A machine can be correctly supported by vibration isolators and still shake more than expected. When that happens, one of the first checks should be the relationship between the excitation frequency and the natural frequency of the isolated system.

The frequency ratio is:

r=f/f_n​

where f is the excitation frequency and fn is the natural frequency.

As a quick reference, r≈1 indicates resonance risk, while r>√2 marks the beginning of the isolation region in the basic undamped model.

From RPM to Frequency Ratio

Rotating equipment is often specified in RPM rather than Hz. Convert rotational speed first:

f=RPM\60

For a motor running at 1,200 RPM:

f=1200\60=20Hz

If the isolated system has a natural frequency of 6 Hz:

r=20\6≈3.33

So the calculation path is:

1,200 RPM → 20 Hz → 20/6 → r=3.33r=3.33

For fans, pumps, compressors and geared systems, RPM may not represent every important excitation. Blade-pass frequencies, harmonics or gear-mesh frequencies may also need to be checked.

What Does the Frequency Ratio Tell You?

Frequency ratio shows where the operating frequency sits relative to the natural frequency of the isolation system.

*The r=√2 crossover applies to the commonly used undamped base-excitation displacement-transmissibility model. Actual response depends on damping, isolator characteristics and how transmissibility is defined.

Frequency Ratio vs. Transmissibility

Frequency ratio and transmissibility describe different parts of the same system behavior.

Frequency ratio r tells us how far the operating frequency is from the system's natural frequency.

Transmissibility T describes how much vibration passes through the isolation system.

Near r=1, the system enters the vibration amplification zone. Once the operating frequency moves sufficiently beyond resonance, it enters the isolation region.

A transmissibility curve makes this relationship easier to see:

Below Resonance → Resonance Zone → Crossover → Isolation Region

This is also why selecting an isolator from load capacity alone can give a poor result. A mount may support the equipment correctly but still operate too close to resonance.

Engineering Note: Damping helps suppress the resonance peak, which is useful when equipment passes through its natural frequency during start-up or shutdown. Well into the isolation region, however, higher damping does not necessarily produce better isolation.

Variable-Speed Equipment Can Cross Resonance

Maximum RPM alone does not describe the full operating condition of variable-speed equipment.

Take a system with a natural frequency of 8 Hz and a normal operating speed of 1,800 RPM.

At full speed:

f=1800\60=30Hz

The normal operating point is well above resonance.

But during start-up, the machine passes through:

8 Hz×60=480 RPM

At approximately 480 RPM:

r≈1

The isolation system is passing directly through its resonance region.

How long the equipment remains near this speed matters. A motor that accelerates quickly through resonance presents a different problem from equipment that operates continuously around the same frequency.

For this reason, HOAN engineers normally ask for the operating RPM range, rather than only the maximum RPM, when evaluating variable-speed equipment.

Why Pursuing the Highest r Value Can Backfire

Lowering the isolator stiffness reduces natural frequency and can increase the frequency ratio.

But there is a mechanical limit to how far this approach should be taken.

An isolator that is too soft may produce excessive static deflection, reduce the travel available for shock, or allow too much movement in tall equipment with a high center of gravity.

In practice, lowering f_n is useful only while static deflection, available travel and equipment stability remain acceptable.

Wire rope isolators add another consideration: their behavior is not perfectly represented by an ideal linear spring. Load direction, displacement and friction between wire strands influence the actual dynamic response.

Frequency ratio should therefore be treated as a selection tool, not as the final specification.

A Practical Frequency-Ratio Check

Before selecting an isolator, establish three values:

1. Excitation frequency f

Convert RPM to Hz and identify any other significant excitation frequencies.

2. Natural frequency f_n

Use the supported load and actual isolator characteristics.

3. Frequency ratio r

r=f\f_n

Then check the entire operating speed range, especially start-up, shutdown and low-speed operation.

For final selection, frequency ratio should be reviewed together with damping, mounting-point loads, static deflection, available shock travel and installation direction.

For equipment with complex excitation frequencies, variable-speed operation or combined shock and vibration requirements, HOAN Engineering can review the operating parameters and recommend an appropriate wire rope isolator configuration.

Technical Review: HOAN Engineering Team
Xi'an Hoan Microwave Co., Ltd.