IPM Motor (Interior Permanent Magnet Type)

An IPM (Interior Permanent Magnet) motor has a structure where permanent magnets are embedded inside the rotor core. Unlike SPM which attaches magnets to the surface, IPM can utilize the saliency of the iron core. In other words, a difference arises between the d-axis and q-axis inductances.

In addition to magnet torque, Reluctance torque can be used. This is the greatest strength of IPM. The reason it is adopted as the main motor for EV propulsion is that it can achieve both high torque density and a wide constant power operating range.

The torque equation in the dq coordinate system is as follows.

Here, $p$ is the number of pole pairs, $\psi_m$ is the permanent magnet flux linkage, $L_d$, $L_q$ are the d-axis and q-axis inductances, and $i_d$, $i_q$ are the d-axis and q-axis currents.

Exactly. In IPM, the magnets block the d-axis magnetic path, so $L_d < L_q$, and the saliency ratio $\xi = L_q / L_d$ becomes about 1.5 to 3. The larger this saliency ratio, the greater the contribution of reluctance torque.

Also, the voltage equations are important.

From these voltage equations, the voltage limitation at high speeds determines the necessity of field-weakening control.

That's right. In JMAG and Ansys Maxwell, the flux linkage is calculated for each rotation angle to determine the dq-axis inductances. Note that due to nonlinearity, the inductance changes depending on the current magnitude.

It's the diffusion equation using the 2D magnetic vector potential $A_z$.

Here, $\nu$ is the magnetic reluctivity (reciprocal of permeability), $\mathbf{J}_0$ is the external current density, $\mathbf{M}$ is the magnetization vector, and $\sigma$ is the conductivity.

Exactly. The nonlinear B-H characteristic of the iron core is incorporated as $\nu(B)$, and nonlinear iteration is performed using the Newton-Raphson method. In IPM, magnetic saturation is strong, so this nonlinear processing is key to analysis accuracy.

Let me summarize the important points.

• Bridge Mesh: The thin bridge (0.5-1mm) that holds the magnets experiences severe magnetic saturation. Place at least 3 layers of elements here.
• Nonlinear B-H Curve: Characteristics vary greatly depending on the type of electrical steel sheet (35H300, 20HIM, etc.)
• Temperature Dependence of Magnets: The residual flux density of NdFeB magnets decreases with a temperature coefficient of $\alpha_B \approx -0.12\%/°C$.
• Current Phase Angle Sweep: To find the MTPA (Maximum Torque Per Ampere) control point, sweep the $\beta$ angle from 0° to 90°.

JMAG-Designer has an automatic recognition function for thin parts, but don't rely on it too much. Always visually check the mesh quality and ensure the aspect ratio of the bridge part is 5 or less.