准双曲面齿轮螺旋变性半展成数控成形理论与方法研究
|
摘要
螺旋锥齿轮代表了目前最复杂的传动形式和高复杂度的曲面加工类型，由于其重合度高、传动平稳、噪声小、承载能力大、传动比大等优点，被广泛应用于汽车、工程机械、航空航天、船舶等领域。而齿面接触区的形状、大小和位置，对齿轮的平稳运转、使用寿命和噪音具有直接影响。所以，齿面接触区是衡量锥齿轮啮合质量的重要标志之一。本文以Gleason的收缩齿制准双曲面齿轮为研究对象，从改善齿面接触情况、提高生产效率及研究四轴数控机床加工技术的本质出发，以微分几何和齿轮啮合原理为理论基础，采用计算机仿真为方法和手段，对螺旋锥齿轮成形理论及方法进行了深入的研究，并建立了螺旋锥齿轮数控成形仿真系统。
论文的主要成果及创新点如下：
1、基于平面产形轮原理，提出新的螺旋锥齿轮成形理论及加工方法，即螺旋变性半展成法。通过对新加工方法的研究，实现更多自由度的齿面误差修正能力，从本质上避免理论接触区对角现象；完善并增强多轴联动数控铣齿机加工螺旋锥齿轮的能力。
2、将小轮刀盘切削刃形成的曲面看作是阿基米德螺旋面，用以替代小轮精切锥面刀盘的螺旋运动。工件与产形轮仍然按照一定的传动比绕各自的轴线旋转，曲率计算时可以直接利用准双曲面齿轮副在节点处的曲率关系，简化了切齿计算过程。
3、针对国产四轴联动数控铣齿机，提出螺旋锥齿轮“两刀法”加工理论。基于新的螺旋锥齿轮成形理论及加工方法，通过对多轴联动数控铣齿机各轴的灵活有效控制，实现使用双面刀盘精切小轮凹、凸面，提高多轴联动数控机床加工柔性、生产效率和加工精度，实现加工的低成本、高效率、高质量。
4、在理论研究基础上，推导了四轴联动数控铣齿机螺旋锥齿轮成形运动关系，建立了螺旋锥齿轮的数控加工模型，给出了机床运动与调整的全部运动关系。简化了数字化制造环境下螺旋锥齿轮少轴加工工艺过程，并取得了良好接触区。
5、提出了螺旋锥齿轮切削仿真方法，在此基础上实现了刀具和齿坯的布尔运算，实现了所得齿面数据点的存储和重构、切削过程的实时显示，开发出了螺旋锥齿轮数控成形仿真系统。
The most complicated transmission forms and the high complexity in curvedsurface machining types were represented by hypoid gears. Hypoid gears were widelyapplied in automobile, engineering machinery, Aerospace, shipping industry, becausethat hypoid gears had the advantages that high contact ratio, steady transmission,lower noise, large loading capacity, large transmission ratio. The form, size andlocation of tooth flanks contact zone directly affected the stable running, working lifeand noise of hypoid gear drives. The tooth flanks contact zones was one of theimportant symbols to examine the meshing quality of the hypoid gear pairs. Thereductive tooth system of Gleason hypoid gears was the research objects of this paper.The theory and method of the machining technology about hypoid gears wasresearched by the paper, in improving production efficiency, in improving the form oftooth surface contact zone, and in studying the essence of the machining technologyin four axis NC machine tool. The research was based on differential geometry andthe principle of gear engagement. The computer simulation was the method andmeans of the research.
The main results and innovations of this paper is listed as follows:
1. The half-spread-out helix modified roll method based on crown generatinggear principle was proposed, which was the machining method of hypoid gears basedon the new forming theory. The new machining theory was founded. The toothsurface corrections in more degrees of freedom was achieved by study in the newmachining method. The Bias of tooth contact zone was prevented in essence. Thehypoid gears processing capacity of multi-axes synchronous CNC gear millingmachine was improved.
2. The surface which was formed by the cutting edge of cutter for pinion wasregarded as the Archimedes spiral curved surface. It was substituted for the helicalmotion of the cone segmental-blade cutter for pinion. The work-piece and the crowngenerating gear revolved around their axes according certain transmission ratio. Thecurvature rate at nodes of hypoid gear pair could be used directly in curvatureestimation. The process of calculation for cutting was simplified.
3. The “Two Cut” machining theory was proposed, aiming at domestic four-axessynchronous CNC gear milling machine. It was implemented that the alternate bladecutter was used to finish cutting the tooth surfaces of pinion, by flexible and effective controlling the movement axes of the multi-axes synchronous CNC machine, basedon the new forming theory and the new machining method of hypoid gears. Thatimproved the flexible manufacturing, production efficiency and machining precisionof multi-axes synchronous CNC machine. The machining processing of low-cost,high-efficiency, and high-quality was implemented.
4. On the base of theoretical research, the motion relationship of the four-axessynchronous CNC gear milling machine, which was used to machine hypoid gears,was deduced. The NC machining model of hypoid gears was established. All of themotion relationship in motion and settings of machine tool were provided. Themachining process of hypoid gears in four-axes digital manufacturing was simplified,and the form of tooth contact zone was satisfied.
5. The machining simulation method of hypoid gears was proposed, which theBoolean operation of the cutter with work piece was implemented based on. The datapoints of the tooth surface was stored and reconstructed. The real-time display ofmachining process was implemented. The machining simulation system of hypoidgears was developed.
论文的主要成果及创新点如下：
1、基于平面产形轮原理，提出新的螺旋锥齿轮成形理论及加工方法，即螺旋变性半展成法。通过对新加工方法的研究，实现更多自由度的齿面误差修正能力，从本质上避免理论接触区对角现象；完善并增强多轴联动数控铣齿机加工螺旋锥齿轮的能力。
2、将小轮刀盘切削刃形成的曲面看作是阿基米德螺旋面，用以替代小轮精切锥面刀盘的螺旋运动。工件与产形轮仍然按照一定的传动比绕各自的轴线旋转，曲率计算时可以直接利用准双曲面齿轮副在节点处的曲率关系，简化了切齿计算过程。
3、针对国产四轴联动数控铣齿机，提出螺旋锥齿轮“两刀法”加工理论。基于新的螺旋锥齿轮成形理论及加工方法，通过对多轴联动数控铣齿机各轴的灵活有效控制，实现使用双面刀盘精切小轮凹、凸面，提高多轴联动数控机床加工柔性、生产效率和加工精度，实现加工的低成本、高效率、高质量。
4、在理论研究基础上，推导了四轴联动数控铣齿机螺旋锥齿轮成形运动关系，建立了螺旋锥齿轮的数控加工模型，给出了机床运动与调整的全部运动关系。简化了数字化制造环境下螺旋锥齿轮少轴加工工艺过程，并取得了良好接触区。
5、提出了螺旋锥齿轮切削仿真方法，在此基础上实现了刀具和齿坯的布尔运算，实现了所得齿面数据点的存储和重构、切削过程的实时显示，开发出了螺旋锥齿轮数控成形仿真系统。
The most complicated transmission forms and the high complexity in curvedsurface machining types were represented by hypoid gears. Hypoid gears were widelyapplied in automobile, engineering machinery, Aerospace, shipping industry, becausethat hypoid gears had the advantages that high contact ratio, steady transmission,lower noise, large loading capacity, large transmission ratio. The form, size andlocation of tooth flanks contact zone directly affected the stable running, working lifeand noise of hypoid gear drives. The tooth flanks contact zones was one of theimportant symbols to examine the meshing quality of the hypoid gear pairs. Thereductive tooth system of Gleason hypoid gears was the research objects of this paper.The theory and method of the machining technology about hypoid gears wasresearched by the paper, in improving production efficiency, in improving the form oftooth surface contact zone, and in studying the essence of the machining technologyin four axis NC machine tool. The research was based on differential geometry andthe principle of gear engagement. The computer simulation was the method andmeans of the research.
The main results and innovations of this paper is listed as follows:
1. The half-spread-out helix modified roll method based on crown generatinggear principle was proposed, which was the machining method of hypoid gears basedon the new forming theory. The new machining theory was founded. The toothsurface corrections in more degrees of freedom was achieved by study in the newmachining method. The Bias of tooth contact zone was prevented in essence. Thehypoid gears processing capacity of multi-axes synchronous CNC gear millingmachine was improved.
2. The surface which was formed by the cutting edge of cutter for pinion wasregarded as the Archimedes spiral curved surface. It was substituted for the helicalmotion of the cone segmental-blade cutter for pinion. The work-piece and the crowngenerating gear revolved around their axes according certain transmission ratio. Thecurvature rate at nodes of hypoid gear pair could be used directly in curvatureestimation. The process of calculation for cutting was simplified.
3. The “Two Cut” machining theory was proposed, aiming at domestic four-axessynchronous CNC gear milling machine. It was implemented that the alternate bladecutter was used to finish cutting the tooth surfaces of pinion, by flexible and effective controlling the movement axes of the multi-axes synchronous CNC machine, basedon the new forming theory and the new machining method of hypoid gears. Thatimproved the flexible manufacturing, production efficiency and machining precisionof multi-axes synchronous CNC machine. The machining processing of low-cost,high-efficiency, and high-quality was implemented.
4. On the base of theoretical research, the motion relationship of the four-axessynchronous CNC gear milling machine, which was used to machine hypoid gears,was deduced. The NC machining model of hypoid gears was established. All of themotion relationship in motion and settings of machine tool were provided. Themachining process of hypoid gears in four-axes digital manufacturing was simplified,and the form of tooth contact zone was satisfied.
5. The machining simulation method of hypoid gears was proposed, which theBoolean operation of the cutter with work piece was implemented based on. The datapoints of the tooth surface was stored and reconstructed. The real-time display ofmachining process was implemented. The machining simulation system of hypoidgears was developed.
引文
[1]李特文，齿轮啮合原理，上海:上海科学技术出版社，1984
[2] E.Wildhaber,Gear tooth curvature treated simply,American Machinist,1945,89(18):122~125
[3] Wildhaber E., Tooth contact.American Machinist,1946,90(12):110~114
[4] Wildhaber E., Basic relationship of hypoid gear,American Machinist,1946,90(3):108~111
[5] Wildhaber E., Conjugate pitch surface.American Machinist,1946,90
[6] Wildhaber E., Surface curvature, Prod Engry,1956,27(5):184~191
[7]爱.威尔德哈尔泊，锥齿轮及准双曲面齿轮啮合原理，北京：机械工业出版社，1958
[8] Baxter M. L., Basic geometry and tooth contact of hypoid gear, industrialmathe-matics,1961,11(2):19~28
[9] Baxter M. L., Second-order surface generation. J Ind Math;1973，23(2):85~106
[10] Hermann J., Stdtfeld, Gleason Bevel Gear Technology, New York: TheGleason works,1994
[11]冯忆艰，克林贝格螺旋锥齿轮磨齿问题的探讨，煤矿机械，1998(11)：23~24
[12]冯忆艰，失配理论在克林贝格螺旋锥齿轮副中的应用，西安科技学院学报，2000，20(2)：148~150
[13]刘志峰，陈良玉，王延忠等，Klingelnberg摆线锥齿轮轮齿几何分析.东北大学学报(自然科学版)，1999，20(4)：388~391
[14] Stadtfeld H.J., Olerlikon bevel and hypoid gears, Olerlikon BührleAG.,1991
[15]刘惟信，圆锥齿轮与双曲面齿轮传动，北京：人民交通出版社，1980
[16]董学朱，延伸外摆线锥齿轮切齿调整计算法的改进，机械传动，1997，21(4)：41~47
[17]董学朱，延伸外摆线齿准双曲面齿轮几何设计和切齿调整计算新方法，机械传动，1999，23(4)：16~20
[18]董学朱，摆线锥齿轮及准双曲面齿轮设计和制造，北京：机械工业出版社，2003
[19]郑昌启，弧齿锥齿轮传和准双曲面齿轮—啮合原理、轮坯设计、加工调整和齿面分析计算原理，北京：机械工业出版社，1988
[20] Litvin F L, Gutman Y, A Method of Local Synthesis of Gears Grounded on theConnection between the Principal and Geodetic Curvatures of Surfaces, ASMEJournal of Mechanical Design,1981,103:114~125
[21] F.L. Litvin, Y. Zhang, Local synthesis and tooth contact analysis of face-milledspiral bevel gears, Chicago: NASA Lewis Research Center,1991
[22]曾韬，螺旋锥齿轮设计与加工，哈尔滨：哈尔滨工业大学出版社，1989
[23]天津齿轮机床研究所，格利森锥齿轮技术资料译文集(第一分册)，北京：机械工业出版社，1986
[24] Kawasaki K,Tamura H, Duplex spread blade method for cutting hypoid gearswith modified tooth surface, JOURNAL OF MECHANICALDESIGN,1998,120(3):441~447
[25] Gleason Works, Electronic Computer Program Aoo212，1978
[26] Litvin F L,Gutman Y, Methods of Synthesis and Analysis for HypoidGear-Drives of “Formate”and “Helixform”, ASME Journal of MechanicalDesign,1981,103(1):83~110
[27] Gleason Works, Phoenix closed loop system, NY：Rochesger,1991
[28] Gosselin, C. J., Cloutier, L., The Generating Space for Parabolic Motion ErrorSpiral Bevel Gears Cut by the Gleason Method, ASME J.Mech. Des.,1993,115:483~489
[29]王小椿，吴联银，基于空间运动学的传统机床与Free-form型机床运动转换方法的研究，机械工程学报，2001，37(4)：93~98
[30] Litvin F L., Gear Geometry and Applied Theory, New Jersey: PrentieeHall,1994
[31] Litvin F L, Fuentes A, Hayasaka K, Design, manufacture, stress analysis, andexperimental tests of low-noise high endurance spiral bevel gears, Mechanismand Machine Theory,2006,41(1):83~118
[32] S. Vilmos, Optimal machine tool setting for hypoid gears improving loaddistribution, ASME Journal of Mechanical Design,2001,123:577~582
[33] S. Vilmos, Optimal tooth modifications in hypoid gears, ASME Journal ofMechanical Design,2005,127:646~655
[34] V. Simon, ADVANCED DESIGN AND MANUFACTURE OFFACE-HOBBED SPIRAL BEVEL GEARS, Proceedings of the ASME2009International Mechanical Engineering Congress&Exposition.Florida,2009:1~10
[35] Fong Z. H., Tsay C. B., Kinematical Optimization of Spiral Bevel Gears,ASME J. Mech. Des.,1992,114:498~506
[36] Fong Z. H., Mathematical Model of Universal Hypoid Generator withSupplemental Kinematic Flank Correction Motions, ASME J.Mech. Des.,2000,122:136~142
[37] Shih Y.P., Fong Z.H., Flank Correction for Spiral Bevel and Hypoid Gears on aSix-Axis CNC Hypoid Generator, ASME Journal of Mechanical Design,2008,130(6):1~11
[38] C.Y. Lin, C.B. Tsay, Z.H. Fong, Mathematical model of spiral bevel andhypoid gears manufactured by the modified roll method, Mechanism andMachine Theory,1997,32:121~136
[39] C.Y. Lin, C.B. Tsay, Z.H. Fong, Computer-aided manufacturing of spiral beveland hypoid gears by applying optimization techniques, Journal of MaterialsProcessing Technology,2001,114:22~35
[40] S. H. Suh, D. H. Jung, E. S. Lee, Modeling, mplementation, and manufacturingof spiral bevel gears with crown, International journal of advancedmanufacturing technology,2003,21(3):775~786
[41] Suh S.H, Jih W.S, et al, Sculptured surface machining of spiral bevel gears withCNC milling, International Journal of Machine Tools&Manufacture,2001,41(5):833~850
[42] S.H. Suh, E.S. Lee, et al. Geometric error measurement of spiral bevel gearsusing a virtual gear model for STEP-NC, International Journal of MachineTools&Manufacture,2002,42:335~342
[43] F L Litvin, Alfonso Fuentes, Qi Fan, et al, Computerized design, simulation ofmeshing, and contact and stress analysis of face-milled formate generatedspiral bevel gears,Mechanism and Machine Theory,2002,37(5):441~459
[44] F.L Litvin, M.De Donno, A Peng, et al, Integrated computer program forsimulation of meshing and contact of gear drives, Computer Methods inApplied Mechanics and Engineering,2000,181(1):71~85
[45] John Argyris, Alfonso Fuentes, Faydor L. Litvin, Computerized integratedapproach for design and stress analysis of spiral bevel gears, ComputerMethods in Applied Mechanics and Engineering,2002,191(11):1057~1095
[46] Litvin F L, W ang A G, Handschuh R F, Computerized generation andsimulation of meshing and contact of spiral bevel gears w ith improvedgeometry, Computer Methods in Applied Mechanics and Engineering,1998,158:35~64
[47] Galina I. Sheveleva, Andrey E. Volkov, Vladimir I. Medvedev, Algorithms foranalysis of meshing and contact of spiral bevel gears, Mechanism andMaehinetheory,2006,42(2007):198~215
[48]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]，武汉：华中科技大学，2004
[49]南开大学数学系齿轮啮合研究小组，齿轮啮合理论的数学基础，应用数学学报，1976(2)：85～89
[50]陈志新，共轭曲面原理，北京：科学出版社，1974
[51]吴序堂，齿轮啮合原理，北京：机械工业出版社，1982
[52]郑昌启，弧齿锥齿轮和准双曲面齿轮，北京：机械工业出版社，1988
[53]王小椿，点啮合曲面的三阶接触分析，西安交通大学学报，1983，17(3)：1~13
[54]王小椿，线接触曲面的三阶接触分析，西安交通大学学报，1983，17(5)：1~12
[55]王小椿，吴序堂，点接触齿面三阶接触分析的进一步探讨—V/H检验法的理论，西安交通大学学报，1987，21(2)：l~13
[56]吴序堂，王小椿，李峰，曲线齿锥齿轮三阶接触分析法的原理及传动质量评价，机械工程学报，1994，30(3)：47~57
[57]王小椿，吴序堂，弧齿锥齿轮和双曲线齿轮的三阶接触分析和优化切齿计算，齿轮，1989，13(2)：1~10
[58]王小椿，吴序堂，空间点啮合齿面的接触特性对安装误差的敏感性分析，西安交通大学学报，1990，24(6)：45~57
[59]方宗德，刘涛，邓效忠，基于传动误差设计的弧齿锥齿轮啮合分析，航空学报，2002，23(3)：226～230
[60]邓效忠，杨宏斌，牛嗥，高齿弧齿锥齿轮的设计与性能试验，中国机械工程，1999，10(8)：864～866
[61]西安交通大学机制教研室齿轮研究组，弧齿锥齿轮与准双曲面齿轮加工调整原理，上海：上海科学技术出版社，1979
[62]吴序堂，准双曲面齿轮的变性全展成加工法原理，齿轮，1984，8(3)：1~8
[63]吴序堂，刀倾半展成法加工准双曲面齿轮的原理及机床调整，西安交大科学技术报告，1951：81~169
[64]吴序堂，准双曲面齿轮啮合原理及其在刀倾半展成加工中的应用，西安交通大学学报，1981，15(1)：9~24
[65]吴序堂，格里生制准双曲面齿轮刀倾全展成切齿法的研究，机械工程学报，1985，21(2)：54~69
[66]吴序堂，格里生制曲线齿锥齿轮变性半展成切齿原理，西安交通大学学报，1984，18(5)：1~14
[67]曾韬，美国格里森SGM编制原理，制造技术与机床，1979，4：17~26
[68]张洪飚，郑昌启，Gleason准双曲面齿轮螺旋成形法切齿计算原理(上)，汽车技术，1982(8)：32~38
[69]张洪飚，郑昌启，Gleason准双曲面齿轮螺旋成形法切齿计算原理(下)，汽车技术，1982(8)：25~29
[70] Wang X C, Wu L，Li B, Zhang Y, Study on kiematics transformation fromtraditional machine tool to free-form ones based on spatial kinematics, JixieGongcheng Xuebao/Chinese Journal of Mechanical Engineering,2001,37(4):93~98
[71] Wang Z Y, Yu S Q，Zeng T, Compensation of machining errors of CNC spiralbevel gear grinding machine, Nongye Jixie Xuebao/Transactions of theChinese Society of Agricultural Machinery,2009,40(1):222~226
[72]王志永，于水琴，曾韬，数控磨齿机与“M类”铣齿机加工参数的转换，制造技术与机床，2007(7)：94~97
[73]王志永，于水琴，曾韬，数控磨齿机与“T类”铣齿机加工参数的转换，制造技术与机床，2007(9)：75~77
[74]吴训成，毛世民，吴序堂，点啮合齿面主动设计研究，机械工程学报，2000，36(4)：70~73
[75]王延忠，周云飞等，基于通用五坐标数控机床螺旋锥齿轮NC加工研究，中国机械工程，2001，12(8)：903~906
[76]王延忠，周云飞，李左章，螺旋锥齿轮空间曲面NC加工插补误差分析，华中理工大学学报，2002，30(2):9~12
[77]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，中国机械工程，2009，20(22)：2733~2737
[78]张华，邓效忠，四轴数控螺旋锥齿轮铣齿机变性法铣齿研究，中国机械工程，2007，18(14)：1652~1655
[79]张华，曹雪梅，邓效忠等，四轴联动数控螺旋锥齿轮铣齿机的齿长曲率修正，农业机械学报，2010，41(7)：205~209
[80]郑昌启，螺旋锥齿轮轮齿加载接触分析计算原理，机械工程学报，1993，29(4)：50~54
[81]方宗德，齿轮轮齿承载接触分析(LTCA)的模型和方法，机械传动，1998，22(2)：1~3
[82]方宗德，邓效忠等，考虑边缘接触的弧齿锥齿轮承载接触分析，机械工程学报，2002，38(9)：69~72
[83]张金良，方宗德等，弧齿锥齿轮齿面接触应力分析，机械科学与技术，2007，26(10)：1268~1272
[84]李敬财，螺旋锥齿轮数字化制造基础应用技术研究[博士学位论文]，天津：天津大学，2008
[85]孙殿柱，董学朱，真实齿面啮合分析，机械工程学报，2000，36(8)：98~101
[86]张军辉，方宗德等，基于NURBS的弧齿锥齿轮真实齿面的数字化仿真，航空动力学报，2009，24(7)：1672~1676
[87]熊越东，王太勇等，螺旋锥齿轮数控铣齿加工过程几何仿真研究，机床与液压，2005(6)：1~3
[88]熊越东，基于虚拟现实技术的螺旋锥齿轮CNC加工仿真理论与方法研究
[博士学位论文]，天津：天津大学，2005
[89]张威，王太勇等，面向刀倾展成法的运动学转换简化算法及仿真，机械工程学报，2008,44(3)：123~129
[90]张威，准双曲面齿轮数控加工理论与仿真研究[博士学位论文]，天津：天津大学，2006
[91]于水琴，曾韬，数控螺旋锥齿轮磨齿机加工仿真系统的研究，机械制造，2008，46(523)：5~7
[92]王志永，曾韬，PhoenixⅡ数控螺旋锥齿轮铣齿机加工仿真，计算机仿真，2009，26(1)：280~283
[93]王志永，曾韬，PhoenixⅡ螺旋锥齿轮磨齿机加工仿真系统的研究，系统仿真学报，2009，21(13)：4171~4173
[94]唐进元，蒲太平等，螺旋锥齿轮双重双面法多轴联动数控加工计算机仿真研究，制造技术与机床，2008(2)：25~29
[95]纪玉坤，曹利新，基于UG的五轴数控机床加工仿真，计算机仿真，2006(1)：215~218
[96]熊越东，王太勇等，螺旋锥齿轮数控加工参数转换计算方法，组合机床与自动化加工技术，2006(8)：7~9
[97] Zhang Wei,Wang Taiyong,Xiong Yuedong, et al, Virtual system solution ofCNC machine for spiral bevel and hypoid gears, Transactions of TianjinUniversity,2006,12(5):373~377
[98] Yuan Xing, Shengfeng Qin, Taiyong Wang, et al, Subdivision surfacemodeling for spiral bevel gear manufacturing,The International Journal ofAdvanced Manufacturing Technology,2011,53(4):63~70
[99] Taiyong Wang, Yuan Xing, Lin Zhao, et al, NC machining of spiral bevel gearand hypoid gear based on unity transformation model,Transactions of TianjinUniversity,2011,17(4):264~269
[100]韩佳颖，王太勇等，基于解析计算的螺旋锥齿轮切削仿真算法，农业机械学报，2010，41(12)：223~227
[101]韩佳颖，王太勇等，准双曲面齿轮切削仿真及齿面偏差分析，机械设计，2010，27(12)：84~87
[102]徐彦伟，张连洪等，弧齿锥齿轮成形三维虚拟仿真研究，中国机械工程，2008，11(19)：2703~2707
[103]李敬财，王太勇等，基于数字化制造的螺旋锥齿轮齿面误差修正理论研究，农业机械学报，2008，39(5)：174~177
[104]Wang Taiyong, Li Jingcai, He Gaiyun, et al, Numerical approach to determininginstantaneous contact region for conjugate surfaces, Chinese Journal ofMechanical Engineering (English Edition),2008,21(4):15~17
[105]董学朱，齿轮啮合理论基础，北京：机械工业出版社，1989
[106] Goldrich R.N., Theory of Six Axes CNC Generation of Sprial Bevel and HypoidGears, AGMA Fall Technical Meeting, Pittsburgh,1989
[107] Hermann J Stadfeld, The G-LAB Expert System, a Third Dimension inDeveloping Bevel Gears, The Gleason Works,1994
[108] Hermann J Stadfeld, Phoenix CB Computer-Controlled Building, Measurementand Truing of Stick Blade Cutter Heads, The Gleason Works,1997
[109] Stadfeld H.J., A Closed and Fast Solution Formulation for Practice OrientedOptimization of Real Sprial Bevel and Hypoid Gear Flank Geometry, AGMAFall Technical Meeting, Toronto,1989
[110] Gosselin C., Nonaka T., Shiono Y., Identification of the Machine Settings ofReal Hypoid Gear Tooth Surfaces, ASME Journal of Mechanical Design,1998,(120):429~440
[111]罗珺，虚拟加工中心系统及四轴联动切削运动学研究[硕士学位论文]，天津：天津大学，2006
[112]李鹏，虚拟制造中加工中心切削过程仿真系统的研究与开发[硕士学位论文]，天津：天津大学，2004
[113]王晓斌，基于三维实体的数控加工仿真系统的研究[硕士学位论文]，天津：天津大学，2003
[2] E.Wildhaber,Gear tooth curvature treated simply,American Machinist,1945,89(18):122~125
[3] Wildhaber E., Tooth contact.American Machinist,1946,90(12):110~114
[4] Wildhaber E., Basic relationship of hypoid gear,American Machinist,1946,90(3):108~111
[5] Wildhaber E., Conjugate pitch surface.American Machinist,1946,90
[6] Wildhaber E., Surface curvature, Prod Engry,1956,27(5):184~191
[7]爱.威尔德哈尔泊，锥齿轮及准双曲面齿轮啮合原理，北京：机械工业出版社，1958
[8] Baxter M. L., Basic geometry and tooth contact of hypoid gear, industrialmathe-matics,1961,11(2):19~28
[9] Baxter M. L., Second-order surface generation. J Ind Math;1973，23(2):85~106
[10] Hermann J., Stdtfeld, Gleason Bevel Gear Technology, New York: TheGleason works,1994
[11]冯忆艰，克林贝格螺旋锥齿轮磨齿问题的探讨，煤矿机械，1998(11)：23~24
[12]冯忆艰，失配理论在克林贝格螺旋锥齿轮副中的应用，西安科技学院学报，2000，20(2)：148~150
[13]刘志峰，陈良玉，王延忠等，Klingelnberg摆线锥齿轮轮齿几何分析.东北大学学报(自然科学版)，1999，20(4)：388~391
[14] Stadtfeld H.J., Olerlikon bevel and hypoid gears, Olerlikon BührleAG.,1991
[15]刘惟信，圆锥齿轮与双曲面齿轮传动，北京：人民交通出版社，1980
[16]董学朱，延伸外摆线锥齿轮切齿调整计算法的改进，机械传动，1997，21(4)：41~47
[17]董学朱，延伸外摆线齿准双曲面齿轮几何设计和切齿调整计算新方法，机械传动，1999，23(4)：16~20
[18]董学朱，摆线锥齿轮及准双曲面齿轮设计和制造，北京：机械工业出版社，2003
[19]郑昌启，弧齿锥齿轮传和准双曲面齿轮—啮合原理、轮坯设计、加工调整和齿面分析计算原理，北京：机械工业出版社，1988
[20] Litvin F L, Gutman Y, A Method of Local Synthesis of Gears Grounded on theConnection between the Principal and Geodetic Curvatures of Surfaces, ASMEJournal of Mechanical Design,1981,103:114~125
[21] F.L. Litvin, Y. Zhang, Local synthesis and tooth contact analysis of face-milledspiral bevel gears, Chicago: NASA Lewis Research Center,1991
[22]曾韬，螺旋锥齿轮设计与加工，哈尔滨：哈尔滨工业大学出版社，1989
[23]天津齿轮机床研究所，格利森锥齿轮技术资料译文集(第一分册)，北京：机械工业出版社，1986
[24] Kawasaki K,Tamura H, Duplex spread blade method for cutting hypoid gearswith modified tooth surface, JOURNAL OF MECHANICALDESIGN,1998,120(3):441~447
[25] Gleason Works, Electronic Computer Program Aoo212，1978
[26] Litvin F L,Gutman Y, Methods of Synthesis and Analysis for HypoidGear-Drives of “Formate”and “Helixform”, ASME Journal of MechanicalDesign,1981,103(1):83~110
[27] Gleason Works, Phoenix closed loop system, NY：Rochesger,1991
[28] Gosselin, C. J., Cloutier, L., The Generating Space for Parabolic Motion ErrorSpiral Bevel Gears Cut by the Gleason Method, ASME J.Mech. Des.,1993,115:483~489
[29]王小椿，吴联银，基于空间运动学的传统机床与Free-form型机床运动转换方法的研究，机械工程学报，2001，37(4)：93~98
[30] Litvin F L., Gear Geometry and Applied Theory, New Jersey: PrentieeHall,1994
[31] Litvin F L, Fuentes A, Hayasaka K, Design, manufacture, stress analysis, andexperimental tests of low-noise high endurance spiral bevel gears, Mechanismand Machine Theory,2006,41(1):83~118
[32] S. Vilmos, Optimal machine tool setting for hypoid gears improving loaddistribution, ASME Journal of Mechanical Design,2001,123:577~582
[33] S. Vilmos, Optimal tooth modifications in hypoid gears, ASME Journal ofMechanical Design,2005,127:646~655
[34] V. Simon, ADVANCED DESIGN AND MANUFACTURE OFFACE-HOBBED SPIRAL BEVEL GEARS, Proceedings of the ASME2009International Mechanical Engineering Congress&Exposition.Florida,2009:1~10
[35] Fong Z. H., Tsay C. B., Kinematical Optimization of Spiral Bevel Gears,ASME J. Mech. Des.,1992,114:498~506
[36] Fong Z. H., Mathematical Model of Universal Hypoid Generator withSupplemental Kinematic Flank Correction Motions, ASME J.Mech. Des.,2000,122:136~142
[37] Shih Y.P., Fong Z.H., Flank Correction for Spiral Bevel and Hypoid Gears on aSix-Axis CNC Hypoid Generator, ASME Journal of Mechanical Design,2008,130(6):1~11
[38] C.Y. Lin, C.B. Tsay, Z.H. Fong, Mathematical model of spiral bevel andhypoid gears manufactured by the modified roll method, Mechanism andMachine Theory,1997,32:121~136
[39] C.Y. Lin, C.B. Tsay, Z.H. Fong, Computer-aided manufacturing of spiral beveland hypoid gears by applying optimization techniques, Journal of MaterialsProcessing Technology,2001,114:22~35
[40] S. H. Suh, D. H. Jung, E. S. Lee, Modeling, mplementation, and manufacturingof spiral bevel gears with crown, International journal of advancedmanufacturing technology,2003,21(3):775~786
[41] Suh S.H, Jih W.S, et al, Sculptured surface machining of spiral bevel gears withCNC milling, International Journal of Machine Tools&Manufacture,2001,41(5):833~850
[42] S.H. Suh, E.S. Lee, et al. Geometric error measurement of spiral bevel gearsusing a virtual gear model for STEP-NC, International Journal of MachineTools&Manufacture,2002,42:335~342
[43] F L Litvin, Alfonso Fuentes, Qi Fan, et al, Computerized design, simulation ofmeshing, and contact and stress analysis of face-milled formate generatedspiral bevel gears,Mechanism and Machine Theory,2002,37(5):441~459
[44] F.L Litvin, M.De Donno, A Peng, et al, Integrated computer program forsimulation of meshing and contact of gear drives, Computer Methods inApplied Mechanics and Engineering,2000,181(1):71~85
[45] John Argyris, Alfonso Fuentes, Faydor L. Litvin, Computerized integratedapproach for design and stress analysis of spiral bevel gears, ComputerMethods in Applied Mechanics and Engineering,2002,191(11):1057~1095
[46] Litvin F L, W ang A G, Handschuh R F, Computerized generation andsimulation of meshing and contact of spiral bevel gears w ith improvedgeometry, Computer Methods in Applied Mechanics and Engineering,1998,158:35~64
[47] Galina I. Sheveleva, Andrey E. Volkov, Vladimir I. Medvedev, Algorithms foranalysis of meshing and contact of spiral bevel gears, Mechanism andMaehinetheory,2006,42(2007):198~215
[48]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]，武汉：华中科技大学，2004
[49]南开大学数学系齿轮啮合研究小组，齿轮啮合理论的数学基础，应用数学学报，1976(2)：85～89
[50]陈志新，共轭曲面原理，北京：科学出版社，1974
[51]吴序堂，齿轮啮合原理，北京：机械工业出版社，1982
[52]郑昌启，弧齿锥齿轮和准双曲面齿轮，北京：机械工业出版社，1988
[53]王小椿，点啮合曲面的三阶接触分析，西安交通大学学报，1983，17(3)：1~13
[54]王小椿，线接触曲面的三阶接触分析，西安交通大学学报，1983，17(5)：1~12
[55]王小椿，吴序堂，点接触齿面三阶接触分析的进一步探讨—V/H检验法的理论，西安交通大学学报，1987，21(2)：l~13
[56]吴序堂，王小椿，李峰，曲线齿锥齿轮三阶接触分析法的原理及传动质量评价，机械工程学报，1994，30(3)：47~57
[57]王小椿，吴序堂，弧齿锥齿轮和双曲线齿轮的三阶接触分析和优化切齿计算，齿轮，1989，13(2)：1~10
[58]王小椿，吴序堂，空间点啮合齿面的接触特性对安装误差的敏感性分析，西安交通大学学报，1990，24(6)：45~57
[59]方宗德，刘涛，邓效忠，基于传动误差设计的弧齿锥齿轮啮合分析，航空学报，2002，23(3)：226～230
[60]邓效忠，杨宏斌，牛嗥，高齿弧齿锥齿轮的设计与性能试验，中国机械工程，1999，10(8)：864～866
[61]西安交通大学机制教研室齿轮研究组，弧齿锥齿轮与准双曲面齿轮加工调整原理，上海：上海科学技术出版社，1979
[62]吴序堂，准双曲面齿轮的变性全展成加工法原理，齿轮，1984，8(3)：1~8
[63]吴序堂，刀倾半展成法加工准双曲面齿轮的原理及机床调整，西安交大科学技术报告，1951：81~169
[64]吴序堂，准双曲面齿轮啮合原理及其在刀倾半展成加工中的应用，西安交通大学学报，1981，15(1)：9~24
[65]吴序堂，格里生制准双曲面齿轮刀倾全展成切齿法的研究，机械工程学报，1985，21(2)：54~69
[66]吴序堂，格里生制曲线齿锥齿轮变性半展成切齿原理，西安交通大学学报，1984，18(5)：1~14
[67]曾韬，美国格里森SGM编制原理，制造技术与机床，1979，4：17~26
[68]张洪飚，郑昌启，Gleason准双曲面齿轮螺旋成形法切齿计算原理(上)，汽车技术，1982(8)：32~38
[69]张洪飚，郑昌启，Gleason准双曲面齿轮螺旋成形法切齿计算原理(下)，汽车技术，1982(8)：25~29
[70] Wang X C, Wu L，Li B, Zhang Y, Study on kiematics transformation fromtraditional machine tool to free-form ones based on spatial kinematics, JixieGongcheng Xuebao/Chinese Journal of Mechanical Engineering,2001,37(4):93~98
[71] Wang Z Y, Yu S Q，Zeng T, Compensation of machining errors of CNC spiralbevel gear grinding machine, Nongye Jixie Xuebao/Transactions of theChinese Society of Agricultural Machinery,2009,40(1):222~226
[72]王志永，于水琴，曾韬，数控磨齿机与“M类”铣齿机加工参数的转换，制造技术与机床，2007(7)：94~97
[73]王志永，于水琴，曾韬，数控磨齿机与“T类”铣齿机加工参数的转换，制造技术与机床，2007(9)：75~77
[74]吴训成，毛世民，吴序堂，点啮合齿面主动设计研究，机械工程学报，2000，36(4)：70~73
[75]王延忠，周云飞等，基于通用五坐标数控机床螺旋锥齿轮NC加工研究，中国机械工程，2001，12(8)：903~906
[76]王延忠，周云飞，李左章，螺旋锥齿轮空间曲面NC加工插补误差分析，华中理工大学学报，2002，30(2):9~12
[77]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，中国机械工程，2009，20(22)：2733~2737
[78]张华，邓效忠，四轴数控螺旋锥齿轮铣齿机变性法铣齿研究，中国机械工程，2007，18(14)：1652~1655
[79]张华，曹雪梅，邓效忠等，四轴联动数控螺旋锥齿轮铣齿机的齿长曲率修正，农业机械学报，2010，41(7)：205~209
[80]郑昌启，螺旋锥齿轮轮齿加载接触分析计算原理，机械工程学报，1993，29(4)：50~54
[81]方宗德，齿轮轮齿承载接触分析(LTCA)的模型和方法，机械传动，1998，22(2)：1~3
[82]方宗德，邓效忠等，考虑边缘接触的弧齿锥齿轮承载接触分析，机械工程学报，2002，38(9)：69~72
[83]张金良，方宗德等，弧齿锥齿轮齿面接触应力分析，机械科学与技术，2007，26(10)：1268~1272
[84]李敬财，螺旋锥齿轮数字化制造基础应用技术研究[博士学位论文]，天津：天津大学，2008
[85]孙殿柱，董学朱，真实齿面啮合分析，机械工程学报，2000，36(8)：98~101
[86]张军辉，方宗德等，基于NURBS的弧齿锥齿轮真实齿面的数字化仿真，航空动力学报，2009，24(7)：1672~1676
[87]熊越东，王太勇等，螺旋锥齿轮数控铣齿加工过程几何仿真研究，机床与液压，2005(6)：1~3
[88]熊越东，基于虚拟现实技术的螺旋锥齿轮CNC加工仿真理论与方法研究
[博士学位论文]，天津：天津大学，2005
[89]张威，王太勇等，面向刀倾展成法的运动学转换简化算法及仿真，机械工程学报，2008,44(3)：123~129
[90]张威，准双曲面齿轮数控加工理论与仿真研究[博士学位论文]，天津：天津大学，2006
[91]于水琴，曾韬，数控螺旋锥齿轮磨齿机加工仿真系统的研究，机械制造，2008，46(523)：5~7
[92]王志永，曾韬，PhoenixⅡ数控螺旋锥齿轮铣齿机加工仿真，计算机仿真，2009，26(1)：280~283
[93]王志永，曾韬，PhoenixⅡ螺旋锥齿轮磨齿机加工仿真系统的研究，系统仿真学报，2009，21(13)：4171~4173
[94]唐进元，蒲太平等，螺旋锥齿轮双重双面法多轴联动数控加工计算机仿真研究，制造技术与机床，2008(2)：25~29
[95]纪玉坤，曹利新，基于UG的五轴数控机床加工仿真，计算机仿真，2006(1)：215~218
[96]熊越东，王太勇等，螺旋锥齿轮数控加工参数转换计算方法，组合机床与自动化加工技术，2006(8)：7~9
[97] Zhang Wei,Wang Taiyong,Xiong Yuedong, et al, Virtual system solution ofCNC machine for spiral bevel and hypoid gears, Transactions of TianjinUniversity,2006,12(5):373~377
[98] Yuan Xing, Shengfeng Qin, Taiyong Wang, et al, Subdivision surfacemodeling for spiral bevel gear manufacturing,The International Journal ofAdvanced Manufacturing Technology,2011,53(4):63~70
[99] Taiyong Wang, Yuan Xing, Lin Zhao, et al, NC machining of spiral bevel gearand hypoid gear based on unity transformation model,Transactions of TianjinUniversity,2011,17(4):264~269
[100]韩佳颖，王太勇等，基于解析计算的螺旋锥齿轮切削仿真算法，农业机械学报，2010，41(12)：223~227
[101]韩佳颖，王太勇等，准双曲面齿轮切削仿真及齿面偏差分析，机械设计，2010，27(12)：84~87
[102]徐彦伟，张连洪等，弧齿锥齿轮成形三维虚拟仿真研究，中国机械工程，2008，11(19)：2703~2707
[103]李敬财，王太勇等，基于数字化制造的螺旋锥齿轮齿面误差修正理论研究，农业机械学报，2008，39(5)：174~177
[104]Wang Taiyong, Li Jingcai, He Gaiyun, et al, Numerical approach to determininginstantaneous contact region for conjugate surfaces, Chinese Journal ofMechanical Engineering (English Edition),2008,21(4):15~17
[105]董学朱，齿轮啮合理论基础，北京：机械工业出版社，1989
[106] Goldrich R.N., Theory of Six Axes CNC Generation of Sprial Bevel and HypoidGears, AGMA Fall Technical Meeting, Pittsburgh,1989
[107] Hermann J Stadfeld, The G-LAB Expert System, a Third Dimension inDeveloping Bevel Gears, The Gleason Works,1994
[108] Hermann J Stadfeld, Phoenix CB Computer-Controlled Building, Measurementand Truing of Stick Blade Cutter Heads, The Gleason Works,1997
[109] Stadfeld H.J., A Closed and Fast Solution Formulation for Practice OrientedOptimization of Real Sprial Bevel and Hypoid Gear Flank Geometry, AGMAFall Technical Meeting, Toronto,1989
[110] Gosselin C., Nonaka T., Shiono Y., Identification of the Machine Settings ofReal Hypoid Gear Tooth Surfaces, ASME Journal of Mechanical Design,1998,(120):429~440
[111]罗珺，虚拟加工中心系统及四轴联动切削运动学研究[硕士学位论文]，天津：天津大学，2006
[112]李鹏，虚拟制造中加工中心切削过程仿真系统的研究与开发[硕士学位论文]，天津：天津大学，2004
[113]王晓斌，基于三维实体的数控加工仿真系统的研究[硕士学位论文]，天津：天津大学，2003
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |