Resonance

 Examples of highly resonant mechanical systems are bells and tuning forks. Resonance is an operating condition where an excitation frequency is near a natural frequency of the machine structure. A natural frequency is a frequency at which a structure will vibrate if deflected and then let go. A typical structure will have many natural frequencies. When resonance occurs, the resulting vibration levels can be very high and can cause rapid damage. Under no circumstances should a machine be operated at a speed corresponding to a resonance! In a machine that produces a broad spectrum of vibration energy, a resonance shows up in the vibration spectrum as a peak whose frequency is constant even as the machine speed is varied. The peak may be quite sharp, or may be broad; depending on the amount of effective damping the structure has at the frequency in question. In order to determine if a machine has prominent resonances, one of several tests can be performed to find them:

The "Bump Test" -- The machine is impacted with a heavy mass such as a wooden four by four or the booted heel of the foot of a football player while recording vibration data. If a resonance is there, the machine vibration will be at the natural frequency as it dies away.

The "Run Up" or "Coast Down" -- The machine is turned on, or turned off, while taking vibration data and tachometer data. The time wave form will show maxima when the RPM matches natural frequencies.

"Variable Speed Test" -- With a machine whose speed can be varied over a wide range, the speed can be varied while taking vibration and tachometer data. The data are interpreted as in the run up test.

The figure below shows an idealized response curve of a mechanical resonance. The behavior of a resonant system when subjected to an external force is interesting and somewhat counter intuitive. It depends strongly on the frequency of the excitation force. If the forcing frequency is lower than the natural frequency -- in other words to the left of the peak -- then the system behaves like a spring, and the displacement is proportional to the force. The spring of the spring-mass combination making up the resonant system is dominant in determining the response of the system. In this spring-controlled region, the system behaves in agreement with our intuition, responding with greater motion as greater force is applied to it, and the motion is in phase with the force.

In the region above the natural frequency, the situation is different. Here, the mass is the controlling element, and the system looks like a mass to an input force. This means its acceleration is proportional to the applied force, and the displacement is relatively constant with changing frequency. The displacement is out of phase with the force in this region -- when you push against the system, it moves toward you and vice versa!

At the resonance itself, the system looks completely different to an applied force. Here, the mass and spring elements effectively cancel each other out, and the force sees only the damping, or friction, in the system. If the system is lightly damped, it is like pushing on air. When you push on it, it recedes from you on its own. Consequently, you cannot apply much force to the system at resonance, and if you continue to try, the vibration amplitude builds up to very high values. It is the damping that controls the motion of a resonant system at its natural frequency.

Examples of resonances in machines are the so-called critical frequencies of rotating shafts.

The phase angle between the excitation source vibration and the response of the structure is always 90 degrees at the natural frequency

In the case of long rotors such as turbines, the natural frequencies are called "critical frequencies" or "critical speeds," and care must be taken that these machines are not operated at speeds where 1X or 2X correspond to these critical frequencies.

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