Design and Disturbance Suppression of a Permanent Magnet Flexible Spherical Wrist Driven by Rotating Magnetic Coaxial Effect

doi:10.12141/j.issn.1000-565X.240377

Abstract

Abstract:

Current permanent magnet spherical joints commonly face issues such as complex electromagnetic drive structures, difficulties in coupled magnetic field modeling, magnetic moment singularities, and insufficient resistance to external disturbances. To solve the problems, this study developed a permanent magnet flexible direct-drive spherical joint with an embedded fully suspended permanent magnet rotor as the core based on the rotational fixed-axis effect, where the rotor axis of the permanent magnet always tends to align with the axis of rotation of the magnetic field. The new stator consists of a three-axis orthogonal nested combination of two sets of saddle coils and one set of Helmholtz coils. To solve the redundancy issue of magnetic moment control variables, a three-phase current formula was used to superimpose the spatial universal rotating magnetic field with the yaw and pitch angles as independent control variables. This enables the decoupling of the yaw and pitch magnetic moments of the permanent magnet rotor in the rotating magnetic field, as well as the realization of the universal spherical joint’s two-degree-of-freedom motion (yaw and pitch) under the guidance of the rotating magnetic field’s axis. Furthermore, the system stability was proved using the Lyapunov function, and a non-singular fast terminal sliding mode control method optimized by a fuzzy algorithm was applied to suppress chatter and reduce trajectory errors at the output end. The theoretical simulation results verified the effectiveness of the controller. Compared with sliding mode control method without fuzzy algorithm optimization,when external disturbance is applied, the sliding mode controller with fuzzy algorithm optimization can effectively suppress chattering, improve tracing speed, reduce output trajectory errors. Simulations and experiments show that the spherical joint has a simple electromagnetic structure, along with convenient analytical modeling of the magnetic field. The input current variables correspond one-to-one with the output magnetic moment variables. The system exhibits good anti-interference capability and effective chatter suppression, achieving fast tracking of the desired trajectory for the spherical joint. The dynamic tracking performance is excellent, and the system demonstrates improved adaptability in complex environments.

Key words: permanent magnet flexible spherical joint, rotating magnetic coaxial effect, spatial universal rotatingmagnetic field, sliding mode control, trajectory tracking

CLC Number:

TP241

ZHANG Yongshun, LIU Zhijun, LIU Zhenhu, WANG Li. Design and Disturbance Suppression of a Permanent Magnet Flexible Spherical Wrist Driven by Rotating Magnetic Coaxial Effect[J]. Journal of South China University of Technology(Natural Science Edition), 2025, 53(4): 102-112.

Figures/Tables 15

Fig.1

Table 1

Fig.2

Fig.3

Fig.4

Table 2

Table 3

Fuzzy rule table"

$e ˙ 、$ $e 、$ $k 1 i$	NB	NS	ZO	PS	PB
NB	PB	PM	PS	NS	NM
NS	PM	PS	PM	NS	NS
ZO	PS	PS	ZO	ZO	NS
PS	PS	NS	NS	NS	NM
PB	NS	NM	NS	NM	NB

Table 3

Fig.5

Fig.6

Fig.7

Fig.8

Fig.9

Fig.10

Fig.11

Fig.12

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参数	数值
x轴转动惯量J_x /（kg·m²）	0.167 5×10^-2
y轴转动惯量J_y /（kg·m²）	0.214 9×10^-2
z轴转动惯量J_z /（kg·m²）	0.102 9×10^-2
永磁体绕z轴转动惯量J_z₂/（kg·m²）	0.002 2×10^-2
永磁体磁矢量幅值m₀/（A·m^-2）	127.2
阻尼系数k	0.2
转差角δ/rad	π/24
负载m/kg	1
负载到磁铁旋转中心距离r/m	0.1

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