05 / CHAPTER 12
Wave studio: pump vibration
Use frequency evidence to distinguish imbalance, cavitation, and structural response.
ANCHOR EQUATION
Vibration evidence
In symbols: f = ω/(2π)
Frequency evidence helps separate imbalance, cavitation, and structural response.
Vibration evidence needs frequency and phase
A pump vibration trace is a signal whose dominant frequencies can reveal imbalance, blade-pass forcing, looseness, or cavitation. The diagnosis is a model comparison, not a label attached to any one peak.
Convert the shaft rate into candidate frequencies
If the shaft rotates at f_rot revolutions per second, angular speed is ω = 2πf_rot. A feature with N repeating blades or vanes produces blade-pass frequency f_b = N f_rot. Fourier amplitude identifies periodic content; phase between acceleration and pressure signals can distinguish forcing from response.
A 1800 rpm pump runs at f_rot = 30 Hz. A six-vane impeller gives blade-pass frequency 180 Hz. A spectral peak near 60 Hz may be a 2× imbalance or alignment feature, but the frequency alone is not proof.
Sampling can invent evidence
A sample rate of 200 Hz cannot represent a 180 Hz component reliably without filtering; aliasing can move it to a false low frequency. Record sample rate, sensor location, and operating condition with every spectrum.
Work it: Given a spectrum with peaks at 30, 60, and 180 Hz for a six-vane pump, write two competing hypotheses and name one additional measurement that would discriminate them.