrical noise and fluctuations in instrument resolutions can be better revealed by it. Theory & Apparatus In this section of the report the justifications for the three measurement methods as well as circuit diagrams of the three measurement apparatus are provided. Basic current and voltage measurement method: The experimental rig shown in Figure 1 has a cantilever beam with a pair of 120 strain gauges attached one on the upper and one on the lower beam surfaces. The strain-setting device is a bolt with a metric thread. The strain produced at the surface of a deflected cantilever beam varies along its length. Close to the gripping point (where the strain gauges are mounted) it has a maximum value of: (Eq.1) where: - deflection of the end of the beam (max of 45 mm), d - beam thickness (0.8mm in the rig) and L - beam length (250 mm in the rig). Figure 1: The experimental rig. Wheatstone bridge measurement method: The purpose of this experiment is to improve the results obtained in experiment 1 by the previous measurement method by using a Wheatstone bridge (Figure 2) that comprises of four nominally identical 120 strain gauges. Figure 2: Wheatstone bridge Ideally, if the bridge resistors are identical no voltage will be registered at the meter but this is not so practically and a small voltage of about 2 mV is detectable. This is because the resistors are not exactly identical. Wheatstone bridge and amplifier method: The output of the Wheatstone bridge is a very small differential signal that can be amplified using a high-gain differential amplifier. The amplifier needs to be able to amplify differential signals of up to about 3mV and produce an output in the range of about 1V to 5V. It should have a high Common Mode Rejection Ratio (CMRR) and a (reasonably) high input impedance. Procedure 1st Method: Objectives: 1. To predict the strain (in microstrains) to expect during this experiment and evaluate in the context of the actual strain measured. 2. A scale is provided to measure the end deflections of the beam but it is not a very accurate measuring device. The aim is to develop an alternate way to measure more accurately. 3. The third objective is to measure the number of turns so as to calculate end deflection. Procedures: The maximum strain is predicted to be: max = 864 microstrains This is as per the following calculation: Strain is equal to: Where: - deflection of the end of the beam (max of 45 mm), d - beam thickness (0.8mm in the rig) and L - beam length (250 mm in the rig). Figure 3: The basic measurement circuit For the purpose of the experiment it is taken: VS = 15V R1 = 3k. The resistor value is taken at the nearest whole value at 3000 = 3 k Steps Adopted during the Experiments: Two sets of experiments were conducted. In the first set the upper strain gauge was used and the following steps adopted. The circuit is set up as per Figure 3 using the strain gauge. A digital voltmeter is used to measure all voltages (ensuring that no strain is applied) in the circuit: (supply), across (- ) and across the strain gauge (). The resolution of the meter when measuring is noted. The resistance of the strain gauge is also measured. Next, a series of different levels of strain is applied using the strain-setting device and the voltage across the strain gauge is measured. Frequent checks are also made to observe if the supply voltage changes. All these are noted down in a log book. In the 2nd set of experiments the lower strain gauge was used and the same steps as in the 1st set of experiments was adopted. 2nd Method: In the Wheatstone bridge experiments, as per Figure 2, the value of is taken as: Where = +/- 15 (Taken) The nearest standard value is taken at 3000 = 3 k Steps Adopted during the Experiment: Since it is known that all the resistors in the bridge are not exactly identical a small voltage (about 2mV) is detected by the meter it is proposed that a balancing system be devised so that no voltage is detectable when no strain is applied. The bridge is set up with the upper strain gauge and three inactive gauges (Figure 2). No strain is applied and the supply voltage and those across both bridge diagonals are measured. The proposed balancing method in Step 1 is applied and the value of the balancing resistance is measured. Various levels of strain are applied and the misbalances in resistance across the bridge are measured. The above process is repeated with two strain gauges - the upper and the lower - active and the other two gauges inactive. The proposed balancing system: The following diagram illustrates the manner in which the bridge is expected to be balanced. Figure 4: The balancing set of resistors It is expected that adjusting appropriately will balance the bridge. The efficacy of the Wheatstone bridge method over the previous one is that the bridge is capable of generating more stable voltages when it is evenly balanced. Thus, it is predicted that this method would produce more efficient results than the previous one. 3rd Method: Steps Adopted during the Experiment: A suitable amplifier circuit is designed and the expected gain from it measured. The designed circuit is constructed. Next, the circuit is connected to the Wheatstone bridge with two active gauges. The digital voltmeter is left connected across the bridge. The bridge is balanced and the output from the amplifier measured. Some strain is applied and the input and output from the amplifier is measured. The gain is also verified. Next, various levels of gain are applied and the output voltage from the amplifier measured. An oscilloscope is used to measure the noise in the output of the amplifier. This is also done for the input. A 1 V DC input is applied to both inputs of the amplifier and the outputs measured. A simple design instrumentation amplifier is used instead of a common differential one because it is both popular and cheap and easily available from 'Analog Devices'. It is connected to the bridge in a similar way to a differential one using (-) for inverting input and (+) for non-inverting one. The amplifier brand is 'AD620' and its specifications (derived from datasheet) are given below: DC PERFORMANCE ("B GRADE") 50 mV max, Input Offset Voltage 0.6 mV/8C max, Input Offset Drift 1.0 nA max, Input Bias Current 100 dB min Common-Mode Rejection Ratio (G = 10) LOW NOISE 9 nV/Hz, @ 1 kHz, Input Voltage Noise 0.28 mV p-p Noise (0.1 Hz to 10 Hz) AC SPECIFICATIONS 120 kHz Bandwidth (G = 100) 15 ms Settling Time to 0.01% The circuit design of the amplifier is as follows: Required gain is defined by the labeled external resistor . = For 3mV input and 3 V output gain is 1000 and = 49.4 This method is a recommended one and no actual experiments have been conducted. It is expected to be the most efficient of the three methods studied here. This is so because the amplifier is capable of maximizing the small differential signals of the normal Wheatstone bridge and this can reveal occurrence of electrical noise and fluctuations of instrument resolutions. Results 1st Method: Measured voltages: = 15.33 V ( - ) = 14.185 V = 1.145 V Voltage resolution of voltmeter: 2000 mV Strain gauge resistance: = 121.08 Table 1: Tabulated data recorded at upper strain gauge: Strain (mm) Voltage (V) Predicted Strain (In microstrains) 0 1.145 0 5 1.146 96 10 1.146 192 15 1.146 288 20 1.147 384 25 1.147 480 30 1.147 576 35 1.148 672 Graph 1: The plotted values of the voltage against the predicted strain for the above table. Table 2: Tabulated data recorded at lower strain gauge: Graph 2: The plotted values of the predicted strains and the voltages as per table above. 2nd Method: a) !st set of experiments with one active and three inactive strain gauges: = 15.34 V (bridge diagonals) = 2.31 V (imbalance) = 0.002 V After applying the balancing equipment, the value of the balancing resistance: = 67.3 k Table 3: Tabulated values of measured strain and voltage in active strain gauge: Strain (mm) Voltage (mV) Predicted Strain (In microstrains) 0 0.02 0 5 0.1 96 10 0.2 192 15 0.4 288 20 0.5 384 25 0.6 480 30 0.8 576 35 0.9 672 Graph 3: Plotted values of the predicted strain and the voltages as per above table. b) 2nd set of experiments using two active (upper and lower) and two inactive strain gauges: = 15.35 V (bridge diagonals) = 2.31 V (imbalance) = 0.0013 V After applying balancing equipment, the balancing resistance: = 12.8 k Table 4: Tabulated strain and voltage values Strain (mm) Voltage (mV) Predicted Strain (In microstrains) 0 0.013 0 5 0.2 96 10 0.5 192 15 0.7 288 20 1.0 384 25 1.3 480 30 1.5 576 35 1.8 672 Graph 4: Plotted values of predicted strain and voltages as per table above. Discussion In experiments 1 & 2 under the 1st method it is found that the plotted lines in graph 1 & 2 corresponding respectively to the two experiments have opposite gradients. This is because of the positioning of the upper strain gauge and the lower one in respect of the rest of the circuit. When strain is applied in the upper gauge the resistance within increases with slight increase in voltage. On the other hand increasing strain in the lower gauge causes the voltage to drop slightly. What is important is that the 1st method is definitely not very effective when it comes to indicating increase in strain compared to the 2nd method. Graphs 3 & 4, which are for experiments 3 & 4 under the Wheatstone bridge method, show a more sensitive demonstration of increase in strain. Both Graphs 3 & 4 have plotted lines that have a stiff gradient indicating uniform increase in voltage with increase in strain. Experiment 4, conducted with two active and two inactive, strain gauges gives the most uniform plotted line as per graph 4 indicating that it is the most effective experiment of the 4 conducted. It also demonstrates that it is the more effective way of utilizing a Wheatstone bridge to measure applied strain. Conclusion It is well known that measuring strain is a very delicate affair as the amount of strain applicable is often so small that the effects on the circuit are minimal. Thus, indications that demonstrate application of strain are also very feeble. Nevertheless, the 2nd method of using a balanced Wheatstone bridge with 4 strain gauges seems to be effective enough to give positive and consistent indication of application of strain at increasing levels. It is envisaged that the 3rd proposed method of using an amplifier with the bridge would be an even more effective one as it would amplify the feeble signals of the bridge and make it more possible to detect changes in applied strain. Also, such amplification would greatly reduce other interference like electrical noise and instrument resolution problems. Reference (Bibliography) Measuring Strain with Strain Gauges, National Instruments, 2006. Extracted on 17th May, 2006, from: http://zone.ni.com/devzone/conceptd.nsf/webmain/C83E9B93DE714DB08625686600704DB1OpenDocument Other data acquired from laboratory manuals and log books. Read More