Induction-Motor Slip & Spectral-Candidate Worksheet
Calculate motoring slip and selected frequency candidates from the contemporaneous supply fundamental,even pole count and measured rotor speed. A frequency match is not a fault diagnosis or severity assessment.
Document one steady motoring state
The model is restricted to a rotating induction motor below synchronous speed with slip less than50%. Use the supply fundamental and speed measured during the same stable acquisition. It is not a start-up,plugging,generating or synchronous-motor model.
Synchronous speed Nₛ
Shaft frequency fᵣ
Slip s
Mechanical speed difference
Rotor electrical slip frequency
Classical MCSA spacing Δf
Lower current candidate
Upper current candidate
2× supply reference
Rotor slot/bar passing
Equations and distinct meanings
| Quantidade | Equation | Limite |
|---|---|---|
| synchronous speed | Nₛ=120fₛ/P | r/min for fₛ in Hz and even pole count P. |
| slip ratio | s=(Nₛ−N)/Nₛ | Dimensionless;this worksheet accepts steady motoring0<s<0.5. |
| mechanical speed difference | fΔm=(Nₛ−N)/60 | Hz of mechanical rotational-speed difference. |
| rotor electrical slip frequency | fslip,e=s fₛ=(P/2)fΔm | Electrical rotor frequency;not the broken-bar sideband spacing. |
| classical first-order MCSA spacing | Δf=2s fₛ | Distance from fₛ to each candidate sideband. |
| classical first-order candidates | fL,U=fₛ(1∓2s) | Candidate current components;no amplitude or fault conclusion. |
| rotor slot/bar passing | fZ=Z N/60=Zfᵣ | Geometric passing frequency when Z is verified;not a defect frequency by itself. |
Sources and applicability
IEC Electropedia defines synchronous speed as the rotational speed resulting from system frequency and pole count,and IEV411-46-07 defines slip as the synchronous-to-actual rotor-speed difference expressed per unit or percent of synchronous speed. These vocabulary definitions support the kinematic portion;they do not prescribe a fault diagnosis.
Peer-reviewed experimental MCSA research reports broken-bar-related current candidates at (1±2s)fₛ and emphasizes that amplitudes depend on fault severity,load and excitation frequency. See Zhu et al.,“Practical Aspects of Broken Rotor Bars Detection in PWM Voltage-Source-Inverter-Fed Squirrel-Cage Induction Motors,”2013,DOI 10.1155/2013/128368. More recent experimental/review literature also documents leakage,load sensitivity and the need for corroborating features.
These equations are ordinary induction-machine kinematics and research-derived spectral candidates,not ISO10816,ISO1940 or an ISO fault-severity method. The former related links to withdrawn ISO10816/ISO1940 did not establish the calculator’s formulas or diagnostic rules and were removed.
O que foi corrigido
The former page calculated rotor electrical slip as s·fₛ and then multiplied it by the full pole count to create “pole pass frequency.” Classical broken-bar current spacing is 2s·fₛ. The former result was correct only by coincidence for two poles;it was2× too high for four poles,3× for six and4× for eight.
It then labelled fₛ±n·PPF as rotor-bar sidebands inside a section that required bar count,although those sidebands did not use bar count. The replacement separates the first-order MCSA candidates from the optional geometric slot/bar passing frequency and removes higher-order unsourced tables.
Defaults,presets,URL/history persistence,prefix parsing,typical-slip bands,“always present”2×line claims,automatic fault lists,dB severity claims and the unsafe instant power-off diagnostic rule were removed. The result now starts blank,requires contemporaneous acquisition evidence and rejects odd/non-integer poles,supersynchronous speed,standstill/start-up and slip at or above50%.
Use and interpretation
- Frequency resolution must separate a sideband spaced only2sfₛ from the supply fundamental;document window length,window function,sampling and leakage.
- Use the actual supply/converter fundamental and measured rotor speed from the same load state. Nominal50/60Hz and nameplate speed can move the candidates outside a narrow spectral bin.
- A visible candidate is not specific to one fault,and an absent candidate does not prove a healthy rotor. Compare load-matched baselines and multiple observables.
- Do not perform ad-hoc energized or power-interruption tests from this page. Follow the equipment owner’s approved electrical-safety and diagnostic procedure.
