圆弧面包络环面蜗杆传动研究
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摘要
由轴截面廓线为圆弧的砂轮磨削加工所得的环面蜗杆和以此蜗杆包络加工出的蜗轮构成的一种新型的环面蜗杆传动,简称为圆弧面包络环面蜗杆传动。研究圆弧面包络环面蜗杆传动旨在开发研制传动效率高、承载能力大的新型蜗杆减速装置。论文的主要研究内容如下:
根据微分几何知识和齿轮啮合理论,用运动学法推导出圆弧面砂轮与被磨削环面蜗杆的啮合函数、啮合方程,以及砂轮齿面接触线方程和蜗杆齿面方程。
根据微分几何知识和齿轮啮合理论,由蜗杆齿面方程推导出蜗杆与蜗轮共轭齿面的啮合函数和啮合方程以及蜗轮齿面瞬时接触线方程;给出了圆弧面包络环面蜗杆传动的一、二类界限函数以及齿面接触参数等。
依据蜗杆传动主要设计参数对蜗轮齿面瞬时接触线分布形状的影响,分析了圆弧面包络环面蜗杆传动的啮合性能及其变化;围绕提高承载能力、改善润滑状况的目标,研究了实现良好啮合条件下的蜗杆传动的主要设计参数,并相应地给出了理想啮合条件下各主要设计参数的优选方法;对圆弧面包络环面蜗杆传动的接触线分布状况与圆弧圆柱蜗杆传动做了比较。
Hourglass enveloping worm drive with circular helicoid generatrix, is a novel hourglass worm drive, which is formed by a new hourglass worm and its enveloping worm gear, and the new hourglass worm is grinded by the wheel with a section profile of circular. The aim of study on this drive is developing a new worm reducer with high efficiency and heavy load. The contents are as follows:
Based on the theories of differential geometry and gear meshing, meshing function and meshing equation between grinding wheel with circular and the grinded worm are established by kinematics method. Grinding wheel tooth surface contact line equation and worm tooth surface equations are also deduced.
On the basis of the theories of differential geometry and gear meshing, meshing function, meshing equation and worm wheel tooth surface contact line equation between the worm wheel and the worm are established by the worm tooth surface equations. The first kind of boundary function, the second kind of boundary function and the tooth face contact parameters are provided.
According to the influence on distributed shape of worm wheel tooth surface contact line by the main design parameters of worm drive, the meshing performance of hourglass enveloping worm drive with circular helicoid generatrix and the transformation of it are carried out. Then, each transmission parameter about achieving the good meshing condition is given to sharpen the bearing capacity and to improve lubrication condition, and each optimal method of main design variable is given under the ideal meshing condition. Finally, the distributed condition of contact line between the hollow flank worm drive and the hourglass enveloping worm drive with circular helicoid generatrix is compared.
根据微分几何知识和齿轮啮合理论,用运动学法推导出圆弧面砂轮与被磨削环面蜗杆的啮合函数、啮合方程,以及砂轮齿面接触线方程和蜗杆齿面方程。
根据微分几何知识和齿轮啮合理论,由蜗杆齿面方程推导出蜗杆与蜗轮共轭齿面的啮合函数和啮合方程以及蜗轮齿面瞬时接触线方程;给出了圆弧面包络环面蜗杆传动的一、二类界限函数以及齿面接触参数等。
依据蜗杆传动主要设计参数对蜗轮齿面瞬时接触线分布形状的影响,分析了圆弧面包络环面蜗杆传动的啮合性能及其变化;围绕提高承载能力、改善润滑状况的目标,研究了实现良好啮合条件下的蜗杆传动的主要设计参数,并相应地给出了理想啮合条件下各主要设计参数的优选方法;对圆弧面包络环面蜗杆传动的接触线分布状况与圆弧圆柱蜗杆传动做了比较。
Hourglass enveloping worm drive with circular helicoid generatrix, is a novel hourglass worm drive, which is formed by a new hourglass worm and its enveloping worm gear, and the new hourglass worm is grinded by the wheel with a section profile of circular. The aim of study on this drive is developing a new worm reducer with high efficiency and heavy load. The contents are as follows:
Based on the theories of differential geometry and gear meshing, meshing function and meshing equation between grinding wheel with circular and the grinded worm are established by kinematics method. Grinding wheel tooth surface contact line equation and worm tooth surface equations are also deduced.
On the basis of the theories of differential geometry and gear meshing, meshing function, meshing equation and worm wheel tooth surface contact line equation between the worm wheel and the worm are established by the worm tooth surface equations. The first kind of boundary function, the second kind of boundary function and the tooth face contact parameters are provided.
According to the influence on distributed shape of worm wheel tooth surface contact line by the main design parameters of worm drive, the meshing performance of hourglass enveloping worm drive with circular helicoid generatrix and the transformation of it are carried out. Then, each transmission parameter about achieving the good meshing condition is given to sharpen the bearing capacity and to improve lubrication condition, and each optimal method of main design variable is given under the ideal meshing condition. Finally, the distributed condition of contact line between the hollow flank worm drive and the hourglass enveloping worm drive with circular helicoid generatrix is compared.
引文
[1]齿轮手册编委会,齿轮手册(上、下册),北京:机械工业出版社,2001
[2]成大先,机械设计手册-机械传动(单行本),北京:化学工业出版社,2000
[3]王树人,圆弧圆柱蜗杆传动,天津:天津大学出版社,1991
[4]王树人,齿轮啮合理论简明教程,天津:天津大学出版社,2005
[5]段路茜,TI蜗杆传动啮合理论研究及优化设计[博士学位论文],天津:天津大学,2004
[6]王树人,刘平娟,圆柱蜗杆传动啮合原理.天津:天津科技出版社,1982
[7]詹东安,交错轴渐开线型共轭副的啮合理论及应用研究[博士学位论文],西安:西安交通大学,1998
[8]刘洪斌,基于渐开线齿轮形修磨轮包络蜗杆传动理论研究及精加工TI蜗杆的新方法[博士学位论文],天津:天津大学,2001
[9]傅则绍等,新型蜗杆传动,西安:陕西科学技术出版社,1990
[10]殷李森,圆弧螺旋面包络环面蜗杆传动,机械传动,2001,34(2):34~36
[11]韩红臣,近似的TI蜗杆传动研究[硕士学位论文],天津:天津大学2006
[12]郑惠江,TI蜗杆加工关键技术研究[硕士学位论文],天津:天津大学2004
[13]谭建平,张光辉,球面二次包络弧面蜗杆传动的理论研究,重庆大学学报,1988,11(1):42~51
[14]沈蕴方,李寅年,徐月琴,“圆环面双包络环面蜗杆传动”的理论研究与参数分析,全国齿轮传动学术年会论文集,1983
[15]李尚信,许冯平,蒋伯英,平面二次包络环面蜗杆传动的接触分析,大庆石油学院学报,1992,16(1):67~7
[16]卢华武,硬齿面副TI传动的加工与试验研究[硕士学位论文],天津:天津大学2007
[17]肖延萍,TI传动的参数化设计及存在装配误差时齿面接触分析[硕士学位论文],天津:天津大学2004
[18] An Zhaoda, Jia Baoxian. An Investigation of Concave-Convex Profile of A Cylindrical Worm Drive. Proceedings of International Conference on Gearing,Zhengzhou ,1988
[19] Sakai T. , Maki M. . An investigation on secondary action on skew gears..ASME,The Mechanisms Conference and International Symposium on Gearing and Transmission,1972,vol.1
[20]文庆明,周良墉,直廓环面蜗杆几何参数和修形的优化设计,新技术新工艺,2000,(12):16~18
[21]沈蕴方,容尔谦等,空间啮合原理及SG-71型蜗轮副,北京:冶金工业出版社,1983
[22]毛梦云,路懿,滚珠环面蜗杆传动的加工和啮合分析,机械工程学报,1989,25(2):42~ 49
[23]张光挥,王进戈,杨念增,滚锥包络环面蜗轮副的研制与实验,重庆大学学报,1992,15(5):8~11
[24]王进戈,张光挥,滚锥包络环面蜗杆传动的理论研究与参数优化,重庆大学学报,1992,15(2):58~64
[25]朱景梓,段德荣,渐开线二次包络弧面蜗杆传动的研究,全国齿轮传动学术年会论文集,1983
[26]秦大同,颜佳,张光辉,平面包络环面蜗杆基于坐标测量的高精度制造方法,机械工程学报,1997, 33(1):59~65
[27]张焕,胡晓波,曹文思,环面蜗杆齿面啮合线的计算机仿真技术,机械设计与研究,2002,18(6):30~32
[28]谭昕,张仲甫,平面二次包络环面蜗杆副的数字制造,中国机械工程,2003,14(8):649~652
[29]张希康,IT型渐开面蜗轮传动螺旋角的合理选择,机械工程学报,1982,18(3):86~92
[30]张希康,TI蜗杆传动瞬时接触线分析及其应用,齿轮,1987, 11(5):1~5
[31]张希康,TI蜗杆传动瞬时接触线分析及其应用(二),齿轮,1987, 11(6):1~5
[32] S. Wang, D. Zhan, etc. Tooth contact analysis of hourglass involute worm mating with involute helical gear,Mechanism and Machine Theory,2002,37(7):685~691
[33]詹东安,吴序堂.TI蜗杆与渐开线斜齿轮传动的接触分析,重型机械,1997;(5): 5~8
[34]詹东安,吴序堂等,双包络TI蜗杆传动的二次包络分析,重型机械,1998;(5):25~28
[35]秦大同,张光辉,锥面二次包络环面蜗杆传动齿面接触及运动精度的研究,重庆大学学报,1993,16(1):45~51
[36] V. Simon.Stress Analysis in Double Enveloping Worm Gears by Finite Element Method,Transactions of the ASME Journal of Mechanical Design,1993,115:179~185
[37]吴大任,齿轮啮合原理,北京:科学出版社,1985
[38]毕庆贞,TI蜗杆的三维造型和精确磨削加工方法[硕士学位论文],天津:天津大学,2003
[39]孙桓,陈作模,机械原理,北京:高等教育出版社,1996
[40] Daizhong Su,Datong Qin.Integration of numerical analysis, virtual simulation and finite element analysis for the optimum design of worm gearing.Journal of Materials Processing Technology,2003,138:429~435
[41] D.Su.A new approach combining numerical analysis and three-dimensional simulation for design of worm gearing with preferable localized tooth contact, Proceedings of 1998 ASME Design Engineering Technical Mechanisms conference, 1998
[42] D.Su,F. Yang and C. R.Gentle.Analysis of tooth stresses, mesh stiffness and loaded transmission errors of involute worm gears.International Journal of Gearing and Transmissions,2000,(3):36~44
[43]张志涌,精通Matlab 6.5版教程,北京:北京航空航天大学出版社,2003
[44]崔兴元,ZC1蜗杆传动可控修形的接触区特性分析及计算机代数系统在ZC1蜗杆传动中的研究[硕士学位论文],天津:天津大学,1990
[45]郜庆路,球面二次包络环面蜗杆传动的啮合原理与啮合性能[硕士学位论文],焦作:焦作工学院,2000
[46]齐麟,张亚雄等,蜗杆传动设计(下册),北京:机械工业出版社,1987
[47]胡来榕等,双包络蜗杆传动的研究与发展,湖北工学院学报,2000,1~5
[48] Zhan Dongan . Tooth analysis of worm-gear drive based on dressing gears.Transactions of tianjin University,2000,6(2):126~129
[49] Dongan Zhan, Daizhong Su, Richard Gentle.A Novel 3D Modelling Approach Utilizing Virtual Reality Machining Principles,Proceedings of the 11th World Congress in Mechanism and Machine Science,2000,699~03
[50]董明,王树人,双自由度锥面包络圆柱蜗杆传动齿形参数的优化设计,机械传动,1994,18(4):4~8
[51]孙月海,郑惠江,毕庆贞等,精确磨削单包络TI蜗杆的方法,中国科学E辑,2005,35(7):737~745
[52]王树人,圆弧圆柱蜗杆传动啮合原理的新进展,全国齿轮传动学术年会论文集,1983
[53] Wang Xiaochun, Wu Xutang.Contact Analysis of Local~Contact Worm Gearing and optimal Design of Worm Gear Hob,Proceedings of International Conference on Gearing ,Zhengzhou,1988
[54]傅则绍,微分几何与齿轮啮合原理,山东:石油大学出版社,1999
[55]岑勇,倾轴直齿渐开面包络环面蜗杆副啮合特性分析,全国齿轮传动学术年会论文集,1983
[2]成大先,机械设计手册-机械传动(单行本),北京:化学工业出版社,2000
[3]王树人,圆弧圆柱蜗杆传动,天津:天津大学出版社,1991
[4]王树人,齿轮啮合理论简明教程,天津:天津大学出版社,2005
[5]段路茜,TI蜗杆传动啮合理论研究及优化设计[博士学位论文],天津:天津大学,2004
[6]王树人,刘平娟,圆柱蜗杆传动啮合原理.天津:天津科技出版社,1982
[7]詹东安,交错轴渐开线型共轭副的啮合理论及应用研究[博士学位论文],西安:西安交通大学,1998
[8]刘洪斌,基于渐开线齿轮形修磨轮包络蜗杆传动理论研究及精加工TI蜗杆的新方法[博士学位论文],天津:天津大学,2001
[9]傅则绍等,新型蜗杆传动,西安:陕西科学技术出版社,1990
[10]殷李森,圆弧螺旋面包络环面蜗杆传动,机械传动,2001,34(2):34~36
[11]韩红臣,近似的TI蜗杆传动研究[硕士学位论文],天津:天津大学2006
[12]郑惠江,TI蜗杆加工关键技术研究[硕士学位论文],天津:天津大学2004
[13]谭建平,张光辉,球面二次包络弧面蜗杆传动的理论研究,重庆大学学报,1988,11(1):42~51
[14]沈蕴方,李寅年,徐月琴,“圆环面双包络环面蜗杆传动”的理论研究与参数分析,全国齿轮传动学术年会论文集,1983
[15]李尚信,许冯平,蒋伯英,平面二次包络环面蜗杆传动的接触分析,大庆石油学院学报,1992,16(1):67~7
[16]卢华武,硬齿面副TI传动的加工与试验研究[硕士学位论文],天津:天津大学2007
[17]肖延萍,TI传动的参数化设计及存在装配误差时齿面接触分析[硕士学位论文],天津:天津大学2004
[18] An Zhaoda, Jia Baoxian. An Investigation of Concave-Convex Profile of A Cylindrical Worm Drive. Proceedings of International Conference on Gearing,Zhengzhou ,1988
[19] Sakai T. , Maki M. . An investigation on secondary action on skew gears..ASME,The Mechanisms Conference and International Symposium on Gearing and Transmission,1972,vol.1
[20]文庆明,周良墉,直廓环面蜗杆几何参数和修形的优化设计,新技术新工艺,2000,(12):16~18
[21]沈蕴方,容尔谦等,空间啮合原理及SG-71型蜗轮副,北京:冶金工业出版社,1983
[22]毛梦云,路懿,滚珠环面蜗杆传动的加工和啮合分析,机械工程学报,1989,25(2):42~ 49
[23]张光挥,王进戈,杨念增,滚锥包络环面蜗轮副的研制与实验,重庆大学学报,1992,15(5):8~11
[24]王进戈,张光挥,滚锥包络环面蜗杆传动的理论研究与参数优化,重庆大学学报,1992,15(2):58~64
[25]朱景梓,段德荣,渐开线二次包络弧面蜗杆传动的研究,全国齿轮传动学术年会论文集,1983
[26]秦大同,颜佳,张光辉,平面包络环面蜗杆基于坐标测量的高精度制造方法,机械工程学报,1997, 33(1):59~65
[27]张焕,胡晓波,曹文思,环面蜗杆齿面啮合线的计算机仿真技术,机械设计与研究,2002,18(6):30~32
[28]谭昕,张仲甫,平面二次包络环面蜗杆副的数字制造,中国机械工程,2003,14(8):649~652
[29]张希康,IT型渐开面蜗轮传动螺旋角的合理选择,机械工程学报,1982,18(3):86~92
[30]张希康,TI蜗杆传动瞬时接触线分析及其应用,齿轮,1987, 11(5):1~5
[31]张希康,TI蜗杆传动瞬时接触线分析及其应用(二),齿轮,1987, 11(6):1~5
[32] S. Wang, D. Zhan, etc. Tooth contact analysis of hourglass involute worm mating with involute helical gear,Mechanism and Machine Theory,2002,37(7):685~691
[33]詹东安,吴序堂.TI蜗杆与渐开线斜齿轮传动的接触分析,重型机械,1997;(5): 5~8
[34]詹东安,吴序堂等,双包络TI蜗杆传动的二次包络分析,重型机械,1998;(5):25~28
[35]秦大同,张光辉,锥面二次包络环面蜗杆传动齿面接触及运动精度的研究,重庆大学学报,1993,16(1):45~51
[36] V. Simon.Stress Analysis in Double Enveloping Worm Gears by Finite Element Method,Transactions of the ASME Journal of Mechanical Design,1993,115:179~185
[37]吴大任,齿轮啮合原理,北京:科学出版社,1985
[38]毕庆贞,TI蜗杆的三维造型和精确磨削加工方法[硕士学位论文],天津:天津大学,2003
[39]孙桓,陈作模,机械原理,北京:高等教育出版社,1996
[40] Daizhong Su,Datong Qin.Integration of numerical analysis, virtual simulation and finite element analysis for the optimum design of worm gearing.Journal of Materials Processing Technology,2003,138:429~435
[41] D.Su.A new approach combining numerical analysis and three-dimensional simulation for design of worm gearing with preferable localized tooth contact, Proceedings of 1998 ASME Design Engineering Technical Mechanisms conference, 1998
[42] D.Su,F. Yang and C. R.Gentle.Analysis of tooth stresses, mesh stiffness and loaded transmission errors of involute worm gears.International Journal of Gearing and Transmissions,2000,(3):36~44
[43]张志涌,精通Matlab 6.5版教程,北京:北京航空航天大学出版社,2003
[44]崔兴元,ZC1蜗杆传动可控修形的接触区特性分析及计算机代数系统在ZC1蜗杆传动中的研究[硕士学位论文],天津:天津大学,1990
[45]郜庆路,球面二次包络环面蜗杆传动的啮合原理与啮合性能[硕士学位论文],焦作:焦作工学院,2000
[46]齐麟,张亚雄等,蜗杆传动设计(下册),北京:机械工业出版社,1987
[47]胡来榕等,双包络蜗杆传动的研究与发展,湖北工学院学报,2000,1~5
[48] Zhan Dongan . Tooth analysis of worm-gear drive based on dressing gears.Transactions of tianjin University,2000,6(2):126~129
[49] Dongan Zhan, Daizhong Su, Richard Gentle.A Novel 3D Modelling Approach Utilizing Virtual Reality Machining Principles,Proceedings of the 11th World Congress in Mechanism and Machine Science,2000,699~03
[50]董明,王树人,双自由度锥面包络圆柱蜗杆传动齿形参数的优化设计,机械传动,1994,18(4):4~8
[51]孙月海,郑惠江,毕庆贞等,精确磨削单包络TI蜗杆的方法,中国科学E辑,2005,35(7):737~745
[52]王树人,圆弧圆柱蜗杆传动啮合原理的新进展,全国齿轮传动学术年会论文集,1983
[53] Wang Xiaochun, Wu Xutang.Contact Analysis of Local~Contact Worm Gearing and optimal Design of Worm Gear Hob,Proceedings of International Conference on Gearing ,Zhengzhou,1988
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