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## Section 10, Vibration Phase Relative to Resonance

If a force is slowly applied to a spring system, the force and its resulting deflection will move in the same direction at the same time, or "in phase" with each other. If a vibrating force is applied to the same object or "spring system," and if the frequency of that vibrating force is below the critical speed range or resonance range, then the force and resulting deflection will remain in phase. However, when the vibration frequency enters the resonance frequency or the critical speed range, the force starts to precede the resulting deflection. The resulting deflection will time-lag the force. When the vibration frequency reaches the actual critical speed or resonance frequency, the force will precede the deflection by 90°. As the frequency increases further, the force increases its lead until the force finally precedes the resultant deflection by 180°. The 180° relationship will remain the same for all frequencies above the resonant frequency range, until the second resonance frequency range is approached. Then the process starts all over again with another phase angle reversal, and so on. This phenomenon is shown in the resonance diagram of a rotor's vibration amplitude and phase relative to resonance of some part, such as the rotor support system, part of a steel base or beam, or more rarely, resonance of the rotor itself.

To be able to visualize this phenomenon using a very practical illustration, assume that the circles represent a "perfectly" round rotor shaft. The heavy dot represents the angular position of unbalance in the rotor. The marker represents where the marks (or deflection) will occur relative to the unbalance force, at frequencies below, at, and above the resonance speed. The arbitrary reference mark represents what will be seen via a vibration instrument that reveals phase through a strobelight. The marker represents the angle at which it will scribe a mark on the shaft's "highspot." (Before electronic instruments were available, phase was indicated in this way.)

This explains why balancing with an electronic instrument will give certain phase angle readings in one situation and a complete reversal in another. If all the readings are taken below the resonant speed range, readings will be consistent from one rotor or machine to another, even when they are of very different construction. "Above resonance" readings from one machine to another will also be consistent with each other.

Below the resonance speed range, the rotor is still trying to rotate about the geometric centerline of the shaft, but it is being forced off center by the centrifugal force due to unbalance (causing a vibration). However, above the resonance speed range, the rotor rotates not about its geometric centerline, but about the rotor's center-of-mass. For all practical purposes, rotation about the center-of-mass occurs from a frequency that is approximately above the resonance speed range on up. Increasing the speed still further will not appreciably change this condition, except for a very gradual diminishing displacement amplitude, until the next resonance range is approached.

The various resonance ranges can be due to the rotor's or some non-rotating part's 1st, 2nd, 3rd, or 4th resonances. However, it more likely to go through, for example, the 1st resonance of the machine's deck; the next resonance due to the 1st resonance of the rotor's support pedestal, followed by a 1st resonance of a span of the attached pipe.

Although the resonance speed range varies from machine part to machine part, depending on several variables, it is safe to assume that for medium speed machines (below approximately 4000 rpm) the resonance range starts at approximately 20 percent below the resonance peak and continues on to approximately 20 percent above the peak. To be safe, many specialists suggest that a machine's vibration frequency (especially running speed) should be at least 25 percent away from the peak resonance frequency.

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