平面二包环面蜗杆副多参数修正接触型式分析
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摘要
本文以斜平面二次包络环面蜗杆副为研究对象,在空间啮合理论的基础上,推论出三参数修正的啮合方程、接触线方程、蜗轮齿面方程。修正型蜗杆副公认存在两种接触线型式Ⅰ型和Ⅱ型.通过理论推导和仿真计算,做出了在蜕变点瞬时将出现一包接触线“复现”在齿面上,并将复现时刻的接触线定义为Ⅲ型接触线,Ⅲ型接触线出现在齿面上时,Ⅰ型和Ⅱ型必然同时出现在Ⅲ型接触线的前后瞬时,并用动画仿真演示了三种接触线型式的演变过程。
对不同型式的接触线进行性能分析,并讨论了单参数修正及三参数组成的混合修正时,不同的修正量下接触线变化规律及啮合性能的比较。
分析了蜗杆副的误差对蜗杆副的性能影响,通过理论研究得到了修正型二次包络环面蜗杆副轴向安装误差时齿面上接触线型式的判断方法:使用MATLAB软件求解Ⅰ型和Ⅱ型二界函数曲线,得出I型接触线簇构成的蜗轮曲面存在两条二界曲线,即蜗轮齿面上存在两个二界点,而Ⅱ型接触线簇不存包络线,不存在二界点。针对三参数修正下二界曲线方程,进行化简求解,得出判断存在二界点的方程,根据方程值的正负及是否为零来判断二界点的个数进而判断接触线的型式。用动画仿真演示了存在轴向误差时Ⅲ型接触线在蜗轮齿面上的演化过程及接触线的转化规律。
In this thesis, planar double-enveloping worm gear pairs is the research object, combined with space Meshing theory, derived from the multi-parameter modification of the mesh equation . The contact line type of original type Worm were analysised, Contact line type of amend-type worm gear pair were recognized are typeⅠand typeⅡT hrough the point of theoretical research of transformation point , the instantaneous contact line of the transformation point will appear first-enveloping contact line in the tooth surface, before and after the transformation point of the instantaneous were typeⅠandⅡcontact line in the tooth surface, the contact line type is defined as the typeⅢ. animation instantaneous contact line of the typeⅢhas rendered the process
Different types of contact line performance analysis and discussion of the single parameter modification and amendment of three parameters simultaneously, the changing of the contact line and meshing performance comparison under different correction variation,
The oretical research was supported by Modified Double Enveloping Worm Gear tooth surface when the axial misalignment of the contact line type judging method: using MATLAB software to solveⅠandⅡtype 2 boundary curves, there are two curves of I-type worm gear surface contact line, there are not two curves ofⅡ-type worm gear surface contact line. Under the three-parameter correction for the second boundary curve to determine the second boundary point then determine the number of contact line of type. Simulation with animation shows the existence of axial error of typeⅢcontact line in the worm tooth surface contact line evolution and transformation rules
对不同型式的接触线进行性能分析,并讨论了单参数修正及三参数组成的混合修正时,不同的修正量下接触线变化规律及啮合性能的比较。
分析了蜗杆副的误差对蜗杆副的性能影响,通过理论研究得到了修正型二次包络环面蜗杆副轴向安装误差时齿面上接触线型式的判断方法:使用MATLAB软件求解Ⅰ型和Ⅱ型二界函数曲线,得出I型接触线簇构成的蜗轮曲面存在两条二界曲线,即蜗轮齿面上存在两个二界点,而Ⅱ型接触线簇不存包络线,不存在二界点。针对三参数修正下二界曲线方程,进行化简求解,得出判断存在二界点的方程,根据方程值的正负及是否为零来判断二界点的个数进而判断接触线的型式。用动画仿真演示了存在轴向误差时Ⅲ型接触线在蜗轮齿面上的演化过程及接触线的转化规律。
In this thesis, planar double-enveloping worm gear pairs is the research object, combined with space Meshing theory, derived from the multi-parameter modification of the mesh equation . The contact line type of original type Worm were analysised, Contact line type of amend-type worm gear pair were recognized are typeⅠand typeⅡT hrough the point of theoretical research of transformation point , the instantaneous contact line of the transformation point will appear first-enveloping contact line in the tooth surface, before and after the transformation point of the instantaneous were typeⅠandⅡcontact line in the tooth surface, the contact line type is defined as the typeⅢ. animation instantaneous contact line of the typeⅢhas rendered the process
Different types of contact line performance analysis and discussion of the single parameter modification and amendment of three parameters simultaneously, the changing of the contact line and meshing performance comparison under different correction variation,
The oretical research was supported by Modified Double Enveloping Worm Gear tooth surface when the axial misalignment of the contact line type judging method: using MATLAB software to solveⅠandⅡtype 2 boundary curves, there are two curves of I-type worm gear surface contact line, there are not two curves ofⅡ-type worm gear surface contact line. Under the three-parameter correction for the second boundary curve to determine the second boundary point then determine the number of contact line of type. Simulation with animation shows the existence of axial error of typeⅢcontact line in the worm tooth surface contact line evolution and transformation rules
引文
[1]郑州机械研究所分度蜗轮课题组.精密传动中包络蜗杆传动副的应用[J].齿轮,1978(4):21-23
[2]张光辉.平面二次包络环面蜗杆传动的研究与应用[J].重庆大学学报,1978(4):7一10
[3]张光辉,王朝晋.活动标架的应用及对Baxter诱导法曲率公式的改进[J]..重庆大学学报,1983(2)1-12
[4]孟惠荣,唐劲松.可展环面蜗杆传动齿面承载能力的研究[J].机械工程学报,1993(6)
[5]熊旭辉,胡来瑢,朱敬成.角修正可展环面蜗杆副的接触润滑性能和开槽工艺参数优化[J]..湖北工学院学报.1999,61(14):87-91
[6]甘正清,王树人.圆弧圆柱蜗杆副(zcl)可控啮合研究及滚刀研究告[R]..1991.10
[7]秦大同.二次包络环面蜗杆失配啮合传动的研究[D].重庆:重庆大学,1993
[8]秦大同,张光辉.二次包络环面蜗杆传动齿面修形的效果[J].重庆大学学报,1993.16(l):7-l3
[9]王树人,张海兵.zCesl蜗杆传动可控修形研究[J].天津大学学报,l989(l):64-71
[10]周良墉环面蜗杆的曲率修形原理[J].机械工程学报,2002(2):112-115
[11]周良墉环面蜗杆修型的实质[J].机械传动,2004(6):48-51
[12]文庆明周良墉徐华平面包络环面蜗杆修型的研究[J].机械设计与研究,2009(1)57-64 [13〕侯力,张光辉.一种包络蜗杆传动啮合分析的数求解方法.机械,1994,21(3):23-27
[14]谭昕.平面二次包络环面蜗杆副数字化造型理论及仿真研究[D].武汉:武汉理工大学,2003
[15] Sherif D.EI Wakil.Processes and Design for Manufacturing.1989 by Prentice-Hall[J]. Inc.Adivision of Simon&Schuster Englewood Clifs, New Jersey 607-632
[16]周祖德,余文勇,陈幼平.数字制造的概念与科学问题[J].中国机械工程,2001(1):25-27
[17]孙昌佑,李光步.孙传文.一种平面二次包络环面蜗杆副的特征建模方法[J].武汉理工大学学报,2006,30(5):881-884
[18]谭昕,徐盛林.平面二次包络环面蜗轮理论齿面重构数字化造型算法研究[J].新技术新工艺:热加工工艺技术与装备,2007,10(10):71-74
[19]黄安贻,夏江敬,张仲甫.平面包络环面蜗杆啮合齿面的结构特性及其应用[J].武汉理工学校学报:信息与管理工程版,2003,25(2):67-70
[20]马龙,吴新跃.平面二次包络环面蜗杆蜗轮副实体建模[J].2006,(6):62-64
[21]谭昕,徐盛,周红.基于数值方法的平面二次包络蜗轮理论齿面的离散建模[J].机械传动,2005,29(3):3-5
[22]陆源.二次包络环面蜗杆传动直接数字化建模研究[D].重庆:重庆大学,2007
[23] LU Hong, HUANG Anyi, XIA Jiangjing. Measuring the Gear Surface of the Plane -Generated Double Enveloping Hourglass Worm Pair[A]. Proc.of 1999 International Conference on Advanced Manufacturing Technology , Xi’an China [D]1 Jiang Zhong De. New York :Science Preff LTD ,1999,396 - 398
[24]秦东兴.平面包络环面蜗杆传动弹性啮合研究[D].重庆:重庆大学,1999
[25]吴(日韦)平面二包蜗杆副的在线自动编程及仿真系统的研究[D].南昌:南昌大学,2005
[26] M.-Y.Yang,T.-M.Lee and J-G.Choi. A New Spindle Current Regulation Algorithm for the CNC End Milling rocess.Int Jadv Manuf Technol (2002)19:471-483
[27]胡来瑢.空间啮合理论(上、下册)[M].北京:煤炭工业出版社,1986
[28]孙昌佑林青孙传文平面二次包络环面蜗轮的特征建模[J].上海师范大学学报:2006(5)48-52
[29]杨朝丽.平面二次包络环面蜗杆传动的运动分析与模糊优化研究[D].昆明:昆明理工大学,2003
[30]张跃敏.修正型二次包络环面蜗杆副接触形态研究[D].焦作:河南理工大学,2008
[31]尹明泽,丁春利等.精通MATLAB 6[M]北京:清华大学出版社,2002年
[32]周良墉.平面二次包络蜗杆传动的参数优化设计[c].全国平面二包蜗杆传动学术与生产经验交流会论文集。2007,8.
[33]张跃敏,王小林,谢刚.修正型斜平面二次包络环面蜗杆副的接触型式[J].机械传动2009,33(1):22-24
[34]董学朱.环面蜗杆传动设计和修形[M].1版.北京:机械工业出版社,2004.
[35]王红梅,董学朱.平面二次包络环面蜗杆副的失配修形[J].农业机械学报,1998,29(3):16-21
[36]张亚雄,齐麟,胡松春等.蜗杆传动设计(下册)[M].北京:机械工业出版社1987:171-172
[37]徐戊矫,制造误差与承载变形耦合条件下平面二次包络环面蜗杆的啮合控制研究[D].重庆:重庆大学,2005
[38] Qin.D.ct.al.Influence of machining and asscmbling errors on tooth contact of hourglassworm gcaring[J].Trans,of the JSME..1991. 57(541)
[39] D Wang,N.Yao. A Study on the Practical Mathematical Model for Evaluating the Profile Error of the Solid of Revolution[J]. Proceedings of CIRPC on ference on PE & MS, 1991,(9):664-671
[40] Ee Meng Lim,etc..Error Compensation for Sculptured Surface Productions by the application of Control-Surface Strategy Using Predicted Machining Errors[J].,Journal of Manufacturing Science and Engineering,Transations of the AS ME ,.1997,1(119)402-409
[41] J.C.Liang,.A Comprehension Error Compensation System for Correcting Geometr ic,Thermal,and Cuting Force-Included Errors[J].,InternationalJo urnal Ad van ced Technology,1997(13),708-712
[42] Maisheng Hong,etc.Separation Techniques and the New Method for Error and ErrorM otion Measure ment"P roceedings of CIRP Conference PE & MS Sep .1991,17- 21
[43] Cheng Liang Yuan,etc. Use of Error Separation Technique in the On-line Comp rehensive Measurement of Size-Form Error of Deep Holes[J].Proceedings of CIRPC onference PE& MS 1991,(9):187-191
[44]谭昕,张仲甫.平面二次包络环面蜗杆副的数字制造[J].中国机械工程,2003,8(14):649-653
[45] W. Shi *, D. Qin, W. Xu. Meshing control of the double-enveloping hourglassworm gearing under the conditions of existing the errors and the load[J]. Mechanism and Machine Theory 39 (2004) 61–74
[46]黄安贻.平面二次包络环面蜗杆副数控加工与可制造性研究[D].武汉:武汉理工大学,2005
[2]张光辉.平面二次包络环面蜗杆传动的研究与应用[J].重庆大学学报,1978(4):7一10
[3]张光辉,王朝晋.活动标架的应用及对Baxter诱导法曲率公式的改进[J]..重庆大学学报,1983(2)1-12
[4]孟惠荣,唐劲松.可展环面蜗杆传动齿面承载能力的研究[J].机械工程学报,1993(6)
[5]熊旭辉,胡来瑢,朱敬成.角修正可展环面蜗杆副的接触润滑性能和开槽工艺参数优化[J]..湖北工学院学报.1999,61(14):87-91
[6]甘正清,王树人.圆弧圆柱蜗杆副(zcl)可控啮合研究及滚刀研究告[R]..1991.10
[7]秦大同.二次包络环面蜗杆失配啮合传动的研究[D].重庆:重庆大学,1993
[8]秦大同,张光辉.二次包络环面蜗杆传动齿面修形的效果[J].重庆大学学报,1993.16(l):7-l3
[9]王树人,张海兵.zCesl蜗杆传动可控修形研究[J].天津大学学报,l989(l):64-71
[10]周良墉环面蜗杆的曲率修形原理[J].机械工程学报,2002(2):112-115
[11]周良墉环面蜗杆修型的实质[J].机械传动,2004(6):48-51
[12]文庆明周良墉徐华平面包络环面蜗杆修型的研究[J].机械设计与研究,2009(1)57-64 [13〕侯力,张光辉.一种包络蜗杆传动啮合分析的数求解方法.机械,1994,21(3):23-27
[14]谭昕.平面二次包络环面蜗杆副数字化造型理论及仿真研究[D].武汉:武汉理工大学,2003
[15] Sherif D.EI Wakil.Processes and Design for Manufacturing.1989 by Prentice-Hall[J]. Inc.Adivision of Simon&Schuster Englewood Clifs, New Jersey 607-632
[16]周祖德,余文勇,陈幼平.数字制造的概念与科学问题[J].中国机械工程,2001(1):25-27
[17]孙昌佑,李光步.孙传文.一种平面二次包络环面蜗杆副的特征建模方法[J].武汉理工大学学报,2006,30(5):881-884
[18]谭昕,徐盛林.平面二次包络环面蜗轮理论齿面重构数字化造型算法研究[J].新技术新工艺:热加工工艺技术与装备,2007,10(10):71-74
[19]黄安贻,夏江敬,张仲甫.平面包络环面蜗杆啮合齿面的结构特性及其应用[J].武汉理工学校学报:信息与管理工程版,2003,25(2):67-70
[20]马龙,吴新跃.平面二次包络环面蜗杆蜗轮副实体建模[J].2006,(6):62-64
[21]谭昕,徐盛,周红.基于数值方法的平面二次包络蜗轮理论齿面的离散建模[J].机械传动,2005,29(3):3-5
[22]陆源.二次包络环面蜗杆传动直接数字化建模研究[D].重庆:重庆大学,2007
[23] LU Hong, HUANG Anyi, XIA Jiangjing. Measuring the Gear Surface of the Plane -Generated Double Enveloping Hourglass Worm Pair[A]. Proc.of 1999 International Conference on Advanced Manufacturing Technology , Xi’an China [D]1 Jiang Zhong De. New York :Science Preff LTD ,1999,396 - 398
[24]秦东兴.平面包络环面蜗杆传动弹性啮合研究[D].重庆:重庆大学,1999
[25]吴(日韦)平面二包蜗杆副的在线自动编程及仿真系统的研究[D].南昌:南昌大学,2005
[26] M.-Y.Yang,T.-M.Lee and J-G.Choi. A New Spindle Current Regulation Algorithm for the CNC End Milling rocess.Int Jadv Manuf Technol (2002)19:471-483
[27]胡来瑢.空间啮合理论(上、下册)[M].北京:煤炭工业出版社,1986
[28]孙昌佑林青孙传文平面二次包络环面蜗轮的特征建模[J].上海师范大学学报:2006(5)48-52
[29]杨朝丽.平面二次包络环面蜗杆传动的运动分析与模糊优化研究[D].昆明:昆明理工大学,2003
[30]张跃敏.修正型二次包络环面蜗杆副接触形态研究[D].焦作:河南理工大学,2008
[31]尹明泽,丁春利等.精通MATLAB 6[M]北京:清华大学出版社,2002年
[32]周良墉.平面二次包络蜗杆传动的参数优化设计[c].全国平面二包蜗杆传动学术与生产经验交流会论文集。2007,8.
[33]张跃敏,王小林,谢刚.修正型斜平面二次包络环面蜗杆副的接触型式[J].机械传动2009,33(1):22-24
[34]董学朱.环面蜗杆传动设计和修形[M].1版.北京:机械工业出版社,2004.
[35]王红梅,董学朱.平面二次包络环面蜗杆副的失配修形[J].农业机械学报,1998,29(3):16-21
[36]张亚雄,齐麟,胡松春等.蜗杆传动设计(下册)[M].北京:机械工业出版社1987:171-172
[37]徐戊矫,制造误差与承载变形耦合条件下平面二次包络环面蜗杆的啮合控制研究[D].重庆:重庆大学,2005
[38] Qin.D.ct.al.Influence of machining and asscmbling errors on tooth contact of hourglassworm gcaring[J].Trans,of the JSME..1991. 57(541)
[39] D Wang,N.Yao. A Study on the Practical Mathematical Model for Evaluating the Profile Error of the Solid of Revolution[J]. Proceedings of CIRPC on ference on PE & MS, 1991,(9):664-671
[40] Ee Meng Lim,etc..Error Compensation for Sculptured Surface Productions by the application of Control-Surface Strategy Using Predicted Machining Errors[J].,Journal of Manufacturing Science and Engineering,Transations of the AS ME ,.1997,1(119)402-409
[41] J.C.Liang,.A Comprehension Error Compensation System for Correcting Geometr ic,Thermal,and Cuting Force-Included Errors[J].,InternationalJo urnal Ad van ced Technology,1997(13),708-712
[42] Maisheng Hong,etc.Separation Techniques and the New Method for Error and ErrorM otion Measure ment"P roceedings of CIRP Conference PE & MS Sep .1991,17- 21
[43] Cheng Liang Yuan,etc. Use of Error Separation Technique in the On-line Comp rehensive Measurement of Size-Form Error of Deep Holes[J].Proceedings of CIRPC onference PE& MS 1991,(9):187-191
[44]谭昕,张仲甫.平面二次包络环面蜗杆副的数字制造[J].中国机械工程,2003,8(14):649-653
[45] W. Shi *, D. Qin, W. Xu. Meshing control of the double-enveloping hourglassworm gearing under the conditions of existing the errors and the load[J]. Mechanism and Machine Theory 39 (2004) 61–74
[46]黄安贻.平面二次包络环面蜗杆副数控加工与可制造性研究[D].武汉:武汉理工大学,2005