Detailed description of bearing vibration displacement, speed and acceleration

In the condition monitoring and fault diagnosis of bearings, vibration signals are often used for analysis. Quantities commonly used in vibration analysis include vibration displacement, vibration speed and vibration acceleration.

In previous articles, we introduced the selection and principles of vibration displacement, velocity, and acceleration signals in vibration analysis. In fact, as long as you understand the essential meaning and differences of these three, these corresponding selection problems will be easily solved. Therefore, this article will give a certain introduction from the meaning and relationship of vibration displacement, velocity and acceleration.

Definitions and relationships of vibration displacement, velocity, and acceleration

First, assume that the initial position of a particle is a position on the horizontal axis. After the vibration starts, the distance difference A between the particle in the vibration direction and the initial position at any time is the displacement. It takes t all the time for the particle to reach this position, then the velocity of the particle at this time is the differential of A with respect to t. With the same logic, the differential of the particle vibration velocity with respect to time is the acceleration of the vibration. On the contrary, the acceleration of vibration is the integral of vibration velocity over time, and the velocity of vibration is the integral of vibration displacement over time.

In vibration, the maximum distance A between the particle and the original point is the amplitude of the sine wave. When this particle passes through the 0 position, its speed reaches its maximum value. The particle reaches the maximum value of acceleration at the previous peak. In other words, the vibration speed leads the displacement by 90°, and the vibration acceleration leads the speed by 90°.

Why is peak-to-peak value used for vibration displacement?

As can be seen from the previous definition, the displacement of vibration is the distance between the particle 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 each moment. Among them, the farthest distance between the particle and the initial position has the greatest impact on mechanical equipment among all displacement values of the entire vibration. At the same time, for a vibration, the maximum deformation experienced by the equipment is the distance between the two peak values, which is the peak-to-peak value of the vibration displacement. In the vibration waveform in the above figure, it 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. Therefore, when measuring the displacement value of vibration, the peak-to-peak value is generally taken.

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

In the meaning of vibration speed, we introduced that the differential of the vibration displacement with respect to time is the vibration speed. From a physical meaning, the speed of vibration covers two factors: 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. For vibration, we know that the vibration speed is a reciprocating alternating variable, so we use an effective equivalent speed actual value to represent the vibration speed during this period.

Of course, the speed value also has peak and peak values, but for a period of time, the impact of the peak value of the speed on the equipment occurs when the peak value appears, and it is impossible to describe the overall vibration speed, so we use the effective value to equate it.

Why is the peak value used for vibration acceleration?

During a period of vibration, the more drastic the change in particle velocity, the greater the impact on the material itself. Considering the impact of vibration on equipment, the peak value of vibration acceleration is taken to measure the impact of vibration acceleration on equipment.

In fact, if you multiply the mass of a particle by its acceleration, you 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.

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