Resonance is simply the natural frequency of a component or combination of components (assembly). All structures have a resonant frequency. If you impact the structure with enough force to make it move, it will vibrate briefly at its natural frequency. A structure will have a resonant frequency in each of its 3 directional planes (x, y and z, or as we call them, horizontal, vertical and axial). Resonance serves to amplify the vibration due to whatever vibration force is present at (or near) that resonant frequency. It is important to note that resonance does not cause vibration - it amplifies it. 
Resonance problems occur in two primary forms. They are:
Critical speeds - occurs when a component rotates at its own natural frequency. 
  • A "critical speed" is simply when the rotational speed (rpm) coincides with the natural frequency of the rotor (cpm).
  • The tiniest amount of residual unbalance (something that is always present) is enough to cause huge amounts of vibration when rotating at a critical.
  • Rotors that are sped up or slowed down slowly are susceptible to this (i.e. turbines). In these cases, the critical speed is usually well known.
  • The most common problem related to unknown critical speeds is probably belts. Belts rotating at their resonant frequency (or having a nearby source of excitation of that resonant frequency) can vibrate excessively and cause other problems. For example, if the natural frequency of the belts coincides with the rpm of the fan, the belts will vibrate at their natural frequency.
  • 2nd and 3rd criticals also may occur if the rotor speed gets high enough.
Structural resonances - This is far more common than a critical speed problem. It becomes a problem when some forcing frequency comes close (+/- 10%) to the resonant (natural) frequency of a structure.
  • The structure can be the machine housing itself or some nearby structure such as a hand rail or I-beam.
  • A common example of this is a vertical pump. Due to the lack of a support at the top of the unit, these typically have very low resonant frequencies (~ 300 cpm). While running, this is not a problem but during start-up or coast-down, the unit experiences a "shudder" as it passes through the structural resonance (this is not a critical speed - it is a structural resonant frequency).
  • The structure itself will vibrate excessively - do not confuse with a critical speed.
  • The "shape" of the structure's vibration is an important clue and is known as a "mode shape".
  • Testing for the structure's natural frequency is crucial (required) to confirming a resonance problem.
Resonance, once diagnosed, can be simple to correct. It can also be extremely complex and difficult
to correct. The trick is in the diagnosis. But how do you diagnose it ? 
One method for determining a critical speed is a "Coast Down/Start Up Plot". This plot consists of the 1x vibration amplitude being collected simultaneously with a 1x rpm phase reading as the machine coasts to a stop or goes from stopped to full running speed. This test requires a 1x rpm reference (from a photoeye or some other speed tracking signal) in order to track the amplitude and phase at that frequency. Two things are observed as the rotor passes through a critical:
  • The 1x rpm amplitude will increase until the rotor reaches it's critical and then decrease to the normal level as the speed continues to change.
  • Phase will shift 180° as the rotor passes through the critical. This is due to the rotor changing from a rigid rotor (while operating below it's critical) to a flexible rotor (while operating above it's critical). It practical terms, on a rigid rotor, the heavy spot pulls the rotor around as it rotates. On a flexible rotor, the heavy spot pushes the rotor around as it rotates.
Structural resonances can be first suspected by several characteristics:
  • Disproportionately high amplitude at a single frequency (the resonant frequency) in the direction in which the resonant frequency is being excited.
  • A "mode shape" analysis shows the structure vibrating in a way that models resonance. Those models are covered on the next page.
Neither of those characteristics confirms resonance as a problem. A test must be performed that actually determines the natural frequency of the structure in question - a "bump test". Although there are high-tech methods available for this test (and some work very well), this test can be as simple as bumping the structure (causing it to vibrate) while it is not running and measuring the response (i.e. the frequency it vibrates at). A simple method for doing this involves collecting a 2 second sample (time domain plot) while bumping the structure, measuring the period of one cycle and converting it to a frequency. The time sample may have to be adjusted depending on the resonant frequency being measured (longer sample for very low resonant frequencies, shorter sample for high frequencies).
If the measured response of the structure (i.e. it's resonant frequency) is within about 10% of the forcing frequency (i.e. the rpm of the machine although it can be at any frequency), resonance should be considered a problem. The closer the two frequencies are, the more of a problem it is.
To correct a resonance problem, there are 4 methods:
  • Stiffen the structure - This method raises the resonant frequency of the structure. 
  • Add mass to the structure - This method lowers the resonant frequency.
  • Change exciting frequency - Change the speed of the machine.
  • Add a dynamic absorber to the structure - This method attaches the equivalent of a tuning fork to the structure. This attachment is tuned to have the same resonant frequency as the structure and sets up an out-of-phase signal that has the effect of cancelling out (reducing) the signal being generated by the structure. The dynamic absorber must be properly sized to handle the forces being generated.