渐开线环形齿球齿轮传动理论研究
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摘要
随着现代齿轮传动技术的发展,在一些新兴的需要多自由度传动的领域,比如机器人领域、仿生技术领域、矢量推进技术领域等,采用传统的单自由度齿轮传动机构给研究工作带来了一定难度,因而,当Trallfa球齿轮——世界上第一种双自由度齿轮传动机构问世时,立即引起了工程界的广泛关注。但是由于Trallfa球齿轮的离散锥形轮齿存在加工难度大、齿廓承载能力低等缺陷,因此,并没有得到推广应用。此后一些学者对Trallfa球齿轮的齿形设计作了一些改进,出现了离散圆弧齿、离散渐开线环形齿、离散锥形齿等双自由度球齿轮传动机构,但由于都没能突破离散齿的齿形设计局限,因此在降低加工难度和提高承载能力方面的效果不佳。本文研究的渐开线环形齿球齿轮轮齿在球面上连续分布,克服了离散齿的局限,具有易于加工和承载能力较高的特点。目前,在传动的基本原理和运动学分析等方面进行了初步研究,但是作为双自由度齿轮传动机构,其传动特性比传统齿轮复杂,必须经过更加深入的传动理论研究才能为其传动技术的进一步发展奠定良好的理论基础。本论文研究工作的主要任务就是深入研究渐开线环形齿球齿轮传动的若干理论问题,建立一个相对完整的球齿轮传动理论体系,也期望能对双自由度齿轮传动技术的发展起到一定的推动作用。论文的研究工作包括以下几个部分:
1.研究了球齿轮副的双自由度共轭齿面啮合问题。建立了球齿轮副的双参数运动学模型,对球齿轮副的两种基本机构——理想机构与万向节式机构进行了运动学原理分析。在此基础上,分析了球齿轮相啮合齿面在接触点处的相对运动情况,建立了球齿轮副的双参数啮合方程,据此得到了相应的啮合面方程及共轭齿面方程。采用计算机仿真方法对两种球齿轮机构的双自由度共轭齿面啮合原理进行了分析与验证,结果表明,理想机构与万向节式机构的相啮合齿面都是共轭齿面。
2.采用滑动系数作为衡量球齿轮齿面滑动磨损程度的重要指标。结合球齿轮副的双自由度啮合原理及滑动系数的基本定义,对球齿轮齿面的滑动系数计算方法进行了研究,并给出了具体的计算公式,其齿面的滑动系数是关于运动参数——偏摆角φ_y1和方位角φ_z1的二元函数,并与球齿轮沿空间两个分方向运动的角速度比ε有关。据此,对球齿轮理想机构与万向节式机构的齿面滑动系数进行了分析计算,由两种球齿轮机构滑动系数分布规律分析可知:球齿轮齿廓中部的滑动磨损最轻,齿顶次之,齿根磨损最为严重。而且,在万向节式机构中,安装轴对齿面滑动磨损的影响是良性的。
3.进行了球齿轮齿面接触特性分析与应力分析。通过理论证明,球齿轮是马鞍面与凸面之间的接触:除极轴重合位置为线接触外,其余位置都为点接触。建立了用于计算机仿真计算的球齿轮齿面啮合模型,通过求解5个方程组成的非线性方程组,可以得到齿面上瞬时接触点的位置,据此对球齿轮副接触点轨迹进行了研究。采用曲率分析法与齿面分离拓扑法相结合对球齿轮的接触椭圆进行了理论与仿真计算,得到了接触椭圆在球齿轮齿面上的分布规律。采用有限元法,对球齿轮齿廓强度最弱的中凸齿进行了接触应力与弯曲应力的有限元计算。结果表明:接触应力在齿面上呈椭圆状分布;在不计重合度时,接触应力在齿中部较小,在齿根部与齿顶部较大;在考虑重合度时,齿根部与齿顶部的接触应力明显减小;弯曲应力较小,最大值出现在轮齿中部。
4.分析研究了安装误差对球齿轮机构传动误差的影响。分别建立了球齿轮副的两种最常用机构——万向节式机构与指向机构的传动误差模型与指向误差模型。分别建立了两种机构在存在安装误差——定轴与动轴的轴向偏差(包括竖直与水平轴向偏差)及中心距误差时的运动学模型。在此基础上,对万向节式机构的传动误差进行了计算与分析;分别采用两种指向误差的评价方法,对指向机构的指向误差进行了计算与分析。结果对球齿轮机构的装配及其传动误差的测量具有重要的参考价值。
5.采用磨削加工方法解决球齿轮精加工问题。根据球齿轮的齿形特点,分别采用成形法与范成法两种方法对球齿轮磨削加工方法进行了研究。针对成形法磨削,根据磨削加工所需的自由度要求,设计了磨削机床及指状砂轮,分析了机床运动链之间的运动关系及指状砂轮的磨削原理。针对范成法磨削加工,同样设计了磨削机床及盘形砂轮,建立了球齿轮与盘形砂轮之间的共轭啮合运动方程式,详细分析了由盘形砂轮加工球齿轮渐开线齿面及齿根过渡曲面的生成原理。最后,在建立盘形砂轮数学模型的基础上,得到了采用盘形砂轮加工球齿轮齿廓曲面的数学模型,据此可进行机床加工参数的设置与调整。
With the development of modern gear transmission technology, in some rising fields which need multi-degree-of-freedom transmission, such as the fields of robotics, bionics, and vector propulsion, and so on, the traditional single-degree-of-freedom gear mechanisms increase the difficulty about the research work. So, Trallfa spherical gear, the first 2-DOF gear mechanism, is focused on in engineering immediately. However, since Trallfa spherical gear with discrete cone-shaped concave teeth has two disadvantages: difficulty to manufacture and low load capacity, it hasn’t been used widly. Afterword, some researchers redesigned the tooth of Trallfa spherical gear, and some 2-DOF gear mechanisms appeared, such as spherical gear with discrete circular arc teeth, spherical gear with discrete ring-involute teeth, spherical gear with discrete cone teeth and so on. These teeth designs haven’t broken through the limitation of discrete teeth; therefore the difficulties in manufacture and low load capacity haven’t been improved evidently. A spherical gear with continuous ring-involute tooth studied in this paper overcomes the defects of discrete teeth and has the advantages of easy manufacture and good load capacity. Some basic researches about its transmission theory and kinematic analysis have been made. However, as a 2-DOF gear driven mechanism, the transmission characteristics of the spherical gear with continuous ring-involute tooth are more complex than the traditional gears, and therefore it is very necessary to make in-depth research in theory for the progress of its transmission technology. This thesis is dedicated to solving some problems in theory about the spherical gear transmission, in order to set up a relatively whole system of transmission theory of the spherical gear, and promote the development of 2-DOF gear transmission technology. The major research efforts include the following aspects.
1. The 2-DOF meshing theory of conjugate surfaces of the spherical gear pair is studied. The two-parameter kinematic model of the spherical gear pair is established, and the kinematic analysis of two basic mechanisms, the ideal mechanism and the gimbal mechanism, is performed. And then, the relative movement between two teeth surfaces in mesh is analyzed and based on the two-parameter meshing model, the equations of the meshing cone surface and conjugate surface are established. The simulation of the conjugate meshing principle of the ideal mechanism and the gimbal mechanism indicates that the teeth surfaces in mesh are the conjugate surfaces.
2. Sliding ratio is an important index which can evaluate the wear of spherical gear tooth surface. According to the 2-DOF meshing theory of the spherical gear and the basic definition of sliding ratio, the calculating method of the sliding ratio of the spherical gear is studied, and the specific equation is received, which is a dual function with the swaying angleφ_y1 and the azimuth angleφ_z1 and relates to the angle velocity ratioεalong with two respective motion directions. Then, the sliding ratios of the teeth surfaces in mesh in the ideal mechanism and the gimbal mechanism are computed and analyzed and according to the distribution of sliding ratio, the following rules can be gotten: wear on tooth middle part is slight; wear on tooth tip is relatively severer; wear on tooth base is the severest. In addition, in the gimbal mechanism, the installed axes have a good effect on sliding wear of tooth surface of the spherical gear.
3. The tooth contact characteristics analysis and stress analysis for the spherical gear are investigated. Theoretical derivation validates that tooth contact form of the meshing spherical gears is a point contact between a convexity and a saddle surface except the position in which the polar axes of two spherical gears are collinear to each other. Then, the meshing model of the spherical gear pair for computer simulation is set up, and the position of instantaneous contact point of two spherical gears can be gotten using the nonlinear solver composed of five equations. Furthermore, the contact point paths of the spherical gear in mesh are studied. Combined the curvature analysis method with the tooth surface separation topology method, the contact ellipse of the spherical gear pair is calculated and simulated, and the distributing rule is gained. Finite element analysis is applied to perform contact stress analysis and bending stress analysis of the convex tooth, the weakest tooth. The result indicates that: the distributing form of contact stress is an ellipse; regardless of contact ratio, contact stress is large on tooth base and tooth tip, and contact stress is little on tooth middle part; considering contact ratio, contact stress is evidently decreased on tooth base and tooth tip; bending stress is little, and the maximum of bending stress occurs on tooth middle part.
4. The effect of assemble errors on the transmission error of the spherical gear mechanism is analyzed and simulated. The transmission error model and pointing error models of two mechanisms of the spherical gear sets in common use, the gimbal mechanism and the pointing mechanism, are set up, respectively. After that, the kinematic models of two mechanisms with assemble errors are built, and the assemble errors comprise the vertical and horizontial axial misalignment of the fixed axis and rotating axis, and the center distance error of two spherical gears, respectively. With these models above, the transmission errors of the gimbal mechanism are simulated and analyzed, and using two computation methods, the pointing errors of the pointing mechanism are simulated and analyzed. The results are useful for the installation and measurement of the spherical gear pairs in practice.
5. Grinding method is the key for solving the finishing machining problem of the spherical gear. According to tooth surface characteristics of the spherical gear, with forming method and generating method, respectively, the grinding manufacture of the spherical gear are researched. To grinding with the forming method, according to the required degrees of freedom, a grinding machine and a fingerlike grinding wheel are designed, then the relationship of motions of the machine is analyzed and the grinding principle of the fingerlike grinding wheel is studied. To grinding with the generating method, similarly, a grinding mchine and plate grinding wheels are designed, and then the conjugate meshing kinematic equations are set up. The generating process of the involute tooth surface and the tooth base surface with the plate grinding wheels are introduced in detail. In the end, based on the mathematical models of the plate grinding wheels, the mathematical models of the spherical gear pair are received and the machining parameters can be set and adjusted.
1.研究了球齿轮副的双自由度共轭齿面啮合问题。建立了球齿轮副的双参数运动学模型,对球齿轮副的两种基本机构——理想机构与万向节式机构进行了运动学原理分析。在此基础上,分析了球齿轮相啮合齿面在接触点处的相对运动情况,建立了球齿轮副的双参数啮合方程,据此得到了相应的啮合面方程及共轭齿面方程。采用计算机仿真方法对两种球齿轮机构的双自由度共轭齿面啮合原理进行了分析与验证,结果表明,理想机构与万向节式机构的相啮合齿面都是共轭齿面。
2.采用滑动系数作为衡量球齿轮齿面滑动磨损程度的重要指标。结合球齿轮副的双自由度啮合原理及滑动系数的基本定义,对球齿轮齿面的滑动系数计算方法进行了研究,并给出了具体的计算公式,其齿面的滑动系数是关于运动参数——偏摆角φ_y1和方位角φ_z1的二元函数,并与球齿轮沿空间两个分方向运动的角速度比ε有关。据此,对球齿轮理想机构与万向节式机构的齿面滑动系数进行了分析计算,由两种球齿轮机构滑动系数分布规律分析可知:球齿轮齿廓中部的滑动磨损最轻,齿顶次之,齿根磨损最为严重。而且,在万向节式机构中,安装轴对齿面滑动磨损的影响是良性的。
3.进行了球齿轮齿面接触特性分析与应力分析。通过理论证明,球齿轮是马鞍面与凸面之间的接触:除极轴重合位置为线接触外,其余位置都为点接触。建立了用于计算机仿真计算的球齿轮齿面啮合模型,通过求解5个方程组成的非线性方程组,可以得到齿面上瞬时接触点的位置,据此对球齿轮副接触点轨迹进行了研究。采用曲率分析法与齿面分离拓扑法相结合对球齿轮的接触椭圆进行了理论与仿真计算,得到了接触椭圆在球齿轮齿面上的分布规律。采用有限元法,对球齿轮齿廓强度最弱的中凸齿进行了接触应力与弯曲应力的有限元计算。结果表明:接触应力在齿面上呈椭圆状分布;在不计重合度时,接触应力在齿中部较小,在齿根部与齿顶部较大;在考虑重合度时,齿根部与齿顶部的接触应力明显减小;弯曲应力较小,最大值出现在轮齿中部。
4.分析研究了安装误差对球齿轮机构传动误差的影响。分别建立了球齿轮副的两种最常用机构——万向节式机构与指向机构的传动误差模型与指向误差模型。分别建立了两种机构在存在安装误差——定轴与动轴的轴向偏差(包括竖直与水平轴向偏差)及中心距误差时的运动学模型。在此基础上,对万向节式机构的传动误差进行了计算与分析;分别采用两种指向误差的评价方法,对指向机构的指向误差进行了计算与分析。结果对球齿轮机构的装配及其传动误差的测量具有重要的参考价值。
5.采用磨削加工方法解决球齿轮精加工问题。根据球齿轮的齿形特点,分别采用成形法与范成法两种方法对球齿轮磨削加工方法进行了研究。针对成形法磨削,根据磨削加工所需的自由度要求,设计了磨削机床及指状砂轮,分析了机床运动链之间的运动关系及指状砂轮的磨削原理。针对范成法磨削加工,同样设计了磨削机床及盘形砂轮,建立了球齿轮与盘形砂轮之间的共轭啮合运动方程式,详细分析了由盘形砂轮加工球齿轮渐开线齿面及齿根过渡曲面的生成原理。最后,在建立盘形砂轮数学模型的基础上,得到了采用盘形砂轮加工球齿轮齿廓曲面的数学模型,据此可进行机床加工参数的设置与调整。
With the development of modern gear transmission technology, in some rising fields which need multi-degree-of-freedom transmission, such as the fields of robotics, bionics, and vector propulsion, and so on, the traditional single-degree-of-freedom gear mechanisms increase the difficulty about the research work. So, Trallfa spherical gear, the first 2-DOF gear mechanism, is focused on in engineering immediately. However, since Trallfa spherical gear with discrete cone-shaped concave teeth has two disadvantages: difficulty to manufacture and low load capacity, it hasn’t been used widly. Afterword, some researchers redesigned the tooth of Trallfa spherical gear, and some 2-DOF gear mechanisms appeared, such as spherical gear with discrete circular arc teeth, spherical gear with discrete ring-involute teeth, spherical gear with discrete cone teeth and so on. These teeth designs haven’t broken through the limitation of discrete teeth; therefore the difficulties in manufacture and low load capacity haven’t been improved evidently. A spherical gear with continuous ring-involute tooth studied in this paper overcomes the defects of discrete teeth and has the advantages of easy manufacture and good load capacity. Some basic researches about its transmission theory and kinematic analysis have been made. However, as a 2-DOF gear driven mechanism, the transmission characteristics of the spherical gear with continuous ring-involute tooth are more complex than the traditional gears, and therefore it is very necessary to make in-depth research in theory for the progress of its transmission technology. This thesis is dedicated to solving some problems in theory about the spherical gear transmission, in order to set up a relatively whole system of transmission theory of the spherical gear, and promote the development of 2-DOF gear transmission technology. The major research efforts include the following aspects.
1. The 2-DOF meshing theory of conjugate surfaces of the spherical gear pair is studied. The two-parameter kinematic model of the spherical gear pair is established, and the kinematic analysis of two basic mechanisms, the ideal mechanism and the gimbal mechanism, is performed. And then, the relative movement between two teeth surfaces in mesh is analyzed and based on the two-parameter meshing model, the equations of the meshing cone surface and conjugate surface are established. The simulation of the conjugate meshing principle of the ideal mechanism and the gimbal mechanism indicates that the teeth surfaces in mesh are the conjugate surfaces.
2. Sliding ratio is an important index which can evaluate the wear of spherical gear tooth surface. According to the 2-DOF meshing theory of the spherical gear and the basic definition of sliding ratio, the calculating method of the sliding ratio of the spherical gear is studied, and the specific equation is received, which is a dual function with the swaying angleφ_y1 and the azimuth angleφ_z1 and relates to the angle velocity ratioεalong with two respective motion directions. Then, the sliding ratios of the teeth surfaces in mesh in the ideal mechanism and the gimbal mechanism are computed and analyzed and according to the distribution of sliding ratio, the following rules can be gotten: wear on tooth middle part is slight; wear on tooth tip is relatively severer; wear on tooth base is the severest. In addition, in the gimbal mechanism, the installed axes have a good effect on sliding wear of tooth surface of the spherical gear.
3. The tooth contact characteristics analysis and stress analysis for the spherical gear are investigated. Theoretical derivation validates that tooth contact form of the meshing spherical gears is a point contact between a convexity and a saddle surface except the position in which the polar axes of two spherical gears are collinear to each other. Then, the meshing model of the spherical gear pair for computer simulation is set up, and the position of instantaneous contact point of two spherical gears can be gotten using the nonlinear solver composed of five equations. Furthermore, the contact point paths of the spherical gear in mesh are studied. Combined the curvature analysis method with the tooth surface separation topology method, the contact ellipse of the spherical gear pair is calculated and simulated, and the distributing rule is gained. Finite element analysis is applied to perform contact stress analysis and bending stress analysis of the convex tooth, the weakest tooth. The result indicates that: the distributing form of contact stress is an ellipse; regardless of contact ratio, contact stress is large on tooth base and tooth tip, and contact stress is little on tooth middle part; considering contact ratio, contact stress is evidently decreased on tooth base and tooth tip; bending stress is little, and the maximum of bending stress occurs on tooth middle part.
4. The effect of assemble errors on the transmission error of the spherical gear mechanism is analyzed and simulated. The transmission error model and pointing error models of two mechanisms of the spherical gear sets in common use, the gimbal mechanism and the pointing mechanism, are set up, respectively. After that, the kinematic models of two mechanisms with assemble errors are built, and the assemble errors comprise the vertical and horizontial axial misalignment of the fixed axis and rotating axis, and the center distance error of two spherical gears, respectively. With these models above, the transmission errors of the gimbal mechanism are simulated and analyzed, and using two computation methods, the pointing errors of the pointing mechanism are simulated and analyzed. The results are useful for the installation and measurement of the spherical gear pairs in practice.
5. Grinding method is the key for solving the finishing machining problem of the spherical gear. According to tooth surface characteristics of the spherical gear, with forming method and generating method, respectively, the grinding manufacture of the spherical gear are researched. To grinding with the forming method, according to the required degrees of freedom, a grinding machine and a fingerlike grinding wheel are designed, then the relationship of motions of the machine is analyzed and the grinding principle of the fingerlike grinding wheel is studied. To grinding with the generating method, similarly, a grinding mchine and plate grinding wheels are designed, and then the conjugate meshing kinematic equations are set up. The generating process of the involute tooth surface and the tooth base surface with the plate grinding wheels are introduced in detail. In the end, based on the mathematical models of the plate grinding wheels, the mathematical models of the spherical gear pair are received and the machining parameters can be set and adjusted.
引文
[1]孙殿柱.真实齿面啮合理论.北京:科学出版社,2006.7
[2] Liu Z Q, Li G X, Li H M. Research on cone tooth spherical gear transmission of robot flexible joint. ASME, 1990, 26:56-60
[3]李瑰贤.机器人关节内环面齿准椭球齿轮传动及其图形仿真,哈尔滨工业大学,1991.2
[4]张昆,冯立群.机器人柔性手腕的球面齿轮设计研究,清华大学学报:自然科学版,1994年2期
[5] Yang S C, Chen C K, Li K Y. A geometric model of a spherical gear with a double degree of freedom. Journal of Materials Processing Technology. 2002, 123:219-224
[6]潘存云,尚建忠.球齿轮机构及其应用.机械科学与技术(江苏),1997,26(1):43-45
[7]潘存云.球齿轮传动原理与加工方法研究.博士学位论文.国防科学技术大学,2001
[8] Johnson K L. Contact Mechanics. Combridge University Press, 1985
[9] Chen N. Curvatures and sliding ratios of conjugate surfaces. Transactions of the ASME, 1998, 20:126-132
[10]孙桓.机械原理.人民教育出版社,1982
[11] Colbourne J R. The Geometry of Involute Gearing. Springer-Verlag, New York,1987
[12] Litvin F L. Theory of Gearing, NASA, 1989
[13]吴序堂.齿轮啮合原理.北京:机械工业出版社,1982
[14]林菁.基于啮合角函数的平面圆齿轮共轭齿廓啮合理论研究.博士学位论文.东北大学,1998
[15] Tsay C B, Jeng J W, Feng H S. A mathematical model of the ZE-type worm gear set. Mech. Mach. Theory, 1995, 30(6):777-789
[16] Litvin F L, Fuentes A. Gear Geometry and Applied Theory. Cambridge University Press, 2004
[17] Litvin F L, Fuentes A, Hayasaka K. Design, manufacture, stress analysis, and experimental tests of low-noise high endurance spiral bevel gears. Mechanism and Machine Theory, 2006, 41:83-113
[18] Argyris J, Fuentes A, Litvin F L. Computerized integrated approach for designand stress analysis of spiral bevel gears. Comput. Methods Appl. Mech. Engry., 2002, 191:1057-1095
[19] Zhang Y, Wu Z. Offset face gear drives: tooth geometry and contact analysis. ASME J. Mech. Des., 1997,119:114-119
[20] Litvin F L, Wang A G, Handschuh R F. Computerized design and analysis of face-milled, uniform tooth height spiral bevel gear drives. ASME J. Mech. Des., 1996, 118:573-579
[21] Lin T J, Ou H, Li R F. A finite element method for 3D static and dynamic contact/impact analysis of gear drives. Computer methods in applied mechanics and engineering, 2007, 196:1716-1728
[22] Simon V. Stress analysis in worm gears with ground concave worm profile. Mech. Mach. Theory, 1996, 31(8):1121-1130
[23] D.Barkah, B.Shafiq, D.Dooner. 3D mesh generation for static stress determination in spiral noncircular gears used for torque balancing. J. Mech. Des., 2002,124:313-319
[24]米克朗公司高性能加工中心VCP/UCP 800/1000 Duro系列.WMEM,2003,6:30-31
[25] Dudley D W. The Evolution of the Gear Art. AGMA, 1969
[26]李华敏,韩元莹,王知行等.渐开线齿轮的几何原理与计算.北京:机械工业出版社,1985
[27] Buckingham E. Analytical Mechanics of Gears. 2nd., Dover, N.Y., 1963
[28] Litvin F L. Theory of Gearing. NASA Publication RP-1212, Washington DC, 1989
[29] Litvin F L. Development of Gear Technology and Theory of Gearing. University of Illinois at Chicago, Illinois, 1998
[30] Litvin F L, Lu J, Townsend D P, et al. Computerized simulation of conventional helical involute gears and modification of geometry. Mechanism and Machine Theory,1999, 34:123-147
[31] Olivier T. The Evolution of the Gear Art, AGMA, 1977
[32] Peng A. Computerized Design and Stress Analysis of Spiral Bevel Gears with Geodetic Path of Contact. Ph.D. thesis, University of Illinois at Chicago, 2000
[33] Kolchin N I. Analytical Calculations of Planar and Spatial Gearing. Leninggrad, Mashgis(in Russion), 1949
[34] Wildhaber E. Basic Relationships of Hypoid Gears. Amer.,1946, 3(90):108-111
[35] Dudley D W. Gear Handbook: The design, manufacture and application of gears.McGraw-hill, New, York, 1962
[36]张启先.空间机构的分析与综合.北京:机械工业出版社,1984
[37] Colbourne J R. The Curvature of Surfaces Formed by Cutting Edge. Mechanism and Machine Theory, 1994, 29(5):767-775
[38] Colbourne J R. Undercutting in worm and worm-gears. American Gear Manufactures Association, Virginia, 1993
[39] Litvin F L. Applied Theory of Gearing: State of the Art. Special 50th Anniversary Design Issue of ASME, 1995, 117:128-134
[40] Litvin F L, Seol I H. Computerized determination of gear tooth surface as envelope to two parameter family of surfaces. Comput. Methods Appl. Mech. Engrg., 1996, 138:213-225
[41] Feng P H, Litvin F L. Determination of principal curvatures and contact ellipse for profile crowned helical gears. ASME J. Mech. Des., 1999, 121:107-111
[42] Lo J S, Tseng C H, Tsay C B. A study on the bearing contact of roller gear cams. Comput. Methods Appl. Mech. Engrg., 2001, 190:4649-4662
[43] Fong Z H, Chiang T W, Tsay C W. Mathematical model for parametric tooth profile of spur gear using line of action. Mathematical and Computer Modelling, 2002, 36:603-614
[44] Boxter M L. Basic Geometry and tooth contact of hypoid gears. Industrial Mathetmati(2), 1962
[45] Ito N, Takahashi K. Differential geometrical conditions of hypoid gears with conjugate tooth surfaces. ASME J. Mech. Des., 2000, 122:323-330
[46] Liu C C, Tsay C B. Contact characteristic of beveloid gears. Mechanism and Machine Theory, 2002, 37:333-350
[47] Zhang Y, Litvin F L, Maruyama N, et al. Computerized analysis of meshing and contact of gear real tooth surfaces. ASME J. Mech. Des., 1994, 116:677-682
[48] Kim D. Computerized simulation of meshing for finishing operations of production of spur and helical gears, Ph.D. thesis, University of Illinois of Chicago, 1995
[49] Litvin F L, Fuentes A, Ignacio G P, et al. Modified involute helical gears: computerized design, simulation of meshing and stress analysis, Comput. Methods Appl. Mech. Engrg., 2003, 192:3619-3655
[50] Litvin F L, Ignacio G P, Fuentes A, et al. Generalized concept of meshing and contact of involute crossed helical gears and its application. Comput. Methods Appl. Mech. Engrg., 2005, 194:3710-3745
[51] Litvin F L, Fuentes A, Ignacio G P, et al. New version of Novikov-Widhaber helical gears: computerized design, simulation of meshing and stress analysis. Comput. Methods Appl. Mech. Engrg., 2002, 191:5707-5740
[52] Tsay C B. Helical gears with involute shaped teeth: geometry, computer simulation, tooth contact analysis, and stress analysis, Journal of Mechanisms, Transmissions, and Automation in Design, 1988,110: 482-491
[53] Litvin F L, Wang A G, Handschuh R F. Computerized generation and simulation of meshing and Contact of spiral bevel gears with improved geometry. Comput. Methods Appl. Mech. Engrg., 1998, 158:35-64
[54] Litvin F L, Fuentes A, Fan Q, et al. Computerized design, simulation of meshing, and contact and stress analysis of face-milled formate generated spiral bevel gears. Mechanism and Machine Theory, 2002, 37:441-559
[55] Simon V. Computer simulation of tooth contact analysis of mismatched spiral bevel gears, Mechanism and Machine Theory, 2007, 42:365-381
[56] Litvin F L, Kin V. Computerized simulation of meshing and bearing contact for single-enveloping worm-gear drives. ASME J. Mech. Des., 1992, 114:313-316
[57] Donno M D, Litvin F L. Computerized design, generation and simulation of meshing of a spiroid worm-gear drive with a ground double-crowned worm. ASME J. Mech. Des., 1999, 121:264-273
[58] Tseng R T, Tsay C B. Contact characteristics of cylindrical gears with curvilinear shaped teeth. Mech. Mach. Theory, 2004, 39:905-919
[59] Chang S H, Chuang T D, Lu S S. Tooth contact analysis of face-gear drives. International Journal of Mechanical Sciences, 2000, 42:487-502
[60] Litvin F L, Donno M D, Peng A, et al. Integrated computer program for simulation of meshing and contact of gear drives. Comput. Methods Appl. Mech. Engrg., 2000, 181:71-85
[61] Litvin F L, Sheveleva G I, Vecchiato D, et al. Modified approach for tooth contact analysis of gear drives and automatic determination of guess values. Methods Appl. Mech. Engrg., 2005, 194:2927-2946
[62] Vogel O, Griewank A, B?r G. Direct gear tooth contact analysis for hypoid bevel gears. Comput. Methods Appl. Mech. Engrg., 2002, 191:3965-3982
[63] Sheveleva G I, Volkov A E, Medvedev V I. Algorithms for analysis of meshing and contact of spiral bevel gears. Mechanism and Machine Theory, 2007, 42:198-215
[64] Gosselin C, Cloutier L, Nguyen Q D. A general formulation for the calculation of the load sharing and transmission error under load of spiral bevel and hypoid gears. Mech. Mach. Theory, 1995, 30(3):433-450
[65] Gosselin C, Guertin T, Remond D. Simulation and experimental measurement of the transmission error of real hypoid gears under load. ASME J. Mech. Des., 2000, 122:109-122
[66] Falah B, Gosselin C, Cloutier L. Experimental and numerical investigation of the meshing cycle and contact ratio in spiral bevel gears. Mech. Mach. Theory., 1998, 33:21-37
[67] Zhang Y, Fang Z. Analysis of transmission errors under load of helical gears with modified tooth surfaces. ASME J. Mech. Des., 1997, 119:120-126
[68] Zhang Y, Fang Z. Analysis of tooth contact and load distribution of helical gears with crossed axes. Mechanism and Machine Theory, 1999, 34:41-57
[69] Li S T. Effect of addendum on contact strength, bending strength and basic performance parameters of a pair of spur gears. Mechanism and Machine Theory, 2008, xxx:xxx-xxx
[70] Simon V. Computer aided loaded tooth contact analysis in cylindrical worm gears. ASME J. Mech. Des., 2005, 127:973-981
[71]贾鹏,许洪斌.齿轮齿面接触分析TCA技术及发展动态.长春大学学报,2006, 16 (2):40-41
[72]傅则绍.微分几何与齿轮啮合原理.石油大学出版社,1999
[73]肖来元,廖道训,易传云.基于MATLAB的数字化共轭曲面求解及仿真研究.2003, 22(3):355-357
[74] Chang H L, Tsai Y C. A mathematical model of parametric tooth profiles for spur gears. ASME J. Mech. Des., 1992, 114:8-16
[75] Sung L M, Tsai Y C. A study on the mathematical models and contact ratios of extended cycloid and cycloid bevel gear sets. Mech. Mach. Theory, 1997, 32(1):39-50
[76] Bair B W. Computer aided design of elliptical gears with circular-arc teeth. Mechanism and Machine Theory, 2004, 39:153-168
[77] Bair B W, Chen C F, Chen S F. Mathematical model and characteristic analysis of elliptical gears manufactured by circular-arc shaper cutters. ASME J. Mech. Des., 2007, 129:210-217
[78] Litvin F L, Ignacio G P, Kenji Y, et al. Generation of planar and helical ellipticalgears by application of rack-cutter, hob, and shaper. Comput. Methods Appl. Mech. Engrg., 2007, 196:4321-4336
[79] Bair B W. Computer aided design of elliptical gears. ASME J. Mech. Des., 2002, 124:787-793
[80] Bair B W. Computer aided design of elliptical gears. ASME J. Mech. Des., 2002, 124:787-793
[81] Chang S L, Tsay C B. Computerized tooth profile generation and undercut analysis of noncircular gears manufactured with shaper cutters. ASME J. Mech. Des., 1998, 120:92-99
[82] Xiao D C, Lee C. A contact point method for the design of form cutters for helical gears. Journal of Engineering for Industry of the ASME, 1994, 116:387-391
[83] Chao L C, Tsay C B. Contact characteristics of spherical gears. Mech. Mach. Theory, 2008, 43:1317-1331
[84] Lu J, Litvin F L, Chen J S. Load share and finite element stress analysis for double circular-arc helical gears. Mathl. Comput. Modelling, 1995, 21(10):13-30
[85] Seol I H, Litvin F L. Computerized design, generation and simulation of meshing and contact of worm-gear drives with improved geometry. Comput. Methods Appl. Mech. Engrg., 1996, 138:73-103
[86] Liu C C, Chen J H, Tsay C B. Meshing simulations of the worm gear cut by a straight-edged flyblade and the ZK-type worm with a non-90°crossing angle. Mech. Mach. Theory, 2006, 41:987-1002
[87] Fang H S, Tsay C B. Mathematical model and bearing contacts of the ZN-type worm gear set cut by oversize hob cutters. Mech. Mach. Theory, 2000, 35:1689-1708
[88] Janninck W K. Contact surface topology of worm gear teeth. Gear Technology, 1988, 4:31-47
[89] Tseng J T, Tsay C B. Undercutting and contact characteristics of cylindrical gears with curvilinear shaped teeth generated by hobbing. ASME J. Mech. Des., 2006, 128:634-643
[90] Litvin F L, Lu J. Computerized design and generation of double circular-arc helical gears with low transmission errors. Comput. Methods Appl. Mech. Engrg., 1995, 127:57-86
[91] Litvin F L, Kim D H. Computerized design, generation and simulation ofmeshing of modified involute spur gears with localized bearing contact and reduced level of transmission errors. ASME J. Mech. Des., 1997, 119:96-100
[92] Litvin F L, Seol I H, Kim D, et al. Kinematic and geometric models of gear drives. ASME J. Mech. Des., 1996, 118:544-550
[93] Simon V. The influence of misalignments on mesh performances of hypoid gears. Mech. Mach. Theory, 1998, 33:1277-1291
[94] Argyris J, Fuentes A, Litvin F L. Computerized integrated approach for design and stress analysis of spiral bevel gears. Comput. Methods Appl. Mech. Engry., 2002, 191:1057-1095
[95] Seol I H. The design, generation, and simulation of meshing of worm-gear drive with longitudinally localized contacts. ASME J. Mech. Des., 2000, 122:201-206
[96] Fang H S, Tsay C B. Mathematical model and bearing contacts of the ZK-type worm gear set cut by oversize hob cutters. Mech. Mach. Theory, 1996, 31(3):271-282
[97] Litvin F L, Zhang Y, Wang J C. Design and geometry of face-gear drives. ASME J. Mech. Des., 1992, 114:642-647
[98] Litvin F L, Chen J S, Sep T M, et al. Computerized simulation of transmission errors and shift of bearing contact for face-milled hypoid gear drive. ASME J. Mech. Des., 1995, 117:262-268
[99] Litvin F L, Chen N X, Lu J. Computerized design and generation of low-noise helical gears with modified surface topology. ASME J. Mech. Des., 1995, 117:254-261
[100] Litvin F L, Fan Q, Vecchiato D, et al. Computerized generation and simulation of meshing of modified spur and helical gears manufactured by shaving. Comput. Methods Appl. Mech. Engrg., 2001, 190:5037-5055
[101] Litvin F L, Ignacio G P, Yukishima K. Design, simulation of meshing, and contact stresses for an improved worm gear drive. Mech. Mach. Theory, 2007, 42:940-959
[102] Chen Y C, Tsay C B. Contact ratios and transmission errors of a helical gear set with involute-teeth pinion and modified-circular-arc-teeth gear. JSME International Journal, Series C, 2001, 44(3):867-874
[103] Bonori G, Barbieri M, Pellicano F. Optimum profile modifications of spur gears by means of genetic algorithms. Journal of Sound and vibration, 2008, 313:603-616
[104] Umeyama M, Kato M, Inoue K. Effects of gear dimensions and tooth surface modifications on the loaded transmission error of a helical gear pair. ASME J. Mech. Des., 1998, 120:119-125
[105] Lee C K. Manufacturing process of a cylindrical crown gear drive with a controllable fourth order polynomial function of transmission error. Journal of Materials Processing Technology, 2008, 209(1):3-13
[106] Gosselin C, Gingras D, Brousseau J, et al. A review of the current contact stress and deformation formulations compared to finite element analysis. Proceedings of the Inter Gearing’94, 1994:155-160
[107] Brauer J. A general finite element model of involute gears. Finite Elements in Analysis and Design, 2004, 40:1857-1872
[108] Simon V. Stress analysis in double enveloping worm gears by finite element method. ASME J. Mech. Des., 1993, 115:179-185
[109] Barone S, Borgianni L, Forte P. Evaluation of the effect of misalignment and profile modification in face gear drive by a finite element meshing simulation. J. Mech. Des., ASME, 2004, 126:916-924
[110] Lu J. Generation, meshing, contact and stress analysis of double circular-arc helical gears, Ph.D. thesis. University of Illinois at Chicago, 1994
[111] Simon V. FEM stress analysis in hypoid gears. Mech. Mach. Theory, 2000, 35:1197-1220
[112] Sfakiotakis V G, Vaitsis J P, Anifantis N K. Numerical simulation of conjugate spur gear action. Computers and Structures, 2001, 79:1153-1160
[113] Wang J D, Ian M H. Error analysis on finite element modeling of involute spur gears. ASME J. Mech. Des., 2006, 128:90-97
[114] Li S T. Finite element analyses for contact strength and bending strength of a pair of spur gears with machining errors, assembly error and tooth modifications. Mech. Mach. Theory, 2007, 42:88-114
[115] Filiz I H, Eyercioglu O. Evaluation of gear tooth stresses by finite element method. ASME J. Engineering for industry, 1995, 117:232-239
[116] Litvin F L, Ignacio G P, Fuentes A, et al. Topology of modified surfaces of involute helical gears with line contact developed for improvement of bearing contact, reduction of transmission errors, and stress analysis. Mathematical and Computer Modeling, 2005, 42:1063-1078
[117] Fuentes A, Litvin F L, Baxter M R, et al. Design and stress analysis of low-noiseadjusted bearing contact spiral bevel gears. Journal of Mechanical Design, 2002, 124:524-532
[118] Chen Y C, Tsay C B. Stress analysis of a helical gear set with localized bearing contact. Finite Elements in Analysis and Design, 2002, 38:707-723
[119] Bibel G D, Kumar A, Reddy S, et al. Contact stress analysis of spiral bevel gears using finite element analysis. ASME J. Mech. Des., 1995, 117:235-240
[120] Cavdar K, Karpat F, Babalik F C. Computer aided analysis of bending strength of involute spur gears with asymmetric profile. ASME J. Mech. Des., 2005, 127:477-484
[121] Stegemiller M E, Houser D R. A three-dimensional analysis of the base flexibility of gear teeth. ASME J. Mech. Des., 1993, 115:186-192
[122] Celik M. Comparison of three teeth and whole body models in spur gear analysis. Mech. Mach. Theory, 1999, 34:1227-1235
[123] Moriwaki I, Fukuda T, Watabe Y. Global local finite element method (FLFEM) in gear tooth stress analysis. ASME J. Mech. Des., 1993, 115:1008-1012
[124] Kawalec A, Wiktor J. Tooth root strength of spur and helical gears manufactured with gear-shaper cutters. ASME J. Mech. Des., 2008, 130:1-5
[125] Li S T. Deformation and bending stress analysis of a three-dimensional, thin-rimmed gear. ASME J. Mech. Des., 2002, 124:129-135
[126] Radzevich S P. A way to improve the accuracy of hobbed involute gears. ASME J. Mech. Des., 2007, 129:1076-1085
[127] Radzevich S P. Investigation of the tooth geometry of a hob for machining of involute gears (in the tool-in-use Reference system). Journal of Manufacturing Science and Engineering, 2007, 129:750-759
[128] Tsay C B, Liu W Y, Chen Y C. Spur gear generation by shaper cutters. Journal of Materials Processing Technology, 2000, 104:271-279
[129] Zhang Y, Xu H. Pitch cone design and avoidance of contact envelope and tooth undercutting for conical worm gear drives. ASME J. Mech. Des., 2003, 125:169-177
[130] Cao X M, Fang Z D, Xu H, et al. Design of pinion machine tool-settings for spiral bevel gears by controlling contact path and transmission errors. Chinese Journal of Aeronautics, 2008, 21:179-186
[131] Litvin F L, Chen N X. Generation of gear tooth surfaces by application of CNC Machines. NASA, 1994
[132] Wang P Y, Fong Z H. Mathematical model of face-milling spiral bevel gear with modified radial motion (MRM) correction. Mathematical and Computer Modelling, 2005, 41:1307-12-323
[133] Fong Z H, Tsay C B. Kinematical optimization of spiral bevel gears. ASME J. Mech. Des., 1992, 114:498-506
[134] Innocenti C. Analysis of meshing of beveloid gears. Mech. Mach. Theory, 1997, 32(3):363-373
[135] Radzevich S P. A novel design of cylindrical hob for machining of precision involute gears. Journal of Mechanical Design, 2007, 129:334-345
[136] Liu C C, Tsay C B. Mathematical models and contact simulations of concave beveloid gear. ASME J. Mech. Des., 2002, 124:753-760
[137] Chen C F, Tsay C B. Computerized tooth profile generation and analysis of characteristics of elliptical gears with circular-arc teeth. Journal of Materials Processing Technology, 2004, 148:226-234
[138] Bair B W, Sung M H, Wang J S, et al. Tooth profile generation and analysis of oval gears with circular-arc teeth. Mech. Mach. Theory, 2008, xxx:xxx-xxx
[139]李左章.螺旋锥齿轮NC加工的理论、方法及控制技术研究:博士学位论文.武汉:华中科技大学,2001
[140] Litvin F L, Zhang Y, Kieffer J, et al. Identification and minimization of deviations of real gear tooth surfaces. ASME J. Mech. Des., 1991, 113(1):55-62
[141] Litvin F L, Kuan C, Wang J C, et al. Minimization of deviations of gear real tooth surfaces determined by coordinate measurements. ASME J. Mech. Des.,1993, 115(4):995-1001
[142] Kin V. Computerized analysis of gear meshing based on coordinate measurement data. ASME J. Mech. Des., 1994, 116:738-744
[143] Gosselin C, Nonaka T, Shiono Y, et al. Identification of the machine settings of real hypoid gear tooth surfaces. ASME J. Mech. Des., 1998, 120:429-440
[144] M&M Precision System. The CNC Gear Inspection System for the Spiral Bevel Gears-QC 3000 Manual, Ohio, 1990
[145] Sohne K. The CNC Inspection System for the Spiral Bevel Gears-HP-KEG Software Manual, Remscheid, Huecheswagen Factory, Germany, 1990
[146] Lemanski A J. AGMA paper 85FTM10, 1995
[147] Krenzer T J. AGMA paper 84FTM4, 1994
[148] Litvin F L. Development of gear technology and theory of gearing. NASA RP1406, 1998
[149] Tsai Y C, Jehng W K. Rapid prototyping and manufacturing technology and applied to forming of spherical gear sets with skew axes. Journal of Materials Processing Technology, 1999, 95:169-179
[150] Tsai Y C, Jehng W K. A kinematics parametric method to generate new tooth profiles of gear sets with skew axes. Mech. Mach. Theory, 1999, 34:857-876
[151] Jehng W K. Computer solid modeling technologies applied to develop and form mathematical parametric tooth profiles of bevel gear and skew gear sets. Journal of Materials Processing Technology, 2002, 122:160-172
[152] Yang S C, Chen C K, Li K Y. A geometric model of a spherical gear with a double degree of freedom, Journal of Materials Processing Technology 2002, 123:219-224
[153] Yang S C. A rack-cutter surface used to generate a spherical gear with discrete ring-involute teeth. Int. J. Adv. Manuf. Technol., 2005, 27:14-20
[154]刘志全,李瑰贤,李华敏.机器人柔性关节准椭球面齿轮传动—节曲面的优化设计.机器人,1990,12(3):36-41
[155]李瑰贤,刘志全,李华敏.机器人柔性关节准椭球面齿轮传动—齿形分析与设计.机器人,1991,13(4):7-12
[156] Li G X, Li H M, Bi Z M. Meching analysis on the quasi—ellipsoidal gear transmission with inner—toroidal teeth the flexible joint on robot. Chinese Journal of Mechanical Engineering, 1992, 5:34-36
[157]李华敏,吴波.圆锥形凹齿球面齿轮传动.哈尔滨工业大学学报,1997,29(1):96-99
[158] Li H M, Li G X, Wang X F. The theory and design of the quasi—ellipsoidal gear transmission with inner—toroidal teeth in the joint of robot.亚洲机器人会议论文, 1991
[159]刘志全.机器人柔性关节椭球面齿轮传动的原理与设计:硕士学位论文.哈尔滨:哈尔滨工业大学,1989
[160]毕诸明.机器人关节内环面齿准椭球齿轮传动及其图形仿真:硕士学位论文.哈尔滨:哈尔滨工业大学,1991
[161]郭吉丰,童忠钫,黄善均,李华敏.HRGP—1喷漆机器人挠性手腕的传动原理及设计.第三届全国机器人会议论文集
[162]郭吉丰.机器人柔性手腕球面传动的原理与设计:硕士学位论文.哈尔滨:哈尔滨工业大学,1992
[163]吴波.机器人绕性手腕图形仿真结构改进:硕士学位论文.哈尔滨:哈尔滨工业大学,1994
[164]常山,陈荣增.球面齿轮传动的强度研究.热能动力工程,1994, 9(1):54-58
[165]林国成,常山.球面齿轮传动的强度分析.机械传动,1993, 17(4):14-17
[166]袁斌,何兆太.双自由度锥形凹齿球面齿轮传动.黄石高等专科学校学报,2004,20(2):43-44
[167] Liu H R. A new kind of spherical gear and its application in a robot’s wrist joint. Robot Comput Integr Manuf(2008), doi:10.1016/j.rcim.2008.07.002
[168]潘存云,温熙森.渐开线环形齿球齿轮传动原理与运动分析.机械工程学报,2005, 41(5):1-9
[169]潘存云,温熙森.渐开线球齿轮齿廓曲面方程的推导.国防科技大学学报,2004, 26(4):93-98
[170]赵亚平,魏文军.点接触齿面滑动率计算方法及其对交错轴渐开线斜齿轮传动的应用.中国机械工程,2006,17(8):40-43
[171]黄锡恺.机械原理.人民教育出版社,1981
[172]李常义.渐开线环形齿球齿轮传动强度计算方法研究:硕士学位论文.长沙:国防科技大学,2004
[173]博弈创作室编著.APDL参数化有限元分析技术及其应用实例.中国水利水电出版社,2001
[174]李小清.螺旋锥齿轮数控加工与误差修正技术研究:博士学位论文.华中科技大学,2004
[175]肖卫国,郝崇恩,李高风.三轴飞行模拟转台误差研究.系统仿真学报,2001,13(5):678-680
[176]刘延斌,金光,何惠阳.轴仿真转台指向误差的建模研究.哈尔滨工业大学学报,2005,37(5):701-704
[177] Bailey M W, Juchem H O. The advantages of CBN grinding: low cutting forces and improved workpiece integrity. IDR, 1998, 3:83 -89
[178] Rowe W B, Black S C. Temperatures in CBN grinding. IDR, 1995, 4:165-169
[179]吴武辉.球齿轮数控磨齿机结构设计与分析:硕士学位论文.国防科学技术大学,2006
[2] Liu Z Q, Li G X, Li H M. Research on cone tooth spherical gear transmission of robot flexible joint. ASME, 1990, 26:56-60
[3]李瑰贤.机器人关节内环面齿准椭球齿轮传动及其图形仿真,哈尔滨工业大学,1991.2
[4]张昆,冯立群.机器人柔性手腕的球面齿轮设计研究,清华大学学报:自然科学版,1994年2期
[5] Yang S C, Chen C K, Li K Y. A geometric model of a spherical gear with a double degree of freedom. Journal of Materials Processing Technology. 2002, 123:219-224
[6]潘存云,尚建忠.球齿轮机构及其应用.机械科学与技术(江苏),1997,26(1):43-45
[7]潘存云.球齿轮传动原理与加工方法研究.博士学位论文.国防科学技术大学,2001
[8] Johnson K L. Contact Mechanics. Combridge University Press, 1985
[9] Chen N. Curvatures and sliding ratios of conjugate surfaces. Transactions of the ASME, 1998, 20:126-132
[10]孙桓.机械原理.人民教育出版社,1982
[11] Colbourne J R. The Geometry of Involute Gearing. Springer-Verlag, New York,1987
[12] Litvin F L. Theory of Gearing, NASA, 1989
[13]吴序堂.齿轮啮合原理.北京:机械工业出版社,1982
[14]林菁.基于啮合角函数的平面圆齿轮共轭齿廓啮合理论研究.博士学位论文.东北大学,1998
[15] Tsay C B, Jeng J W, Feng H S. A mathematical model of the ZE-type worm gear set. Mech. Mach. Theory, 1995, 30(6):777-789
[16] Litvin F L, Fuentes A. Gear Geometry and Applied Theory. Cambridge University Press, 2004
[17] Litvin F L, Fuentes A, Hayasaka K. Design, manufacture, stress analysis, and experimental tests of low-noise high endurance spiral bevel gears. Mechanism and Machine Theory, 2006, 41:83-113
[18] Argyris J, Fuentes A, Litvin F L. Computerized integrated approach for designand stress analysis of spiral bevel gears. Comput. Methods Appl. Mech. Engry., 2002, 191:1057-1095
[19] Zhang Y, Wu Z. Offset face gear drives: tooth geometry and contact analysis. ASME J. Mech. Des., 1997,119:114-119
[20] Litvin F L, Wang A G, Handschuh R F. Computerized design and analysis of face-milled, uniform tooth height spiral bevel gear drives. ASME J. Mech. Des., 1996, 118:573-579
[21] Lin T J, Ou H, Li R F. A finite element method for 3D static and dynamic contact/impact analysis of gear drives. Computer methods in applied mechanics and engineering, 2007, 196:1716-1728
[22] Simon V. Stress analysis in worm gears with ground concave worm profile. Mech. Mach. Theory, 1996, 31(8):1121-1130
[23] D.Barkah, B.Shafiq, D.Dooner. 3D mesh generation for static stress determination in spiral noncircular gears used for torque balancing. J. Mech. Des., 2002,124:313-319
[24]米克朗公司高性能加工中心VCP/UCP 800/1000 Duro系列.WMEM,2003,6:30-31
[25] Dudley D W. The Evolution of the Gear Art. AGMA, 1969
[26]李华敏,韩元莹,王知行等.渐开线齿轮的几何原理与计算.北京:机械工业出版社,1985
[27] Buckingham E. Analytical Mechanics of Gears. 2nd., Dover, N.Y., 1963
[28] Litvin F L. Theory of Gearing. NASA Publication RP-1212, Washington DC, 1989
[29] Litvin F L. Development of Gear Technology and Theory of Gearing. University of Illinois at Chicago, Illinois, 1998
[30] Litvin F L, Lu J, Townsend D P, et al. Computerized simulation of conventional helical involute gears and modification of geometry. Mechanism and Machine Theory,1999, 34:123-147
[31] Olivier T. The Evolution of the Gear Art, AGMA, 1977
[32] Peng A. Computerized Design and Stress Analysis of Spiral Bevel Gears with Geodetic Path of Contact. Ph.D. thesis, University of Illinois at Chicago, 2000
[33] Kolchin N I. Analytical Calculations of Planar and Spatial Gearing. Leninggrad, Mashgis(in Russion), 1949
[34] Wildhaber E. Basic Relationships of Hypoid Gears. Amer.,1946, 3(90):108-111
[35] Dudley D W. Gear Handbook: The design, manufacture and application of gears.McGraw-hill, New, York, 1962
[36]张启先.空间机构的分析与综合.北京:机械工业出版社,1984
[37] Colbourne J R. The Curvature of Surfaces Formed by Cutting Edge. Mechanism and Machine Theory, 1994, 29(5):767-775
[38] Colbourne J R. Undercutting in worm and worm-gears. American Gear Manufactures Association, Virginia, 1993
[39] Litvin F L. Applied Theory of Gearing: State of the Art. Special 50th Anniversary Design Issue of ASME, 1995, 117:128-134
[40] Litvin F L, Seol I H. Computerized determination of gear tooth surface as envelope to two parameter family of surfaces. Comput. Methods Appl. Mech. Engrg., 1996, 138:213-225
[41] Feng P H, Litvin F L. Determination of principal curvatures and contact ellipse for profile crowned helical gears. ASME J. Mech. Des., 1999, 121:107-111
[42] Lo J S, Tseng C H, Tsay C B. A study on the bearing contact of roller gear cams. Comput. Methods Appl. Mech. Engrg., 2001, 190:4649-4662
[43] Fong Z H, Chiang T W, Tsay C W. Mathematical model for parametric tooth profile of spur gear using line of action. Mathematical and Computer Modelling, 2002, 36:603-614
[44] Boxter M L. Basic Geometry and tooth contact of hypoid gears. Industrial Mathetmati(2), 1962
[45] Ito N, Takahashi K. Differential geometrical conditions of hypoid gears with conjugate tooth surfaces. ASME J. Mech. Des., 2000, 122:323-330
[46] Liu C C, Tsay C B. Contact characteristic of beveloid gears. Mechanism and Machine Theory, 2002, 37:333-350
[47] Zhang Y, Litvin F L, Maruyama N, et al. Computerized analysis of meshing and contact of gear real tooth surfaces. ASME J. Mech. Des., 1994, 116:677-682
[48] Kim D. Computerized simulation of meshing for finishing operations of production of spur and helical gears, Ph.D. thesis, University of Illinois of Chicago, 1995
[49] Litvin F L, Fuentes A, Ignacio G P, et al. Modified involute helical gears: computerized design, simulation of meshing and stress analysis, Comput. Methods Appl. Mech. Engrg., 2003, 192:3619-3655
[50] Litvin F L, Ignacio G P, Fuentes A, et al. Generalized concept of meshing and contact of involute crossed helical gears and its application. Comput. Methods Appl. Mech. Engrg., 2005, 194:3710-3745
[51] Litvin F L, Fuentes A, Ignacio G P, et al. New version of Novikov-Widhaber helical gears: computerized design, simulation of meshing and stress analysis. Comput. Methods Appl. Mech. Engrg., 2002, 191:5707-5740
[52] Tsay C B. Helical gears with involute shaped teeth: geometry, computer simulation, tooth contact analysis, and stress analysis, Journal of Mechanisms, Transmissions, and Automation in Design, 1988,110: 482-491
[53] Litvin F L, Wang A G, Handschuh R F. Computerized generation and simulation of meshing and Contact of spiral bevel gears with improved geometry. Comput. Methods Appl. Mech. Engrg., 1998, 158:35-64
[54] Litvin F L, Fuentes A, Fan Q, et al. Computerized design, simulation of meshing, and contact and stress analysis of face-milled formate generated spiral bevel gears. Mechanism and Machine Theory, 2002, 37:441-559
[55] Simon V. Computer simulation of tooth contact analysis of mismatched spiral bevel gears, Mechanism and Machine Theory, 2007, 42:365-381
[56] Litvin F L, Kin V. Computerized simulation of meshing and bearing contact for single-enveloping worm-gear drives. ASME J. Mech. Des., 1992, 114:313-316
[57] Donno M D, Litvin F L. Computerized design, generation and simulation of meshing of a spiroid worm-gear drive with a ground double-crowned worm. ASME J. Mech. Des., 1999, 121:264-273
[58] Tseng R T, Tsay C B. Contact characteristics of cylindrical gears with curvilinear shaped teeth. Mech. Mach. Theory, 2004, 39:905-919
[59] Chang S H, Chuang T D, Lu S S. Tooth contact analysis of face-gear drives. International Journal of Mechanical Sciences, 2000, 42:487-502
[60] Litvin F L, Donno M D, Peng A, et al. Integrated computer program for simulation of meshing and contact of gear drives. Comput. Methods Appl. Mech. Engrg., 2000, 181:71-85
[61] Litvin F L, Sheveleva G I, Vecchiato D, et al. Modified approach for tooth contact analysis of gear drives and automatic determination of guess values. Methods Appl. Mech. Engrg., 2005, 194:2927-2946
[62] Vogel O, Griewank A, B?r G. Direct gear tooth contact analysis for hypoid bevel gears. Comput. Methods Appl. Mech. Engrg., 2002, 191:3965-3982
[63] Sheveleva G I, Volkov A E, Medvedev V I. Algorithms for analysis of meshing and contact of spiral bevel gears. Mechanism and Machine Theory, 2007, 42:198-215
[64] Gosselin C, Cloutier L, Nguyen Q D. A general formulation for the calculation of the load sharing and transmission error under load of spiral bevel and hypoid gears. Mech. Mach. Theory, 1995, 30(3):433-450
[65] Gosselin C, Guertin T, Remond D. Simulation and experimental measurement of the transmission error of real hypoid gears under load. ASME J. Mech. Des., 2000, 122:109-122
[66] Falah B, Gosselin C, Cloutier L. Experimental and numerical investigation of the meshing cycle and contact ratio in spiral bevel gears. Mech. Mach. Theory., 1998, 33:21-37
[67] Zhang Y, Fang Z. Analysis of transmission errors under load of helical gears with modified tooth surfaces. ASME J. Mech. Des., 1997, 119:120-126
[68] Zhang Y, Fang Z. Analysis of tooth contact and load distribution of helical gears with crossed axes. Mechanism and Machine Theory, 1999, 34:41-57
[69] Li S T. Effect of addendum on contact strength, bending strength and basic performance parameters of a pair of spur gears. Mechanism and Machine Theory, 2008, xxx:xxx-xxx
[70] Simon V. Computer aided loaded tooth contact analysis in cylindrical worm gears. ASME J. Mech. Des., 2005, 127:973-981
[71]贾鹏,许洪斌.齿轮齿面接触分析TCA技术及发展动态.长春大学学报,2006, 16 (2):40-41
[72]傅则绍.微分几何与齿轮啮合原理.石油大学出版社,1999
[73]肖来元,廖道训,易传云.基于MATLAB的数字化共轭曲面求解及仿真研究.2003, 22(3):355-357
[74] Chang H L, Tsai Y C. A mathematical model of parametric tooth profiles for spur gears. ASME J. Mech. Des., 1992, 114:8-16
[75] Sung L M, Tsai Y C. A study on the mathematical models and contact ratios of extended cycloid and cycloid bevel gear sets. Mech. Mach. Theory, 1997, 32(1):39-50
[76] Bair B W. Computer aided design of elliptical gears with circular-arc teeth. Mechanism and Machine Theory, 2004, 39:153-168
[77] Bair B W, Chen C F, Chen S F. Mathematical model and characteristic analysis of elliptical gears manufactured by circular-arc shaper cutters. ASME J. Mech. Des., 2007, 129:210-217
[78] Litvin F L, Ignacio G P, Kenji Y, et al. Generation of planar and helical ellipticalgears by application of rack-cutter, hob, and shaper. Comput. Methods Appl. Mech. Engrg., 2007, 196:4321-4336
[79] Bair B W. Computer aided design of elliptical gears. ASME J. Mech. Des., 2002, 124:787-793
[80] Bair B W. Computer aided design of elliptical gears. ASME J. Mech. Des., 2002, 124:787-793
[81] Chang S L, Tsay C B. Computerized tooth profile generation and undercut analysis of noncircular gears manufactured with shaper cutters. ASME J. Mech. Des., 1998, 120:92-99
[82] Xiao D C, Lee C. A contact point method for the design of form cutters for helical gears. Journal of Engineering for Industry of the ASME, 1994, 116:387-391
[83] Chao L C, Tsay C B. Contact characteristics of spherical gears. Mech. Mach. Theory, 2008, 43:1317-1331
[84] Lu J, Litvin F L, Chen J S. Load share and finite element stress analysis for double circular-arc helical gears. Mathl. Comput. Modelling, 1995, 21(10):13-30
[85] Seol I H, Litvin F L. Computerized design, generation and simulation of meshing and contact of worm-gear drives with improved geometry. Comput. Methods Appl. Mech. Engrg., 1996, 138:73-103
[86] Liu C C, Chen J H, Tsay C B. Meshing simulations of the worm gear cut by a straight-edged flyblade and the ZK-type worm with a non-90°crossing angle. Mech. Mach. Theory, 2006, 41:987-1002
[87] Fang H S, Tsay C B. Mathematical model and bearing contacts of the ZN-type worm gear set cut by oversize hob cutters. Mech. Mach. Theory, 2000, 35:1689-1708
[88] Janninck W K. Contact surface topology of worm gear teeth. Gear Technology, 1988, 4:31-47
[89] Tseng J T, Tsay C B. Undercutting and contact characteristics of cylindrical gears with curvilinear shaped teeth generated by hobbing. ASME J. Mech. Des., 2006, 128:634-643
[90] Litvin F L, Lu J. Computerized design and generation of double circular-arc helical gears with low transmission errors. Comput. Methods Appl. Mech. Engrg., 1995, 127:57-86
[91] Litvin F L, Kim D H. Computerized design, generation and simulation ofmeshing of modified involute spur gears with localized bearing contact and reduced level of transmission errors. ASME J. Mech. Des., 1997, 119:96-100
[92] Litvin F L, Seol I H, Kim D, et al. Kinematic and geometric models of gear drives. ASME J. Mech. Des., 1996, 118:544-550
[93] Simon V. The influence of misalignments on mesh performances of hypoid gears. Mech. Mach. Theory, 1998, 33:1277-1291
[94] Argyris J, Fuentes A, Litvin F L. Computerized integrated approach for design and stress analysis of spiral bevel gears. Comput. Methods Appl. Mech. Engry., 2002, 191:1057-1095
[95] Seol I H. The design, generation, and simulation of meshing of worm-gear drive with longitudinally localized contacts. ASME J. Mech. Des., 2000, 122:201-206
[96] Fang H S, Tsay C B. Mathematical model and bearing contacts of the ZK-type worm gear set cut by oversize hob cutters. Mech. Mach. Theory, 1996, 31(3):271-282
[97] Litvin F L, Zhang Y, Wang J C. Design and geometry of face-gear drives. ASME J. Mech. Des., 1992, 114:642-647
[98] Litvin F L, Chen J S, Sep T M, et al. Computerized simulation of transmission errors and shift of bearing contact for face-milled hypoid gear drive. ASME J. Mech. Des., 1995, 117:262-268
[99] Litvin F L, Chen N X, Lu J. Computerized design and generation of low-noise helical gears with modified surface topology. ASME J. Mech. Des., 1995, 117:254-261
[100] Litvin F L, Fan Q, Vecchiato D, et al. Computerized generation and simulation of meshing of modified spur and helical gears manufactured by shaving. Comput. Methods Appl. Mech. Engrg., 2001, 190:5037-5055
[101] Litvin F L, Ignacio G P, Yukishima K. Design, simulation of meshing, and contact stresses for an improved worm gear drive. Mech. Mach. Theory, 2007, 42:940-959
[102] Chen Y C, Tsay C B. Contact ratios and transmission errors of a helical gear set with involute-teeth pinion and modified-circular-arc-teeth gear. JSME International Journal, Series C, 2001, 44(3):867-874
[103] Bonori G, Barbieri M, Pellicano F. Optimum profile modifications of spur gears by means of genetic algorithms. Journal of Sound and vibration, 2008, 313:603-616
[104] Umeyama M, Kato M, Inoue K. Effects of gear dimensions and tooth surface modifications on the loaded transmission error of a helical gear pair. ASME J. Mech. Des., 1998, 120:119-125
[105] Lee C K. Manufacturing process of a cylindrical crown gear drive with a controllable fourth order polynomial function of transmission error. Journal of Materials Processing Technology, 2008, 209(1):3-13
[106] Gosselin C, Gingras D, Brousseau J, et al. A review of the current contact stress and deformation formulations compared to finite element analysis. Proceedings of the Inter Gearing’94, 1994:155-160
[107] Brauer J. A general finite element model of involute gears. Finite Elements in Analysis and Design, 2004, 40:1857-1872
[108] Simon V. Stress analysis in double enveloping worm gears by finite element method. ASME J. Mech. Des., 1993, 115:179-185
[109] Barone S, Borgianni L, Forte P. Evaluation of the effect of misalignment and profile modification in face gear drive by a finite element meshing simulation. J. Mech. Des., ASME, 2004, 126:916-924
[110] Lu J. Generation, meshing, contact and stress analysis of double circular-arc helical gears, Ph.D. thesis. University of Illinois at Chicago, 1994
[111] Simon V. FEM stress analysis in hypoid gears. Mech. Mach. Theory, 2000, 35:1197-1220
[112] Sfakiotakis V G, Vaitsis J P, Anifantis N K. Numerical simulation of conjugate spur gear action. Computers and Structures, 2001, 79:1153-1160
[113] Wang J D, Ian M H. Error analysis on finite element modeling of involute spur gears. ASME J. Mech. Des., 2006, 128:90-97
[114] Li S T. Finite element analyses for contact strength and bending strength of a pair of spur gears with machining errors, assembly error and tooth modifications. Mech. Mach. Theory, 2007, 42:88-114
[115] Filiz I H, Eyercioglu O. Evaluation of gear tooth stresses by finite element method. ASME J. Engineering for industry, 1995, 117:232-239
[116] Litvin F L, Ignacio G P, Fuentes A, et al. Topology of modified surfaces of involute helical gears with line contact developed for improvement of bearing contact, reduction of transmission errors, and stress analysis. Mathematical and Computer Modeling, 2005, 42:1063-1078
[117] Fuentes A, Litvin F L, Baxter M R, et al. Design and stress analysis of low-noiseadjusted bearing contact spiral bevel gears. Journal of Mechanical Design, 2002, 124:524-532
[118] Chen Y C, Tsay C B. Stress analysis of a helical gear set with localized bearing contact. Finite Elements in Analysis and Design, 2002, 38:707-723
[119] Bibel G D, Kumar A, Reddy S, et al. Contact stress analysis of spiral bevel gears using finite element analysis. ASME J. Mech. Des., 1995, 117:235-240
[120] Cavdar K, Karpat F, Babalik F C. Computer aided analysis of bending strength of involute spur gears with asymmetric profile. ASME J. Mech. Des., 2005, 127:477-484
[121] Stegemiller M E, Houser D R. A three-dimensional analysis of the base flexibility of gear teeth. ASME J. Mech. Des., 1993, 115:186-192
[122] Celik M. Comparison of three teeth and whole body models in spur gear analysis. Mech. Mach. Theory, 1999, 34:1227-1235
[123] Moriwaki I, Fukuda T, Watabe Y. Global local finite element method (FLFEM) in gear tooth stress analysis. ASME J. Mech. Des., 1993, 115:1008-1012
[124] Kawalec A, Wiktor J. Tooth root strength of spur and helical gears manufactured with gear-shaper cutters. ASME J. Mech. Des., 2008, 130:1-5
[125] Li S T. Deformation and bending stress analysis of a three-dimensional, thin-rimmed gear. ASME J. Mech. Des., 2002, 124:129-135
[126] Radzevich S P. A way to improve the accuracy of hobbed involute gears. ASME J. Mech. Des., 2007, 129:1076-1085
[127] Radzevich S P. Investigation of the tooth geometry of a hob for machining of involute gears (in the tool-in-use Reference system). Journal of Manufacturing Science and Engineering, 2007, 129:750-759
[128] Tsay C B, Liu W Y, Chen Y C. Spur gear generation by shaper cutters. Journal of Materials Processing Technology, 2000, 104:271-279
[129] Zhang Y, Xu H. Pitch cone design and avoidance of contact envelope and tooth undercutting for conical worm gear drives. ASME J. Mech. Des., 2003, 125:169-177
[130] Cao X M, Fang Z D, Xu H, et al. Design of pinion machine tool-settings for spiral bevel gears by controlling contact path and transmission errors. Chinese Journal of Aeronautics, 2008, 21:179-186
[131] Litvin F L, Chen N X. Generation of gear tooth surfaces by application of CNC Machines. NASA, 1994
[132] Wang P Y, Fong Z H. Mathematical model of face-milling spiral bevel gear with modified radial motion (MRM) correction. Mathematical and Computer Modelling, 2005, 41:1307-12-323
[133] Fong Z H, Tsay C B. Kinematical optimization of spiral bevel gears. ASME J. Mech. Des., 1992, 114:498-506
[134] Innocenti C. Analysis of meshing of beveloid gears. Mech. Mach. Theory, 1997, 32(3):363-373
[135] Radzevich S P. A novel design of cylindrical hob for machining of precision involute gears. Journal of Mechanical Design, 2007, 129:334-345
[136] Liu C C, Tsay C B. Mathematical models and contact simulations of concave beveloid gear. ASME J. Mech. Des., 2002, 124:753-760
[137] Chen C F, Tsay C B. Computerized tooth profile generation and analysis of characteristics of elliptical gears with circular-arc teeth. Journal of Materials Processing Technology, 2004, 148:226-234
[138] Bair B W, Sung M H, Wang J S, et al. Tooth profile generation and analysis of oval gears with circular-arc teeth. Mech. Mach. Theory, 2008, xxx:xxx-xxx
[139]李左章.螺旋锥齿轮NC加工的理论、方法及控制技术研究:博士学位论文.武汉:华中科技大学,2001
[140] Litvin F L, Zhang Y, Kieffer J, et al. Identification and minimization of deviations of real gear tooth surfaces. ASME J. Mech. Des., 1991, 113(1):55-62
[141] Litvin F L, Kuan C, Wang J C, et al. Minimization of deviations of gear real tooth surfaces determined by coordinate measurements. ASME J. Mech. Des.,1993, 115(4):995-1001
[142] Kin V. Computerized analysis of gear meshing based on coordinate measurement data. ASME J. Mech. Des., 1994, 116:738-744
[143] Gosselin C, Nonaka T, Shiono Y, et al. Identification of the machine settings of real hypoid gear tooth surfaces. ASME J. Mech. Des., 1998, 120:429-440
[144] M&M Precision System. The CNC Gear Inspection System for the Spiral Bevel Gears-QC 3000 Manual, Ohio, 1990
[145] Sohne K. The CNC Inspection System for the Spiral Bevel Gears-HP-KEG Software Manual, Remscheid, Huecheswagen Factory, Germany, 1990
[146] Lemanski A J. AGMA paper 85FTM10, 1995
[147] Krenzer T J. AGMA paper 84FTM4, 1994
[148] Litvin F L. Development of gear technology and theory of gearing. NASA RP1406, 1998
[149] Tsai Y C, Jehng W K. Rapid prototyping and manufacturing technology and applied to forming of spherical gear sets with skew axes. Journal of Materials Processing Technology, 1999, 95:169-179
[150] Tsai Y C, Jehng W K. A kinematics parametric method to generate new tooth profiles of gear sets with skew axes. Mech. Mach. Theory, 1999, 34:857-876
[151] Jehng W K. Computer solid modeling technologies applied to develop and form mathematical parametric tooth profiles of bevel gear and skew gear sets. Journal of Materials Processing Technology, 2002, 122:160-172
[152] Yang S C, Chen C K, Li K Y. A geometric model of a spherical gear with a double degree of freedom, Journal of Materials Processing Technology 2002, 123:219-224
[153] Yang S C. A rack-cutter surface used to generate a spherical gear with discrete ring-involute teeth. Int. J. Adv. Manuf. Technol., 2005, 27:14-20
[154]刘志全,李瑰贤,李华敏.机器人柔性关节准椭球面齿轮传动—节曲面的优化设计.机器人,1990,12(3):36-41
[155]李瑰贤,刘志全,李华敏.机器人柔性关节准椭球面齿轮传动—齿形分析与设计.机器人,1991,13(4):7-12
[156] Li G X, Li H M, Bi Z M. Meching analysis on the quasi—ellipsoidal gear transmission with inner—toroidal teeth the flexible joint on robot. Chinese Journal of Mechanical Engineering, 1992, 5:34-36
[157]李华敏,吴波.圆锥形凹齿球面齿轮传动.哈尔滨工业大学学报,1997,29(1):96-99
[158] Li H M, Li G X, Wang X F. The theory and design of the quasi—ellipsoidal gear transmission with inner—toroidal teeth in the joint of robot.亚洲机器人会议论文, 1991
[159]刘志全.机器人柔性关节椭球面齿轮传动的原理与设计:硕士学位论文.哈尔滨:哈尔滨工业大学,1989
[160]毕诸明.机器人关节内环面齿准椭球齿轮传动及其图形仿真:硕士学位论文.哈尔滨:哈尔滨工业大学,1991
[161]郭吉丰,童忠钫,黄善均,李华敏.HRGP—1喷漆机器人挠性手腕的传动原理及设计.第三届全国机器人会议论文集
[162]郭吉丰.机器人柔性手腕球面传动的原理与设计:硕士学位论文.哈尔滨:哈尔滨工业大学,1992
[163]吴波.机器人绕性手腕图形仿真结构改进:硕士学位论文.哈尔滨:哈尔滨工业大学,1994
[164]常山,陈荣增.球面齿轮传动的强度研究.热能动力工程,1994, 9(1):54-58
[165]林国成,常山.球面齿轮传动的强度分析.机械传动,1993, 17(4):14-17
[166]袁斌,何兆太.双自由度锥形凹齿球面齿轮传动.黄石高等专科学校学报,2004,20(2):43-44
[167] Liu H R. A new kind of spherical gear and its application in a robot’s wrist joint. Robot Comput Integr Manuf(2008), doi:10.1016/j.rcim.2008.07.002
[168]潘存云,温熙森.渐开线环形齿球齿轮传动原理与运动分析.机械工程学报,2005, 41(5):1-9
[169]潘存云,温熙森.渐开线球齿轮齿廓曲面方程的推导.国防科技大学学报,2004, 26(4):93-98
[170]赵亚平,魏文军.点接触齿面滑动率计算方法及其对交错轴渐开线斜齿轮传动的应用.中国机械工程,2006,17(8):40-43
[171]黄锡恺.机械原理.人民教育出版社,1981
[172]李常义.渐开线环形齿球齿轮传动强度计算方法研究:硕士学位论文.长沙:国防科技大学,2004
[173]博弈创作室编著.APDL参数化有限元分析技术及其应用实例.中国水利水电出版社,2001
[174]李小清.螺旋锥齿轮数控加工与误差修正技术研究:博士学位论文.华中科技大学,2004
[175]肖卫国,郝崇恩,李高风.三轴飞行模拟转台误差研究.系统仿真学报,2001,13(5):678-680
[176]刘延斌,金光,何惠阳.轴仿真转台指向误差的建模研究.哈尔滨工业大学学报,2005,37(5):701-704
[177] Bailey M W, Juchem H O. The advantages of CBN grinding: low cutting forces and improved workpiece integrity. IDR, 1998, 3:83 -89
[178] Rowe W B, Black S C. Temperatures in CBN grinding. IDR, 1995, 4:165-169
[179]吴武辉.球齿轮数控磨齿机结构设计与分析:硕士学位论文.国防科学技术大学,2006