螺旋弹簧临界屈曲失稳的平衡方程

目前，针对螺旋弹簧失稳现象的研究主要基于当量柱模型，将弹簧等效为柱模型，忽略其绕轴线的转动．该文建立了三维螺旋弹簧模型，通过曲线Frenet坐标系和主轴坐标系，建立了描述弹簧螺旋中心线的空间变形和截面扭转变形的平衡方程．采用小变形假设，通过对弹簧挠度变量采用Taylor级数展开，并忽略其高阶小量，平衡方程可以被简化为扭转角和弧长的函数，使获得方程的数值解成为可能．同时，讨论了作用于弹簧圆心位置的轴向力引起的弹簧约束端反作用力，为平衡方程的求解确定了边界载荷条件．该文的研究工作为进一步研究受压螺旋弹簧的后屈曲性奠定了基础．

Equilibrium Equations for 3D Critical Buckling of Helical Springs

In most cases, the research on the buckling of helical spring is based on column, the spring is equivalent to column and the torsion around the axial line is ignored. The 3D helical spring model was considered,and its equilibrium equations were established by introducing two coordinate systems, named Frenet and principal axis coordinate systems, to describe the spatial deformation of center line and the torsion of cross section of spring respectively. By using small deformation assumption, the variables on deflection could be expanded by Taylor’s series and the terms of high orders were ignored. So the equations could be simplified to the functions of twist angle and arc length, which was possible to be solved in numerical method. The reaction loads of spring caused by axial load subjected at the center point were also discussed, which provided boundary conditions to gain the solution of equilibrium equations. This present work can be helpful to the continued research on the behavior of post buckling of compressed helical spring.