谐波齿轮间隙装配下柔轮齿圈的力学特性及轮齿定位研究  

Research on Tooth Positioning and Mechanical Properties of Flexspline Tooth Rings with Harmonic Gear Clearance Assembly

作　　者：邢静忠[1,2] 杨子钰 陈晓霞[1,2] 姚云鹏[2] Xing Jingzhong;Yang Ziyu;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》2022年第12期7-15,共9页Journal of Mechanical Transmission

基　　金：国家自然科学基金(51575390);天津市自然基金重点项目(19JCZDJC38700,18JCZDJC39000)。

摘　　要：现有理论认为变形后柔轮齿圈中性线为整圈贴合凸轮轮廓的等距线,未考虑配合间隙和中面伸长的影响。为揭示配合间隙装配状态下柔轮的力学特性和齿圈变形后的轮齿定位,以椭圆凸轮波发生器为例,考虑柔轮内壁与波发生器外圈间隙和柔性轴承游隙引起的配合间隙及齿圈中面伸长,建立了柔轮齿圈变形的接触力学模型;引入变形后包角为未知参数,依据包角内用椭圆等距线表示的齿圈中线的曲率及力平衡条件确定齿圈内力;根据短轴处的位移条件和包角处的曲率条件及弧长关系,运用能量法迭代计算了包角、非接触区的大小及齿圈的内力和变形。以有限元模型结果为参照,对比验证了理论结果和轮齿定位偏差。理论分析和数值模拟均表明,受中面伸长的影响,零间隙配合的实际包角远小于90°,整圈贴合凸轮并不符合实际;降低配合间隙可有效增大轴承承载区,降低柔性轴承的径向负载和磨损;考虑包角和周向伸长,可以获得更准确的轮齿定位。研究为谐波齿轮的结构设计和啮合分析奠定了更准确的基础。The current theory considers that the shape of the deformed flexspline tooth ring neutral line is an isometric line of the cam,which ignores the effect of fit clearance and neutral line’s elongation.To reveal the mechanical properties and the tooth positioning on deformed flexspline tooth rings with fit clearance,taking elliptical cam wave generator as an example and considering the fit clearance caused by the clearance between the inner wall of flexsplines,the outer surface of wave generators,the clearance of flexible bearings and the elongation of neutral lines,a contact mechanical model of tooth rings is established.The wrap angle after deformation is introduced as an unknown parameter,and the internal forces in tooth rings in the wrap angle is determined according to the curvature of the neutral line of tooth rings represented by the elliptic equidistant line and the equilibrium equations of the forces.The size of non-contact area,and the internal forces and deformation of tooth ring is solved iteratively with Energy Method according to the displacement conditions on minor axis and the curvature condition at wrap angle and arc length relationship.Based on the results of finite element model,the theoretical results and tooth positions are compared and verified.Both the theoretical analysis and the numerical simulation show that the actual wrap angle of zero clearance fit is far less than 90°,and the full round fitting cam is not true because of the elongation of the neutral line.Reducing fit clearance can effectively increase the contact area and reduce the radial load and the wear of flexible bearings.Considering the wrap angle and the circumferential elongation,more accurate tooth positioning may lead to a more accurate foundation for structural design and meshing analysis of harmonic gears.

关 键 词：谐波齿轮传动 椭圆凸轮波发生器 配合间隙 力学分析 能量法 

分 类 号：TH132.41[机械工程—机械制造及自动化]