Machines

Building a PMSM or induction machine from parameters, and the analysis tools built around it: skew, bEMF and cogging, the IM equivalent circuit, performance curves and maps, mass estimation, and the PDF report.

Turn the module on from Addons → Machines Module before anything below is available; it adds a Machine workflow tab and a Model → New Machine menu item, and hides the plain-geometry tools that a parametric machine model does not need.

Topologies

New Machine asks for a topology first, since it decides which parameter fields follow: PMSM (inner rotor, surface or interior permanent magnets), PMSM – Outrunner (the magnet ring on the outside, the stator inside), IM (squirrel-cage induction machine, inner rotor) and IM – Outrunner. The two outrunner variants mirror their inner-rotor counterpart's parameters and analysis tools; only the geometry construction differs.

Slot/pole combination

Set the number of stator slots and rotor poles directly, or open the Slot/Pole Advisor next to the field: for a concentrated (fractional-slot) winding it lists valid combinations in your slots-per-pole-per-phase range together with each one's winding factor, so you can compare candidates before committing to a geometry. A distributed winding instead expects an integer slots-per-pole-per-phase and does not need the advisor.

Geometry parameters

The remaining Machine tab fields build the cross-section: stator outer/inner diameter, slot shape (opening, tooth width, back-iron), rotor outer diameter and air gap, and, for a PMSM, magnet shape and embrace (surface-mounted) or the pocket geometry of an interior-magnet rotor. Changing a geometry field rebuilds the shapes but not the mesh — Generate Mesh still needs a press before you solve, exactly as for a hand-drawn model (see Meshing). Winding parameters (layout, layers, turns, chording, fill factor, end-winding extension) and phase excitation are the same fields as Coils & circuits — windings; the machine module only adds the automatic per-slot coil construction, not a new set of options.

Outrunner geometry notes

The two outrunner topologies reuse their inner-rotor counterpart's parameter set almost unchanged — same slot shape fields, same magnet/pocket fields — but three things differ in how the cross-section is actually built:

• the stator sits on the inside and the rotor ring on the outside, so Stator Outer Diameter and Rotor Outer Diameter swap which one bounds the air gap — the air gap is still entered the same way, it just now separates the stator's outside from the rotor's inside;
• the inner stator's tooth geometry is built at a half-slot-pitch rotation relative to the inner-rotor case, so a Custom Rotor DXF sector drawn for one orientation will not simply drop into the other without re-checking its angular alignment against the stator slots;
• for the IM outrunner, the squirrel cage sits in the outer ring exactly as it would in an inner rotor — Number of Bars and the cage wiring below behave identically, only the bar ring's radius changes.

Everything else on this page — skew, bEMF/cogging, the equivalent circuit, performance analysis, mass estimation, the PDF report — applies to an outrunner exactly as described for its inner-rotor counterpart.

Custom rotors

Beyond the built-in parametric rotor shapes, Custom Rotor lets you import a DXF drawing of one rotor sector (or one pole) and have Nabla mirror and array it into the full rotor, using the same sector/symmetry copy settings as the parametric rotors. This is the escape hatch for a rotor geometry — a Halbach array, an unusual squirrel-cage bar shape, a trapezoidal-tooth IM rotor — that the parametric fields cannot express directly.

The squirrel cage

For an IM topology, Number of Bars generates one region per rotor bar plus the end rings, wires each bar into its own short-circuited loop with the two end rings, and names each bar's coil so it shows up individually in post-processing (bar current, bar joule loss). Rebuilding the rotor geometry regenerates this cage wiring; if you have added your own stator circuit wiring by hand, do so only after the rotor geometry is final, since a rotor rebuild resets the rotor-side circuit.

Skew

Skew Slices (default 1, meaning no skew) splits the rotor — the rotor bars for an IM, the magnet or lamination stack for a PMSM — into that many axial slices, each offset by a fraction of one slot pitch, and solves and couples all slices together in one run. It is the standard technique for suppressing slot-harmonic torque ripple and cogging. It is substantially more expensive than a single-slice run (of the order of 6–7× the matrix size and 10–12× the wall time for the same mesh, and the solver log prints a measured cost estimate for the run), and it does not combine with an axisymmetric problem type or with second-order elements across more than one slice.

Back-EMF, cogging torque and Ld/Lq

For a PMSM, the Machine tab's analysis buttons run a short automated sequence of solves and report the results as a graph plus a summary value, without you having to set each operating point by hand:

• Back-EMF — a single static solve at the no-load operating point extracts the permanent-magnet flux linkage directly, and the peak line-to-neutral back-EMF at your rated speed follows from it (e_peak = ω_e·|λ_PM|) — no time-stepped no-load run is needed;
• Cogging Torque — a transient, current-free sweep of one electrical period that reports the ripple torque from magnet/slot interaction alone;
• Ld/Lq — injects test currents along the rotor's own d and q axes and reads back the resulting flux linkages, giving the two synchronous inductances a performance-analysis run needs.

Stator or rotor skew changes these results: back-EMF and cogging are evaluated from the axial average across all skew slices, not just the centre slice, so a skewed run correctly shows the ripple reduction skewing is meant to produce.

The IM equivalent circuit

Extract Equivalent Circuit runs a short sequence of simulations — a no-load solve and one or more reduced-frequency locked-rotor solves — and fits the classic per-phase equivalent circuit (stator resistance and leakage reactance, magnetizing branch, referred rotor resistance and leakage reactance) from the results. Two extraction methods trade run time against accuracy: the default combines a nonlinear no-load solve with a locked-rotor time-harmonic solve at a quarter of rated frequency; Fast instead uses a single skew slice and a trimmed steady-state window, at some accuracy cost on a heavily skewed rotor. A successful extraction unlocks the analytical performance curves below, which are derived from the circuit rather than from further transient solves.

Performance analysis

Once the equivalent circuit (IM) or Ld/Lq and bEMF (PMSM) are available, the Performance Analysis tab derives, without further FEM solves:

• Torque vs. speed / slip — the analytical torque curve, anchored to your simulated operating point rather than a pure textbook circuit;
• Current and power factor vs. speed — phase current and PF from the circuit's input impedance, likewise anchored against the FEM solve at one operating point;
• Efficiency and loss curves — combine the circuit with a two-anchor (no-load and loaded) iron-loss fit, split into stator iron, rotor iron, and stator/cage copper loss series, plus a single-point loss breakdown pie chart;
• Efficiency map — a torque–speed heatmap of efficiency over the drive's whole envelope, with iso-efficiency contour lines and labels.

Set the supply (fixed voltage, or a drive's DC bus voltage with Star/Delta connection and optional SVPWM) under Performance Input first; the curves reconcile phase-to-neutral and line-to-line quantities for you once the connection is set. A Max Iph vs. drive Vdc warning appears on the torque-vs-speed curve wherever the requested current cannot actually be delivered at that speed by the given bus voltage — read it before trusting the curve at high speed.

Mass estimation

The Machine summary's Mass Estimation triangulates each simulation region on demand and multiplies its area by the axial length and the assigned material's density, so no extra input is needed beyond materials already assigned for the field solve; a model with sector symmetry is scaled up by the number of symmetric sectors automatically.

PDF report

Model → Create Report writes a self-contained PDF for a solved PMSM or IM model (including their outrunner variants): a parameter table, key waveforms (phase current/voltage, flux linkage, torque), a loss summary, and field images, without disturbing whatever step or plot selection you currently have on screen. Only sections your model actually has data for are offered — a section that needs the equivalent circuit or the calculated parameters is hidden rather than shown empty until that data exists.

Worked example: a PMSM from parameters to a performance map

This walks the whole pipeline once, top to bottom, for a surface-mounted PMSM. Each step links to the section above that covers it in detail.

1. Enable the module — Addons → Machines Module, then Model → New Machine and pick PMSM (see Topologies).
2. Pick a slot/pole combination — for a concentrated winding, open the Slot/Pole Advisor and choose a combination with a high winding factor and low cogging-torque risk rather than typing numbers in blind (see Slot/pole combination).
3. Fill in the cross-section — stator and rotor diameters, air gap, slot shape, magnet shape/embrace, then the winding fields (layers, turns, fill factor) shared with Coils & circuits (see Geometry parameters). Press Generate Mesh once the shapes look right (see Meshing).
4. Run the automated analyses — Back-EMF for the no-load voltage, Cogging Torque to check ripple before committing to the design, and Ld/Lq so a performance run has both synchronous inductances available (see Back-EMF, cogging torque and Ld/Lq). Skew slices, if you use them, feed into all three automatically.
5. Set the supply under Performance Input — voltage source or a drive's DC bus with Star/Delta and optional SVPWM — then open Performance Analysis for torque-vs-speed, current/PF, efficiency and loss curves, and the efficiency map, all derived from the bEMF/Ld/Lq you just extracted without another transient solve (see Performance analysis).
6. Check the mass and write the PDF report once you are happy with the design (see Mass estimation and PDF report).

The induction-machine path follows the same shape, with two swaps: no bEMF/cogging/Ld/Lq step — instead run Extract Equivalent Circuit once the squirrel cage is wired (see The squirrel cage) — and Performance Analysis then works from that circuit instead of from PM flux and inductances.

Next steps

• Coils & circuits — the winding fields the machine module drives.
• Motion — the rotary motion zone a machine model always uses.
• Thermal — running a heat-conduction pass on the same cross-section.
• Automation — scripting this same pipeline from Python or an MCP client.
• Back to the contents.