TEAM problem 30B - Single-phase induction machine

This induction machine is one of the International TEAM Workshop series of benchmark problems used to challenge and test finite element analysis software. Shown is a half-model of the device, which has a periodic boundary condition on the plane of symmetry. A complete description of this problem is given in the paper by Kent Davey, "Analytic Analysis of Single and Three Phase Induction Motors." It was solved using the MagNet transient 2d with motion solver in a single transient run, as a velocity-driven problem. The velocity was specified as a staircase function spending 100ms at each speed, enough time for the transients to die out. The time step size varied from 1 ms per time step during the first 80 ms at each speed to 0.25 ms per time step during the last 20 ms at each speed. The average torque was calculated from the transient waveforms in the last 20 ms at each speed.

Results

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The average torque at different speeds from zero to synchronous speed (blue trace), compared to the analytic results (red trace). The analytic solution uses some approximations, so with this good a match there is no telling which is closer to the actual torque value.

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The ripple torque, which close to synchronous speed is larger than the average torque. This implies that during part of the cycle the magnetic forces work against the rotor motion.