球面渐开线螺旋锥齿轮接触区调整方法研究
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摘要
螺旋锥齿轮用于传递相交轴的运动与动力，相比于直齿锥齿轮，螺旋锥齿轮具有重合度大、承载能力高、传动平稳、强度高，对安装误差的敏感性小等优点，广泛应用于舰船、航空和国防技术装备以及汽车，机床、工程机械和矿山机械等各种机械产品中。螺旋锥齿轮的加工技术一直受到广泛的关注。成立于1865年的美国格里森公司，是国际上锥齿轮加工机床和技术的主要领跑者，它所生产的螺旋锥齿轮是目前应用最广泛的一种锥齿轮。由于格里森公司固有的加工原理，使得机床结构非常复杂，加工调整计算十分繁杂、困难，是最难以操作使用的机床之一。另一方面，格里森的“近似替代”和“局部共轭”原理导致加工的两齿面往往不能正确啮合，出现接触区不良、噪音增大、强度下降等弊端。为了改善齿轮的啮合状态，获得较好的接触区，需要对机床和刀具进行复杂的调整和反复的试切、检验，增加了制造成本，加工一对齿轮的生产周期长，且齿轮需要配对使用。这样加工出来的齿轮不是球面渐开线齿形，因而也就不具备互换性、瞬时传动比恒定等优良特性。
本文的研究基于产形线切齿法原理，利用产形线切齿原理可以获得具有球面渐开线齿廓的螺旋锥齿轮。球面渐开线是锥齿轮的理论齿廓，具有渐开线齿廓的一切优良特性。产形线切齿法原理提供了球面渐开线螺旋锥齿轮的切齿方法和切齿装备的设计制造方案。本文在上述研究工作的基础上，从空间啮合原理出发，对这种新型球面渐开线螺旋锥齿轮的接触和啮合状态进行了分析和研究。螺旋锥齿轮的啮合特性和接触分析对传动性能有很大影响，直接影响齿轮的使用和加工，因此有必要对其开展深入的研究。本文的研究内容主要包括以下几个方面：
（1）系统研究了球面渐开线螺旋锥齿轮的齿面生成运动过程，阐述了左旋、右旋以及凸、凹齿面形成的切齿运动关系。在此基础上，运用坐标变换原理推导了齿面的数学模型，从啮合原理的角度对所推导的右旋凹齿面方程进行了分析，给出了啮合方程、接触线方程和与之共轭的左旋凸齿面方程的表达式。并对接触线方程与产形线方程的同一性进行了对比分析。这部分研究内容从理论上为产形线切齿法原理提供了支持，同时也是开展齿面研究和接触分析的基础。
（2）对所推导的左、右旋凸、凹齿面的啮合特性进行了研究，计算了各自曲面的法曲率，主曲率、确定了主方向，计算了理论上线接触的螺旋锥齿轮齿面的诱导法曲率，推导了曲面的曲率干涉界限线和啮合界限线的表达式。为进一步研究齿面接触区的调整提供依据。
（3）对于理论上线接触共轭的球面渐开线螺旋锥齿轮提出了通过改变产形线半径将线接触转化为点接触的接触区调整方法。分析并推导了产形线半径的计算公式，对调整后的点接触共轭齿面的诱导法曲率计算公式进行了推导，为轮齿接触分析奠定了基础。
（4）采用轮齿接触分析（TCA）方法对调整后的点接触共轭齿轮副的接触区进行了模拟。首先将两齿面方程及法向量方程转化至同一坐标系中，建立由矢量方程表示的接触方程。其次将矢量方程表示的接触方程转化为数量方程并运用MATLAB软件进行非线性方程组的求解，求解的方法是迭代法，为此需要确定合理的迭代初值，文中分析了迭代初值的选择方法。最后将非线性方程组的求解结果以图形的形式进行表达，获得了接触迹线，为了获得更直观的接触区，计算了以瞬时接触点为中心的接触椭圆的各项参数，并绘制了由接触椭圆长轴所组成的接触区。对轮齿接触分析的结果进行实验验证。将所加工的螺旋锥齿轮模型进行传动实验，获得实际的接触区，并对模拟和实验的结果进行分析说明。
（5）为了揭示外在因素对齿轮接触区的影响，本文分析了齿轮副安装误差对接触区的影响规律。通过建立包含安装误差的接触方程并对其进行求解的方法，分别对小轮安装距误差H、大轮安装距误差J、齿轮副轴间距偏差V和轴交角偏差对接触迹线的位置和形态的影响进行了研究并得到了相关结论。在此基础上，进一步对各项误差对接触迹线的综合影响进行了分析，得出了对齿轮安装有指导意义的调整规律。
Spiral bevel gear used to transmit motion and power between intersect axis, comparedto straight bevel gears, spiral bevel gear has many advantages, such as the large toothcontact ratio, higher load capacity, steady transmission, high strength, and insensitive toinstall errors, etc. It is widely used in ships, aviation, defense technology and equipment aswell as automotive, machine tools, construction machinery, mining machinery and othermachinery products. The processing technology of spiral bevel gear has been widelyconcerned. The Gleason Works that founded in1865in the United States is in a leadingposition in bevel gear cutting machines and technology; the spiral bevel gears manufacturedby Gleason Works are the most widely used bevel gears. Due to the inherent Gleasonprocessing principle, The Gleason machines which have complicated machine structure arehard to calculation and adjustment of processing, the machines are one of the most difficultto operate. On the other hand, the principle of “Approximate substitution” and “Locationconjugate” made the tooth surface can not properly engaged, which result too manydisadvantages such as the inexpectant contact area, high-noise and decrease strength,etc. Inorder to improve the gear engagement and obtain better contact area, Machines and toolsneed to be complex adjusted and the gears should be cutting and inspection repeatedly. Thecosts of manufacturing increased, and the production period prolonged, furthermore, thegears should be used in pair. In this way, the tooth profile of spiral bevel gear is not thespherical involutes, so it does not have interchangeable, constant of instantaneoustransmission ratio and other fine features.
This study based on the principle of involute gear cutting on the tracing line, using theprinciple can obtain the spiral bevel gears with spherical involute tooth profile. Sphericalinvolute is the theoretical tooth profile of bevel gear; it has all the good characteristics ofinvolute tooth profile. The principle of involute gear cutting on the tracing line provides thecutting methods of spherical involute spiral bevel gears and the design and manufacturingsolutions of the processing equipments. Based on the above works, the situation of contactand engagement of this new type of spherical involute spiral bevel gear were analyzed andstudied in meshing. Meshing characteristics and contact analysis of spiral bevel gear drivehas great influence on the performance of transmission, it has a direct impact on the gearusing and processing, so it is necessary to carry out in-depth research. The main contents ofthis paper include the following aspects:
(1) The generating movement of the spherical involute spiral bevel gear tooth surfaces has been studied systematically in this paper. The generating of concave tooth surface andconvex tooth surface both of right-and left-handed spiral bevel gear have been described indetail. On this basis, the mathematical model of the tooth surface has been derived bycoordinate transformation, the right-handed concave tooth surface equation has beenanalyzed from the perspective of meshing theory, the meshing equation, and the contact lineequation and the left-handed convex tooth surface equation were derived. A comparativeanalysis of contact line and tracing line was carried out to prove that the two are the samecurve. This part of research provides support for the tracing line method in theory, and alsoprovides the basis for carrying out research on tooth surfaces and contact analysis.
(2) The meshing characteristics of the left and right-handed convex and concave toothsurface were studied, the normal curvature and the principal curvatures of each surfacewere calculated, the main direction also determined. The induced normal curvature of spiralbevel gear tooth surface that line contact in theory were calculated, the expressions whichdescribe the curvature interference limit line and the meshing limit line were derived. Theyall provide the basis for further research to adjust tooth contact area.
(3) The method of contact adjustment of spiral bevel gear was proposed in this part,the contact patterns of gears from line-contact changes to point-contact by changing theradius of generating line. The method how to determine the reasonable radius of generatingline was analyzed, and the formula for calculating the radius of the generating line wasderived. After that, the formulas of induced normal curvature which applicable to thepoint-contact conjugate tooth surface were deduced. The works lay the foundation for thetooth contact analysis.
(4) The tooth contact analysis method was used to simulating the meshing and contactof gear drives which change to point-contact by changing the radius of generating line. First,the gears should be change into the same coordinate system, and then established contactequation represented by vectors. Second, the contact equation represented by vectors needconverted into numerical formula and MATLAB software was used for solving nonlinearequations. Iterative method is used to solve the nonlinear equations, in order to obtain thereasonable initial value of iteration, the way how to choose reasonable initial value ofiteration was analyzed. Finally, the results of nonlinear equations were plotted in graphical,so the contact trace was obtained. In order to obtain an intuitive contact area, the parametersof the contact ellipse which take instantaneous point as the center were calculated, thecontact region formed by the major axis of contact ellipses was drawed. The results of toothcontact analysis were confirmed by experiment. The actual contact area has been gained, and the difference between simulation and experiment was analyzed.
(5) With the purpose of revealing the influence of external factors on the gear contactarea, the influence of installation error on contact area was researched in this paper byestablishing and solving contacts equations that contains the installation error. The effectsof pinion installation error H, gear installation error J, gear shaft deviation V, andaxis angle deviation on location and shape of contact trace were researched and someconclusions were gained. On this basis, further research on comprehensive effects ofinstallation error on contact trace has been analyzed, and then the adjustment rules guidinggear installation were proposed.
本文的研究基于产形线切齿法原理，利用产形线切齿原理可以获得具有球面渐开线齿廓的螺旋锥齿轮。球面渐开线是锥齿轮的理论齿廓，具有渐开线齿廓的一切优良特性。产形线切齿法原理提供了球面渐开线螺旋锥齿轮的切齿方法和切齿装备的设计制造方案。本文在上述研究工作的基础上，从空间啮合原理出发，对这种新型球面渐开线螺旋锥齿轮的接触和啮合状态进行了分析和研究。螺旋锥齿轮的啮合特性和接触分析对传动性能有很大影响，直接影响齿轮的使用和加工，因此有必要对其开展深入的研究。本文的研究内容主要包括以下几个方面：
（1）系统研究了球面渐开线螺旋锥齿轮的齿面生成运动过程，阐述了左旋、右旋以及凸、凹齿面形成的切齿运动关系。在此基础上，运用坐标变换原理推导了齿面的数学模型，从啮合原理的角度对所推导的右旋凹齿面方程进行了分析，给出了啮合方程、接触线方程和与之共轭的左旋凸齿面方程的表达式。并对接触线方程与产形线方程的同一性进行了对比分析。这部分研究内容从理论上为产形线切齿法原理提供了支持，同时也是开展齿面研究和接触分析的基础。
（2）对所推导的左、右旋凸、凹齿面的啮合特性进行了研究，计算了各自曲面的法曲率，主曲率、确定了主方向，计算了理论上线接触的螺旋锥齿轮齿面的诱导法曲率，推导了曲面的曲率干涉界限线和啮合界限线的表达式。为进一步研究齿面接触区的调整提供依据。
（3）对于理论上线接触共轭的球面渐开线螺旋锥齿轮提出了通过改变产形线半径将线接触转化为点接触的接触区调整方法。分析并推导了产形线半径的计算公式，对调整后的点接触共轭齿面的诱导法曲率计算公式进行了推导，为轮齿接触分析奠定了基础。
（4）采用轮齿接触分析（TCA）方法对调整后的点接触共轭齿轮副的接触区进行了模拟。首先将两齿面方程及法向量方程转化至同一坐标系中，建立由矢量方程表示的接触方程。其次将矢量方程表示的接触方程转化为数量方程并运用MATLAB软件进行非线性方程组的求解，求解的方法是迭代法，为此需要确定合理的迭代初值，文中分析了迭代初值的选择方法。最后将非线性方程组的求解结果以图形的形式进行表达，获得了接触迹线，为了获得更直观的接触区，计算了以瞬时接触点为中心的接触椭圆的各项参数，并绘制了由接触椭圆长轴所组成的接触区。对轮齿接触分析的结果进行实验验证。将所加工的螺旋锥齿轮模型进行传动实验，获得实际的接触区，并对模拟和实验的结果进行分析说明。
（5）为了揭示外在因素对齿轮接触区的影响，本文分析了齿轮副安装误差对接触区的影响规律。通过建立包含安装误差的接触方程并对其进行求解的方法，分别对小轮安装距误差H、大轮安装距误差J、齿轮副轴间距偏差V和轴交角偏差对接触迹线的位置和形态的影响进行了研究并得到了相关结论。在此基础上，进一步对各项误差对接触迹线的综合影响进行了分析，得出了对齿轮安装有指导意义的调整规律。
Spiral bevel gear used to transmit motion and power between intersect axis, comparedto straight bevel gears, spiral bevel gear has many advantages, such as the large toothcontact ratio, higher load capacity, steady transmission, high strength, and insensitive toinstall errors, etc. It is widely used in ships, aviation, defense technology and equipment aswell as automotive, machine tools, construction machinery, mining machinery and othermachinery products. The processing technology of spiral bevel gear has been widelyconcerned. The Gleason Works that founded in1865in the United States is in a leadingposition in bevel gear cutting machines and technology; the spiral bevel gears manufacturedby Gleason Works are the most widely used bevel gears. Due to the inherent Gleasonprocessing principle, The Gleason machines which have complicated machine structure arehard to calculation and adjustment of processing, the machines are one of the most difficultto operate. On the other hand, the principle of “Approximate substitution” and “Locationconjugate” made the tooth surface can not properly engaged, which result too manydisadvantages such as the inexpectant contact area, high-noise and decrease strength,etc. Inorder to improve the gear engagement and obtain better contact area, Machines and toolsneed to be complex adjusted and the gears should be cutting and inspection repeatedly. Thecosts of manufacturing increased, and the production period prolonged, furthermore, thegears should be used in pair. In this way, the tooth profile of spiral bevel gear is not thespherical involutes, so it does not have interchangeable, constant of instantaneoustransmission ratio and other fine features.
This study based on the principle of involute gear cutting on the tracing line, using theprinciple can obtain the spiral bevel gears with spherical involute tooth profile. Sphericalinvolute is the theoretical tooth profile of bevel gear; it has all the good characteristics ofinvolute tooth profile. The principle of involute gear cutting on the tracing line provides thecutting methods of spherical involute spiral bevel gears and the design and manufacturingsolutions of the processing equipments. Based on the above works, the situation of contactand engagement of this new type of spherical involute spiral bevel gear were analyzed andstudied in meshing. Meshing characteristics and contact analysis of spiral bevel gear drivehas great influence on the performance of transmission, it has a direct impact on the gearusing and processing, so it is necessary to carry out in-depth research. The main contents ofthis paper include the following aspects:
(1) The generating movement of the spherical involute spiral bevel gear tooth surfaces has been studied systematically in this paper. The generating of concave tooth surface andconvex tooth surface both of right-and left-handed spiral bevel gear have been described indetail. On this basis, the mathematical model of the tooth surface has been derived bycoordinate transformation, the right-handed concave tooth surface equation has beenanalyzed from the perspective of meshing theory, the meshing equation, and the contact lineequation and the left-handed convex tooth surface equation were derived. A comparativeanalysis of contact line and tracing line was carried out to prove that the two are the samecurve. This part of research provides support for the tracing line method in theory, and alsoprovides the basis for carrying out research on tooth surfaces and contact analysis.
(2) The meshing characteristics of the left and right-handed convex and concave toothsurface were studied, the normal curvature and the principal curvatures of each surfacewere calculated, the main direction also determined. The induced normal curvature of spiralbevel gear tooth surface that line contact in theory were calculated, the expressions whichdescribe the curvature interference limit line and the meshing limit line were derived. Theyall provide the basis for further research to adjust tooth contact area.
(3) The method of contact adjustment of spiral bevel gear was proposed in this part,the contact patterns of gears from line-contact changes to point-contact by changing theradius of generating line. The method how to determine the reasonable radius of generatingline was analyzed, and the formula for calculating the radius of the generating line wasderived. After that, the formulas of induced normal curvature which applicable to thepoint-contact conjugate tooth surface were deduced. The works lay the foundation for thetooth contact analysis.
(4) The tooth contact analysis method was used to simulating the meshing and contactof gear drives which change to point-contact by changing the radius of generating line. First,the gears should be change into the same coordinate system, and then established contactequation represented by vectors. Second, the contact equation represented by vectors needconverted into numerical formula and MATLAB software was used for solving nonlinearequations. Iterative method is used to solve the nonlinear equations, in order to obtain thereasonable initial value of iteration, the way how to choose reasonable initial value ofiteration was analyzed. Finally, the results of nonlinear equations were plotted in graphical,so the contact trace was obtained. In order to obtain an intuitive contact area, the parametersof the contact ellipse which take instantaneous point as the center were calculated, thecontact region formed by the major axis of contact ellipses was drawed. The results of toothcontact analysis were confirmed by experiment. The actual contact area has been gained, and the difference between simulation and experiment was analyzed.
(5) With the purpose of revealing the influence of external factors on the gear contactarea, the influence of installation error on contact area was researched in this paper byestablishing and solving contacts equations that contains the installation error. The effectsof pinion installation error H, gear installation error J, gear shaft deviation V, andaxis angle deviation on location and shape of contact trace were researched and someconclusions were gained. On this basis, further research on comprehensive effects ofinstallation error on contact trace has been analyzed, and then the adjustment rules guidinggear installation were proposed.
引文
[1]邓效忠,魏冰阳.锥齿轮设计的新方法[M].北京:科学出版社,2012.
[2]齿轮手册编.齿轮手册[M].北京:机械工业出版社,2004.
[3]李强,宿宝龙,闫洪波,等.螺旋锥齿轮加工机床发展综述[J].机床与液压2012,40(8):164-166.
[4] Y.C. Tsai, P.C. Chin. Surface Geometry of Straight and Spiral Bevel Gears [J].Journal of Mechanisms, Transmissions, and Automation in Design1987,109(4):443-449.
[5] R. L. Huston, J.J. Coy. Ideal Spiral Bevel Gears—A New Approach to SurfaceGeometry [J]. Transactions of theASME1981,103(1):127-132.
[6]四川省机械工业局编.齿轮刀具设计理论基础（下）[M].北京:机械工业出版社,1982.
[7]谷凤民,周亮,段建中,等.弧齿锥齿轮的一种新型精确设计方法[J].机械设计与制造,2008,12:12-13.
[8] M. J. Al-Daccak, J. Angeles, M. A. Gonzalez-Palacios. The Modeling of BevelGears Using the Exact Spherical Involute [J]. Transactions of the ASME1994,116(2):363-368.
[9] R.L. Huston, J.J. Coy. Surface Geometry of Circular Cut Spiral Bevel Gears[J].ASME J. Mech. Des.,104(3):743–748.
[10] F.L. Litvin, A. Fuentes: Gear Geometry and Applied Theory[M]. Cambridge,University Press,2004.
[11] CHUNG-YUNN LIN and CHUNG-BIAU TSAY, ZHANG-HUA FONG.MATHEMATICAL MODEL OF SPIRAL BEVEL AND HYPOID GEARSMANUFACTURED BY THE MODIFIED ROLL Method,[J]. Mech. Mach. Theory,1997,32(2):121-136.
[12]曾韬.螺旋锥齿轮设计与加工[M].哈尔滨：哈尔滨工业大学出版社,1989.
[13]胡来瑢.空间啮合原理及应用(下)[M].煤炭工业出版社,1989.
[14] F. L. Litvin, Wei-Jiung Tsung, J.J. Coy, et al. Method for Generation of Spiral BevelGears With Conjugate Gear Tooth Surfaces, Journal of Mechanisms, Transmissions,and Automation in Design.1987.109(2):163-170.
[15]郑昌启,弧齿锥齿轮传和准双曲面齿轮—啮合原理、轮坯设计、加工调整和齿面分析计算原理[M].北京：机械工业出版社,1988.
[16]樊红卫,谷霁红.螺旋锥齿轮设计与制造的研究现状与展望[J].机械制造2009.47(540):47-49.
[17]李兆文,王太勇,陈正洪.螺旋锥齿轮技术的研究现状[J].工具技术,2007,41(10):3-6.
[18]遇立基. CIMT’99展出的数控齿轮加工机床.制造技术与机床,1999,12:6～7.
[19]彭福华.渐开线齿轮产形线切齿法[M].长春:吉林科学技术出版社,2008.
[20]彭福华.球面渐开线齿形收缩齿制弧齿锥齿轮的切齿方法:中国,200610017213.0[P].2008-04-02.
[21]杨兆军,彭福华,张学成.球面渐开线齿形弧齿锥齿轮切齿法与机床:中国,200810051354.3[P].2009-03-25.
[22]彭福华,杨兆军,于立娟.球面渐开线齿形阿基米德螺线齿锥齿轮切齿法与机床:中国,200810051355.8[P].2009-03-25.
[23]彭福华,呼咏,李春光.收缩齿制球面渐开线齿形斜直齿锥齿轮加工方法:中国,200810051356.2[P].2009-03-25.
[24] Yankun Wang, Zhaojun Yang, Linan Li. The Equation of Meshing of Spiral BevelGears Manufactured by Generating-Line Method. Open Mech. Eng. J.2011,5(1):51-55.
[25] Linan Li, Zhaojun Yang, Yankun Wang. Cutting Geometry and Base-Cone Parametersof Manufacturing Hypoid Gears by Generating-Line Method. Open Mech. Eng.J.2011,5(1):19-25.
[26]张学成,李春光,李桂娇.弧齿锥齿轮齿面发生线切齿法探讨[J].机械传动,2009,6:21-24.
[27]张学成,呼咏,杨兆军.基于齿面发生线的弧齿锥齿轮切齿运动分析[J].北京工业大学学报,2010,36(11):1441-1446.
[28]呼咏,张学成,杨兆军,等.球面渐开线齿形弧齿锥齿轮精密切齿方法[J].北京工业大学学报,2011,37(5):641-647.
[29] Zhang, X C, Wang, X, Yu, L J, Yang, Z J. Study on the generation of spiral bevelgears with spherical involute tooth profile by the tracing line[J]. P I MECH ENG C-JMEC,2012,226(C4):1097-1106.
[30]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锥齿轮啮合及加工原理[M].北京:机械工业出版社,1986.
[31]北京齿轮厂.格利森锥齿轮技术资料译文集第二分册格利森锥齿轮设计及计算[M].北京:机械工业出版社,1983.
[32]北京齿轮厂.格利森锥齿轮技术资料译文集第三分册格利森锥齿轮强度分析及计算[M].北京:机械工业出版社,1984.
[33]天津齿轮机床研究所.格利森锥具轮技术资料译文集第五分册格利森锥齿轮加工方法及轮齿接触分析[M].北京:机械工业出版社,1982.
[34]天津齿轮机床研究所.格利森锥具轮技术资料译文集第六分册格利森锥齿轮的检验及安装[M].北京:机械工业出版社,1983.
[35]董学朱.摆线齿锥齿轮及准双曲面齿轮设计和制造[M].北京:机械工业出版社,2003.
[36] Е.А.Андрущенко,蒋朝明.奥利康公司的齿轮加工[J].齿轮,1983,1:41-43.
[37] Gleason Seminar. Spiral bevel and hypoid gear technology update[R].Beijing:Gleason Corporation,2007.
[38]刘鹄然,陈良玉,刘志峰.奥利康与克林根贝尔格制铣齿机工作原理的新认识[J].机械传动,1998,22(3):36-37.
[39]董学朱.摆线齿锥齿轮连续分齿法铣齿原理的研究[J].机械传动,1999,23(2):29-30.
[40]胡来容.等高弧齿锥齿轮副的啮合理论研究(上)[J].焦作矿业学院学报.1991,3:1-21.
[41] Lelkes M, Márialigeti J, Play D. Numerical Determination of Cutting Parameters forthe Control of Klingelnberg Spiral Bevel Gear Geometry[J].ASME J. Mech. Des.2002,124(4):761–771.
[42] Litvin F L, Wang A G, Handschuh R F. Comput erized design and analysis of face-milled, uniform tooth height spiral bevel gear drives[J].Mechanical Design,2006(118):573-579.
[43] M.L.Baxter. Basie Geometry and Tooth Contact of Hypoid Gear[J]. IndustrialMathematics.1961,11(2):l-28.
[44] M.L.Baxter. Seeond Order Surface Generation[J]. Industrial Mathematies,1973,23(2):85-106.
[45]中国机械工业年委员会.中国机械通用零部件工业年鉴[M].机械工业出版社,2003.
[46] Stadtfeld H L. Advanced bevel gear technology[M].The Gleason Works,2000.
[47]庄中.格里森弧齿锥齿轮磨齿技术的发展[J].汽车工艺与材料,2004,9:11-18.
[48] Shih, Yi-Pei, Chen, Shi-Duang. Free-form flank correction in helical gear grindingusing a five-axis computer numerical control gear profile grinding machine. Journalof Manufacturing Science and Engineering[J]. Transactions of the ASME,2012,134(4):041006-1-041006-13.
[49] Wu L Y, Wei H Q, Wang X C. Geometric parameters of extended epicycloid geartooth surface generated on free-form bevel gear milling machines[J]. Journal of Xi'anJiaotong University,2001,35(3):322-325.
[50] Chang S L, Tsay C B, Nagata S. A General Mathematical Model for Gears by CNCHobbing Machines[J].1997, ASME J. Mech. Des.119():108–113.
[51]肖冬生,曾韬,殷盛福. GLEASON PHOENIX ⅡCNC磨齿机B轴运动分析[J].制造技术与机床,2005,(1):55-56.
[52]樊奇,让·德福.格里森专家制造系统(GEMS)开创弧齿锥齿轮及双曲面齿轮数字化制造新纪元[J].世界制造技术与装备市场,2005,4:87-93.
[53]周军辉刘宝生陈建平徐华兵.基于PHOENIX系列磨齿机的磨齿参数设计[J].精密制造与自动,2003,155(3):40-42.
[54]吴训成,陈志恒,胡宁.曲线齿锥齿轮点啮合齿面主动控制加工技术[M].机械工程学报,2005,41(10):97-101.
[55] Stadtfeld H J. The Universal Motion Concept for Bevel Gear Production,1999[C].Fourth World Congress on Gearing and Power Transmissions, Paris:595–607.
[56] LING Chung-yunn, TSAY Chung-biau. FONG Zhang-hua. Computer-aidedmanufacturing of spiral bevel and hypoid gears by applying optimization techniques[J]. Journal of Materials Processing Technology,2001,114(1):22-35.
[57] WANG Pei-yu, Fong ZHANG-hua. Adjustability improvement of face-milling spiralbevel gears by modified radial motion (MRM) method [J]. Mechanism and MachineTheory,2005,40(1):69-89.
[58] SHIH Yi-pei, FONG Zhang-hua. Flank modification methodology for face-hobbinghypoid gears based on ease-off topography [J]. Journal of Mechanical Design,2007,129(12):1294-1302.
[59] Shih, Yi-Pei. A novel ease-off flank modification methodology for spiral bevel andhypoid gears [J]. MECHANISM AND MACHINE THEORY,2010,45(8):1108-1124
[60] WANG Pei-yu, FONG Zhang-hua. Fourth-order kinematic synthesis for face-millingspiral bevel gears with modified radial motion (MRM) correction [J]. Journal ofMechanical Design,2006,128(2):457-467.
[61] WANG Pei-yu, FONG Zhang-hua. Mathematical model of face-milling spiral bevelgear with modified radial motion (MRM) correction [J]. Mathematical and ComputerModelling,2005,41(11-12):1307-1323.
[62] FAN Q. Enhanced Algorithms of Contact Simulation for Hypoid Gear DrivesProduced by Face-Milling and Face-Hobbing Processes[J]. Journal of MechanicalDesign.2007,129(1):31-37.
[63] FAN Q, Computerized Modeling and Simulation of Spiral Bevel and Hypoid GearsManufactured by Gleason Face Hobbing Process[J]. ASME Journal of MechanicalDesign.2006,128(6):1315-1327.
[64] FAN Q, DAFOE R S, SWANGER J W. Higher-order tooth flank form error correctionfor face-milled spiral bevel and hypoid gears [J]. Journal of Mechanical Design,2008,130(7):072601.1-072601.7.
[65] FAN Q. Tooth surface error correction for face-hobbed hypoid gears [J]. Journal ofMechanical Design,2010,132(1):011004.1-011004.8.
[66] Hua, Zhao, Piao, Sheng, The measurement and evaluation method of global errorof spiral bevel gear[J] Advanced Materials Research, v204-210, p1299-1304,2011
[67] Kin V. Computerized Analysis of Gear Meshing Based on Coordinate MeasurementData[J].ASME Journal of Mechanical Design.1994,116(3):738-744.
[68] Kawasaki, Kazumasa. Accuracy measurement and evaluation of straight bevel gearmanufactured by end mill using CNC milling machine Journal of MechanicalDesign[J], Transactions of the ASME,2009,131(1):0110011-0110018.
[69]董红涛.弧齿锥齿轮技术研究的现状和发展趋势[J].机械传动,2012,36(10):115-118.
[70]马云. CIMT99磨齿机展品简评[J].磨床与磨削,2000,1:16-18.
[71]乐美豪.2005年的中国齿轮制造业[J].制造技术与机床,2007,2:44-47.
[72]王红利,钟晓玲. CIMT99从CCMT2010看数控齿轮加工机床的快速发展[J].制造技术与机床,2010,7:56-62.
[73]马云. CIMT2012齿轮装备精品荟萃[J].世界制造与装备技术市场,2012,6:82-87.
[74]李丽霞,李培军,刘新状.机床调整误差对弧齿锥齿轮大轮齿面形状影响规律的研究[J].机械传动,2006,30(4):1315..
[75]唐进元,聂金安,王智泉.螺旋锥齿轮HFT法加工的反调修正方法[J].中南大学学报(自然科学版),2012,43(6):2142-2149.
[76]唐进元,聂金安,王智泉.螺旋锥齿轮机床五轴联动数学模型创成算法[J].中南大学学报(自然科学版),2011,42(10):3033-3039
[77]唐进元；王智泉；李友元；基于优化算法的Free-form型机床各轴运动方程及其对齿面误差的影响[J].国防科技大学学报,2011,33(5):64-68.
[78]周超;唐进元;曾韬;卢延峰.螺旋锥齿轮磨齿机砂轮位置误差与齿轮齿面误差的关系[J].机械工程学报,2008,44(2):94-101.
[79]王志永,曾韬.弧齿锥齿轮基于比例修正参数的齿形误差修正[J].机械工程学报,2010,46(1):43-47.
[80]王志永,于水琴,曾韬.机床误差对螺旋锥齿轮齿形的影响规律[J].农业机械学报,2009,40(6):199-202.
[81]王志永,于水琴,曾韬.数控螺旋锥齿轮磨齿机机床加工误差补偿[J].农业机械学报,2009,40(1):222-226.
[82]周凯红,唐进元,曾韬.基于预定啮合特性的点啮合齿轮的CNC制造技术[J].机械工程学报,2009,45(9):173-182.
[83]许浩,曾韬.网络化螺旋锥齿轮齿面加工集成制造系统[J].工程图学学报,2006,2:43-50..
[84]张婧,王太勇,郑惠江,等.螺旋锥齿轮四轴联动数控两刀法加工[J].天津大学学报,2013,46(8):749-753.
[85]王时龙,孙守利,周杰,等.滚刀几何误差与齿轮几何精度的映射规律研究[J].机械工程学报,2013,49(19):119-125.
[86]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面齿轮加工调整原理[M].上海：上海科学技术出版社，1979.
[87] Litvin F L, Gutman Y. A Method of Local Synthesis of Gears Grounded on theConnection Between the Principal and Geodetic Curvatures Surfaces[J]. ASME J. ofMech. Design,1981,103:114-125.
[88]郑昌启,弧齿锥齿轮和准双曲面齿轮[M].北京:机械工业出版社,1988.
[89] Litvin F L. Theory of gearing[M]. Nauka,(in Russion),1968.
[90] L itvin F L, WangA G, Handschuh R F. Computerized Generation and Simu lation ofMeshing and Contact of Spiral Bevel Gears with Improved Geometry[J]. ComputerMethods in Applied Mechanics and Engineering,1998,158(1-2):35-64.
[91] Argyris, J., Fuentes, A., and Litvin, F. L., Computerized Integrated Approach forDesign and Stress Analysis of Spiral Bevel Gears.[J] Comput. Methods Appl. Mech.Eng.,2002,191(11):1057–1095.
[92] Fuentes, A., Litvin, F. L., Mullins, B. R., et al. Design and Stress Analysis ofLow-Noise Adjusted Bearing Contact Spiral Bevel Gears[J].ASME J. Mech. Des.,2002,124(3):524–532.
[93] F.L.Litvin,Y.Gutman. A Methods of Local Synthesis of Gears Ground on theConnections Between the Principal and Geodetic Curvatures of Surfaces[J]. ASMEJournal of Mechanical Design,1981.103(1):114-125.
[94] Litvin F L, Vecchiato D, Gurovich E, et al. Computerized Deve lopments in Design,Generation, Simulation of Meshing, and Stress Analysis of Gear Drives[J]. Meccanica,2005,40(3):291-324.
[95] Litvin F L, Vecchiato D, Yukishima K, et al. Reduction of Noise of Loaded andUnloaded Misaligned Gear Drives[J]. Computer Methods in Applied Mechanics andEngineering,2006,195(41):5523~5536.
[96] Baxter M L. Basic geometry and tooth contact of hypoid gears [J]. IndustrialMathematics,1961,11(2):1-28.
[97] Gleason Works. Understanding tooth contact analysis[M]. New York: University ofRochester Press,1981.
[98] Fan Q, Lowell W. New developments in tooth contact analysis (TCA) and loadedTCA f or spiral bevel and hypoid gear drives[J]. Gear Technology,2007,24(3):26-35.
[99] Sheveleva G I, Volkov A E, Medvedev V I. Algorithms for analysis of meshing andcontact of spiral bevel gear[J]. Mechanism and Machine Theory,2007,42(2):198-215.
[100] Litvin F L. Gear geometry and applied theory[M]. New Jersey: Prentice Hall PTR,1994:107-281.
[101]F.L. Litvin, M. De Donno, A. Peng, etc. Integrated Computer Program for Simulationof Meshing and Contact of Gear Drives[J]. Comput. Methods Appl. Mech. Engrg.2000,181(1-3):71-85.
[102]F.L. Litvin, A.G. Wang, R.F. Handschuh. Computerized generation and simulation ofmeshing and contact of spiral bevel gears with improved geometry[J]. Comput.MethodsAppl. Mech. Engrg.1998,158(1-2):35-64.
[103]Simon V V. Infuence of tooth modifications on tooth contact in face-hobbed spiralbevel gears[J]. Mechanism and machine theory,2011,46(12):1980-1998.
[104]Litivin F. L.,Sheveleva G. I.,Vecchiato D. et al. A modified approach for toothcontact analysis of gear drives and automatic determination of guess values.Computer Methods in Applied Mechanics and Engineering,2005,194(27-29):2927~2946.
[105]Litvin F L, Vecchiato D, Fuentes A, et al. Automatic determination of guess valuesfor simulation of meshing of gear drives [J]. Computer Methods in AppliedMechanics and Engineering,2004,193(33):3745-3758.
[106] Achtmann J, B r G. Optimized bearing ellipses of hypoid gears[J]. Journal ofMechanical Design,2003,125(4):739~745.
[107] Litvin F.L., Chen N.X., Chen J.S.. Computerized determination of curvature relationsand contact ellipse for conjugate surfaces[J]. Computer Methods in AppliedMechanics and Engineering,1995,125(1-4):151~170.
[108] Litvin, F T，Chen J S. Application of Finite Element Analysis for Determination ofLoad Share，Real Contact Ratio，Precision of Motion and Stress Analysis， ASMEJournal of Mechanical Design[J],1996,118(4):561-567.
[109] Fuentes, A., Litvin, F., Mullins, B., Woods, R., and Handschuh, R. F..Design andStress Analysis of Low-Noise Adjusted Bearing Contact Spiral Bevel Gears. ASMEJ. Mech. Des.,2002,124(3):524–532.
[110] Litvin F L, Fuen tes A, H ayasaka K. Design, manufacture, stress analysis, andexperimental tests of low-noise high endurance spiral bevel gears [J]. Mechanism andMachine Theory,2006,(41):83-118.
[111] Litvin F L, Fuentes Alfonso, Fan Qi, e t a l. Computerized design, simulation ofmeshing, and contact and stress analysis of face-milled formate generated spiral bevelgears [J]. Mechanism and Machine Theory,2002,37(5):441~459.
[112]Vilmos V. Simon, Machine-Tool Settings to Reduce the Sensitivity of Spiral BevelGears to Tooth Errors and Misalignments[J]. Journal of Mechanical Design,2008,130(8):082603-1-082603-10.
[113]Gosselin C, Guertin T, Simulation and Experimental Measurement of theTransmission Error of Real Hypoid Gears Under Load[J]. ASME Journal MechanicalDesign.2000,122(1):109-122.
[114] Gosselin C, Cloutier L, Nguyen Q D, A General Formulation for the Calculation ofthe Load Sharing and Transmission Error Under Load Sharing and TransmissionError Under Load of Spiral Bevel And Hypoid Gears[J]. Mech. Mach. Theory.1995,30(3):433-450.
[115] Gosselin C, Gagnon P, Cloutier L. Accurate Tooth Stiffness of Spiral Bevel GearTeeth by the Finite Strip Method[J]. ASME Journal of Mech. Des.1998,120(4):599-605.
[116] Sugimoto M, Maruyama N, Nakayama A, et al. Effect of tooth contact and geardimensions on transmission errors of loaded hypoid gears[J]. Transactions of theASME, Journal of Mechanical Design.1991,113(2):182-187.
[117] Falah B， Gosselin C， Experimental and numerical investigation of the meshingcycle and contact ratio in spiral bevel gears，Mech. Mach. Theory[J]，1998，33(1/2)，21-37.
[118]曾韬.螺旋锥齿轮设计中的轮坯修正.航空标准化与质量,1981,5：51~56
[119]曾韬.格里森磨齿机展成凸轮分析.制造技术与机床,1978,5：6~11,5.
[120]曾韬.美国格里森编制原理.制造技术与机床,1979,4：17~26,6.
[121]董学朱.准双曲面齿轮刀倾全展成切齿调整计算方法.齿轮,1988,12(5)：1-7.
[122]董学朱,金志民,叶海建.弧齿锥齿轮和准双曲面齿轮齿面接触区的计算机辅助分析.北京农业工程大学学报,1989,9(3):48-57.
[123]郑昌启.局部共轭的“密切抛物面”原理及其在弧齿锥齿轮切齿计算中的应用研究[J].重庆大学学报(自然科学版),1978,3:1-42.
[124]吴序堂.准双曲面齿轮啮合原理及其在刀倾半展成加工中的应用.西安交通大学学报,1981,15(1)：9~24.
[125]吴序堂.格里生制曲线齿锥齿轮变性半展成切齿原理.西安交通大学学报,1984,18(5):1~14.
[126]吴序堂.格里森制准双曲面齿轮刀倾全展成切齿法的研究.机械工程学报,1985,21(2)：54~69.
[127]王小椿.点啮合曲面的三阶接触分析.西安交通大学学报,1983,17(3):1~13.
[128]王小椿.线接触曲面的三阶接触分析.西安交通大学学报,1983,17(5):1~12.
[129]王小椿,吴序堂,点接触齿面三阶接触分析的进一步探讨—V/H检验理论.西安交通大学学报,1987,21(2):1~13.
[130]吴序堂,王小椿,李峰.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):47~57.
[131]田行斌,方宗德.弧齿锥齿轮加工参数的全局优化设计.航空动力学报,2000,15(l):75~77.
[132]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[J].机械科学与技术,1999,18(6):956-960.
[133]刘光磊,樊红卫,谷霁红,江平.一种弧齿锥齿轮传动性能优化方法[J].航空学报,2010,31(8):1680-1687.
[134]刘光磊,樊红卫,谷霁红,江平.弧齿锥齿轮传动误差曲线优化的半变性法[J].航空动力学报,2010,25(8):1888-1893.
[135]刘光磊,樊红卫.航空弧齿锥齿轮磨削齿面的主动优化设计[J].西北工业大学学报2011,29(3):394-399.
[136]张华,邓效忠.基于局部综合法的非零正传动弧齿锥齿轮副设计[J].农业机械学报2007,38(10):150-153.
[137]张华,邓效忠.基于局部综合的非零变位弧齿锥齿轮切齿仿真[J].农业机械学报2007,38(5):204-206.
[138]张华,邓效忠,曹雪梅.弧齿锥齿轮的TCA分析及切齿试验[J].拖拉机与农用运输车,2003(3):24-26.
[139]张华,曹雪梅,邓效忠,等.四轴联动数控螺旋锥齿轮铣齿机的齿长曲率修正,农业机械学报,2010,41(7):205-209.
[140]刘光磊,樊红卫,谷霁红,等.一种弧齿锥齿轮传动性能优化方法.航空学报,2010,31(8):1680-1687.
[141]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):
[142]黄昌华,郑昌启,李润方.弧齿锥齿轮和准双曲面齿轮承载啮合性能分析系统研究[J].自然科学进展,1992,5.
[143]方宗德，齿轮轮齿承载接触分析(LTCA)的模型和方法，机械传动[J]，1998，22(2):1-3.
[144]方宗德,邓效忠,任东锋,等.考虑边缘接触的弧齿锥齿轮承载接触分析[J],机械工程学报,2002,38(9):69-72.
[145]黄昌华,温诗铸,李润方,等.弧齿锥齿轮和准双曲面齿轮润滑加载接触分析[J].清华大学学报(自然科学版),1996,36(4):48-53.
[146]王延忠,周云飞,周济,等.考虑轮齿制造误差的螺旋锥齿轮加载接触分析[J],机械科学与技术,2002,21(2):224-227.
[147]王延忠,鄂中凯,陈良玉.航空发动机弧齿锥齿轮加载接触分析[J],机械设计与制造,1996,(3):20-22.
[148]王延忠,陈良玉,鄂中凯,等.弧齿锥齿轮轮齿边缘接触分析[J],机械设计与制造,1996,(6):23-25.
[149]王延忠,李左章,周云飞,等.螺旋锥齿轮基于离散点描述齿面接触分析研究[J],机械科学与技术,2002,21(1):3-9.
[150]王延忠,周云飞,周济,等.基于弹流润滑的弧齿锥齿轮的加工修正方法[J].机械工程学报,2002,38(7):70~75.
[151]王延忠,周云飞,周济,等.高速弧齿锥齿轮弹流润滑特性分析[J].华中科技大学学报,2001,29(12):4~7.
[152]唐进元，卢延峰，周超.有误差的螺旋锥齿轮接触分析[J],机械工程学报，2008,44(7):16-23.
[153]唐进元,卢延峰,周超,螺旋锥齿轮齿面接触分析改进算法研究[J].航空动力学报,2009,24(1):189-195.
[154]唐进元,陈嫦,蒲太平.考虑误差、轴变形和轴承刚度的弧齿锥齿轮LTCA[J].机械传动,2010,34(5):5-8.
[155]唐进元,蒲太平.基于有限元法的螺旋锥齿轮啮合刚度计算[J].机械械工程学报,2011,47(11):23-29.
[156]邓效忠,方宗德,魏冰阳,等.高重合度弧齿锥齿轮加工参数设计与重合度测定[J],机械工程学报,2004,40(6):95-99.
[157]王三民；沈允文.具有最佳加载接触性能的弧齿锥齿轮主动设计研究[J],机械科学与技术,2001,21(1):3-9.
[158]王三民,哀茄,陈作模.弧齿锥齿轮计及误差的轮齿接触分析[J],西北工业大学学报,1994,12(2):164-168.
[159]苏进展,方宗德,蔡香伟.弧齿锥齿轮计数字化齿面啮合仿真分析与实验[J],西北工业大学学报,2012,30(4):565-569.
[160]苏进展,方宗德.弧齿锥齿轮误差敏感性优化设计[J],航空动力学报,2012,27(1):183-189.
[161]李天兴,邓效忠,李聚波，等.螺旋锥齿轮齿面误差分析与自动反馈修正[J],航空动力学报,2011,26(5):1194-1200.
[162]刘光磊,樊红卫.航空弧齿锥齿轮磨削齿面的主动优化设计[J],西北工业大学学报,2011,29(3):394-399.
[163]曹雪梅,方宗德,许诺.弧齿锥齿轮的齿面主动设计及实验验证[J],机械工程学报,2008,44(7):209-214.
[164]苏进展,方宗德,谷建功.螺旋锥齿轮齿面误差修正[J],农业机械学报,2010,41(3):200-103.
[165]孟凡净.克林根贝格螺旋锥齿轮接触区域分析[D],淮南：安徽理工大学,2007.
[166]张瑞亮.双圆弧弧齿锥齿轮传动啮合特性的研究[D],山西太原：太原理工大学,2010.
[167]陈兴明.含安装误差的修形直齿-面齿轮传动齿面接触分析的研究[D],长沙：中南大学,2012.
[168]吴序堂.齿轮啮合原理（第二版）[M],西安：西安交通大学出版社,2009.
[2]齿轮手册编.齿轮手册[M].北京:机械工业出版社,2004.
[3]李强,宿宝龙,闫洪波,等.螺旋锥齿轮加工机床发展综述[J].机床与液压2012,40(8):164-166.
[4] Y.C. Tsai, P.C. Chin. Surface Geometry of Straight and Spiral Bevel Gears [J].Journal of Mechanisms, Transmissions, and Automation in Design1987,109(4):443-449.
[5] R. L. Huston, J.J. Coy. Ideal Spiral Bevel Gears—A New Approach to SurfaceGeometry [J]. Transactions of theASME1981,103(1):127-132.
[6]四川省机械工业局编.齿轮刀具设计理论基础（下）[M].北京:机械工业出版社,1982.
[7]谷凤民,周亮,段建中,等.弧齿锥齿轮的一种新型精确设计方法[J].机械设计与制造,2008,12:12-13.
[8] M. J. Al-Daccak, J. Angeles, M. A. Gonzalez-Palacios. The Modeling of BevelGears Using the Exact Spherical Involute [J]. Transactions of the ASME1994,116(2):363-368.
[9] R.L. Huston, J.J. Coy. Surface Geometry of Circular Cut Spiral Bevel Gears[J].ASME J. Mech. Des.,104(3):743–748.
[10] F.L. Litvin, A. Fuentes: Gear Geometry and Applied Theory[M]. Cambridge,University Press,2004.
[11] CHUNG-YUNN LIN and CHUNG-BIAU TSAY, ZHANG-HUA FONG.MATHEMATICAL MODEL OF SPIRAL BEVEL AND HYPOID GEARSMANUFACTURED BY THE MODIFIED ROLL Method,[J]. Mech. Mach. Theory,1997,32(2):121-136.
[12]曾韬.螺旋锥齿轮设计与加工[M].哈尔滨：哈尔滨工业大学出版社,1989.
[13]胡来瑢.空间啮合原理及应用(下)[M].煤炭工业出版社,1989.
[14] F. L. Litvin, Wei-Jiung Tsung, J.J. Coy, et al. Method for Generation of Spiral BevelGears With Conjugate Gear Tooth Surfaces, Journal of Mechanisms, Transmissions,and Automation in Design.1987.109(2):163-170.
[15]郑昌启,弧齿锥齿轮传和准双曲面齿轮—啮合原理、轮坯设计、加工调整和齿面分析计算原理[M].北京：机械工业出版社,1988.
[16]樊红卫,谷霁红.螺旋锥齿轮设计与制造的研究现状与展望[J].机械制造2009.47(540):47-49.
[17]李兆文,王太勇,陈正洪.螺旋锥齿轮技术的研究现状[J].工具技术,2007,41(10):3-6.
[18]遇立基. CIMT’99展出的数控齿轮加工机床.制造技术与机床,1999,12:6～7.
[19]彭福华.渐开线齿轮产形线切齿法[M].长春:吉林科学技术出版社,2008.
[20]彭福华.球面渐开线齿形收缩齿制弧齿锥齿轮的切齿方法:中国,200610017213.0[P].2008-04-02.
[21]杨兆军,彭福华,张学成.球面渐开线齿形弧齿锥齿轮切齿法与机床:中国,200810051354.3[P].2009-03-25.
[22]彭福华,杨兆军,于立娟.球面渐开线齿形阿基米德螺线齿锥齿轮切齿法与机床:中国,200810051355.8[P].2009-03-25.
[23]彭福华,呼咏,李春光.收缩齿制球面渐开线齿形斜直齿锥齿轮加工方法:中国,200810051356.2[P].2009-03-25.
[24] Yankun Wang, Zhaojun Yang, Linan Li. The Equation of Meshing of Spiral BevelGears Manufactured by Generating-Line Method. Open Mech. Eng. J.2011,5(1):51-55.
[25] Linan Li, Zhaojun Yang, Yankun Wang. Cutting Geometry and Base-Cone Parametersof Manufacturing Hypoid Gears by Generating-Line Method. Open Mech. Eng.J.2011,5(1):19-25.
[26]张学成,李春光,李桂娇.弧齿锥齿轮齿面发生线切齿法探讨[J].机械传动,2009,6:21-24.
[27]张学成,呼咏,杨兆军.基于齿面发生线的弧齿锥齿轮切齿运动分析[J].北京工业大学学报,2010,36(11):1441-1446.
[28]呼咏,张学成,杨兆军,等.球面渐开线齿形弧齿锥齿轮精密切齿方法[J].北京工业大学学报,2011,37(5):641-647.
[29] Zhang, X C, Wang, X, Yu, L J, Yang, Z J. Study on the generation of spiral bevelgears with spherical involute tooth profile by the tracing line[J]. P I MECH ENG C-JMEC,2012,226(C4):1097-1106.
[30]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锥齿轮啮合及加工原理[M].北京:机械工业出版社,1986.
[31]北京齿轮厂.格利森锥齿轮技术资料译文集第二分册格利森锥齿轮设计及计算[M].北京:机械工业出版社,1983.
[32]北京齿轮厂.格利森锥齿轮技术资料译文集第三分册格利森锥齿轮强度分析及计算[M].北京:机械工业出版社,1984.
[33]天津齿轮机床研究所.格利森锥具轮技术资料译文集第五分册格利森锥齿轮加工方法及轮齿接触分析[M].北京:机械工业出版社,1982.
[34]天津齿轮机床研究所.格利森锥具轮技术资料译文集第六分册格利森锥齿轮的检验及安装[M].北京:机械工业出版社,1983.
[35]董学朱.摆线齿锥齿轮及准双曲面齿轮设计和制造[M].北京:机械工业出版社,2003.
[36] Е.А.Андрущенко,蒋朝明.奥利康公司的齿轮加工[J].齿轮,1983,1:41-43.
[37] Gleason Seminar. Spiral bevel and hypoid gear technology update[R].Beijing:Gleason Corporation,2007.
[38]刘鹄然,陈良玉,刘志峰.奥利康与克林根贝尔格制铣齿机工作原理的新认识[J].机械传动,1998,22(3):36-37.
[39]董学朱.摆线齿锥齿轮连续分齿法铣齿原理的研究[J].机械传动,1999,23(2):29-30.
[40]胡来容.等高弧齿锥齿轮副的啮合理论研究(上)[J].焦作矿业学院学报.1991,3:1-21.
[41] Lelkes M, Márialigeti J, Play D. Numerical Determination of Cutting Parameters forthe Control of Klingelnberg Spiral Bevel Gear Geometry[J].ASME J. Mech. Des.2002,124(4):761–771.
[42] Litvin F L, Wang A G, Handschuh R F. Comput erized design and analysis of face-milled, uniform tooth height spiral bevel gear drives[J].Mechanical Design,2006(118):573-579.
[43] M.L.Baxter. Basie Geometry and Tooth Contact of Hypoid Gear[J]. IndustrialMathematics.1961,11(2):l-28.
[44] M.L.Baxter. Seeond Order Surface Generation[J]. Industrial Mathematies,1973,23(2):85-106.
[45]中国机械工业年委员会.中国机械通用零部件工业年鉴[M].机械工业出版社,2003.
[46] Stadtfeld H L. Advanced bevel gear technology[M].The Gleason Works,2000.
[47]庄中.格里森弧齿锥齿轮磨齿技术的发展[J].汽车工艺与材料,2004,9:11-18.
[48] Shih, Yi-Pei, Chen, Shi-Duang. Free-form flank correction in helical gear grindingusing a five-axis computer numerical control gear profile grinding machine. Journalof Manufacturing Science and Engineering[J]. Transactions of the ASME,2012,134(4):041006-1-041006-13.
[49] Wu L Y, Wei H Q, Wang X C. Geometric parameters of extended epicycloid geartooth surface generated on free-form bevel gear milling machines[J]. Journal of Xi'anJiaotong University,2001,35(3):322-325.
[50] Chang S L, Tsay C B, Nagata S. A General Mathematical Model for Gears by CNCHobbing Machines[J].1997, ASME J. Mech. Des.119():108–113.
[51]肖冬生,曾韬,殷盛福. GLEASON PHOENIX ⅡCNC磨齿机B轴运动分析[J].制造技术与机床,2005,(1):55-56.
[52]樊奇,让·德福.格里森专家制造系统(GEMS)开创弧齿锥齿轮及双曲面齿轮数字化制造新纪元[J].世界制造技术与装备市场,2005,4:87-93.
[53]周军辉刘宝生陈建平徐华兵.基于PHOENIX系列磨齿机的磨齿参数设计[J].精密制造与自动,2003,155(3):40-42.
[54]吴训成,陈志恒,胡宁.曲线齿锥齿轮点啮合齿面主动控制加工技术[M].机械工程学报,2005,41(10):97-101.
[55] Stadtfeld H J. The Universal Motion Concept for Bevel Gear Production,1999[C].Fourth World Congress on Gearing and Power Transmissions, Paris:595–607.
[56] LING Chung-yunn, TSAY Chung-biau. FONG Zhang-hua. Computer-aidedmanufacturing of spiral bevel and hypoid gears by applying optimization techniques[J]. Journal of Materials Processing Technology,2001,114(1):22-35.
[57] WANG Pei-yu, Fong ZHANG-hua. Adjustability improvement of face-milling spiralbevel gears by modified radial motion (MRM) method [J]. Mechanism and MachineTheory,2005,40(1):69-89.
[58] SHIH Yi-pei, FONG Zhang-hua. Flank modification methodology for face-hobbinghypoid gears based on ease-off topography [J]. Journal of Mechanical Design,2007,129(12):1294-1302.
[59] Shih, Yi-Pei. A novel ease-off flank modification methodology for spiral bevel andhypoid gears [J]. MECHANISM AND MACHINE THEORY,2010,45(8):1108-1124
[60] WANG Pei-yu, FONG Zhang-hua. Fourth-order kinematic synthesis for face-millingspiral bevel gears with modified radial motion (MRM) correction [J]. Journal ofMechanical Design,2006,128(2):457-467.
[61] WANG Pei-yu, FONG Zhang-hua. Mathematical model of face-milling spiral bevelgear with modified radial motion (MRM) correction [J]. Mathematical and ComputerModelling,2005,41(11-12):1307-1323.
[62] FAN Q. Enhanced Algorithms of Contact Simulation for Hypoid Gear DrivesProduced by Face-Milling and Face-Hobbing Processes[J]. Journal of MechanicalDesign.2007,129(1):31-37.
[63] FAN Q, Computerized Modeling and Simulation of Spiral Bevel and Hypoid GearsManufactured by Gleason Face Hobbing Process[J]. ASME Journal of MechanicalDesign.2006,128(6):1315-1327.
[64] FAN Q, DAFOE R S, SWANGER J W. Higher-order tooth flank form error correctionfor face-milled spiral bevel and hypoid gears [J]. Journal of Mechanical Design,2008,130(7):072601.1-072601.7.
[65] FAN Q. Tooth surface error correction for face-hobbed hypoid gears [J]. Journal ofMechanical Design,2010,132(1):011004.1-011004.8.
[66] Hua, Zhao, Piao, Sheng, The measurement and evaluation method of global errorof spiral bevel gear[J] Advanced Materials Research, v204-210, p1299-1304,2011
[67] Kin V. Computerized Analysis of Gear Meshing Based on Coordinate MeasurementData[J].ASME Journal of Mechanical Design.1994,116(3):738-744.
[68] Kawasaki, Kazumasa. Accuracy measurement and evaluation of straight bevel gearmanufactured by end mill using CNC milling machine Journal of MechanicalDesign[J], Transactions of the ASME,2009,131(1):0110011-0110018.
[69]董红涛.弧齿锥齿轮技术研究的现状和发展趋势[J].机械传动,2012,36(10):115-118.
[70]马云. CIMT99磨齿机展品简评[J].磨床与磨削,2000,1:16-18.
[71]乐美豪.2005年的中国齿轮制造业[J].制造技术与机床,2007,2:44-47.
[72]王红利,钟晓玲. CIMT99从CCMT2010看数控齿轮加工机床的快速发展[J].制造技术与机床,2010,7:56-62.
[73]马云. CIMT2012齿轮装备精品荟萃[J].世界制造与装备技术市场,2012,6:82-87.
[74]李丽霞,李培军,刘新状.机床调整误差对弧齿锥齿轮大轮齿面形状影响规律的研究[J].机械传动,2006,30(4):1315..
[75]唐进元,聂金安,王智泉.螺旋锥齿轮HFT法加工的反调修正方法[J].中南大学学报(自然科学版),2012,43(6):2142-2149.
[76]唐进元,聂金安,王智泉.螺旋锥齿轮机床五轴联动数学模型创成算法[J].中南大学学报(自然科学版),2011,42(10):3033-3039
[77]唐进元；王智泉；李友元；基于优化算法的Free-form型机床各轴运动方程及其对齿面误差的影响[J].国防科技大学学报,2011,33(5):64-68.
[78]周超;唐进元;曾韬;卢延峰.螺旋锥齿轮磨齿机砂轮位置误差与齿轮齿面误差的关系[J].机械工程学报,2008,44(2):94-101.
[79]王志永,曾韬.弧齿锥齿轮基于比例修正参数的齿形误差修正[J].机械工程学报,2010,46(1):43-47.
[80]王志永,于水琴,曾韬.机床误差对螺旋锥齿轮齿形的影响规律[J].农业机械学报,2009,40(6):199-202.
[81]王志永,于水琴,曾韬.数控螺旋锥齿轮磨齿机机床加工误差补偿[J].农业机械学报,2009,40(1):222-226.
[82]周凯红,唐进元,曾韬.基于预定啮合特性的点啮合齿轮的CNC制造技术[J].机械工程学报,2009,45(9):173-182.
[83]许浩,曾韬.网络化螺旋锥齿轮齿面加工集成制造系统[J].工程图学学报,2006,2:43-50..
[84]张婧,王太勇,郑惠江,等.螺旋锥齿轮四轴联动数控两刀法加工[J].天津大学学报,2013,46(8):749-753.
[85]王时龙,孙守利,周杰,等.滚刀几何误差与齿轮几何精度的映射规律研究[J].机械工程学报,2013,49(19):119-125.
[86]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面齿轮加工调整原理[M].上海：上海科学技术出版社，1979.
[87] Litvin F L, Gutman Y. A Method of Local Synthesis of Gears Grounded on theConnection Between the Principal and Geodetic Curvatures Surfaces[J]. ASME J. ofMech. Design,1981,103:114-125.
[88]郑昌启,弧齿锥齿轮和准双曲面齿轮[M].北京:机械工业出版社,1988.
[89] Litvin F L. Theory of gearing[M]. Nauka,(in Russion),1968.
[90] L itvin F L, WangA G, Handschuh R F. Computerized Generation and Simu lation ofMeshing and Contact of Spiral Bevel Gears with Improved Geometry[J]. ComputerMethods in Applied Mechanics and Engineering,1998,158(1-2):35-64.
[91] Argyris, J., Fuentes, A., and Litvin, F. L., Computerized Integrated Approach forDesign and Stress Analysis of Spiral Bevel Gears.[J] Comput. Methods Appl. Mech.Eng.,2002,191(11):1057–1095.
[92] Fuentes, A., Litvin, F. L., Mullins, B. R., et al. Design and Stress Analysis ofLow-Noise Adjusted Bearing Contact Spiral Bevel Gears[J].ASME J. Mech. Des.,2002,124(3):524–532.
[93] F.L.Litvin,Y.Gutman. A Methods of Local Synthesis of Gears Ground on theConnections Between the Principal and Geodetic Curvatures of Surfaces[J]. ASMEJournal of Mechanical Design,1981.103(1):114-125.
[94] Litvin F L, Vecchiato D, Gurovich E, et al. Computerized Deve lopments in Design,Generation, Simulation of Meshing, and Stress Analysis of Gear Drives[J]. Meccanica,2005,40(3):291-324.
[95] Litvin F L, Vecchiato D, Yukishima K, et al. Reduction of Noise of Loaded andUnloaded Misaligned Gear Drives[J]. Computer Methods in Applied Mechanics andEngineering,2006,195(41):5523~5536.
[96] Baxter M L. Basic geometry and tooth contact of hypoid gears [J]. IndustrialMathematics,1961,11(2):1-28.
[97] Gleason Works. Understanding tooth contact analysis[M]. New York: University ofRochester Press,1981.
[98] Fan Q, Lowell W. New developments in tooth contact analysis (TCA) and loadedTCA f or spiral bevel and hypoid gear drives[J]. Gear Technology,2007,24(3):26-35.
[99] Sheveleva G I, Volkov A E, Medvedev V I. Algorithms for analysis of meshing andcontact of spiral bevel gear[J]. Mechanism and Machine Theory,2007,42(2):198-215.
[100] Litvin F L. Gear geometry and applied theory[M]. New Jersey: Prentice Hall PTR,1994:107-281.
[101]F.L. Litvin, M. De Donno, A. Peng, etc. Integrated Computer Program for Simulationof Meshing and Contact of Gear Drives[J]. Comput. Methods Appl. Mech. Engrg.2000,181(1-3):71-85.
[102]F.L. Litvin, A.G. Wang, R.F. Handschuh. Computerized generation and simulation ofmeshing and contact of spiral bevel gears with improved geometry[J]. Comput.MethodsAppl. Mech. Engrg.1998,158(1-2):35-64.
[103]Simon V V. Infuence of tooth modifications on tooth contact in face-hobbed spiralbevel gears[J]. Mechanism and machine theory,2011,46(12):1980-1998.
[104]Litivin F. L.,Sheveleva G. I.,Vecchiato D. et al. A modified approach for toothcontact analysis of gear drives and automatic determination of guess values.Computer Methods in Applied Mechanics and Engineering,2005,194(27-29):2927~2946.
[105]Litvin F L, Vecchiato D, Fuentes A, et al. Automatic determination of guess valuesfor simulation of meshing of gear drives [J]. Computer Methods in AppliedMechanics and Engineering,2004,193(33):3745-3758.
[106] Achtmann J, B r G. Optimized bearing ellipses of hypoid gears[J]. Journal ofMechanical Design,2003,125(4):739~745.
[107] Litvin F.L., Chen N.X., Chen J.S.. Computerized determination of curvature relationsand contact ellipse for conjugate surfaces[J]. Computer Methods in AppliedMechanics and Engineering,1995,125(1-4):151~170.
[108] Litvin, F T，Chen J S. Application of Finite Element Analysis for Determination ofLoad Share，Real Contact Ratio，Precision of Motion and Stress Analysis， ASMEJournal of Mechanical Design[J],1996,118(4):561-567.
[109] Fuentes, A., Litvin, F., Mullins, B., Woods, R., and Handschuh, R. F..Design andStress Analysis of Low-Noise Adjusted Bearing Contact Spiral Bevel Gears. ASMEJ. Mech. Des.,2002,124(3):524–532.
[110] Litvin F L, Fuen tes A, H ayasaka K. Design, manufacture, stress analysis, andexperimental tests of low-noise high endurance spiral bevel gears [J]. Mechanism andMachine Theory,2006,(41):83-118.
[111] Litvin F L, Fuentes Alfonso, Fan Qi, e t a l. Computerized design, simulation ofmeshing, and contact and stress analysis of face-milled formate generated spiral bevelgears [J]. Mechanism and Machine Theory,2002,37(5):441~459.
[112]Vilmos V. Simon, Machine-Tool Settings to Reduce the Sensitivity of Spiral BevelGears to Tooth Errors and Misalignments[J]. Journal of Mechanical Design,2008,130(8):082603-1-082603-10.
[113]Gosselin C, Guertin T, Simulation and Experimental Measurement of theTransmission Error of Real Hypoid Gears Under Load[J]. ASME Journal MechanicalDesign.2000,122(1):109-122.
[114] Gosselin C, Cloutier L, Nguyen Q D, A General Formulation for the Calculation ofthe Load Sharing and Transmission Error Under Load Sharing and TransmissionError Under Load of Spiral Bevel And Hypoid Gears[J]. Mech. Mach. Theory.1995,30(3):433-450.
[115] Gosselin C, Gagnon P, Cloutier L. Accurate Tooth Stiffness of Spiral Bevel GearTeeth by the Finite Strip Method[J]. ASME Journal of Mech. Des.1998,120(4):599-605.
[116] Sugimoto M, Maruyama N, Nakayama A, et al. Effect of tooth contact and geardimensions on transmission errors of loaded hypoid gears[J]. Transactions of theASME, Journal of Mechanical Design.1991,113(2):182-187.
[117] Falah B， Gosselin C， Experimental and numerical investigation of the meshingcycle and contact ratio in spiral bevel gears，Mech. Mach. Theory[J]，1998，33(1/2)，21-37.
[118]曾韬.螺旋锥齿轮设计中的轮坯修正.航空标准化与质量,1981,5：51~56
[119]曾韬.格里森磨齿机展成凸轮分析.制造技术与机床,1978,5：6~11,5.
[120]曾韬.美国格里森
[121]董学朱.准双曲面齿轮刀倾全展成切齿调整计算方法.齿轮,1988,12(5)：1-7.
[122]董学朱,金志民,叶海建.弧齿锥齿轮和准双曲面齿轮齿面接触区的计算机辅助分析.北京农业工程大学学报,1989,9(3):48-57.
[123]郑昌启.局部共轭的“密切抛物面”原理及其在弧齿锥齿轮切齿计算中的应用研究[J].重庆大学学报(自然科学版),1978,3:1-42.
[124]吴序堂.准双曲面齿轮啮合原理及其在刀倾半展成加工中的应用.西安交通大学学报,1981,15(1)：9~24.
[125]吴序堂.格里生制曲线齿锥齿轮变性半展成切齿原理.西安交通大学学报,1984,18(5):1~14.
[126]吴序堂.格里森制准双曲面齿轮刀倾全展成切齿法的研究.机械工程学报,1985,21(2)：54~69.
[127]王小椿.点啮合曲面的三阶接触分析.西安交通大学学报,1983,17(3):1~13.
[128]王小椿.线接触曲面的三阶接触分析.西安交通大学学报,1983,17(5):1~12.
[129]王小椿,吴序堂,点接触齿面三阶接触分析的进一步探讨—V/H检验理论.西安交通大学学报,1987,21(2):1~13.
[130]吴序堂,王小椿,李峰.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):47~57.
[131]田行斌,方宗德.弧齿锥齿轮加工参数的全局优化设计.航空动力学报,2000,15(l):75~77.
[132]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[J].机械科学与技术,1999,18(6):956-960.
[133]刘光磊,樊红卫,谷霁红,江平.一种弧齿锥齿轮传动性能优化方法[J].航空学报,2010,31(8):1680-1687.
[134]刘光磊,樊红卫,谷霁红,江平.弧齿锥齿轮传动误差曲线优化的半变性法[J].航空动力学报,2010,25(8):1888-1893.
[135]刘光磊,樊红卫.航空弧齿锥齿轮磨削齿面的主动优化设计[J].西北工业大学学报2011,29(3):394-399.
[136]张华,邓效忠.基于局部综合法的非零正传动弧齿锥齿轮副设计[J].农业机械学报2007,38(10):150-153.
[137]张华,邓效忠.基于局部综合的非零变位弧齿锥齿轮切齿仿真[J].农业机械学报2007,38(5):204-206.
[138]张华,邓效忠,曹雪梅.弧齿锥齿轮的TCA分析及切齿试验[J].拖拉机与农用运输车,2003(3):24-26.
[139]张华,曹雪梅,邓效忠,等.四轴联动数控螺旋锥齿轮铣齿机的齿长曲率修正,农业机械学报,2010,41(7):205-209.
[140]刘光磊,樊红卫,谷霁红,等.一种弧齿锥齿轮传动性能优化方法.航空学报,2010,31(8):1680-1687.
[141]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):
[142]黄昌华,郑昌启,李润方.弧齿锥齿轮和准双曲面齿轮承载啮合性能分析系统研究[J].自然科学进展,1992,5.
[143]方宗德，齿轮轮齿承载接触分析(LTCA)的模型和方法，机械传动[J]，1998，22(2):1-3.
[144]方宗德,邓效忠,任东锋,等.考虑边缘接触的弧齿锥齿轮承载接触分析[J],机械工程学报,2002,38(9):69-72.
[145]黄昌华,温诗铸,李润方,等.弧齿锥齿轮和准双曲面齿轮润滑加载接触分析[J].清华大学学报(自然科学版),1996,36(4):48-53.
[146]王延忠,周云飞,周济,等.考虑轮齿制造误差的螺旋锥齿轮加载接触分析[J],机械科学与技术,2002,21(2):224-227.
[147]王延忠,鄂中凯,陈良玉.航空发动机弧齿锥齿轮加载接触分析[J],机械设计与制造,1996,(3):20-22.
[148]王延忠,陈良玉,鄂中凯,等.弧齿锥齿轮轮齿边缘接触分析[J],机械设计与制造,1996,(6):23-25.
[149]王延忠,李左章,周云飞,等.螺旋锥齿轮基于离散点描述齿面接触分析研究[J],机械科学与技术,2002,21(1):3-9.
[150]王延忠,周云飞,周济,等.基于弹流润滑的弧齿锥齿轮的加工修正方法[J].机械工程学报,2002,38(7):70~75.
[151]王延忠,周云飞,周济,等.高速弧齿锥齿轮弹流润滑特性分析[J].华中科技大学学报,2001,29(12):4~7.
[152]唐进元，卢延峰，周超.有误差的螺旋锥齿轮接触分析[J],机械工程学报，2008,44(7):16-23.
[153]唐进元,卢延峰,周超,螺旋锥齿轮齿面接触分析改进算法研究[J].航空动力学报,2009,24(1):189-195.
[154]唐进元,陈嫦,蒲太平.考虑误差、轴变形和轴承刚度的弧齿锥齿轮LTCA[J].机械传动,2010,34(5):5-8.
[155]唐进元,蒲太平.基于有限元法的螺旋锥齿轮啮合刚度计算[J].机械械工程学报,2011,47(11):23-29.
[156]邓效忠,方宗德,魏冰阳,等.高重合度弧齿锥齿轮加工参数设计与重合度测定[J],机械工程学报,2004,40(6):95-99.
[157]王三民；沈允文.具有最佳加载接触性能的弧齿锥齿轮主动设计研究[J],机械科学与技术,2001,21(1):3-9.
[158]王三民,哀茄,陈作模.弧齿锥齿轮计及误差的轮齿接触分析[J],西北工业大学学报,1994,12(2):164-168.
[159]苏进展,方宗德,蔡香伟.弧齿锥齿轮计数字化齿面啮合仿真分析与实验[J],西北工业大学学报,2012,30(4):565-569.
[160]苏进展,方宗德.弧齿锥齿轮误差敏感性优化设计[J],航空动力学报,2012,27(1):183-189.
[161]李天兴,邓效忠,李聚波，等.螺旋锥齿轮齿面误差分析与自动反馈修正[J],航空动力学报,2011,26(5):1194-1200.
[162]刘光磊,樊红卫.航空弧齿锥齿轮磨削齿面的主动优化设计[J],西北工业大学学报,2011,29(3):394-399.
[163]曹雪梅,方宗德,许诺.弧齿锥齿轮的齿面主动设计及实验验证[J],机械工程学报,2008,44(7):209-214.
[164]苏进展,方宗德,谷建功.螺旋锥齿轮齿面误差修正[J],农业机械学报,2010,41(3):200-103.
[165]孟凡净.克林根贝格螺旋锥齿轮接触区域分析[D],淮南：安徽理工大学,2007.
[166]张瑞亮.双圆弧弧齿锥齿轮传动啮合特性的研究[D],山西太原：太原理工大学,2010.
[167]陈兴明.含安装误差的修形直齿-面齿轮传动齿面接触分析的研究[D],长沙：中南大学,2012.
[168]吴序堂.齿轮啮合原理（第二版）[M],西安：西安交通大学出版社,2009.
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