Critical Speed & Resonance Separation Margin Calculator
Calculate critical speed and separation margin using system stiffness, equivalent mass, operating speed, maximum speed, damping ratio, and excitation type.
Enter the known values and review the calculated result
Input parameters
Use consistent values and select the intended engineering units.
Operating conditions
System properties
Damping
Excitation
Results
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Method, application and limitations
Review the calculation method, intended application and engineering assumptions before using the result in a design decision.
Formula and calculation method
Critical speed formula:
ωn = √(k / m)
fn = ωn / (2π)
ncrit = fn · 60
Excitation frequency:
- 1× rotational speed: fexc = n / 60
- 2× rotational speed: fexc = 2 · (n / 60)
- Gear mesh: fexc = (n / 60) · z
- External cyclic: fexc = f
Separation margin formula:
nexc = fexc · 60
SM = min(|(ncrit − nexc,operating) / ncrit|, |(ncrit − nexc,max) / ncrit|) · 100
where:
- ωn — natural angular frequency (rad/s)
- fn — natural frequency (Hz)
- ncrit — critical speed (rpm)
- SM — separation margin (%)
- k — system stiffness (N/m)
- m — equivalent mass (kg)
- n — operating speed (rpm)
- nmax — maximum speed (rpm)
- z — number of gear teeth (-)
- f — external cyclic excitation frequency (Hz)
- fexc — excitation frequency (Hz)
- nexc — excitation speed equivalent (rpm)
When to use this calculator
When to use this calculator:
- Check whether the operating speed range overlaps the calculated resonance zone.
- Calculate the critical speed from system stiffness and equivalent mass.
- Evaluate separation margin between the critical speed and selected excitation speed.
- Compare the calculated separation margin with the required separation margin.
- Analyze 1× speed, 2× speed, gear mesh, or external cyclic excitation against the natural frequency.
How to interpret the result
Critical speed is defined as the rotational speed corresponding to the system natural frequency calculated from system stiffness and equivalent mass.
Separation margin is defined as the smaller percentage distance between critical speed and excitation speed at operating speed or maximum speed.
Critical speed increases when system stiffness increases and decreases when equivalent mass increases.
Separation margin decreases when the selected excitation speed moves closer to the calculated critical speed.
- Safe — no resonance crossing is detected, amplification factor is not greater than 20, the excitation is outside the resonance band, and separation margin is not below the required separation margin.
- Warning — excitation is inside the resonance band or separation margin is lower than the required separation margin.
- Unsafe — resonance crossing is detected or the amplification factor is greater than 20.
- Invalid — at least one required input violates the JS validation conditions.
The result is used to evaluate whether the selected operating speed range should avoid the calculated resonance zone.
Calculation example
Example:
A user wants to check whether a rotating system operating up to 1800 rpm has enough separation from its calculated critical speed for 1× rotational excitation.
- n — Operating speed = 1200 rpm
- nmax — Maximum speed = 1800 rpm
- SMreq — Required separation margin = 20%
- k — System stiffness = 1,000,000 N/m
- m — Equivalent mass = 25 kg
- ζ — Damping ratio value = 0.03
- Excitation type = 1× rotational speed
ncrit = 1909.9 rpm
SM = 5.8%
Assumptions and limitations
- The system natural angular frequency is calculated as √(k / m).
- The critical speed is calculated from natural frequency using ncrit = fn · 60.
- The selected excitation type defines the excitation frequency calculation.
- The resonance bandwidth is calculated as 2 · ζ · fn.
- The amplification factor is calculated from the frequency ratio and damping ratio.
- The resonance zone is centered around the calculated critical speed.