矩形截面非圆柱螺旋弹簧的自由振动分析.doc

矩形截面非圆柱螺旋弹簧的模态分析 郝颖 虞爱民 （同济大学航空航天与力学学院, 上海 200092） 摘要：对矩形截面非圆柱（锥形、桶形、双曲形）螺旋弹簧的自由振动问题进行了研究。在弹簧的运动微分方程中，首次考虑了簧丝截面的翘曲变形对固有频率的影响。本文采用改进的Riccati传递矩阵法对包括14个自由度的一阶变系数常微分方程组进行了求解。为了证明理论的有效性，对两端固支矩形截面非圆柱螺旋弹簧的固有频率进行了求解，同时给出了各种参数变化对两端固支矩形截面锥形弹簧固有频率的影响。计算表明，翘曲变形对矩形截面非圆柱螺旋弹簧的固有频率有着重大的影响，在自由振动分析中必须加以考虑。 关键词：非圆柱螺旋弹簧；翘曲变形；改进的Riccati传递矩阵法；固有频率；模态 中图分类号：O326；TU323 文献标识码：A Modal analysis of non-cylindrical helical springs with rectangular cross-section HAO Ying YU Ai-min (School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, China) Abstract：Free vibration analysis of non-cylindrical (conical, barrel, and hyperboloidal types) helical springs with rectangular cross-section is performed. The effect of the warping deformation of wire cross-section on the natural frequencies is first studied in the differential equations of motion of the springs. Improved Riccati transfer matrix method is introduced to solve the first order ordinary differential equations with variable coefficients, which consist of 14 degrees of freedom. The natural frequencies of non-cylindrical helical springs with rectangular cross-section and clamped-clamped boundary condition are simulated to validate the proposed method, and the effects of various parameters on the natural frequencies of the clamped–clamped conical springs with rectangular cross-section are also investigated. Calculations show that the warping effect upon the natural frequencies is prominent, which should be considered in the free vibration analysis of the springs. Key words: non-cylindrical helical spring; warping deformation; improved Riccati transfer matrix method; natural frequency; mode shape 引言 车辆的悬架系统是提高车辆平顺性和安全性、减少由动载荷引起零部件损坏的关键。为使车辆悬架系统的布置更加紧凑，在汽车工业中广泛使用变刚度的螺旋弹簧，其中最受青睐的就是变中径、变节距的非圆柱螺旋弹簧。 簧丝截面为非圆形的非圆柱螺旋弹簧，具有蓄存能量大、有效平缓应力分布、压并高度低，压缩量大等优良性能，因此被广泛用于发动机阀门、离合器和自动变速等装置上。随着非圆截面非圆柱螺旋弹簧在工程中应用的日益广泛，对其计算方法提出了许多新的要求。Epstein研究了锥形弹簧的自由振动问题，他在理论上得到了在几种边界条件下该弹簧的一阶频率。继他的开创性工作之后，非圆柱螺旋弹簧振动特性的研究已经受到普遍的关