Explanation Given: Weight of motor is 400 lb . Equivalent Spring constant is 1200 lb/in . . Unbalance mass of rotor is 1 -oz . Distance of unbalance mass from axis is 8 in . . Amplitude of vibration is 0.06 in . . Concept used: Write the expression for amplitude of vibration for the rotating unbalance mass system of motor as per the given condition. x m ≥ r ( m M ) ( ω f 2 ω n 2 ) 1 − ( ω f 2 ω n 2 ) ...... (1) Here, x m is the magnitude of maximum amplitude of vibration, r is the distance between the unbalance mass from axis of rotation, ω n is the natural circular frequency of system, ω f is forced frequency of rotation, m is the unbalance mass of rotor and M is the mass of motor. Divide equation (1) by ( ω f 2 ω n 2 ) . x m ≥ r ( m M ) 1 ( ω f 2 ω n 2 ) − 1 ...... (2) Write the expression for natural circular frequency of system. ω n = k M ...... (3) Here, k is the equivalent stiffness of spring. Calculation: Substitute 1200 lb/in . for k and 400 lb 32.2 ft/s 2 for M in equation (3). ω n = 1200 lb/in ( 12 in/1 ft ) ( 400 / 32.2 ) lb-s 2 /ft = 34.047 rad/s In-Phase motion: Substitute 0.06 in for x m , 8 in . for r , 1 -oz for m , 400 lb 32.2 ft/s 2 for M and 34.047 rad/s 2 for ω n in equation (1). 0.06 in . ( 1 ft 12 in . ) ≥ ( 8 in . ( 1 ft 12 in . ) ) [ ( 1 -oz ( 1 lb 16 -oz ) ( 1 32.2 ft/s 2 ) 400 32.2 ) ( ω f 2 ( 34.047 ) 2 ) ] 1 − ( ω f 2 ( 34.047 ) 2 ) ( ω f 2 ( 34

12th Edition

ISBN: 9781259977305

Author: BEER, Ferdinand P. (ferdinand Pierre), Johnston, E. Russell (elwood Russell), Cornwell, Phillip J., SELF, Brian P.

Publisher: Mcgraw-hill Education,

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Free Damped Vibrations

Free vibration is a type of vibration in which the external force is removed after giving the initial displacement to a body/system. In other words, in this type of vibration, force is applied at the initial displacement of the system, and after the init…

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Chapter 19.4, Problem 19.116P

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The range of allowable values of motor speed.

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Chapter 19.4, Problem 19.115P

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The range of allowable values of motor speed.

Solution Summary: The author explains the range of allowable values of motor speed and the amplitude of vibration for the rotating unbalance mass system.

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The range of allowable values of motor speed.

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