Understanding Resonance in Mechanical Systems

Definition: What is Resonance?

Resonance is a physical phenomenon that occurs when a system is subjected to a periodic force at a frequency that matches one of its own natural frequencies. When this frequency matching occurs, the system begins to vibrate with extremely large amplitudes. The energy from the input force is transferred to the system very efficiently, causing the vibration to build up dramatically. The only factor that limits the amplitude at resonance is the system’s damping.

The Link Between Natural Frequency and Resonance

To understand resonance, you must first understand natural frequency. Every physical object has a set of natural frequencies at which it will vibrate if disturbed. These are determined by its mass and stiffness. Resonance is what happens when you continuously “push” the object at the exact same rate as one of its natural frequencies.

A classic analogy is pushing a child on a swing:

• The swing, with the child on it, has a specific natural frequency based on the length of the ropes (stiffness) and the mass of the child.
• If you give the swing a single push, it will oscillate at its natural frequency and eventually stop due to damping (air resistance and friction).
• If you time your pushes to perfectly match the swing’s natural frequency, each push adds more energy to the system, and the swing goes higher and higher. This is resonance.
• If you push at the wrong frequency (too fast or too slow), your pushes will be out of sync with the swing’s motion, and you won’t be able to build up a large amplitude.

Why is Resonance a Problem in Machinery?

In rotating machinery, resonance is a highly destructive and dangerous condition. The “push” is provided by any periodic force generated by the machine’s operation, such as unbalance, misalignment, or blade pass forces. If the frequency of one of these forces aligns with a natural frequency of the machine’s rotor, foundation, support structure, or attached piping, the consequences can be severe:

• Extreme Vibration Levels: Amplitudes can be amplified 10, 50, or even hundreds of times, depending on the amount of damping.
• High Dynamic Stresses: The large deflections cause immense stress on components, leading to rapid fatigue.
• Catastrophic Failure: Resonance can lead to cracked shafts, failed bearings, broken welds, and complete structural failure in a very short amount of time.
• Excessive Noise: The high vibration levels radiate as loud and often tonal noise.

Symptoms and Identification of Resonance

Resonance has a very distinct set of symptoms that help in its diagnosis:

• Highly Directional Vibration: The vibration is typically much higher in one direction (e.g., horizontal) than in others.
• Sharp Peak in Vibration vs. Speed: The vibration is only high within a very narrow speed range. As the machine speeds up or slows down past this point, the vibration drops off dramatically.
• A 180-Degree Phase Shift: As the machine’s speed passes through the resonant frequency, the phase of the vibration will shift by 180 degrees. This is a definitive confirmation of resonance.
• Difficult to Balance: Attempting to balance a rotor that is operating on a resonance is often ineffective or may even make the problem worse. The balance correction weights will be unusually large or small, and the vibration may move to a different location.

Resonance is confirmed experimentally using an impact (or bump) test to identify the structure’s natural frequencies, or by performing a run-up/coast-down test to observe the amplitude and phase changes as the machine passes through the suspected resonance.

How to Solve a Resonance Problem

Since resonance is a frequency-matching problem, the solution always involves changing the frequency of either the “pusher” or the “pushee”:

1. Change the Forcing Frequency: This usually means changing the machine’s operating speed. This is the simplest solution if it is feasible.
2. Change the Natural Frequency: This is the most common solution.
   • To increase the natural frequency, you must increase the stiffness of the resonant component (e.g., by adding a brace or a gusset).
   • To decrease the natural frequency, you can either decrease the stiffness or add mass to the component.
3. Add Damping: In some cases where the frequencies cannot be changed, adding damping (e.g., with viscoelastic materials or specialized dampers) can reduce the amplitude of the resonant peak to an acceptable level.

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