双圆弧弧齿锥齿轮传动的三维建模及切齿啮合模拟与分析
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摘要
作为一种新型齿轮传动方式，双圆弧弧齿锥齿轮传动不论在齿线方向、还是在齿高方向，均为凸、凹齿廓相啮合，因而它比一般的弧齿锥齿轮传动的承载能力高，使用寿命长；并且在啮合过程中两齿面间容易形成润滑油膜，具有良好的跑合性能，所以对它的应用和研究日益受到人们的重视。
本论文首先根据双圆弧齿轮传动的啮合理论，结合其齿形特点和弧齿锥齿轮的加工原理，进行了双圆弧弧齿锥齿轮的切齿啮合分析，得到了切齿啮合过程中的啮合方程、产形轮齿面方程以及双圆弧弧齿锥齿轮的通用齿面方程，为下一步生成双圆弧弧齿锥齿轮的三维模型打下了基础。
在上述工作的基础上，综合应用计算机图形学理论、C语言、VC++语言、AUTOLISP编程以及CAD技术，编制了一交互式图形系统和双圆弧弧齿锥齿轮的三维建模软件。其中，C语言是计算部分，AUTOLISP语言是模型建立部分，VC++语言完成程序界面的生成。在参数界面中，不但有各个参数的编辑框，而且还有锥齿轮的结构图和双圆弧齿轮的基本齿形图，这样可以一边参照图形一边进行设计，从而大大提高了设计效率；另一方面，点击相应按扭后，可以马上得到这种双圆弧弧齿锥齿轮的三维模型。同时也可直接输入齿轮参数和齿形参数，来生成相应齿轮的三维模型，从而证明了前面推导的双圆弧弧齿锥齿轮通用齿面方程式的正确性。
在实体建模程序中，以双圆弧弧齿锥齿轮的加工原理为基础，借助绘图软件AutoCAD，模拟了双圆弧弧齿锥齿轮铣刀盘刀齿形状、轮齿毛坯形状等，进而根据产形轮与被加工齿坯之间的共轭啮合关系，进行了双圆弧弧齿锥齿轮的实体建模及加工过程模拟，在屏幕上动态显示刀具及被加工齿轮的相对位置及其加工时的运动轨迹和规律。
最后，通过比较双圆弧弧齿锥齿轮齿面理论方程与加入刀位及刀位角误差后的齿面方程，应用上述软件和通过进一步的数值计算，进行了无误差的理论齿形与加入刀位及刀位角误差后所得到的实际齿形之间的定量分析，比较直观、方便、准确地对刀位及刀位角误差对双圆弧弧齿锥齿轮的齿形以及传动的影响进行了初步研究。
As a new type gear transmission, double circular arc profile bevel gearing carries out its transmission by means of meshing between convex-concave tooth profile in both of the direction of tooth trace and the direction of tooth depth, so it has advantage of high load capacity, long service life, easy forming hydrodynamic oil film between teeth as well as high quality of running-in etc. Therefore, more attention has been paid to its application and research in recent years.
In this dissertation, first, based on the theory of W-N gearing, characteristic of tooth profile as well as the processing principle of helical bevel gear, a cutting meshing analysis about double circular arc profile bevel gear was carried out, the equation of meshing in the process of cutting tooth, the surface equation of generating gear as well as the general tooth surface equation of double circular arc profile bevel gear were obtained. Which established a foundation for building three-dimensional model of double circular arc profile bevel gear.
Second, based on works mentioned above, an interactive graphic system, i.e. an interactive parametric three-dimensional model-building software about double circular arc profile bevel gear were established according to computer graphics, C language, VC++ language, AUTOLISP programmed and CAD technology, in which, language C completed complicated calculation, AUTOLISP language finished model-building, VC++ language accomplished the generation of program interface. In parametric interface of this software, there is not only the editor frame of every parameter but also the standard schemes of double circular arc profile and the structural scheme of bevel gear .We can design the gearing according to the schemes efficiently. On the other hand, after clicking corresponding button, we can get the three-dimensional model at once. Simultaneity it can generate the three-dimensional model of corresponding gear in a minute after by directly inputting gear parameters and the parameters of tooth form, which could prove th
at the general tooth surface equation of double circular arc profile bevel gear obtained above was correct.
In the solid model building program, based on the cutting tooth theory of double circular arc profile spiral bevel gear and AutoCAD software, a series of computer simulations about solid model building and cutting tooth process of the gear were curried out. The cutter's tooth shape, the processed gear blank shape and its conjugated tooth profile shape as well as visual movement relationship between generating gear and processed gear blank etc. were obtained. The relative position of cutter and processed gear as well as the movement trace and rule in the cutting process can be showed dynamically on screen.
Finally, by means of comparing the theoretical tooth surface equation with the tooth surface equation included errors of cutter position and cutter position angle, the quantitative analysis of the theoretical tooth shape and the tooth shape considering the errors of cutter position and cutter position angle was curried out based on the software above. From which, the effect of errors of cutter position as well as cutter position angle on the processed tooth shape and transmitting behavior of this kind of gearing was studied.
本论文首先根据双圆弧齿轮传动的啮合理论，结合其齿形特点和弧齿锥齿轮的加工原理，进行了双圆弧弧齿锥齿轮的切齿啮合分析，得到了切齿啮合过程中的啮合方程、产形轮齿面方程以及双圆弧弧齿锥齿轮的通用齿面方程，为下一步生成双圆弧弧齿锥齿轮的三维模型打下了基础。
在上述工作的基础上，综合应用计算机图形学理论、C语言、VC++语言、AUTOLISP编程以及CAD技术，编制了一交互式图形系统和双圆弧弧齿锥齿轮的三维建模软件。其中，C语言是计算部分，AUTOLISP语言是模型建立部分，VC++语言完成程序界面的生成。在参数界面中，不但有各个参数的编辑框，而且还有锥齿轮的结构图和双圆弧齿轮的基本齿形图，这样可以一边参照图形一边进行设计，从而大大提高了设计效率；另一方面，点击相应按扭后，可以马上得到这种双圆弧弧齿锥齿轮的三维模型。同时也可直接输入齿轮参数和齿形参数，来生成相应齿轮的三维模型，从而证明了前面推导的双圆弧弧齿锥齿轮通用齿面方程式的正确性。
在实体建模程序中，以双圆弧弧齿锥齿轮的加工原理为基础，借助绘图软件AutoCAD，模拟了双圆弧弧齿锥齿轮铣刀盘刀齿形状、轮齿毛坯形状等，进而根据产形轮与被加工齿坯之间的共轭啮合关系，进行了双圆弧弧齿锥齿轮的实体建模及加工过程模拟，在屏幕上动态显示刀具及被加工齿轮的相对位置及其加工时的运动轨迹和规律。
最后，通过比较双圆弧弧齿锥齿轮齿面理论方程与加入刀位及刀位角误差后的齿面方程，应用上述软件和通过进一步的数值计算，进行了无误差的理论齿形与加入刀位及刀位角误差后所得到的实际齿形之间的定量分析，比较直观、方便、准确地对刀位及刀位角误差对双圆弧弧齿锥齿轮的齿形以及传动的影响进行了初步研究。
As a new type gear transmission, double circular arc profile bevel gearing carries out its transmission by means of meshing between convex-concave tooth profile in both of the direction of tooth trace and the direction of tooth depth, so it has advantage of high load capacity, long service life, easy forming hydrodynamic oil film between teeth as well as high quality of running-in etc. Therefore, more attention has been paid to its application and research in recent years.
In this dissertation, first, based on the theory of W-N gearing, characteristic of tooth profile as well as the processing principle of helical bevel gear, a cutting meshing analysis about double circular arc profile bevel gear was carried out, the equation of meshing in the process of cutting tooth, the surface equation of generating gear as well as the general tooth surface equation of double circular arc profile bevel gear were obtained. Which established a foundation for building three-dimensional model of double circular arc profile bevel gear.
Second, based on works mentioned above, an interactive graphic system, i.e. an interactive parametric three-dimensional model-building software about double circular arc profile bevel gear were established according to computer graphics, C language, VC++ language, AUTOLISP programmed and CAD technology, in which, language C completed complicated calculation, AUTOLISP language finished model-building, VC++ language accomplished the generation of program interface. In parametric interface of this software, there is not only the editor frame of every parameter but also the standard schemes of double circular arc profile and the structural scheme of bevel gear .We can design the gearing according to the schemes efficiently. On the other hand, after clicking corresponding button, we can get the three-dimensional model at once. Simultaneity it can generate the three-dimensional model of corresponding gear in a minute after by directly inputting gear parameters and the parameters of tooth form, which could prove th
at the general tooth surface equation of double circular arc profile bevel gear obtained above was correct.
In the solid model building program, based on the cutting tooth theory of double circular arc profile spiral bevel gear and AutoCAD software, a series of computer simulations about solid model building and cutting tooth process of the gear were curried out. The cutter's tooth shape, the processed gear blank shape and its conjugated tooth profile shape as well as visual movement relationship between generating gear and processed gear blank etc. were obtained. The relative position of cutter and processed gear as well as the movement trace and rule in the cutting process can be showed dynamically on screen.
Finally, by means of comparing the theoretical tooth surface equation with the tooth surface equation included errors of cutter position and cutter position angle, the quantitative analysis of the theoretical tooth shape and the tooth shape considering the errors of cutter position and cutter position angle was curried out based on the software above. From which, the effect of errors of cutter position as well as cutter position angle on the processed tooth shape and transmitting behavior of this kind of gearing was studied.
引文
[1] 邵家辉．圆弧齿轮(第2版)．机械工业出版社，1994
[2] 李进宝等．双圆弧弧齿锥齿轮传动特性及应用研究．中国机械工程．1994，(5)
[3] 吴大任．微分几何讲义．高等教育出版社，1982
[4] 吴大任、骆家舜．齿轮啮合原理．科学出版社，1985
[5] 胡来容．空间啮合原理及应用．机械工业出版社，1987
[6] 李进宝．双圆弧弧齿锥齿轮制造工艺与试验．机械传动学会齿轮传动学术年会应征论文选编，1983
[7] 武宝林等．双圆弧弧齿锥齿轮传动的切齿啮合分析．机械科学与技术，2002，21(5)：726～729
[8] 胡进、蔡春源、鄂中凯．双圆弧齿轮齿形参数的研究．东北工学院学报，1990，(11)：18～23
[9] 陶升元、刘军．圆弧齿轮齿面方程及诱导法曲率的探讨．淮南矿业学院学报，1988，(3)：25～30
[10] 陈启松、江耕华译．圆弧齿轮传动．科技译丛，太原工学院
[11] 段德荣．双圆弧齿轮传动的啮合分析．太原工业大学学报，1985，(4)
[12] 董学朱．齿轮啮合理论基础．机械工业出版社，1989
[13] 北京齿轮厂．螺旋锥齿轮 科学出版社，1974
[14] [苏联]Φ．李特文．齿轮啮合原理，上海科学技术出版社，1984
[15] 齿轮手册．机械工业出版社
[16] 机械零件设计手册．冶金工业出版社
[17] 蔡颖、薛庆等．CAD／CAM原理与应用．机械工业出版社，1999
[18] [美] D．F．罗杰斯．计算机图形学的算法基础．科学出版社，1987
[19] 宁汝新、徐弘山．机械制造中的CAD／CAM技术．北京理工大学出版社，1991
[20] 章一鸣．计算机辅助机械设计．北京理工大学出版社，1992
[21] AutoCAD 2002／2000 Visual LISP开发指南．清华大学出版社，2001
[22] 林龙震．AutoCAD窗口设计技巧与ADS程序设计参考．清华大学出版社，1994
[23] 俞长高、蒋锡藩．机械制造中的计算机辅助设计．机械工业出版社
[24] 刘方爱等．C语言程序设计．石油大学出版社，1995
[25] 汤德忠、李正吾．CAD／CAM应用技术．机械工业出版社，1988
[26] 孙家广等．计算机图形学．清华大学出版社，1998
[27] 黄少昌．计算机辅助机械设计技术基础．清华大学出版社，1988
[28] Hawkes B. The CAD/CAM Process. Pitman, 1988
[29] R.H. Johnson. Solid Mokdelling:A State-of-the-art Report. Massachusetts, 1985
[30] S.K. Newsletter. Solid Modeling In Computer Graphics: Technology, Applications, Technology & Business Communication Inc.,Sudbury, Massachusetts, 1984
[31] A. Seireg. Analysis and Synthesis of Circular Arc Gear by Interactive Graphics. Transactions of the ASME, March 1986, vol.108
[32] Li Jinbao. Study on Double Circular Arc Profile Spiral Bevel Gear Transmission. Chinese journal of Mechanical Engineering, 1995,8
[33] Li, J, Shao. J and R.L. Huston. Meshing analysis of double circular arc profile spiral bevel gears. Proceedings of international conference on gearing, 1998
[34] J. Li and R.L. Huston. Design and analysis of double circular arc profile spiral bevel gears. Proceedings of the Ixth ICPR, 1987
[35] L. Bexter. Second-order Surface Generation. Industrial Mathematics Vol. 23, Part 2,1973
[36] L. Litvin. Method for Generation of Spiral Bevel Gear with conjugate Gear Tooth Surface. Journal of mechanisms, Transmissions, and automation in Design, June, 1987 Vol, 109
[37] H. Chang, R.L. Huston, J.J. cov. A Computer Aided design Procedure For Generating Gear Teeth. AD-A 166082 Oct., 1984
[38] 孙珠峰、吴金平．Visual C++基础培训教程．人民邮电出版社，2002
[39] 邓力、张廷健等．双自由度包络法推导双圆弧齿轮齿面方程．机械传动，2001，(3)：36～39
[40] 段德荣、常彦伟．准端面双圆弧齿轮及齿面方程．机械传动，2000，(2)：10～14
[41] 綦耀光．双圆弧齿轮凸凹弧啮合规律与啮合刚度计算．石油机械，1998，(2)：28～30
[42] 毋荣亮．圆弧齿线双圆弧齿轮的基本原理．太原理工大学学报，1997，(3)：72～77
[43] 张秀亲、张应顺．存在误差时双圆弧齿轮啮合的理论分析．太原工业大学学报，1995，(2)：28～33
[44] 张秀亲、张应顺．分阶式双圆弧齿轮的优化设计．煤矿机械，1996，(4)：9～10
[45] 周广仁、谭建荣等．计算机辅助设计与绘图．高等教育出版社，2000
[46] 谭荣伟．AutoCAD 2000三维建模技巧与范例．清华大学出版社，2000
[47] 洪汉玉．圆弧齿线双圆弧齿轮啮合分析及计算机图形系统研究．太原工业大学硕士学位论文，1991
[48] 张云石、张云杰等．3D Studio MAX R4应用培训教程．电子工业出版社，2001
[49] 谭浩强、张基温、唐永炎．C语言程序设计教程．高等教育出版社，1998
[50] 尚红权．双圆弧锥齿轮传动啮合模拟及分析．太原工业大学硕士学位论文，1998
[2] 李进宝等．双圆弧弧齿锥齿轮传动特性及应用研究．中国机械工程．1994，(5)
[3] 吴大任．微分几何讲义．高等教育出版社，1982
[4] 吴大任、骆家舜．齿轮啮合原理．科学出版社，1985
[5] 胡来容．空间啮合原理及应用．机械工业出版社，1987
[6] 李进宝．双圆弧弧齿锥齿轮制造工艺与试验．机械传动学会齿轮传动学术年会应征论文选编，1983
[7] 武宝林等．双圆弧弧齿锥齿轮传动的切齿啮合分析．机械科学与技术，2002，21(5)：726～729
[8] 胡进、蔡春源、鄂中凯．双圆弧齿轮齿形参数的研究．东北工学院学报，1990，(11)：18～23
[9] 陶升元、刘军．圆弧齿轮齿面方程及诱导法曲率的探讨．淮南矿业学院学报，1988，(3)：25～30
[10] 陈启松、江耕华译．圆弧齿轮传动．科技译丛，太原工学院
[11] 段德荣．双圆弧齿轮传动的啮合分析．太原工业大学学报，1985，(4)
[12] 董学朱．齿轮啮合理论基础．机械工业出版社，1989
[13] 北京齿轮厂．螺旋锥齿轮 科学出版社，1974
[14] [苏联]Φ．李特文．齿轮啮合原理，上海科学技术出版社，1984
[15] 齿轮手册．机械工业出版社
[16] 机械零件设计手册．冶金工业出版社
[17] 蔡颖、薛庆等．CAD／CAM原理与应用．机械工业出版社，1999
[18] [美] D．F．罗杰斯．计算机图形学的算法基础．科学出版社，1987
[19] 宁汝新、徐弘山．机械制造中的CAD／CAM技术．北京理工大学出版社，1991
[20] 章一鸣．计算机辅助机械设计．北京理工大学出版社，1992
[21] AutoCAD 2002／2000 Visual LISP开发指南．清华大学出版社，2001
[22] 林龙震．AutoCAD窗口设计技巧与ADS程序设计参考．清华大学出版社，1994
[23] 俞长高、蒋锡藩．机械制造中的计算机辅助设计．机械工业出版社
[24] 刘方爱等．C语言程序设计．石油大学出版社，1995
[25] 汤德忠、李正吾．CAD／CAM应用技术．机械工业出版社，1988
[26] 孙家广等．计算机图形学．清华大学出版社，1998
[27] 黄少昌．计算机辅助机械设计技术基础．清华大学出版社，1988
[28] Hawkes B. The CAD/CAM Process. Pitman, 1988
[29] R.H. Johnson. Solid Mokdelling:A State-of-the-art Report. Massachusetts, 1985
[30] S.K. Newsletter. Solid Modeling In Computer Graphics: Technology, Applications, Technology & Business Communication Inc.,Sudbury, Massachusetts, 1984
[31] A. Seireg. Analysis and Synthesis of Circular Arc Gear by Interactive Graphics. Transactions of the ASME, March 1986, vol.108
[32] Li Jinbao. Study on Double Circular Arc Profile Spiral Bevel Gear Transmission. Chinese journal of Mechanical Engineering, 1995,8
[33] Li, J, Shao. J and R.L. Huston. Meshing analysis of double circular arc profile spiral bevel gears. Proceedings of international conference on gearing, 1998
[34] J. Li and R.L. Huston. Design and analysis of double circular arc profile spiral bevel gears. Proceedings of the Ixth ICPR, 1987
[35] L. Bexter. Second-order Surface Generation. Industrial Mathematics Vol. 23, Part 2,1973
[36] L. Litvin. Method for Generation of Spiral Bevel Gear with conjugate Gear Tooth Surface. Journal of mechanisms, Transmissions, and automation in Design, June, 1987 Vol, 109
[37] H. Chang, R.L. Huston, J.J. cov. A Computer Aided design Procedure For Generating Gear Teeth. AD-A 166082 Oct., 1984
[38] 孙珠峰、吴金平．Visual C++基础培训教程．人民邮电出版社，2002
[39] 邓力、张廷健等．双自由度包络法推导双圆弧齿轮齿面方程．机械传动，2001，(3)：36～39
[40] 段德荣、常彦伟．准端面双圆弧齿轮及齿面方程．机械传动，2000，(2)：10～14
[41] 綦耀光．双圆弧齿轮凸凹弧啮合规律与啮合刚度计算．石油机械，1998，(2)：28～30
[42] 毋荣亮．圆弧齿线双圆弧齿轮的基本原理．太原理工大学学报，1997，(3)：72～77
[43] 张秀亲、张应顺．存在误差时双圆弧齿轮啮合的理论分析．太原工业大学学报，1995，(2)：28～33
[44] 张秀亲、张应顺．分阶式双圆弧齿轮的优化设计．煤矿机械，1996，(4)：9～10
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