Electric motors play a vital role in the electrification of transportation systems. Along with enabling the operation of vehicles, these motors work as generators during regenerative braking. Electric motors with high power density and efficiency improve the maximum distance traveled on a single charge. Achieving high power density and efficiency in electric motors is thus a standard design goal. Modeling and simulation can be used to ensure that these requirements, among others, are met.
Here, we’ll first briefly cover different motor types and the approaches for modeling them.
Modeling various motors types
Several types of electric motors are used in automotive applications. Radial flux motors are the most commonly used motor type. However, axial motors are becoming increasingly popular since they can be compact and well-suited for in-wheel applications.
Another popular type of motor is the linear motor, which is used in transportation systems that employ magnetic levitation techniques. All three of these motor types can be modeled with fully coupled multiphysics modeling capabilities.
Linear motors can be modeled effectively in 2D, while 3D is more suitable when end-winding effects are of interest. For axial motors, 3D modeling is typically used for axial motors because of the geometrical structure. An equivalent 2D design can be modeled by rolling out the cross section in parallel to the axis of rotation. Radial flux motors can also be modeled in 2D and 3D, with 2D being the most common case.
Some effects like the rotor skew cannot be reproduced in plain 2D, but 2.5D provides a good approximation. In 2.5D modeling, multiple 2D cross-sections corresponding to various skewing angles can be modeled together to gain results similar to 3D with only a small fraction of the computational effort. 3D modeling is typically only used to capture multiphysics effects that are extremely hard to capture in 2D and to verify the accuracy of existing 2D models.
Multiphysics modeling of e-motors
Electric motors operate through a combination of electromagnetic fields, mechanical forces, heat transfer, and other physical phenomena. They require multiphysics simulation for a complete understanding. By building finite element models that include multiphysics effects, performance is closer to real-world applications, and designs can be optimized early in product development.
One of the primary steps in modeling an electric motor is computing the electromagnetic fields. This computation is required to examine the machine’s electromagnetic torque for a given electrical excitation. Additionally, electromagnetic losses obtained from this type of simulation can be used with a heat transfer model to compute the temperature rise. The primary effect of temperature on the electromagnetic analysis can be considered by including temperature-dependent material properties, such as linearized resistivity.
This will result in a two-way coupled multiphysics model. Similarly, different types of multiphysics phenomena can be modeled by coupling a wide range of relevant physics phenomena, as shown in Figure 1.
Figure 1. The multiphysics phenomena involved in electric motor modeling.
Electrothermal modeling
Modeling electromagnetic motors involves modeling the stator and rotor geometry, which includes laminated electrical steel, permanent magnets, and multiphase windings. The primary results from the electromagnetics analysis are torque, electromagnetic losses, and efficiency, which can be obtained as a function of torque and speed.
Some of the losses that are of interest are the eddy current losses in the permanent magnets and the iron losses in the laminated steel, a soft magnetic material with nonlinear B-H characteristics. The eddy current losses can be computed based on the electrical conductivity of the magnets. The iron losses in the steel can be computed with standard loss models like Steinmetz or Bertotti, or taken from a loss data curve, which provides loss as a function of magnetic flux density and frequency.
Since many of these loss models are frequency dependent (meaning different harmonics contribute to the loss differently), simulation data in the time domain is converted to the frequency domain with the help of the fast Fourier transform (FFT).
Based on the computed loss, the temperature rise of the motor can be determined with an electrothermal model. The rise in temperature affects the material properties of copper windings and permanent magnets. These material properties can be modeled as a function of temperature. This results in a fully coupled electrothermal model.
Figure 2 shows an efficiency map obtained from a fully coupled electrothermal model. It shows a reduction in peak torque with an increase in speed due to the rise in temperature of the permanent magnets. Modifying the design to improve the efficiency at critical operating points increases the vehicle’s driving range.
Figure 2. An example of an efficiency map for a surface-mount permanent magnet motor, including thermal effects.
Coupling electromagnetics with structural analysis
Electromagnetic forces in the air gap between the stator and the rotor could cause the stator and motor housing to vibrate, leading to acoustic noise. To better understand a motor’s structural and acoustic behavior, the electromagnetic stator forces can be used as an excitation in a structural mechanics model (resulting in stress and strain). The mechanical vibrations can then be coupled with pressure acoustics to determine the noise.
Figure 3 shows the von Mises stress on a stator due to electromagnetic forces and the resulting acoustic noise levels. This type of multiphysics analysis is essential for understanding an electric vehicle’s (EV’s) noise, vibration, and harness behavior.
Figure 3. The fourth harmonic vibrational mode of a surface-mount permanent magnet motor at 7000 rpm.
Time-periodic electromagnetics
When modeling highly inductive devices such as electric motors, the traditional transient method can be used for electromagnetic analysis. However, using this method to compute steady-state results requires solving for multiple electrical cycles.
To simplify the computation of a steady state, the time-periodic formulation can be used instead, which solves for steady-state results directly. In this approach, the electromagnetic field is solved for all times at once, and periodicity is imposed in time. The time-periodic formulation is particularly well-suited for periodic systems with anharmonic properties. This can be because of a non-harmonic excitation or a nonlinear material property.
Apart from finding steady-state conditions directly, the time-periodic method reduces complexity in coupling electromagnetics with other physics. Since the time constant of an electromagnetics model is extremely small compared to heat transfer, the traditional transient approach would need to continue the electromagnetic simulation until nominal thermal conditions have been reached. This may require many electrical cycles.
With the time-periodic approach, the fully coupled physics phenomena can be solved in one go, with the electromagnetics model solving for the time-periodic conditions and the thermal model solving for the thermal steady-state conditions. This results in a significant reduction in computation time. To summarize, the time-periodic approach is well suited for multiphysics problems.
E-motor design optimization
An e-motor is typically designed to meet certain performance requirements. Obtaining the design parameters that result in higher power density and efficiency is crucial for EVs. This makes the optimization study essential in the design process.
Different optimization methods can be used, including parameter optimization, shape optimization, and topology optimization. Each method requires defining an objective function and a set of constraints. The objectives and constraints can be defined based on a single physics or multiphysics phenomena. For example, you could define an objective as maximizing the average torque the motor develops while constraining the volume of permanent magnets and stress on the rotor bridge in an interior permanent magnet motor.
In parameter optimization, optimal dimensions can be obtained for various motor geometry parameters (such as the magnet thickness and width, back iron thickness, etc.), for a given set of objective functions and constraints. Shape optimization finds the optimal shape of a surface or a part. Figure 4 shows how the surface of an interior magnet rotor can be optimized to minimize the torque ripple. Finally, topology optimization optimizes the material distribution, which helps reduce weight without compromising performance.
These methods can incorporate objectives based on multiple physics to find an optimal design for multiphysics machines more easily.
Figure 4. The magnetic flux density distribution in a shape-optimized interior magnet rotor.
Simulation is a key design component
Improving the driving range and reducing the costs of EVs helps with the widespread adoption of these systems. Part of achieving electric vehicle goals is designing highly efficient and cost-effective motors.
Simulation reduces development time significantly and is thus an important aspect of product development. Using multiphysics simulation, engineers can model electric motors with effects that closely align with real-world behavior. Furthermore, optimizing such designs leads to creating advanced and competitive products on the market.
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