GVSU EGR 345  EGR 345 Lab 10  Torsion (2 pages)
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EGR 345 Lab 10  Torsion
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Lecture Notes
 Pages:
 2
 School:
 Grand Valley State University
 Course:
 Egr 345  Dynamic System Modeling and Control
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egr345 lab guide 4 1 4 0 1 Lab 10 Torsion 4 0 1 1 Purpose To predicat and experimentally verify the period of oscillation for a torsional pendulum 4 0 1 2 Background Theory Suppose a large symmetric rotating mass has a rotational inertia J and a twisting rod has a torsional spring coefficient K Recall the basic torsional relationships d 2 T T J J dt T K K 0 We can calculate the torsional spring coefficient using the basic mechanics of materials JG T L Finally consider the rotating mass on the end of a torsional rod d1 h1 J 1 G d 2 T J L dt h2 d2 egr345 lab guide 4 2 4 0 1 3 Prelab 1 Calculate the equation for the natural frequency for a rotating mass with a torsional spring 2 Set up a Mathcad sheet that will accept material properties and a diameter of a round shaft and determine the spring coefficient accept geometry for a rectangular mass and calculate the polar moment of inertia use the spring coefficient and polar moment of inertia to estimate the natural frequency use previous values to estimate the oscillations using Runge Kutta plot the function derived using the homogeneous and particular solutions 4 0 1 4 Equipment Computer with 4 0 1 5 Experimental 1 1 Calibrate the potentiometer so that the relationship between the output voltage and angle is known Plot this on a graph and verify that it is linear before connecting it to the mass 2 Set up the apparatus and connect the potentiometer to the mass Apply a static torque and measure the deflected position Use this to calculate a coefficient for the torsional spring 3 Apply a torque to offset the mass and release it so that it oscillates Estimate the natural frequency by counting cycles over a long period of time 4 Set up LabVIEW to measure the angular position of the large mass The angular position of the mass will be measured with a potentiometer 5 Determine if the initial angle of deflection changes the frequency of oscillation 6 Compare the theoretical and experimental values
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