Detailed description of vibration displacement, velocity, acceleration

Detailed description of vibration displacement, velocity, acceleration

Vibration signals are often analysed in the condition monitoring and fault diagnosis of bearings. Commonly used quantities for vibration analysis include vibration displacement, vibration velocity and vibration acceleration.

In previous articles we have introduced the vibration displacement, velocity and acceleration signals in the vibration analysis of the selection and its principles. In fact, as long as we understand the essential meanings and differences of these three, the problem of selecting these correspondences will be solved. Therefore, this article from the vibration of the displacement, velocity, acceleration of the meaning and relationship between certain aspects of the introduction.



Definition of vibration displacement, velocity, acceleration and relationship
The figure above is a simple vibration diagram, we use this figure to illustrate some concepts.

First of all, assuming that the initial position of a point of mass for a position on the horizontal axis, when the vibration begins, the point of mass in any moment from the direction of vibration and the initial position of the distance between the difference between A is the displacement. The point of mass to reach this position all the time t, then the speed of this point of mass is A on t differential. By the same logic, the differential of the vibrational velocity of a point of mass with respect to time is the acceleration of the vibration. Conversely, the acceleration of the vibration is the integral of the velocity of the vibration with respect to time, and the velocity of the vibration is the integral of the displacement of the vibration with respect to time.

The figure above is a time domain plot of this vibration and it is easy to see that the maximum distance A of the mass from the original point in this vibration is the amplitude of the sine wave. This mass reaches its maximum velocity as it passes through position 0. The mass reaches the maximum value of acceleration at the place of the previous peak. In other words the velocity of the vibration exceeds the displacement by 90° and the acceleration of the vibration exceeds the velocity by 90°.



Why are peak-to-peak values used for vibrational displacements?

As can be seen from the previous definition, the displacement of a vibration is the distance between the point of mass in the vibration and the initial position. Throughout the time domain, the position of the vibration is constantly changing, and there is a displacement value at every moment. Of these, the distance of the mass point furthest from the initial position is the most influential for a mechanical device out of all the displacement values throughout the vibration. Also for a vibration, the maximum amount of deformation experienced by the equipment is the distance between the two peaks, which is the peak-to-peak value of this vibration displacement. In the vibration waveform shown above is the sum of the absolute values of the vibration amplitudes, on both sides of the horizontal axis. The maximum deformation of the equipment experiencing vibration has the greatest impact on the equipment itself, so when measuring the displacement value of vibration, the peak value is generally taken.

Why is the RMS value used for the speed of vibration?

In the meaning of the velocity of vibration, we introduced that the velocity of vibration is the differential of the displacement of vibration with respect to time. In physical terms, the velocity of vibration covers both the displacement and frequency of vibration. The concept of effective value is actually an equivalent concept, which equates an alternating quantity to an equivalent value. In the case of vibration, we know that the vibration velocity is a reciprocal alternating quantity, so we use an RMS equivalent of the actual value of the velocity to represent the velocity of the vibration during this period of time.

Of course there are peaks and valleys, but for a time period, the peaks and valleys of the velocity have an effect on the equipment that occurs when the peaks and valleys occur, which does not describe the overall vibration velocity, so we use an RMS equivalent.

Why are peak values used for acceleration of vibration?

The more drastic the change in the velocity of a mass in a section of vibration, the greater the effect on the material itself. Considering the effect of vibration on equipment, the peak value of the acceleration of vibration is taken as a measure of the effect of the acceleration of vibration on the equipment.

In fact, if the reader multiplies the mass of the mass point by the acceleration they will get a unit of force. It is not difficult to find that the acceleration of vibration is actually the "impact" of vibration, the maximum impact on the equipment, is the peak value of this impact.

Why use displacement signals for low speed vibration? Velocity signals for medium speed motion? High-speed motion with acceleration signals?

We know from the introduction of vibration displacement, velocity and acceleration:

The displacement of vibration takes into account the amplitude of the vibration;

The velocity of vibration takes into account the amplitude and frequency of vibration;

The acceleration of vibration takes into account the amplitude and frequency of vibration as well as the change in frequency.

Therefore, it can be found that the acceleration of vibration has the highest sensitivity to the frequency of vibration, followed by the velocity, and again by the displacement.

The above figure shows the spectra of displacement, velocity and acceleration signals for the same vibration with an amplitude of 10um. It can be clearly seen that of the same three frequency components, the acceleration signal is strong, the velocity signal is moderate and the displacement signal is not sensitive.

For rotating equipment, the acceleration is more sensitive to high-speed vibration, and the displacement signal is more suitable for low-speed vibration.

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