Multi-objective Optimization Design and Temperature Rise Estimation of In-wheel Electric Machine

doi:10.12382/bgxb.2024.0355

Abstract

Abstract:

According to the high torque density requirement for electric drive system of special vehicle,a multi-physics-based multi-objective optimization design and temperature rise estimation method for in-wheel electric machine is proposed to effectively enhance the peak torque and efficiency,reduce the torque ripple and prevent the in-wheel electric machine from overheating.The electromagnetism finite element model and loss models of in-wheel electric machine are established based on the vehicle mission profile.Non-dominated sorting genetic algorithm-Ⅱ(NSGA-Ⅱ) is applied to optimize the peak torque,torque ripple,efficiency,and heat exchange area of winding.Based on the key geometry parameters and losses characteristics obtained,a temperature rise estimation model for electric wheel lumped parameter thermal network including the electric machine is established to estimate the temperature rise and distribution characteristics under typical working conditions.The accuracy of the temperature rise estimation model is validated through a testbench.The result shows that the peak torque and its efficiency of optimized in-wheel electric machine are increased 5.2% and 1.15%,respectively.The root mean square error of the estimated temperature is less than 4.3℃ compared with experimental result,and the calculation effort is dramatically reduced.

Key words: in-wheel electric machine, multi-objective optimization, thermal network model, temperature rise estimation

GAO Zhuo, LI Junqiu, ZHOU Yang, ZHANG Xiaopeng, TAN Ping, QIU Meng, ZHU Jiahao. Multi-objective Optimization Design and Temperature Rise Estimation of In-wheel Electric Machine[J]. Acta Armamentarii, 2025, 46(4): 240355-.

Figures/Tables 22

Fig.1 Inner rotor E-wheel structure

Fig.2 Design and optimization process of in-wheel electric machine

Fig.3 Loss characteristics of silicon steel plate

Fig.4 Schematic diagram of electric machine thermal network

Table 1 Heat exchange calculation method of electric machine thermal network nodes

热阻计算区域	传热方向	等效热阻计算方法
r1、r2、r4、s5	径向	$\frac{1}{2 \pi \lambda L_{c}} \ln \left(\frac{r_{o}}{r_{i}}\right)$
r3、r5、s2	径向	$\frac{1}{\varphi \lambda L_{c}} \ln \left(\frac{r_{o}}{r_{i}}\right)$
r4-s2	径向	$\frac{L_{c}}{N u \lambda A}$
s1、s3、s3、s4	径向	$\begin{array}{l}\frac{L_{C}}{\lambda\left(A_{o}-A_{i}\right)} \ln \left(\frac{x_{o}}{x_{i}}\right) \text {（梯形）；}\\\frac{L_{c}}{\lambda A}(\text { 矩形 })\end{array}$
s1、s4	周向	$\frac{\varphi}{2 \lambda l} \cdot \frac{r_{i}+r_{o}}{r_{o}-r_{i}}$

Fig.5 E-wheel thermal network

Fig.6 Structure and key design parameters of electric machine

Fig.7 NSGA-Ⅱ optimization procedure

Fig.8 Optimized results

Table 2 Comparison of objectives before and after optimization

优化目标	初始设计	优化设计	优化结果对比/%
$T ¯$ /(N·m)	1147.41	1207.62	5.2
$Δ T T ¯$ /%	3.59	3.65	0.06
η_em/%	85.58	86.73	1.15
A_s/mm²	3419.8	5142.16	50.4

Table 2 Comparison of objectives before and after optimization

优化目标	初始设计	优化设计	优化结果对比/%
$T ¯$ /(N·m)	1147.41	1207.62	5.2
$Δ T T ¯$ /%	3.59	3.65	0.06
η_em/%	85.58	86.73	1.15
A_s/mm²	3419.8	5142.16	50.4

Fig.9 Magnetic density of electric machine

Fig.10 Torque outputs before and after optimization under 2 typical working conditions

Fig.11 Torque harmonics under 2 typical working conditions

Table 3 Torque ripples under 2 working conditions

工况	波动幅值/(N·m)	幅值占比/%	THD/%
峰值扭矩/功率	43.9	3.6	2.9
最高转速	8.9	7.8	6.0

Fig.12 EM loss map

Fig.13 Loss of EM components under 2 typical working conditions

Fig.14 Temperature rise of EM components under the working conditions of peak torque/power

Fig.15 Temperature rise of EM components at maximum speed

Fig.16 Installation position of testbench and temperature sensor

Fig.17 Validation of the end windings temperature rise estimation under the working conditions of peak torque/power

Fig.18 Validation of the end windings temperature rise estimation at maximum speed

Fig.19 Validation of the end windings temperature rise estimation at high environment temperature

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