# Resonance (Electric Motors)

3.14.5
Every mechanical object has properties of mass, stiffness, and damping which determine its natural frequency of oscillation. Mass is the volume of the material times its
density. Stiffness depends on the elasticity of the material. Damping is a measure of the ability of the system to dissipate vibratory energy.
The natural frequency is directly proportional to the stiffness and inversely proportional to the mass. This is the frequency at which the object will tend to self-vibrate when rung by an impact.
Materials such as soft rubber have a high level of damping and a low stiffness and tend to absorb and dissipate vibration. Most hard materials have a higher stiffness and a lower level of damping. The damping factor determines the rate of energy loss to the surroundings. The damping factor is a nonlinear parameter and changes with speed. For a given structure, there is a frequency at which the damping factor approaches zero and therefore very little vibration energy is absorbed.
Resonance and critical speeds are frequencies that are governed by natural frequencies, damping, and vibratory forces. A resonance is a condition in a structure in which the frequency of a vibratory force, such as mass unbalance, is equal to a natural frequency of the system. If the vibratory force is caused by a rotating part, the resonance is called a critical speed.
A structure or object can be excited by one or more vibratory forces. Vibratory forces can be caused by various factors, including design, installation, manufacture, and wear, or the force can have a single constant frequency, as occurs with mass unbalance.
A rotational assembly with any finite unbalance acts as a vibration exciter and will produce a force as it is rotated. This is called the excitation frequency. When the natural frequency and the excitation frequency coincide, a state of resonance is said to exist. As rotational speed approaches the resonant frequency, the effects of the force increases. At resonant frequency, vibration amplitudes can become very large. If the rate of speed is close to the resonant frequency, a very low level of unbalance can still generate unacceptable vibration amplitudes.
As rotational speed reaches the resonant frequency, the support structure will vibrate directly with the exciting force (phase shift = 0°). As the speed increases nearer to resonance, the phase begins to shift until at resonance there is a 90° phase shift. As the rotational speed continues to increase, the phase continues to change until it reaches opposition (phase shift = 180°).
Balancing requires an exact knowledge of both the magnitude and the location of the unbalance, and so balancing speeds close to resonance are to be avoided. A small speed change will cause a large change in both the amount and the angle of the measured signal, and the results will be incorrect.
Sometimes equipment is designed to emphasize the resonant frequency. A tuning fork or piano string produces strong vibrations at the resonant frequency, which is beneficial; however, this is not the case with a stiff rotor, where the exact opposite condition is needed.
Vibrations that have large amplitudes can cause early fatigue failure. The energy expended by such vibrations causes significant power loss and speed reduction. In addition, noise levels from the vibration may be irritating to the operator as well as detrimental to the components surrounding the bearings.
It follows from this that as speeds and densities increase, keeping resonance away from the operating speed is a crucial part of the assembly designer’s job. Ensuring that balancing speeds and tool design avoid resonance is a crucial part of the balancing-machine and tooling manufacturers’ jobs.

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