基于精确几何模型梁单元的螺旋弹簧刚度分析

张健, 齐朝晖, 卓英鹏, 国树东

张健, 齐朝晖, 卓英鹏, 国树东. 基于精确几何模型梁单元的螺旋弹簧刚度分析[J]. 工程力学, 2020, 37(2): 16-22,80. DOI: 10.6052/j.issn.1000-4750.2019.01.0096
引用本文: 张健, 齐朝晖, 卓英鹏, 国树东. 基于精确几何模型梁单元的螺旋弹簧刚度分析[J]. 工程力学, 2020, 37(2): 16-22,80. DOI: 10.6052/j.issn.1000-4750.2019.01.0096
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ZHANG Jian, QI Zhao-hui, ZHUO Ying-peng, GUO Shu-dong. STIFFNESS ANALYSIS OF HELIX SPRING USING EXACT GEOMETRIC BEAM ELEMENT[J]. Engineering Mechanics, 2020, 37(2): 16-22,80. DOI: 10.6052/j.issn.1000-4750.2019.01.0096
Citation: ZHANG Jian, QI Zhao-hui, ZHUO Ying-peng, GUO Shu-dong. STIFFNESS ANALYSIS OF HELIX SPRING USING EXACT GEOMETRIC BEAM ELEMENT[J]. Engineering Mechanics, 2020, 37(2): 16-22,80. DOI: 10.6052/j.issn.1000-4750.2019.01.0096
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基于精确几何模型梁单元的螺旋弹簧刚度分析

  • 大连理工大学工业装备结构分析国家重点实验室, 大连 116024

基金项目: 国家自然科学基金项目（11872137，91748203）
详细信息
    作者简介:

    张健(1987-),男,山西临汾人,博士生,主要从事多体系统动力学研究(E-mail:zhangjian1987@mail.dlut.edu.cn);卓英鹏(1994-),男,河北张家口人,博士生,主要从事机械系统动力学与数值分析研究(E-mail:zhuoyingpeng@mail.dlut.edu.cn);国树东(1982-),男,山东泰安人,博士生,主要从事多体系统学研究(E-mail:gsd0905@mail.dlut.edu.cn).

    通讯作者:

    齐朝晖(1964-),男,辽宁大连人,教授,博士,主要从事多体系统动力学研究(E-mail:zhaohuiq@dlut.edu.cn).

  • 中图分类号: O342;TH135.1

STIFFNESS ANALYSIS OF HELIX SPRING USING EXACT GEOMETRIC BEAM ELEMENT

  • State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian 116024, China

摘要

    摘要
  • 摘要: 以精确几何模型梁单元为基础，对圆截面螺旋弹簧刚度的非线性特性进行了分析。结合弹簧细长结构的变形特点，选取弹簧半径、弹簧高度、螺旋线极角和簧丝截面扭转角作为螺旋弹簧的描述变量；按照Bernoulli梁理论，通过形心曲线切矢量和簧丝截面扭转角建立截面坐标系；基于大转动梁的变形虚功率，获得螺旋弹簧曲率矢量，构建弹簧变形虚功率；应用柔体建模过程的滤除高频震荡分量方法修正弹簧系统动力学方程求得弹簧刚度，提高计算效率。数值算例表明，计算结果符合弹簧刚度的受力变形规律。同时与弹簧经典理论算法和传统有限元方法进行对比，验证了分析方法的正确性和合理性。
    Abstract: Based on the exact geometric beam element model, the nonlinear stiffness characteristic of helix spring with circular cross-sections was investigated. The way to choose descriptive variables of spring model was combined with deformation characteristics of slender helix spring, and the spring radius, height, helix polar angle and torsion angle of the cross-section of spring wire were selected as the descriptive variables of helix spring. According to the Bernoulli beam theory, the cross-section coordinate system was established by the centroid curve tangent vector and torsion angle of the cross-section. Spring deformation virtual power equation was built using curvature vector of helix spring which was based on the deformation virtual power of large rotating beam. The deformation virtual power equation of spring was built by using the method of removing high-frequency vibrations in flexible body systems. As validated by numerical examples, the results conformed to the deformation law of spring stiffness. In addition, compared with the classical theory algorithm and the traditional finite element method, the results proved the validity and rationality of the analytical procedure.
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    • 参考文献(17)
  • [1] Liu H, Kim D. Estimation of valve spring surge amplitude using the variable natural frequency and the damping ratio[J]. International Journal of Automotive Technology, 2011, 12(5):631-638.
    [2] Bartolozzi R, Frendo F. Stiffness and strength aspects in the design of automotive coil springs for McPherson front suspensions:A case study[J]. Proceedings of the Institution of Mechanical Engineers, Part D:Journal of Automobile Engineering, 2011, 225(10):1377-1391.
    [3] 尚汉冀. 内燃机配气凸轮机构设计与计算[M]. 上海:复旦大学出版社, 1988:57-65. Shang Hanji. Design and calculation of valve cam mechanism for internal combustion engine[M]. Shanghai:Fudan University Press, 1988:57-65. (in Chinese)
    [4] Iritani T, Shozaki A, Sheng B. Prediction of the dynamic characteristics in valve train design of a diesel engine[J]. SAE Technical Paper, 2002, 4332(1):1-7.
    [5] Zeng S, Chen S F. Finite element analysis of spatial curved beam in large deformation[J]. Journal of Southeast University, 2010(26):591-596.
    [6] 谈梅兰, 王鑫伟, 周勇. 高效的三维曲梁单元[J]. 计算力学学报, 2005(1):78-82. Tan Meilan,Wang Xinwei, Zhou Yong. An efficient finite element of spatial curved beams[J]. Chinese Journal of Computational Mechanics, 2005(1):78-82. (in Chinese)
    [7] 张英会,刘辉航,王德成. 弹簧手册[M]. 北京:机械工业出版社, 2017:370-373. Zhang Yinghui, Liu Huihang, Wang Decheng. Spring manual[M]. Beijing:Machinery Industry Press, 2017:370-373. (in Chinese)
    [8] 郝颖, 虞爱民. 考虑翘曲效应的圆柱螺旋弹簧的振动分析[J]. 力学学报, 2011, 43(3):561-569. Hao Ying, Yu Aimin. Vibration analysis of cylindrical helical springs considering warping deformation effect[J]. Chinese Journal of Theoretical and Applied Mechanics, 2011(3):561-569. (in Chinese)
    [9] Shabana A A. An absolute nodal coordinate formulation for the large rotation and deformation analysis of flexible bodies[R]. Chicago:Department of Mechanical and Industrial Engineering, University of Illinois at Chicago, 1996.
    [10] Shabana A A. Three dimensional absolute nodal coordinate formulation for beam elements theory[J]. Journal of Mechanical Design, 2001, 123(4):614-621.
    [11] 田强, 张云清, 陈立平, 等. 柔性多体系统动力学绝对节点坐标方法研究进展[J]. 力学进展, 2010, 40(2):189-202. Tian Qiang, Zhang Yunqing, Chen Liping, et al. Advances in the absolute nodal coordinate method for the flexible multibody dynamics[J]. Advances in Mechanics, 2010, 40(2):189-202. (in Chinese)
    [12] 汤宏伟, 钟宏志. 考虑杆件初弯曲的网壳弹塑性稳定性的弱形式求积元分析[J]. 工程力学, 2019, 36(1):168-177. Tang Hongwei, Zhong Hongzhi. Elasto-plastic stability analysis of latticed sheels with initially curved members by weak-form quadrature elements[J]. Engineering Mechanics, 2019, 36(1):168-177. (in Chinese)
    [13] 叶康生, 吴可伟. 空间杆系结构的弹塑性大位移分析[J]. 工程力学, 2013, 30(11):1-8. Ye Kangsheng, Wu Kewei. Elasto-plastic large displacement analysis of spatial skeletal structures[J]. Engineering Mechanics, 2013, 30(11):1-8. (in Chinese)
    [14] Simo J C,Vu-Quoc L. A three-dimensional finite-strain rod model. Part II:Computational aspects[J]. Computer Methods in Applied Mechanics & Engineering, 1986, 58(1):79-116.
    [15] 齐朝晖,方慧青,张志刚,等. 基于曲率离散的几何非线性空间梁单元[J]. 应用数学和力学, 2014(5):498-509. Qi Zhaohui, Fang Huiqing, Zhang Zhigang, et al. Geometric nonlinear spatial beam elements with curvature interpolations[J]. Applied Mathematics and Mechanics, 2014(5):498-509. (in Chinese)
    [16] 齐朝晖. 多体系统动力学[M]. 北京:科学出版社, 2008:175-178. Qi Zhaohui. Dynamics of multibody systems[M]. Beijing:Science Press, 2008:175-178. (in Chinese)
    [17] 齐朝晖, 曹艳, 王刚. 多柔体系统数值分析的模型降噪方法[J]. 力学学报, 2018(4):863-870. Qi Zhaohui, Cao Yan, Wang Gang. Model smoothing methods in numerical analysis of flexible multibody systems[J]. Chinese Journal of Theoretical and Applied Mechanics, 2018(4):863-870. (in Chinese)
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出版历程
  • 收稿日期:  2019-03-05
  • 修回日期:  2019-08-28
  • 刊出日期:  2020-05-26

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