The nature of vibration

A lot can be learned about a machine’s condition and possible mechanical problems by
noting its vibration characteristics. We can now learn the characteristics, which characterize a vibration signal. Referring back to the mass-spring body, we can study the characteristics of vibration by plotting the movement of the mass with respect to time.

The sign wave shown is represents one complete cycle, that is the weight moved from its rest position to its upper limit back through its rest position to its lower limit and then returned to its rest position. Continued vibration of this spring mass system would only repeat the characteristics shown in this single cycle.
This one cycle of motion contains all the information necessary to measure the vibration of this system. Continued motion of the mass will simply repeat the same cycle. This motion is called periodic and harmonic
Some of the characteristics of this vibratory motion are PERIOD, FREQUENCY, DISPLACEMENT, VELOCITY, ACCELERATION, AMPLITUDE and PHASE.

PERIOD
The period of the vibration, represented by the letter T, is the time required to complete one oscillation. That is the total time required for the mass to move from the rest position to the upper limit, back through the rest position to the lower limit, and return to the rest position .

FREQUENCY
Frequency is the number of complete oscillations completed in a unit time, or simply expressed as 1/T. Generally it is measured express frequency in terms of cycles per minute, since we measure the rotational speed of machinery in revolutions per minute. This allows examination of the vibration frequency in terms of multiples of the rotational speed. The two times rotational speed is known as the second harmonic, and the three times rotational speed is the third harmonic. Rotational speed is also known as the fundamental frequency.

DISPLACEMENT
The displacement of the mass can be seen. The peak-to-peak distance is measured from the upper limit to the lower limit, and is usually measured in mils or thousandths
of an inch (.001 inch). In the metric system, the displacement is measured in microns or millionths of a meter (.000001 meter or .001 millimeter).

VELOCITY
The velocity of a vibrating object is continually changing. At the upper and lower limits, the object stops and reverses its direction of travel, thus its velocity at these two points is zero. While passing through the neutral or position of rest, the velocity is at its maximum. Since the velocity is continually changing with respect to time, the peak or maximum velocity is always measured and commonly expressed in inches-per-second peak. In the metric system, vibration velocity is measured in meters per second peak. When expressing the vibration characteristic in terms of velocity, both the displacement and frequency are considered. Remember velocity is inches-per-second, and thus the displacement [inches] and the frequency [times per second] are considered.

ACCELERATION
Acceleration is the rate of change of velocity with respect to time. It can also be expressed as the rate of change in distance with respect to time, with respect to time. That is it is the change in displacement with respect to time squared. Normally, vibration acceleration is measured in terms of G’s or number of times the normal force due to gravity. Gravitational force has been standardized as 32.1739 feet per second per second or 386.087 inches per second per second. In the metric system, the standard for gravity is 980.665 centimeters per second per second. Once again, acceleration is measured as G’s peak.

PHASE
Phase is the position of a vibrating object with respect to another object at a given point in time.