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

See similar textbooks

Concept explainers

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.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 19.5, Problem 19.144P

Chapter 19.5, Problem 19.146P

Students have asked these similar questions

A 36-lb motor is bolted to a light horizontal beam that has a static deflection of 0.075 in. due to the weight of the motor. Knowing that the unbalance of the rotor is equivalent to a weight of 0.64 oz located 6.25 in. from the axis of rotation, determine the amplitude of the vibration of the motor at a speed of 900 rpm, assuming (a ) that no damping is present, (b ) that the damping factor c/cc is equal to 0.055.

A 2-kg block is supported by a spring with a constant of k= 128 N/m and a dashpot with a coefficient of viscous damping of c=0.6 N.s/m. The block is in equilibrium when it is struck from below by a hammer that imparts to the block an upward velocity of 0.4 m/s. Determine (a) the logarithmic decrement,(b) the maximum upward displacement of the block from equilibrium after two cycles.

In the case of the forced vibration of a system, determine the range of values of the damping factor c/cc for which the magnification factor will always decrease as the frequency ratio wf/wn increases.

Chapter 19 Solutions

Vector Mechanics for Engineers: Dynamics

Ch. 19.1 - A particle moves in simple harmonic motion....Ch. 19.1 - A particle moves in simple harmonic motion....Ch. 19.1 - Prob. 19.3P Ch. 19.1 - Prob. 19.4P Ch. 19.1 - Prob. 19.5P Ch. 19.1 - Prob. 19.6P Ch. 19.1 - A simple pendulum consisting of a bob attached to...Ch. 19.1 - A simple pendulum consisting of a bob attached to...Ch. 19.1 - A 10-Ib block A rests on a 40-Ib plate B that is...Ch. 19.1 - A 5-kg fragile glass vase is surrounded by packing...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.