圆柱齿超环面行星蜗杆传动的强度计算分析
|
摘要
随着现代工业对机械设备及机械传动系统的要求越来越高,世界传动系统研究的重点逐渐向高速、重载、长寿命、低成本等方面发展,超环面行星蜗杆传动这一新型传动应运而生,成为近年来国内外学者研究的热点。本文主要研究了圆柱齿超环面行星蜗杆传动的强度计算分析,完成了以下工作:
推导出了圆柱齿超环面行星蜗杆传动的接触强度计算公式,通过四因素三水平的正交试验,研究出接触应力大小的主要影响因素及影响规律,并基于以上研究,确定中心距为接触强度设计参数,给出超环面行星蜗杆传动的接触强度计算方法。
推导出圆柱齿超环面行星蜗杆传动的行星轮齿及内齿圈齿的弯曲强度计算公式,分别通过正交试验,研究出其弯曲应力大小的影响因素及影响规律,基于以上研究,确定圆柱滚子的滚针轴承内径及内齿圈螺旋齿厚分别为圆柱滚子及内齿圈的弯曲强度设计参数,通过选定合适的圆柱滚子半径系数来完成该机构的弯曲强度设计。
建立了该减速器各个部件的精确三维实体模型。借助有限元分析软件ABAQUS对此模型进行数值计算,分别得到了中心蜗杆、行星轮、超环面内齿圈的应力云图。通过分析得到中心蜗杆、行星轮、内齿圈接触面上的接触应力和圆柱滚子齿及超环面内齿圈螺旋齿的弯曲应力,分析结果验证了接触强度及弯曲强度计算公式的正确及设计方法的正确性。
With the increasingly demand of machinery and mechanical transmission system of modern industrial, the development of transmission in the world mainly focus on high-speed, the high loading capacity, long life, low cost and other aspects. The toroidal drive, as a new type of drive, emerged and was studied by scholars at home and abroad as a hot spot in recent years. Strength of the cylindrical teeth-type toroidal drive is the main object in my paper which is showed as follows:
The calculation formulas of contact stress are derived. Through four factors and three levels of the orthogonal test, the influencing factors and the changing law of the mechanism pressure angle are obtained. Based on the above studies, the centre distance is identified as the design parameter of contact strength and the design model of the contact strength of toroidal drive are given.
The calculation formulas of bending stress of planetary tooth and stator tooth are derived respectively. Through the orthogonal test, the influencing factors and the changing law of the bending stress are given respectively. Based on the above studies, the inner diameter are identified as the design parameter of bending strength of planetary tooth and the tooth thickness identified as the design parameter of bending strength of the stator. Choosing the appropriate coefficient of cylindrical roller, the design of the bending strength of the toroidal drive is acquired.
In this paper, the solid model of the cylindrical teeth-type of toroidal drive reducer is created in the software of UG. The finite analysis software ABAQUS can provide valuable data of this model. The stresses of the toroidal drive reducer for the sun worm, the planet gear and the stator are can be get with the finite analysis simulation. The analysis results confirmed that the strength of toroidal drive could meet the design requirement. We can verify that contact and bending strength calculation formulas of toroidal drive are reliable by analyzing the contact stress of the contact surface of sun worm, planetary gear and stator and the bending stress of the cylindrical roller and stator tooth. The analysis results verified that contact and bending strength calculation formulas of toroidal drive are appropriate.
推导出了圆柱齿超环面行星蜗杆传动的接触强度计算公式,通过四因素三水平的正交试验,研究出接触应力大小的主要影响因素及影响规律,并基于以上研究,确定中心距为接触强度设计参数,给出超环面行星蜗杆传动的接触强度计算方法。
推导出圆柱齿超环面行星蜗杆传动的行星轮齿及内齿圈齿的弯曲强度计算公式,分别通过正交试验,研究出其弯曲应力大小的影响因素及影响规律,基于以上研究,确定圆柱滚子的滚针轴承内径及内齿圈螺旋齿厚分别为圆柱滚子及内齿圈的弯曲强度设计参数,通过选定合适的圆柱滚子半径系数来完成该机构的弯曲强度设计。
建立了该减速器各个部件的精确三维实体模型。借助有限元分析软件ABAQUS对此模型进行数值计算,分别得到了中心蜗杆、行星轮、超环面内齿圈的应力云图。通过分析得到中心蜗杆、行星轮、内齿圈接触面上的接触应力和圆柱滚子齿及超环面内齿圈螺旋齿的弯曲应力,分析结果验证了接触强度及弯曲强度计算公式的正确及设计方法的正确性。
With the increasingly demand of machinery and mechanical transmission system of modern industrial, the development of transmission in the world mainly focus on high-speed, the high loading capacity, long life, low cost and other aspects. The toroidal drive, as a new type of drive, emerged and was studied by scholars at home and abroad as a hot spot in recent years. Strength of the cylindrical teeth-type toroidal drive is the main object in my paper which is showed as follows:
The calculation formulas of contact stress are derived. Through four factors and three levels of the orthogonal test, the influencing factors and the changing law of the mechanism pressure angle are obtained. Based on the above studies, the centre distance is identified as the design parameter of contact strength and the design model of the contact strength of toroidal drive are given.
The calculation formulas of bending stress of planetary tooth and stator tooth are derived respectively. Through the orthogonal test, the influencing factors and the changing law of the bending stress are given respectively. Based on the above studies, the inner diameter are identified as the design parameter of bending strength of planetary tooth and the tooth thickness identified as the design parameter of bending strength of the stator. Choosing the appropriate coefficient of cylindrical roller, the design of the bending strength of the toroidal drive is acquired.
In this paper, the solid model of the cylindrical teeth-type of toroidal drive reducer is created in the software of UG. The finite analysis software ABAQUS can provide valuable data of this model. The stresses of the toroidal drive reducer for the sun worm, the planet gear and the stator are can be get with the finite analysis simulation. The analysis results confirmed that the strength of toroidal drive could meet the design requirement. We can verify that contact and bending strength calculation formulas of toroidal drive are reliable by analyzing the contact stress of the contact surface of sun worm, planetary gear and stator and the bending stress of the cylindrical roller and stator tooth. The analysis results verified that contact and bending strength calculation formulas of toroidal drive are appropriate.
引文
[1]王丽娟,黄清世,邹雯.齿轮发展研究综述[J].机械研究及应用,2008,21(1):17-18.
[2]周良墉.环面蜗杆修行原理及制造技术[M].长沙:国防科技大学出版社,2005.
[3] Kuehnle M R, Peeken H, Troeder C, and Cerniak S. The Toroidal drive [J]. Mechanical Engineering. 1981(2): 32-39.
[4] Peeken H. The Toroidal Drive—a new concept in mechanical transmission [J], Design Engineering Conference, 1979, 26 (9): 21-28.
[5] Peeken H, Troeder Chr, Ciemiak S, and Kuehnle M R. Development and construction of toroidal[J]. Construction, 1979, 31(11): 421-428.
[6] Peeken H, Troeder C, and Tooten K H. Borechnung und Messung der Lastverteilung im Toroidgetriebe [J]. Konstruction, 1984, 36(3): 81-86.
[7] Peeken H. DrerKoordinaten Messtechnik zur Kontrolle Raumlich Gekrummter Zahnflanken. Werkstatt und Betrieb [J]. 1982, 115(11): 721-723.
[8] Cierniak S. Rollverhalten von Kugeln zwischen geschrankten Rinnen. Konstruktion [J]. 1981, 33(4):155-158.
[9] Cierniak S.Construction optimal Design for Toroidal Drive [J].International Conference on Planetary Drive, 1998.
[10] Tooten K H. Optimierung des Kraftubertragungsverhaltens in Getrieben mitWalzkon-takten [J]. Antriebstechnik, 1985, 24(7):49-55.
[11]聂行健,陈定方.螺环减速机的试制[J].武汉水运工程学报, 1984, 8(1):13-17.
[12]聂行健,陈定方.螺环行星减速机构[P].中华人民共和国, ZL CN85201789U.
[13]聂行健,陈定方.螺环行星减速器的分析和试制[J].机械设计,1988,12(1):66-71.
[14] Lizhong Xu. Study on loads and contact stresses for toroidal drive[J]. Chinese journal of mechanical engineering, 1997, 6(4): 275-278.
[15]许立忠,曲继方.滚柱式超环面蜗杆传动传动弹流润滑研究[J].润滑与密封,1997, 15(6): 36-38.
[16]许立忠,赵永生.滚柱式超环面行星蜗杆传动啮合特性和接触应力研究[J].工程设计, 1998, 1(8): 35-37.
[17]杨育林,许立忠,赵永生.滚柱式超环面行星蜗杆传动接触疲劳强度研究[J].中国机械工程, 1998, 9(6): 19-24.
[18]许立忠,王灵忠,赵永生.超环面行星蜗杆传动啮合特性研究[J].农业机械学报, 1998, 28(4): 139-143.
[19] Xu Lizhong, Huang Zhen. Mesh Theory for Toroidal drive[J]. Journal of Mechanical Design, 1998, (1): 35-37.
[20]许立忠,曲继方.超环面行星蜗杆传动效率研究[J].机械工程学报. 1998, (5): 20-24.
[21]许立忠,黄真.超环面行星蜗杆传动摩擦理论研究[J].中国工程科学(中国工程院院刊),2002, 4(3): 63-67.
[22]许立忠,杨育林,黄真.超环面行星蜗杆传动弹流润滑状态研究[J].机械工程学报. 2002, (9): 114-117.
[23] Lizhong Xu, Zhen Huang. Efficiency for Toroidal drive[C]. Proceedings of the11th World Congress in Mechanism and Machine Science. Tianjin, China. April 1-4, 2004.
[24]蔡毅,许立忠.滚锥齿超环面行星蜗杆传动的优化设计[J].机械设计, 2005, 22(10): 58-60.
[25] Ligang Yao. Xiaojun Xu. Huamin Li. The intelligent CAD system for toroidal drive[C]. Proc. Of 18th Int Conference on Computer in Engineering. China, 1995: 744-746.
[26] Yao Ligang, Xu Xiaojun, Li Huamin. Research on NC manufacturing the stator of toroidal drive system[C]. Proc. Of ICIM95. China, 1995: 881-884.
[27]姚立纲,郑建祥,李尚信等.超环面行星蜗杆传动的啮合分析[J].大庆石油学院学报,1996,20(3):129-132
[28]姚立刚、徐晓俊、李华敏、李尚信。包络法加工超环面行星蜗杆传动定子的研究[J].机械传动, 1996.
[29] Yao Ligang, Xu Xiaojun. Li Huamin. Theory and Practice of Toroidal Drive[C]. Inter. Conf. on Gearing Theory and Practice, 1998, 12.
[30] Yao Ligang, Li Shangxin, Li Huamin. Research on Manufacturing the Worm Tooth Profile of Toroidal Drive by Flyblady[C]. The 1st Inter Conf. on Mechanical Engineering, Shanghai, China. 2000, 11.
[31] Guo wu Wei, Ligang Yao and Zhihuan Wu. Research on Optimum Design and Simulation for Toroidal Drive[C]. In: Tian Huang, Proceedings of the 11th World Congress in Mechanism and Machine Science, April 1-4, 2004, Tianjin, China: 756-759.
[32] Ligang Yao, Jian S. Dai, Guowu Wei and Huamin Li. Geometric Modeling and Meshing Characteristic of the Toroidal Drive[J]. ASME Journal of Mechanical Design.
[33]魏国武超环面行星蜗杆传动的关键技术研究[D].福州:福州大学工学硕士学位论文. 2004:2-3.
[34]姚立纲,魏国武,蔡英杰.超环面行星蜗杆传动的多目标优化设计研究[J].福州大学学报1000-2243(2004)05-0583-05
[35] L Yao,J S Dai and H Li.Mathematical modeling and manufacturing of the internal toroidal tooth profile.Journal of Mechanical Engineering Science,2004,218(9)1043-10517.
[36]姚立纲魏国武.超环面行星蜗杆传动啮合齿廓的几何形状分析[J].现代制造工程2005(2)
[37]魏国武,姚立纲,朱晓林。超环面行星蜗杆传动的运动学和动力学仿真[J].机械设计与研究1006-2343(2005)05-052-04
[38]魏国武,姚立纲,杨蓉,蔡英杰。内超环面齿轮加工的根切问题研究[J].福州大学学报1000-2243(2005)03-0309-04
[39] Ligang Yao, Jian S. Dai, Guowu Wei and Yingjie Cai. Comparative analysis of meshing characteristics with respect to different meshing rollers of the toroidal drive[J]. 2006, 41(7): 863-881.
[40]蔡英杰,姚立纲,魏国武。超环面行星蜗杆传动中超环面蜗杆的数控加工[J].现代制造工程1671—3133(2007)10—0012—03
[41] Guowu Wei, Ligang Yao, Yingjie Cai, Jian S. Dai. Latency errors in the mathematical modelling and meshing chatacterictics of the toroidal drive[J]. Mathematical and Computer Modelling 47(9-10) 2008: 827-854.
[42]杨蓉,姚立纲,魏国武,吕苇白。超环面行星蜗杆传动系统自由振动特性分析[J].厦门理工学院学报号]1008-3804(2009)01-0042—05
[43]张春丽.新型行星蜗杆传动的啮合理论与实验研究[D].哈尔滨:哈尔滨工业大学,1999.
[44]徐晓俊,张春丽,董申.新型超环面传动的内齿轮齿面展成原理.机械传动,1999,9(6):32-34
[45]张春丽,徐晓俊,董申.在数控铣床上加工超环面蜗杆的数值简单计算方法.机械传动, 1999, 23(2): 13-15.
[46]杨传民.螺环传动装置的效率[J].机械设计, 1997, (2): 35-38.
[47]谭援强,杨世平,王亮等.圆柱齿超环面行星蜗杆传动的压力角[J].机械工程学报,2010,46(21):29-34.
[48]王亮.超环面行星蜗杆传动设计制造基础及运动特性研究[D].湘潭:湘潭大学硕士论文, 2009.
[49] Xu Lizhong and Sunhou Fan, Design and torque control of an electromechanical integrating toroidal drive. Mechanism and Machine Theory 41(2), 2006: 230-245.
[50]许立忠,蔡毅.机电集成超环面传动集成原理和磁力分析[J].机械设计与研究. 2006, 22(1): 60-61.
[51] Lizhong Xu, Xin Liu. Mesh analysis and torque fluctuation for electromechanical integrated toroidal drive. Mechanism and Machine Theory 41(6), 2008: 771-789.
[52]许立忠,杨育林,黄忠.超环面行星蜗杆传动研究综述[J],中国工程学报,2000,2(6):84-88.
[53]许立忠.超环面行星蜗杆传动综合设计理论与制造技术研究[D].秦皇岛:燕山大学博士学位论文. 1999.
[54]吴序堂.齿轮啮合原理[M].北京:机械工业出版社. 1982.
[55]傅则绍主编.微分几何与齿轮啮合原理[M].山东:石油大学出版社. 1999.
[56]刘鸿文主编.材料力学[M].北京:高等教育出版社. 2003.
[57]赵腾伦主编. ABAQUS6.6在机械工程中的应用[M].北京:中国水利水电出版社, 2007.
[58]崔忠圻.金属学与热处理[M].北京:机械工业出版社. 1995.
[59]机械设计手册编委会.机械设计手册新版(第3卷)[M].北京:机械工业出版社,2004.
[2]周良墉.环面蜗杆修行原理及制造技术[M].长沙:国防科技大学出版社,2005.
[3] Kuehnle M R, Peeken H, Troeder C, and Cerniak S. The Toroidal drive [J]. Mechanical Engineering. 1981(2): 32-39.
[4] Peeken H. The Toroidal Drive—a new concept in mechanical transmission [J], Design Engineering Conference, 1979, 26 (9): 21-28.
[5] Peeken H, Troeder Chr, Ciemiak S, and Kuehnle M R. Development and construction of toroidal[J]. Construction, 1979, 31(11): 421-428.
[6] Peeken H, Troeder C, and Tooten K H. Borechnung und Messung der Lastverteilung im Toroidgetriebe [J]. Konstruction, 1984, 36(3): 81-86.
[7] Peeken H. DrerKoordinaten Messtechnik zur Kontrolle Raumlich Gekrummter Zahnflanken. Werkstatt und Betrieb [J]. 1982, 115(11): 721-723.
[8] Cierniak S. Rollverhalten von Kugeln zwischen geschrankten Rinnen. Konstruktion [J]. 1981, 33(4):155-158.
[9] Cierniak S.Construction optimal Design for Toroidal Drive [J].International Conference on Planetary Drive, 1998.
[10] Tooten K H. Optimierung des Kraftubertragungsverhaltens in Getrieben mitWalzkon-takten [J]. Antriebstechnik, 1985, 24(7):49-55.
[11]聂行健,陈定方.螺环减速机的试制[J].武汉水运工程学报, 1984, 8(1):13-17.
[12]聂行健,陈定方.螺环行星减速机构[P].中华人民共和国, ZL CN85201789U.
[13]聂行健,陈定方.螺环行星减速器的分析和试制[J].机械设计,1988,12(1):66-71.
[14] Lizhong Xu. Study on loads and contact stresses for toroidal drive[J]. Chinese journal of mechanical engineering, 1997, 6(4): 275-278.
[15]许立忠,曲继方.滚柱式超环面蜗杆传动传动弹流润滑研究[J].润滑与密封,1997, 15(6): 36-38.
[16]许立忠,赵永生.滚柱式超环面行星蜗杆传动啮合特性和接触应力研究[J].工程设计, 1998, 1(8): 35-37.
[17]杨育林,许立忠,赵永生.滚柱式超环面行星蜗杆传动接触疲劳强度研究[J].中国机械工程, 1998, 9(6): 19-24.
[18]许立忠,王灵忠,赵永生.超环面行星蜗杆传动啮合特性研究[J].农业机械学报, 1998, 28(4): 139-143.
[19] Xu Lizhong, Huang Zhen. Mesh Theory for Toroidal drive[J]. Journal of Mechanical Design, 1998, (1): 35-37.
[20]许立忠,曲继方.超环面行星蜗杆传动效率研究[J].机械工程学报. 1998, (5): 20-24.
[21]许立忠,黄真.超环面行星蜗杆传动摩擦理论研究[J].中国工程科学(中国工程院院刊),2002, 4(3): 63-67.
[22]许立忠,杨育林,黄真.超环面行星蜗杆传动弹流润滑状态研究[J].机械工程学报. 2002, (9): 114-117.
[23] Lizhong Xu, Zhen Huang. Efficiency for Toroidal drive[C]. Proceedings of the11th World Congress in Mechanism and Machine Science. Tianjin, China. April 1-4, 2004.
[24]蔡毅,许立忠.滚锥齿超环面行星蜗杆传动的优化设计[J].机械设计, 2005, 22(10): 58-60.
[25] Ligang Yao. Xiaojun Xu. Huamin Li. The intelligent CAD system for toroidal drive[C]. Proc. Of 18th Int Conference on Computer in Engineering. China, 1995: 744-746.
[26] Yao Ligang, Xu Xiaojun, Li Huamin. Research on NC manufacturing the stator of toroidal drive system[C]. Proc. Of ICIM95. China, 1995: 881-884.
[27]姚立纲,郑建祥,李尚信等.超环面行星蜗杆传动的啮合分析[J].大庆石油学院学报,1996,20(3):129-132
[28]姚立刚、徐晓俊、李华敏、李尚信。包络法加工超环面行星蜗杆传动定子的研究[J].机械传动, 1996.
[29] Yao Ligang, Xu Xiaojun. Li Huamin. Theory and Practice of Toroidal Drive[C]. Inter. Conf. on Gearing Theory and Practice, 1998, 12.
[30] Yao Ligang, Li Shangxin, Li Huamin. Research on Manufacturing the Worm Tooth Profile of Toroidal Drive by Flyblady[C]. The 1st Inter Conf. on Mechanical Engineering, Shanghai, China. 2000, 11.
[31] Guo wu Wei, Ligang Yao and Zhihuan Wu. Research on Optimum Design and Simulation for Toroidal Drive[C]. In: Tian Huang, Proceedings of the 11th World Congress in Mechanism and Machine Science, April 1-4, 2004, Tianjin, China: 756-759.
[32] Ligang Yao, Jian S. Dai, Guowu Wei and Huamin Li. Geometric Modeling and Meshing Characteristic of the Toroidal Drive[J]. ASME Journal of Mechanical Design.
[33]魏国武超环面行星蜗杆传动的关键技术研究[D].福州:福州大学工学硕士学位论文. 2004:2-3.
[34]姚立纲,魏国武,蔡英杰.超环面行星蜗杆传动的多目标优化设计研究[J].福州大学学报1000-2243(2004)05-0583-05
[35] L Yao,J S Dai and H Li.Mathematical modeling and manufacturing of the internal toroidal tooth profile.Journal of Mechanical Engineering Science,2004,218(9)1043-10517.
[36]姚立纲魏国武.超环面行星蜗杆传动啮合齿廓的几何形状分析[J].现代制造工程2005(2)
[37]魏国武,姚立纲,朱晓林。超环面行星蜗杆传动的运动学和动力学仿真[J].机械设计与研究1006-2343(2005)05-052-04
[38]魏国武,姚立纲,杨蓉,蔡英杰。内超环面齿轮加工的根切问题研究[J].福州大学学报1000-2243(2005)03-0309-04
[39] Ligang Yao, Jian S. Dai, Guowu Wei and Yingjie Cai. Comparative analysis of meshing characteristics with respect to different meshing rollers of the toroidal drive[J]. 2006, 41(7): 863-881.
[40]蔡英杰,姚立纲,魏国武。超环面行星蜗杆传动中超环面蜗杆的数控加工[J].现代制造工程1671—3133(2007)10—0012—03
[41] Guowu Wei, Ligang Yao, Yingjie Cai, Jian S. Dai. Latency errors in the mathematical modelling and meshing chatacterictics of the toroidal drive[J]. Mathematical and Computer Modelling 47(9-10) 2008: 827-854.
[42]杨蓉,姚立纲,魏国武,吕苇白。超环面行星蜗杆传动系统自由振动特性分析[J].厦门理工学院学报号]1008-3804(2009)01-0042—05
[43]张春丽.新型行星蜗杆传动的啮合理论与实验研究[D].哈尔滨:哈尔滨工业大学,1999.
[44]徐晓俊,张春丽,董申.新型超环面传动的内齿轮齿面展成原理.机械传动,1999,9(6):32-34
[45]张春丽,徐晓俊,董申.在数控铣床上加工超环面蜗杆的数值简单计算方法.机械传动, 1999, 23(2): 13-15.
[46]杨传民.螺环传动装置的效率[J].机械设计, 1997, (2): 35-38.
[47]谭援强,杨世平,王亮等.圆柱齿超环面行星蜗杆传动的压力角[J].机械工程学报,2010,46(21):29-34.
[48]王亮.超环面行星蜗杆传动设计制造基础及运动特性研究[D].湘潭:湘潭大学硕士论文, 2009.
[49] Xu Lizhong and Sunhou Fan, Design and torque control of an electromechanical integrating toroidal drive. Mechanism and Machine Theory 41(2), 2006: 230-245.
[50]许立忠,蔡毅.机电集成超环面传动集成原理和磁力分析[J].机械设计与研究. 2006, 22(1): 60-61.
[51] Lizhong Xu, Xin Liu. Mesh analysis and torque fluctuation for electromechanical integrated toroidal drive. Mechanism and Machine Theory 41(6), 2008: 771-789.
[52]许立忠,杨育林,黄忠.超环面行星蜗杆传动研究综述[J],中国工程学报,2000,2(6):84-88.
[53]许立忠.超环面行星蜗杆传动综合设计理论与制造技术研究[D].秦皇岛:燕山大学博士学位论文. 1999.
[54]吴序堂.齿轮啮合原理[M].北京:机械工业出版社. 1982.
[55]傅则绍主编.微分几何与齿轮啮合原理[M].山东:石油大学出版社. 1999.
[56]刘鸿文主编.材料力学[M].北京:高等教育出版社. 2003.
[57]赵腾伦主编. ABAQUS6.6在机械工程中的应用[M].北京:中国水利水电出版社, 2007.
[58]崔忠圻.金属学与热处理[M].北京:机械工业出版社. 1995.
[59]机械设计手册编委会.机械设计手册新版(第3卷)[M].北京:机械工业出版社,2004.