Pumps & Systems, November 2008

Mechanical resonance occurs when an external source amplifies the vibration level of a mass or structure at its natural frequency. For a rotating mass like a motor or a pump, this occurs at the critical speed(s). Electrical resonance amplifies the magnitude of voltage or current, or both.

The increase in amplitude, whether mechanical or electrical, places more stress on motor and pump components, negatively affects operation (e.g., increased vibration, instability and energy consumption) and leads to premature failure.

Fed by an external energy source, resonance may continue increasing in magnitude until a fault occurs. Mechanical resonance can break motor, drive and pump components; electrical resonance can cause motor windings to fail. This article discusses both types of resonance and provides solutions for each.

## Mechanical System Resonance

The motor and load-such as a pump-comprise a "two-mass system" and are usually connected by power transmission devices such as gearboxes, belts and couplings. As Figure 1 illustrates, each of these connecting components twists slightly like a spring when the motor applies torque. Mechanical system resonance, which can occur if any natural frequencies are within the speed range, is typically caused by compliance ("springiness" or lack of stiffness) between a motor and its load. Evidence of the problem includes increased vibration at a natural frequency. The motor may also emit a pure tone like that of a tuning fork, start "growling" or become unstable.

Every two-mass system has at least one frequency where it wants to oscillate, which is its mechanical resonance frequency. In a variable-frequency drive (VFD) and motor application, multiple resonant (natural) frequencies are possible.

## Solutions for Mechanical Resonance

If only one resonant frequency is an issue, a good solution is to stiffen the "springs" of the system (Figure 1) to raise its resonant frequency. This can be accomplished by using less compliant components-e.g., replacing helical couplings with stiffer "bellows" couplings or substituting shorter and thicker shafts for longer and thinner ones. To stiffen belt drives, use wider or shorter belts, belts with steel banding or parallel (multiple) belts. Installing stiffer gearboxes and stiffening the frame or base of the machine can also help reduce mechanical resonance problems.

VFDs. As mentioned earlier, VFD and motor applications may exhibit multiple resonant frequencies. The solution for mechanical resonance problems in most of these cases is to program the VFD to "skip" problem-causing resonant frequencies, which prevents the motor from operating in speed ranges associated with resonance or vibration.

Load-to-motor inertia. Another way to attack mechanical resonance problems is to reduce the ratio of load-to-motor inertias. For example, if a motor is physically much smaller than the pump it drives, it will be harder to control than a larger motor and will be more susceptible to mechanical resonance. Using a motor with a larger physical size will improve the load-to-motor inertia ratio and therefore decrease resonance problems. Of course, such a solution might not be practical, because it may require major modifications of the electrical and mechanical systems.

Motor base modification. Modifying the motor base is another way to reduce mechanical system resonance. The motor manufacturer can usually supply the information needed to calculate the system resonant frequency of an installed motor: motor weight, center of gravity and static deflection. Bases in typical installations are not truly stiff, so the actual resonant frequency of the system will probably be lower than calculations show. If this frequency is at or near operating speed, it may be necessary to change the resonant (reed critical) frequency of the motor to prevent an enormous increase in vibration amplitude.

Common ways to accomplish this include altering the stiffness of the base, modifying the weight of the motor/base combination or changing (usually lowering) the center of gravity (see Figure 2). (Note: In motors with sleeve bearings, a reed critical speed of about 40 to 50 percent of running speed can cause vibration due to oil whip or oil whirl.)

## Electrical System Resonance

In addition to excitation of mechanical resonance, electrical power system resonance is also possible and often associated with the presence of harmonics.