法向圆弧锥齿轮数控加工技术研究
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摘要
法向圆弧锥齿轮是基于Bertrand共轭原理发展起来的一种新型传动形式，除具有接触强度高、承载能力大、对误差敏感度低、接触域容易控制等优良性能外，还具有良好的工艺性，十分便于采用指状或盘状铣刀进行成形法加工。目前，该种新型齿轮副尚处在理论研究阶段，将其引入工程实践有重要的应用价值。本文正是在数控技术迅猛发展的背景下，研究了法向圆弧锥齿轮数控加工理论。
论文从微分几何学基本概念入手，首先研究了Bertrand共轭曲面的几何性质与内在联系，接着引出了一种典型的Bertrand曲面，即法向圆弧曲面，该种曲面也是本文所研究的法向圆弧锥齿轮的齿廓面。法向圆弧曲面结构简单，沿母线法线共面，并且有许多重要的几何性质，在机械传动和曲面加工中有着广泛的应用前景。论文随后较为系统的研究了斜航式法向圆弧锥齿轮共轭原理，分析了节锥面上斜航线的特征，给出了斜航式法向圆弧锥齿轮廓面方程、准线应满足的基本条件、共轭曲面的诱导曲率、不干涉条件与准线曲率轴之间的关系，并基于UG软件平台建立了一对斜航式法向圆弧锥齿轮实体模型，这些都为后面的加工研究奠定了理论基础。在上面的基础上，论文详细研究了法向圆弧锥齿轮在数控机床上进行加工的原理，包括刀具的选择与参数的确定、刀具与工件间的接触条件、工件与机床坐标系的位置关系、刀具与锥齿轮廓面间的曲率干涉以及加工时刀具与工件之间的相对运动，最后编制了斜航式法向圆弧锥齿轮齿廓面的加工宏程序。
本文是基于数控技术对法向圆弧锥齿轮加工原理进行的研究。由于该种齿轮可在兼顾加工工艺性的基础上选择准线，那么当准线为斜航线时，不仅形成的齿廓面为便于加工的规律曲面，而且仍具有一般圆弧螺旋齿轮的优良传动性。由此可见，对该种齿轮数控加工技术的研究在工程上是具有重要价值的。
As a new type transmission pair based on Bertrand conjugation principle, normal circular-arc spiral bevel gears have many good characters, such as high contact strength ,large bearing capacity, low error sensitivity and the aptness to be controlled easily. It also has well technological function and convenience for machining. At the present time, the research on this gear is not sufficient. It is worth studying for the need of engineering. In the background of NC technology, the processing theory of the normal circular-arc bevel gears is studied.
Starting with the basic conceptions of differential geometry, the geometry nature and inner relationship of Bertrand conjugation surface are studied first. Then the normal circular-arc surface is put forward which is a typical Bertrand surface. There are some geometry characters about normal circular-arc surface, for example, it is simple in structure, and the normal lines along generatrix line are in one plane, so there are the extensive applying prospects in mechanical transmission and surface processing. Then the conjugation theory of loxodrome normal circular-arc bevel gears is studied. The characters of loxodrome line are analyzed. The tooth profile of loxodrome normal circular-arc bevel gears, the primary condition the directrix line must be satisfied, the relative curvature of the conjugating surfaces, the relations between non-interventional condition and curvature axle of the directrix line is provided. The modeling of the normal circular-arc gear is established with the soft of UG. The theory be studied all above have established the foundation for the following study. After that, the NC machining theory of normal circular-arc bevel gears is studied, including the designing and manufacture of the tool, the movement of the machine, the adjustment of the tool under the condition of tangency and non-interventional condition and so on. Finally the NC program of loxodrome normal circular-arc bevel gears is provided.
The machimng theory of normal circular-arc is studied on base of NC technology. Not only does the loxodrome normal circular-arc bevel gears has regular tooth surface, but also has the virtue transmission as common circular-arc bevel gears. The NC machining theory of normal circular-arc is important for the need of engineering indeed.
论文从微分几何学基本概念入手，首先研究了Bertrand共轭曲面的几何性质与内在联系，接着引出了一种典型的Bertrand曲面，即法向圆弧曲面，该种曲面也是本文所研究的法向圆弧锥齿轮的齿廓面。法向圆弧曲面结构简单，沿母线法线共面，并且有许多重要的几何性质，在机械传动和曲面加工中有着广泛的应用前景。论文随后较为系统的研究了斜航式法向圆弧锥齿轮共轭原理，分析了节锥面上斜航线的特征，给出了斜航式法向圆弧锥齿轮廓面方程、准线应满足的基本条件、共轭曲面的诱导曲率、不干涉条件与准线曲率轴之间的关系，并基于UG软件平台建立了一对斜航式法向圆弧锥齿轮实体模型，这些都为后面的加工研究奠定了理论基础。在上面的基础上，论文详细研究了法向圆弧锥齿轮在数控机床上进行加工的原理，包括刀具的选择与参数的确定、刀具与工件间的接触条件、工件与机床坐标系的位置关系、刀具与锥齿轮廓面间的曲率干涉以及加工时刀具与工件之间的相对运动，最后编制了斜航式法向圆弧锥齿轮齿廓面的加工宏程序。
本文是基于数控技术对法向圆弧锥齿轮加工原理进行的研究。由于该种齿轮可在兼顾加工工艺性的基础上选择准线，那么当准线为斜航线时，不仅形成的齿廓面为便于加工的规律曲面，而且仍具有一般圆弧螺旋齿轮的优良传动性。由此可见，对该种齿轮数控加工技术的研究在工程上是具有重要价值的。
As a new type transmission pair based on Bertrand conjugation principle, normal circular-arc spiral bevel gears have many good characters, such as high contact strength ,large bearing capacity, low error sensitivity and the aptness to be controlled easily. It also has well technological function and convenience for machining. At the present time, the research on this gear is not sufficient. It is worth studying for the need of engineering. In the background of NC technology, the processing theory of the normal circular-arc bevel gears is studied.
Starting with the basic conceptions of differential geometry, the geometry nature and inner relationship of Bertrand conjugation surface are studied first. Then the normal circular-arc surface is put forward which is a typical Bertrand surface. There are some geometry characters about normal circular-arc surface, for example, it is simple in structure, and the normal lines along generatrix line are in one plane, so there are the extensive applying prospects in mechanical transmission and surface processing. Then the conjugation theory of loxodrome normal circular-arc bevel gears is studied. The characters of loxodrome line are analyzed. The tooth profile of loxodrome normal circular-arc bevel gears, the primary condition the directrix line must be satisfied, the relative curvature of the conjugating surfaces, the relations between non-interventional condition and curvature axle of the directrix line is provided. The modeling of the normal circular-arc gear is established with the soft of UG. The theory be studied all above have established the foundation for the following study. After that, the NC machining theory of normal circular-arc bevel gears is studied, including the designing and manufacture of the tool, the movement of the machine, the adjustment of the tool under the condition of tangency and non-interventional condition and so on. Finally the NC program of loxodrome normal circular-arc bevel gears is provided.
The machimng theory of normal circular-arc is studied on base of NC technology. Not only does the loxodrome normal circular-arc bevel gears has regular tooth surface, but also has the virtue transmission as common circular-arc bevel gears. The NC machining theory of normal circular-arc is important for the need of engineering indeed.
引文
[1]齿轮手册编辑委员会．齿轮手册(上)．北京：机械工业出版社，2001．
[2]段振云．白川德共轭曲面的基本原理与斜航式法向圆弧螺旋锥齿轮传动的研究：(博士学位论文)．大连：大连理工大学，2002．
[3]杨春兰．齿轮工程词典．北京：机械工业出版社，1994．
[4]陈万先，黄道田．CNC机床加工螺旋锥齿轮的展成原理分析．湖北工学院学报，2002(3)：13-15．
[5]徐永年，张廷健．圆弧齿轮在我国的发展和应用．郑州机械研究所，1999(5)：88-89．
[6]M. L. Baxter. Basic Geometry of Hypiod Gears. Industrial Mathematic. Part2, 1961.
[7]Gleason works., Calculating Instructions Generated Spiral Bevel Gears, SGM, Gears Engineering Standard, Gleason works. Rochester, N. Y. 1962.
[8]Gleason works., Calculating Instructions Generated Hypid Gears, HGM, Gear Engeering Standard, Gleason works. N. Y. 1962.
[9]魏冰阳，邓效忠．弧齿锥齿轮数字化设计和集成制造．机械传动，2003(4)：32-35．
[10]邹昊．克林贝格锥齿轮的加工及特点．机械工程师，2004(11)：40-41．
[11]邹昊，张友良．新型圆锥齿轮——克林贝格锥齿轮及其加工机床．江苏石油化工学院学报，2002(3)：37-39．
[12]李海翔，李朝阳．圆弧齿轮研究的进展．现代制造工程，2005(3)：19-21．
[13]王秀叶．圆弧齿轮在我国的发展和应用．山东建材，2002(1)：38-39．
[14]范绍唐，王巧英．圆弧齿轮制造工艺探讨．太原重型机械学院学报，2001(3)：208-213．
[15]张静，杨宏斌，邓效忠等．我国锥齿轮技术的现状和发展动向．河南科技大学学报，2003(1)：40-43．
[16]张生昌．对传统机床进行数控化改造是提高我国工业化水平的一条重要途径．机械与电子，1997(1)．
[17]Wiener, Dieter. CNC Technology and the System Independent Manufacture of Spiral Bevel Gear. Gear Techol, 1992, 9(5):22-27.
[18]Kollluri S P, T seng A A. Simulation of CNC Controller Features in Graphics Based Programming. Computer in Industry, 1989(1): 135-140.
[19]Zhang Y, Litvin F L, Maruyama N, et al. Computerized analysis of meshing and contact of gear real tooth surfaces. ASME Journal of Mechanical Design, 1994, 116(9):667-682.
[20]Litv in F L. ASME Jounal of Mechanical Design, 1987,109: 163-170.
[21]Wang X C, et al. Advanced Theories of Hypoid Gears. Elsevier, 1994.
[22]Hermann J Stdtfeld. Gleason Bevel Gear Technology. The Gleason Works, 1994.
[23]S. H. Suh, et al. SculPtured surface machining of spiral bevel gears with CNC milling. Machine Tool&Manufacture, 2001, (41).
[24]吴晓铃，袁丽娟，徐万里．中国齿轮传动的历史与进展．机械传动，2004(5)：62-64．
[25]邵家辉．圆弧齿轮．北京：机械工业出版社，1994．
[26]Hennann J Stadfeld. Handbook of bevel and hypoid gears. Rochater Institute of Technology, 1993.
[27]张波，王苏平，周磊．UGNX2基础教程．北京：清华大学出版社，2005．
[28]朱凯，黄业清，冯辉．UG中文版机械设计实战训练．北京：人民邮电出版社，2004．
[29]张方瑞，于鹰宇，程鸣．UGNX2高级实例教程．北京：电子工业出版社，2005．
[30]黄恺，李雷，林爱琴．弧齿锥齿轮三维参数化设计．机床与液压，2005(10)：183-184．
[31]马秋成，韩利芬，罗毅宁．基于UG平台的齿轮CAD技术研究。机械设计与制造，2001(3)：32-33．
[32]周学良，阮景奎．基于UG／Open的齿轮参数化建模．湖北汽车工业学院学报，2004(6)：23-25．
[33]林莉．基于UG的齿轮参数化设计．机械制造与研究，2006(7)：76-81．
[34]徐雪松，毕凤荣，西红杰．基于UG的渐开线斜齿轮参数化建模研究．机械设计与制造，2003(6)：47-48．
[35]沈智慧，刘扬，林益平．利用UG软件实现齿轮的精确建模．包装工程，2001(6)：44-45．
[36]陈蔚芳，王宏涛．机床数控技术及应用．北京：科学出版社，2005．
[37]孙德茂．数控机床铣削加工直接编程技术．北京：机械工业出版社，2005．
[38]陈海舟．数控铣削加工宏程序及应用实例．北京：机械工业出版社，2006．
[39]袁明伟，谭积明，蒋丽．宏程序在数控加工中的应用．电气技术自动化，2005(7)：110-112．
[40]丰飞．用户宏程序在数控加工中的应用．新技术新工艺，2006(1)：41-43．
[41]杨世平，朱忠喜，杨湘军．基于宏指令的规则曲面数控加工程序的开发应用．机械设计与制造，2003(6)：52-53．
[42]余盛．非圆曲线的宏程序数控铣削编制．机械工人，2003(12)：45-46．
[2]段振云．白川德共轭曲面的基本原理与斜航式法向圆弧螺旋锥齿轮传动的研究：(博士学位论文)．大连：大连理工大学，2002．
[3]杨春兰．齿轮工程词典．北京：机械工业出版社，1994．
[4]陈万先，黄道田．CNC机床加工螺旋锥齿轮的展成原理分析．湖北工学院学报，2002(3)：13-15．
[5]徐永年，张廷健．圆弧齿轮在我国的发展和应用．郑州机械研究所，1999(5)：88-89．
[6]M. L. Baxter. Basic Geometry of Hypiod Gears. Industrial Mathematic. Part2, 1961.
[7]Gleason works., Calculating Instructions Generated Spiral Bevel Gears, SGM, Gears Engineering Standard, Gleason works. Rochester, N. Y. 1962.
[8]Gleason works., Calculating Instructions Generated Hypid Gears, HGM, Gear Engeering Standard, Gleason works. N. Y. 1962.
[9]魏冰阳，邓效忠．弧齿锥齿轮数字化设计和集成制造．机械传动，2003(4)：32-35．
[10]邹昊．克林贝格锥齿轮的加工及特点．机械工程师，2004(11)：40-41．
[11]邹昊，张友良．新型圆锥齿轮——克林贝格锥齿轮及其加工机床．江苏石油化工学院学报，2002(3)：37-39．
[12]李海翔，李朝阳．圆弧齿轮研究的进展．现代制造工程，2005(3)：19-21．
[13]王秀叶．圆弧齿轮在我国的发展和应用．山东建材，2002(1)：38-39．
[14]范绍唐，王巧英．圆弧齿轮制造工艺探讨．太原重型机械学院学报，2001(3)：208-213．
[15]张静，杨宏斌，邓效忠等．我国锥齿轮技术的现状和发展动向．河南科技大学学报，2003(1)：40-43．
[16]张生昌．对传统机床进行数控化改造是提高我国工业化水平的一条重要途径．机械与电子，1997(1)．
[17]Wiener, Dieter. CNC Technology and the System Independent Manufacture of Spiral Bevel Gear. Gear Techol, 1992, 9(5):22-27.
[18]Kollluri S P, T seng A A. Simulation of CNC Controller Features in Graphics Based Programming. Computer in Industry, 1989(1): 135-140.
[19]Zhang Y, Litvin F L, Maruyama N, et al. Computerized analysis of meshing and contact of gear real tooth surfaces. ASME Journal of Mechanical Design, 1994, 116(9):667-682.
[20]Litv in F L. ASME Jounal of Mechanical Design, 1987,109: 163-170.
[21]Wang X C, et al. Advanced Theories of Hypoid Gears. Elsevier, 1994.
[22]Hermann J Stdtfeld. Gleason Bevel Gear Technology. The Gleason Works, 1994.
[23]S. H. Suh, et al. SculPtured surface machining of spiral bevel gears with CNC milling. Machine Tool&Manufacture, 2001, (41).
[24]吴晓铃，袁丽娟，徐万里．中国齿轮传动的历史与进展．机械传动，2004(5)：62-64．
[25]邵家辉．圆弧齿轮．北京：机械工业出版社，1994．
[26]Hennann J Stadfeld. Handbook of bevel and hypoid gears. Rochater Institute of Technology, 1993.
[27]张波，王苏平，周磊．UGNX2基础教程．北京：清华大学出版社，2005．
[28]朱凯，黄业清，冯辉．UG中文版机械设计实战训练．北京：人民邮电出版社，2004．
[29]张方瑞，于鹰宇，程鸣．UGNX2高级实例教程．北京：电子工业出版社，2005．
[30]黄恺，李雷，林爱琴．弧齿锥齿轮三维参数化设计．机床与液压，2005(10)：183-184．
[31]马秋成，韩利芬，罗毅宁．基于UG平台的齿轮CAD技术研究。机械设计与制造，2001(3)：32-33．
[32]周学良，阮景奎．基于UG／Open的齿轮参数化建模．湖北汽车工业学院学报，2004(6)：23-25．
[33]林莉．基于UG的齿轮参数化设计．机械制造与研究，2006(7)：76-81．
[34]徐雪松，毕凤荣，西红杰．基于UG的渐开线斜齿轮参数化建模研究．机械设计与制造，2003(6)：47-48．
[35]沈智慧，刘扬，林益平．利用UG软件实现齿轮的精确建模．包装工程，2001(6)：44-45．
[36]陈蔚芳，王宏涛．机床数控技术及应用．北京：科学出版社，2005．
[37]孙德茂．数控机床铣削加工直接编程技术．北京：机械工业出版社，2005．
[38]陈海舟．数控铣削加工宏程序及应用实例．北京：机械工业出版社，2006．
[39]袁明伟，谭积明，蒋丽．宏程序在数控加工中的应用．电气技术自动化，2005(7)：110-112．
[40]丰飞．用户宏程序在数控加工中的应用．新技术新工艺，2006(1)：41-43．
[41]杨世平，朱忠喜，杨湘军．基于宏指令的规则曲面数控加工程序的开发应用．机械设计与制造，2003(6)：52-53．
[42]余盛．非圆曲线的宏程序数控铣削编制．机械工人，2003(12)：45-46．
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