基于球面渐开线齿面生成原理的弧齿锥齿轮新型铣削加工方法
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摘要
弧齿锥齿轮具有重合系数大、传动平稳、强度高等特性，被广泛应用于航空、舰船和国防技术装备以及机床、汽车、工程机械和矿山机械等各种机械产品中。球面渐开线齿形属于理想的弧齿锥齿轮齿形。但是球面渐开线齿形弧齿锥齿轮齿面是空间螺旋面，齿面数学模型较为复杂，从而使得现有的齿面切制加工工艺极其复杂，机床和刀具造价昂贵。实际切齿加工过程中，弧齿锥齿轮切齿加工采用的是工程近似法，锥齿轮齿形以背锥展开平面上假想的当量圆柱齿轮齿形来近似代替，并追求刀具设计、制造简单，用直线刃回转形成的圆锥螺旋面作为刀刃的切削表面，以包络展成的方式加工出弧齿锥齿轮齿面。如此切制的齿面严格来说不是球面渐开线齿面，失去了可互换性、瞬时传动比恒定等诸多性能，出现了诸如传动噪音大、接触区不良、强度降低等弊病。为了获得比较好的齿面接触性能，必须对机床和刀具参数进行反复的调整，这使得高精密弧齿锥齿轮的造价比较昂贵，而且需要花费大量的时间进行锥齿轮齿面的对滚调整。此外弧齿锥齿轮加工的核心关键技术一直被国外封锁，严重制约了我国在弧齿锥齿轮加工技术方面的进步。
本文基于球面渐开线齿面生成原理，突破现有弧齿锥齿轮加工的格里森切齿体制，提出了两种全新的弧齿锥齿轮铣削加工方法。一种是以齿面的圆弧形发生线作为切齿刀刃，通过三轴联动的方式即可加工出无原理误差的弧齿锥齿轮齿面的方法。另一种方法是基于前一种加工方法的研究，以若干离散点近似代替弧齿锥齿轮齿面的圆弧形发生线，通过更为简单的二轴联动方式即可实现弧齿锥齿轮齿面的铣削加工。论文的主要研究工作包括以下几方面：
1、对弧齿锥齿轮齿面的生成原理进行了分析。球面渐开线齿形弧齿锥齿轮齿面的生成过程是由其圆弧形发生线随着基圆锥相切面——（Q）平面在基圆锥上纯滚动生成。其中凹齿面是由齿面发生线由大端向小端的方向生成，而凸齿面则刚好相反。文中运用空间三维建模和解析几何的知识对齿面生成过程的各运动关系进行推算和分析。
2、基于球面渐开线齿面的生成原理，提出了一种全新的弧齿锥齿轮铣削加工方法。该方法以齿面发生线作为切齿刀刃，以齿面生成运动的逆运动作为切齿运动，仅需三轴联动即可切制出弧齿锥齿轮齿面。本文运用空间几何学的知识分别对不同旋向的弧齿锥齿轮的凸、凹齿面的切制运动进行了推算和分析，并建立了弧齿锥齿轮齿面切制生成的运动模型。
3、根据三轴联动铣齿加工新方法对刀具的要求，对切齿刀具进行了设计。所设计的刀具在铣齿加工过程中高速旋转，形成一个半球状的刀刃，并与假想的（Q）平面截交生成齿面发生线。运用结构设计和空间几何学的知识对切齿刀具的几何外形和关键几何参数进行了设计和推算，并运用CATIA软件分别建立了加工凹齿面的外刃铣刀和加工凸齿面的内刃铣刀的三维模型。
4、进行了三轴联动铣齿机构的设计，并运用VERICUT软件进行了三轴联动切齿加工仿真。由切齿运动的分析可知，切齿加工过程中所需的三个联动运动分别为：齿坯的自转运动ω1、齿坯绕着刀刃端点的旋转运动ω2和齿坯沿着调整区与切削区交界线方向的直线移动V。对以上三个运动所需的机构分别进行了设计，并运用CATIA软件分别建立了其三维模型以及三者的装配模型。为了进一步验证所设计的三轴联动机构和切齿新方法的可行性，运用VERICUT软件分别建立了切齿机床的简化模型、齿坯模型、刀具模型，并运用MATLAB、EXCEL软件编制了数控加工程序，最后进行了弧齿锥齿轮铣削加工仿真。
5、在三轴联动铣齿新方法研究的基础上，提出了一种切齿运动更为简单的二轴联动切齿新方法。该方法以若干离散点代替弧齿锥齿轮齿面的圆弧形发生线，通过点铣削包络展成的方式进行锥齿轮齿面的加工。首先对运用该方法切齿加工过程中所需的两个联动运动进行了分析和推算，然后对切齿运动所需的机床结构和刀具进行了设计，最后运用CATIA软件建立了该切齿机床关键机构的三维模型，并对运用该机构实现弧齿锥齿轮齿面加工所需的各个运动进行了分析。
6、运用VERICUT仿真软件对本文所提出的二轴联动铣齿新方法进行了切齿加工仿真分析。首先运用VERICUT软件分别建立了切齿机床、刀具和弧齿锥齿轮齿坯的三维模型。然后运用MATLAB和EXCEL软件编制了切齿加工所需的数控程序。最后在VERICUT的加工仿真环境下，调用仿真软件内置的sin840d控制系统，添加所编制的数控程序，进行了弧齿锥齿轮的切齿加工仿真。
7、进行了二轴联动数控切齿机床原理样机的研制，切齿加工实验以及齿面偏差测量。根据切齿运动分析和两轴联动切齿机床的结构设计要求，在现有XK716数控铣床的基础上进行改装，添加了关键功能部件，研制出了切齿机床原理样机。并进行了锥齿轮齿坯的设计加工和切齿刀具的选购。然后运用所设计的切齿机床进行了切齿实验，切制出了弧齿锥齿轮样件。最后运用3906T型齿轮测量中心对加工出的弧齿锥齿轮齿面偏差进行了测量，结果显示：齿面法向偏差在-0.0227mm~0.0097mm之间。由切齿实验和齿面偏差测量结果进一步验证了所提出的弧齿锥齿轮二轴联动切齿新方法。
Spiral bevel gears have advantages of large coincidence degree, steady transmission andhigh strength. And they are widely used in fields of aerospace, ships, national defenseequipment and kinds of machines, such as machine tools, automotive vehicle, engineeringmachine and mining machine. And the tooth profile of spherical involute is ideal profile ofspiral bevel gear. However, the surface of spiral bevel gear with spherical involute is spatialspiral surface, and it’s mathematical model is relatively complicated, thus making theprocessing technology of spiral bevel gear more complicated, and the cost of machine tooland cutting tool more expensive. In the cutting process of spiral bevel gear, the machiningmethod is the method of engineering approximation, and the tooth profile of bevel gear isapproximated by the profile of equivalent cylindrical gear which is unwrapped on the backcone. In order to pursue that the cutting tool can be designed and manufactured more simply,the machined surface of cutting edge is designed as conical helicoid which is formed by thestraight line. And it is used to cut the surface of spiral bevel gear by the method of envelopeexpansion. Strictly speaking, the tooth profile generated by this method is not the sphericalinvolute. And many excellent properties are lost, such as interchangeability, constanttransmission ratio. Many disadvantages appear, such as large transmission noise, adversecontact area, strength reduction and so on. In order to gain better performance of toothcontact, parameters of machine tool and cutting tool must be adjusted iteratively. These makethat we must cost much time to adjust the tooth contact. In addition, the key cuttingtechnology of spiral bevel gears has been blocked by the foreign countries. Thus thetechnology progress of spiral bevel gears in my country has been restricted seriously.
Base on the generating principle of tooth surface with spherical involute, two new millingmethods of spiral bevel gears are proposed in the paper which breaks through the existingcutting system of Gleason. The first method is that the surface generating line is used ascutting edge, and the tooth surface can be machined out through three axes linkage. Theother is that based on the research of first method, the arc generating-line is approximated bysome dispersed points, and the tooth surface can be machined through two axes linkage. Themain research contents of this paper are as follows:
1. The generating principle of tooth surface was analyzed. The tooth surface of spiralbevel gear with spherical involute is formed by the arc generating-line’s pure rolling on thebase cone. The concave tooth surface is generated by generating line from the big end to theother end. And the generation of convex surface is opposite exactly. The relationshipbetween the movements in the cutting process was calculated and analyzed by usingknowledge of three-dimensional modeling and analytic geometry.
2. Based on the the generating principle of tooth surface with spherical involute, a newcutting method was proposed. The generating line of tooth surface is used as cutting edge,and the cutting movement is the inverse movement of surface generation. The tooth surfacecan be machined out through three axes linkage by using this method. The cutting motions ofsurfaces with different revolving direction were calculated and analyzed by using knowledge of space geometry. And the motion model of surface cutting was built.
3. The new cutting tool was designed according to the requirements of tool based on thenew method in this paper. When the tool rotates at high speed in the cutting process, it willform a half-spherical cutting edge. The intersection of this half-spherical cutting edge and (Q)face is the generating line of tooth surface. The geometric shape and key parameters weredesigned and caculated by using knowledge of structure design and space geometry. And thethree dimensional models of tools were built up by using CATIA software.
4. The three axes linkage mechanism was designed, and the cutting simulation was carriedout by using VERICUT software. According to the analysis of cutting motion, three linkagemotions in the cutting process are as follow: spin motion of gear blank (ω1), rotary motionthat gear blank rotates around the endpoint of cutting edge (ω2), linear movement that gearblank moves along the boundary line between cutting zone and adjustment region (V). Themechanisms for above motions were designed. And the three dimensional models of thesemechanisms and their assembly product were built up by using CATIA software. In order toverify the feasibility of the three axes linkage mechanism and new cutting method, models ofmachine tool, gear blank and cutting tool were built by using VERICUT software. And NCprogram was compiled by using software of MATLAB and EXCEL. At last, the cuttingsimulation of spiral bevel gear was carried out.
5. Based on the research of the three axes linkage method, a more simple cutting methodwas proposed, by which spiral bevel gear can be machined with two axes linkage. The arcgenerating-line of tooth surface is approximated by some dispersed points, and tooth surfacewas machined with the mode of envelope expansion. Firstly, two linkage motions in thecutting process were calculated and analyzed. Then mechanisms of machine tool and cuttingtool were designed. At last, the three-dimensional model of cutting tool was built up by usingCATIA software. And how the designed mechanism completes motions in the cuttingprocess was analyzed.
6. In order to verify the feasibility of the two axes linkage mechanism and the cuttingmethod, cutting simulation analysis of two axes linkage method was carried out by usingVERICUT software. Firstly, models of machine tool, cutting tool and gear blank were builtby using VERICUT software. And then, NC program was compiled by using software ofMATLAB and EXCEL. At last, in the simulation environment of VERICUT, sin840d controlsystem was called, the compiled NC program was added, and the two axes linkage cuttingsimulation of spiral bevel gear was carried out.
7. The principle prototype of two axes linkage NC cutting machine was successfullydeveloped, and the cutting experiment and the measurement of profile deviation were carriedout. According to the analysis of cutting motions and the designed machine structure, aprinciple prototype of cutting machine was developed by refitting and adding key functionelements on the XK716NC milling machine. Taking a concrete spiral bevel gear forexample, the gear blank was designed, and the cutting tool was purchased. Then the cuttingexperiment was carried out by using the designed machine tool. At last, the measurement ofprofile deviation was carried out by using3906T gear measuring center. The measurementresults show that the surface normal deviation is between-0.0227mm and0.0097mm. These verify the feasibility of two axes linkage milling method which is proposed in this paper.
本文基于球面渐开线齿面生成原理，突破现有弧齿锥齿轮加工的格里森切齿体制，提出了两种全新的弧齿锥齿轮铣削加工方法。一种是以齿面的圆弧形发生线作为切齿刀刃，通过三轴联动的方式即可加工出无原理误差的弧齿锥齿轮齿面的方法。另一种方法是基于前一种加工方法的研究，以若干离散点近似代替弧齿锥齿轮齿面的圆弧形发生线，通过更为简单的二轴联动方式即可实现弧齿锥齿轮齿面的铣削加工。论文的主要研究工作包括以下几方面：
1、对弧齿锥齿轮齿面的生成原理进行了分析。球面渐开线齿形弧齿锥齿轮齿面的生成过程是由其圆弧形发生线随着基圆锥相切面——（Q）平面在基圆锥上纯滚动生成。其中凹齿面是由齿面发生线由大端向小端的方向生成，而凸齿面则刚好相反。文中运用空间三维建模和解析几何的知识对齿面生成过程的各运动关系进行推算和分析。
2、基于球面渐开线齿面的生成原理，提出了一种全新的弧齿锥齿轮铣削加工方法。该方法以齿面发生线作为切齿刀刃，以齿面生成运动的逆运动作为切齿运动，仅需三轴联动即可切制出弧齿锥齿轮齿面。本文运用空间几何学的知识分别对不同旋向的弧齿锥齿轮的凸、凹齿面的切制运动进行了推算和分析，并建立了弧齿锥齿轮齿面切制生成的运动模型。
3、根据三轴联动铣齿加工新方法对刀具的要求，对切齿刀具进行了设计。所设计的刀具在铣齿加工过程中高速旋转，形成一个半球状的刀刃，并与假想的（Q）平面截交生成齿面发生线。运用结构设计和空间几何学的知识对切齿刀具的几何外形和关键几何参数进行了设计和推算，并运用CATIA软件分别建立了加工凹齿面的外刃铣刀和加工凸齿面的内刃铣刀的三维模型。
4、进行了三轴联动铣齿机构的设计，并运用VERICUT软件进行了三轴联动切齿加工仿真。由切齿运动的分析可知，切齿加工过程中所需的三个联动运动分别为：齿坯的自转运动ω1、齿坯绕着刀刃端点的旋转运动ω2和齿坯沿着调整区与切削区交界线方向的直线移动V。对以上三个运动所需的机构分别进行了设计，并运用CATIA软件分别建立了其三维模型以及三者的装配模型。为了进一步验证所设计的三轴联动机构和切齿新方法的可行性，运用VERICUT软件分别建立了切齿机床的简化模型、齿坯模型、刀具模型，并运用MATLAB、EXCEL软件编制了数控加工程序，最后进行了弧齿锥齿轮铣削加工仿真。
5、在三轴联动铣齿新方法研究的基础上，提出了一种切齿运动更为简单的二轴联动切齿新方法。该方法以若干离散点代替弧齿锥齿轮齿面的圆弧形发生线，通过点铣削包络展成的方式进行锥齿轮齿面的加工。首先对运用该方法切齿加工过程中所需的两个联动运动进行了分析和推算，然后对切齿运动所需的机床结构和刀具进行了设计，最后运用CATIA软件建立了该切齿机床关键机构的三维模型，并对运用该机构实现弧齿锥齿轮齿面加工所需的各个运动进行了分析。
6、运用VERICUT仿真软件对本文所提出的二轴联动铣齿新方法进行了切齿加工仿真分析。首先运用VERICUT软件分别建立了切齿机床、刀具和弧齿锥齿轮齿坯的三维模型。然后运用MATLAB和EXCEL软件编制了切齿加工所需的数控程序。最后在VERICUT的加工仿真环境下，调用仿真软件内置的sin840d控制系统，添加所编制的数控程序，进行了弧齿锥齿轮的切齿加工仿真。
7、进行了二轴联动数控切齿机床原理样机的研制，切齿加工实验以及齿面偏差测量。根据切齿运动分析和两轴联动切齿机床的结构设计要求，在现有XK716数控铣床的基础上进行改装，添加了关键功能部件，研制出了切齿机床原理样机。并进行了锥齿轮齿坯的设计加工和切齿刀具的选购。然后运用所设计的切齿机床进行了切齿实验，切制出了弧齿锥齿轮样件。最后运用3906T型齿轮测量中心对加工出的弧齿锥齿轮齿面偏差进行了测量，结果显示：齿面法向偏差在-0.0227mm~0.0097mm之间。由切齿实验和齿面偏差测量结果进一步验证了所提出的弧齿锥齿轮二轴联动切齿新方法。
Spiral bevel gears have advantages of large coincidence degree, steady transmission andhigh strength. And they are widely used in fields of aerospace, ships, national defenseequipment and kinds of machines, such as machine tools, automotive vehicle, engineeringmachine and mining machine. And the tooth profile of spherical involute is ideal profile ofspiral bevel gear. However, the surface of spiral bevel gear with spherical involute is spatialspiral surface, and it’s mathematical model is relatively complicated, thus making theprocessing technology of spiral bevel gear more complicated, and the cost of machine tooland cutting tool more expensive. In the cutting process of spiral bevel gear, the machiningmethod is the method of engineering approximation, and the tooth profile of bevel gear isapproximated by the profile of equivalent cylindrical gear which is unwrapped on the backcone. In order to pursue that the cutting tool can be designed and manufactured more simply,the machined surface of cutting edge is designed as conical helicoid which is formed by thestraight line. And it is used to cut the surface of spiral bevel gear by the method of envelopeexpansion. Strictly speaking, the tooth profile generated by this method is not the sphericalinvolute. And many excellent properties are lost, such as interchangeability, constanttransmission ratio. Many disadvantages appear, such as large transmission noise, adversecontact area, strength reduction and so on. In order to gain better performance of toothcontact, parameters of machine tool and cutting tool must be adjusted iteratively. These makethat we must cost much time to adjust the tooth contact. In addition, the key cuttingtechnology of spiral bevel gears has been blocked by the foreign countries. Thus thetechnology progress of spiral bevel gears in my country has been restricted seriously.
Base on the generating principle of tooth surface with spherical involute, two new millingmethods of spiral bevel gears are proposed in the paper which breaks through the existingcutting system of Gleason. The first method is that the surface generating line is used ascutting edge, and the tooth surface can be machined out through three axes linkage. Theother is that based on the research of first method, the arc generating-line is approximated bysome dispersed points, and the tooth surface can be machined through two axes linkage. Themain research contents of this paper are as follows:
1. The generating principle of tooth surface was analyzed. The tooth surface of spiralbevel gear with spherical involute is formed by the arc generating-line’s pure rolling on thebase cone. The concave tooth surface is generated by generating line from the big end to theother end. And the generation of convex surface is opposite exactly. The relationshipbetween the movements in the cutting process was calculated and analyzed by usingknowledge of three-dimensional modeling and analytic geometry.
2. Based on the the generating principle of tooth surface with spherical involute, a newcutting method was proposed. The generating line of tooth surface is used as cutting edge,and the cutting movement is the inverse movement of surface generation. The tooth surfacecan be machined out through three axes linkage by using this method. The cutting motions ofsurfaces with different revolving direction were calculated and analyzed by using knowledge of space geometry. And the motion model of surface cutting was built.
3. The new cutting tool was designed according to the requirements of tool based on thenew method in this paper. When the tool rotates at high speed in the cutting process, it willform a half-spherical cutting edge. The intersection of this half-spherical cutting edge and (Q)face is the generating line of tooth surface. The geometric shape and key parameters weredesigned and caculated by using knowledge of structure design and space geometry. And thethree dimensional models of tools were built up by using CATIA software.
4. The three axes linkage mechanism was designed, and the cutting simulation was carriedout by using VERICUT software. According to the analysis of cutting motion, three linkagemotions in the cutting process are as follow: spin motion of gear blank (ω1), rotary motionthat gear blank rotates around the endpoint of cutting edge (ω2), linear movement that gearblank moves along the boundary line between cutting zone and adjustment region (V). Themechanisms for above motions were designed. And the three dimensional models of thesemechanisms and their assembly product were built up by using CATIA software. In order toverify the feasibility of the three axes linkage mechanism and new cutting method, models ofmachine tool, gear blank and cutting tool were built by using VERICUT software. And NCprogram was compiled by using software of MATLAB and EXCEL. At last, the cuttingsimulation of spiral bevel gear was carried out.
5. Based on the research of the three axes linkage method, a more simple cutting methodwas proposed, by which spiral bevel gear can be machined with two axes linkage. The arcgenerating-line of tooth surface is approximated by some dispersed points, and tooth surfacewas machined with the mode of envelope expansion. Firstly, two linkage motions in thecutting process were calculated and analyzed. Then mechanisms of machine tool and cuttingtool were designed. At last, the three-dimensional model of cutting tool was built up by usingCATIA software. And how the designed mechanism completes motions in the cuttingprocess was analyzed.
6. In order to verify the feasibility of the two axes linkage mechanism and the cuttingmethod, cutting simulation analysis of two axes linkage method was carried out by usingVERICUT software. Firstly, models of machine tool, cutting tool and gear blank were builtby using VERICUT software. And then, NC program was compiled by using software ofMATLAB and EXCEL. At last, in the simulation environment of VERICUT, sin840d controlsystem was called, the compiled NC program was added, and the two axes linkage cuttingsimulation of spiral bevel gear was carried out.
7. The principle prototype of two axes linkage NC cutting machine was successfullydeveloped, and the cutting experiment and the measurement of profile deviation were carriedout. According to the analysis of cutting motions and the designed machine structure, aprinciple prototype of cutting machine was developed by refitting and adding key functionelements on the XK716NC milling machine. Taking a concrete spiral bevel gear forexample, the gear blank was designed, and the cutting tool was purchased. Then the cuttingexperiment was carried out by using the designed machine tool. At last, the measurement ofprofile deviation was carried out by using3906T gear measuring center. The measurementresults show that the surface normal deviation is between-0.0227mm and0.0097mm. These verify the feasibility of two axes linkage milling method which is proposed in this paper.
引文
[1]中国齿轮专业协会.中国齿轮工业年鉴[M].北京：北京理工大学出版社，2006.
[2] Litvin F L, Fuentes A, Hayasaka K. Design, manufacture, stress analysis, and experimental tests oflow-noise high endurance spiral bevel gears [J]. Mechanism and Machine Theory,2006,41(1):83-118.
[3] FuentesA, Litvin F L, Mullins B R, et al. Design and StressAnalysis of Low-NoiseAdjusted BearingContact Spiral Bevel Gears [J]. Journal of Mechanical Design,2002,124(3):524-532.
[4]李兆文，王勇，陈正洪.螺旋锥齿轮技术的研究现状[J].工具技术，2007,4l(l0):3-6.
[5]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.
[6]周凯红,李淑.螺旋锥齿轮技术的历史、现状和展望[J].桂林航天工业高等专科学校学报,2008,3:4-8.
[7] Litvin F L, FuentesA. Gear geometry and applied theory [M]. Cambridge University Press,2004.
[8] Ma N, Xu W J, Wang X Y, et al. Mathematical modeling for finishing tooth surfaces of spiral bevelgears using pulse electrochemical dissolution [J]. Int J Adv Manuf Technol,2011,54(9-12):979-986.
[9] Deng X B, Hua L, Han X H. Three-dimensional FE modelling simulation of cold rotary forging ofspiral bevel gear [J]. IRONMAKING&STEELMAKING,2011,38(2):101-111.
[10] Yang Z J, Wang Y K, Li L N, et al. Mathematical Model of Spiral Bevel Gears Manufactured byGenerating Line Method [C]. Advanced Materials Research,2011,154-155:103-108.
[11]胡来瑢.空间啮合原理及应用[M].煤炭工业出版社，1987.
[12]曾韬.螺旋锥齿轮设计与加工[M].哈尔滨工业大学出版社,1989.
[13] Simon V V. Influence of tooth modifications on tooth contact in face-hobbed spiral bevel gears [J].Mechanism and machine theory,2011,46(12):1980-1998.
[14] Simon V. Influence of tooth errors and misalignments on tooth contact in spiral bevel gears [J].Mechanism and machine theory,2008,43(10):1253-1267.
[15] Gonzalez-Perez I, Fuentes A, Hayasaka, K. Analytical determination of basic machine-tool settingsfor generation of spiral bevel gears from blank data [J]. Journal of mechanical design,2010,132(10):1-11.
[16]彭东林，戴政远，郑连清，等.弧齿锥齿轮铣齿机传动误差检测系统研究[J].仪器仪表学报，1999,20（3）：280-284.
[17]曹雪梅，张华，方宗德.航空弧齿锥齿轮承载传动误差的分析与设计[J].航空动力学报，2009，24（11）：2618-2624.
[18]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.
[19]天津齿轮机床研究所，西安交通大学.格里森锥齿轮技术资料译文集[M].机械工业出版社，1986.
[20] Gleason Seminar. Spiral bevel and hypoid gear technology update [R]. Beijing: Gleason Corporation,2007.
[21]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.
[22] Handschuh R F, Bill R C. Recent manufacturing advances for spiral bevel gears [J]. SAETransactions,1991:2793-2804.
[23] Park N G, Lee H W. The spherical involute bevel gear: its geometry, kinematic behavior andstandardization [J]. Journal of mechanical science and technology,2011,25(4):1023-1034.
[24]李特文.齿轮啮合原理[M].上海：上海科学技术出版社，1984.
[25]北京齿轮厂.螺旋锥齿轮[M].科学出版社,1974.
[26]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.
[27] Stadtfeld H L.Advanced bevel gear technology [M]. The Gleason Works,2000.
[28]李敦信，包润阁，王德友.锥齿轮加工简化计算[M].机械工业出版社，1978.
[29] Zhu C D, Guan Q, Wang H. Twin symmetry roll axial rolling: new method of plastic formingprofiles demonstrated using manufacture of spiral bevel gears [J]. Ironmaking&steelmaking,2011,38(3):211-217.
[30] Stadtfeld H J. Handbook of Bevel and Hypoid Gears: Calculation, Manufacturing, and Optimization[M]. NY: Rochester Institute of Technology,1993.
[31]刘立民.奥利康制弧齿锥齿轮XN型齿的应用[J].现代零部件，2006,3:100-101.
[32] Liu G L, Fan H W, Pinion tooth surface generation strategy of spiral bevel gears [J]. Chinese journalof mechanical engineering,2012,25(4):753-759.
[33] Watanabe M, Maki M, Hirokawa S. A study on forging of spiral bevel gear [C]. Proceedings of theasme international design engineering technical conferences and computers and information inengineering conference,2008,7:799-806.
[34]西安交通大学机制教研室齿轮研究组.弧齿锥齿轮和准双曲线齿轮加工调整原理[M].上海科学技术出版社，1979.
[35]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.
[36]毛世民，吴序堂.任意指定接触基准点的切齿理论——对格里森半展成法加工弧齿维齿轮和准双曲面齿轮方法的改进[J].西安交通大学学报，1985,19（5）：1-10.
[37]李普华.弧齿锥齿轮和准双曲面齿轮加工技术[J].机电工程技术，2010,39（7）：134-135.
[38]李广财，吴亚龙，杨兆军.零度弧齿锥齿轮加工工艺简介[J].一重技术，2004,2:44-45.
[39]《齿轮制造工艺手册——滚、插、磨、剃、刨》编委会.齿轮制造工艺手册——滚、插、磨、剃、刨[M].机械工业出版社，2010.
[40] Fan Q. Computerized modeling and simulation of spiral bevel and hypoid gears manufactured bygleason face hobbing process [J]. Journal of mechanical design,2006,128(6):1315-1327.
[41] Baxter M L. Basic geometry and tooth contact of hypoid gears [J]. Industrial Mathematics,1961,11(2):1-28
[42] Baxter M L. Second order surface generation [J]. Industrial Mathematics,1973,23(2):85-106.
[43] Litvin F L. Development of gear technology and theory of gearing [M]. National Aeronautics andSpace Administration, Lewis Research Center,1997.
[44] Е.А.Андрущенко,蒋朝明.奥利康公司的齿轮加工[J].齿轮，1983,41-43.
[45]卢佳，董苗苗.克林根贝尔格锥齿轮铣齿机工作原理的基础分析——AMK852实践[J].科技创新与应用，2012，3：56-57.
[46]汪有刚.浅析克林根贝尔格制锥齿轮的加工及特点[J].民营科技，2013,1:20.
[47]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四册[M]，机械工业出版社，1986.
[48] Litvin F L, Wang A G, Handschuh R F. Computerized generation and simulation of meshing andcontact of spiral bevel gears with improved geometry [J]. Computer methods in applied mechanics&engineering,1998,158:35-64.
[49] Handschuh R F, Bibel G D. Experimental and analytical study of aerospace spiral bevel gear toothfillet stresses [J]. Journal of mechanical design,1999,121(4):565-572.
[50]蒋文兵.螺旋锥齿轮五轴联动数控加工的研究[D].郑州:郑州大学，2003.
[51]遇立基.CIMT’99展出的数控齿轮加工机床[J].制造技术与机床，1999，12:6-7.
[52]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，2004，9:11-13.
[53]刘小龙.螺旋锥齿轮切、磨齿技术的发展及面临的挑战[J].汽车齿轮，2010，4：42-50.
[54] Alves J T, Guingand M, de Vaujany J P. Designing and manufacturing spiral bevel gears using5-axiscomputer numerical control (CNC) milling machines [J]. J. Mech. Des.,2013,135(2):1-6.
[55] Zhou K H, Tang J Y. Envelope-approximation theory of manufacture technology for point-contacttooth surface on six-axis CNC hypoid [J]. Mechanism and machine theory,2011,46(6):806-819.
[56]刘凯.弧齿锥齿轮数控铣齿机运动分析及控制系统研究[D].南京：南京航空航天大学，2007.
[57] Harmann J.Stadtfeld.锥齿轮齿形加工的第二次革命——Hermann J.Stadtfeld先生在W&B杂志上介绍的锥齿轮加工技术最新发展的情况[J].世界制造技术与装备市场，2004,5:71-75.
[58] Fan Q, DaFoe R S, Swanger J W. New developments in computerized design and manufacturing ofspiral bevel and hypoid gears [C]. International conference on mechanical transmissions,2006,1-2:128-133.
[59] SIGMA∑POOL集团.SIGMA∑POOL齿轮技术集团——国际齿轮界的强强联合[J].机电国际市场，2000，6:36-37.
[60]李先广.当今制齿技术及制齿机床[J].现代制造工程，2002,11:66-68.
[61]李先广，刘飞，曹华军.齿轮加工机床的绿色设计与制造技术[J].机械工程学报，2009,45（11）：140-145.
[62]乐美豪.中国齿轮制造业50年[J].机电国际市场，2000,5:5-8.
[63]吴训成，毛世民，吴序堂.点接触齿面在控制误差敏感性条件下的二阶参数设计[J].西安交通大学学报，1999,33（11）：86-89.
[64]毛世民，吴序堂.新型万能曲线齿锥齿轮加工机床的运动学[J].制造技术与机床，1997,6:22-24.
[65]林经德，刘鹄然.摆线齿螺旋锥齿轮铣齿机工作原理的新认识[J].机械研究与应用，1998，11（2）：17-18.
[66]刘鹄然，刘厚根，李国顺.在螺旋锥齿轮数控铣齿机上实现刀倾法加工小轮[J].现代机械.1998，4:54-57.
[67]马云.CCMT2012制齿装备精品荟萃[J].世界制造技术与装备市场，2012,6:82-87.
[68]恩宝贵.中国机床工业到了向世界制造技术高峰冲锋的时候[J].制造技术与机床，2012,6:13-18.
[69]张卫青，张明德，郭晓东，等.全数控锥齿轮铣齿机运动控制方法及切齿实验研究[J].中国机械工程，2009,20（22）：2733-2737.
[70]张曙，朱志浩，樊留群.中国机床工业综述:过去、现在与将来[J].世界制造技术与装备市场，2011,5：54-62.
[71]王红利，钟晓玲.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.
[72]李先广.机床制造业绿色制造运行模式及其特征主线研究[D].重庆：重庆大学，2012.
[73]李朋.相约南京CCMT,盛览创新装备[J].现代零部件，2012,4:42-46.
[74]李翼龙，郭志全，刘明涛，等.基于FEM的数控弧齿铣齿机立柱结构静、动态设计[J].天津科技大学学报，2012,27（1）：52-56.
[75]王红利.从CIMT2007看齿轮加工机床的发展趋势[J].制造技术与机床，2007,3:40-44.
[76]毛世民，聂钢，范超毅，等.准渐开线齿锥齿轮的齿面展成[J].中国机械工程，1999,10（12）：1325-1327.
[77]苏智剑，吴序堂.基于计算机数字控制弧齿锥齿轮加工机床的准双曲面齿轮的制造[J].机械工程学报，2007,43（5）：57-63.
[78]李建刚，吴序堂，贺敬良，等.CNC铣齿机床加工曲线齿锥齿轮仿真系统的研究[J].系统仿真学报，2003,15（4）：499-501.
[79]吴序堂.齿轮啮合原理[M].北京：机械工业出版社，1982.
[80]李建刚，毛世民，苏智剑.五轴联动数控工具磨床加工模拟系统的开发[J].工具技术，2001，35（6）：18-19.
[81]张军辉，方宗德，王成.基于NURBS的弧齿锥齿轮真实齿面的数字化仿真[J].航空动力学报，2009,24(7):1672-1676.
[82]苏进展，方宗德，蔡香伟.弧齿锥齿轮数字化齿面啮合仿真分析与试验[J].西北工业大学学报，2012,30（4）：565-569.
[83]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.
[84]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.
[85]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.
[86]方宗德，曹雪梅，沈云波.弧线齿面齿轮的齿面设计与加工[J].航空动力学报，2010,25（1）：224-227.
[87]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）：200-203.
[88]刘光磊，樊红卫，谷霁红，等.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.
[89]曹雪梅，方宗德，许浩.弧齿锥齿轮的齿面主动设计及试验验证[J].机械工程学报，2008，44（7）：209-214.
[90] Jia J S, Cao X M. Generation and TCA of Straight Bevel Gear Drive with Modified Geometry [J].Applied mechanics and materials,2011,86:403-406.
[91] Cao X M, Fang Z D, Xu H. Design of pinion machine tool-settings for spiral bevel gears bycontrolling contact path and transmission errors [J]. Chinese journal of aeronautics,2008,21(2):179-186.
[92] Zhang J H, Fang Z D, Cao X M, et al. The modified pitch cone design of the hypoid gear:Manufacture, stress analysis and experimental tests [J]. Mechanism and machine theory,2007,42(2):147-158.
[93] Wei B Y, Deng X Z, Fang Z D. Study on ultrasonic-assisted lapping of gears [J]. Internationaljournal of machine tools&manufacture,2007,47(12-13):2051-2056.
[94]曹雪梅，方宗德，张金良，等.弧齿锥齿轮的齿面主动设计[J].机械工程学报，2007,43（8）：155-158.
[95]邓效忠，方宗德，魏冰阳.接触路径对弧齿锥齿轮接触应力和弯曲应力的影响[J].中国机械工程，2003,14（22）：1895-1898.
[96]刘凯，赵东标.弧齿锥齿轮数控加工和齿面接触点求解算法研究[J].小型微型计算机系统，2008，29（3）：572-576.
[97]刘凯，赵东标，黄沛建.弧齿锥齿轮数控展成运动轨迹规划方法[J].华南理工大学学报(自然科学版)，2007,35（8）：32-37.
[98] Liu K, Zhao D B. Algorithms of generation motion and direct interpolation for spiral bevel gear ncmachining [J]. Transactions of nanjing university of aeronautics&astronautics,2007,24(3):257-264.
[99]刘凯，赵东标.弧齿锥齿轮数控加工主动控制方法研究[J].机械科学与技术，2007,26（8）：973-976.
[100]王延忠，周云飞，李左章，等.基于通用五坐标数控机床螺旋锥齿轮NC加工研究[J].中国机械工程，2001,12（8）：903-906.
[101]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.
[102]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.
[103]李小清，周云飞，李左章，等.螺旋锥齿轮数控展成轨迹生成及直接插补算法[J].华中科技大学学报(自然科学版)，2002,30（10）：38-40.
[104]王延忠，周云飞，李左章，等.螺旋锥齿轮空间曲面NC加工插补误差分析[J].华中科技大学学报(自然科学版)，2002,30（2）：9-12.
[105]李小清，周云飞，王延忠，等.螺旋锥齿轮拟合齿面啮合特性分析方法[J].中国机械工程，2003，14（13）：1139-1143.
[106]王延忠，周云飞，周济，蔡春源.高速弧齿锥齿轮点接触瞬态等温弹流数值分析[J].华中科技大学学报，2001，29（12）：4-7.
[107]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.
[108] Wang Y Z, Wu C H, Gong K, et al. Loaded tooth contact analysis of orthogonal face-gear drives [J].Proceedings of the institution of mechanical engineers part c-journal of mechanical engineeringscience,2012,226(C9):2309-2319.
[109]徐彦伟，张连洪.弧齿锥齿轮齿面点坐标求解及模型建立[J].机床与液压，2012，40（21）：138-142.
[110]李敬财，徐文丽，李清，等.基于层片分割算法弧齿锥齿轮及准双面齿轮五轴数控切削仿真[J].机械传动，2011,35（3）：7-10.
[111]韩佳颖，王太勇，李清，郑慧江.基于解析计算的螺旋锥齿轮切削仿真算法[J].农业机械学报，2010,41（12）：223-227.
[112]徐彦伟，张连洪，魏巍.重型弧齿锥齿轮铣齿机数控加工模型建立与仿真[J].农业机械学报，2009,40（10）：211-215.
[113]熊越东，王太勇，张威.螺旋锥齿轮数控加工参数转换计算方法[J].组合机床与自动化加工技术，2006,8:5-8.
[114]魏巍.面向齿轮传动性能的螺旋锥齿轮铣齿机精度设计方法研究[D].天津：天津大学，2011.
[115]徐彦伟.弧齿锥齿轮铣齿机主动精度设计方法研究[D].天津：天津大学，2010.
[116] Zhou K H, Tang J Y. Envelope-approximation theory of manufacture technology for point-contacttooth surface on six-axis CNC hypoid generator [J]. Mechanism and machine theory,2011,46(6):806-819.
[117] Zhou K H, Tang J Y, Zeng T. New geometry of generating spiral bevel gear [C]. Proceedings of theASME international design engineering technical conferences and computers and information inengineering conference,2008,7:335-342.
[118]唐进元，卢延峰，周超.有误差的螺旋锥齿轮传动接触分析[J].机械工程学报，2008,44（7）：16-23.
[119]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].机械工程学报，2011,47（11）：23-29.
[120]唐进元，黄云飞，周超，等.弧齿锥齿轮展成齿面的几何建模[J].计算机仿真，2009,26（2）：293-297.
[121]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.
[122]周超，唐进元，曾韬，等.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.
[123]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.
[124]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.
[125] Chen S H, Yan H Z, Ming X Z. Error modeling and analysis of spiral bevel gear grinder based onmulti-body system theory [J]. Joumal of central south university of technology,2008,15(5):706-711.
[126]陈书涵.螺旋锥齿轮磨削误差产生机制及修正技术研究[D].长沙：中南大学，2009.
[127] Zhao Y P, Wei W J, Dong X Z. Some problems on the2DOF theory of gearing [J]. Mechanism andmachine theory,2008,43(8):1024-1037.
[128]董学朱.齿轮啮合理论基础[M].北京：机械工业出版社，1989.
[129]董学朱.李海涛，魏文军.双自由度齿轮啮合理论及应用[M].北京：机械工业出版社，2011.
[130]董学朱.弧齿锥齿轮半展成切齿调整计算新方法[J].齿轮，1988,12（4）：1-5.
[131]董学朱.弧齿锥齿轮变性全展成切齿调整计算新方法[J].齿轮，1987，11（6）：6-21.
[132]董学朱.弧齿锥齿轮刀倾全展成切齿调整计算新方法[J].北京农业工程大学学报，1988,8（3）：68-81.
[133]董学朱.弧齿锥齿轮和准双曲面齿轮切齿调整计算新方法——按大轮齿面任一基准点配切小轮的原理[J].北京农业工程大学学报，1990,10（1）：16-27.
[134]曾韬.关于《共轭曲面原理》的若干问题——与陈志新同志商榷[J].齿轮，1982,1:38-42.
[135]曾韬.螺旋锥齿轮设计中的轮坯修正[J].航空标准化，1981,5:52-56.
[136]杨丰，曾韬.弧齿锥齿轮齿面接触区的边缘检测技术[J].现代制造工程，2007,1:95-97.
[137]王裕清，武良臣，等.弧齿锥齿轮接触区理论与切削过程仿真[M].北京：煤炭工业出版社，2004.
[138]王裕清，王小林，梁剑.弧齿锥齿轮实体造型数学模型及其实现[J].中国机械工程，2007,18（14）：1660-1663.
[139]王裕清，祝运攀.弧齿锥齿轮接触斑点图像采集及预处理[J].河南理工大学学报(自然科学版)，2009,28（2）：194-198.
[140]武良臣，王裕清.锥齿轮和双曲线齿轮副接触斑点稳定性分析[J].机械工艺师，2000,10:59-60.
[141]刘冠华，马永寿，吴锐.弧齿锥齿轮轮坯修正新方法[J].机械工程师，2004，5：57.
[142] Fan Q. Optimization of face cone element for spiral bevel and hypoid gears [J]. Journal ofmechanical design,2011,133(9):1-7.
[143] Simon V. Load distribution in spiral bevel gears [J]. Journal of mechanical design,2007,129(2):201-209.
[144] Sheveleva G I, VolkovAE, Medvedev V I.Algorithms for analysis of meshing and contact ofspiral bevel gears [J]. Mechanism and machine theory,2007,42(2):198-215.
[145]刘凯，陆永华，赵东标.参数曲线自适应加减速控制方法在弧齿锥齿轮数控加工中的应用[J].机械工程学报，2009,45（12）：198-204.
[146] Ma N, Xu W J, Wang X Y, et al. Prediction method for surface finishing of spiral bevel gear toothbased on least square support vector machine [J]. Journal of central south university of technology,2011,18(3):685-689.
[147] Safavi S M, Mirian S S, Abedinzadeh R. Use of PLC module to control a rotary table to cut spiralbevel gear with three-axis CNC milling [J]. International journal of advanced manufacturingtechnology,2010,49(9-12):1069-1077.
[148] Shih Y P, Fong Z H. Flank correction for spiral bevel and hypoid gears on a six-axis CNC hypoidgenerator [J]. Journal of mechanical design,2008,130(6):1-11
[149] Wang P Y, Fong Z H. Fourth-order kinematic synthesis for face-milling spiral bevel gears withmodified radial motion (MRM) correction [J].2006,128(2):457-467.
[150] Simon V. Head-cutter for optimal tooth modi. cations in spiral bevel gears [J]. Mechanism andmachine theory,2009,44(7):1420-1435.
[151] Gosselin C, Masseth J, Liang W. Cutter interchangeability for spiral-bevel and hypoid gearmanufacturing [C]. Chicago: ASME/AGMA2003International Power Transmission and GearingConference,2003.
[152] Simon V V. Advanced manufacture of spiral bevel gears on cnc hypoid generating machine [J].Journal of mechanical design,2010,132(3):1-8.
[153] Simon V V. Machine-tool settings to reduce the sensitivity of spiral bevel gears to tooth errors andmisalignments [J]. Journal of mechanical design,2008,130(8):1-10.
[154] Artoni A, Gabiccini M, Kolivand M. Ease-off based compensation of tooth surface deviations forspiral bevel and hypoid gears: Only the pinion needs corrections [J]. Mechanism and machine theory,2013,61:84-101.
[155] Wang P Y, Fan S C, Huang Z G. Spiral bevel gear dynamic contact and tooth impact analysis [J].Journal of mechanical design,2011,133(8):1-6.
[156] Shih Y P. A novel ease-off flank modification methodology for spiral bevel and hypoid gears [J].Mechanism and machine theory,2010,45(8):1108-1124.
[157] Alves J T, Guingand M, de Vaujany J P. Set of functions for the calculation of bendingdisplacements for spiral bevel gear teeth [J]. Mechanism and machine theory,2010,45(2):349-363.
[158] Simon V. Computer simulation of tooth contact analysis of mismatched spiral bevel gears [J].Mechanism and machine theory,2007,42(3):365-381.
[159]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.
[160]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.
[161]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].2009-03-05.
[162]洪肇斌，杨兆军，张学成，等.基于齿面发生线的弧齿锥齿轮铣削加工仿真分析[J].吉林大学学报(工学版)，2013,43（2）：334-339.
[163]陈爱平，张韵风，侯欣芸译.齿轮的功用及加工[M].北京：机械工业出版社，2010.
[164]秦荣荣，崔可维.机械原理[M].长春：吉林科学技术出版社，2000.
[165]张宝珠.齿轮加工速查手册[M].北京：机械工业出版社，2010.
[166]朱孝录.齿轮传动设计手册第二版[M].北京：化学工业出版社，2010.
[167] Yang Z J, Hong Z B, Wang B C, et al. New tooth profile design of spiral bevel gears with sphericalinvolute [J]. Intl. J. Adv. Comput. Technolog.,2012,4(19):462-469.
[168] Hong Z B, Yang Z J, Zhang X C, et al. New modeling method of spiral bevel gears with sphericalinvolute based on CATIA [C]. Proc. SPIE Int. Soc. Opt. Eng.,2011,7997:79970Y.
[169]李云龙，曹岩.数控机床加工仿真系统VERICUT[M].西安：西安交通大学出版社，2005.
[170]杨胜群.VERICUT数控加工仿真技术[M].北京：清华大学出版社，2010.
[171] Hong Z B, Yang Z J, Wang B C, et al. Simulation analysis of spiral bevel gear tooth surfacegeneration based on VERICUT [J]. Applied mechanics and materials,2013,273:175-179.
[172]徐彦伟，张连洪，刘德全，等.弧齿锥齿轮成形三维虚拟仿真研究[J].中国机械工程，2008,19（22）：2703-2707.
[173]张艳，桂贵生.基于VERICUT的数控加工仿真及优化[J].现代制造技术与装备，2008,4:75-77.
[174]朱正祥.基于VERICUT数控铣齿机加工仿真的研究与应用[J].机床与液压，2008,36（9）：118-120.
[175]刘保柱，苏彦华，张宏林.MATLAB7.0从入门到精通[M].北京：人民邮电出版社，2010.
[176]于润伟，朱晓慧. MATLAB基础及应用（第2版）[M].北京：机械工业出版社，2008.
[177]宋放之.数控机床多轴加工技术实用教程[M].北京：清华大学出版社，2010.
[2] Litvin F L, Fuentes A, Hayasaka K. Design, manufacture, stress analysis, and experimental tests oflow-noise high endurance spiral bevel gears [J]. Mechanism and Machine Theory,2006,41(1):83-118.
[3] FuentesA, Litvin F L, Mullins B R, et al. Design and StressAnalysis of Low-NoiseAdjusted BearingContact Spiral Bevel Gears [J]. Journal of Mechanical Design,2002,124(3):524-532.
[4]李兆文，王勇，陈正洪.螺旋锥齿轮技术的研究现状[J].工具技术，2007,4l(l0):3-6.
[5]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.
[6]周凯红,李淑.螺旋锥齿轮技术的历史、现状和展望[J].桂林航天工业高等专科学校学报,2008,3:4-8.
[7] Litvin F L, FuentesA. Gear geometry and applied theory [M]. Cambridge University Press,2004.
[8] Ma N, Xu W J, Wang X Y, et al. Mathematical modeling for finishing tooth surfaces of spiral bevelgears using pulse electrochemical dissolution [J]. Int J Adv Manuf Technol,2011,54(9-12):979-986.
[9] Deng X B, Hua L, Han X H. Three-dimensional FE modelling simulation of cold rotary forging ofspiral bevel gear [J]. IRONMAKING&STEELMAKING,2011,38(2):101-111.
[10] Yang Z J, Wang Y K, Li L N, et al. Mathematical Model of Spiral Bevel Gears Manufactured byGenerating Line Method [C]. Advanced Materials Research,2011,154-155:103-108.
[11]胡来瑢.空间啮合原理及应用[M].煤炭工业出版社，1987.
[12]曾韬.螺旋锥齿轮设计与加工[M].哈尔滨工业大学出版社,1989.
[13] Simon V V. Influence of tooth modifications on tooth contact in face-hobbed spiral bevel gears [J].Mechanism and machine theory,2011,46(12):1980-1998.
[14] Simon V. Influence of tooth errors and misalignments on tooth contact in spiral bevel gears [J].Mechanism and machine theory,2008,43(10):1253-1267.
[15] Gonzalez-Perez I, Fuentes A, Hayasaka, K. Analytical determination of basic machine-tool settingsfor generation of spiral bevel gears from blank data [J]. Journal of mechanical design,2010,132(10):1-11.
[16]彭东林，戴政远，郑连清，等.弧齿锥齿轮铣齿机传动误差检测系统研究[J].仪器仪表学报，1999,20（3）：280-284.
[17]曹雪梅，张华，方宗德.航空弧齿锥齿轮承载传动误差的分析与设计[J].航空动力学报，2009，24（11）：2618-2624.
[18]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.
[19]天津齿轮机床研究所，西安交通大学.格里森锥齿轮技术资料译文集[M].机械工业出版社，1986.
[20] Gleason Seminar. Spiral bevel and hypoid gear technology update [R]. Beijing: Gleason Corporation,2007.
[21]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.
[22] Handschuh R F, Bill R C. Recent manufacturing advances for spiral bevel gears [J]. SAETransactions,1991:2793-2804.
[23] Park N G, Lee H W. The spherical involute bevel gear: its geometry, kinematic behavior andstandardization [J]. Journal of mechanical science and technology,2011,25(4):1023-1034.
[24]李特文.齿轮啮合原理[M].上海：上海科学技术出版社，1984.
[25]北京齿轮厂.螺旋锥齿轮[M].科学出版社,1974.
[26]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.
[27] Stadtfeld H L.Advanced bevel gear technology [M]. The Gleason Works,2000.
[28]李敦信，包润阁，王德友.锥齿轮加工简化计算[M].机械工业出版社，1978.
[29] Zhu C D, Guan Q, Wang H. Twin symmetry roll axial rolling: new method of plastic formingprofiles demonstrated using manufacture of spiral bevel gears [J]. Ironmaking&steelmaking,2011,38(3):211-217.
[30] Stadtfeld H J. Handbook of Bevel and Hypoid Gears: Calculation, Manufacturing, and Optimization[M]. NY: Rochester Institute of Technology,1993.
[31]刘立民.奥利康制弧齿锥齿轮XN型齿的应用[J].现代零部件，2006,3:100-101.
[32] Liu G L, Fan H W, Pinion tooth surface generation strategy of spiral bevel gears [J]. Chinese journalof mechanical engineering,2012,25(4):753-759.
[33] Watanabe M, Maki M, Hirokawa S. A study on forging of spiral bevel gear [C]. Proceedings of theasme international design engineering technical conferences and computers and information inengineering conference,2008,7:799-806.
[34]西安交通大学机制教研室齿轮研究组.弧齿锥齿轮和准双曲线齿轮加工调整原理[M].上海科学技术出版社，1979.
[35]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.
[36]毛世民，吴序堂.任意指定接触基准点的切齿理论——对格里森半展成法加工弧齿维齿轮和准双曲面齿轮方法的改进[J].西安交通大学学报，1985,19（5）：1-10.
[37]李普华.弧齿锥齿轮和准双曲面齿轮加工技术[J].机电工程技术，2010,39（7）：134-135.
[38]李广财，吴亚龙，杨兆军.零度弧齿锥齿轮加工工艺简介[J].一重技术，2004,2:44-45.
[39]《齿轮制造工艺手册——滚、插、磨、剃、刨》编委会.齿轮制造工艺手册——滚、插、磨、剃、刨[M].机械工业出版社，2010.
[40] Fan Q. Computerized modeling and simulation of spiral bevel and hypoid gears manufactured bygleason face hobbing process [J]. Journal of mechanical design,2006,128(6):1315-1327.
[41] Baxter M L. Basic geometry and tooth contact of hypoid gears [J]. Industrial Mathematics,1961,11(2):1-28
[42] Baxter M L. Second order surface generation [J]. Industrial Mathematics,1973,23(2):85-106.
[43] Litvin F L. Development of gear technology and theory of gearing [M]. National Aeronautics andSpace Administration, Lewis Research Center,1997.
[44] Е.А.Андрущенко,蒋朝明.奥利康公司的齿轮加工[J].齿轮，1983,41-43.
[45]卢佳，董苗苗.克林根贝尔格锥齿轮铣齿机工作原理的基础分析——AMK852实践[J].科技创新与应用，2012，3：56-57.
[46]汪有刚.浅析克林根贝尔格制锥齿轮的加工及特点[J].民营科技，2013,1:20.
[47]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四册[M]，机械工业出版社，1986.
[48] Litvin F L, Wang A G, Handschuh R F. Computerized generation and simulation of meshing andcontact of spiral bevel gears with improved geometry [J]. Computer methods in applied mechanics&engineering,1998,158:35-64.
[49] Handschuh R F, Bibel G D. Experimental and analytical study of aerospace spiral bevel gear toothfillet stresses [J]. Journal of mechanical design,1999,121(4):565-572.
[50]蒋文兵.螺旋锥齿轮五轴联动数控加工的研究[D].郑州:郑州大学，2003.
[51]遇立基.CIMT’99展出的数控齿轮加工机床[J].制造技术与机床，1999，12:6-7.
[52]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，2004，9:11-13.
[53]刘小龙.螺旋锥齿轮切、磨齿技术的发展及面临的挑战[J].汽车齿轮，2010，4：42-50.
[54] Alves J T, Guingand M, de Vaujany J P. Designing and manufacturing spiral bevel gears using5-axiscomputer numerical control (CNC) milling machines [J]. J. Mech. Des.,2013,135(2):1-6.
[55] Zhou K H, Tang J Y. Envelope-approximation theory of manufacture technology for point-contacttooth surface on six-axis CNC hypoid [J]. Mechanism and machine theory,2011,46(6):806-819.
[56]刘凯.弧齿锥齿轮数控铣齿机运动分析及控制系统研究[D].南京：南京航空航天大学，2007.
[57] Harmann J.Stadtfeld.锥齿轮齿形加工的第二次革命——Hermann J.Stadtfeld先生在W&B杂志上介绍的锥齿轮加工技术最新发展的情况[J].世界制造技术与装备市场，2004,5:71-75.
[58] Fan Q, DaFoe R S, Swanger J W. New developments in computerized design and manufacturing ofspiral bevel and hypoid gears [C]. International conference on mechanical transmissions,2006,1-2:128-133.
[59] SIGMA∑POOL集团.SIGMA∑POOL齿轮技术集团——国际齿轮界的强强联合[J].机电国际市场，2000，6:36-37.
[60]李先广.当今制齿技术及制齿机床[J].现代制造工程，2002,11:66-68.
[61]李先广，刘飞，曹华军.齿轮加工机床的绿色设计与制造技术[J].机械工程学报，2009,45（11）：140-145.
[62]乐美豪.中国齿轮制造业50年[J].机电国际市场，2000,5:5-8.
[63]吴训成，毛世民，吴序堂.点接触齿面在控制误差敏感性条件下的二阶参数设计[J].西安交通大学学报，1999,33（11）：86-89.
[64]毛世民，吴序堂.新型万能曲线齿锥齿轮加工机床的运动学[J].制造技术与机床，1997,6:22-24.
[65]林经德，刘鹄然.摆线齿螺旋锥齿轮铣齿机工作原理的新认识[J].机械研究与应用，1998，11（2）：17-18.
[66]刘鹄然，刘厚根，李国顺.在螺旋锥齿轮数控铣齿机上实现刀倾法加工小轮[J].现代机械.1998，4:54-57.
[67]马云.CCMT2012制齿装备精品荟萃[J].世界制造技术与装备市场，2012,6:82-87.
[68]恩宝贵.中国机床工业到了向世界制造技术高峰冲锋的时候[J].制造技术与机床，2012,6:13-18.
[69]张卫青，张明德，郭晓东，等.全数控锥齿轮铣齿机运动控制方法及切齿实验研究[J].中国机械工程，2009,20（22）：2733-2737.
[70]张曙，朱志浩，樊留群.中国机床工业综述:过去、现在与将来[J].世界制造技术与装备市场，2011,5：54-62.
[71]王红利，钟晓玲.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.
[72]李先广.机床制造业绿色制造运行模式及其特征主线研究[D].重庆：重庆大学，2012.
[73]李朋.相约南京CCMT,盛览创新装备[J].现代零部件，2012,4:42-46.
[74]李翼龙，郭志全，刘明涛，等.基于FEM的数控弧齿铣齿机立柱结构静、动态设计[J].天津科技大学学报，2012,27（1）：52-56.
[75]王红利.从CIMT2007看齿轮加工机床的发展趋势[J].制造技术与机床，2007,3:40-44.
[76]毛世民，聂钢，范超毅，等.准渐开线齿锥齿轮的齿面展成[J].中国机械工程，1999,10（12）：1325-1327.
[77]苏智剑，吴序堂.基于计算机数字控制弧齿锥齿轮加工机床的准双曲面齿轮的制造[J].机械工程学报，2007,43（5）：57-63.
[78]李建刚，吴序堂，贺敬良，等.CNC铣齿机床加工曲线齿锥齿轮仿真系统的研究[J].系统仿真学报，2003,15（4）：499-501.
[79]吴序堂.齿轮啮合原理[M].北京：机械工业出版社，1982.
[80]李建刚，毛世民，苏智剑.五轴联动数控工具磨床加工模拟系统的开发[J].工具技术，2001，35（6）：18-19.
[81]张军辉，方宗德，王成.基于NURBS的弧齿锥齿轮真实齿面的数字化仿真[J].航空动力学报，2009,24(7):1672-1676.
[82]苏进展，方宗德，蔡香伟.弧齿锥齿轮数字化齿面啮合仿真分析与试验[J].西北工业大学学报，2012,30（4）：565-569.
[83]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.
[84]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.
[85]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.
[86]方宗德，曹雪梅，沈云波.弧线齿面齿轮的齿面设计与加工[J].航空动力学报，2010,25（1）：224-227.
[87]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）：200-203.
[88]刘光磊，樊红卫，谷霁红，等.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.
[89]曹雪梅，方宗德，许浩.弧齿锥齿轮的齿面主动设计及试验验证[J].机械工程学报，2008，44（7）：209-214.
[90] Jia J S, Cao X M. Generation and TCA of Straight Bevel Gear Drive with Modified Geometry [J].Applied mechanics and materials,2011,86:403-406.
[91] Cao X M, Fang Z D, Xu H. Design of pinion machine tool-settings for spiral bevel gears bycontrolling contact path and transmission errors [J]. Chinese journal of aeronautics,2008,21(2):179-186.
[92] Zhang J H, Fang Z D, Cao X M, et al. The modified pitch cone design of the hypoid gear:Manufacture, stress analysis and experimental tests [J]. Mechanism and machine theory,2007,42(2):147-158.
[93] Wei B Y, Deng X Z, Fang Z D. Study on ultrasonic-assisted lapping of gears [J]. Internationaljournal of machine tools&manufacture,2007,47(12-13):2051-2056.
[94]曹雪梅，方宗德，张金良，等.弧齿锥齿轮的齿面主动设计[J].机械工程学报，2007,43（8）：155-158.
[95]邓效忠，方宗德，魏冰阳.接触路径对弧齿锥齿轮接触应力和弯曲应力的影响[J].中国机械工程，2003,14（22）：1895-1898.
[96]刘凯，赵东标.弧齿锥齿轮数控加工和齿面接触点求解算法研究[J].小型微型计算机系统，2008，29（3）：572-576.
[97]刘凯，赵东标，黄沛建.弧齿锥齿轮数控展成运动轨迹规划方法[J].华南理工大学学报(自然科学版)，2007,35（8）：32-37.
[98] Liu K, Zhao D B. Algorithms of generation motion and direct interpolation for spiral bevel gear ncmachining [J]. Transactions of nanjing university of aeronautics&astronautics,2007,24(3):257-264.
[99]刘凯，赵东标.弧齿锥齿轮数控加工主动控制方法研究[J].机械科学与技术，2007,26（8）：973-976.
[100]王延忠，周云飞，李左章，等.基于通用五坐标数控机床螺旋锥齿轮NC加工研究[J].中国机械工程，2001,12（8）：903-906.
[101]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.
[102]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.
[103]李小清，周云飞，李左章，等.螺旋锥齿轮数控展成轨迹生成及直接插补算法[J].华中科技大学学报(自然科学版)，2002,30（10）：38-40.
[104]王延忠，周云飞，李左章，等.螺旋锥齿轮空间曲面NC加工插补误差分析[J].华中科技大学学报(自然科学版)，2002,30（2）：9-12.
[105]李小清，周云飞，王延忠，等.螺旋锥齿轮拟合齿面啮合特性分析方法[J].中国机械工程，2003，14（13）：1139-1143.
[106]王延忠，周云飞，周济，蔡春源.高速弧齿锥齿轮点接触瞬态等温弹流数值分析[J].华中科技大学学报，2001，29（12）：4-7.
[107]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.
[108] Wang Y Z, Wu C H, Gong K, et al. Loaded tooth contact analysis of orthogonal face-gear drives [J].Proceedings of the institution of mechanical engineers part c-journal of mechanical engineeringscience,2012,226(C9):2309-2319.
[109]徐彦伟，张连洪.弧齿锥齿轮齿面点坐标求解及模型建立[J].机床与液压，2012，40（21）：138-142.
[110]李敬财，徐文丽，李清，等.基于层片分割算法弧齿锥齿轮及准双面齿轮五轴数控切削仿真[J].机械传动，2011,35（3）：7-10.
[111]韩佳颖，王太勇，李清，郑慧江.基于解析计算的螺旋锥齿轮切削仿真算法[J].农业机械学报，2010,41（12）：223-227.
[112]徐彦伟，张连洪，魏巍.重型弧齿锥齿轮铣齿机数控加工模型建立与仿真[J].农业机械学报，2009,40（10）：211-215.
[113]熊越东，王太勇，张威.螺旋锥齿轮数控加工参数转换计算方法[J].组合机床与自动化加工技术，2006,8:5-8.
[114]魏巍.面向齿轮传动性能的螺旋锥齿轮铣齿机精度设计方法研究[D].天津：天津大学，2011.
[115]徐彦伟.弧齿锥齿轮铣齿机主动精度设计方法研究[D].天津：天津大学，2010.
[116] Zhou K H, Tang J Y. Envelope-approximation theory of manufacture technology for point-contacttooth surface on six-axis CNC hypoid generator [J]. Mechanism and machine theory,2011,46(6):806-819.
[117] Zhou K H, Tang J Y, Zeng T. New geometry of generating spiral bevel gear [C]. Proceedings of theASME international design engineering technical conferences and computers and information inengineering conference,2008,7:335-342.
[118]唐进元，卢延峰，周超.有误差的螺旋锥齿轮传动接触分析[J].机械工程学报，2008,44（7）：16-23.
[119]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].机械工程学报，2011,47（11）：23-29.
[120]唐进元，黄云飞，周超，等.弧齿锥齿轮展成齿面的几何建模[J].计算机仿真，2009,26（2）：293-297.
[121]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.
[122]周超，唐进元，曾韬，等.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.
[123]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.
[124]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.
[125] Chen S H, Yan H Z, Ming X Z. Error modeling and analysis of spiral bevel gear grinder based onmulti-body system theory [J]. Joumal of central south university of technology,2008,15(5):706-711.
[126]陈书涵.螺旋锥齿轮磨削误差产生机制及修正技术研究[D].长沙：中南大学，2009.
[127] Zhao Y P, Wei W J, Dong X Z. Some problems on the2DOF theory of gearing [J]. Mechanism andmachine theory,2008,43(8):1024-1037.
[128]董学朱.齿轮啮合理论基础[M].北京：机械工业出版社，1989.
[129]董学朱.李海涛，魏文军.双自由度齿轮啮合理论及应用[M].北京：机械工业出版社，2011.
[130]董学朱.弧齿锥齿轮半展成切齿调整计算新方法[J].齿轮，1988,12（4）：1-5.
[131]董学朱.弧齿锥齿轮变性全展成切齿调整计算新方法[J].齿轮，1987，11（6）：6-21.
[132]董学朱.弧齿锥齿轮刀倾全展成切齿调整计算新方法[J].北京农业工程大学学报，1988,8（3）：68-81.
[133]董学朱.弧齿锥齿轮和准双曲面齿轮切齿调整计算新方法——按大轮齿面任一基准点配切小轮的原理[J].北京农业工程大学学报，1990,10（1）：16-27.
[134]曾韬.关于《共轭曲面原理》的若干问题——与陈志新同志商榷[J].齿轮，1982,1:38-42.
[135]曾韬.螺旋锥齿轮设计中的轮坯修正[J].航空标准化，1981,5:52-56.
[136]杨丰，曾韬.弧齿锥齿轮齿面接触区的边缘检测技术[J].现代制造工程，2007,1:95-97.
[137]王裕清，武良臣，等.弧齿锥齿轮接触区理论与切削过程仿真[M].北京：煤炭工业出版社，2004.
[138]王裕清，王小林，梁剑.弧齿锥齿轮实体造型数学模型及其实现[J].中国机械工程，2007,18（14）：1660-1663.
[139]王裕清，祝运攀.弧齿锥齿轮接触斑点图像采集及预处理[J].河南理工大学学报(自然科学版)，2009,28（2）：194-198.
[140]武良臣，王裕清.锥齿轮和双曲线齿轮副接触斑点稳定性分析[J].机械工艺师，2000,10:59-60.
[141]刘冠华，马永寿，吴锐.弧齿锥齿轮轮坯修正新方法[J].机械工程师，2004，5：57.
[142] Fan Q. Optimization of face cone element for spiral bevel and hypoid gears [J]. Journal ofmechanical design,2011,133(9):1-7.
[143] Simon V. Load distribution in spiral bevel gears [J]. Journal of mechanical design,2007,129(2):201-209.
[144] Sheveleva G I, VolkovAE, Medvedev V I.Algorithms for analysis of meshing and contact ofspiral bevel gears [J]. Mechanism and machine theory,2007,42(2):198-215.
[145]刘凯，陆永华，赵东标.参数曲线自适应加减速控制方法在弧齿锥齿轮数控加工中的应用[J].机械工程学报，2009,45（12）：198-204.
[146] Ma N, Xu W J, Wang X Y, et al. Prediction method for surface finishing of spiral bevel gear toothbased on least square support vector machine [J]. Journal of central south university of technology,2011,18(3):685-689.
[147] Safavi S M, Mirian S S, Abedinzadeh R. Use of PLC module to control a rotary table to cut spiralbevel gear with three-axis CNC milling [J]. International journal of advanced manufacturingtechnology,2010,49(9-12):1069-1077.
[148] Shih Y P, Fong Z H. Flank correction for spiral bevel and hypoid gears on a six-axis CNC hypoidgenerator [J]. Journal of mechanical design,2008,130(6):1-11
[149] Wang P Y, Fong Z H. Fourth-order kinematic synthesis for face-milling spiral bevel gears withmodified radial motion (MRM) correction [J].2006,128(2):457-467.
[150] Simon V. Head-cutter for optimal tooth modi. cations in spiral bevel gears [J]. Mechanism andmachine theory,2009,44(7):1420-1435.
[151] Gosselin C, Masseth J, Liang W. Cutter interchangeability for spiral-bevel and hypoid gearmanufacturing [C]. Chicago: ASME/AGMA2003International Power Transmission and GearingConference,2003.
[152] Simon V V. Advanced manufacture of spiral bevel gears on cnc hypoid generating machine [J].Journal of mechanical design,2010,132(3):1-8.
[153] Simon V V. Machine-tool settings to reduce the sensitivity of spiral bevel gears to tooth errors andmisalignments [J]. Journal of mechanical design,2008,130(8):1-10.
[154] Artoni A, Gabiccini M, Kolivand M. Ease-off based compensation of tooth surface deviations forspiral bevel and hypoid gears: Only the pinion needs corrections [J]. Mechanism and machine theory,2013,61:84-101.
[155] Wang P Y, Fan S C, Huang Z G. Spiral bevel gear dynamic contact and tooth impact analysis [J].Journal of mechanical design,2011,133(8):1-6.
[156] Shih Y P. A novel ease-off flank modification methodology for spiral bevel and hypoid gears [J].Mechanism and machine theory,2010,45(8):1108-1124.
[157] Alves J T, Guingand M, de Vaujany J P. Set of functions for the calculation of bendingdisplacements for spiral bevel gear teeth [J]. Mechanism and machine theory,2010,45(2):349-363.
[158] Simon V. Computer simulation of tooth contact analysis of mismatched spiral bevel gears [J].Mechanism and machine theory,2007,42(3):365-381.
[159]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.
[160]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.
[161]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].2009-03-05.
[162]洪肇斌，杨兆军，张学成，等.基于齿面发生线的弧齿锥齿轮铣削加工仿真分析[J].吉林大学学报(工学版)，2013,43（2）：334-339.
[163]陈爱平，张韵风，侯欣芸译.齿轮的功用及加工[M].北京：机械工业出版社，2010.
[164]秦荣荣，崔可维.机械原理[M].长春：吉林科学技术出版社，2000.
[165]张宝珠.齿轮加工速查手册[M].北京：机械工业出版社，2010.
[166]朱孝录.齿轮传动设计手册第二版[M].北京：化学工业出版社，2010.
[167] Yang Z J, Hong Z B, Wang B C, et al. New tooth profile design of spiral bevel gears with sphericalinvolute [J]. Intl. J. Adv. Comput. Technolog.,2012,4(19):462-469.
[168] Hong Z B, Yang Z J, Zhang X C, et al. New modeling method of spiral bevel gears with sphericalinvolute based on CATIA [C]. Proc. SPIE Int. Soc. Opt. Eng.,2011,7997:79970Y.
[169]李云龙，曹岩.数控机床加工仿真系统VERICUT[M].西安：西安交通大学出版社，2005.
[170]杨胜群.VERICUT数控加工仿真技术[M].北京：清华大学出版社，2010.
[171] Hong Z B, Yang Z J, Wang B C, et al. Simulation analysis of spiral bevel gear tooth surfacegeneration based on VERICUT [J]. Applied mechanics and materials,2013,273:175-179.
[172]徐彦伟，张连洪，刘德全，等.弧齿锥齿轮成形三维虚拟仿真研究[J].中国机械工程，2008,19（22）：2703-2707.
[173]张艳，桂贵生.基于VERICUT的数控加工仿真及优化[J].现代制造技术与装备，2008,4:75-77.
[174]朱正祥.基于VERICUT数控铣齿机加工仿真的研究与应用[J].机床与液压，2008,36（9）：118-120.
[175]刘保柱，苏彦华，张宏林.MATLAB7.0从入门到精通[M].北京：人民邮电出版社，2010.
[176]于润伟，朱晓慧. MATLAB基础及应用（第2版）[M].北京：机械工业出版社，2008.
[177]宋放之.数控机床多轴加工技术实用教程[M].北京：清华大学出版社，2010.