# Vibration with velocity and acceleration.

1. Feb 15, 2009

### cams

if we have a machine is running at 6,000 rpm. It is vibrating at 1 mil Pk-Pk. Calculate the velocity & acceleration of the vibration in mm/s & mm/S2. Explain the calculation.

can any body provide me the formulas?

2. Feb 15, 2009

### Cyrus

I have no idea, but I would like to see the answer posted once you find it.

3. Feb 15, 2009

### cams

i try to find the answer by searching in internet but no answer is found.

will wait for somebody help us

4. Feb 15, 2009

### brewnog

Displacement = Velocity / (Pi x frequency)

Stick to SI units and you'll be ok.

Acceleration is the derivative of velocity with respect to time.

5. Feb 15, 2009

### FredGarvin

These kinds of questions assume that the vibration is a single frequency and are in a sin wave. That should give you all the information you need. You have the frequency and the peak amplitude, i.e. displacement.

6. Feb 15, 2009

### cams

what is pi mean?

freq=6000

displacement= 1 mil pk to pk

where is the acceleration?

7. Feb 15, 2009

### dlgoff

Pi = 3.14

8. Feb 15, 2009

### cams

if the unit of displacement is 1 mil what will be the RPM for frequency?

what is a standard unit for them?

9. Feb 15, 2009

### rbeale98

you need to convert your frequency into Hz, which is rotations per second. So divide your RPM by 60.

10. Feb 25, 2009

### cams

so

frequency =3600/60=60 HZ

velocity= 1*3.16*60=189.6 m/s

now how i can calculate the acceleration?

11. Feb 25, 2009

### minger

That is maximum velocity. The maximum acceleration will be the derivative of the velocity, i.e. if:
$$v = A\sin(Bt)$$
Then,
$$a = AB\cos(Bt)$$
In other words, your maximum accleration will be the maximum velocity times the frequency (by way of chain rule).

12. Feb 27, 2009

### Dr.D

The displacement was given as 1 mil p-p, which means 0.0005 inches 0 to peak. If you are going to work in SI, this dimension in inches has to be converted to meters. There is no need to work in SI, since working in inches will be just as good, but you need to be aware of what your units are. Also, it did not look to me like you had accounted for the fact that you want only half of the peak-to-peak value when you want to describe the amplitude of the displacement sinusoid.

PS: Since your requirement specified that you want velocity and acceleration in mm/s and mm/s^2, then it is in fact necessary to convert this dimension to mm.

13. Apr 5, 2009

### onlinevib

In short, assuming pure sinusoidal vibration at 6.000cpm (pure unbalance, for example):

velocity: 5,642 mm/s rms
displacement: 3545 mm/s2 rms

Rms values are those commonly used in ISO standards, for pk or pk-pk values you would have to multiply by sqrt(2) and 2*sqrt(2) respectively.

Formulas are derived from the fact that velocity is the integral of acceleration and displacement the integral of velocity, and assuming sinusoidal vibration at one single frequency* , I've compiled them, with an online calculator to do these conversions in: http://onlinevib.synthasite.com/Vibration-calculator.php

Hope this helps!

* In fact, you are also assuming zero mean acceleration, velocity and displacement, i.e. the machine vibrates around an equilibrium point and does not move around (if it moves from its foundation you'd better turn it off :-) )

14. Apr 5, 2009

### andresdelsol

what a great answers!

15. Jan 16, 2012