主动悬架用非均匀齿圆筒型永磁直线电机多目标分层优化设计

doi:10.12382/bgxb.2022.0756

摘要/Abstract

摘要：

针对直线电机式电磁主动悬架推力波动大、推力密度低的问题,提出一种非均匀齿结构的Halbach圆筒型永磁直线电机。利用解析法对该电机的边端力模型进行推导,并进一步分析非均匀边端齿结构对电机输出性能的影响。根据分析结果选取边端齿的轴向长度和径向削短高度、永磁体高度和径向充磁的长度、内部齿的长度5个参数作为优化因子,以电机输出推力最大和推力波动最小为优化目标进行田口法和响应面法优化,得到参数的最优值。试制了原理样机并搭建了实验平台,对电机进行空载与负载实验,验证了所提结构及其设计优化方法的有效性。

关键词: 圆筒型永磁直线电机, 主动悬架, Halbach永磁阵列, 多目标优化, 推力波动

Abstract:

A Halbach tubular permanent magnet linear motor with a non-uniform teeth structure is proposed in this study to solve the problems of high ripple and low force density of a linear electromagnetic active suspension system. The end force model is derived using the analytical method, and the effects of non-uniform teeth structure on the output performance of the motor are analyzed. Based on the analysis results, five parameters, including the axial length and radial cut length of the end teeth, thickness and radial-magnetization length of the permanent magnet, and length of the inner teeth, are selected as optimization factors. Taguchi and response surface methods are adopted to optimize the maximum output force and minimum ripple of force simultaneously, and the optimal parameters are obtained. Finally, a prototype is manufactured and an experimental platform is set up to carry out the no-load and load experiments to verify the effectiveness of the proposed structure and its optimization methods.

Key words: tubular permanent magnet linear machine, active suspension, Halbach PM array, multi-objective optimization, force ripple

中图分类号:

TM359.4

颜建虎, 李彪, 时岩, 张凌宇, 衡培然. 主动悬架用非均匀齿圆筒型永磁直线电机多目标分层优化设计[J]. 兵工学报, 2023, 44(1): 40-50.

YAN Jianhu, LI Biao, SHI Yan, ZHANG Lingyu, HENG Peiran. Multi-objective Stratified Optimization Design of Tubular Permanent Magnet Linear Motors with Nonuniform Teeth for Active Suspension[J]. Acta Armamentarii, 2023, 44(1): 40-50.

图/表 23

图1 主动悬架示意图

Fig.1 Diagram of active suspension

表1 TPLM设计目标

Table 1 Design objectives of TPLM

参数	数值
额定电磁推力/N	220
最大电磁推力/N	650
最大行程/mm	±20
最大安装长度/mm	150
最大直径/mm	80

图2 绕组配置示意图

Fig.2 Winding configuration modes

表2 初始模型的主要参数

Table 2 Main parameters of the preliminary design model

电机参数	数值	电机参数	数值
极对数p	5	气隙直径D_δ/mm	40
极距τ_p/mm	10	初级轭高H_y/mm	3
气隙δ/mm	1	内部齿长L_t/mm	2.9
绕组匝数N	56	永磁体长L_m/mm	5
频率f/Hz	60	永磁体高H_m/mm	3.5
初级长度L_p/mm	100	边端齿高H_b/mm	18
次级长度L_s/mm	140	边端齿长L_b/mm	2.9

图3 初始模型空载仿真结果

Fig.3 No-load simulation results of the preliminary model

图4 负载电磁推力仿真结果

Fig.4 Simulation results of loaded electromagnetic force

图5 电机推力积分路径示意图

Fig.5 Schematic diagram of motor force integration paths

图6 He和Lb的参数化分析

Fig.6 Parametric analysis of He and Lb

图7 边端齿对推力特性的影响

Fig.7 Effects of end teeth on force characteristics

图8 优化流程图

Fig.8 Optimization flow chart

表3 田口法参数及水平

Table 3 Parameters and levels of Taguchi method

参数	取值范围/ mm	水平
参数	取值范围/ mm	1	2	3	4
L_t	2.9~3.2	2.9	3.0	3.1	3.2
L_b	2.8~3.4	2.8	3.0	3.2	3.4
H_e	1.0~4.0	1.0	2.0	3.0	4.0
H_m	3.0~6.0	3.0	4.0	5.0	6.0
L_m	5.5~7.0	5.5	6.0	6.5	7.0

表4 田口法实验及其结果

Table 4 Taguchi experiments and results

实验编号	L_t	L_b	H_e	H_m	L_m	R₁/N	R₂/%
1	1	1	1	1	1	585.4	7.58
2	1	2	2	2	2	649.5	5.93
3	1	3	3	3	3	682.4	6.83
4	1	4	4	4	4	694.2	10.43
5	2	1	2	3	4	687.1	6.67
6	2	2	1	4	3	711.0	6.37
7	2	3	4	1	2	603.0	6.38
8	2	4	3	2	1	652.7	5.38
9	3	1	3	4	2	725.7	8.89
10	3	2	4	3	1	698.9	9.72
11	3	3	1	2	4	666.3	7.16
12	3	4	2	1	3	617.6	3.82
13	4	1	4	2	3	676.0	8.80
14	4	2	3	1	4	627.8	5.32
15	4	3	2	4	1	735.8	5.71
16	4	4	1	3	2	710.2	7.39

图9 不同参数水平的平均值

Fig.9 Average values of different parameter levels

表5 田口法实验结果分析

Table 5 Experimental results using Taguchi method

优化目标		L_t	L_b	H_e	H_m	L_m
R₁	方差	2764.9	41.6	70.9	26612.6	47.3
	方差比重/%	9.36	0.14	0.24	90.10	0.16
R₂	方差	12.5	12.4	30.0	17.9	9.2
	方差比重/%	15.24	15.12	36.59	21.86	11.19

表6 响应面法参数及水平

Table 6 Parameters and levels of RSM

参数	水平
参数	-1	0	1
L_t	2.9	3.0	3.1
L_b	3.0	3.2	3.4
H_e	1.0	2.0	3.0
H_m	3.0	4.0	5.0
L_m	6.0	6.5	7.0

表7 响应面法实验及其结果

Table 7 RSM experiments and results

实验编号	L_t/mm	L_b/mm	H_e/mm	H_m/mm	L_m/mm	F_e/N	F_a/%
1	-1	-1	0	0	0	651.95	5.22
2	1	-1	0	0	0	668.96	5.13
3	-1	1	0	0	0	651.95	5.07
4	1	1	0	0	0	669.05	4.72
5	0	0	-1	-1	0	609.28	4.52
︙	︙	︙	︙	︙	︙	︙	︙
38	0	1	0	-1	0	610.63	3.89
39	0	-1	0	1	0	691.93	5.90
40	0	1	0	1	0	692.05	5.45
41	0	0	0	0	0	660.76	4.59

图10 平均推力及推力波动的响应曲面

Fig.10 Response surfaces of average force and ripple

表8 优化前后参数对比

Table 8 Comparison of parameters before and after optimization

参数	初始值/mm	优化值/mm
L_t	2.9	3.1
L_b	2.9	3.3
H_e	0	2.0
H_m	3.5	4.2
L_m	5.0	6.4

图11 优化前后结果对比

Fig.11 Results before and after optimization

图12 TPLM样机

Fig.12 TPLM prototype

图13 测试平台

Fig.13 Experiment platform

图14 空载感应电动势

Fig.14 No-load EMF

图15 不同q轴电流下的电磁推力

Fig.15 Electromagnetic force under different q-axial currents

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