Resonance & Critical Speed Simulator

When running speed approaches a natural frequency, even small unbalance becomes large vibration. This simulator shows the response of a single-degree-of-freedom system excited by rotating unbalance.

Magnification factor —× —

Frequency ratio r = n / fn: —
Phase shift: —
Separation from critical: —
Quality factor Q: —

Amplitude response

Phase response

These tools are intended for preliminary assessment and training. Decisions on critical equipment should be based on on-site measurement and expert evaluation.

How to use

Enter the measured or calculated natural frequency (bump test, coast-down).
Choose the damping ratio; steel structures are typically 0.02–0.08.
Move the speed slider and watch magnification and phase change around the natural frequency.

Theory & formulas

For a system excited by rotating unbalance, dimensionless amplitude is M = r² / √((1 − r²)² + (2ζr)²), with r = n / f_n.

Phase shift φ = atan2(2ζr, 1 − r²) is 90° at resonance and approaches 180° above it. A 90° phase change during coast-down confirms a resonance.

Quality factor Q ≈ 1 / (2ζ). Many machine specifications require 10–20% separation between running speed and a critical speed; the default here is 15%.

Frequently asked questions

Can balancing fix resonance?

Partly. Balancing reduces the exciting force and lowers vibration, but if running speed is close to a natural frequency the system stays sensitive to small forces. A lasting fix moves the natural frequency by changing stiffness, mass or damping.