Excite a brake disc with a defined hammer impulse and simultaneously measure the response with a microphone – you can compute the part's transfer function. It is the mathematical foundation of modern modal analysis – and the standard for any clean resonance analysis.
What does a transfer function describe?
X(f) is the FFT of the excitation, Y(f) the FFT of the response. H(f) is complex: magnitude = gain, phase = phase shift.
Why direct division is dangerous
Excitation is noisy, response is noisy, and at some frequencies X(f) is near zero. Robust estimation:
Coherence – the quality metric
γ² ∈ [0, 1]. γ² = 1: response fully explained by excitation, FRF trustworthy. γ² < 0.8: caution – noise/nonlinearities distort the FRF.
Extracting modal parameters
Natural frequencies sit at maxima of |H(f)|.
Excitation in practice
| Type | Pro | Con |
|---|---|---|
| Hammer impulse | simple, broadband, contactless | low energy at high frequencies |
| Loudspeaker sweep | tunable range, high energy | more complex setup |
| Shaker pseudo-random | statistically optimal, good coherence | mass attachment |
How SonicTC.AT uses FRFs
1–4 FRFs per part. Automatic extraction of first 6–12 modes, per-bin coherence check, master build and inline comparison. Coherence < 0.9 in a relevant range triggers a warning.
