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Unformatted text preview: 2- 39 Problems and Solutions Section 2.5(2.51 through 2.58) 2.51A lathe can be modeled as an electric motor mounted on a steel table. The table plus the motor have a mass of 50 kg. The rotating parts of the lathe have a mass of 5 kg at a distance 0.1 m from the center. The damping ratio of the system is measured to be != 0.06 (viscous damping) and its natural frequency is 7.5 Hz. Calculate the amplitude of the steady-state displacement of the motor, assuming r!= 30 Hz. Soltuion: Given: m= 50 kg, 5=om, e= 0.1m, 06.=!, !n=7.5Hz Let !r=30 Hz So, r=!r!n=4From Equation (2.84), 22222222)]4)(06.(2[)41(450)1.)(5()2()1(!+!=+!=rrrmemXo"X= 0.011m X = 1.1 cm 2.52The system of Figure 2.18 produces a forced oscillation of varying frequency. As the frequency is changed, it is noted that at resonance, the amplitude of the displacement is 10 mm. As the frequency is increased several decades past resonance the amplitude of the displacement remains fixed at 1 mm. Estimate the damping ratio for the system. Solution: Equation (2.84) is 2222)2()1(rrrmemXo!+"=At resonance, X= 10 mm = !21memo!2110=emmoWhen ris very large, 1=emXmoand X= 1 mm, so 1=emmoTherefore, 10(1) = !...
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This note was uploaded on 03/31/2009 for the course MECHANICAL MAE351 taught by Professor J.g.lee during the Spring '09 term at Korea Advanced Institute of Science and Technology.
- Spring '09