A combustion engine sounds different at idle than at 4,000 rpm. An e-drive changes its excitation structure with speed. A pure FFT on such signals shows a smeared cloud, not a clear cause. The solution is order analysis.

What is an order?

An order is a multiple of rotation frequency. At n = 3,000 rpm, rotation frequency is frot = 50 Hz. A 600 Hz component equals the 12th order – mechanically coupled to rotation.

order = f / frot
  • Order 1: rotor unbalance
  • Order 2: misalignment, shaft bend
  • Order Z (tooth count): gear meshing
  • Order 6 / 12 (e-machine): poles × phases excitation
  • Order 0.5 / 1.5: subharmonics, often bearing damage or belt whip

Why FFT fails at variable speed

If speed changes during measurement, all order-coupled frequencies move along. They smear across the spectrum – energy that should sit on a sharp line spreads over 50 bins. The order becomes invisible.

Order tracking: angle-synchronous resampling

Resample the signal at equal angle steps of the shaft (instead of equal time steps), using an encoder or trigger track. The subsequent FFT delivers an order spectrum: an order appears on the same bin regardless of speed.

Math

xθ(k) = x(tk) with θ(tk) = k · Δθ
X(o) = Σk=0K−1 xθ(k) · e−j 2π o k / K

The Campbell diagram

Most powerful NVH visualisation: x = speed, y = frequency, colour = amplitude. Orders appear as straight lines through the origin (slope = order). Structure resonances show as horizontal lines. Crossings of an order with a resonance produce resonance excitation – often the root cause of comfort issues.

Practical example: e-drive run-up

0 → 6,000 rpm in 8 s. Campbell shows:

  • Strong 24th order (pole pairs × phases).
  • Weak 48th order – switching harmonics.
  • Horizontal line at 1,240 Hz – housing resonance.
  • At 3,100 rpm the 24th order crosses this resonance – audible whine.