弹簧丝横截面上各内力对锥形弹簧刚度的影响  

Influence of various internal forces of spring wire on stiffness of conical spring

作　　者：李峥彬 钱宁伟 肖奉英 沈逸舟 黄模佳[1] LI Zhengbin;QIAN Ningwei;XIAO Fengying;SHEN Yizhou;HUANG Mojia(Institute of Engineering Mechanics,Nanchang University,Nanchang 330031,China)

机构地区：[1]南昌大学工程力学系,江西南昌330031

出　　处：《南昌大学学报（工科版）》2022年第2期176-182,共7页Journal of Nanchang University(Engineering & Technology)

摘　　要：横截面上的内力包括扭矩、弯矩、轴力和剪力。锥形螺旋弹簧刚度的经典表达式由外力所做功等于弹簧丝的扭转变形能获得,但经典表达式未考虑弹簧丝倾斜度与弹簧丝弯曲变形的关系及其对弹簧刚度的影响,也未考虑弹簧径径比(弹簧丝直径d和锥形弹簧圈最大半径R1之比d/R1)与弹簧丝剪切变形的关系及其对弹簧刚度的影响。求解弹簧丝在扭转、弯曲、剪切以及轴力作用下的组合变形能,利用外力功等于弹簧丝的组合变形能,推导出包含弹簧丝倾斜度及弹簧径径比影响的弹簧刚度表达式,该锥形弹簧刚度表达式可退化为圆柱弹簧刚度计算式、可退化为锥形螺旋弹簧的经典表达式。当弹簧丝倾斜度和弹簧径径比较大时,由锥形弹簧刚度经典表达式得到的计算值与有限元仿真结果的误差达7%,而新给出的锥形弹簧刚度表达式计算值与有限元结果的误差在1%之内,新给出的锥形螺旋弹簧刚度表达式对锥形螺旋弹簧的工程设计和应用具有指导意义。Internal forces in cross section include torque,bending moment,axial force and shear force.The classical expression of the stiffness of conical coil spring was based on the assumption that the work of the external force equals to the torsional deformation energy of spring wires.However,in the classical expression,the relationship between the inclination and the bending deformation of spring wires and its influence on the spring stiffness were not considered.The relationship between the ratio d/R1(i.e.,the ratio of the diameter d of spring wire to the maximum radius R1 of conical spring coil)and the shear deformation of the spring wire and its influence on the spring stiffness were also not considered.The deformation energy of torsion,bending,shearing and axial force on the spring wire was given.According to the external force work equal to the combined deformation energy of the spring wire,the spring stiffness expression with the effect of the spring wire inclination and the spring diameter-diameter ratio was derived.The expression of the conical spring stiffness could be degenerated into the classical expressions for the cylindrical spring and the conical coil spring.When the inclination and the diameter of the spring were relatively large,the error between the results of the classical expression and the finite element methods was 7%,while the error between the results of our conical spring stiffness expression and the finite element methods was less than 1%.Our expression of the conical coil spring stiffness has guiding significance in the engineering design and application.

关 键 词：弹簧刚度 锥形螺旋弹簧 弹簧丝倾斜度 弹簧径径比 弹簧丝变形能 

分 类 号：TH135[机械工程—机械制造及自动化]