One of the Augury fault cards that can be assigned to any component (motor, gearbox, pump, fan, a whole asset, etc…) is called Resonance. It is a very complicated topic; it can be difficult to understand, difficult to diagnose, and sometimes can be difficult or costly to repair.
To understand what Resonance is, first we must define some terms.
- Natural Frequency: Also known as ringing frequency, this is the frequency of the free oscillation of a structure displaced from its equilibrium. An example is a tuning fork or a bell… when you hit it, the frequency your ears hear is the Natural Frequency. It is independent of any input signal and is a property of a structure. It is dictated by the mass, stiffness, and dampening of a structure. When energy is input to the structure by impacting it and it is allowed to vibrate undisturbed, it will vibrate (ring) at the natural frequency.
- Forcing Frequency: for the purpose of this discussion, a forcing frequency is the frequency of energy input to a structure. An example of this is the running speed (aka operating frequency) of a shaft in rotating equipment. Every shaft has some slight residual unbalance, and if the shaft is rotating at 1800 rpm, then energy is being input by the shaft at 1800 rpm. If the shaft is connected to a vane pump that has 9 pumping vanes in it, then those vanes are passing one stationary part of that equipment 9 times for every shaft rotation… so the forcing frequency would by 9 * shaft speed = 9 * 1800 = 16,200rpm.
- Resonance: Resonance occurs when a forcing frequency coincides with a natural frequency and causes the magnitude of the forced input vibration to be amplified. Following the example above for a shaft rotating at 1800 rpm, if the natural frequency of the structure just so happens to also be 1800 rpm, then the machine is in Resonance.
Every structure has Natural Frequencies, and every rotating equipment has Forcing Frequencies. However, Resonance only happens when these frequencies line up with each other. A natural frequency of a structure is generally unchanged throughout its life, but a forcing frequency can change. For instance, when the motor runs at different speeds (VFD), it is effectively changing its forcing frequency.
To complicate things further, resonance can exist in a structure but might not actually be a problem. This is the case when there is a noticeable change in vibration at certain machine speeds, but the amplitude of vibration isn’t so high that it is dangerous or causing machine damage. See above image, where there is a resonance at 37 Hz, but the amplitude of vibration for that type of machine is not a concern (0.25ips versus 0.35ips). Resonance is a concern when the amplitude of vibration during resonance conditions is creating so much movement and energy that it can cause reliability problems. The beginning of this article mentioned that Resonance is a fault card that Augury can assign. In actuality, Resonance is a condition, and it only becomes a fault when vibration amplitudes become a concern.
- Resonance in Monitor might mean that there is evidence of a possible resonance condition, but maybe we haven’t seen enough of the running speeds to determine whether the amplitudes are too high. It can also mean that Resonance has been identified, but we are watching it to see how much time it spends at high amplitudes to weigh a decision on whether repairs are worth pursuing.
- Resonance in Alarm or Danger means that the vibration amplitudes are high and could be causing premature machine damage, could cause instantaneous failure, or could be dangerous from a safety perspective.
So, think you have a good handle on Resonance? Well, let me throw another wrench in the mix. Remember above when I said “Every structure has Natural Frequencies, and every rotating equipment has Forcing Frequencies?” Take note of the plural on Frequencies. Not only can a whole structure have a Natural Frequency, but different pieces of an asset can each have its own Natural Frequency, meaning you’re not just dealing with one frequency, but many frequencies. And we already talked about how there can be multiple forcing frequencies in rotating equipment, not just shaft speed and rotor mesh, but gear mesh frequencies, bearing frequencies, or even frequencies specific to the machine design and what it’s doing (such as fluid dynamic frequencies).
Here's a free body diagram of a simple vertical pump with a free-standing pipe coming off the side (humor the drawing, it’s just an example!).
The motor, the pump, and the pipe each have their own natural frequency. Not only that, but combinations of attachments each have a natural frequency, and finally, the entire structure mounted to the base has a natural frequency. Testing to find out which part of the asset might be causing resonance and the type of resonance can be extremely exhausting and could require several very advanced test methods. Anytime an Augury machine is marked with a Resonance fault card, we can’t really tell which component might be at fault or where improvements should be made. So, troubleshooting probably needs to start by making a couple adjustments at a time and watching for changes in vibration.
What to do
Which leads to the big question. What do we do about a Resonance fault? Well, if resonance only exists when a natural frequency and forcing frequency align… then just move a frequency so they don’t align anymore. Simple to say, harder to do. Let’s start by trying to move the Forcing Frequency, which can be done by setting operating instructions or implementing speed interlocks (to prevent the machine from turning at the known problematic frequencies). When Augury identifies Resonance, we can also provide information such as the frequency range where Resonance is a problem. If a natural frequency is at 32Hz, the communication might be to avoid speeds between 28 and 36 Hz. See below for trend data, and how that data looks once the speed and vibration are plotted together.
In the above plot, you see apparently random spikes in the vibration amplitude trend (top trend). But these are not random. Looking more closely at that data and the corresponding speeds (bottom trend), those high vibration amplitudes are due to a resonance around 32 Hz!
If you plot the motor speed data against the vibration amplitude, you can see the vibration is elevated when the motor is running between 28 and 36 Hz. If this speed is something easy to avoid, then simply setting speed limitations will improve the reliability of the asset.
The reason this is a frequency range instead of just one frequency is because of a structural property called dampening. Increasing dampening in a structure can reduce the amplitude of vibration, and might slightly move the resonance frequency. However, increasing dampening can make the range of frequencies where resonance occurs even wider, meaning you have to avoid operation at more speeds. If you can lower the amplitude caused by resonance enough that it no longer becomes a concern, then dampening might be an option. Otherwise, adding dampening might make your operating vibrations worse. This leads us to our second option for frequencies to move during Resonance: the Natural Frequency.
The Natural Frequency can be manipulated slightly by adjusting dampening, but not appreciably. The best way to change a Natural Frequency is by adjusting the Mass or Stiffness. Increasing mass or decreasing stiffness moves the Natural Frequency to a lower frequency. Decreasing mass or increasing stiffness moves the Natural Frequency to a higher frequency. An easy analogy is a guitar string. If you pluck the string, then twist the tuning knob to tighten it, that causes the frequency to rise (increased stiffness). If you add a mass to the string and play it, it will vibrate at a lower frequency (increased mass). By moving a Natural Frequency away from speeds where Forcing Frequencies might line up with it, you can prevent resonance from happening.
Natural Frequency n= Stiffness (k)Mass (m)
Whenever attempting to adjust the Natural Frequency of a machine, it’s important to discuss this with the Original Equipment Manufacturer (OEM). Sometimes they have easy solutions or suggestions to fight Resonance. Or they might let you know if your intended design changes might damage the machine.
Lastly, if you really need to attempt adjusting your natural frequency, it is a good idea to get extra testing or simulations done to make sure the changes you want to make will have an appreciable effect. Additional forms of testing include Modal Impact Analysis (the crude form of this is called a Bump Test), Operating Deflection Shape analysis (ODS), or possibly Motion Amplification to help identify the bending mode.
Summary
Resonance is a naturally occurring physical reaction that occurs between the natural frequency of a structure and the forcing frequency of the rotating equipment. These frequencies exist in all rotating equipment and only become a problem when they align and cause vibration amplitudes that increase the stress on the equipment’s components. It can be complicated to identify and correct due to the multiple components and multiple frequencies that exist for each component. When resonant faults are identified, it is important to correct them to avoid overstressing the equipment. This continuous stress for long duration run times eventually leads to repeat failures with no obvious root cause.