Analytical Investigations of Nonlinear Stiffness Characteristics of Halbach-Cylinder Magnetic Springs for Heavy-Load Capacity

Quasi-zero stiffness (QZS) has become a promising way of realizing low-frequency vibration isolation, where magnetic springs have been widely adopted for constructing negative stiffness. However, existing single-layer magnetic springs often have a small-amplitude negative stiffness, so the loading c...

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Main Authors: Zhongsheng Chen, Yangyi Zhang, Yeping Xiong, Ankang Wang
Format: Article
Language:English
Published: MDPI AG 2025-05-01
Series:Applied Sciences
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Online Access:https://www.mdpi.com/2076-3417/15/9/5099
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author Zhongsheng Chen
Yangyi Zhang
Yeping Xiong
Ankang Wang
author_facet Zhongsheng Chen
Yangyi Zhang
Yeping Xiong
Ankang Wang
author_sort Zhongsheng Chen
collection DOAJ
description Quasi-zero stiffness (QZS) has become a promising way of realizing low-frequency vibration isolation, where magnetic springs have been widely adopted for constructing negative stiffness. However, existing single-layer magnetic springs often have a small-amplitude negative stiffness, so the loading capacity is low. In order to address this issue, this paper presents novel Halbach-cylinder magnetic springs (HCMSs) by using the Halbach array. Firstly, stiffness formulas of basic single-layer magnetic springs are analytically built based on the Amperian current model. The stiffness of the HCMS is derived from combining multiple single-layer magnetic springs. Then, nonlinear stiffness characteristics of both single-layer magnetic springs and HCMSs are investigated in terms of the amplitude, the uniformity, and the displacement range of negative stiffness. Analytical results show that HCMSs can generate negative stiffness with different equilibrium positions, and the amplitude of negative stiffness of HCMSs is much larger than that of single-layer magnetic springs. The amplitude of negative stiffness is in conflict with the uniformity, so a trade-off design is needed. In addition, increasing the number of layers of Halbach cylinders can be adopted to realize larger-amplitude and wider-range negative stiffness. This study will provide new insights into designing QZS with heavy-load capacity.
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spelling doaj-art-c49c7642a6a94e47be8f8133f2f56ed72025-08-20T01:49:24ZengMDPI AGApplied Sciences2076-34172025-05-01159509910.3390/app15095099Analytical Investigations of Nonlinear Stiffness Characteristics of Halbach-Cylinder Magnetic Springs for Heavy-Load CapacityZhongsheng Chen0Yangyi Zhang1Yeping Xiong2Ankang Wang3School of Engineering Science, Shandong Xiehe University, Jinan 250107, ChinaCollege of Railway Transportation, Hunan University of Technology, Zhuzhou 412007, ChinaFaculty of Engineering and Physical Sciences, University of Southampton, Southampton SO16 7QF, UKCollege of Railway Transportation, Hunan University of Technology, Zhuzhou 412007, ChinaQuasi-zero stiffness (QZS) has become a promising way of realizing low-frequency vibration isolation, where magnetic springs have been widely adopted for constructing negative stiffness. However, existing single-layer magnetic springs often have a small-amplitude negative stiffness, so the loading capacity is low. In order to address this issue, this paper presents novel Halbach-cylinder magnetic springs (HCMSs) by using the Halbach array. Firstly, stiffness formulas of basic single-layer magnetic springs are analytically built based on the Amperian current model. The stiffness of the HCMS is derived from combining multiple single-layer magnetic springs. Then, nonlinear stiffness characteristics of both single-layer magnetic springs and HCMSs are investigated in terms of the amplitude, the uniformity, and the displacement range of negative stiffness. Analytical results show that HCMSs can generate negative stiffness with different equilibrium positions, and the amplitude of negative stiffness of HCMSs is much larger than that of single-layer magnetic springs. The amplitude of negative stiffness is in conflict with the uniformity, so a trade-off design is needed. In addition, increasing the number of layers of Halbach cylinders can be adopted to realize larger-amplitude and wider-range negative stiffness. This study will provide new insights into designing QZS with heavy-load capacity.https://www.mdpi.com/2076-3417/15/9/5099quasi-zero stiffnessheavy loadlarge-amplitude negative stiffnessmagnetic springHalbach arraysHalbach-cylinder magnetic spring
spellingShingle Zhongsheng Chen
Yangyi Zhang
Yeping Xiong
Ankang Wang
Analytical Investigations of Nonlinear Stiffness Characteristics of Halbach-Cylinder Magnetic Springs for Heavy-Load Capacity
Applied Sciences
quasi-zero stiffness
heavy load
large-amplitude negative stiffness
magnetic spring
Halbach arrays
Halbach-cylinder magnetic spring
title Analytical Investigations of Nonlinear Stiffness Characteristics of Halbach-Cylinder Magnetic Springs for Heavy-Load Capacity
title_full Analytical Investigations of Nonlinear Stiffness Characteristics of Halbach-Cylinder Magnetic Springs for Heavy-Load Capacity
title_fullStr Analytical Investigations of Nonlinear Stiffness Characteristics of Halbach-Cylinder Magnetic Springs for Heavy-Load Capacity
title_full_unstemmed Analytical Investigations of Nonlinear Stiffness Characteristics of Halbach-Cylinder Magnetic Springs for Heavy-Load Capacity
title_short Analytical Investigations of Nonlinear Stiffness Characteristics of Halbach-Cylinder Magnetic Springs for Heavy-Load Capacity
title_sort analytical investigations of nonlinear stiffness characteristics of halbach cylinder magnetic springs for heavy load capacity
topic quasi-zero stiffness
heavy load
large-amplitude negative stiffness
magnetic spring
Halbach arrays
Halbach-cylinder magnetic spring
url https://www.mdpi.com/2076-3417/15/9/5099
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AT yepingxiong analyticalinvestigationsofnonlinearstiffnesscharacteristicsofhalbachcylindermagneticspringsforheavyloadcapacity
AT ankangwang analyticalinvestigationsofnonlinearstiffnesscharacteristicsofhalbachcylindermagneticspringsforheavyloadcapacity