Modern electric cars with four-wheel-drive architecture usually employ two electric machines: one primary drive motor and one auxiliary drive motor. During aggressive acceleration, both motors can deliver torque together, while during steady-speed cruising, only the primary motor is energized and the auxiliary motor is left to rotate in a trailing state. If a permanent-magnet synchronous motor is used as the auxiliary drive, its back-EMF and drag losses may be unacceptable because the rotor magnets continuously induce losses in the iron core even when the inverter is turned off or the machine is in a free-running state. For this reason, AC induction motors have become very attractive for the auxiliary drive position in high-performance electric cars. Induction motors have lower cogging torque, simpler construction, low cost and excellent reliability. More importantly, they exhibit very low drag torque when de-energized, which is a crucial advantage for auxiliary drive systems in electric cars.
This article describes the complete electromagnetic design and multi-objective optimization process of an AC induction motor used for the auxiliary drive of an electric car. The motor is required to be compact, lightweight, exhibit high power density, high efficiency and low drag torque. In order to reach these targets, we combined classical sizing formulas, fully parameterized finite-element models, and a commercial multi-objective optimization platform. The selected design was then manufactured and tested on a prototype. The measured results show excellent agreement with the simulations, proving that the workflow is efficient and accurate for developing induction auxiliary drive motors in modern electric cars.
1. Main Parameters and Basic Sizing of the Motor
The fundamental data for the motor originate from the vehicle requirements of a high-performance electric car. The auxiliary motor is not required to provide very high continuous torque, but it must have a sufficiently high peak torque and wide constant-power speed range for dynamic overtaking and four-wheel-drive launch. The installation space inside the electric car is restricted, so the stator outer diameter is limited to 210 mm. Table 1 lists the main design data.
| Parameter | Value |
|---|---|
| Peak power / kW | 150 |
| Peak torque / (N·m) | 290 |
| Maximum speed / (r/min) | 15000 |
| Number of pole pairs | 2 |
| Cooling method | Water cooling |
| Insulation class | H |
The active volume of the machine can be estimated with the classical sizing equation used in electric machine design for electric car traction motors:
$$
\frac{D_{i}^{2} L_{\mathrm{ef}} \cdot n}{P’} = \frac{6.1 \times 10^{8}}{\alpha’ K_{\mathrm{Nm}} K_{\mathrm{dp}} A B_{\delta}}
$$
where \(D_{i}\) is the stator bore diameter, \(L_{\mathrm{ef}}\) is the effective core length, \(n\) is the motor speed in r/min, \(P’\) is the apparent electromagnetic power, \(\alpha’\) is the pole-arc coefficient, \(K_{\mathrm{Nm}}\) is the air-gap field waveform coefficient, \(K_{\mathrm{dp}}\) is the winding factor, \(A\) is the electric loading and \(B_{\delta}\) is the air-gap flux density.
For the water-cooled high-power-density traction motor used in an electric car, the typical range of electromagnetic loadings is much higher than that of an industrial induction motor. Based on our previous experience and on the allowable thermal limits, we selected a reasonable set of electromagnetic loadings and obtain an effective core length of 120 mm. The pole count is four, because two pole pairs provide an acceptable balance between inverter switching frequency, flux weakening performance, and end-winding length for this class of automotive induction machines.
2. Air-Gap Length Selection
The air-gap length \(\delta\) has a strong influence on torque capability, magnetizing current, power factor and NVH behavior. If the air gap is increased, the magnetic reluctance rises, the magnetizing current increases, and the torque per ampere is reduced. In a variable-frequency induction motor supplied by a voltage-source inverter, the stator current must increase to maintain the required air-gap flux when the gap becomes larger. Conversely, an extremely small air gap can generate audible magnetic noise and make the mechanical assembly difficult. We considered the manufacturing capabilities of the electric car motor supplier and NVH requirements, and set the air-gap length to 0.4 mm.
3. Stator and Rotor Slot Combination Selection
The number of rotor slots directly affects the harmonic leakage, stray load loss, torque ripple and mechanical strength of the rotor lamination. A smaller number of rotor slots usually causes higher zigzag leakage and larger torque ripple, while a larger rotor slot count increases the current density in the rotor bars and weakens the mechanical robustness of the rotor cage. Since this motor is a four-pole, 48-slot stator machine, candidate rotor slot numbers are 38, 50, 58, 64, 70 and 74. For a grid-fed asynchronous motor, a 64-slot rotor can produce so-called “synchronous cusps” during startup, but in an inverter-fed induction motor for an electric car, the field-oriented controller handles startup smoothly, so this concern is less important.
We performed electromagnetic finite-element simulations for all six slot combinations. The stator current at peak torque, the maximum torque, torque ripple ratio, torque-per-current ratio and efficiency are compared in Table 2.
| Rotor slots | Stator current / A | Max torque / N·m | Torque ripple / % | Torque per current | Efficiency / % |
|---|---|---|---|---|---|
| 38 | 365.5 | 292.71 | 3.23 | 0.801 | 85.39 |
| 50 | 359.2 | 289.73 | 2.95 | 0.807 | 85.49 |
| 58 | 355.7 | 286.14 | 2.32 | 0.804 | 85.53 |
| 64 | 353.4 | 279.86 | 3.90 | 0.792 | 85.55 |
| 70 | 351.1 | 282.07 | 2.52 | 0.803 | 85.56 |
| 74 | 349.5 | 281.65 | 2.30 | 0.806 | 85.55 |
The results show that the rotor slot number has the greatest effect on torque ripple. With the 38-slot rotor, the torque ripple reaches 3.23 %, while with 74 slots the ripple is only 2.30 %. However, a 74-slot rotor lamination has very narrow teeth and may not satisfy the mechanical stress requirement at a maximum speed of 15,000 r/min. The 58-slot and 70-slot combinations both give low torque ripple and acceptable mechanical strength. Considering manufacturing constraints and rotor die reliability, we selected the 70-slot rotor for further design.
4. Fully Parameterized Finite-Element Model
4.1 Stator Lamination Model
The electromagnetic model is first built in the RMxprt module of ANSYS, using the “three-phase induction motor” template. All dimensions that have a significant influence on performance are defined as parametric variables. The stator inner diameter, stator tooth width and stator slot height are chosen as key variables. The non-critical dimensions such as slot opening width, slot opening height and wedge height are initially set to fixed empirical values. This reduces the number of optimization variables and improves the efficiency of the optimizer.
| Fixed parameter | Symbol / expression | Variable parameter | Symbol |
|---|---|---|---|
| Stator outer diameter | 210 mm | Stator inner diameter | \(D_{\mathrm{is}}\) |
| Slot opening width | \(B_{\mathrm{s0}}\) | Stator tooth width | \(B_{\mathrm{ts}}\) |
| Slot opening height | \(H_{\mathrm{s0}}\) | Stator slot height | \(H_{\mathrm{s2}}\) |
| Wedge height | \(H_{\mathrm{s1}}\) |
4.2 Winding Configuration
The stator winding is a single-layer concentric winding with an average coil pitch of 10 slots, which allows simple automatic winding insertion. With the DC-bus voltage and current limits determined by the inverter of the electric car, the number of series turns per phase is first calculated using standard magnetic-circuit equations. The winding turns are treated as fixed during optimization because changing them substantially alters the entire torque-speed characteristic and is rarely necessary after the initial sizing.
To ensure that the conductor cross-section automatically matches the slot area as the geometry variables change, the slot-fill factor is constrained to a maximum value of 82 %. The wire diameter and the number of parallel strands are allowed to be selected automatically by the software. This technique avoids the tedious manual recalculation of strand dimensions during each optimization iteration and greatly improves modeling speed.
4.3 Rotor Model and End Ring Design
The rotor lamination is modeled in a similar way as the stator. A die-cast aluminum cage is chosen for low cost and mass production suitability. The rotor bar shape is identical to the rotor slot geometry, so no additional conductor shape definition is required. Table 4 gives the fixed and variable rotor parameters.
| Fixed parameter | Symbol / expression | Variable parameter | Symbol |
|---|---|---|---|
| Rotor outer diameter | \(D_{\mathrm{is}} – 2\delta\) | Rotor inner diameter | \(D_{\mathrm{ir}}\) |
| Rotor slot opening height | \(H_{\mathrm{r0}}\) | Rotor slot number | \(Z_{\mathrm{r}}\) |
| Rotor slot shoulder height | \(H_{\mathrm{r1}}\) | Rotor tooth width | \(B_{\mathrm{tr}}\) |
| Rotor slot bottom radius | \(R_{\mathrm{r}}\) | Rotor slot height | \(H_{\mathrm{r2}}\) |
The area of the end ring is calculated according to the peak rotor-bar current and the allowable current density in the end ring. In addition, the end-ring shape must provide enough cross-sectional area while satisfying the axial length constraint of the electric car auxiliary drive unit. We designed the end rings with a slightly trapezoidal profile so that the mean radius of the end ring is close to the mean radius of the rotor bars, reducing the additional end leakage reactance.
5. Finite-Element Electromagnetic Simulation
After the RMxprt calculation is complete, a two-dimensional finite-element model is generated automatically from the parametric machine model. Symmetric or anti-symmetric boundary conditions are used where appropriate to reduce computation time. The meshes are refined in the air gap and in the rotor bars to capture the skin effect and harmonic flux accurately at high speed.
The motor is supplied by an ideal three-phase sinusoidal voltage source, representing the fundamental output of the inverter. The instantaneous phase voltages are defined as:
$$
u_{a} = \sqrt{2} U_{\mathrm{ph}}\sin\!\left(\frac{2\pi p n t}{60}\right)
$$
$$
u_{b} = \sqrt{2} U_{\mathrm{ph}}\sin\!\left(\frac{2\pi p n t}{60} – \frac{2\pi}{3}\right)
$$
$$
u_{c} = \sqrt{2} U_{\mathrm{ph}}\sin\!\left(\frac{2\pi p n t}{60} – \frac{4\pi}{3}\right)
$$
where \(U_{\mathrm{ph}}\) is the RMS phase voltage, \(p\) is the number of pole pairs, \(n\) is the rotational speed in r/min and \(t\) is time in seconds. For the peak-torque operating point, the motor is controlled at the optimal slip frequency so that the maximum torque per inverter volt-ampere is obtained. The electromagnetic torque and stator current are calculated after the steady-state time-periodic solution converges.
For high-power-density traction motors in electric cars, the peak torque point is not only a measure of acceleration performance but also the point with the highest current and copper loss. The objective of the design is to obtain as much torque as possible for a given stator current or, equivalently, to increase the torque-per-ampere ratio. A larger torque-per-ampere ratio yields three direct benefits for the electric car:
- It reduces copper loss in the stator winding, so the cooling system becomes less challenging;
- It lowers the current density and thus improves the inverter overload capability;
- It may allow the use of a power module with a smaller current rating, reducing system cost.
6. Multi-Objective Optimization
6.1 Optimization variables and constraints
The initial design is established by conventional magnetic-circuit sizing. We then optimize the lamination geometric parameters using the modal-based optimizer integrated with the finite-element model. Six parameters are selected as variables, with their initial values and ranges shown in Table 5. The lower and upper bounds are chosen around the initial values so that the slot dimensions remain compatible with a stamping die and with the fixed stator outer diameter.
| Variable | Initial value / mm | Range / mm |
|---|---|---|
| Stator inner diameter \(D_{\mathrm{is}}\) | 126 | 113.4 – 138.6 |
| Stator tooth width \(B_{\mathrm{ts}}\) | 4.8 | 4.3 – 5.3 |
| Stator slot height \(H_{\mathrm{s2}}\) | 18 | 16.2 – 19.8 |
| Rotor tooth width \(B_{\mathrm{tr}}\) | 3.11 | 2.8 – 3.5 |
| Rotor slot height \(H_{\mathrm{r2}}\) | 16.63 | 15 – 18.3 |
During the optimization, the slot-fill factor is not allowed to exceed 82 %. The stator and rotor tooth flux densities must also remain below a saturation level. The peak torque is evaluated at the base-speed operating point where the inverter voltage is just reaching its maximum output.
6.2 Optimization formulation
The design problem can be stated as a constrained multi-objective optimization problem:
$$
\min_{\mathbf{x}} \mathbf{F}(\mathbf{x}) = \bigl( -f_{\mathrm{torque}}(\mathbf{x}),\ f_{\mathrm{current}}(\mathbf{x}),\ -f_{\mathrm{efficiency}}(\mathbf{x}) \bigr)
$$
where \(\mathbf{x}\) contains the geometric variables in Table 5, \(f_{\mathrm{torque}}\) is the peak electromagnetic torque, \(f_{\mathrm{current}}\) is the required stator current at a given voltage, and \(f_{\mathrm{efficiency}}\) is the motor efficiency at the peak torque operating point. Instead of giving all three objectives the same weight, we treat the peak torque and stator current as the primary objectives because the auxiliary drive motor is only used intermittently in the electric car. Efficiency, although important, has a lower priority because the motor spends most of its time in a zero-torque drag state. Nevertheless, efficiency is included as a secondary objective to prevent the optimizer from producing a design with excessively small rotor bars and high rotor losses.
Using the optiSLang software coupled with the finite-element model, a total of 584 feasible designs were evaluated. The algorithms automatically selected the most appropriate method between gradient-based search, evolutionary strategy, adaptive response surface and other techniques. The evaluated results are presented as a four-dimensional Pareto solution set, with the three objectives displayed on independent axes and the achievable torque as the horizontal manifold. The Pareto front clearly shows the trade-off between torque and current: for a given rotor slot geometry, producing a larger torque always requires a larger stator current.
6.3 Selection of the final design
To reduce the complexity of the three-dimensional Pareto front, we first project the solutions onto the torque–current plane. From the projected front, we identify the lower envelope corresponding to the minimum current required for each torque value. Points lying above this envelope are discarded because they cannot achieve the same torque with lower current. This filtering yields 93 candidate designs that satisfy the primary objective of “maximum output torque under minimum current” or, equivalently, “maximum torque-per-current ratio”.
Subsequently, we compare the efficiency values of these 93 remaining designs. Because the auxiliary drive in an electric car only runs for short time intervals, the efficiency difference is relatively small among the candidate designs. Still, we choose the design with the highest efficiency among the filtered set. This step follows the analytical hierarchy process concept: first prioritize the torque/current objective; then use the secondary efficiency objective to make the final selection. The final optimization result is summarized in Table 6.
| Variable | Initial value / mm | Final value / mm |
|---|---|---|
| Stator inner diameter \(D_{\mathrm{is}}\) | 126 | 129.3 |
| Stator tooth width \(B_{\mathrm{ts}}\) | 4.8 | 4.85 |
| Stator slot height \(H_{\mathrm{s2}}\) | 18 | 16.2 |
| Rotor tooth width \(B_{\mathrm{tr}}\) | 3.11 | 3.21 |
| Rotor slot height \(H_{\mathrm{r2}}\) | 16.63 | 16.9 |
7. Performance Comparison Before and After Optimization
Using the same voltage and current limits, we calculate the external torque-speed and power-speed characteristics of the motor before and after optimization. In the constant-torque region, the optimized motor produces approximately 310 N·m while the initial design produces 298 N·m. Therefore the multi-objective optimization increases the peak torque by nearly 4 % without any increase in the rated inverter current. This improvement comes from a better balance between the stator bore diameter and the tooth/slot widths, which reduces the magnetic saturation in the teeth and allows the active material to be used more effectively.
In the flux-weakening region, the post-optimization torque curve follows the expected inverse-speed hyperbola closely. The high-speed torque capability is not noticeably degraded by the geometric changes, because the selected stator slot height reduction lowers the leakage inductance appropriately, allowing the motor to produce sufficient torque at high speed. The efficiency map of the optimized motor is slightly higher than that of the initial design. The maximum efficiency increases from 94.8 % to 95.0 %. The high-efficiency region is centered in the middle-to-high speed range, which matches the typical operating condition of an auxiliary drive motor in an electric car.
8. Prototype Manufacturing and Experimental Verification
In order to validate the simulation model and the selected optimization, we manufactured a prototype using the finalized lamination dimensions. The stator laminations and rotor laminations were fabricated by progressive dies, and the rotor cage was aluminum die-cast. The stator winding was inserted using an automatic winding machine with the same slot-fill factor as in the model. The water-cooled housing and end shields were also dimensioned to satisfy the electric car installation envelope. The prototype was then installed on a dynamometer test bench.
An external-characteristic test was performed by measuring the motor torque and speed under inverter supply while maintaining the DC-bus voltage and current limits as specified. The measured torque and power curves match the finite-element predictions very closely over the whole speed range up to the maximum speed of 15,000 r/min. The small discrepancy observed at high speed is mainly attributed to the additional mechanical loss, iron losses caused by punching stress, and the difference between the assumed and actual winding end-leakage inductance. The test results also confirm that the motor can continuously run at the rated auxiliary power condition without violating the temperature rise limit.
The measured torque ripple is acceptable for the gearbox and drive shaft NVH behavior. In driving tests, the electric car equipped with this induction auxiliary motor shows no additional noise or vibration compared with a permanent-magnet auxiliary motor during synchronous operation. More importantly, when the motor is not energized and the rotor is dragged by the wheels, the no-load drag torque is substantially lower than that of a permanent-magnet machine, contributing to an improvement in the overall driving range of the electric car on highway cycles.
9. Conclusion
We have presented a complete design and optimization methodology for an AC induction motor used as the auxiliary drive in an electric car. The following conclusions can be drawn from this work:
- The combination of a magnetic-circuit sizing formula with a fully parameterized finite-element model greatly speeds up the initial dimensioning. The use of a commercial multi-objective optimization platform eliminates the need for cumbersome manual iteration and gives a more comprehensive view of the design space.
- Only the sensitive dimensions should be set as optimization variables. Non-critical dimensions can be fixed to empirical values. Reducing the number of variables is very important because the number of required finite-element evaluations grows rapidly with every additional variable.
- For an auxiliary drive motor in an electric car, the optimization objectives must be defined according to the actual driving cycle. Maximizing the torque-per-current ratio should be the first priority. Efficiency is a secondary objective because the auxiliary motor is mostly used in short transient events. This hierarchical approach leads to a more accurate selection of the final design.
- The prototype test results confirm that the final optimized motor meets all the performance targets for an electric car auxiliary drive. The measured external characteristic agrees well with the finite-element simulation. Therefore, the proposed methodology is effective for engineering practice and can save considerable time in motor development projects.
In summary, the AC induction motor is still a competitive candidate for auxiliary drives in high-performance electric cars. With advanced multi-objective optimization tools, the induction motor can be designed to achieve high torque density, high efficiency and low drag torque simultaneously. These characteristics are essential for modern electric cars that require both excellent acceleration and long driving range.