锥面包络环面蜗杆传动数字建模方法  

Digital Modeling of Cone-generated Enveloping Torus Worm

作　　者：刘志 卢红[3] 匡鑫 夏亮 Liu Zhi;Lu Hong;Kuang Xin;Xia Liang(School of Electromechanical and Automobile Engineering,Huanggang Normal University,Huanggang 438000,China;Hubei Zhongke Research Institute of Indusrial Technology,Huanggang 438000,China;School of Mechanical and Electronic Engineering,Wuhan University of Technology,Wuhan 430070,China)

机构地区：[1]黄冈师范学院机电与汽车工程学院,湖北黄冈438000 [2]湖北省中科产业技术研究院,湖北黄冈438000 [3]武汉理工大学机电工程学院,湖北武汉430070

出　　处：《机械传动》2020年第10期60-67,共8页Journal of Mechanical Transmission

基　　金：国家自然科学基金(51675393);湖北省教育厅科研计划重点项目(D20192903);黄冈市级科技计划项目(XQYF2020000031);校级科研项目(201814903)。

摘　　要：包络环面蜗杆传动的啮合性能对齿廓的几何精度和啮合质量要求严格,齿廓的模型精度将直接影响其应用性能。针对锥面包络环面蜗杆传动复杂型面表征问题,提出其精确数字模型构建方法。建立了锥面包络环面蜗杆活动标架,运用微分几何学、运动学、包络原理和空间坐标转换等方法,推导了蜗杆工作齿廓在不同坐标系统下的啮合方程及其数字模型,并给出了蜗杆齿底与齿顶环面的母线方程。结合包络运动起始区间和蜗杆工作齿廓边界,建立了蜗杆数字模型的约束条件。根据蜗杆工作齿廓成型原理,设计了表征其工作齿廓的复杂多元非线性数学模型的求解算法,计算出了蜗杆工作齿廓的全部瞬时接触线簇及其啮合点云,并给出了蜗杆齿廓接触线分布状态。在蜗杆齿廓点云基础上,运用曲线曲面拟合技术得到了蜗杆数字化实体模型。建模实例表明,蜗杆数字模型准确,模型求解算法收敛有效,蜗杆齿廓误差在10-9级。研究结果可为锥面包络环面蜗杆和相应二次包络蜗轮滚刀的精密数字制造等奠定模型基础。The meshing performance of enveloping tours worm drive requires the envelope lines to be matched strictly in accordance with the established relationship,the accuracy of tooth profile will directly affect its application performance.Aiming at the complicate meshing surface representation issue of cone-generated enveloping torus worm,the digital modeling method of this worm is proposed.The modeling frame is established firstly,and the meshing equations of the working tooth profile in different coordinate systems for the worm are deduced by applying differential geometry,kinematics,envelope theory and space coordinate transformation method,and the digital models of the working tooth profile of the worm are established,simultaneously,the generatrices equation of bottom and addendum surface are worked out.In addition,the constraint conditions of the worm digital models are constructed according to the enveloping process and boundary conditions of tooth profile.The solving algorithm for the complex nonlinear mathematical models is also designed based on the forming principle of the envelope surface,the instantaneous contact line and all meshing point cloud for the tooth profile are calculated,the distribution of contact line of worm tooth profile is also given.The digital solid model of worm is obtained by using curve and surface fitting technology based on the point cloud of worm tooth profile.The modeling experiment demonstrate that the digital model of worm is accurate,the designed solving algorithm of the model is effective as well as convergence,the worm tooth profile is of high precision,and the error of the worm tooth profile is at the level of 10-9.The research results can lay an accurate model foundation for precision digital manufacturing of cone-generated envelope torus worm and corresponding cone-generated double-envelope worm gear hob.

关 键 词：锥面包络环面蜗杆 啮合型面 数字模型 算法 

分 类 号：TH132.44[机械工程—机械制造及自动化]