Cogging Torque⚠ unverified
Electrical / Motors · Compute an approximate cogging torque of a slotted machine
Parameters
| Input | Symbol | Unit | Default | Description |
|---|---|---|---|---|
| Teeth | Teeth | — | 1.0 | Number of stator teeth (slots) |
| B | B | T | 1.0 | Air-gap magnetic flux density |
| A | A | m**2 | 1.0 | Effective air-gap area |
| Output | Symbol | Unit | Description |
|---|---|---|---|
| result | Tcog | N.m | Approximate cogging torque, in newton-metres (N.m) |
The science & history
Understanding the Parameters
-
$N_{teeth}$ — the slotting that creates the periodic reluctance variation; cogging repeats many times per revolution (related to the least common multiple of slots and poles).
-
$B$, $A$ — set the magnetic energy stored in the air gap; more flux over more area means a stronger tendency to "cog" toward aligned positions.
-
$T_{cog}$ — a ripple, not a useful driving torque; it averages to zero over a revolution.
Derivation (an estimate)
Cogging is a reluctance effect: the magnetic circuit's stored energy $W$ depends on rotor position $\theta$ because a magnet facing a tooth (low reluctance) stores different energy than one facing a slot opening. Torque is the position gradient of that energy,
$$T_{cog} = -\frac{\partial W}{\partial \theta}.$$
Estimating the air‑gap energy from the flux ($\sim B A$) and the angular period from the tooth count ($\sim 2\pi/N_{teeth}$ per feature) yields the order‑of‑magnitude scaling used here, $T_{cog} \sim B A\,N_{teeth}/2\pi$. It is only an estimate — accurate cogging prediction needs finite‑element analysis of the exact slot/pole geometry.
Mitigation. Because cogging comes from the interaction of discrete slots and poles, it is reduced by skewing the slots or magnets, choosing fractional slots‑per‑pole, shaping the pole/tooth edges, or going slotless — all of which smear out the alignment preference.
History
Cogging became a central concern with the rise of high‑energy permanent magnets (ferrite, then rare‑earth NdFeB) in servo and BLDC motors from the 1980s, where smooth low‑speed torque is essential. Skewing and fractional‑slot windings are the standard countermeasures.
Related Concepts: Motor Torque, Back Emf, Synchronous Speed
Notes: Registry calculator cogging-torque (unverified). An order‑of‑magnitude estimate only; real
cogging depends on detailed geometry and is computed by FEA.