How the wizard thinks — intersection, not lookup
Each symptom maps onto a set of candidate causes drawn from the suction side, the hydraulics, the system and the mechanical train. A symptom seen alone may point at a dozen causes; several symptoms seen together usually point at one or two. The wizard therefore scores every cause by the number of selected symptom sets it appears in (intersection depth), breaks ties by specificity — a cause that explains three of three symptoms outranks one that explains three of twenty-five — and shows the top five with the check that confirms each and the action that cures it. Example: "vibration at all flows" alone lists over thirty candidates; add "excessive power" and only the causes common to both sets survive — a foreign object in the impeller, internal rub, and misalignment rise to the top.
1 · Naming a spectrum peak
Every peak is named by its ratio to running speed. With \(N\) = speed in rpm, \(Z\) = number of impeller vanes and running frequency \(f_{1\times}=N/60\) Hz:
Rolling-element bearing defect tones come from the bearing geometry — element count \(N_b\), element diameter \(B_d\), pitch diameter \(D_p\), contact angle \(\theta\), with \(f_r=N/60\) Hz. The full forms, and the order-of-running-speed approximations this tool uses when only the element count is known:
$$BPFO=\frac{N_b f_r}{2}\left(1-\frac{B_d}{D_p}\cos\theta\right)\approx 0.4\,N_b f_r\qquad BPFI=\frac{N_b f_r}{2}\left(1+\frac{B_d}{D_p}\cos\theta\right)\approx 0.6\,N_b f_r\qquad BSF\approx 0.5\,N_b f_r$$| Symbol | Meaning | Units |
|---|---|---|
| \(N\) | shaft speed | rpm |
| \(Z\) | number of impeller vanes | — |
| \(f_{1\times},\,f_r\) | running-speed (1×) frequency, \(N/60\) | Hz |
| \(f_{vane}\) | vane-pass frequency — blade tips passing the cutwater | Hz |
| \(f_{whirl},\,f_{recirc}\) | fluid-film whirl; suction-recirculation band | Hz |
| \(BPFO,\ BPFI,\ BSF\) | ball-pass frequencies, outer / inner race / rolling element | Hz |
| \(N_b,\ B_d,\ D_p,\ \theta\) | rolling-element count; element and pitch diameters; contact angle | —, mm, mm, ° |
2 · Frequency fingerprints (condensed)
| Spectrum peak | Classic attribution | Verdict |
|---|---|---|
| 1× RPM | unbalance or bent shaft; plugged impeller; misalignment if axial > ½ radial; grows ≈ with speed² | 🟡 investigate |
| 2× RPM | coupling angular misalignment; loose rotor parts; double-volute clearance effects | 🟡 investigate |
| vane-pass (\(Z\times\) RPM) | vane-to-cutwater gap too small; eccentric impeller; recirculation can also show it | 🟡 investigate |
| 0.5× RPM | oil whirl — tracks speed faithfully near 0.45–0.5× | 🔴 act |
| 0.42–0.48× RPM, frequency locks | rotor-dynamic instability (oil whip) — escalating fault; plan shutdown | 🔴 act now |
| 0.65–0.95× RPM | suction recirculation — appears at part load, fades at very low flow; moves with the throttle, not with speed | 🟡 raise flow |
| several × RPM, non-integer | rolling-element bearing defect tones — match against BPFO/BSF/BPFI | 🔴 confirm & replace |
| random low frequency | cavitation or internal recirculation (cavitation energy sits at 10–50 kHz) | 🟡 restore NPSH |
| random high frequency | usually a resonance being excited — confirm with a ≈ 90° phase shift at the peak | 🟡 detune |
3 · Why the triage order is fixed
Non-invasive checks — a gauge reading, a dial sweep, a spectrum — cost minutes and risk nothing; disassembly costs crane time and spares, invites reassembly faults of its own, and destroys evidence: erosion patterns and rub marks get cleaned away before anyone photographs them. So the order is always process data → free mechanical checks → spectrum analysis → disassembly, and each stage either names the fault or earns the right to the next. The priors support it: across rotating machinery roughly 40% of vibration problems trace to unbalance and another 40% to misalignment — 80–90% of the total before hydraulics even enter, and both are visible to the free checks.
Worked example (anchor)
Process pump at 3,000 rpm, 6 impeller vanes, 9 rolling elements per bearing. The analyzer and the chart produce exactly:
| Feature | Order | Frequency | Suspect |
|---|---|---|---|
| Running speed | 1× | 50 Hz | unbalance / bent shaft |
| Twice running | 2× | 100 Hz | misalignment / looseness |
| Vane-pass | 6× | 300 Hz | cutwater gap / eccentric impeller |
| Oil-whirl / whip band | 0.42–0.48× | 21 – 24 Hz | rotor-dynamic instability |
| Recirculation band | 0.65–0.95× | 32.5 – 47.5 Hz | suction recirculation |
| Outer race (Nb = 9) | ≈ 3.6× | 180 Hz | BPFO defect tone |
| Inner race (Nb = 9) | ≈ 5.4× | 270 Hz | BPFI defect tone |
Same machine, symptom side: ticking "vibrates / noisy at all flows" and "excessive power consumption" leaves three causes standing in both sets — foreign object in the impeller, internal rub, misalignment — and the wizard ranks them top, with the dial-check, hand-barring and inspection steps that confirm each.
Engineering criteria applied
- Intersection logic — causes ranked by how many selected symptom sets contain them, tie-broken by specificity (hit count ÷ total symptom coverage), then by cause number.
- Sub-synchronous discipline — the band below 1× is shaded red on the chart: whirl, whip, stall and recirculation all live there; a peak that locks at 0.42–0.48× is an escalating instability, not a nuisance.
- Bearing tones — outer race ≈ 0.4·Nb orders, rolling element ≈ 0.5·Nb, inner race ≈ 0.6·Nb; confirm against the full geometry formula before ordering parts.
- Triage order — process data → free mechanical checks → spectrum → teardown; never open the pump on suspicion alone: performance drop, noise or abnormal driver load are the facts that justify it.