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High-Efficiency Dynamic Modeling of a Helical Spring Element Based on the Geometrically Exact Beam Theory
Shock and Vibration ( IF 1.6 ) Pub Date : 2020-06-19 , DOI: 10.1155/2020/8254606
Jian Zhang 1 , Zhaohui Qi 1 , Gang Wang 2 , Shudong Guo 1
Affiliation  

This paper presents a modeling study of the dynamics of a helical spring element with variable pitch and radius considering both the static stiffness and dynamic response by using the geometrically exact beam theory. The geometrically exact beam theory based on the Euler–Bernoulli beam hypothesis is described, of which the shear deformations are ignored. Unlike the traditional spliced curved beam element method, the helical spring element is described with curvature vector and axial strain by establishing and spline-interpolating a function of the radius, the height, the polar angle, and the torsion angle of the whole spring. In addition, a model smoothing method is developed and applied in the numerical analysis to filter the high-frequency oscillation component of the flexible multibody systems, so as to correct the system dynamic equations and improve the calculation efficiency when solving the static equilibrium of the spring. This study also carries out five numerical trials to validate the above dynamic procedure of the helical spring element. The example of the spring static stiffness design shows that the proposed helical spring procedure enables one to deal with practical engineering applications.

中文翻译:

基于几何精确梁理论的螺旋弹簧元件高效动态建模

本文利用几何精确梁理论,对静态螺距和动态响应都考虑到了螺距和半径可变的螺旋弹簧元件的动力学进行了建模研究。描述了基于欧拉-伯努利梁假设的几何精确梁理论,其中忽略了剪切变形。与传统的拼接弯曲梁单元法不同,螺旋弹簧单元通过建立并通过样条插值法对整个弹簧的半径,高度,极角和扭转角进行函数化,以曲率矢量和轴向应变来描述。此外,开发了一种模型平滑方法并将其应用于数值分析中,以过滤柔性多体系统的高频振荡分量,从而解决了弹簧的静态平衡时,可以校正系统动力学方程,提高计算效率。这项研究还进行了五个数值试验,以验证上述螺旋弹簧元件的动态过程。弹簧静态刚度设计的示例表明,提出的螺旋弹簧程序使人们能够处理实际的工程应用。
更新日期:2020-06-19
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