ME_375_Lab_Report__2 - ME 375 VIBRATIONS LABORATORY Lab...

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ME 375 – VIBRATIONS LABORATORY __________________________ Lab Report Two October 11th, 2007 Section 2 Group 3 Submitted by: Sheyla M Matos-Camacho Submitted to: Chris Hudson (TA) Partners: John Fake Hoang Nguyen
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I. INTRODUCTION During the past four weeks, the experiments in the laboratory was targeted examine the response of a single degree of freedom vibratory system given the initial conditions (velocity and displacement) and compared them to the experimental data. The two mechanical systems studied were the translational and torsional, for which the governing differential equation of motion was developed using the physical characteristics and a dynamic response of the system to initial displacement. The experiments covered free vibration for a linear viscous and coulomb friction damping for single degree of freedom systems; acquisition of data for translational test stand; data comparison for the translational test stand; data acquisition for the torsional test stand and the finally data comparison for the torsional test stand. This report demonstrates the linearity for translational system and non-linearity for torsional systems. Through the use of MATLAB® and the model created through Simulink®, a more accurate comparison for the data acquired. The calculations performed include the log decrement, the coulomb friction (or dissipative force) from the equation shown in the appendix, mass, volume for the torsional disk, angle, voltage and the calibration factor. The graphs shown also include the analytical or simulated against the measured data. Figure1. a) Translational systems and b) rotational system For the translational system the linear differential equation of motion is given by: 0 = + + kx x c x M This equation may also be written as: 0 2 2 = + + x x x n n ϖ ζϖ Where: M = Mass c = damping coefficient k = spring constant ζ = damping ratio ϖ n = undamped natural frequency For the rotational system the linear differential equation of motion is given by:
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0 = + + θ θ θ Kt Ff J This equation may also be written as: 0 2 2 = + + θ ϖ θ ζϖ θ n n Where: J = Mass moment of inertia F f = damping coefficient K t = torsional spring constant ζ = damping ratio ϖ n = undamped natural frequency
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II. Results For the second group of experiments, the first week evaluated the data acquisition for the translational system. The top transducer calibration factor was calculated to be 0.3886V/mm. The period for the cycle was taken from the graph in figure 3, to be .14 s. The graph also demonstrated that the system decay was under the natural frequency ω n , similarly the stiffness was calculated to be 886.3 N/m with a mass of 0.44 kg. It was expected that our damping ratio ξ was less than one and equal to 0.0552 giving then a damping coefficient of 2.18 N-s/m. The damping ratio of a physical system may be determined from experimental data using the log- decrement method shown in Figure 1. The translational data was acquired from SigLab’s function vos.
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