锥形摆线行星传动基础理论及实验研究
|
摘要
精密传动是以高精度传递运动为主要目的的一类机械传动形式,在航空航天、武器装备、数控机床、机器人、精密机械、印刷包装机械、交通运输机械、医疗器械等领域应用十分广泛,是制造装备业和国防工业极其重要的基础件。锥形摆线行星传动是依据普通摆线针轮行星传动的针齿半径改变时对应的系列变幅摆线互为等距线而提出的新型传动。该传动可以通过调整锥形摆线啮合副的轴向位置调整啮合的间隙,利用多齿啮合的误差均化效应获得高的传动精度。系统深入地开展关于锥形摆线行星传动的理论和设计方法、制造关键技术和实验研究,奠定其工程应用的基础,具有重要的理论意义和工程实用价值。
本文的主要内容如下:
①根据齿轮啮合原理的运动学法,讨论了平行轴内啮合行星传动的啮合方程,给出了行星轮共轭齿廓方程的一般表达式,建立了锥形摆线行星传动的啮合理论;论证了变截面摆线行星传动针齿齿廓半径沿轴向变化时所对应的系列短幅摆线互为等距线;针对变截面摆线传动,给出了针齿半径沿轴向线性变化的锥形摆线轮和非线性变化的鼓形行星轮的设计实例,从而验证了理论推导的正确性;给出了横截面为抛物线的行星轮的齿廓曲面方程,讨论了行星轮齿廓曲面的多样性;分别讨论了变截面摆线传动和抛物线柱面行星传动的齿廓曲率特性。
②提出了以锥形摆线轮大端面为设计基准的设计方法,完成了锥形摆线啮合副齿廓曲面的设计;提出了基于锥形摆线的N型传动、NN型传动和双圆盘摆线行星传动三种结构形式,并针对不同的结构形式,给出了计算实例。
③分析了锥形啮合副的受力情况,提出了锥形啮合副的接触应力计算方法;采用有限元方法完成了分别使用独立销套和整体销套的悬臂梁式输出机构和简支梁式输出机构的应力应变分析。
④应用Microsoft Visual C++6.0编制了锥形摆线行星传动的可视化设计分析软件系统,实现N型、N-N型传动和双圆盘摆线传动各参数、齿廓的自动计算,以及力学特性等的计算机辅助设计。
⑤提出了用指锥刀具/磨具直接形成零件轴向锥形,而零件截面摆线或圆弧齿通过展成方式形成的“指锥包络”切削加工方法和圆弧面砂轮磨削法,并分别进行了加工仿真。在此基础上,研制出三台套实验样机。
⑥提出了变截面行星啮合副齿廓曲面的坐标测量和误差评定方法。编制了基于三坐标测量机变截面摆线轮齿廓曲面的通用自动测量程序,完成了样机齿廓曲面的精度检测;提出了采用最小二乘法的数据处理方法,对锥形啮合副的齿距偏差、齿廓偏差和锥度误差等保证锥形摆线行星传动运动精度和平稳性的重要指标进行了评定。
⑦完成了实验台的研制和和改装,分别开展了普通摆线行星传动减速机、双圆盘摆线行星传动、双圆盘锥形摆线行星传动样机的实验研究,包括传动效率、传动精度、回差等。实验结果表明,三台减速器均具有高的传动效率,双圆盘摆线行星传动样机可以承受较大的轴向载荷,双圆盘锥形摆线行星传动通过调整啮合零件轴向位置可以调整啮合的间隙。
Precision transmission is a kind of mechanical transmission mainly for high precision, which is extensively applied to many industry fields such as aviation and spaceflight, weaponry and equipment, NC machine tools, robot, precision machinery, printing and packaging machinery, transportation machinery, medical apparatus and so on. It is an important basic element in manufacturing equipment industry and national defense industry. The conic cycloidal gear planetary transmission is proposed as a new cycloidal gearing based on the theory that series of epicycloids are equidistant curves with radius of pins variable along its axis. The conic cycloid gearing can realize lower backlash by adjusting the axial location of the variable cross cycloid gear pair, and can gain higher transmission precision by error averaging with multi-tooth meshing. Therefore, it has important theoretical significance and reference value in the engineering practice to develop studies deeply and systematically on the related basic theory, machining and measuring, experiments of new conic cycloidal gearing.
Major contents of the dissertation are as follows:
①According to gear geometry kinematics, the meshing equation of parallel internal planetary drive is discussed, the general equation of conjugate surfaces of planet gear is derived, and the meshing theory of conic cycloidal gearing is developed. It is proved that series of epicycloids are equidistant curves with radius of pins variable along its axis. Design examples of linear variable cross section cycloid gear as conic cycloid gear and nonlinear as drum cycloid gear are given, and the numerical work is presented to demonstrate the correction of formulations. Profile equation of planetary gear whose cross section is a parabola is given, and diversity of profile surface of planetary gear is also discussed. Profile’s curvature of variable cross section cycloidal gear and paraboloid planetary gear is discussed respectively.
②The design method using the large end face of conic cycloidal gear as design standard is put forward, with which the profile surfaces of the conic cycloidal meshing pair are designed. Three innovative structural designs as N gearing, NN gearing and double-disc cycloidal gearing are developed based on conic cycloid gearing. And calculation examples for different structural designs are given respectively.
③The force condition of the conic meshing pair is studied, and contact strength calculation method is proposed. Stress and strain analysis of the output mechanism concerning about cantilever beam type and simple supported beam type with separate pin sleeve and unique pin sleeve is carried out respectively with Finite Element Method.
④The Windows-based visual analysis software system for the conic cycloidal gearing is developed with the Microsoft Visual C++6.0, which can realize automatic calculation on design parameters and profiles, and computer assistant design on mechanics of the N gearing, the NN gearing and double-disc cycloidal gearing.
⑤New cutting/grinding method called“finger cone enveloping”is put forward, that is, the axis direction cone of the gear is shaped by finger conic cutter or grinder, and cycloid or arc profile is formed by enveloping. Machining simulations are respectively carried out. Three sets of prototype are developed by using this method.
⑥The method of coordinate measurement and error evaluation on variable cross section cycloidal gear’s profile surface is proposed. A general automatic measuring program of variable section cycloidal gear’s profile surface is developed based on coordinate measurement machine. The precision measurement on profile surface of prototypes has been finished. Date processing method based on the least squares method is developed, and pitch error, profile error and conic error of conic cycloidal meshing pair are evaluated, which are important indexes to guarantee smooth motion and precision of conic cycloidal gear pair.
⑦Experimental equipments are developed or refitted. Experimental study on three sets of prototype is carried out, which includes transmission efficiency, backlash and precision. The results show that three sets of prototype all have higher efficiency, double-disc cycloidal gearing can work well with larger axial loads, and can also adjusted the meshing clearance by adjusting the axial location of the meshing pair.
本文的主要内容如下:
①根据齿轮啮合原理的运动学法,讨论了平行轴内啮合行星传动的啮合方程,给出了行星轮共轭齿廓方程的一般表达式,建立了锥形摆线行星传动的啮合理论;论证了变截面摆线行星传动针齿齿廓半径沿轴向变化时所对应的系列短幅摆线互为等距线;针对变截面摆线传动,给出了针齿半径沿轴向线性变化的锥形摆线轮和非线性变化的鼓形行星轮的设计实例,从而验证了理论推导的正确性;给出了横截面为抛物线的行星轮的齿廓曲面方程,讨论了行星轮齿廓曲面的多样性;分别讨论了变截面摆线传动和抛物线柱面行星传动的齿廓曲率特性。
②提出了以锥形摆线轮大端面为设计基准的设计方法,完成了锥形摆线啮合副齿廓曲面的设计;提出了基于锥形摆线的N型传动、NN型传动和双圆盘摆线行星传动三种结构形式,并针对不同的结构形式,给出了计算实例。
③分析了锥形啮合副的受力情况,提出了锥形啮合副的接触应力计算方法;采用有限元方法完成了分别使用独立销套和整体销套的悬臂梁式输出机构和简支梁式输出机构的应力应变分析。
④应用Microsoft Visual C++6.0编制了锥形摆线行星传动的可视化设计分析软件系统,实现N型、N-N型传动和双圆盘摆线传动各参数、齿廓的自动计算,以及力学特性等的计算机辅助设计。
⑤提出了用指锥刀具/磨具直接形成零件轴向锥形,而零件截面摆线或圆弧齿通过展成方式形成的“指锥包络”切削加工方法和圆弧面砂轮磨削法,并分别进行了加工仿真。在此基础上,研制出三台套实验样机。
⑥提出了变截面行星啮合副齿廓曲面的坐标测量和误差评定方法。编制了基于三坐标测量机变截面摆线轮齿廓曲面的通用自动测量程序,完成了样机齿廓曲面的精度检测;提出了采用最小二乘法的数据处理方法,对锥形啮合副的齿距偏差、齿廓偏差和锥度误差等保证锥形摆线行星传动运动精度和平稳性的重要指标进行了评定。
⑦完成了实验台的研制和和改装,分别开展了普通摆线行星传动减速机、双圆盘摆线行星传动、双圆盘锥形摆线行星传动样机的实验研究,包括传动效率、传动精度、回差等。实验结果表明,三台减速器均具有高的传动效率,双圆盘摆线行星传动样机可以承受较大的轴向载荷,双圆盘锥形摆线行星传动通过调整啮合零件轴向位置可以调整啮合的间隙。
Precision transmission is a kind of mechanical transmission mainly for high precision, which is extensively applied to many industry fields such as aviation and spaceflight, weaponry and equipment, NC machine tools, robot, precision machinery, printing and packaging machinery, transportation machinery, medical apparatus and so on. It is an important basic element in manufacturing equipment industry and national defense industry. The conic cycloidal gear planetary transmission is proposed as a new cycloidal gearing based on the theory that series of epicycloids are equidistant curves with radius of pins variable along its axis. The conic cycloid gearing can realize lower backlash by adjusting the axial location of the variable cross cycloid gear pair, and can gain higher transmission precision by error averaging with multi-tooth meshing. Therefore, it has important theoretical significance and reference value in the engineering practice to develop studies deeply and systematically on the related basic theory, machining and measuring, experiments of new conic cycloidal gearing.
Major contents of the dissertation are as follows:
①According to gear geometry kinematics, the meshing equation of parallel internal planetary drive is discussed, the general equation of conjugate surfaces of planet gear is derived, and the meshing theory of conic cycloidal gearing is developed. It is proved that series of epicycloids are equidistant curves with radius of pins variable along its axis. Design examples of linear variable cross section cycloid gear as conic cycloid gear and nonlinear as drum cycloid gear are given, and the numerical work is presented to demonstrate the correction of formulations. Profile equation of planetary gear whose cross section is a parabola is given, and diversity of profile surface of planetary gear is also discussed. Profile’s curvature of variable cross section cycloidal gear and paraboloid planetary gear is discussed respectively.
②The design method using the large end face of conic cycloidal gear as design standard is put forward, with which the profile surfaces of the conic cycloidal meshing pair are designed. Three innovative structural designs as N gearing, NN gearing and double-disc cycloidal gearing are developed based on conic cycloid gearing. And calculation examples for different structural designs are given respectively.
③The force condition of the conic meshing pair is studied, and contact strength calculation method is proposed. Stress and strain analysis of the output mechanism concerning about cantilever beam type and simple supported beam type with separate pin sleeve and unique pin sleeve is carried out respectively with Finite Element Method.
④The Windows-based visual analysis software system for the conic cycloidal gearing is developed with the Microsoft Visual C++6.0, which can realize automatic calculation on design parameters and profiles, and computer assistant design on mechanics of the N gearing, the NN gearing and double-disc cycloidal gearing.
⑤New cutting/grinding method called“finger cone enveloping”is put forward, that is, the axis direction cone of the gear is shaped by finger conic cutter or grinder, and cycloid or arc profile is formed by enveloping. Machining simulations are respectively carried out. Three sets of prototype are developed by using this method.
⑥The method of coordinate measurement and error evaluation on variable cross section cycloidal gear’s profile surface is proposed. A general automatic measuring program of variable section cycloidal gear’s profile surface is developed based on coordinate measurement machine. The precision measurement on profile surface of prototypes has been finished. Date processing method based on the least squares method is developed, and pitch error, profile error and conic error of conic cycloidal meshing pair are evaluated, which are important indexes to guarantee smooth motion and precision of conic cycloidal gear pair.
⑦Experimental equipments are developed or refitted. Experimental study on three sets of prototype is carried out, which includes transmission efficiency, backlash and precision. The results show that three sets of prototype all have higher efficiency, double-disc cycloidal gearing can work well with larger axial loads, and can also adjusted the meshing clearance by adjusting the axial location of the meshing pair.
引文
[1] Dudley D W. The evolution of the gear art [J]. Washington D.C.: AGMA ,1969.
[2] Dudley D W. Gear technology past, present and future [J]. Zheng Zhou: Proceedingsof International Conference on Gearing, 1988.
[3]唐定国,陈国民.齿轮传动技术的展望[J].机械工程学报, 1993, 29 (5) : 35-41.
[4] RotoPRECISION Inc. Mectrol Dojen Zero Backlash Speed Reducers. http://www.rotolube.com,1999.
[5] MOTION TECHNOLOGIES. Twinspin/Solution for Precision. http://motiontech.com.au, 2003.
[6] Prabhakar Nagabhusan, Marlboro, Mass. Adjustable Cycloidal Speed Reducer. United States Patent, 5145468. 1992/09/08.
[7]陈兵奎.锥形摆线轮行星传动装置[P].中国, ZLO3117879.0, 2005/02/16.
[8]陈兵奎,王淑妍,李朝阳.双圆盘摆线轮行星传动装置[P].中国, 200510057463.2, 2005/12/23.
[9]陈兵奎,蒋旭君,王淑妍.新型锥形摆线轮行星传动初步研究[J].现代制造工程, 2005, (2):14～15.
[10]冯澄宙.渐开线少齿差形星传动[M].人民教育出版社, 1982.
[11]饶振纲.行星传动机构设计(第二版)[M].国防工业出版社, 1994.6.
[12]郑州工学院机械原理及机械零件教研室编.摆线针轮行星传动[M].科学出版社, 1978.2.
[13] Jeffry D.Stoehr. Choosy about gears[J]. Tooling & Production, 2001.
[14]范又功等.谐波齿轮发展动向[J].航空制造工程, 1993(3):17-18.
[15]北京谐波齿轮传动技术研究所.谐波传动技术的新发展[J].齿轮, 1991(2):52-55.
[16]辛洪兵等.谐波传动技术及其研究动向[J].北京轻工业学院学报, 1999(3):30-36.
[17]孙慧.谐波传动综述[J].长岭技术与经济, 1996(2):44-51.
[18]北京谐波齿轮传动技术研究所.谐波传动技术及谐波减速机[J].新技术新工艺, 1994(3):12-13.
[19] J·G·Blanche and D·C·H·Yang. Cycloid Drives With Machining Tolerances [J]. ASME J.Mech.Transm, Automn Des Vol.111, 1989: 337-344.
[20] D·C·H·Yang and J·G·Blanche. Design and Application Guidences for Cycloid Drives with Machining Tolerances[J]. Mech.Mach.Theory,Vol.25(5),1990:487-501.
[21]沈允文等. RV减速器及其在机器人上的应用[J] .齿轮, 1988, 12 (5) :51-54.
[22]林章炎等. RV传动机构发展概述及设计新思想[J].机械工程师, 1991, (5) :18-20.
[23]徐永贤等. RV传动的弹性误差分析[J].大连铁道学院学报, 1999, 20(2):12-17.
[24]徐永贤等. RV传动刚度计算方法[J].大连铁道学院学报, 1999, 20(2):18-22.
[25]徐永贤等. RV传动输出机构的刚性误差分析[J].大连铁道学院学报, 1996, 17(4):41-47.
[26]刘洪斌等. RV传动的动力学研究[J].天津大学学报, 1999, 32(6): 661-661.
[27]李瑰贤等.变厚齿轮RV减速器系统扭振动力学分析[J].机械传动, 1999,23 (4):20-22.
[28]王刚等. RV减速机动力学建模方法研究[J].机械设计, 1999, 16(3) :19-22.
[29]董向阳等. RV传动机构的受力分析[J].上海交大学报, 1996, 30(5):65-71.
[30]戚厚军等. RV传动中摆线轮齿形修正的反求设计方法[J].天津职业技术师范学院学报, 1999(1):6-9.
[31]何卫东等.高精度RV传动的受力分析及传动效率[J].机械工程学报, 1996,32(4):104-110.
[32]何卫东等.机器人用高精度RV传动中变形轮修形对回差的影响[J].机械传动, 1999, 23(1):24-28.
[33]何卫东等.机器人用高精度RV减速器中摆线轮的优化新齿形[J].机械工程学报, 2000, 36(3):51-55.
[34]吴俊飞,李瑰贤等.机器人用变厚齿轮RV减速器回差分析与计算[J].机械设计, 2000, 17(3):24-26, 29.
[35]郭燕利等.平面二次包络环面蜗轮副研究综述与展望[J].机械, 2000, 27: 209-210.
[36]张光辉.侧隙可调式平面包络环面蜗杆传动研究[P].中国, 99117383.x, 2000.06.28.
[37]孙英时等.三片摆线轮减速机针齿与摆线轮啮合实际作用力分析[J].大连铁道学院学报, 2002, 23(2):20-23.
[38]关天民等.三片摆线轮新型针摆传动及其受力分析[J].大连铁道学院学报, 1999, 20(3):48-51.
[39]王海燕等. K-H-V双摆线钢球行星传动减速器齿廓曲线参数的选择[J].西北轻工业学院学报, 1994, 12:77-83.
[40]李思益等. K-H-V双摆线钢球行星传动减速器振动的初步分析与计算[J].西北轻工业学院学报, 1994, 12:64-68.
[41]李思益等.双摆线钢球的啮合与传动[J].西北轻工业学院学报, 1994, 12:69-72.
[42]安子军等.双摆线无隙钢球传动间隙调节力矩分析[J].机械传动, 1995, 19(4):1-4.
[43] F.L. Litvin, Alberto Demenego, Daniele Vecchiato. Formation by branches of envelope to parametric families of surfaces and curves [J]. Computer methods in applied mechanics and engineering, 190 (2001) 4587-4608.
[44] F.L. Litvin, A.M. Egelja, M. De Donno. Computerized determination of singularities and envelopes to families of contact lines on gear tooth surfaces [J]. Computer methods in appliedmechanics and engineering, 158 (1998) 23-24.
[45] F.L. Litvin, Pin-hao Feng. Computerized design, generation, and simulation of meshing rotors of screw compressor [J].Mech. Mach. Theory, Vol.32, (2),: 137-160,1997.
[46] Daniele Vecchiato, Alberto Demenego, John Argyris, Faydor L. Litvin. Geometry of a cycloidal pump [J]. Comput. Methods Appl. Mech. Engrg, 190 (2001) 2309-2330.
[47] Alberto Demenego, Daniele Vecchiato, Faydor L. Litvin, Nicola Nervegna, Salvatore Manco. Design and simulation of meshing of a cycloidal pump [J]. Mechanism and Machine Theory, 37 (2002) 311-332.
[48] F.L. Litvin, Pin-hao Feng. Computerized Design and Generation of Cycloidal Gearings [J] Mech. Mach. Theory, Vol.31, (7): 891-911, 1996.
[49] Joong-Ho Shin, Soon-Man Kwon. On the lobe profile design in a cycloid reducer using instant velocity center [J]. Mechanism and Machine Theory, 41 (2006) 596-616.
[50] Joong-Ho Shin, Sewon Chang, Soon-Man Kwon, Hoon-Ki Choi. New shape design method of an epicycloidal gear for an epicycloid drive [J]. Proc. of SPIE, Vol. 6040 60401G: 1-6.
[51] Ta-Shi Lai. Design and machining of the epicycloid planet gear of cycloid drives [J] International Journal of Advanced Manufacturing Technology, v28, n7-8, April, 2006: 665-670.
[52] Ta-Shi Lai. Geometric design of roller drives with cylindrical meshing elements [J]. Mechanism and Machine Theory, 40 (2005): 55–67.
[53] H.S. Yan, T.S.Lai. Geometry design an elementary planetary gear train with cylindrical tooth-profiles [J]. Mechanismand Machine Theory, 37 (8) (2002) 757-767.
[54] Vecchiato D., DemenegoA, Argyris J, et al. Geometry of aCycloidal Pump [J].ComPut Methods Appl Mech Engrg, 2001, 190:2309-2330.
[55] Mimmia G C, Pennacchi E. Non-undercuting conditions in internal gears [J].Mechanism and Machine Theory, 2000, 5:477-490.
[56] Vogesang H, Verhulsdonk B, et al. pulsation problems in rotary lobe PumP [J].Vorld Pump February, 1999(2):16-21.
[57] Tong Shih-His, Yang Daniel C H.On the generation of new lobe pumps for higher pumping flowrate [J]. Mechanism and Machine Theory, 2000, 35:997-1012.
[58] Chen C-K, Yang S-C.Geometric modeling for cylindrical and helical gear pumps with circular arc teeth [J].Proc lnstn Mech Engrs part C, 2000, 214(4):599-607.
[59] D.W. Botsiber, L. Kingston. Design and performance of the cycloid speed reducer [J]. Machine Design, 28 (1956) 65–69.
[60] X. Li, W. He, L. Li, L.C. Schmidt. A new cycloid drive with high-load capacity and highefficiency [J] ASME Journalof Mechanical Design, 126 (2004): 683-686.
[61] J. Davidson, K.H. Hunt, Robots and Screw Theory. Applications of Kinematics and Statics to Robotics [J]. OxfordUniversity Press, 2004.
[62] J.S. Dai, D.R. Kerr. Geometric analysis and optimization of symmetrical Watt 6-bar mechanisms [J] Journal of Mechanical Engineering Science, Proceedings of IMechE 205 (C1) (1991): 275-280.
[63] E.P. Pollitt. Some applications of the cycloid machine design [J]. ASME Journal of Engineering for Industry, 82 (1960):407-414.
[64]李力行,洪淳赫.摆线针轮行星传动中摆线轮齿形通用方程式的研究[J].大连铁道学院学报, 1992,13(1):7-122.
[65]高兴岐.多齿差摆线针轮行星传动的齿形及啮合特性的理论分析[J].机械传动, 2000, 4(4):11-14.
[66]孟继安等.内啮合摆线齿轮泵齿廓特征参数化设计探讨[J].化工机械, 1990(3): 145-150.
[67]侯东海等.少齿差摆线齿轮啮合原理及几何参数选择[J].机械传动, 1995, 19 (3): 24-27.
[68]侯东海,司春华,吕伴功.少齿差摆线齿轮泵啮合原理及几何参数选择[J].机械传动, 1995, 19(3):24-27.
[69]李荣堂等.多齿差内啮合圆弧摆线齿轮泵的开发[J].石油化工设备技术,1994,15 (4): 26-30.
[70]李荣堂,史发科.多齿差内啮合圆弧摆线齿轮泵的开发[J].石油化工设备技术, 1994, 15 (4):25-30.
[71]徐秀生.多齿差圆弧摆线式内啮合齿轮泵的设计[J].水泵技术, 1996(3):26-31.
[72]王乾廷,桂贵生.用切触线法加工曲线轮廓[J].合肥工业大学学报(自然科学版), 2003,26(3):193-196.
[73]张敬东.摆线齿轮的数控加工[J].现代制造工程, 2005(3):49-50.
[74]张德泉,李真等.摆线轮齿廓曲线CNC成形磨削机理[J].天津大学学报, 1998.4(31):454-458.
[75]腾献银等.摆线齿轮齿廓展成的CAD研究[J].机械设计, 2004.21(3):12-13.
[76]雷宏等.摆线齿廓成形磨削的研究[J].煤矿机械, 1994(4):35-38.
[77]严勇等.摆线齿轮成形磨齿工艺[J].机械工艺师, 1994(4):8-9.
[78] Liang Xichang, Shao Ming, Chen Da. Research of New Technologies in Gear-Machining [J]. Chinese Journal of Mechanical Engineering, 1994, 7(3):188-192.
[79]梁锡昌.摆线齿轮数控砂带磨法[P].中国专利, 0410022009.4.
[80]梁锡昌.摆线齿轮数控磨齿方法及装置[P].中国专利, 0410022109.1.
[81]刘殿忠,田嘉.用少齿差行星传动机构实现短幅外摆线齿形的范成磨削装置[J].煤矿机械, 2004(8):72-74.
[82]哈兰涛等.开放式摆线磨齿机的数控系统研究[J].上海工程技术大学学报, 2003.17(3):217-220.
[83]王强.摆线齿轮公法线测量法及程序设计[J].机械工艺师, 1991(10):22-24.
[84]虞培清,王则胜.摆线轮跨齿测量数值计算方法[J].现代制造工程, 2005(2):103-104.
[85]李真,庄葆华,吴迈等.摆线齿轮误差测量仪[J].工具技术, 1996, 30(5):39-42.
[86]梅向明,黄敬之.微分几何(第二版)[M].高等教育出版社, 1988.2.
[87]李特文.齿轮啮合原理(第二版)[M].上海科学技术出版社,1984.12.
[88]南开大学数学系齿轮研究小组.齿轮啮合理论的数学基础(一) [J].数学的实践与认识, 1976(1):52-62.
[89]南开大学数学系齿轮研究小组.齿轮啮合理论的数学基础(二) [J].数学的实践与认识, 1976(2):41-58.
[90]南开大学数学系齿轮研究小组.齿轮啮合理论的数学基础(三) [J].应用数学学报. 1976, 1(1):84-88.
[91]吴大任,骆家舜.齿轮啮合理论[M].北京,科学出版社, 1985.
[92]北京钢铁学院(数力系、机械系).包络法及其在空间啮合理论的应用[J]. 1975-1982.
[93]李力行等.摆线针轮行星传动的齿形修正及受力分析[J].机械工程学报, 1986, 22(1):40-49
[94] Shu Xiao-Long. Determination of load sharing factor for planetary gearing with small tooth number difference [J]. Mech. Mach. Theory, 1995,30(2):313-321.
[95] W.Mierzejewski, T.Szopa. Loads of planet wheels in planetary gears [J]. Journal of Mechanical Design, 1993, 115(4):1019-1023.
[96] Ahmet Kahraman. Load sharing characteristics of planetary transmission [J]. Mech. Mach. Theory, 1994, 29(8):1151-1165.
[97] S.P Velex. An extended model for the analysis of the dynamic behavior of planetary trains [J]. Journal of Mechanical Design, 1995,117(2):241-247.
[98] Wilcox L. E.. Finite element analysis pinpoint gear-tooth stress [J]. Machines Design, 1978,50(4):11-13.
[99] Tianmin Guan, Dongsheng Zhang, Lei Lei. Method of force bearing analysis and finite element analysis on contacting state of tooth surface for new typed FA planetary transmission of cycloidal needle-wheel[J]. Journal of machine design, 2005,22(3):31-34.
[100] Pinxiang Zhang, Hailiang Hu, Min Zhang. Finite element analysis of cycloidal gear [J]. Drive System Technique, 40-47.
[101]刘国庆,杨庆东. Ansys工程应用教程[M] .北京,中国铁道出版社, 2003.
[102] Li Lixing, etc. The computer aided design of cycloid drive [J]. Chinese Journal of MechanicalEngineering, 1990,3(2): 221-231
[103]王燕.面向对象的理论设计与C++实践[M].北京:清华大学出版社, 1991. 27-53.
[104]钱能. C++程序设计教程(第一版)[M].北京:清华大学出版社, 1999.4.
[105]王华.叶爱亮等. VISUAL C++编程实例与技巧[M].北京:机械工业出版社,1999.1. 233-250.
[106] Michael J. Yong. Visual C++从入门到精通[M].北京:电子工业出版社, 1999,(1): 355-683.
[107]网冠科技. Visual C++时尚编程百例[M].北京.机械工业出版社. 2001.3. 244-247.
[108]编程高手工作室. Visual C++编程高手(Ⅰ)(Ⅱ) [M] .北京:北京希望电子出版社, 2001.4
[109]鸿志创作组. Visual C++编程指南(第一版) [M].北京:科学出版社, 1999:72-75.
[110] JB/T10419-2005.摆线针轮行星传动摆线齿轮和针轮精度.
[111]熊有伦.线轮廓度和面轮廓度的评定和判别[J].计量学报, 1991(12):108-116.
[112] Zhai Haiyun, Li Zhen, Chen Lincai, Bi Fengjie. Error Processing Method of Cycloidal Gear Measurement Using 3D Coordinates Measuring Machine [J]. Chinese Journal of Mechanical Engineering, 1998, 11(3):196-200.
[113]柏永新.齿轮精度综合检验[M].上海:上海科学技术出版社,1986,41-281
[114]袁孔铎.误差理论及应用[M].北京:冶金工业出版社,1980,71-239
[115]毛英泰.误差理论与精度分析[M].北京:国防工业出版社,1982.6, 185-334
[116]汪仁树.行星轮系的运动精度研究[J].机械工程学报, 1988, 24(1) :15-19
[117]李充宁,刘继岩等. 2K-V型行星传动中摆线轮啮合的传动精度研究[J].机械工程学报, 2001, 37(4):61-65.
[118] C.Bard, D.Remond, D.Play. Comparison of Experimental Measurement and Numberical Calculation of Gear Transmission Error under Various Dynamic Conditions [J]. Ninth World Congress on the Theory of Machines and Mechanisms, Milan: 1995,(1):585-591.
[119] D.J.Sweeney, R.B.Randall. Gear Transmission Error Measurement Using Phase Demodulation [J]. Journal of Mechanical Engineering Science, 1996, 210(3):201-213.
[120]杜小平.机构的传动误差分析与可靠性计算[J].机械, 1995, 22 (4):16-18.
[121]盛鸿亮.齿轮机构精度分析中若干概念问题的研讨[J].光学技术, 1989, (3):44-46.
[122]汪仁树.行星轮系的运动精度研究[J].机械工程学报, 1988, 24(1):15-19.
[123]徐墨林.齿轮机构运动精度的分析与计算[J].锦州工学院学报.1984, (2):1-13.
[124]张永材,蔺天存.齿轮传动误差的检测[J].机械科学与技术.1992, (2):65-69.
[125]李真.摆线齿轮误差的研究[J].机械传动, 1992,16 (3):24-28.
[126]钱向勇.少齿差变位齿轮的回差分析[J].第二届中国仪器仪表学会学术年会交流资料,南京:1987, 1-9.
[127]罗其江.精密齿轮传动回差测试的新方法[J].航天部七三零六研究所, 1987,1-6..
[128]王印.摆线针轮减速机运动误差基本计算公式[J] .齿轮, 1987, 11(5):23-24.
[129]李宝田,李印玺.摆线针轮减速机传动误差的初步探讨[J].齿轮.1991,15(4) :42-45.
[130]刘鹤坤.谐波齿轮传动的回差及刚度测试[J].第五次航空减速器设计、工艺和实验方法学术交流会论文集, 1985:83-87.
[131]机械设计手册(第四版)[M].北京:化学工业出版社, 2002.
[132]齿轮手册(第二版)[M].北京:机械工业出版社, 2000.
[133]《现代机械传动手册》编辑委员会.现代机械传动手册[M].机械工业出版社, 2002.
[134]电机工程手册编辑委员会.机械工程手册(机械零部件设计卷)(第二版)[M].机械工业出版社, 1996.
[135]《机械设计手册》编写组编.机床设计手册(部件、构件及总体设计)[M].机械工业出版社, 1986.1.
[2] Dudley D W. Gear technology past, present and future [J]. Zheng Zhou: Proceedingsof International Conference on Gearing, 1988.
[3]唐定国,陈国民.齿轮传动技术的展望[J].机械工程学报, 1993, 29 (5) : 35-41.
[4] RotoPRECISION Inc. Mectrol Dojen Zero Backlash Speed Reducers. http://www.rotolube.com,1999.
[5] MOTION TECHNOLOGIES. Twinspin/Solution for Precision. http://motiontech.com.au, 2003.
[6] Prabhakar Nagabhusan, Marlboro, Mass. Adjustable Cycloidal Speed Reducer. United States Patent, 5145468. 1992/09/08.
[7]陈兵奎.锥形摆线轮行星传动装置[P].中国, ZLO3117879.0, 2005/02/16.
[8]陈兵奎,王淑妍,李朝阳.双圆盘摆线轮行星传动装置[P].中国, 200510057463.2, 2005/12/23.
[9]陈兵奎,蒋旭君,王淑妍.新型锥形摆线轮行星传动初步研究[J].现代制造工程, 2005, (2):14～15.
[10]冯澄宙.渐开线少齿差形星传动[M].人民教育出版社, 1982.
[11]饶振纲.行星传动机构设计(第二版)[M].国防工业出版社, 1994.6.
[12]郑州工学院机械原理及机械零件教研室编.摆线针轮行星传动[M].科学出版社, 1978.2.
[13] Jeffry D.Stoehr. Choosy about gears[J]. Tooling & Production, 2001.
[14]范又功等.谐波齿轮发展动向[J].航空制造工程, 1993(3):17-18.
[15]北京谐波齿轮传动技术研究所.谐波传动技术的新发展[J].齿轮, 1991(2):52-55.
[16]辛洪兵等.谐波传动技术及其研究动向[J].北京轻工业学院学报, 1999(3):30-36.
[17]孙慧.谐波传动综述[J].长岭技术与经济, 1996(2):44-51.
[18]北京谐波齿轮传动技术研究所.谐波传动技术及谐波减速机[J].新技术新工艺, 1994(3):12-13.
[19] J·G·Blanche and D·C·H·Yang. Cycloid Drives With Machining Tolerances [J]. ASME J.Mech.Transm, Automn Des Vol.111, 1989: 337-344.
[20] D·C·H·Yang and J·G·Blanche. Design and Application Guidences for Cycloid Drives with Machining Tolerances[J]. Mech.Mach.Theory,Vol.25(5),1990:487-501.
[21]沈允文等. RV减速器及其在机器人上的应用[J] .齿轮, 1988, 12 (5) :51-54.
[22]林章炎等. RV传动机构发展概述及设计新思想[J].机械工程师, 1991, (5) :18-20.
[23]徐永贤等. RV传动的弹性误差分析[J].大连铁道学院学报, 1999, 20(2):12-17.
[24]徐永贤等. RV传动刚度计算方法[J].大连铁道学院学报, 1999, 20(2):18-22.
[25]徐永贤等. RV传动输出机构的刚性误差分析[J].大连铁道学院学报, 1996, 17(4):41-47.
[26]刘洪斌等. RV传动的动力学研究[J].天津大学学报, 1999, 32(6): 661-661.
[27]李瑰贤等.变厚齿轮RV减速器系统扭振动力学分析[J].机械传动, 1999,23 (4):20-22.
[28]王刚等. RV减速机动力学建模方法研究[J].机械设计, 1999, 16(3) :19-22.
[29]董向阳等. RV传动机构的受力分析[J].上海交大学报, 1996, 30(5):65-71.
[30]戚厚军等. RV传动中摆线轮齿形修正的反求设计方法[J].天津职业技术师范学院学报, 1999(1):6-9.
[31]何卫东等.高精度RV传动的受力分析及传动效率[J].机械工程学报, 1996,32(4):104-110.
[32]何卫东等.机器人用高精度RV传动中变形轮修形对回差的影响[J].机械传动, 1999, 23(1):24-28.
[33]何卫东等.机器人用高精度RV减速器中摆线轮的优化新齿形[J].机械工程学报, 2000, 36(3):51-55.
[34]吴俊飞,李瑰贤等.机器人用变厚齿轮RV减速器回差分析与计算[J].机械设计, 2000, 17(3):24-26, 29.
[35]郭燕利等.平面二次包络环面蜗轮副研究综述与展望[J].机械, 2000, 27: 209-210.
[36]张光辉.侧隙可调式平面包络环面蜗杆传动研究[P].中国, 99117383.x, 2000.06.28.
[37]孙英时等.三片摆线轮减速机针齿与摆线轮啮合实际作用力分析[J].大连铁道学院学报, 2002, 23(2):20-23.
[38]关天民等.三片摆线轮新型针摆传动及其受力分析[J].大连铁道学院学报, 1999, 20(3):48-51.
[39]王海燕等. K-H-V双摆线钢球行星传动减速器齿廓曲线参数的选择[J].西北轻工业学院学报, 1994, 12:77-83.
[40]李思益等. K-H-V双摆线钢球行星传动减速器振动的初步分析与计算[J].西北轻工业学院学报, 1994, 12:64-68.
[41]李思益等.双摆线钢球的啮合与传动[J].西北轻工业学院学报, 1994, 12:69-72.
[42]安子军等.双摆线无隙钢球传动间隙调节力矩分析[J].机械传动, 1995, 19(4):1-4.
[43] F.L. Litvin, Alberto Demenego, Daniele Vecchiato. Formation by branches of envelope to parametric families of surfaces and curves [J]. Computer methods in applied mechanics and engineering, 190 (2001) 4587-4608.
[44] F.L. Litvin, A.M. Egelja, M. De Donno. Computerized determination of singularities and envelopes to families of contact lines on gear tooth surfaces [J]. Computer methods in appliedmechanics and engineering, 158 (1998) 23-24.
[45] F.L. Litvin, Pin-hao Feng. Computerized design, generation, and simulation of meshing rotors of screw compressor [J].Mech. Mach. Theory, Vol.32, (2),: 137-160,1997.
[46] Daniele Vecchiato, Alberto Demenego, John Argyris, Faydor L. Litvin. Geometry of a cycloidal pump [J]. Comput. Methods Appl. Mech. Engrg, 190 (2001) 2309-2330.
[47] Alberto Demenego, Daniele Vecchiato, Faydor L. Litvin, Nicola Nervegna, Salvatore Manco. Design and simulation of meshing of a cycloidal pump [J]. Mechanism and Machine Theory, 37 (2002) 311-332.
[48] F.L. Litvin, Pin-hao Feng. Computerized Design and Generation of Cycloidal Gearings [J] Mech. Mach. Theory, Vol.31, (7): 891-911, 1996.
[49] Joong-Ho Shin, Soon-Man Kwon. On the lobe profile design in a cycloid reducer using instant velocity center [J]. Mechanism and Machine Theory, 41 (2006) 596-616.
[50] Joong-Ho Shin, Sewon Chang, Soon-Man Kwon, Hoon-Ki Choi. New shape design method of an epicycloidal gear for an epicycloid drive [J]. Proc. of SPIE, Vol. 6040 60401G: 1-6.
[51] Ta-Shi Lai. Design and machining of the epicycloid planet gear of cycloid drives [J] International Journal of Advanced Manufacturing Technology, v28, n7-8, April, 2006: 665-670.
[52] Ta-Shi Lai. Geometric design of roller drives with cylindrical meshing elements [J]. Mechanism and Machine Theory, 40 (2005): 55–67.
[53] H.S. Yan, T.S.Lai. Geometry design an elementary planetary gear train with cylindrical tooth-profiles [J]. Mechanismand Machine Theory, 37 (8) (2002) 757-767.
[54] Vecchiato D., DemenegoA, Argyris J, et al. Geometry of aCycloidal Pump [J].ComPut Methods Appl Mech Engrg, 2001, 190:2309-2330.
[55] Mimmia G C, Pennacchi E. Non-undercuting conditions in internal gears [J].Mechanism and Machine Theory, 2000, 5:477-490.
[56] Vogesang H, Verhulsdonk B, et al. pulsation problems in rotary lobe PumP [J].Vorld Pump February, 1999(2):16-21.
[57] Tong Shih-His, Yang Daniel C H.On the generation of new lobe pumps for higher pumping flowrate [J]. Mechanism and Machine Theory, 2000, 35:997-1012.
[58] Chen C-K, Yang S-C.Geometric modeling for cylindrical and helical gear pumps with circular arc teeth [J].Proc lnstn Mech Engrs part C, 2000, 214(4):599-607.
[59] D.W. Botsiber, L. Kingston. Design and performance of the cycloid speed reducer [J]. Machine Design, 28 (1956) 65–69.
[60] X. Li, W. He, L. Li, L.C. Schmidt. A new cycloid drive with high-load capacity and highefficiency [J] ASME Journalof Mechanical Design, 126 (2004): 683-686.
[61] J. Davidson, K.H. Hunt, Robots and Screw Theory. Applications of Kinematics and Statics to Robotics [J]. OxfordUniversity Press, 2004.
[62] J.S. Dai, D.R. Kerr. Geometric analysis and optimization of symmetrical Watt 6-bar mechanisms [J] Journal of Mechanical Engineering Science, Proceedings of IMechE 205 (C1) (1991): 275-280.
[63] E.P. Pollitt. Some applications of the cycloid machine design [J]. ASME Journal of Engineering for Industry, 82 (1960):407-414.
[64]李力行,洪淳赫.摆线针轮行星传动中摆线轮齿形通用方程式的研究[J].大连铁道学院学报, 1992,13(1):7-122.
[65]高兴岐.多齿差摆线针轮行星传动的齿形及啮合特性的理论分析[J].机械传动, 2000, 4(4):11-14.
[66]孟继安等.内啮合摆线齿轮泵齿廓特征参数化设计探讨[J].化工机械, 1990(3): 145-150.
[67]侯东海等.少齿差摆线齿轮啮合原理及几何参数选择[J].机械传动, 1995, 19 (3): 24-27.
[68]侯东海,司春华,吕伴功.少齿差摆线齿轮泵啮合原理及几何参数选择[J].机械传动, 1995, 19(3):24-27.
[69]李荣堂等.多齿差内啮合圆弧摆线齿轮泵的开发[J].石油化工设备技术,1994,15 (4): 26-30.
[70]李荣堂,史发科.多齿差内啮合圆弧摆线齿轮泵的开发[J].石油化工设备技术, 1994, 15 (4):25-30.
[71]徐秀生.多齿差圆弧摆线式内啮合齿轮泵的设计[J].水泵技术, 1996(3):26-31.
[72]王乾廷,桂贵生.用切触线法加工曲线轮廓[J].合肥工业大学学报(自然科学版), 2003,26(3):193-196.
[73]张敬东.摆线齿轮的数控加工[J].现代制造工程, 2005(3):49-50.
[74]张德泉,李真等.摆线轮齿廓曲线CNC成形磨削机理[J].天津大学学报, 1998.4(31):454-458.
[75]腾献银等.摆线齿轮齿廓展成的CAD研究[J].机械设计, 2004.21(3):12-13.
[76]雷宏等.摆线齿廓成形磨削的研究[J].煤矿机械, 1994(4):35-38.
[77]严勇等.摆线齿轮成形磨齿工艺[J].机械工艺师, 1994(4):8-9.
[78] Liang Xichang, Shao Ming, Chen Da. Research of New Technologies in Gear-Machining [J]. Chinese Journal of Mechanical Engineering, 1994, 7(3):188-192.
[79]梁锡昌.摆线齿轮数控砂带磨法[P].中国专利, 0410022009.4.
[80]梁锡昌.摆线齿轮数控磨齿方法及装置[P].中国专利, 0410022109.1.
[81]刘殿忠,田嘉.用少齿差行星传动机构实现短幅外摆线齿形的范成磨削装置[J].煤矿机械, 2004(8):72-74.
[82]哈兰涛等.开放式摆线磨齿机的数控系统研究[J].上海工程技术大学学报, 2003.17(3):217-220.
[83]王强.摆线齿轮公法线测量法及程序设计[J].机械工艺师, 1991(10):22-24.
[84]虞培清,王则胜.摆线轮跨齿测量数值计算方法[J].现代制造工程, 2005(2):103-104.
[85]李真,庄葆华,吴迈等.摆线齿轮误差测量仪[J].工具技术, 1996, 30(5):39-42.
[86]梅向明,黄敬之.微分几何(第二版)[M].高等教育出版社, 1988.2.
[87]李特文.齿轮啮合原理(第二版)[M].上海科学技术出版社,1984.12.
[88]南开大学数学系齿轮研究小组.齿轮啮合理论的数学基础(一) [J].数学的实践与认识, 1976(1):52-62.
[89]南开大学数学系齿轮研究小组.齿轮啮合理论的数学基础(二) [J].数学的实践与认识, 1976(2):41-58.
[90]南开大学数学系齿轮研究小组.齿轮啮合理论的数学基础(三) [J].应用数学学报. 1976, 1(1):84-88.
[91]吴大任,骆家舜.齿轮啮合理论[M].北京,科学出版社, 1985.
[92]北京钢铁学院(数力系、机械系).包络法及其在空间啮合理论的应用[J]. 1975-1982.
[93]李力行等.摆线针轮行星传动的齿形修正及受力分析[J].机械工程学报, 1986, 22(1):40-49
[94] Shu Xiao-Long. Determination of load sharing factor for planetary gearing with small tooth number difference [J]. Mech. Mach. Theory, 1995,30(2):313-321.
[95] W.Mierzejewski, T.Szopa. Loads of planet wheels in planetary gears [J]. Journal of Mechanical Design, 1993, 115(4):1019-1023.
[96] Ahmet Kahraman. Load sharing characteristics of planetary transmission [J]. Mech. Mach. Theory, 1994, 29(8):1151-1165.
[97] S.P Velex. An extended model for the analysis of the dynamic behavior of planetary trains [J]. Journal of Mechanical Design, 1995,117(2):241-247.
[98] Wilcox L. E.. Finite element analysis pinpoint gear-tooth stress [J]. Machines Design, 1978,50(4):11-13.
[99] Tianmin Guan, Dongsheng Zhang, Lei Lei. Method of force bearing analysis and finite element analysis on contacting state of tooth surface for new typed FA planetary transmission of cycloidal needle-wheel[J]. Journal of machine design, 2005,22(3):31-34.
[100] Pinxiang Zhang, Hailiang Hu, Min Zhang. Finite element analysis of cycloidal gear [J]. Drive System Technique, 40-47.
[101]刘国庆,杨庆东. Ansys工程应用教程[M] .北京,中国铁道出版社, 2003.
[102] Li Lixing, etc. The computer aided design of cycloid drive [J]. Chinese Journal of MechanicalEngineering, 1990,3(2): 221-231
[103]王燕.面向对象的理论设计与C++实践[M].北京:清华大学出版社, 1991. 27-53.
[104]钱能. C++程序设计教程(第一版)[M].北京:清华大学出版社, 1999.4.
[105]王华.叶爱亮等. VISUAL C++编程实例与技巧[M].北京:机械工业出版社,1999.1. 233-250.
[106] Michael J. Yong. Visual C++从入门到精通[M].北京:电子工业出版社, 1999,(1): 355-683.
[107]网冠科技. Visual C++时尚编程百例[M].北京.机械工业出版社. 2001.3. 244-247.
[108]编程高手工作室. Visual C++编程高手(Ⅰ)(Ⅱ) [M] .北京:北京希望电子出版社, 2001.4
[109]鸿志创作组. Visual C++编程指南(第一版) [M].北京:科学出版社, 1999:72-75.
[110] JB/T10419-2005.摆线针轮行星传动摆线齿轮和针轮精度.
[111]熊有伦.线轮廓度和面轮廓度的评定和判别[J].计量学报, 1991(12):108-116.
[112] Zhai Haiyun, Li Zhen, Chen Lincai, Bi Fengjie. Error Processing Method of Cycloidal Gear Measurement Using 3D Coordinates Measuring Machine [J]. Chinese Journal of Mechanical Engineering, 1998, 11(3):196-200.
[113]柏永新.齿轮精度综合检验[M].上海:上海科学技术出版社,1986,41-281
[114]袁孔铎.误差理论及应用[M].北京:冶金工业出版社,1980,71-239
[115]毛英泰.误差理论与精度分析[M].北京:国防工业出版社,1982.6, 185-334
[116]汪仁树.行星轮系的运动精度研究[J].机械工程学报, 1988, 24(1) :15-19
[117]李充宁,刘继岩等. 2K-V型行星传动中摆线轮啮合的传动精度研究[J].机械工程学报, 2001, 37(4):61-65.
[118] C.Bard, D.Remond, D.Play. Comparison of Experimental Measurement and Numberical Calculation of Gear Transmission Error under Various Dynamic Conditions [J]. Ninth World Congress on the Theory of Machines and Mechanisms, Milan: 1995,(1):585-591.
[119] D.J.Sweeney, R.B.Randall. Gear Transmission Error Measurement Using Phase Demodulation [J]. Journal of Mechanical Engineering Science, 1996, 210(3):201-213.
[120]杜小平.机构的传动误差分析与可靠性计算[J].机械, 1995, 22 (4):16-18.
[121]盛鸿亮.齿轮机构精度分析中若干概念问题的研讨[J].光学技术, 1989, (3):44-46.
[122]汪仁树.行星轮系的运动精度研究[J].机械工程学报, 1988, 24(1):15-19.
[123]徐墨林.齿轮机构运动精度的分析与计算[J].锦州工学院学报.1984, (2):1-13.
[124]张永材,蔺天存.齿轮传动误差的检测[J].机械科学与技术.1992, (2):65-69.
[125]李真.摆线齿轮误差的研究[J].机械传动, 1992,16 (3):24-28.
[126]钱向勇.少齿差变位齿轮的回差分析[J].第二届中国仪器仪表学会学术年会交流资料,南京:1987, 1-9.
[127]罗其江.精密齿轮传动回差测试的新方法[J].航天部七三零六研究所, 1987,1-6..
[128]王印.摆线针轮减速机运动误差基本计算公式[J] .齿轮, 1987, 11(5):23-24.
[129]李宝田,李印玺.摆线针轮减速机传动误差的初步探讨[J].齿轮.1991,15(4) :42-45.
[130]刘鹤坤.谐波齿轮传动的回差及刚度测试[J].第五次航空减速器设计、工艺和实验方法学术交流会论文集, 1985:83-87.
[131]机械设计手册(第四版)[M].北京:化学工业出版社, 2002.
[132]齿轮手册(第二版)[M].北京:机械工业出版社, 2000.
[133]《现代机械传动手册》编辑委员会.现代机械传动手册[M].机械工业出版社, 2002.
[134]电机工程手册编辑委员会.机械工程手册(机械零部件设计卷)(第二版)[M].机械工业出版社, 1996.
[135]《机械设计手册》编写组编.机床设计手册(部件、构件及总体设计)[M].机械工业出版社, 1986.1.