双圆弧弧齿锥齿轮的参数化建模及力学特性模拟分析
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摘要
双圆弧弧齿锥齿轮是将圆弧齿廓点啮合传动形式运用于锥齿轮传动的一种新型的齿轮传动方式，其基本齿廓是分阶式双圆弧齿形，现有的分析表明，它具有承载能力高、使用寿命长、加工简单等优点，是一种具有广阔应用前景的新型弧齿锥齿轮传动方式。
双圆弧弧齿锥齿轮采用等高齿，在轮齿任意法截面内具有完全相同的齿形，由于采用平面齿轮原理加工，能形成点接触共轭齿面，符合齿廓啮合的基本定律。短齿形的采用，按内端法面模数进行设计，保证了内端轮齿具有足够高的弯曲强度。FSH型分阶式双圆弧齿形(短齿形)，其轮齿从内端到外端的齿形分布，是由短齿型向超短齿型逐步过渡，如果合理选用重合度，适当利用轮齿外端粗厚部分，则锥齿轮的承载能力及使用寿命可以得到更大的提高。
本文阐述了弧齿锥齿轮副点啮合共轭齿面的形成原理，同时还论述了双圆弧弧齿锥齿轮基本啮合原理，推导了弧齿锥齿轮的齿面方程；并按照等强度设计的原则选用FSH型分阶式双圆弧齿形(短齿形)进行研究。由于齿面形状比较复杂，很难通过基准齿形的空间旋转、平移等变化形成准确的齿面，所以要建立一个准确可靠的双圆弧弧齿锥齿轮的有
Double circular arc spiral bevel gears is a new gear transmission mode by using arc gear teeth dot mesh transmission method as spiral bevel gears transmission method. Its basic gear tooth profile is double circular arc spiral bevel gear tooth profile. Analysis proves that this tooth profile has much advantage, such as its high bearing loads and its long use life-span and its easy manufacture process.
Double circular arc spiral bevel gears apply equal-high gear tooth, and its gear profile is equal in any vertical plane, this gear profile can form dot-contact conjugate gear surface for adopting plane gear theory to make gear, and this gear profile abide by the gear profile meshing elementary rule, the apply of short-tooth and the design of according to small-section vertical plane modulus assure that small-section gear surface own very high bend strength. To FSH step double circular arc spiral bevel gears tooth (short-tooth ) , its gear teeth of distributing from small-section to big-section
双圆弧弧齿锥齿轮采用等高齿，在轮齿任意法截面内具有完全相同的齿形，由于采用平面齿轮原理加工，能形成点接触共轭齿面，符合齿廓啮合的基本定律。短齿形的采用，按内端法面模数进行设计，保证了内端轮齿具有足够高的弯曲强度。FSH型分阶式双圆弧齿形(短齿形)，其轮齿从内端到外端的齿形分布，是由短齿型向超短齿型逐步过渡，如果合理选用重合度，适当利用轮齿外端粗厚部分，则锥齿轮的承载能力及使用寿命可以得到更大的提高。
本文阐述了弧齿锥齿轮副点啮合共轭齿面的形成原理，同时还论述了双圆弧弧齿锥齿轮基本啮合原理，推导了弧齿锥齿轮的齿面方程；并按照等强度设计的原则选用FSH型分阶式双圆弧齿形(短齿形)进行研究。由于齿面形状比较复杂，很难通过基准齿形的空间旋转、平移等变化形成准确的齿面，所以要建立一个准确可靠的双圆弧弧齿锥齿轮的有
Double circular arc spiral bevel gears is a new gear transmission mode by using arc gear teeth dot mesh transmission method as spiral bevel gears transmission method. Its basic gear tooth profile is double circular arc spiral bevel gear tooth profile. Analysis proves that this tooth profile has much advantage, such as its high bearing loads and its long use life-span and its easy manufacture process.
Double circular arc spiral bevel gears apply equal-high gear tooth, and its gear profile is equal in any vertical plane, this gear profile can form dot-contact conjugate gear surface for adopting plane gear theory to make gear, and this gear profile abide by the gear profile meshing elementary rule, the apply of short-tooth and the design of according to small-section vertical plane modulus assure that small-section gear surface own very high bend strength. To FSH step double circular arc spiral bevel gears tooth (short-tooth ) , its gear teeth of distributing from small-section to big-section
引文
[1] 王秀业．圆弧齿轮在我国的发展和应用．山东建材，2002(1)：38-39
[2] 唐定国，陈国民．齿轮传动技术的现状与展望．机械工程学报，1993(5)：35-42
[3] 王声堂，杨歧华，蒋荣孝．21世纪齿轮行业发展战略的建议．机械传动，1992(5)：46-49
[4] 陈荣增．圆弧齿圆柱齿轮传动．北京：高等教育出版社，1995．2
[5] 邵家辉．圆弧齿轮(第4版)．北京：机械工业出版社，1994．12
[6] 陶柯，杨林，金晶立．弧齿锥齿轮啮合过程的载荷分配及应力计算方法．沈阳工业大学学报，1995，17(1)：56-58
[7] 郑夕健，鄂中凯，邢俊干．弧齿锥齿轮齿根应力的影响因素分析．沈阳建筑工程学院学报，1994，13(1)：5-7
[8] 闰颂，吴继泽．接触区等对弧齿锥齿轮弯曲强度的影响．北京航空航天大学学报，1996，22(1)：99-103
[9] 张秀亲．双圆弧弧齿锥齿轮齿根应力沿齿长分布的研究．工程设计学报，2002(9)：215—218
[10] Arai, Norishisa, Kawamoto. Shigeru; Yoneda, Haruaki. Study of spiral bevel gear(Analysis of tooth root stress by three-dimensinal finite element method).Nippon Kikai Gakkai Ronbunshu, C Hen/Transactions of the Japan Society of Mechenical Engineers, 1991,57(538):2114-2117.
[11] Fong, Z.H., Tsay, Chung-Biau, Mathematical Model for the tooth geometry of circular-cut spiral bevel gears, Journal of Mechanisms, Transmissions, and Automation in Design, 1991, 113(2): 174-181
[12] Bibel, George., Handschuh, Robert. Meshing of a spiral bevel gear set with 3D finite element analysis. American Society of Mechanical Engineers, 1996, 88: 703-708[13]Oda, Satoshi, Koide, Takao, etc., Tooth deflection and bendings moment of WN gear tooth due to concentrated load (Haseg symMarC gear),JSME International Journal .Series C: Dynamics .Control, Robotics, Design and Menufacturing, 1993, 36(3):386-392.
[14]Gu, Shoufeng, Lian, Xiaoming, Yan, Lei. Automatic generation and densification of 3-D finite element mesh for helical gear tooth]. Qinghua Daxue Xuebao/Journal of Tsinighua University, 1996,36(8):77-82.
[15]ArgyrisJ., LitvinF. L, Computerized integrated approach for design and stress analydid of spiral bevel gears. Computer Methods in Applied Mechanics and Engineering, 2002, 191 (11-12):1057-1095
[16]Litvin F. L., LU, J. Computerized design and generation of double circular-arc helical gears with low transmission errors .Computer Methods in Applied Mechanics and Engineering, 1995,v 127,n1-4,Nov. p57-86
[17] Simon, VilmosV., Optimal tooth modification in hypoid gears, Proceedings of the ASME Design Engineering Technical Conference , 2003,v 4 B, p 875-884
[18] Kalashnikov,A.S., Kalashnikov, S. N., Technological processes of gear manufacture from blanks with pre-formed teeth (practice at the Likhachev Automobile works ), Soviet Engineering Research , 1990, v 10, n 11. p 38-42
[19]Shunmugam, m. s., Rao, B. S., Jayaprakash, V., Establishing gear tooth surface geometry and normal deviation part 2 - bevel gears , Mechanism & Machine Theory, v 33, n 5, Jul, 1998, p525-534
[20] Ping-Hsun Lin and Hsiang Hsi Lin The University of Memphis, Memphis, Tennessee, Fred B. Oswald and Dennis P. Townsend Lewis Research Center, Cleveland, Ohio. "Using Dynamic Analysis for Compact Gear Design" NASA/TM—1998-207419 ARL-TR-1818 DETC98/PTG - 5785 . September 1998
[21] Faydor L. Litvin University of Illinois at Chicago, Chicago, IllinoisAlfonso Fuentes Polytehnic University of Cartagena, Cartagena, Spain. gnacio Gonzalez-Perez, Luca Carnevali, and Kazumasa Kawasaki, University of Illinois at Chicago, Chicago, Illinois "Modified Involute Helical Gears:Computerized Design, Simulation of Meshing, and Stress Analysis" NASA/CR—2003-212229, ARL-CR-514 June 2003.
[22] Haber R, Shaphard M S, Abel JF et al., A general two-dimensional graphical finite element preprocess utilizing discrete transfinite mapping Int J Num Meth Eng, 1981,17(7):1015～1044.
[23] Durocher L L, Gasper A.A, versastile two-dimensionel mesh generator with automatic band width reduction, compu & Struct, 1979,10(4): 561～575
[24] 张晋西，郭学琴．齿轮三维参数化建模与加工运动仿真．机械设计，2002，3，NO3
[25] 王铁，邵家辉，陈永康．超短齿硬齿面双圆弧齿轮传动的强度计算和应用．机械传动，1993(3)：72-81
[26] 张秀亲．双圆弧弧齿锥齿轮齿面方程的推导．太原工业大学学报，1996(12)：78—81．
[27] 张秀亲．双圆弧弧齿锥齿轮齿根应力沿齿长分布的研究．工程设计学报，2002(9)：215—218．
[28] 张秀亲．双圆弧弧齿锥齿轮的有限元分析．煤矿机械，1997(1)：19—20
[29] 武宝林．双圆弧弧齿锥齿轮的切齿啮合分析．机械科学与技术，2002(9)：726—729
[30] 姚俊红．双圆弧弧齿锥齿轮的三维建模．德州学院学报，2002(12)：97—99．
[31] 姚俊红．双圆弧弧齿锥齿轮的实体建模方法及加工过程模拟．机械设计，2003(6)：23—24．
[32] 陆惟信．圆锥齿轮与双曲面齿轮传动．北京：人民交通出版社1980年12月
[33] 姚俊红．双圆弧弧齿锥齿轮传动的三维建模及切齿啮合分析．天津工业大学硕士学位论文，2003
[34] 谭小红．双圆弧弧齿轮维建模与仿真．太原理工大学硕士学位论文，2004[35] 许贤泽．齿轮弯曲强度的有限元分析法．武测科技，1996，4：P25～P28
[36] 杨生华．齿轮接触有限元分析．计算力学学报，2003(2)：P329～P332
[37] 朱景梓，邵家辉，李进宝．双圆弧弧齿锥齿轮啮合原理及设计制造．太原工学院内部发行，1982
[38] 李进宝．双圆弧弧齿锥齿轮设计与分析．1987
[39] 王裕清，武良臣．弧齿锥齿轮接触区理论与切削过程仿真．北京：煤炭工业出版社，2004
[40] 邱宣怀，机械设计(第四版)．北京：高等教育出版社，1997，7
[41] 孙江宏．Pro／ENGINEER结构分析与运动仿真．北京：中国铁道出版社，2004
[42] 张亚欧．ANSYS7.0有限元分析实用教程．北京：清华大学出版社，2004，7
[2] 唐定国，陈国民．齿轮传动技术的现状与展望．机械工程学报，1993(5)：35-42
[3] 王声堂，杨歧华，蒋荣孝．21世纪齿轮行业发展战略的建议．机械传动，1992(5)：46-49
[4] 陈荣增．圆弧齿圆柱齿轮传动．北京：高等教育出版社，1995．2
[5] 邵家辉．圆弧齿轮(第4版)．北京：机械工业出版社，1994．12
[6] 陶柯，杨林，金晶立．弧齿锥齿轮啮合过程的载荷分配及应力计算方法．沈阳工业大学学报，1995，17(1)：56-58
[7] 郑夕健，鄂中凯，邢俊干．弧齿锥齿轮齿根应力的影响因素分析．沈阳建筑工程学院学报，1994，13(1)：5-7
[8] 闰颂，吴继泽．接触区等对弧齿锥齿轮弯曲强度的影响．北京航空航天大学学报，1996，22(1)：99-103
[9] 张秀亲．双圆弧弧齿锥齿轮齿根应力沿齿长分布的研究．工程设计学报，2002(9)：215—218
[10] Arai, Norishisa, Kawamoto. Shigeru; Yoneda, Haruaki. Study of spiral bevel gear(Analysis of tooth root stress by three-dimensinal finite element method).Nippon Kikai Gakkai Ronbunshu, C Hen/Transactions of the Japan Society of Mechenical Engineers, 1991,57(538):2114-2117.
[11] Fong, Z.H., Tsay, Chung-Biau, Mathematical Model for the tooth geometry of circular-cut spiral bevel gears, Journal of Mechanisms, Transmissions, and Automation in Design, 1991, 113(2): 174-181
[12] Bibel, George., Handschuh, Robert. Meshing of a spiral bevel gear set with 3D finite element analysis. American Society of Mechanical Engineers, 1996, 88: 703-708[13]Oda, Satoshi, Koide, Takao, etc., Tooth deflection and bendings moment of WN gear tooth due to concentrated load (Haseg symMarC gear),JSME International Journal .Series C: Dynamics .Control, Robotics, Design and Menufacturing, 1993, 36(3):386-392.
[14]Gu, Shoufeng, Lian, Xiaoming, Yan, Lei. Automatic generation and densification of 3-D finite element mesh for helical gear tooth]. Qinghua Daxue Xuebao/Journal of Tsinighua University, 1996,36(8):77-82.
[15]ArgyrisJ., LitvinF. L, Computerized integrated approach for design and stress analydid of spiral bevel gears. Computer Methods in Applied Mechanics and Engineering, 2002, 191 (11-12):1057-1095
[16]Litvin F. L., LU, J. Computerized design and generation of double circular-arc helical gears with low transmission errors .Computer Methods in Applied Mechanics and Engineering, 1995,v 127,n1-4,Nov. p57-86
[17] Simon, VilmosV., Optimal tooth modification in hypoid gears, Proceedings of the ASME Design Engineering Technical Conference , 2003,v 4 B, p 875-884
[18] Kalashnikov,A.S., Kalashnikov, S. N., Technological processes of gear manufacture from blanks with pre-formed teeth (practice at the Likhachev Automobile works ), Soviet Engineering Research , 1990, v 10, n 11. p 38-42
[19]Shunmugam, m. s., Rao, B. S., Jayaprakash, V., Establishing gear tooth surface geometry and normal deviation part 2 - bevel gears , Mechanism & Machine Theory, v 33, n 5, Jul, 1998, p525-534
[20] Ping-Hsun Lin and Hsiang Hsi Lin The University of Memphis, Memphis, Tennessee, Fred B. Oswald and Dennis P. Townsend Lewis Research Center, Cleveland, Ohio. "Using Dynamic Analysis for Compact Gear Design" NASA/TM—1998-207419 ARL-TR-1818 DETC98/PTG - 5785 . September 1998
[21] Faydor L. Litvin University of Illinois at Chicago, Chicago, IllinoisAlfonso Fuentes Polytehnic University of Cartagena, Cartagena, Spain. gnacio Gonzalez-Perez, Luca Carnevali, and Kazumasa Kawasaki, University of Illinois at Chicago, Chicago, Illinois "Modified Involute Helical Gears:Computerized Design, Simulation of Meshing, and Stress Analysis" NASA/CR—2003-212229, ARL-CR-514 June 2003.
[22] Haber R, Shaphard M S, Abel JF et al., A general two-dimensional graphical finite element preprocess utilizing discrete transfinite mapping Int J Num Meth Eng, 1981,17(7):1015～1044.
[23] Durocher L L, Gasper A.A, versastile two-dimensionel mesh generator with automatic band width reduction, compu & Struct, 1979,10(4): 561～575
[24] 张晋西，郭学琴．齿轮三维参数化建模与加工运动仿真．机械设计，2002，3，NO3
[25] 王铁，邵家辉，陈永康．超短齿硬齿面双圆弧齿轮传动的强度计算和应用．机械传动，1993(3)：72-81
[26] 张秀亲．双圆弧弧齿锥齿轮齿面方程的推导．太原工业大学学报，1996(12)：78—81．
[27] 张秀亲．双圆弧弧齿锥齿轮齿根应力沿齿长分布的研究．工程设计学报，2002(9)：215—218．
[28] 张秀亲．双圆弧弧齿锥齿轮的有限元分析．煤矿机械，1997(1)：19—20
[29] 武宝林．双圆弧弧齿锥齿轮的切齿啮合分析．机械科学与技术，2002(9)：726—729
[30] 姚俊红．双圆弧弧齿锥齿轮的三维建模．德州学院学报，2002(12)：97—99．
[31] 姚俊红．双圆弧弧齿锥齿轮的实体建模方法及加工过程模拟．机械设计，2003(6)：23—24．
[32] 陆惟信．圆锥齿轮与双曲面齿轮传动．北京：人民交通出版社1980年12月
[33] 姚俊红．双圆弧弧齿锥齿轮传动的三维建模及切齿啮合分析．天津工业大学硕士学位论文，2003
[34] 谭小红．双圆弧弧齿轮维建模与仿真．太原理工大学硕士学位论文，2004[35] 许贤泽．齿轮弯曲强度的有限元分析法．武测科技，1996，4：P25～P28
[36] 杨生华．齿轮接触有限元分析．计算力学学报，2003(2)：P329～P332
[37] 朱景梓，邵家辉，李进宝．双圆弧弧齿锥齿轮啮合原理及设计制造．太原工学院内部发行，1982
[38] 李进宝．双圆弧弧齿锥齿轮设计与分析．1987
[39] 王裕清，武良臣．弧齿锥齿轮接触区理论与切削过程仿真．北京：煤炭工业出版社，2004
[40] 邱宣怀，机械设计(第四版)．北京：高等教育出版社，1997，7
[41] 孙江宏．Pro／ENGINEER结构分析与运动仿真．北京：中国铁道出版社，2004
[42] 张亚欧．ANSYS7.0有限元分析实用教程．北京：清华大学出版社，2004，7