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工程科学与技术:2013,45(3):171-175
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旋转刀盘母面成形的弧齿线圆柱齿轮数学建模
(1.四川大学 制造科学与工程学院;2.重庆大学 机械传动国家重点实验室)
Mathematical Modeling of Rotary Cutter Arc Tooth Line of Cylindrical Gear Shaped by Origin Face of Rotary Cutter
(1.School of Manufacturing Sci. and Eng.,Sichuan Univ.;2.State Key Lab. of Mechanical Transmission,Chongqing Univ.)
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投稿时间:2012-07-10    修订日期:2013-01-25
中文摘要: 将空间啮合理论用于齿轮的齿面数学方程推导,建立了可用于理论分析的采用旋转刀盘为成形母面的弧齿线圆柱齿轮齿面数学方程。通过观察分析齿轮加工中刀盘与齿胚的运动关系,将弧齿线圆柱齿轮齿面分割为3个主要构成曲面,建立了加工过程中的动态与静态坐标系,依据曲面包络理论建立工作曲面的曲面数学方程,根据坐标转换关系建立了齿底和齿根曲面方程;在此基础上建立齿面方程。输出齿面的点云数据,通过逆向工程拟合取得可用于编辑裁剪的齿轮曲面,再根据曲面之间的关系裁剪曲面,最终生成齿轮3D模型实体。此方法建立了精确的弧齿线圆柱齿轮3D模型,并且与采用模拟加工方法生成的模型一致,为精确地进行有限元分析提供了基础;而由此方法获得的曲面方程可用于对弧齿线圆柱齿轮的理论分析。
Abstract:Spatial engaging theory was used to deduce mathematical equation of gear surface. Mathematical equation of arc tooth line of cylindrical gear surface shaped by origin face of rotary cutter,which could be used for both theoretical analysis and computer simulation,was built by dividing arc tooth line of cylindrical tooth surface into three main component surface,establishing dynamic and static coordinate system in machining process,constructing working surface mathematical equations based on theory of conjugate surface,deriving tooth bottom surface equation and tooth root surface equation from coordinate transformation and establishing equations of gear surface on this basis.Point cloud data of the tooth surface was calculated and output,tooth surface was tailored on the relationship between gear surfaces,and 3D model entities of arc tooth line of cylindrical gear was obtained.The arc tooth line cylindrical gear 3D model obtained by this method was consistent with the model generated by the method of simulating machining means.
文章编号:201200535     中图分类号:    文献标志码:
基金项目:机械传动国家重点实验室(重庆大学)开放基金资助项目(SKLMT-KFKT-200901);西华大学重点实验室开放基金资助项目(szjj2011-041)
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肖华军,侯力,董璐,蒋易强,魏永峭.旋转刀盘母面成形的弧齿线圆柱齿轮数学建模[J].工程科学与技术,2013,45(3):171-175.
Xiao Huajun,Hou Li,Dong Lu,Jiang Yiqiang,Wei Yongqiao.Mathematical Modeling of Rotary Cutter Arc Tooth Line of Cylindrical Gear Shaped by Origin Face of Rotary Cutter[J].Advanced Engineering Sciences,2013,45(3):171-175.