考虑翘曲效应的圆柱螺旋弹簧的振动分析

以空间曲梁理论为基础对簧丝截面为矩形的圆柱螺旋弹簧的自由振动特性进行了研究. 在弹簧的运动微分方程中, 所有的位移函数和广义翘曲坐标均定义在横截面的形心主轴上, 同时考虑了翘曲变形对弹簧固有频率的影响. 通过精确地应用符号运算软件MATHEMATICA可以得到振动模态的显式表达式, 固有频率则可用搜索的方法来确定. 在较宽的范围内, 给出了各种参数变化, 如簧丝截面的宽高比(a/ b = 0.6 ~ 1.7)、螺旋角(\bar {\alpha } = 5^\circ ~ 12.5^ \circ)、弹簧工作圈数(n = 6 ~ 12)和圆柱螺旋线半径(R = 4~ 10mm)对固有频率的影响. 为了证明解析法的有效性, 对两端固支和一端固支、一端自由矩形截面圆柱螺旋弹簧的固有频率和振动模态进行了求解, 并同ANSYS三维实体单元(Solid45)的结果和文献的结果进行了比较. 计算表明: 用解析方法得到的解和用数值方法得到的结果吻合得很好. 

VIBRATION ANALYSIS OF CYLINDRICAL HELICAL SPRINGS CONSIDERING WARPING DEFORMATION EFFECT

The free vibrational behavior of cylindrical helical springs with rectangular cross sections is analytically investigated in this paper based on spatial curved beam theory.In the differential equations of motion of the springs,all displacement functions and a generalized warping coordinate are defined at the centroid principal axes and the warping effect upon the natural frequencies is also considered in present study.Explicit analytical expressions which give the vibrating mode shapes are derived by rigoro...