基于统一数学表达的弧面分度凸轮廓面方程的研究
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摘要
应用单参数曲面族包络面理论,计算和分析了弧面分度凸轮机构。通过齐次坐标变换,推导建立了圆柱滚子、圆锥滚子以及双曲线滚子的弧面分度凸轮轮廓曲面模型的统一数学表达式。通过实例,验证了该方法和模型的正确性。为压力角及主曲率表达式的推导奠定了基础;同时,为计算机辅助设计和制造空间凸轮提供了参考。
Based on the theory of envelopes for the single parameter family of surfaces,the globoidal indexing cams mechanism are calculated and analyzed. The unifi mathematical expressions of the contour surface geometry for globoidal cams with cylindrical,conical,and hyperbolic meshing turret-rollers are derived by homogeneous coordinate transformation. The correctness of the method and model is verified by an example. A foundation for the derivation of the expression of pressure angle and main curvature is laid,and a reference for computer aided design and manufacture of spatial cams is provided.
Based on the theory of envelopes for the single parameter family of surfaces,the globoidal indexing cams mechanism are calculated and analyzed. The unifi mathematical expressions of the contour surface geometry for globoidal cams with cylindrical,conical,and hyperbolic meshing turret-rollers are derived by homogeneous coordinate transformation. The correctness of the method and model is verified by an example. A foundation for the derivation of the expression of pressure angle and main curvature is laid,and a reference for computer aided design and manufacture of spatial cams is provided.
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].湘潭:湘潭大学,2015:57-62.
[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,2016:21-28.
[3]张三.弧面分度凸轮工作轮廓曲面数字化模型设计[J].现代制造工程,2015(9):132-137.
[4] LI Lei,FENG Xianying,PING Zi,et al. 3D modeling and simulation of a new type of globoidal indexing cam mechanism[J]. Applied Mechanics and Materials,2010,973(26):931-935.
[5] WANG Lin,YIN Mingfu. The parametric design and simulation for globoidal indexing cam mechanism[J]. Applied Mechanics and Materials,2014(599/600/601):517-521.
[6] YAN H S,CHEN H H. Geometry design of globoidal cams with generalized meshing turret-rollers[J]. Journal of Mechanical Design,1996,118(2):243-249.
[7]常宗瑜,张策,杨玉虎.用包络理论生成空间分度凸轮的啮合曲面[J].机械设计,2000,17(2):10-11.
[8]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.
[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,2011:37-42.
[10]李俭,殷国富.圆锥滚子直动从动件圆锥凸轮机构廓面方程的解析方法[J].机械设计,2003,20(11):13-15.
[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,2016:20-31.
[13]何雪涛,程源,黄钟,等.齐次坐标变换在空间机构分析中的应用[J].北京化工大学学报(自然科学版),1999,26(1):43-46.
[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]刘德平.计算机辅助设计与制造[M].北京:中国铁道出版社,2012:78-91.
[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,2016:21-28.
[3]张三.弧面分度凸轮工作轮廓曲面数字化模型设计[J].现代制造工程,2015(9):132-137.
[4] LI Lei,FENG Xianying,PING Zi,et al. 3D modeling and simulation of a new type of globoidal indexing cam mechanism[J]. Applied Mechanics and Materials,2010,973(26):931-935.
[5] WANG Lin,YIN Mingfu. The parametric design and simulation for globoidal indexing cam mechanism[J]. Applied Mechanics and Materials,2014(599/600/601):517-521.
[6] YAN H S,CHEN H H. Geometry design of globoidal cams with generalized meshing turret-rollers[J]. Journal of Mechanical Design,1996,118(2):243-249.
[7]常宗瑜,张策,杨玉虎.用包络理论生成空间分度凸轮的啮合曲面[J].机械设计,2000,17(2):10-11.
[8]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.
[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,2011:37-42.
[10]李俭,殷国富.圆锥滚子直动从动件圆锥凸轮机构廓面方程的解析方法[J].机械设计,2003,20(11):13-15.
[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,2016:20-31.
[13]何雪涛,程源,黄钟,等.齐次坐标变换在空间机构分析中的应用[J].北京化工大学学报(自然科学版),1999,26(1):43-46.
[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]刘德平.计算机辅助设计与制造[M].北京:中国铁道出版社,2012:78-91.