Purpose:Theory:andEquipment:Procedure:Results:Dynamics SystemModeling- and ControlsEGR 345 Lab #6Torsional SpringBrian MalkowskiAndrew EdlerOctober, 12 1999Purpose: To study torsional oscillation using Labview and data collection.Theory:A large symmetric rotating mass has a rotational inertia J, and a twisting rod has a torsional spring coefficient K. the basic torsional relationships are as follows:The natural frequency of an oscillating system can be found by the following derivation.or whereand Equipment:(2) CDT (#217126 & 12196)(2) DMM (#23116 & 23117)(2) wire harnesses(2) Dell Computer (#125 &124)Wooden Block (rotating mass)202)(dtdJLJGTLJGTKKTdtdJJTHolding fixtureTorsional spring (shaft)Rotating massRqFigure 6.12dtdJLJGT02dtdJLJGAtheLGJJA120 LJGJiA1)sin()cos(11tLJGJitLJGJhsradLJGJ1HzLJGJf121Carbon Steel (rotating mass)1 PVC pipe (torsional spring)1 Aluminum rod (torsional spring)Calipers (#2428301)(2) Potentiometer (Bourns 3540S-1-103 10K +- 5% & 1K ohm #53C1)Various clampsGlue Gun (#8841)ProtractorOhaus ScaleStopwatchProcedure:For this experimental procedure, two different apparatuses were set up. One apparatus consist of a PVC pipe as the torsional spring and a weighted block of wood as the rotating mass. The second apparatus consist of an aluminum rod as a torsional spring and a block of carbon steel as the rotating mass. The apparatus design was set up according to Figure 1 from above. A potentiometer was mounted to the bottom of the rotating mass at its center of rotation. A constant voltage was then ran through the pot. As the mass rotated the pot changes the resistance, therefor changing the voltage. A Labview program was designed to record thechange in voltage over time. From this data we can estimate the natural frequency PVC/weighted wood apparatus:1. A PVC pipe was rigidly attached to a table. A wooden block was then attached to the end of the PVC pipe, at a distance of twenty-four inches. C-clamps were then used toweight the ends of the block.2. The apparatus was then calibrated. For every degree the mass rotated the voltage changed 0.001 volts. 3. The mass was then rotated and the voltage measurements were recorded.4. The frequency of the oscillating system was measured by using a stopwatch to measure the time for the system to complete 10 cycles.Aluminum/carbon steel apparatus:1. The aluminum rod was threaded into the center of the carbon steel block2. A flat was ground on the aluminum rod so that the rod could be securely clamped using a setscrew type clamp.3. The apparatus was calibrated with Labview readings. The voltage output changed by .016 V for every degree of apparatus rotation.4. The system was deflected and voltage output data was collected using Labview.5. The frequency of the oscillating system was measured by using a stopwatch to measure the time for the system to complete 10 cycles.Results:The calculated natural frequencies were calculated with the assumption that there were no damping effects on the system. The calculations for the theoretical natural frequency are in Appendix A. The datafor both PVC and metal are plotted in Appendix B. By counting the time between peaks in the data, we were able to determine the frequency of the systems as seen in Labview. Figure 6.1* The discrepancy is between experimental and calculatedFigure 6.2Conclusion:In general the data for the metal system agreed well, while there was obvious errors in the PVC data. Some of the error in the PVC data can be attributed to the methodof calculating the polar moment of inertia of the clamps. It was assumed that the clamps could be treated as a solid block at the ends of the board. Stopwatch LabView CalculatedPVC 0.56 0.625 0.406Metal 2.91 2.86 2.963Frequency (Hz)Stopwatch LabViewPVC 37.93 16.01Metal 1.79 1.69% DiscrepancyAppendix A: MathCAD CalculationsPVC apparatusWe had to calculate the moment of inertia about the rod, JPVCDPVCout0.85 inHPVC24 inDPVCin0.59 inIxDPVCoutDPVCin432IyDPVCoutDPVCin432JPVCIxIyJPVC8.973 104in4Next we had to calulated the moment of inertia on the wood plank including the masses at the end of the plankThis portion is for the boardMboard1.64 lbLboard24 inWboard3.5 inIxxboard112MboardLboard2Ixxboard78.72 lb in2Iyyboard112MboardWboard2Iyyboard1.674 lb in2JboardIxxboardIyyboardJboard80.394 lb in2Now we have to concider the massesMmass4.20 lbD 11 inJ0Mmass3.5 in( )22 in( )212JmassJ0MmassD2JtotalJboard2 JmassJtotal1.108 103lb in2GPVC5.004 105lbfin2fPVC12( )JPVCGPVCHPVCJtotalfPVC0.406 s1Stop watch calculation:Cycles 4Time 7.14 sfCyclesTimef 0.56 s1Steel apparatusWe had to calculate the moment of inertia about the rod, JPVCDrod0.249 inHrod19.09 inJrod32Drod4Jrod3.774 104in4Next we had to calulated the moment of inertia on the mass.Mst15.45 lbLst7 inWst4 inJstmass112MstLst2Wst2Jstmass83.688 lb in2Grod3.8 106lbfin2fst12( )JrodGrodHrodJstmassfst2.963 s1Stop watch calculation:Cycles 10Time 3.44 sfCyclesTimef 2.907 s1Appendix BImput Voltage vs Time(Metal Rod)00.050.10.150.20.250.30.350.40 1 2 3 4Time (s)Voltage (v)Input Voltage vs Readings(PVC Pipe)1.391.41.411.421.431.441.451.461.471.480 500 1000 1500 2000 2500 3000Data PointsVoltage
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