弧面分度凸轮机构压力角的通用表达式研究
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摘要
针对弧面分度凸轮机构参数缺乏通用数学模型的情况,应用包络面理论,通过齐次坐标的矩阵变换,提出了一种基于统一数学表达的弧面分度凸轮轮廓曲面的建模方法.以圆柱滚子、圆锥滚子和双曲线滚子为研究对象,推导建立了弧面分度凸轮廓面模型的统一数学模型,在此基础上进一步推导出了压力角的通用解析表达式,为弧面分度凸轮的精确设计与制造提供了理论基础.
Due to the lack of general mathematical model for the parameters of the globoidal indexing cam mechanism,a method of modeling the contour for the globoidal indexing cam based on the unified mathematical expression is proposed by applying the envelope theory and the matrix transformation of the homogeneous coordinates. Taking the globoidal cams with cylindrical,conical,and hyperbolic meshing turret-rollers as the research objects,the unified mathematical model of profile model for the globoidal indexing cam is derived. On this basis,the general analytic expression of pressure angle is further derived,which provides a theoretical basis for the precise design and manufacture of the globoidal indexing cam.
Due to the lack of general mathematical model for the parameters of the globoidal indexing cam mechanism,a method of modeling the contour for the globoidal indexing cam based on the unified mathematical expression is proposed by applying the envelope theory and the matrix transformation of the homogeneous coordinates. Taking the globoidal cams with cylindrical,conical,and hyperbolic meshing turret-rollers as the research objects,the unified mathematical model of profile model for the globoidal indexing cam is derived. On this basis,the general analytic expression of pressure angle is further derived,which provides a theoretical basis for the precise design and manufacture of the globoidal indexing cam.
引文
[1]李海.弧面凸轮加工的廓面误差分析与测量方案设计[D].湖南:湘潭大学,2015.
[2]纪姝婷.弧面凸轮机构制造误差及曲面特性研究[D].北京:北京工业大学,2016.
[3]Yan H S,Chen H H. Geometry design of globoidal cams with generalized meshing turret-rollers[J]. J Mech Design,1996,118(2):243-249.
[4]方代正,张淳,曹西京.钢球滚子弧面凸轮分度机构的设计与压力角计算[J].机械科学与技术,2003,22(S1):154-156.
[5]Li L,Feng X Y,Zhang Z P,et al. Profile surface construction and pressure angle analysis of a new type of globoidal indexing cam[J]. App Mech Mat,2010,979(29):1608-1614.
[6]刘明,丁江民.弧面分度凸轮压力角计算及滚子运动分析[J].机械传动,2008,32(6):104-106,134.
[7]杨玮,曹巨江.弧面凸轮机构的压力角和曲率分析[J].机械科学与技术,2004,23(1):74-76.
[8]赵雪妮,曹巨江,孙立新.锥滚子弧面分度凸轮机构的压力角[J].吉林大学学报(工学版),2003,33(4):55-58.
[9]刘永骏.基于共轭包络理论的齿面加工模拟与仿真研究[D].上海:华东理工大学,2011.
[10]李俭,唐茂,张跃华,等.基于统一数学表达的摆动或直动从动件空间凸轮机构曲面建模研究[J].机械设计,2009,26(6):38-42.
[11]张艳妮.利用经典包络理论求曲线和曲面的包络[J].山东农业工程学院学报,2015,32(7):141,143.
[12]李养成.空间解析几何[M].北京:科学出版社,2016.
[13]刘德平.计算机辅助设计与制造[M].北京:中国铁道出版社,2012.
[14]唐哲敏,黄美发,孙永厚.基于齐次坐标变换的统计装配公差建模[J].计算机集成制造系统,2017,23(3):455-464.
[15]陈维桓.微分几何[M].北京:北京大学出版社,2017.
[2]纪姝婷.弧面凸轮机构制造误差及曲面特性研究[D].北京:北京工业大学,2016.
[3]Yan H S,Chen H H. Geometry design of globoidal cams with generalized meshing turret-rollers[J]. J Mech Design,1996,118(2):243-249.
[4]方代正,张淳,曹西京.钢球滚子弧面凸轮分度机构的设计与压力角计算[J].机械科学与技术,2003,22(S1):154-156.
[5]Li L,Feng X Y,Zhang Z P,et al. Profile surface construction and pressure angle analysis of a new type of globoidal indexing cam[J]. App Mech Mat,2010,979(29):1608-1614.
[6]刘明,丁江民.弧面分度凸轮压力角计算及滚子运动分析[J].机械传动,2008,32(6):104-106,134.
[7]杨玮,曹巨江.弧面凸轮机构的压力角和曲率分析[J].机械科学与技术,2004,23(1):74-76.
[8]赵雪妮,曹巨江,孙立新.锥滚子弧面分度凸轮机构的压力角[J].吉林大学学报(工学版),2003,33(4):55-58.
[9]刘永骏.基于共轭包络理论的齿面加工模拟与仿真研究[D].上海:华东理工大学,2011.
[10]李俭,唐茂,张跃华,等.基于统一数学表达的摆动或直动从动件空间凸轮机构曲面建模研究[J].机械设计,2009,26(6):38-42.
[11]张艳妮.利用经典包络理论求曲线和曲面的包络[J].山东农业工程学院学报,2015,32(7):141,143.
[12]李养成.空间解析几何[M].北京:科学出版社,2016.
[13]刘德平.计算机辅助设计与制造[M].北京:中国铁道出版社,2012.
[14]唐哲敏,黄美发,孙永厚.基于齐次坐标变换的统计装配公差建模[J].计算机集成制造系统,2017,23(3):455-464.
[15]陈维桓.微分几何[M].北京:北京大学出版社,2017.