求解弧面分度凸轮廓面数控加工刀具轨迹通用方程
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摘要
对弧面分度凸轮轮廓曲面进行数控加工编程前需确定刀具轨迹方程。针对不同滚子形状及凸轮轴线与从动盘轴线成任意角度的情况,基于微分几何原理,应用包络面理论建立统一数学模型的弧面凸轮廓面方程。在此基础上进一步推导出数控加工刀具轨迹方程的通用解析表达式。此结果可作为数控加工弧面分度凸轮廓面编程时的数学模型,也可应用于弧面凸轮加工过程的仿真、加工误差分析和廓面修形等方面。
The tool path equation must be determined before the NC machining program for the contour surface of globoidal indexing cam is programmed. In view of the difference of the shape of the rollers and the angle between the axis of globoidal cam and the axis of the follower plate,the profile equation of globoidal cam is established by using envelope theory based on the principle of differential geometry. On this basis,the general analytic expression for the tool path equation of NC machining is further derived. This result can not only be used as a mathematical model for the programming of the NC machining globoidal cam profile,but also can be applied to the simulation for the machining process of the globoidal cam,the analysis of the machining error and the profile modification.
The tool path equation must be determined before the NC machining program for the contour surface of globoidal indexing cam is programmed. In view of the difference of the shape of the rollers and the angle between the axis of globoidal cam and the axis of the follower plate,the profile equation of globoidal cam is established by using envelope theory based on the principle of differential geometry. On this basis,the general analytic expression for the tool path equation of NC machining is further derived. This result can not only be used as a mathematical model for the programming of the NC machining globoidal cam profile,but also can be applied to the simulation for the machining process of the globoidal cam,the analysis of the machining error and the profile modification.
引文
[1]袁惊滔.弧面分度凸轮的三维造型与数控加工[J].精密制造与自动化,2015(1):52-54,57.
[2]窦湘屏,袁光明,刘磊.五轴联动加工中心加工弧面凸轮[J].机械制造与自动化,2010,39(6):45-48,60.
[3]X F Tang,Wei He,Y S Liu.A new one-side finish machining method for profile of globoidal indexing cam in high speed[J].Materials Science Forum,2009,857(626):611-616.
[4]范友君,别瑜,李阳.弧面分度凸轮五轴非等价加工研究[J].机械传动,2015,39(4):168-171.
[5]曹巨江,李言,刘兴亮.弧面凸轮的单侧面磨削加工研究[J].机械科学与技术,2010,29(4):514-518,523.
[6]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.
[7]冯桢,边明杰,王双林,等.弧面分度凸轮精确建模与五轴加工[J].机械传动,2013,37(7):137-139.
[2]窦湘屏,袁光明,刘磊.五轴联动加工中心加工弧面凸轮[J].机械制造与自动化,2010,39(6):45-48,60.
[3]X F Tang,Wei He,Y S Liu.A new one-side finish machining method for profile of globoidal indexing cam in high speed[J].Materials Science Forum,2009,857(626):611-616.
[4]范友君,别瑜,李阳.弧面分度凸轮五轴非等价加工研究[J].机械传动,2015,39(4):168-171.
[5]曹巨江,李言,刘兴亮.弧面凸轮的单侧面磨削加工研究[J].机械科学与技术,2010,29(4):514-518,523.
[6]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.
[7]冯桢,边明杰,王双林,等.弧面分度凸轮精确建模与五轴加工[J].机械传动,2013,37(7):137-139.