三圆弧谐波齿轮空间齿廓设计与扭转刚度的有限元仿真  

Spatial Tooth Profile Design of Triple-circular-arc Harmonic Gears and Finite Element Simulation of Torsional Stiffness

作　　者：邢静忠[1,2] 陈亮 陈晓霞[1,2] 姚云鹏 Xing Jingzhong;Chen Liang;Chen Xiaoxia;Yao Yunpeng(School of Mechanical Engineering,Tiangong University,Tianjin 300387,China;Tianjin Key Laboratory of Modern Mechatronics Equipment Technology,Tiangong University,Tianjin 300387,China)

机构地区：[1]天津工业大学机械工程学院,天津300387 [2]天津工业大学天津市现代机电装备技术重点实验室,天津300387

出　　处：《机械传动》2023年第9期37-43,共7页Journal of Mechanical Transmission

基　　金：国家自然科学基金项目(51575390);天津市自然科学基金项目(19JCZDJC38700)。

摘　　要：为评价齿廓方案的负载传动性能,提升负载传动能力,建立有限元分析(Finite Element Analysis,FEA)仿真模型,揭示了输出端扭转刚度与负载啮合特性的关系。构造三圆弧柔轮齿廓,调整柔轮齿廓的径向变位系数,使柔轮齿廓啮合运动的外包络重叠量最小化,并基于外包络用包络法设计了三圆弧平面齿廓刚轮;在多个横截面内构造径向变位的三圆弧柔轮齿廓,在有限元环境下轴向放样生成柔轮空间齿廓,建立了包含平面齿廓刚轮、空间齿廓柔轮和波发生器外圈的有限元仿真模型;固定刚轮,对柔轮杯底法兰施加不同幅值和转向的负载转矩,仿真计算了啮合力分布与扭转刚度滞回曲线;通过建立啮合齿数与刚度特性的关系,揭示了扭转刚度特性与齿面啮合特性之间的关系。仿真结果表明,啮合齿数与扭转刚度成正相关;使用可测量的扭转刚度迟滞曲线,可以估算啮合齿数等不可测量的啮合特性。In order to improve the transmission capability by exploring the relationship between torsional stiffness on output shaft and load meshing characteristics,a simulation model of finite element analysis(FEA)is built to evaluate the performance of tooth profile under transmission loading.A triple-circular-arc tooth profile of flexspline is constructed,and the radial modification of the tooth profile is adjusted to minimize the outer envelope overlap of meshing motion of the tooth profiles.Then,a triple-circular-arc planar tooth profile of circular splines is designed with the envelop method according to the outer envelope.A triple-circular-arc tooth profile of flexspline with tradial modification is constructed in several cross sections,and the spatial tooth profiles of flexsplines are generated by axial lofting in finite element environment.A finite element simulation model including circular spline with planar tooth profile,cup-shaped flexspline with spatial tooth profile and outer ring of wave generators is established.Transmission torques of different amplitudes in two rotational directions are applied on the flange plate at the bottom of the flexspline engaged with a fixed circular spline,and the meshing force distribution and torsional stiffness hysteresis curves are simulated.The number of meshing teeth in different meshing states can be estimated with the relationship between torsional stiffness and meshing characteristics of tooth profiles.The simulation results show that the number of meshing teeth is positively correlated with the torsional stiffness.Using the measureable hysteresis curve of torsional stiffness,the immeasurable meshing characteristics such as the number of meshing teeth can be estimated.

关 键 词：三圆弧齿廓 空间齿廓 啮合特性 有限元仿真 扭转刚度 

分 类 号：TH132.41[机械工程—机械制造及自动化]