Gene Vogel
EASA Pump and Vibration Specialist
Resonance is a property of all mechanical structures. It can be described as a sensitivity to a certain vibration frequency. For machinery such as electric motors, pumps, turbines, etc., it becomes a problem when small vibratory forces from the machine operation are amplified by mechanical resonance. The result can be very severe vibration levels, even when the exciting forces are small. Often resonance is encountered when a speed change has been implemented, as with retrofitting a VFD or operating a 50 Hz motor on 60 Hz power.
The most common example of resonance is when the structure supporting a machine is resonant at or near the rotating speed of the machine. Even slight vibratory forces from residual unbalance and misalignment will excite the resonant base structure, resulting in severe vibration. The machine components can also be resonant. There are many examples of 2-pole electric motors where a resonant endbracket caused very high axial vibration at 1 x rpm or 2 x rpm.
A second category of resonant conditions occurs when the resonant component is the rotating element of the machine. This is common with gas and steam turbines, centrifugal pumps and 2-pole electric motors. While the result is similar (high vibration when a certain operating speed is reached), this is a more complex phenomenon. When the operating speed reaches the resonant frequency of the rotating element, the rotating element actually distorts and the vibratory forces increase significantly.
There is a need to distinguish between these two types of resonance. The first, where a supporting structure or non-rotating machine component is resonant, is usually referred to as a “structural resonance.” The second, where the rotating element is resonant, is known as the “rotor critical speed.” This leaves the term “critical speed” (without the word “rotor”) somewhere in limbo.
Technically, a critical speed could be either a structural resonance or a rotor critical speed. For the sake of clarity it’s best to avoid using that term. The simple term “resonance” can be applied to both conditions to avoid confusion.
The characteristics of resonance
As described above, the most notable characteristic of resonance is increased vibration when a certain operating speed is reached. It will also be observed that as the operating speed is increased beyond the resonant frequency, the vibration amplitude will decrease somewhat. A graphic representation, termed a Bode plot, of this operating speed vs. vibration amplitude will be helpful (Figure 1). For the sake of illustration, we’ll assume the exciting force is at the rotating speed, as with residual unbalance of the rotor.
The formula for calculating the resonant frequency is:
where ‘K’ is the stiffness of the resonant structure or component, and ‘W’ is the weight (mass). Note that at the core of this formula is:
So increased stiffness will raise the resonant frequency and increased mass will lower it. That’s logical since stiffness is a force that always pushes against motion, while mass has inertia which always pushes with motion. Resonance is what happens when these two opposing forces are equal; they cancel each other out and vibration increases.
The damping factor
But there is a third force at work throughout the speed range. That force is damping. Damping absorbs vibratory energy, converting it to heat. Damping reduces the maximum amplitude of the vibration at resonance and also increases the width of the amplification zone (Figure 2). A common example of damping is shock absorbers on a vehicle. On machinery bases, concrete and grouting add significant damping to a base structure.
These forces (stiffness, mass and damping) determine the characteristics of resonance and are important in the distinction between structural resonance and rotor critical speeds.
With structural resonance, the machine is operating very close to resonant frequency. It is most noticeable when damping is low, since very high vibration amplitude results. Solutions include changing the resonant frequency to move it away from the operating speed by modifying stiffness or mass, and increasing damping to directly reduce the amplitude. There are a variety of methods by which these corrective measures are implemented, and a discussion of them is a topic for another article. The objective here is a comparison to rotor critical speeds.
With a rotor critical speed, the problem is quite different. First of all, the stiffness, mass and damping of the rotor can almost never be changed, and damping is typically very low. No rotor can have an operating speed close to the rotor critical speed. The problem in this case is not that the operating speed is close to resonance, but that at the rotor critical speed the rotor distorts. The rotor becomes what is called a “flexible” rotor rather than a “rigid” rotor.
With a rigid rotor (one that operates below the rotor critical speed), there are numerous unbalance forces distributed along the rotor. The sum of these unbalance forces can be corrected in any two planes along the rotor axis with common two plane dynamic balancing methods. However, once the rotor becomes flexible, above the rotor critical speed, the unbalance forces may be distributed so that the rotor distorts, causing an unbalanced condition that was not present in the rigid mode. This flexible mode unbalance causes increased vibration that persists at higher speeds.
With structural resonance, the force is constant while the vibratory response of the structure changes with speed. With a rotor critical speed, the force changes as the rotor distorts to conform to unbalance forces distributed along the axis of the rotor. The solution to a rotor critical speed is to eliminate the unbalance forces in the various planes along the axis of the rotor. However, it is generally not possible to detect where the unbalance forces are with the rotor in the rigid mode. So it must be operated above the rotor critical speed (in the flexible mode) to detect the effects of the unbalance.
Bending modes
As the speed of a rotor is increased it will go through a series of bending modes: first bending mode, second bending mode, third bending mode, etc. (Figure 3).
Electric motor rotors for large, 2-pole motors may operate above the first rotor critical speed (first bending mode). Seldom are such rotors designed to operate above the second rotor critical speed. Rotors for multistage pumps, steam and gas turbines often do operate above the second rotor critical speed and sometimes above the third rotor critical speed. Rotors that are designed for such “flexible rotor” operation have provisions for additional balancing planes to accommodate dynamic balancing procedures that eliminate the residual unbalance forces that cause flexible rotor distortion. These dynamic balancing procedures require the rotor to spin at operating speed, which can only be done safely with specially designed balancing machines in a spin pit.
Understanding the difference between structural resonance and rotor critical speeds will help clarify discussion with customers, especially when large, 2-pole motors or multistage pumps are the topic of discussion.
Print
