# General vibration concepts for the end-user

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Excessive vibration can be caused by shaking forces (“excitation forces”) that are higher than normal. For example, maybe the rotor imbalance is too high. Such shaking forces could be mechanically sourced (such as the imbalance) or hydraulically based (such as from piping pressure pulsations). They can even be electrically based (such as from uneven air gap in a motor, or from VFD harmonic pulses). In all these cases, high rotor vibration is typically just rotor increased oscillating displacement “x” in response to the shaking force “F” working against the rotor-bearing support stiffness “k”. In equation form, F = k*x, and calculating x for a given F is known as “forced response analysis”.

However, sometimes all of the shaking forces are actually reasonably low, but still excessive vibration is encountered. This can be an unfortunate circumstance during system commissioning, leading to violation of vibration specifications, particularly in variable speed systems where the chances are greater that an excitation force’s frequency will equal a natural frequency over at least part of the running speed range. This situation is known as resonance.

A key reason for performing rotordynamic analysis is to check for the possibility of resonance. Rotordynamic testing likewise should include consideration of possible resonance. In rotor vibration troubleshooting, it is recommended to first investigate imbalance, then misalignment, and then natural frequency resonance, in that order, as likely causes, unless the specific vibration vs. frequency plot (the “spectrum”) or vibration vs. time pulsations indicate other issues (some of these other issues will be discussed in some detail later).

An important concept is the "natural frequency", the number of cycles per minute that the rotor or structure will vibrate at if it is "rapped", like a tuning fork. Pump rotors and casings have many natural frequencies, some of which may be at or close to the operating speed range, thereby causing “resonance”. The vibrating pattern which results when a natural frequency is close to the running speed or some other strong force’s frequency is known as a "mode shape".

Each natural frequency has a different mode shape associated with it, and where this shape moves the most is generally the most sensitive, worst case place for an exciting force such as imbalance to be applied, but similarly is the best place to try a “fix” such as a gusset or some added mass. In resonance, the vibration energy from previous "hits" of the force come full cycle exactly when the next hit takes place. The vibration in the next cycle will then include movement due to all hits up to that point, and will be higher than it would have been for one hit alone (the principle is the same as a child’s paddle-ball). The vibration motion keeps being amplified in this way until its large motion uses up as much energy as that which is being supplied by each new hit. Unfortunately, the motion at this point is generally quite large, and is often damaging to bearings, seals, and internal running clearances (e.g. wear rings).