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Nonlinear
flexibility expression of conical springs with constant pitch
under large deformation conditions and its FEM
verification
Fengying Xiao, Huajie Yin, Chunhua Rao, Risheng Zhu, Mojia Huang, Tengfei Zhao and Zhi Huang |
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Vol. 20 (2025), No. 1, 79–94
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Abstract |
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The conical spring, characterized by its high flexibility and substantial deformation during operation, presents challenges for conventional engineering theories. Existing dense and sparse coil spring theories are limited to small deformation calculations of conical springs, lacking a comprehensive understanding of spring flexibility under significant deformation. Addressing this gap, this paper derives a nonlinear flexibility expression for the large deformation of a conical spring, accounting for the impact of the pitch angle based on the interrelations of parameters in a constant pitch conical spring. Geometric nonlinearity calculations under conditions of substantial deformation are conducted using finite element simulation software. The results demonstrate a close alignment between the expression proposed in this study and finite element outcomes, with a deviation of less than 3%. Conversely, sparse coil spring theory aligns with finite element results only under conditions of minor deformation, with increasing disparities as deformation intensifies. The validated nonlinear flexibility expression presented in this study serves as a pivotal reference for engineering applications, offering valuable insights for the design and utilization of springs in practical scenarios. |
Keywords
constant pitch, conical spring, nonlinear flexibility,
pitch angle, finite element simulation
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Mathematical Subject Classification
Primary: 49S99, 74B05, 74505
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Milestones
Received: 18 August 2024
Revised: 22 December 2024
Accepted: 10 February 2025
Published: 9 March 2025
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Authors |
| Fengying Xiao | |
| Department of Engineering,
Mechanics Nanchang University Nanchang, 330031 China |
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| Huajie Yin | |
| Jiangxi Province Traffic
Construction Engineering Quality Supervision
Administration Nanchang, 330069 China |
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| Chunhua Rao | |
| Department of Engineering,
Mechanics Nanchang University Nanchang, 330031 China |
Jiangxi Transportation Design and
Research Institute Co. Ltd. Nanchang, 330209 China |
| Risheng Zhu | |
| Project Management Office of
Shanghai-Kunming Expressway Liyuan to Dongxiang Section Reconstruction and Expansion Shangrao, 334100 China |
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| Mojia Huang | |
| Department of Engineering,
Mechanics Nanchang University Nanchang, 330031 China |
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| Tengfei Zhao | |
| College of City Construction Jiangxi Normal University Nanchang, 330022 China |
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| Zhi Huang | |
| Jiangxi Gandong Road and Bridge
Construction Group LTD. Fuzhou, 344000 China |
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| © 2025 MSP (Mathematical Sciences Publishers). |
