# Vibration with velocity and acceleration.

• cams
In summary, the conversation discussed how to calculate the velocity and acceleration of a machine vibrating at 6,000 rpm with a displacement of 1 mil Pk-Pk. The formula for displacement is velocity divided by (Pi x frequency). The units should be in SI for accurate results. The formula for acceleration is the derivative of velocity with respect to time. Pi is equal to 3.14 and frequency can be converted to Hz by dividing the RPM by 60. The maximum acceleration is equal to the maximum velocity multiplied by the frequency. It was also mentioned that the displacement should be converted to mm for the required units. For sinusoidal vibration at 6,000 cpm, the velocity would be 5,642 mm/s rms and

#### 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 anybody provide me the formulas?

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

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

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

will wait for somebody help us

Displacement = Velocity / (Pi x frequency)

Stick to SI units and you'll be ok.

Acceleration is the derivative of velocity with respect to time.

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.

brewnog said:
Displacement = Velocity / (Pi x frequency)

Stick to SI units and you'll be ok.

Acceleration is the derivative of velocity with respect to time.

what is pi mean?

freq=6000

displacement= 1 mil pk to pk

where is the acceleration?

Pi = 3.14

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

what is a standard unit for them?

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

rbeale98 said:
you need to convert your frequency into Hz, which is rotations per second. So divide your RPM by 60.

so

frequency =3600/60=60 HZ

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

now how i can calculate the acceleration?

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).

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

what is a standard unit for them?

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.

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 :-) )

cams said:
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 anybody provide me the formulas?

## 1. What is vibration with velocity and acceleration?

Vibration with velocity and acceleration refers to the movement of an object or system in a repeating pattern around a fixed point. Velocity is the speed at which the object is moving, while acceleration is the rate at which the velocity is changing.

## 2. How is vibration with velocity and acceleration measured?

Vibration with velocity and acceleration can be measured using a variety of instruments such as accelerometers and seismographs. These devices measure the movement and changes in velocity and acceleration of an object or system over time.

## 3. What are the factors that affect vibration with velocity and acceleration?

There are several factors that can affect vibration with velocity and acceleration, including the mass of the object or system, the stiffness of the material, and the frequency of the vibration. Additionally, external forces such as wind or earthquakes can also impact vibration.

## 4. What are some examples of vibration with velocity and acceleration?

Vibration with velocity and acceleration can be seen in many natural phenomena, such as the movement of tectonic plates, earthquakes, and ocean waves. It is also commonly observed in man-made structures, such as buildings, bridges, and machines.

## 5. How is vibration with velocity and acceleration used in science and engineering?

Vibration with velocity and acceleration is an important concept in science and engineering, as it helps us understand the behavior and stability of various systems. It is used in fields such as seismology, aerospace engineering, and mechanical engineering to design and analyze structures and machines for optimal performance and safety.

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