What is a vibration of (1.2 G’s at 7,100 cpm) converted down to velocity?

Question

stuck on this question on vibration analysis

 

Answer 1

Adrian, first of all you need to write an equation for given vibration in G's in which is acceleration. The equation is in the form of A*cos(ω*t) representing a simple vibration with one frequency.  Where ω=2*pi*f and t=time.   

 

1 G= 9.8m/s  Hence, A=1.2 G's = 1.2*9.8=11.76 m/s². This is the amplitude of the acceleration curve.

 

7100 cpm means 7100 cycles per minute. Need to convert it to the number of cycles per second in which is f.

 

f=7100 cpm* 1Hz/60cpm=118.3 Hz

 

ω=2*pi*118.3≅744 rad/s

 

Therefore a(t)=11.76*cos(744*t) in which is the acceleration curve. To convert it to velocity, just take the integral with respect to time.

 

v(t)=∫a(t)dt = A/ω*sin(ω*t)=11.76/744*sin(744*t)

v(t)=0.0158*sin(744*t)

 

Note: Vibration analysis is a study of harmonics. For this problem, it is simple harmonics.