Motor Efficiency Map Generation — Loss Separation via Electromagnetic Field FEM and Iso-Efficiency Contour Creation Methods

It's a plot with rotational speed on the horizontal axis and torque on the vertical axis, showing the motor efficiency at each operating point as contour lines. Just like contour lines on a map, you draw lines for "95% efficiency," "90% efficiency," and so on.

It's for evaluating the average efficiency over an EV's driving pattern. Since you can see which operating points are used frequently in driving cycles like WLTP or JC08, you can optimize the design so that the high-efficiency "island" falls in that high-frequency region. For example, an EV that drives a lot on highways would want the high-efficiency region around 8000-12000 rpm, while one mainly for city driving would want it around 3000-5000 rpm.

Exactly. Having just one theoretical maximum efficiency point is not enough. The design philosophy of maximizing "practical efficiency" tailored to actual usage is the most important thing in motor design practice.

The total motor loss can be largely separated into three categories.

• Iron Loss $P_{\mathrm{iron}}$: Losses originating from magnetic flux density variation within the core (iron core). Divided into hysteresis loss and eddy current loss.
• Copper Loss $P_{\mathrm{cu}}$: Heat generation loss (Joule loss) due to the electrical resistance of the windings.
• Mechanical Loss $P_{\mathrm{mech}}$: Bearing friction and rotor windage loss.

Whether these three can be accurately separated and calculated is the key to a high-quality efficiency map.

Good observation. In the low-speed, high-torque region, copper loss is overwhelmingly large. Because large currents are flowing, $I^2R$ is significant. On the other hand, in the high-speed region, iron loss increases rapidly. Iron loss is proportional to the 1st to 2nd power of frequency (≈ rotational speed). So, as speed increases, "the main player switches from copper loss to iron loss." The shape of the efficiency map's contour lines reflects this interplay between the two.

The most widely used model for iron loss is the modified Steinmetz equation (iGSE: improved Generalized Steinmetz Equation). The original Steinmetz equation is for sinusoidal flux, but the flux waveform inside a motor contains harmonics, so iGSE is needed.

Exactly. Eddy current loss is proportional to the square of the steel sheet thickness $d$. $k_e \propto d^2 / (12 \rho)$ ($\rho$ is the electrical resistivity of the steel sheet). That's why high-speed motors use 0.2–0.25mm thick electrical steel sheets. If you pursue even lower iron loss, amorphous cores are also an option. But the cost jumps up.

Sharp observation. Copper's temperature coefficient of resistance is about 0.393%/°C. Based on 20°C, $R_s(T) = R_{s,20}[1 + 0.00393(T - 20)]$. If the winding temperature rises to 120°C, the resistance increases by about 39%. That's why accurate efficiency maps require coupled electromagnetic-thermal analysis. Furthermore, at high frequencies, the effective resistance increases due to skin effect and proximity effect. This is called AC loss.

Right, mechanical loss is not a direct calculation target of electromagnetic FEM. It is generally estimated using the following empirical formula:

$$ P_{\mathrm{mech}} = P_{\mathrm{bearing}} + P_{\mathrm{windage}} = k_b \omega + k_w \omega^3 $$

Bearing loss $k_b \omega$ is proportional to the first power of rotational speed, and windage loss $k_w \omega^3$ increases with the cube. It's common practice to identify $k_b$, $k_w$ from experimental data and incorporate them into the efficiency map.

Exactly. The formula is "output/(output+loss)" that even a middle school student can understand, but calculating the denominator's $P_{\mathrm{cu}}$, $P_{\mathrm{iron}}$, $P_{\mathrm{mech}}$ precisely for each operating point requires the full power of electromagnetic field FEM. Especially the accuracy of $P_{\mathrm{iron}}$ determines the reliability of the efficiency map.