Improvement and Optimization of Rectangular Closed-loop Magnetic Array Adsorption Module for Wall-climbing Robots

doi:10.12382/bgxb.2024.1013

Abstract

Abstract:

In order to improve the magnetic adsorption efficiency and uniform magnetic field distribution in the limited installation space of wall-climbing robots,a Halbach-based rectangular closed-loop magnetic array adsorption module and parameter optimization method are proposed.This module improves the magnetic force attenuation and leakage caused by the end effect of the linear classical Halbach magnetic array adsorption module,and has the characteristics of easy installation and uniform magnetic force distribution.The structural configuration with high adsorption efficiency is determined by establishing a magnetic force attenuation model considering the end effect and studying the influence of magnetic circuit structure change on magnetic field distribution and gradient through simulation.The key structural dimension parameters are extracted and integrated,and a nonlinear regression prediction model is established using the random uniform sampling strategy and the response surface method.The structural parameters are optimized by the particle swarm optimization algorithm to obtain the optimal combination of magnetic adsorption force parameters.The results show that the proposed prediction model exhibits high credibility and accuracy,and its average relative error is only 1.5184%;and the optimized design of the rectangular closed-loop magnetic array adsorption module increases its magnetic performance by 33.54%.The tensile force experiment of magnetic adsorption module and the obstacle clearance test of robot are conducted to verify the effectiveness of optimization process.The wall-climbing robot performs well on curved surfaces and wall environments containing weld obstacles.

Key words: Halbach magnetic array, wall-climbing robot, adsorption module optimization, finite element simulation, response surface methodology

CLC Number:

TP242

SHI Qi, MAO Yunsheng, SHUI Jinpeng, CHEN Liuyi, LIANG Qiyu, SONG Lifei. Improvement and Optimization of Rectangular Closed-loop Magnetic Array Adsorption Module for Wall-climbing Robots[J]. Acta Armamentarii, 2025, 46(9): 241013-.

Figures/Tables 25

Fig.1 Simplified model of the magnetic field of an infinite-length Halbach magnetic array

Fig.2 Simplified model of the magnetic field of a finite-length Halbach magnetic array

Fig.3 Structures of wall-climbing robot and magnetic adsorption module

Fig.4 Program design route of rectangular Halbach magnetic array

Table 1 Comparison of magnetic forces of magnetic arrays with different magnetic circuits

方案	磁路	总磁吸附力/N	磁体数量	磁体体积/mm³	单位体积磁吸附力/(N·mm^-3)
基础方案	八磁路	146.39	8	10×10×10	0.01829
方案1	十二磁路	160.57	8	10×10×10	0.02007
方案2	十六磁路	122.46	12	6×10×10	0.01701
方案3	十九磁路	134.4	13	6×10×10	0.01723
方案4	二十磁路	79.857	16	6×6×10	0.01386
方案5	三十磁路	108.6	21	6×6×10	0.01437

Fig.5 Magnetic force variation of different magnetic circuits under air gap variation

Fig.6 Variation of magnetic force for different magnetic circuits under wall thickness variation

Fig.7 Logic diagram for optimization of main parameters of rectangular Halbach magnetic array structure

Fig.8 Dimension parameters of rectangular Halbach magnetic array structure

Table 2 Key parameter values

参数	数值
H/mm	[7,14]
A_m1/mm	[4,13]
A_m2/mm	[4,13]
t/mm	5
h/mm	3
a/mm	30
b/mm	30
c/mm	15

Fig.9 Static orce of robotic system

Fig.10 Variation of magnetic force with angle for three failure modes within a 180° range

Fig.11 Geometric spatial random uniform sampling process

Table 3 Sample point data for partially safe adsorption magnetic force value domain constraints

序号	A_m1/mm	A_m2/mm	H/mm	F/N
1	10.3357	8.4036	13.8619	104.5255
2	11.3818	13.2948	9.8718	103.5731
3	13.2585	9.49195	13.8918	114.1140
4	13.3671	9.16431	12.0854	106.4561
5	11.2002	8.95901	11.9724	106.5326
6	10.2050	10.6433	12.3298	114.3527
7	11.7911	12.8627	10.0698	107.2076
8	13.8512	9.4308	13.9405	110.7030
9	10.3015	9.2317	13.0263	108.7921
10	10.1867	13.4361	12.6585	115.4847
11	8.9248	12.4708	12.1209	107.4850
12	9.1972	12.5001	13.4336	113.7884
13	13.2405	10.9135	11.5979	113.5201
14	12.6339	11.5551	13.5914	124.6796
15	13.3666	10.9200	13.4765	120.1272
16	11.8380	8.9514	13.9762	113.9812
17	13.4409	9.2477	11.4943	104.5890
18	10.7765	10.3508	10.0264	102.9980
19	11.9956	12.2862	13.3898	125.1924
20	13.1883	13.3964	12.6995	111.1677
21	11.3755	13.0154	11.2925	113.0044
22	12.8944	8.3855	13.3864	108.0141
23	13.0824	13.3945	10.4635	103.6425
24	11.2759	11.0815	9.5889	104.2145
25	10.8567	13.7308	13.7966	117.2943
26	10.4024	10.1996	10.5422	104.7440
27	12.5845	11.8480	10.7926	112.2580
28	8.6519	12.6053	13.6125	110.6508
29	13.0296	12.5655	10.3337	106.7189
30	11.7627	11.4825	9.4877	105.3202

Table 4 Experimental design of Box-Behnken response surface

参数	水平
参数	-1	0	1
A_m1 /mm	8	11	14
A_m2/mm	8	11	14
H/mm	9	11.5	14

Table 5 Verification of accuracies of simulated and predicted values

工况	A_m1/mm	$A m 2$ /mm	H/mm	$F V 1$		相对误差绝对值/%	平均相对误差/%
工况	A_m1/mm	$A m 2$ /mm	H/mm	仿真值	预测值	相对误差绝对值/%	平均相对误差/%
1	12	12	13	124.425	121.8130	2.100	1.2615
2	13	9	14	114.290	113.5540	0.644
3	9	13	14	112.220	112.4042	0.164
4	11	9	12	105.580	107.8368	2.138

Table 5 Verification of accuracies of simulated and predicted values

工况	A_m1/mm	$A m 2$ /mm	H/mm	$F V 1$		相对误差绝对值/%	平均相对误差/%
工况	A_m1/mm	$A m 2$ /mm	H/mm	仿真值	预测值	相对误差绝对值/%	平均相对误差/%
1	12	12	13	124.425	121.8130	2.100	1.2615
2	13	9	14	114.290	113.5540	0.644
3	9	13	14	112.220	112.4042	0.164
4	11	9	12	105.580	107.8368	2.138

Table 6 Simulation value comparison analysis

序号	A_m1/mm	A_m2/mm	H/mm	F_V₁/N			F_V₂/N
序号	A_m1/mm	A_m2/mm	H/mm	原值	h=2mm	h=7mm	F_V₂/N
1	12	11	14	124.425	203.097	20.4155	447.0250
2	13	12	14	127.199	207.129	18.7207	451.6994
3	11	12	14	126.505	203.087	19.9831	446.1402
4	11	11	14	125.524	198.962	19.9558	437.8356

Table 7 Main magnet size optimization before and after comparison

状态	尺寸参数/mm	轭铁厚度/ mm	气隙/mm	模块磁吸附力/N
优化前	10×10×10	5	2	155.110
优化后	12×12×14	1	2	207.129

Table 8 Comparison of existing magnetic circuit patterns

磁路方案	主磁铁尺寸参数/mm	模块磁吸附力/N
开放磁路方案	30×30×14	128.790
三磁路方案^[18]	13×30×14	200.090
方案1	12×12×14	207.129

Fig.12 Magnetic force simulation of triple and open magnetic circuits

Fig.13 Adsorption force test of magnetic adsorption module

Fig.14 Comparison between magnetic force simulated and measured values under various air gaps

Fig.15 Surface adaptive motion for wall-climbing robot

Fig.16 Obstacle-crossing motion of wall-climbing robot

Fig.17 Experimental site of wall-climbing robot overpassing weld seam

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