精锻直齿锥齿轮齿形修形设计技术研究
|
摘要
精锻齿轮,是指齿轮的轮齿直接模锻成形且无需切削加工的齿轮。直齿锥齿轮,以其结构上的可锻性,成为国内外研制最早、发展最快、应用最多的精锻零件之一。同利用切齿加工相比,精锻齿轮在提高寿命、节能、节材等方面具有显著的效果。然而,受技术和装备等水平的影响,7级以上精度的齿轮难以实现批量精锻,限制了精锻齿轮在现代汽车特别是轿车、重型车中的应用。采用齿轮齿形修形技术可有效地改善齿轮传动装置的工作平稳性,降低齿轮的噪声和振动,提高齿轮的承载能力,延长齿轮的使用寿命。圆柱齿轮的齿形修形易于实现,已取得了明显的效果,而圆锥齿轮齿形修形技术,受到齿轮结构的影响,加工出的鼓形量较小且鼓形位置难以调整,达不到齿形修形的根本目的。精锻锥齿轮靠模具成形,研究通过模具型腔修形实现齿轮产品的修形是经济的。
论文综合分析了齿轮齿形修形技术的国内外究现状,以目前难以实现齿形修形的精锻直齿锥齿轮为研究对象,提出并研究实现了精锻直齿锥齿轮的等距化铣修形工艺。该工艺研究应用化学铣切方法,通过对齿轮精锻模电极齿轮的等距修形,实现精锻模具型腔的修形,从而实现精锻锥齿轮的齿形修形。通过在某汽车差速器齿轮的精锻生产证明,应用本研究技术,可以提高精锻齿轮产品运动精度和工作平稳性精度一级,齿轮产品的接触区分布较好,齿面粗糙度得以降低,精锻模具寿命得到提高20%。
通过研究分析证明,提出的等距化铣修形技术,不仅可以方便地实现精锻直齿锥齿轮的齿顶修缘和鼓形齿加工,而且,修形后的表面仍然保持齿轮的渐开线特征。
提出以齿形修形后,精锻齿轮能否顺利脱模作为修形设计的主要依据,并根据修形齿轮的结构特点,建立了计算精锻直齿锥齿轮齿面上任意修形部位点脱模校核的数学模型,编制了通用的修形精锻直齿锥齿轮脱模计算程序。
通过对常用电极齿轮材料—紫铜的化铣实验,认为:化铣液主要成份Fe~(3+)的含量在8-12g/l、化铣温度宜在40-60℃、化铣时间在10分钟以上时,对紫铜材料的化铣速度达到较大值且波动较小,化铣面的表面粗糙程度保持在较低程度;对于一般齿轮的齿形修形量在0.02-0.05mm的情况下,采用本化铣工艺能够保证对紫铜材料化铣的均匀性。
根据直齿锥齿轮的齿形修形技术需要,提出了精锻直齿锥齿轮齿形修形设计综合技术研究路线,认为修形直齿锥齿轮的三维实体建模是本技术研究的基础,论文基于SolidWorks系统,采用尺寸驱动法进行了等距修形直齿锥齿轮的三维实体建模模块开发。
The teeth of gear named fine forging gear can be formed directly by the forging die without chip-removal machining. Especially for the bevel gear, it was the one of fine forging parts which were developed and applied earlier. Compared with the machining gears, some merits can be obtained to the gears made by fine forging technology as high mechanical performance, long life, energy saving and less materials. But due to the limitation of forming technology and equipments, fine-forging bevel gears with high precision better than 7-grade are hardly manufactured in batch and then their application are out of modern automobile industry. It is proved that the transmission stability, precision and service life of gear box can be improved as well as the vibration and noisy can be lightened with the usage of teeth profile modification technology in manufacturing of gears. It is easy to modify the profile of spur gears, and only minimal modification of profile can be obtained in bevel gears even with some certain location. The modification technology of bevel gears then used seldom. In fact it is efficient and effective to modified the teeth profile of fine forging gears if the modification was printed on the forging die previously.
Based on the synthetical analysis of the research and application of the gear modification technology, this thesis put forward and developed the Equidistance Chemical Machining Modification Technology(ECMMT) which is available to the bevel gears modification. The electrode gear, used to form the cavity of fine forging die by the Electrode Discharge Machining(EDM), are modified by the ECMMT. The modification the is "copied" on the die. Large batch of fine forging gears with the special modification therefore are "duplicated" by the unique die. The ECMMT was used in the production of a certain type bevel gear used in the car, as the result, the transmission precision and stability of the bevel gears improved to the 7-grade, the touch area is quite better, the roughness of the teeth face is increased greatly, and the life of forging die is lengthened.
By use of ECMMT, both edge modification and the drum area on the gear tooth surface can be implemented easily, as well, the involute characteristic of the modified teeth of bevel gear keeps the normal gear profile.
One of the principles of gear teeth modification is researched in this thesis, that is whether the forging gear with teeth modification can be lift out of the die cavity or not. And the calculating model is constructed based on the study of the modified bevel gear structure. Further the universal program is developed and tested effective as the tool to design the figure and the location of modification area.
The useful results are obtained by the experiments of chemical milling parameters on copper samples. It's tested that the best chemical milling parameters to reach the excellent machining result are those, the Fe3+ content of electrolyte is 8-12 g/l, the work temperature keeps between 40℃to 60℃, the milling time is not less than 10 minutes. By use of the chemical machining technology with the parameters above, such ideal and operable results as the well-proportioned milling velocity, lower surface roughness and the material equidistance removal of varied surfaces when the milling depth in 0.02-0.05mm.
It is necessary to build the comprehensive research way to design the modification area and size precisely for the straight-teeth bevel gear. In this thesis, the 3-D modeling system of equidistance modification bevel gear is developed based the universal CAD software SolidWorks with main help of the tool integrated in SolidWorks-Size Drive Method.
论文综合分析了齿轮齿形修形技术的国内外究现状,以目前难以实现齿形修形的精锻直齿锥齿轮为研究对象,提出并研究实现了精锻直齿锥齿轮的等距化铣修形工艺。该工艺研究应用化学铣切方法,通过对齿轮精锻模电极齿轮的等距修形,实现精锻模具型腔的修形,从而实现精锻锥齿轮的齿形修形。通过在某汽车差速器齿轮的精锻生产证明,应用本研究技术,可以提高精锻齿轮产品运动精度和工作平稳性精度一级,齿轮产品的接触区分布较好,齿面粗糙度得以降低,精锻模具寿命得到提高20%。
通过研究分析证明,提出的等距化铣修形技术,不仅可以方便地实现精锻直齿锥齿轮的齿顶修缘和鼓形齿加工,而且,修形后的表面仍然保持齿轮的渐开线特征。
提出以齿形修形后,精锻齿轮能否顺利脱模作为修形设计的主要依据,并根据修形齿轮的结构特点,建立了计算精锻直齿锥齿轮齿面上任意修形部位点脱模校核的数学模型,编制了通用的修形精锻直齿锥齿轮脱模计算程序。
通过对常用电极齿轮材料—紫铜的化铣实验,认为:化铣液主要成份Fe~(3+)的含量在8-12g/l、化铣温度宜在40-60℃、化铣时间在10分钟以上时,对紫铜材料的化铣速度达到较大值且波动较小,化铣面的表面粗糙程度保持在较低程度;对于一般齿轮的齿形修形量在0.02-0.05mm的情况下,采用本化铣工艺能够保证对紫铜材料化铣的均匀性。
根据直齿锥齿轮的齿形修形技术需要,提出了精锻直齿锥齿轮齿形修形设计综合技术研究路线,认为修形直齿锥齿轮的三维实体建模是本技术研究的基础,论文基于SolidWorks系统,采用尺寸驱动法进行了等距修形直齿锥齿轮的三维实体建模模块开发。
The teeth of gear named fine forging gear can be formed directly by the forging die without chip-removal machining. Especially for the bevel gear, it was the one of fine forging parts which were developed and applied earlier. Compared with the machining gears, some merits can be obtained to the gears made by fine forging technology as high mechanical performance, long life, energy saving and less materials. But due to the limitation of forming technology and equipments, fine-forging bevel gears with high precision better than 7-grade are hardly manufactured in batch and then their application are out of modern automobile industry. It is proved that the transmission stability, precision and service life of gear box can be improved as well as the vibration and noisy can be lightened with the usage of teeth profile modification technology in manufacturing of gears. It is easy to modify the profile of spur gears, and only minimal modification of profile can be obtained in bevel gears even with some certain location. The modification technology of bevel gears then used seldom. In fact it is efficient and effective to modified the teeth profile of fine forging gears if the modification was printed on the forging die previously.
Based on the synthetical analysis of the research and application of the gear modification technology, this thesis put forward and developed the Equidistance Chemical Machining Modification Technology(ECMMT) which is available to the bevel gears modification. The electrode gear, used to form the cavity of fine forging die by the Electrode Discharge Machining(EDM), are modified by the ECMMT. The modification the is "copied" on the die. Large batch of fine forging gears with the special modification therefore are "duplicated" by the unique die. The ECMMT was used in the production of a certain type bevel gear used in the car, as the result, the transmission precision and stability of the bevel gears improved to the 7-grade, the touch area is quite better, the roughness of the teeth face is increased greatly, and the life of forging die is lengthened.
By use of ECMMT, both edge modification and the drum area on the gear tooth surface can be implemented easily, as well, the involute characteristic of the modified teeth of bevel gear keeps the normal gear profile.
One of the principles of gear teeth modification is researched in this thesis, that is whether the forging gear with teeth modification can be lift out of the die cavity or not. And the calculating model is constructed based on the study of the modified bevel gear structure. Further the universal program is developed and tested effective as the tool to design the figure and the location of modification area.
The useful results are obtained by the experiments of chemical milling parameters on copper samples. It's tested that the best chemical milling parameters to reach the excellent machining result are those, the Fe3+ content of electrolyte is 8-12 g/l, the work temperature keeps between 40℃to 60℃, the milling time is not less than 10 minutes. By use of the chemical machining technology with the parameters above, such ideal and operable results as the well-proportioned milling velocity, lower surface roughness and the material equidistance removal of varied surfaces when the milling depth in 0.02-0.05mm.
It is necessary to build the comprehensive research way to design the modification area and size precisely for the straight-teeth bevel gear. In this thesis, the 3-D modeling system of equidistance modification bevel gear is developed based the universal CAD software SolidWorks with main help of the tool integrated in SolidWorks-Size Drive Method.
引文
[1]孙桓,陈作模主编.机械原理.高等教育出版社,1995
[2]Wang,J and Howard.I.The Torsional Stiffness of involute spur gears.Proc.Instn Mesh Engrs,2004,Vol.218(part c:Journal of Mechanical Engineering Science):131-142
[3]陈若愚.直齿锥齿轮精锻技术.制造技术与机床,1997(11):25-28
[4]渭阳柴油机厂编著.直齿锥齿轮.国防工业出版社,1978
[5]易建军,张明,徐中耀.汽车齿轮修形的工艺及其分析.汽车工艺与材料,1998(10):10-12
[6]李英杰,支秋玲.采用设计齿形修形技术提高工程机械传动装置性能.工程机械,2005(3):56-57
[7]崔焕勇.直齿锥齿轮精锻模具设计及制造新技术研究.山东工业大学硕士学位论文,1996
[8]金海平.汽车齿轮精锻成型.天津汽车,2003(1):20-24
[9]李亚兰等.精锻齿轮模具失效分析及对策.金属热处理,1994(9):30-34
[10]邓克.直伞齿轮精锻技术的应用及发展.安徽工业大学学报,2005(4):169-172
[11]张勇.半轴齿轮温(热)锻成形技术研究.重庆大学硕士学位论文,2003
[12]陈泽中.直齿圆柱齿轮精锻工步分析与实验研究.南昌大学硕士学位论文,1998
[13]田福祥.直伞齿轮精锻模齿模的设计与制造.模具制造,2002(12):28-33
[14]夏巨谌.精密塑性成形工艺.北京:机械工业出版社,1999
[15]Chitkara N R.Near-Net shape forging of spur gear forms:An analysis and some experiments.Int.J.Mech.Sci.,1996,V01.38(8-9):891-916
[16]Neher R.Modern Cold Forging Applications for the Manufacture of Complex Automotive Parts,Journal of Material Processing Technology.1994,Vol.46(1-2):169-183
[17]梁秀春,王振纲,付建华,张如怀.摆辗工艺及设备,重型机械,1995,(5):56-60
[18]王丽莉.摆动辗压技术发展概况.有色矿冶,2002,Vol.18(12):42-45
[19]王广春,马新武,赵国群,姜寿文.摆辗机摆头运动学分析和运动轨迹的数值模拟.金属成形工艺,2000,Vol.18(3):17-19
[20]D.B Willey,A.J.Williams,R.Harris.Preparation and Properties of metal matrix hydride compacts via the rotary forging compaction mute.Journal of Alloys and Compounds,1997,253-254(5):698-703
[21]J.Szymborski,J.Pregowski.Gear manufacture using rotary repressing.Metal Powder Report,1994,Vol.49(11):40-41
[22]胡亚民,车路长.我国摆动辗压技术的发展概况.锻压技术,1996(6):37.39
[23]T.Canta,D.Frunza,D.Sabadus and C.Tintelecan.Some aspects of energy distribution in rotary forming processes.Journal of Materials Processing Technology,1998,80-81(8):195-198
[24]胡亚民.摆辗机的发展态势.机械工人(热加工),1999(4):13-14
[25]胡锐.直齿锥齿轮摆辗成形有限元模拟研究.武汉理工大学硕士学位论文,2006
[26]秦万忠.粉末冶金直齿锥齿轮的模具设计.粉末冶金技术,2000,Vol.18(1):16-22
[27]杨沿平等.汽车精密成型技术现状与发展趋势刍议.2003,Vol.25(6):625-629
[28]崔传勋.工程机械齿轮的修形设计与加工.机械传动,1996,Vol.20(3):50-54
[29]朱传敏,田志仁,宋孔杰.齿轮修形曲线的优化设计.山东工业大学学报,1998,Vol.28(2):122-126
[30]汪强,周锦进.齿轮修形技术及工艺的进展.电加工与模具,2001(5):21-24
[31]寺内喜男.齿形修正对齿轮动载和噪声的影响.汽车齿轮,1984,Vol.8(3):41-43
[32]唐增宝,钟毅芳,陈久荣.修形齿轮的最佳修形量和修形长度的确定.华中理工大学学报,1995,Vol.23(2):125-128
[33]杨廷力,叶新,王玉璞.渐开线高速齿轮的齿高修形.齿轮,1982(3):14-24
[34]李敦信.高速齿轮的修形.见:宋聚福主编.齿轮科技资料汇编.上海:上海科学技术出版社,1985:45-55
[35]仙波正庄.高强度齿轮设计.任宏达译.北京:机械工业出版社,1981:105-205
[36]宋乐民.齿轮修形与齿轮强度.北京:国防工业出版社,1987
[37]Dudlcy B W.Hand Book of Practical Gear Design.New York:Mc GrawHill Co.,1984
[38]陶燕光等.高速齿轮热变形修形的试验研究.齿轮,1988,Vol.12(2):25-28
[39]王统,李伟.齿轮轴三维综合弹性变形和齿向修形曲线的研究.上海交通大学学报,1993,Vol.27(1):64-71
[40]J.J.Zhang,I.I.Esat,Y.H.Shi.Load Analysis with Varing Mesh Stiffness. Computers &Structures,1999,Vol.70(3):273-280
[41]ChungYunn Lin,ChungBiau Tsay,ZhangHua Fong.Computer-aided-manufacturing of spiral bevel and hypoid gears by applying optimization techniques.Journal of Materials Processing Technology,2001,Vol.114(1 ):22-35
[42]Myounggu Park.Failure analysis of an accessory bevel gear installed on a J69turbojet engine.Engineering Failure Analysis,2003,Vol.10(3 ):371-382
[43]K.P.Rajurkar,D.Zhu,J.A.McGeough,J.Kozak,A.De Silva.New Developments in Electro-Chemical Machining.CIRP Annals-Manufacturing Technology,1999,Vol.48(2):567-579
[44]M.Ceilik.Comparison of Three Teeth and Whole Body Models in Spur Gear Analysis.Mechanism and Machine Theory,1999,Vol.34(8):1227-1335
[45]Hsiang Hsi Lin,Fred B.Oswald,Dennis P.Townsend.Dynamic loading of spur gears with linear or parabolic tooth profile modifications.Mechanism and Machine Theory,1994,Vol.29(8):1115-1129
[46]杨生华.齿轮接触有限元分析.计算力学学报,2003,Vol.20(2):189-194
[47]李常义.基于ANSYS的渐开线圆柱齿轮参数化造型与有限元建模及分析技术.机械传动,2004,Vol.28(6):25-29
[48]叶友东.基于ANSYS的渐开线直齿圆柱齿轮有限元分析.煤矿机械,2004(6):43-45
[49]刘道玉.渐开线直齿圆柱齿轮有限元仿真分析.陕西工业学院学报,2004,Vol.20(3):4-6
[50]刘晖.基于参数化的齿轮传动接触有限元分析.大连交通大学硕士论文,2004
[51]F.L.Litvin,G.Sheveleva,D.Vecchiato,I.Gonzalez,A.Fuentes.Modified approach for tooth contact analysis of gear drives and automatic determination of guess values.Computer Methods in Applied Mechanics and Engineering,2000,Vol.181(1-3):71-85
[52]Wang,J.Numerical and Experimental Analysis of Spur Gears in Mesh.Academic Ph.D Thesis Department of Mechanical Engineering,Curtin University of Technology.2003,Perth Australia
[53]王超.齿轮轮齿三维动力接触有限元分析.车辆与动力技术,2004(2):41-45
[54]王勖成,邵敏.有限单元法基本原理与数值方法(第二版)。北京:清华大学出版社,2003
[55]Jerome Bruyere,et al.Statical tolerance analysis of bevel gear by tooth contact analysis and Monte Carlo simulation.Mechanism and Machine Theory,2007,Vol.40(10):1326-1351
[56]O.Vogel,A.Griewank,G.Bar.Direct gear tooth contact analysis for hypoid bevel gears.Computer Methods in Applied Mechanics and Engineering.2002,Vol.191(36):3965-3982
[57]陈霞,夏巨谌等.直齿锥齿轮啮合过程数值模拟.机械设计,2006,Vol.23(4):21-23
[58]金俊松,夏巨谌等.冷精锻修形圆锥齿轮的齿形设计.中国机械工程,2006,Vol.17(19):2038-2041
[59]吴忠鸣,轿车直齿锥齿轮的修形技术研究.武汉:华中科技大学硕士学位论文,2005
[60]崔焕勇,舒其馥,付志刚.直齿锥齿轮精锻模电极齿轮的化铣修形技术.锻压装备与制造技术,2003(4):50-52
[61]Paddy J.Frencha,Pasqualina M.Sarro.Micromachining Technology A Practical Guide to Design,Analysis,and Applications,William Andrew Inc.Published by Elsevier Inc.2006:805-851
[62]吴萌顺.腐蚀工程手册.北京:中国石化出版社,2004
[63]唐余勇.计算直齿锥齿轮近似齿廓方程的等距变换法.哈尔滨工业大学学报.1983(1):20-23
[64]赵洁俊,宋化远.直齿锥齿轮拔模斜度的计算及其应用.锻压机械.1990(6):34-36
[65]左景伊,左禹.腐蚀数据与选材手册.北京:化学工业出版社,2003
[66]胡仁喜.Solidworks中文版标准教程.北京:科学出版社,北京希望电子出版社.2007
[2]Wang,J and Howard.I.The Torsional Stiffness of involute spur gears.Proc.Instn Mesh Engrs,2004,Vol.218(part c:Journal of Mechanical Engineering Science):131-142
[3]陈若愚.直齿锥齿轮精锻技术.制造技术与机床,1997(11):25-28
[4]渭阳柴油机厂编著.直齿锥齿轮.国防工业出版社,1978
[5]易建军,张明,徐中耀.汽车齿轮修形的工艺及其分析.汽车工艺与材料,1998(10):10-12
[6]李英杰,支秋玲.采用设计齿形修形技术提高工程机械传动装置性能.工程机械,2005(3):56-57
[7]崔焕勇.直齿锥齿轮精锻模具设计及制造新技术研究.山东工业大学硕士学位论文,1996
[8]金海平.汽车齿轮精锻成型.天津汽车,2003(1):20-24
[9]李亚兰等.精锻齿轮模具失效分析及对策.金属热处理,1994(9):30-34
[10]邓克.直伞齿轮精锻技术的应用及发展.安徽工业大学学报,2005(4):169-172
[11]张勇.半轴齿轮温(热)锻成形技术研究.重庆大学硕士学位论文,2003
[12]陈泽中.直齿圆柱齿轮精锻工步分析与实验研究.南昌大学硕士学位论文,1998
[13]田福祥.直伞齿轮精锻模齿模的设计与制造.模具制造,2002(12):28-33
[14]夏巨谌.精密塑性成形工艺.北京:机械工业出版社,1999
[15]Chitkara N R.Near-Net shape forging of spur gear forms:An analysis and some experiments.Int.J.Mech.Sci.,1996,V01.38(8-9):891-916
[16]Neher R.Modern Cold Forging Applications for the Manufacture of Complex Automotive Parts,Journal of Material Processing Technology.1994,Vol.46(1-2):169-183
[17]梁秀春,王振纲,付建华,张如怀.摆辗工艺及设备,重型机械,1995,(5):56-60
[18]王丽莉.摆动辗压技术发展概况.有色矿冶,2002,Vol.18(12):42-45
[19]王广春,马新武,赵国群,姜寿文.摆辗机摆头运动学分析和运动轨迹的数值模拟.金属成形工艺,2000,Vol.18(3):17-19
[20]D.B Willey,A.J.Williams,R.Harris.Preparation and Properties of metal matrix hydride compacts via the rotary forging compaction mute.Journal of Alloys and Compounds,1997,253-254(5):698-703
[21]J.Szymborski,J.Pregowski.Gear manufacture using rotary repressing.Metal Powder Report,1994,Vol.49(11):40-41
[22]胡亚民,车路长.我国摆动辗压技术的发展概况.锻压技术,1996(6):37.39
[23]T.Canta,D.Frunza,D.Sabadus and C.Tintelecan.Some aspects of energy distribution in rotary forming processes.Journal of Materials Processing Technology,1998,80-81(8):195-198
[24]胡亚民.摆辗机的发展态势.机械工人(热加工),1999(4):13-14
[25]胡锐.直齿锥齿轮摆辗成形有限元模拟研究.武汉理工大学硕士学位论文,2006
[26]秦万忠.粉末冶金直齿锥齿轮的模具设计.粉末冶金技术,2000,Vol.18(1):16-22
[27]杨沿平等.汽车精密成型技术现状与发展趋势刍议.2003,Vol.25(6):625-629
[28]崔传勋.工程机械齿轮的修形设计与加工.机械传动,1996,Vol.20(3):50-54
[29]朱传敏,田志仁,宋孔杰.齿轮修形曲线的优化设计.山东工业大学学报,1998,Vol.28(2):122-126
[30]汪强,周锦进.齿轮修形技术及工艺的进展.电加工与模具,2001(5):21-24
[31]寺内喜男.齿形修正对齿轮动载和噪声的影响.汽车齿轮,1984,Vol.8(3):41-43
[32]唐增宝,钟毅芳,陈久荣.修形齿轮的最佳修形量和修形长度的确定.华中理工大学学报,1995,Vol.23(2):125-128
[33]杨廷力,叶新,王玉璞.渐开线高速齿轮的齿高修形.齿轮,1982(3):14-24
[34]李敦信.高速齿轮的修形.见:宋聚福主编.齿轮科技资料汇编.上海:上海科学技术出版社,1985:45-55
[35]仙波正庄.高强度齿轮设计.任宏达译.北京:机械工业出版社,1981:105-205
[36]宋乐民.齿轮修形与齿轮强度.北京:国防工业出版社,1987
[37]Dudlcy B W.Hand Book of Practical Gear Design.New York:Mc GrawHill Co.,1984
[38]陶燕光等.高速齿轮热变形修形的试验研究.齿轮,1988,Vol.12(2):25-28
[39]王统,李伟.齿轮轴三维综合弹性变形和齿向修形曲线的研究.上海交通大学学报,1993,Vol.27(1):64-71
[40]J.J.Zhang,I.I.Esat,Y.H.Shi.Load Analysis with Varing Mesh Stiffness. Computers &Structures,1999,Vol.70(3):273-280
[41]ChungYunn Lin,ChungBiau Tsay,ZhangHua Fong.Computer-aided-manufacturing of spiral bevel and hypoid gears by applying optimization techniques.Journal of Materials Processing Technology,2001,Vol.114(1 ):22-35
[42]Myounggu Park.Failure analysis of an accessory bevel gear installed on a J69turbojet engine.Engineering Failure Analysis,2003,Vol.10(3 ):371-382
[43]K.P.Rajurkar,D.Zhu,J.A.McGeough,J.Kozak,A.De Silva.New Developments in Electro-Chemical Machining.CIRP Annals-Manufacturing Technology,1999,Vol.48(2):567-579
[44]M.Ceilik.Comparison of Three Teeth and Whole Body Models in Spur Gear Analysis.Mechanism and Machine Theory,1999,Vol.34(8):1227-1335
[45]Hsiang Hsi Lin,Fred B.Oswald,Dennis P.Townsend.Dynamic loading of spur gears with linear or parabolic tooth profile modifications.Mechanism and Machine Theory,1994,Vol.29(8):1115-1129
[46]杨生华.齿轮接触有限元分析.计算力学学报,2003,Vol.20(2):189-194
[47]李常义.基于ANSYS的渐开线圆柱齿轮参数化造型与有限元建模及分析技术.机械传动,2004,Vol.28(6):25-29
[48]叶友东.基于ANSYS的渐开线直齿圆柱齿轮有限元分析.煤矿机械,2004(6):43-45
[49]刘道玉.渐开线直齿圆柱齿轮有限元仿真分析.陕西工业学院学报,2004,Vol.20(3):4-6
[50]刘晖.基于参数化的齿轮传动接触有限元分析.大连交通大学硕士论文,2004
[51]F.L.Litvin,G.Sheveleva,D.Vecchiato,I.Gonzalez,A.Fuentes.Modified approach for tooth contact analysis of gear drives and automatic determination of guess values.Computer Methods in Applied Mechanics and Engineering,2000,Vol.181(1-3):71-85
[52]Wang,J.Numerical and Experimental Analysis of Spur Gears in Mesh.Academic Ph.D Thesis Department of Mechanical Engineering,Curtin University of Technology.2003,Perth Australia
[53]王超.齿轮轮齿三维动力接触有限元分析.车辆与动力技术,2004(2):41-45
[54]王勖成,邵敏.有限单元法基本原理与数值方法(第二版)。北京:清华大学出版社,2003
[55]Jerome Bruyere,et al.Statical tolerance analysis of bevel gear by tooth contact analysis and Monte Carlo simulation.Mechanism and Machine Theory,2007,Vol.40(10):1326-1351
[56]O.Vogel,A.Griewank,G.Bar.Direct gear tooth contact analysis for hypoid bevel gears.Computer Methods in Applied Mechanics and Engineering.2002,Vol.191(36):3965-3982
[57]陈霞,夏巨谌等.直齿锥齿轮啮合过程数值模拟.机械设计,2006,Vol.23(4):21-23
[58]金俊松,夏巨谌等.冷精锻修形圆锥齿轮的齿形设计.中国机械工程,2006,Vol.17(19):2038-2041
[59]吴忠鸣,轿车直齿锥齿轮的修形技术研究.武汉:华中科技大学硕士学位论文,2005
[60]崔焕勇,舒其馥,付志刚.直齿锥齿轮精锻模电极齿轮的化铣修形技术.锻压装备与制造技术,2003(4):50-52
[61]Paddy J.Frencha,Pasqualina M.Sarro.Micromachining Technology A Practical Guide to Design,Analysis,and Applications,William Andrew Inc.Published by Elsevier Inc.2006:805-851
[62]吴萌顺.腐蚀工程手册.北京:中国石化出版社,2004
[63]唐余勇.计算直齿锥齿轮近似齿廓方程的等距变换法.哈尔滨工业大学学报.1983(1):20-23
[64]赵洁俊,宋化远.直齿锥齿轮拔模斜度的计算及其应用.锻压机械.1990(6):34-36
[65]左景伊,左禹.腐蚀数据与选材手册.北京:化学工业出版社,2003
[66]胡仁喜.Solidworks中文版标准教程.北京:科学出版社,北京希望电子出版社.2007