Why Can an Anti-resonance Have Poor Repeatability?

Problem

Repeated FRF measurements of the same axis show an anti-resonance around 280 Hz whose exact frequency and depth change from run to run, while the main resonance stays put. Controller designs that notch or invert this region inherit the variability. Why would an anti-resonance be less repeatable than its neighboring resonance?

Likely Causes

1. Contact stiffness variation. An anti-resonance frequency is set by a sub-structure’s local stiffness-to-mass ratio. If that stiffness comes through a contact (bolted joint, preloaded bearing, clamped part), it varies with preload and surface condition.
2. Preload changes between runs. Thermal cycles, re-clamping, or even axis position change the preload on the relevant joint, shifting the effective stiffness.
3. Clearance / backlash. With play in the joint, small-amplitude excitation rattles rather than deforming the stiffness — the apparent anti-resonance depends on excitation amplitude.
4. Nonlinearity + excitation level. If stiffness is amplitude-dependent (Hertzian-like contact), different excitation levels linearize the system around different operating points.
5. Measurement artifacts. Anti-resonances are low-signal regions: coherence drops there, so part of the variation can be plain estimation variance.

Measurement Method

• Repeat the FRF at three or more excitation amplitudes without touching the hardware: amplitude dependence indicates nonlinearity or clearance.
• Vary preload deliberately (torque steps on the suspect joint) and track the anti-resonance frequency against preload.
• Check coherence in the anti-resonance region across runs — if coherence is poor, increase averaging or excitation energy there before drawing mechanical conclusions.
• Measure at several axis positions to separate position-dependent structure effects from joint condition.

Engineering Interpretation

A repeatable resonance with a wandering anti-resonance points at the substructure branch, not the main drive path. Rank causes by their experimental signature: amplitude dependence → clearance or nonlinear stiffness; preload dependence → contact stiffness; run-to-run scatter with poor coherence → estimation variance, fix the measurement first. Control design should treat the anti-resonance frequency as an uncertain parameter with the measured range, rather than a fixed value to invert.

What to Test Next

• Build the preload-vs-frequency curve and compare its slope against a Hertzian contact stiffness model.
• Bound the estimation variance contribution by back-to-back repeated runs with identical settings.
• If clearance is confirmed, quantify the rattle threshold amplitude — it defines the valid excitation window for future FRF campaigns.