Explanation Given: Mass of motor is 45 kg . Static deflection is 6 mm . Unbalance equivalent mass is 110 g . Location of unbalance mass from axis is 75 mm . Amplitude of vibration is 0.25 mm . Speed of motor is 300 rpm . Concept used: Write the expression of natural frequency of system. ω n = g δ st ...... (1) Here, ω n is the natural frequency, g is the acceleration due to gravity and δ st is the static deflection. Write the expression for angular frequency of rotation. ω f = 2 π N 60 ...... (2) Here, ω f is the angular frequency of rotation and N is the speed in RPM. Write the expression for the amplitude of periodic force. P m = m ′ r ω f 2 ...... (3) Here, P m is the magnitude of unbalanced force, m ′ is the unbalance mass and r is the distance of unbalance mass from axis of rotation. Write the expression for the spring constant. k = m ω n 2 ...... (4) Here, k is the spring constant and m is the mass of motor. Write the expression for amplitude of damped vibration. x m = P m / k [ 1 − ( ω f ω n ) 2 ] 2 + [ 2 ( c c c ) ( ω f ω n ) ] 2 ...... (5) Here, x m is the maximum vibration, c is the damping coefficient and c c is the critical damping coefficient. Calculation: Substitute 9.81 m/s 2 for g and 6 mm for δ st in equation (1). ω n = 9.81 6 mm ( 1 m 1000 mm ) = 40.435 rad/s Substitute 300 rpm for N in equation (2). ω f = 2 π ( 300 ) 60 = 31 To determine (b) Coefficient of damping c .

Vector Mechanics for Engineers: Dynamics

11th Edition

ISBN: 9780077687342

Author: Ferdinand P. Beer, E. Russell Johnston Jr., Phillip J. Cornwell, Brian Self

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…

Question

Chapter 19.5, Problem 19.145P

To determine

(a)

The damping factor c/cc.

To determine

(b)

Coefficient of damping c.

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Chapter 19.5, Problem 19.144P

Chapter 19.5, Problem 19.146P

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