用扩口杯砂轮磨削螺旋锥齿轮成形法大轮的过程仿真研究
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摘要
螺旋锥齿轮是重要的基础传动元件，其加工原理和加工设备在所有金属切削机床中是最为复杂的。汽车后桥螺旋锥齿轮大轮一般采用拉齿的方法加工，这种大轮称为成形法大轮。为了消除热处理变形，热处理后磨齿是汽车后桥齿轮工艺的发展方向。为此，就必须解决成形法大轮的磨齿问题。成形法大轮的磨削通常有两种方法：瓦古里磨削和扩口杯磨削。本文主要就是研究用扩口杯砂轮来磨削成形法大轮及其相关技术。
目前，国内在用扩口杯砂轮磨削成形法大轮这方面还没有专门人员去研究，因此本课题的研究具有较大的理论意义和经济效益。
文章首先综述了国内外对于如何解决成形法大轮磨齿的研究现状，并对各种磨齿方法进行了比较，得出了采用扩口杯砂轮磨削成形法大轮的必要性和重要意义；在分析了扩口杯磨削原理以及机床加工的数学模型的基础上，充分运用矢量概念，首次给出了采用扩口杯砂轮磨削加工的七轴五联动机床各轴的运动分析；介绍了扩口杯砂轮的选用依据，对砂轮的修形理论以及使用金刚滚轮修整扩口杯砂轮的刀位计算作了重点的推导；为方便分析实际加工的结果及实现机床调整参数的优化，对扩口杯砂轮磨削螺旋锥齿轮成形法大轮进行了加工模拟仿真。仿真结果表明，扩口杯磨削成形法大轮的理论计算是确实可行的。
Spiral bevel and hypoid gear is the important fundamental driving component in mechanical engineering. Its machining principle and equipment is the most complicated in all kinds of stock-removing machines. Rear axle gear, which is called formate gear is always broached. In order to eliminate distortion for heat treatment, after heat treatment, grinding is a trend for rear axle gear process. So the grinding problem about formate gear must be solved. There are two methods for formate gear grinding: Waguri method and flared cup wheel method. This thesis deeply studies the grinding method with flared cup wheel grinding formate gear and related technology.
At present, nobody does a research about using flared cup wheel grinding formate gear in domestic. So the research in the paper is meaningful and has more economical benefit.
This paper firstly summaries present situations of research on how to solve the grinding of the formate gear both in domestic and international, compares all sorts of the grinding methods, provides the necessities and important meaning about the realization of flared cup wheel grinding formate gear; On the basis of understanding the principle of flared cup grinding and the mathematic model of machine tool processing, the concept of vector fully used, the analysis of motion of each axis of machine, which adopts 7-axis system with 5-axis simultaneous motion directly harmonized by computer, is presented firstly; how to choose the flared cup wheel is introduced. The theory of wheel dressed and cutter location calculation of using diamond roller dressing flared cup wheel are discussed emphatically; In order to analyze the results from practice conveniently and optimize machining adjustment parameters, the simulation of spiral bevel and hypoid gear grinded by flared cup wheel is achieved. The result proves the the
ory of flared cup grinding formate gear reasonable.
目前，国内在用扩口杯砂轮磨削成形法大轮这方面还没有专门人员去研究，因此本课题的研究具有较大的理论意义和经济效益。
文章首先综述了国内外对于如何解决成形法大轮磨齿的研究现状，并对各种磨齿方法进行了比较，得出了采用扩口杯砂轮磨削成形法大轮的必要性和重要意义；在分析了扩口杯磨削原理以及机床加工的数学模型的基础上，充分运用矢量概念，首次给出了采用扩口杯砂轮磨削加工的七轴五联动机床各轴的运动分析；介绍了扩口杯砂轮的选用依据，对砂轮的修形理论以及使用金刚滚轮修整扩口杯砂轮的刀位计算作了重点的推导；为方便分析实际加工的结果及实现机床调整参数的优化，对扩口杯砂轮磨削螺旋锥齿轮成形法大轮进行了加工模拟仿真。仿真结果表明，扩口杯磨削成形法大轮的理论计算是确实可行的。
Spiral bevel and hypoid gear is the important fundamental driving component in mechanical engineering. Its machining principle and equipment is the most complicated in all kinds of stock-removing machines. Rear axle gear, which is called formate gear is always broached. In order to eliminate distortion for heat treatment, after heat treatment, grinding is a trend for rear axle gear process. So the grinding problem about formate gear must be solved. There are two methods for formate gear grinding: Waguri method and flared cup wheel method. This thesis deeply studies the grinding method with flared cup wheel grinding formate gear and related technology.
At present, nobody does a research about using flared cup wheel grinding formate gear in domestic. So the research in the paper is meaningful and has more economical benefit.
This paper firstly summaries present situations of research on how to solve the grinding of the formate gear both in domestic and international, compares all sorts of the grinding methods, provides the necessities and important meaning about the realization of flared cup wheel grinding formate gear; On the basis of understanding the principle of flared cup grinding and the mathematic model of machine tool processing, the concept of vector fully used, the analysis of motion of each axis of machine, which adopts 7-axis system with 5-axis simultaneous motion directly harmonized by computer, is presented firstly; how to choose the flared cup wheel is introduced. The theory of wheel dressed and cutter location calculation of using diamond roller dressing flared cup wheel are discussed emphatically; In order to analyze the results from practice conveniently and optimize machining adjustment parameters, the simulation of spiral bevel and hypoid gear grinded by flared cup wheel is achieved. The result proves the the
ory of flared cup grinding formate gear reasonable.
引文
[1] 曾韬．螺旋锥齿轮设计与加工．哈尔滨：哈尔滨工业大学出版社，1989
[2] 北京齿轮厂．螺旋锥齿轮．北京：科学出版社，1974
[3] 李特文．齿轮啮合原理．上海：上海科学技术出版社，1964
[4] Hermann J. Stadtfeld. Handbook of Bevel and Hypoid Gears. Rochester Institute of Technology
[5] 陈志新．共轭曲面原理(上)．北京：科学出版社，1973
[6] 陈志新．共轭曲面原理(中)．北京：科学出版社，1976
[7] 郑昌启．弧齿锥齿轮和准双曲面齿轮．北京：机械工业出版社，1988
[8] 曾韬．格里森磨齿机床展成凸轮分析．机床，1978，(5)
[9] 曾韬．美国格里森《SGM》编制原理．机床，1979，(4)
[10] 吴序掌．齿轮啮合原理．北京：机械工业出版社，1982
[11] Dieter Wiener, Ettlingen. Grinding Sprial Bevel Gears in Small Batch Production. Industrial & Production Engineering, 1987, p83～86
[12] 毛世民，吴序堂．新型万能曲线齿锥齿轮加工机床的运动学．制造技术与机床，1997，(6)：22～24
[13] Theodore J. Krenzer. CNC Bevel Gear Generators and Flared Cup Formate Gear Grinding. The Gleason Works, 1000 University Avenue P. O. Box 22970, Rochester, New York
[14] 李建刚，吴序堂，贺敬良等．CNC 铣齿机床加工曲线齿锥齿轮仿真系统的研究．系统仿真学报，2003，15(4)：499～501
[15] 卢晓勇．螺旋锥齿轮数控机床加工理论的研究：[硕士学位论文]．郑州：郑州大学，2002
[16] The Gleason Works. The Gleason Grinding Process. Customer Training Center,1989
[17] 齿轮手册编委会．齿轮手册(下册)．北京：机械工业出版社，2001
[18] 张悰．螺旋锥齿轮在普通机床上的加工．山西机械，1993(2)：27～31，6
[19] 刘鹄然，刘厚根，李国顺．在螺旋锥齿轮数控铣齿机上实现刀倾法加工小轮．现代机械，1998(4)：54～57
[20] 吕宝占，浮红霞，武良臣．数控机床加工弧齿锥齿轮的研究．煤矿机电，2000 (6)：9～11
[21] 王延忠，周云飞，李左章等．基于通用五坐标数控机床螺旋锥齿轮 NC 加工
研究．中国机械工程，2001，12(8)：903～906
[22] 卢晓勇，侯伯杰，蒋文兵等．螺旋锥齿轮数控加工中的后置处理．郑州大学学报，2002，23(3)：64～66
[23] 李小清，周云飞，李左章等．螺旋锥齿轮数控展成轨迹生成及直接插补算法．华中科技大学学报，2002，30(10)：38～40
[24] 陈万先，黄道田．CNC机床加工螺旋锥齿轮的展成原理分析．湖北工学院报，2002，17(3)：13～15
[25] 王延忠，周云飞，李左章等．螺旋锥齿轮空间曲面NC加工插补误差分析．华中科技大学学报，2002，30(2)：9～12
[26] 翁远松(译)，何敬安(校)．用碗形砂轮对螺旋伞齿轮和准双曲线锥齿轮进行成形磨削．SAE 会刊，1989，98(6)：39～45
[27] 郭晓东，张明德，梁伟．基于 AutoCAD 的锥齿轮切齿过程仿真及软件开发．现代制造工程，2002 (10)：34～36
[28] 吴序堂，王小椿，李锋．曲线齿锥齿轮三阶接触分析法的原理及传动质量评价．机械工程学报，1994，30(3)：47～54
[29] 王小椿，吴序堂．弧齿锥齿轮和双曲线齿轮的三阶接触分析和优化切齿计算．齿轮，1989，13(2)：1～10，41
[30] 李左章．螺旋锥齿轮NC加工的理论、方法及控制技术：[博士学位论文]．武汉：华中科技大学，2001
[31] Litvin, Faydor L.: Fuentes, Alfonso; Fan, Qi; Handschuh, Robert F. Computerized Design, Simulation of Meshing, and Contact and Stress Analysis of Face-milled Formate Generated Spiral Bevel Gears. Mechanism and Machine Theory, v37, n5, May, 2002, p441～459
[32] 袁哲俊，刘华明，唐宜胜．齿轮刀具设计(下册)．北京：新时代出版社，1983
[33] 李建刚．曲线齿锥齿轮加工模拟系统的研究：[硕士学位论文]．西安：西安交通大学，2002
[34] 天津齿轮机床研究所，西安交通大学．格利森锥齿轮技术资料译文集第一分册．北京：机械工业出版社，1986
[35] Tamura, Hisashi: Sakaue, Toshio. Formate Method of Cutting Hypoid Gears. Nippon Kikai Gakkai Ronbunshu, C Hen/Transactions of the Japan Society of Mechanical Engineers, Part C; v55, n509, Jan, 1989, p145～152
[36] 田行斌，方宗德．基于局部综合的弧齿锥齿轮磨齿加工参数设计．机械科学与技术，1999，18(6)：956～957，960
[37] Kondo S. Study on Formate Grinding Method of Constant Depth Tooth Spiral Bevel Gears. Bull JSME, v13, n65, Nov, 1970, p1331～8
[38] Theodore J. Krenzer. CNC Bevel Gear Generators and Flared Cup Gear Grinding. Gear Technology, v10, n4, Jul-Aug, 1993, p18～24
[39] Ito, Norio; Takahashi, Koichi. Equi-depth Tooth Hypoid Gear Using Formate Gear Cutting Method (1st report, Basic Dimensions for Gear Cutting). Nippon Kikai Gakkai Ronbunshu, C Hen/Transactions of the Japan Society of Mechanical Engineers, Part C, v61, n582, Feb, 1995, p373～379
[40] Ito, Norio; Nomura, Kazuhiro. Equi-depth Tooth Hypoid Gear Using Formate Gear Cutting Method (2nd report, Cutting Conditions and Tooth Bearing Pattern). Nippon Kikai Gakkai Ronbunshu, C Hen/Transactions of the Japan Society of Mechanical Engineers, Part C, v61, n582, Feb, 1995, p380～385
[41] Litvin, F.L.; Gutman, Y. Methods of Synthesis and Analysis for Hypoid Gear-drives of Left Double Quote FORMATE Right Double Quote and Left Double Quote HELIXFORM Right Double Quote EM DASH 1. CALCULATIONS FOR MACHINE SETTINGS FOR MEMBER GEAR MANUFACTURE OF THE FORMATE AND HELIXFORM HYPOID GEARS. American Society of Mechanical Engineers (Paper), n80-C2/DET-31, 1980, 8p
[42] Litvin, F.L.; Gutman, Y. Methods of Synthesis and Analysis for Hypoid Gear-drives of Left Double Quote FORMATE Right Double Quote and Left Double Quote HELIXFORM Right Double Quote EM DASH 2. MACHINE SETTING CALCULATIONS FOR THE PINIONS OF FORMATE AND HELIXFORM GEARS. American Society of Mechanical Engineers (Paper), n 80-C2/DET-32, 1980, 12p
[43] Theodore J. Krenzer. Computer Aided Corrective Machine Settings for Manufacturing Bevel and Hypoid Gear Sets. The Gleason Works, Rochester, New York
[44] 邵俊昌，李旭东．AutoCAD ObjectARX 2000 开发技术指南．电子工业出版社，2000
[45] 周军辉，刘宝生，陈建平等．基于PHOENIX 系列磨齿机的磨齿参数设计．起重运输机械，2003(5)：11～13
[2] 北京齿轮厂．螺旋锥齿轮．北京：科学出版社，1974
[3] 李特文．齿轮啮合原理．上海：上海科学技术出版社，1964
[4] Hermann J. Stadtfeld. Handbook of Bevel and Hypoid Gears. Rochester Institute of Technology
[5] 陈志新．共轭曲面原理(上)．北京：科学出版社，1973
[6] 陈志新．共轭曲面原理(中)．北京：科学出版社，1976
[7] 郑昌启．弧齿锥齿轮和准双曲面齿轮．北京：机械工业出版社，1988
[8] 曾韬．格里森磨齿机床展成凸轮分析．机床，1978，(5)
[9] 曾韬．美国格里森《SGM》编制原理．机床，1979，(4)
[10] 吴序掌．齿轮啮合原理．北京：机械工业出版社，1982
[11] Dieter Wiener, Ettlingen. Grinding Sprial Bevel Gears in Small Batch Production. Industrial & Production Engineering, 1987, p83～86
[12] 毛世民，吴序堂．新型万能曲线齿锥齿轮加工机床的运动学．制造技术与机床，1997，(6)：22～24
[13] Theodore J. Krenzer. CNC Bevel Gear Generators and Flared Cup Formate Gear Grinding. The Gleason Works, 1000 University Avenue P. O. Box 22970, Rochester, New York
[14] 李建刚，吴序堂，贺敬良等．CNC 铣齿机床加工曲线齿锥齿轮仿真系统的研究．系统仿真学报，2003，15(4)：499～501
[15] 卢晓勇．螺旋锥齿轮数控机床加工理论的研究：[硕士学位论文]．郑州：郑州大学，2002
[16] The Gleason Works. The Gleason Grinding Process. Customer Training Center,1989
[17] 齿轮手册编委会．齿轮手册(下册)．北京：机械工业出版社，2001
[18] 张悰．螺旋锥齿轮在普通机床上的加工．山西机械，1993(2)：27～31，6
[19] 刘鹄然，刘厚根，李国顺．在螺旋锥齿轮数控铣齿机上实现刀倾法加工小轮．现代机械，1998(4)：54～57
[20] 吕宝占，浮红霞，武良臣．数控机床加工弧齿锥齿轮的研究．煤矿机电，2000 (6)：9～11
[21] 王延忠，周云飞，李左章等．基于通用五坐标数控机床螺旋锥齿轮 NC 加工
研究．中国机械工程，2001，12(8)：903～906
[22] 卢晓勇，侯伯杰，蒋文兵等．螺旋锥齿轮数控加工中的后置处理．郑州大学学报，2002，23(3)：64～66
[23] 李小清，周云飞，李左章等．螺旋锥齿轮数控展成轨迹生成及直接插补算法．华中科技大学学报，2002，30(10)：38～40
[24] 陈万先，黄道田．CNC机床加工螺旋锥齿轮的展成原理分析．湖北工学院报，2002，17(3)：13～15
[25] 王延忠，周云飞，李左章等．螺旋锥齿轮空间曲面NC加工插补误差分析．华中科技大学学报，2002，30(2)：9～12
[26] 翁远松(译)，何敬安(校)．用碗形砂轮对螺旋伞齿轮和准双曲线锥齿轮进行成形磨削．SAE 会刊，1989，98(6)：39～45
[27] 郭晓东，张明德，梁伟．基于 AutoCAD 的锥齿轮切齿过程仿真及软件开发．现代制造工程，2002 (10)：34～36
[28] 吴序堂，王小椿，李锋．曲线齿锥齿轮三阶接触分析法的原理及传动质量评价．机械工程学报，1994，30(3)：47～54
[29] 王小椿，吴序堂．弧齿锥齿轮和双曲线齿轮的三阶接触分析和优化切齿计算．齿轮，1989，13(2)：1～10，41
[30] 李左章．螺旋锥齿轮NC加工的理论、方法及控制技术：[博士学位论文]．武汉：华中科技大学，2001
[31] Litvin, Faydor L.: Fuentes, Alfonso; Fan, Qi; Handschuh, Robert F. Computerized Design, Simulation of Meshing, and Contact and Stress Analysis of Face-milled Formate Generated Spiral Bevel Gears. Mechanism and Machine Theory, v37, n5, May, 2002, p441～459
[32] 袁哲俊，刘华明，唐宜胜．齿轮刀具设计(下册)．北京：新时代出版社，1983
[33] 李建刚．曲线齿锥齿轮加工模拟系统的研究：[硕士学位论文]．西安：西安交通大学，2002
[34] 天津齿轮机床研究所，西安交通大学．格利森锥齿轮技术资料译文集第一分册．北京：机械工业出版社，1986
[35] Tamura, Hisashi: Sakaue, Toshio. Formate Method of Cutting Hypoid Gears. Nippon Kikai Gakkai Ronbunshu, C Hen/Transactions of the Japan Society of Mechanical Engineers, Part C; v55, n509, Jan, 1989, p145～152
[36] 田行斌，方宗德．基于局部综合的弧齿锥齿轮磨齿加工参数设计．机械科学与技术，1999，18(6)：956～957，960
[37] Kondo S. Study on Formate Grinding Method of Constant Depth Tooth Spiral Bevel Gears. Bull JSME, v13, n65, Nov, 1970, p1331～8
[38] Theodore J. Krenzer. CNC Bevel Gear Generators and Flared Cup Gear Grinding. Gear Technology, v10, n4, Jul-Aug, 1993, p18～24
[39] Ito, Norio; Takahashi, Koichi. Equi-depth Tooth Hypoid Gear Using Formate Gear Cutting Method (1st report, Basic Dimensions for Gear Cutting). Nippon Kikai Gakkai Ronbunshu, C Hen/Transactions of the Japan Society of Mechanical Engineers, Part C, v61, n582, Feb, 1995, p373～379
[40] Ito, Norio; Nomura, Kazuhiro. Equi-depth Tooth Hypoid Gear Using Formate Gear Cutting Method (2nd report, Cutting Conditions and Tooth Bearing Pattern). Nippon Kikai Gakkai Ronbunshu, C Hen/Transactions of the Japan Society of Mechanical Engineers, Part C, v61, n582, Feb, 1995, p380～385
[41] Litvin, F.L.; Gutman, Y. Methods of Synthesis and Analysis for Hypoid Gear-drives of Left Double Quote FORMATE Right Double Quote and Left Double Quote HELIXFORM Right Double Quote EM DASH 1. CALCULATIONS FOR MACHINE SETTINGS FOR MEMBER GEAR MANUFACTURE OF THE FORMATE AND HELIXFORM HYPOID GEARS. American Society of Mechanical Engineers (Paper), n80-C2/DET-31, 1980, 8p
[42] Litvin, F.L.; Gutman, Y. Methods of Synthesis and Analysis for Hypoid Gear-drives of Left Double Quote FORMATE Right Double Quote and Left Double Quote HELIXFORM Right Double Quote EM DASH 2. MACHINE SETTING CALCULATIONS FOR THE PINIONS OF FORMATE AND HELIXFORM GEARS. American Society of Mechanical Engineers (Paper), n 80-C2/DET-32, 1980, 12p
[43] Theodore J. Krenzer. Computer Aided Corrective Machine Settings for Manufacturing Bevel and Hypoid Gear Sets. The Gleason Works, Rochester, New York
[44] 邵俊昌，李旭东．AutoCAD ObjectARX 2000 开发技术指南．电子工业出版社，2000
[45] 周军辉，刘宝生，陈建平等．基于PHOENIX 系列磨齿机的磨齿参数设计．起重运输机械，2003(5)：11～13