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.
The power supplied by the electric utility is normally a pure sine wave at the fundamental frequency, commonly 50-Hz or 60-Hz. Connecting non-linear loads to the power system, however, can inject undesirable frequency components called harmonics at multiples of the fundamental frequency. For example, a typical VFD produces these undesirable components at the fifth harmonic (five times the fundamental frequency), as well as at the seventh, 11th, 13th, etc. Examples of non-linear loads include personal computers, uninterruptible power supplies (UPSs) and DC motor drives.
Adding harmonics to the fundamental frequency produces a distorted, non-sinusoidal waveform. Depending on the level of harmonic distortion, harmful effects can range from nuisance tripping and minor faults to damaged motors and pumps and lengthy downtime. Harmonics also increase losses in the power system and electrical equipment.
For motors, the higher frequency harmonic components place additional electrical stress on windings, increase rotor heating and reduce motor life. Potentially the most detrimental effect of harmonics is that they could excite a system resonance that damages motors and pumps or even causes system failure. Harmonics can also cause faulty meter readings, motor bearing failure (due to electrical currents), blown fusing on power-factor-corrected systems and telephone communication interference. Many of these problems may go undetected until the affected equipment fails.
When a VFD or other non-linear device injects a harmonic current at the resonant frequency, the system becomes excited or unstable. A variation of Ohms law (V = IZ) applies for system resonance. When I (amps) and Z (impedance) are simultaneously high, V (voltage) becomes exceptionally high. This causes excessive heating or possibly immediate dielectric failure in capacitors, transformers or other devices.
Another issue is that most manufacturers of VFDs specify a maximum lead length between their equipment and the motor. This specification varies by manufacturer and drive but typically ranges from 50- to 250-ft (15- to 75-m). Because this restriction can make application difficult, impractical or even impossible, many VFD users disregard it, leading to more motor failures and downtime.
If the resonant frequency of the lead conductors falls within the frequency range of the VFD voltage waveform, the conductors themselves will go into resonance. That will amplify the voltage components at (or near) the natural resonant frequency of the conductors, causing voltage spikes that can exceed 2.5 times the DC bus voltage of the inverter section of the VFD.
Solutions for Electrical System Resonance And Harmonics
The obvious solution for preventing voltage spikes in VFD systems is to keep the lead length between the motor and drive within the drive manufacturer's specifications. As mentioned earlier, VFDs also can be programmed to "skip" problem frequencies.
Commonly available solutions for reducing harmonics include line reactors, isolation transformers, filters and higher-pulse VFDs (e.g., 12- or 18-pulse). Carefully consider all the strengths and weaknesses to determine which is best for a particular installation.
The simplest and most common way to reduce harmonics is to add impedance to the system. This solution offers the largest reduction in total harmonic distortion relative to cost. In fact, increasing impedance by just 3 percent will reduce current harmonics about 50 percent in a standard 6-pulse VFD. This solution is often accomplished at the VFD by installing a DC choke or input line reactor, an isolation transformer or combination of these.
Line reactors. Line reactors provide the impedance to reduce harmonic current but are smaller and usually cost less than isolation transformers. Also called inductors, they are available in standard impedance ranges of 1.5, 3, 5 and 7.5 percent of the load impedance.
Applying a line reactor at the drive terminals can help reduce the resonant frequency of the total circuit, but additional losses in the copper and core of the inductor increase overall circuit dampening. While this reduces the peak of the overshoot voltage (voltage spikes), it also increases its duration, which still results in additional stress on the motor windings.
Isolation transformers. An isolation transformer provides several advantages. First and foremost, it provides impedance to the drive, which reduces current distortion. Properly selected, it can be used to match the supply voltage to the rated voltage of the load. If the secondary is grounded, it also isolates ground faults and reduces common mode noise (electrical noise that occurs simultaneously on all conductors of an electrical circuit).
Harmonic filters. Harmonic filters may also be installed, sometimes in combination with reactors and resistors, to reduce the harmonic content of the power system. In its simplest form, the capacitor-inductor combination "traps" or filters out the harmonic current of a single frequency. Low-pass filters are available with capacitors, inductors and resistors that allow only low frequencies to "pass" through them.
Applying a tuned, low-pass filter at the terminals of an inverter can remove all VFD carrier frequency voltages. These application-specific, custom filters were originally designed to limit audible motor noise. While this approach removes all VFD frequencies above the fundamental and affords excellent motor protection, the filters also reduce the fundamental voltage due to inductor losses. This may cause the motor to draw higher fundamental current er to produce rated horsepower.
Conclusion
Whether resonance problems are mechanical, electrical or some combination of the two, early detection and correction are critical. Resonance problems not only degrade the efficiency of the motor-drive system through added losses, but they also may lead to equipment or system damage, costly downtime and lost production.
