A Study on the Stiffness of Frustum-shaped Coil Spring

원추형 코일스프링의 강성에 대한 연구

Springs are widely utilized in machine element. To find out stiffness of frustum-shaped coil spring, the space beam theory using the finite element method is adopted in this paper In three dimensional space, a space frame element is a straight bar of uniform cross section which is capable of resisting axial forces, bending moments about two principal axes in the plane of its cross section and twisting moment about its centroidal axis. The corresponding displacement degrees of freedom are twelve. To find out load vector of coil spring subjected to distributed compression, principle of virtual work is adapted The displacements of nodal points due to small increment of force are calculated by the finite element method and the calculated nodal displacements are added to coordinates of nodal points. The new stiffness matrix of the system using the new coordinates of nodal points is adopted to calculate the another increments of nodal displacements, that is, the step by step method is used in this paper. The results of the finite element method are fairly well agreed with those of various experiments. Using MATLAB program developed in this paper, spring constants and stresses can be predicted by input of few factors.