Tom Bishop, P.E.
EASA Technical Support Specialist
Mechanical resonance can be defined as the amplification of the vibration level of a mass or structure at its natural frequency, caused by excitation from an external source. For a rotating mass, this amplification occurs at the critical speed(s). Electrical resonance causes an amplification of the magnitude of voltage or current, or both. The increase in amplitude, whether mechanical or electrical, increases the stress on motor components and negatively affects operation, e.g., increased vibration, instability, increased energy consumption, and premature failure.
By receiving energy from an external source, the resonant condition can cause the magnitude of the disturbance to continue to increase until a fault occurs. Mechanical resonance can lead to breakage of motor and drive components, and electrical resonance can result in winding failure. In this article we will discuss mechanical and electrical resonance associated with motors and drives, and provide some solutions to address them.
Mechanical system resonance
Mechanical resonance can occur in variable speed applications if there are any natural frequencies within the speed range. In addition to increased vibration at a natural frequency, the motor may emit a pure tone, similar to that of a tuning fork, or it may start “growling” or become unstable. These are indicators of mechanical resonance, typically caused by compliance, or “springiness,” between a motor and its load. The motor and load comprise a “two-mass system” and are usually connected by power transmission devices such as gearboxes, belts, and couplings. As illustrated in Figure 1, each of these connecting components is like a spring; all twist slightly when motor torque is applied. This springiness, or lack of stiffness, is at the root of many mechanical resonance problems.
Every two-mass system has one frequency where it wants to oscillate; that is its mechanical resonance frequency. In a VFD (variable frequency drive) and motor application there can be multiple resonant (natural) frequencies. The solution for resonance in most cases with a VFD is to have the VFD block out the problem resonant frequencies by making them “skip frequencies.” That is, the drive does not allow the motor to operate in speed ranges associated with resonance or vibration.
Solutions for mechanical resonance
If only one resonant frequency is an issue, resonance may be avoided by raising the system resonant frequency by stiffening the “springs” (Figure 1) of the system. This can be accomplished by using less compliant components; for example, replacing helical couplings with stiffer “bellows” couplings. Short and thicker shafts can replace their long and thinner counterparts. Stiffer gearboxes can be used. Using wider belts, belts with steel banding, shorter belts, or parallel (multiple) belts increase the stiffness of belt drives. In addition, stiffening the frame or base of the machine can help reduce mechanical resonance problems.
Another way to reduce the possibility of mechanical resonance problems is to reduce the ratio of load-to-motor inertias. A physically small motor is more susceptible to resonance than a larger motor because it is more difficult to control when it is driving a load many times its size. Increasing the motor physical size and therefore the motor inertia will improve the load-to-motor inertia ratio. However, from a practical perspective, it may not be possible to increase motor size without major modifications to the electrical and mechanical systems.
Motor base modification
Modification or alteration of the motor base is another method of reducing mechanical system resonance. The motor manufacturer can usually supply the following information to aid in determining the system resonant frequency of an installed motor: motor weight, center of gravity, and static deflection. Bases in typical installations are not truly stiff, and because of this the resonant frequency will be lower than that obtained from calculations. If the resonant frequency is at or near operating speed, the motor resonant (reed critical) frequency may need to be changed; otherwise, enormous amplification in the vibration amplitude will occur. This is most commonly accomplished by changing the stiffness of the base, the weight of the base and motor combination, or by changing (usually lowering) the center of gravity (Figure 2). A reed critical speed that is about 40% to 50% of running speed can result in vibration in motors with sleeve bearings due to oil whip or oil whirl.
Electrical system resonance and harmonics
In addition to excitation of mechanical resonance, there is also the possibility of electrical power system resonance, 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 50Hz or 60Hz. However, when certain types of loads are connected to the power system, they can inject undesirable frequency components that are at other than the fundamental frequency. These additional frequency components are termed harmonics. For example, produced by a typical VFD are the 5th (5 times the fundamental), 7th, 11th, 13th, etc. The result of adding these harmonic frequencies to the fundamental frequency is a distorted, non-sinusoidal waveform that increases losses and reduces motor torque. Non-linear loads connected to the power system can also be a source of harmonic distortion. Figure 3 shows a distorted waveform and its associated harmonic components.
A linear load is one in which the current and voltage are proportional to each other. The current waveform will typically have the same shape as the voltage waveform. Some examples of linear loads are induction motors and resistance element heaters. With a non-linear load, the current waveform is shaped differently than the voltage waveform. Examples of non-linear loads include uninterruptible power supplies (UPSs), VFDs and DC motor drives. Non-linear loads also tend to have low power factor.
Depending on the level of harmonic distortion, harmful effects can range from nuisance tripping, to minor faults, to lengthy down time due to seriously damaged equipment. Harmonics also add to power system and electrical equipment losses. In motors the higher frequency harmonic components cause negative effects such as additional winding electrical stress, rotor heating and reduced motor life. The most damaging effect of electrical harmonics is if they excite a system resonance, because it can lead to equipment and possibly system failure.
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 both I (amps) and Z (impedance) are high at the same time, V (voltage) becomes exceptionally high, causing excessive heating or possibly immediate dielectric failure in capacitors, transformers or other devices. In addition, harmonics can cause problems such as incorrect 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.
Lead length between VFDs and motors
Another issue with VFDs and motors is the lead length between them. Most manufacturers of VFDs publish a maximum recommended distance between their equipment and the motor. The restriction of that maximum distance may make application difficult, impractical, or in some cases impossible. Maximum tolerable distances vary by manufacturer and drive, but are typically from 50 to 250 feet (15 to 75 meters). Unfortunately, many users of VFDs have chosen, or have been forced, to disregard the maximum recommended lead length distance, with resultant increase in 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. The conductor resonance then creates an amplification of the voltage components at, or near, the conductor’s natural resonant frequency. This results in voltage spikes that can reach levels in excess of 2.5 times the DC bus voltage of the inverter section of the VFD.
Solutions for electrical system resonance and harmonics
Commonly available solutions for reducing harmonics include line reactors, isolation transformers, filters, and higher pulse (e.g., 12- or 18-pulse) VFDs. All have their strengths and weaknesses and each should be carefully considered to determine which is best for a particular installation.
The simplest and most common method for reducing harmonics is the addition of impedance to the system. This is often accomplished by installing a DC choke or input line reactor or isolation transformer, or combination of these, to the VFD. The simple addition of impedance to a system offers the largest reduction in total harmonic distortion relative to cost. A standard 6-pulse VFD will experience about a 50% reduction in current harmonics just by providing an additional 3% impedance.
A line reactor provides the impedance to reduce harmonic current, similar to an isolation transformer, but with a smaller physical size and usually lower cost. Line reactors, also referred to as inductors, are available in standard impedance ranges of 1.5%, 3%, 5% and 7.5% of the load impedance. If the actual system voltage is at or near 10% below the nominal system rating, the higher impedance 5% and 7.5% values should be avoided.
Applying a line reactor at the drive terminals can help by reducing the resonant frequency of the total circuit. However, because there are additional losses associated with the inductor, both in the copper and in the core, overall circuit dampening increases. While this dampening reduces the overshoot voltage peak, it also increases the duration of the overshoot, thus still resulting in additional stress on the motor windings.
Advantages of isolation transformer
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 load rated voltage. Also, if the secondary is grounded, it isolates ground faults and reduces common mode noise (electrical noise that occurs simultaneously on all conductors of an electrical circuit).
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 acts as a “trap” to filter 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.
A tuned low-pass filter can be applied at the terminals of an inverter to remove all of the 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 reduce the fundamental voltage due to inductor losses and may cause the motor to draw higher fundamental current to produce rated horsepower.
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