摆线锥齿啮合特性及加工装置的研究
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摘要
进动式减速机是一种新型减速机构,但由于作为其关键零部件摆线锥齿轮加工制造困难,成为制约进动式减速机广泛应用的主要因素。国内外对进动传动的研究主要集中于对锥齿轮齿廓的几何形状及其加工方法的研究。本文研究了摆线锥齿轮的啮合特性,并提出一种新的加工方法,对该加工装置进行了研究。
在论述进动啮合理论的基础上,建立了摆线锥齿轮啮合的数学模型,计算推导出空间球面上的齿形方程,为了更直观的研究齿形几何形状,通过坐标变换得出了法截面上的齿形方程,并分析了摆线锥齿轮的多齿啮合性。
根据摆线锥齿轮的加工装置的机构运动学原理,提出了一种实现新的范成加工方法的空间机构。根据该加工装置,确定了刀具的运动轨迹,推导出刀具锥面族包络面方程及刀具锥面族包络面在法截面上的投影方程。用计算机绘出由刀具包络出的齿形图。
根据已建立的啮合数学模型,在MATLAB系统平台上,编制M文件,绘制了法截面上的齿形图,并在此基础上进一步研究了加工装置的齿数、章动角、滚子的顶锥角和锥形齿的锥面角,这些啮合参数对齿廓形状影响的程度和倾向性。
基于摆线锥齿轮加工装置的机构简图,采用PROE wildfire 2.0对此加工装置的仿形杠杆进行三维仿真,并运用有限元分析软件ANSYS对其在加工时的受力情况、变形趋势进行了分析。而且分析了加工装置的刚度对齿轮误差的影响。并引入有限元分析的变形情况,比较了实际齿形与理论齿形的区别。
Nutation driving reducer is a kind of new style reducer, because its essential part cycloid bevel gear processing manufacture difficulty, this has become the primary factor, which restriction nutation driving reducer widespread application. Nutation drive's research mainly concentrates to the geometrical shape of the bevel gear tooth profile and its processing method research in domestic and foreign. This article had studied the cycloid bevel gear's meshing characteristic, and proposed a new processing method, and the research of this processing device was made.
On the base of elaboration the theory of nutation meshing, the mathematical model of the cycloid bevel gear engaging was established. The tooth profile equation in the spatial spherical surface was computed and inferred. For the research of tooth profile more direct-viewing, the tooth profile equation in the plane of normal section was obtained through the coordinate transformation. And the multi-tooth meshing characteristic of the cycloid bevel gear was analyzed.
Base on the organization kinematics principle of cycloid bevel gear's processing device, a kind of spatial mechanism was proposed, which realized a new Fan Cheng of the processing method. According to this processing device, cutting tool's path was determined, the cutting tool conical surface race envelope equation and the cutting tool conical surface race envelope in plane of normal section projection equation was inferred. The tooth profile chart which left by the cutting tool envelope was drawn with the computer.
Based on the mathematical model of the meshing established, in the MATLAB system platform, the M document was established, the tooth profile chart in the plane of normal section was drawn up. These meshing parameter of the cycloid bevel gear's processing device, the number of tooth, the nutation angle, roller's tip cone angle, and the cone-shape tooth's conical surface angle, the degree and orientation of the affects to the to meshing characteristic, was further studied.
Based on the organization diagram of the cycloid bevel gear's processing device, the three dimensional simulation of the processing device was carried on with the PROE wildfire 2.0, and stress situation and distortion tendency was analyzed, with Finite Element Analysis software ANSYS, when the processing device processing.
And the processing device's rigidity influence to the gear's error was analyzed. And according to distortion situation, which obtained by finite element analysis, the actual tooth profile and the theory tooth profile's difference was compared with.
在论述进动啮合理论的基础上,建立了摆线锥齿轮啮合的数学模型,计算推导出空间球面上的齿形方程,为了更直观的研究齿形几何形状,通过坐标变换得出了法截面上的齿形方程,并分析了摆线锥齿轮的多齿啮合性。
根据摆线锥齿轮的加工装置的机构运动学原理,提出了一种实现新的范成加工方法的空间机构。根据该加工装置,确定了刀具的运动轨迹,推导出刀具锥面族包络面方程及刀具锥面族包络面在法截面上的投影方程。用计算机绘出由刀具包络出的齿形图。
根据已建立的啮合数学模型,在MATLAB系统平台上,编制M文件,绘制了法截面上的齿形图,并在此基础上进一步研究了加工装置的齿数、章动角、滚子的顶锥角和锥形齿的锥面角,这些啮合参数对齿廓形状影响的程度和倾向性。
基于摆线锥齿轮加工装置的机构简图,采用PROE wildfire 2.0对此加工装置的仿形杠杆进行三维仿真,并运用有限元分析软件ANSYS对其在加工时的受力情况、变形趋势进行了分析。而且分析了加工装置的刚度对齿轮误差的影响。并引入有限元分析的变形情况,比较了实际齿形与理论齿形的区别。
Nutation driving reducer is a kind of new style reducer, because its essential part cycloid bevel gear processing manufacture difficulty, this has become the primary factor, which restriction nutation driving reducer widespread application. Nutation drive's research mainly concentrates to the geometrical shape of the bevel gear tooth profile and its processing method research in domestic and foreign. This article had studied the cycloid bevel gear's meshing characteristic, and proposed a new processing method, and the research of this processing device was made.
On the base of elaboration the theory of nutation meshing, the mathematical model of the cycloid bevel gear engaging was established. The tooth profile equation in the spatial spherical surface was computed and inferred. For the research of tooth profile more direct-viewing, the tooth profile equation in the plane of normal section was obtained through the coordinate transformation. And the multi-tooth meshing characteristic of the cycloid bevel gear was analyzed.
Base on the organization kinematics principle of cycloid bevel gear's processing device, a kind of spatial mechanism was proposed, which realized a new Fan Cheng of the processing method. According to this processing device, cutting tool's path was determined, the cutting tool conical surface race envelope equation and the cutting tool conical surface race envelope in plane of normal section projection equation was inferred. The tooth profile chart which left by the cutting tool envelope was drawn with the computer.
Based on the mathematical model of the meshing established, in the MATLAB system platform, the M document was established, the tooth profile chart in the plane of normal section was drawn up. These meshing parameter of the cycloid bevel gear's processing device, the number of tooth, the nutation angle, roller's tip cone angle, and the cone-shape tooth's conical surface angle, the degree and orientation of the affects to the to meshing characteristic, was further studied.
Based on the organization diagram of the cycloid bevel gear's processing device, the three dimensional simulation of the processing device was carried on with the PROE wildfire 2.0, and stress situation and distortion tendency was analyzed, with Finite Element Analysis software ANSYS, when the processing device processing.
And the processing device's rigidity influence to the gear's error was analyzed. And according to distortion situation, which obtained by finite element analysis, the actual tooth profile and the theory tooth profile's difference was compared with.
引文
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[19]F.L.Litvin,J.S.Chen and T.M.Sep etc.Computerized Simulation of Transmission Errors and Shift of Bearing Contact for Face-Mille Hypoi Gear Drive.1995,117(6):262-267.
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[32]陶柯,姜芳,田方.进动式锥摆齿轮加工装置的研究.机械传动,2005(1):15-16.
[33]田方,陶柯,姜芳.潜油螺杆泵用进动式减速机的设计与实验.机械传动,2005(1):50-51.
[34]渐开线齿轮行星传动的设计与制造编委会.渐开线齿轮行星传动的设计与制造.北京:机械工业出版社,2002.
[35]王继军,田方,金映丽等.空间球面圆锥外摆线针轮传动.机械设计与制造,1998(4):22-23.
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[38]孙祥.MATLAB 7.0基础教程.北京:清华大学出版社,2006.
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[40]孙靖民.机床结构计算的有限元法.北京:机械工业出版社,1983.
[41]吴春凌.有限元法分析刀具前角对切削加工的影响.有色金属工业,2005,39(3):51-54.
[42]赫顿.有限元分析基础.重庆.重庆大学出版社,2007.
[43]陈精一.ANSYS工程分析实例教程.北京.中国铁道出版社,2007.
[44]刘相新,孟宪颐.ANSYS基础与应用教程.北京:科学出版社,2006.
[45]余强,周京平.PRO/E机械设计与工程应用精选五十例.北京:清华大学出版社,2006.
[46]林清安.PRO/ENGINEER野火3.0中文版基础零件设计.北京:电子工业出版社,2006.
[47]孙江宏,黄小龙,高宏.PRO/ENGINEER结构分析与运动仿真.北京:中国铁道出版社,2004.
[48]陆建中,孙家宁.金属切削原理与刀具.北京:机械工业出版社,1985.
[49]上海市金属切削技术协会.金属切削手册.上海:上海科学技术出版社,2004.
[50]刘志峰等.Klingelnberg摆线锥齿轮轮齿几何分析.东北大学学报,1999(4):388-392.
[51]刘志峰等.Klingelnberg摆线锥齿轮接触分析与预报仿真.东北大学学报,1999(6):594-597.
[52]刘志峰.摆线齿锥齿轮传动原理及啮合性能模糊优化的研究.沈阳:东北大学出版社,2001.
[53]和志华.齿轮加工精度的影响因素分析及改进方法.甘肃冶金,2005,27(3):88-90.
[2]孙永才.谐波圆锥齿轮传动减速器工作原理与设计.齿轮,1984,8(5).
[3]刘维信.机械最优化设计.北京:清华大学出版社,1994.
[4]陈荣.齿轮啮合理论.北京:煤炭工业出版社,1985.
[5]赵建衡,张根保.章动齿轮减速机械原理.中国齿轮制造研究会第三届学术年会暨四川机械传动分会第八届学术年会.重庆,1995.
[6]何韶君,赵清.摆线针轮章动传动的齿廓分析.机械传动,1997(4):8-11.
[7]王克起,杨吉生,张宝丰.新型刚体进动演示仪及其现象分析.天津师范大学学报,2001(3):36-38.
[8]边文莉.坐标变换在弧齿圆锥齿轮切齿调整计算中的应用.佳木斯工学院学报,1993(9):182-185.
[9]西安交通大学机制教研室齿轮研究组编.弧齿锥齿轮和准双曲线齿轮加工调整原理.上海:上海科学出版社,1979.
[10]刘雄伟等.数控加工理论与编程技术.北京:机械工业出版社,1994.
[11]E.Wildhaber.Gear Tooth Curvature Treated Simply.American Machinist,1948(18).
[12]E.Wildhabe.Basic Relationship of Hypoid Gears.American Machinist,1945,90(20).
[13]E.Wildhaber.Basic Relationship of Hypoid Gears.American Machinist,1946,90(3-5).
[14]M.L.Baxter.Basic Geometry and Tooth Contact of Hypoid Gear.Industrial Mathematics,1961(2).
[15]M.L.Baxter.High Reduction Hypoid.Machine Design,1961(27).
[16]M.L.Baxter.Second Order Surface Generation,Industrial Mathematics,1964(2).
[17]F.L.Litvin,Y.Gutman.Method of Synthesis and Analysis for Hypoi Gear-Drives of Formate and Helixform.Journal of Mechanical Design ASME,1981,103(1):83-110.
[18]F.L.Litvin,C.Kuan and J.C.Wang etc.Minimization of Deviations of Gear Real Tooth Surfaces Determined by Coordinate Measurements.Journal of Mechanical Design,ASME,1993,115(12):995-1001.
[19]F.L.Litvin,J.S.Chen and T.M.Sep etc.Computerized Simulation of Transmission Errors and Shift of Bearing Contact for Face-Mille Hypoi Gear Drive.1995,117(6):262-267.
[20]F.L.Litvin,A.G.Wang and R.F.Handschuh.Computerized Design and Analysis of Face-Milled,Uniform Tooth Height Spiral Bevel Gear Drives.Journal of Mechanical Design,ASME,1996,118(12):573-579.
[21]董学朱.延伸外摆线锥齿轮切齿调整计算法的改进.机械传动,1997,21(4):41-47.
[22]吴联银,魏洪钦,王小椿.Free-Form机床展成延伸外摆线锥齿轮的齿面几何研究.西安交通大学学报,2001,35(3):322-325.
[23]罗建勤,吕传贵.延伸外摆线锥齿轮的设计新方法.机械传动,1999,23(3):14-22.
[24]吴序堂.刀倾半展成法加工弧齿锥齿轮的原理及机床调整.西安交通大学科学技术报告,1979.
[25]吴序堂.齿轮啮合原理.北京.机械工业出版社,1982.
[26]吴序堂.准双曲面齿轮的变性全展成加工法原理.齿轮,1984,8(2):1-8.
[27]董学朱.准双曲面齿轮切齿调整计算方法的改进.齿轮,1985,9(6):1-4.
[28]董学朱.弧齿锥齿轮半展成切齿调整计算新方法.齿轮,1988,12(4):1-7.
[29]郑昌启,黄昌华,吕传贵.螺旋锥齿轮轮齿加载接触分析计算原理.机械工程学报,1993,29(4):50-54.
[30]郑昌启.弧齿锥齿轮和准双曲面齿轮的齿面接触分析计算原理.机械工程学报,1981,17(2):1-12.
[31]万小利,梁桂明,魏任之等.准双曲面齿轮设计新方法.机械工程学报,1993,29(6):8-11.
[32]陶柯,姜芳,田方.进动式锥摆齿轮加工装置的研究.机械传动,2005(1):15-16.
[33]田方,陶柯,姜芳.潜油螺杆泵用进动式减速机的设计与实验.机械传动,2005(1):50-51.
[34]渐开线齿轮行星传动的设计与制造编委会.渐开线齿轮行星传动的设计与制造.北京:机械工业出版社,2002.
[35]王继军,田方,金映丽等.空间球面圆锥外摆线针轮传动.机械设计与制造,1998(4):22-23.
[36]郭仁生.机械工程设计分析和MATLAB应用.北京:机械工业出版社,2008.
[37]郭仁生.齿轮传动设计与MATLAB实现.机械,2005(3):38-39.
[38]孙祥.MATLAB 7.0基础教程.北京:清华大学出版社,2006.
[39]王家文,王皓,刘海.MATLAB 7.0编程基础.北京:机械工业出版社,2005.
[40]孙靖民.机床结构计算的有限元法.北京:机械工业出版社,1983.
[41]吴春凌.有限元法分析刀具前角对切削加工的影响.有色金属工业,2005,39(3):51-54.
[42]赫顿.有限元分析基础.重庆.重庆大学出版社,2007.
[43]陈精一.ANSYS工程分析实例教程.北京.中国铁道出版社,2007.
[44]刘相新,孟宪颐.ANSYS基础与应用教程.北京:科学出版社,2006.
[45]余强,周京平.PRO/E机械设计与工程应用精选五十例.北京:清华大学出版社,2006.
[46]林清安.PRO/ENGINEER野火3.0中文版基础零件设计.北京:电子工业出版社,2006.
[47]孙江宏,黄小龙,高宏.PRO/ENGINEER结构分析与运动仿真.北京:中国铁道出版社,2004.
[48]陆建中,孙家宁.金属切削原理与刀具.北京:机械工业出版社,1985.
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