Design and parameter optimization of permanent magnet wheel based on reliable and stable adhesion of bilateral Halbach arrays

doi:10.3785/j.issn.1006-754X.2026.05.142

Chinese Journal of Engineering Design

2026, Vol. 33

Issue (2): 275-284 DOI: 10.3785/j.issn.1006-754X.2026.05.142

Reliability and Quality Design

Design and parameter optimization of permanent magnet wheel based on reliable and stable adhesion of bilateral Halbach arrays

Bingsheng LU¹(

),Donglin TANG¹(

),Yuanyao HU¹,Jianbo CHE¹,Yuanyuan HE^1,²

^1.School of Mechanical and Electrical Engineering, Southwest Petroleum University, Chengdu 610500, China
^2.Sichuan Special Equipment Inspection Institute, Chengdu 610000, China

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Abstract

In order to improve the load-bearing capacity and mobility of permanent magnet adhesion wall-climbing robots on ferromagnetic surfaces, a bilateral Halbach permanent magnet wheel structure is proposed, aiming to address the issues of non-adjustable adhesion force, low overall adhesion force, and large adhesion force fluctuations during circumferential rotation of traditional unilateral Halbach permanent magnet wheels. This structure achieved the enhancement of adhesion performance and effectively suppressed adhesion force fluctuations through the collaborative action of the inner and outer permanent magnet wheels. Based on the theory of magnetic dipoles and the Maxwell stress tensor method, an adhesion force theoretical model of the bilateral Halbach permanent magnet wheel was constructed and its accuracy was verified through the finite element analysis. Meanwhile, parameter indicators for evaluating the adhesion performance of the permanent magnet wheel were established. The influence of the relative rotation angle between the inner and outer permanent magnet wheels on the adhesion force regulation effect was analyzed in detail, and the relative rotation angle was optimized. Finally, an experimental platform for testing permanent magnet wheel adhesion performance was built and the practical research was conducted. The results showed that when the relative rotation angle of the bilateral Halbach permanent magnet wheel was 35°, its average adhesion force reached 187.955 N, and the adhesion force fluctuation coefficient dropped to 0.057. Compared with the traditional unilateral permanent magnet wheel structure, its adhesion force increased by 114.004%, and the adhesion force fluctuation coefficient was reduced by 89.366%. The study demonstrates that the bilateral Halbach permanent magnet wheel structure achieves significant enhancement and controllable adjustment of adhesion performance through the regulation of relative rotation angles, providing theoretical support and practical guidance for the design of high-performance permanent magnet adhesion systems, which is of great significance for improving the reliability and safety of industrial automation equipment.

Key words： wall-climbing robot Halbach permanent magnet wheel adhesion adhesion stability parameter optimization

Received: 16 June 2025 Published: 28 April 2026

CLC:

TH 122

Corresponding Authors: Donglin TANG E-mail: Cobingo@163.com;tdl840451816@163.com

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Cite this article:

Bingsheng LU,Donglin TANG,Yuanyao HU,Jianbo CHE,Yuanyuan HE. Design and parameter optimization of permanent magnet wheel based on reliable and stable adhesion of bilateral Halbach arrays. Chinese Journal of Engineering Design, 2026, 33(2): 275-284.

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https://www.zjujournals.com/gcsjxb/10.3785/j.issn.1006-754X.2026.05.142 OR https://www.zjujournals.com/gcsjxb/Y2026/V33/I2/275

基于双侧Halbach阵列可靠稳定吸附的永磁轮设计与参数优化

为提升永磁吸附爬壁机器人在导磁壁面上的负载能力与机动性能，提出了一种双侧Halbach永磁轮结构，旨在解决传统单侧Halbach永磁轮吸附力不可调、整体吸附力较小以及在周向转动过程中吸附力波动大的问题。该结构通过内、外侧永磁轮的协同作用，实现了吸附性能的增强与吸附力波动的有效抑制。基于磁偶极子理论与麦克斯韦应力张量法，构建了双侧Halbach永磁轮的吸附力理论模型，并通过有限元分析验证了其准确性。同时，构建了评估永磁轮吸附性能的参数指标，重点分析了内、外侧永磁轮之间的相对转角对吸附力调控效果的影响，并对相对转角进行了优化。最后，搭建了永磁轮吸附性能测试实验平台以开展实测研究。结果显示：当双侧Halbach永磁轮的相对转角为35°时，其平均吸附力达到187.955 N，吸附力波动系数降至0.057；相较于传统的单侧永磁轮结构，其平均吸附力提高了114.004%，吸附力波动系数降低了89.366%。研究表明，双侧Halbach永磁轮结构通过相对转角的调节作用，实现了吸附性能的显著增强与可控调节，为高性能永磁吸附系统的设计提供了理论支撑和实践指导，这对提升工业自动化设备的可靠性与安全性具有重要意义。

关键词： 爬壁机器人, Halbach永磁轮式吸附, 吸附稳定性, 参数优化

Fig.1 Structural diagram of bilateral Halbach permanent magnet wheel

Fig.2 Magnetization method of magnetic blocks in the bilateral Halbach permanent magnet wheel

Fig.3 Diagram of distance from magnetic block to observation point

Fig.4 Magnetic flux line distribution of unilateral Halbach permanent magnet wheel

Fig.5 Relationship between adhesion force of unilateral Halbach permanent magnet wheel and wall thickness and wall spacing

Fig.6 Finite element simulation model of unilateral Halbach permanent magnet wheel

Fig.7 Variation curves of adhesion force during circumferential rotation of unilateral Halbach permanent magnet wheel

Fig.8 Variation curves of adhesion force during circumferential rotation of bilateral Halbach permanent magnet wheel

相对转角 $θ r e l / (°)$	平均吸附力 $F m e a n / N$	吸附力波动幅度 $? F$ /N	吸附力波动系数C_F
0	199.878	80.132	0.401
15	199.129	62.873	0.316
30	190.671	24.597	0.129
45	182.377	24.803	0.136
60	174.326	77.083	0.442
75	168.842	117.893	0.698
90	168.052	126.142	0.751

Table 1 Evaluation indicators of adhesion force during circumferential rotation of bilateral Halbach permanent magnet wheel with relative rotation angle of 0°-90°

相对转角 $θ r e l / (°)$	平均吸附力 $F m e a n / N$	吸附力波动幅度 $? F$ /N	吸附力波动系数C_F
30	190.671	24.597	0.129
31	190.137	21.866	0.115
32	189.598	18.960	0.100
33	189.054	16.259	0.086
34	188.506	13.384	0.071
35	187.955	10.713	0.057
36	187.401	11.244	0.060
37	186.845	11.024	0.059
38	186.287	11.364	0.061
39	185.727	12.072	0.065
40	185.167	13.147	0.071
41	184.607	14.769	0.080
42	184.048	16.748	0.091
43	183.489	19.266	0.105
44	182.932	21.952	0.120
45	182.377	24.803	0.136

Table 2 Evaluation indicators of adhesion force during circumferential rotation of bilateral Halbach permanent magnet wheel with relative rotation angle of 30°-45°

Fig.9 Variation curves of adhesion force during circumferential rotation of Halbach permanent magnet wheels

Fig.10 Experimental platform for testing adhesion performance of Halbach permanent magnet wheels

Fig.11 Comparison of adhesion force during circumferential rotation of Halbach permanent magnet wheels


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