双重螺旋法圆弧刀廓加工齿轮副的齿面啮合特性分析
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摘要
为了预控双重螺旋法加工齿轮副的啮合特性,研究基于圆弧刀廓的双重螺旋法加工齿轮副齿廓修形对齿面接触性能的影响。首先推导采用圆弧刀廓、双重螺旋法加工的齿面方程,基于Ease-off分析圆弧刀廓加工对齿面失配量的影响;采用有限元法进行加载接触分析,得到不同刀廓加工齿轮副的接触位置及形状、传动误差、接触压力,对比分析不同刀廓加工齿轮副啮合性能对安装误差的敏感性。研究结果表明:圆弧刀廓修形可改善接触区位置和形状,避免边沿接触,减小传动误差,提高传动平稳性;显著降低工作与非工作齿面最大接触应力,以及边沿接触对安装误差的敏感性,有利于提高齿轮副承载性能和磨损寿命。
In order to pre-control the meshing performance of spiral bevel gears manufactured by duplex helical method, the influence of contact performance of spiral bevel gears with tooth profile modification based on arc blade profile was studied. Firstly, the tooth surface mathematical equation of spiral bevel gear by duplex helical method with arc blade profile was deduced, and the influence of the mismatch of spiral bevel gears with arc blade profile based on Ease-off topology was analyzed. Secondly, the finite element loading contacts analysis of spiral bevel gear pairs was conducted in different shapes of blade profile, and then the contact area, transmission error and the maximum contact stress were gained. Finally, the alignment error sensitivity generated by two different tool shapes was analyzed by comparison. The results show that the contact area can be improved by using the arc blade profile to avoid the tooth edge contact, and to moderate the wave curves of transmission error instability to raise the operation stability. It can decrease the maximum contact stress and the alignment error sensitivity significantly, showing that modifying tooth profile with arc blade profile is propitious to improve the contact performance and to extend the wear life of gear pair.
In order to pre-control the meshing performance of spiral bevel gears manufactured by duplex helical method, the influence of contact performance of spiral bevel gears with tooth profile modification based on arc blade profile was studied. Firstly, the tooth surface mathematical equation of spiral bevel gear by duplex helical method with arc blade profile was deduced, and the influence of the mismatch of spiral bevel gears with arc blade profile based on Ease-off topology was analyzed. Secondly, the finite element loading contacts analysis of spiral bevel gear pairs was conducted in different shapes of blade profile, and then the contact area, transmission error and the maximum contact stress were gained. Finally, the alignment error sensitivity generated by two different tool shapes was analyzed by comparison. The results show that the contact area can be improved by using the arc blade profile to avoid the tooth edge contact, and to moderate the wave curves of transmission error instability to raise the operation stability. It can decrease the maximum contact stress and the alignment error sensitivity significantly, showing that modifying tooth profile with arc blade profile is propitious to improve the contact performance and to extend the wear life of gear pair.
引文
[1]SIMON V.Influence of tooth modifications on tooth contact in face-hobbed spiral bevel gears[J].Mechanism and Machine Theory,2011,46(12):1980-1998.
[2]STADTFELD H J.Guidelines for modern bevel gear grinding[J].Gear Technology,2008,8:42-53.
[3]SIMON V.Head-cutter for optimal tooth modifications in spiral bevel gears[J].Mechanism and Machine Theory,2009,44(7):1420-1435.
[4]聂少武,邓效忠,李天兴,等.基于圆弧刀廓的端面滚切锥齿轮啮合接触分析[J].航空动力学报,2012,27(6):1424-1431.NIE Shaowu,DENG Xiaozhong,Li Tianxing,et al.Tooth meshing contact analysis for bevel gears by face hobbing method based on arc blade profile[J].Journal of Aerospace Power,2012,27(6):1424-1431.
[5]姜宏阳,刘志辉,肖似蹼.基于修根刀具的螺旋锥齿轮齿面优化[J].机械设计,2016(7):8-11.JIANG Hongyang,LIU Zhihui,XIAO Sipu.Tooth surface optimization of spiral bevel gear based on the toprem tools[J].Journal of Machine Design,2016(7):8-11.
[6]杨宏斌,张广杰,梁桂明.弧齿锥齿轮的修形设计与加工[J].机械传动,2008,32(5):93-95.YANG Hongbin,ZHANG Guangjie,Liang Guiming.The modification design and manufacture of spiral bevel gear[J].Journal of Mechanical Transmission,2008,32(5):93-95.
[7]ZHANG Yu,YAN Hongzhi,ZENG Tao,et al.Tooth surface geometry optimization of spiral bevel and hypoid gears generated by duplex helical method with circular profile blade[J].Journal of Central South University,2016,23(3):544-554.
[8]ARTONI A,GABICCINI M,KOLIVAND M.Ease-off based compensation of tooth surface deviations for spiral bevel and hypoid gears:Only the pinion needs corrections[J].Mechanism&Machine Theory,2013,61(1):84-101.
[9]曾韬.螺旋锥齿轮设计与加工[M].哈尔滨:哈尔滨工业大学出版社,1989:240-243.ZENG Tao.Design and manufacture of spiral bevel gears[M].Harbin:Harbin Institute of Technology Press,1989:240-243.
[10]李剑敏,吴跃成,宣海枫,等.基于齿面网格节点变形量的齿廓修形计算方法[J].中国机械工程,2017,28(3):294-299.LI Jianmin,WU Yuechen,XUAN Haifeng,et al.Calculation method of tooth profile modification based on mesh node deformations[J].China Mechanical Engineering,2017,28(3):294-299.
[11]苏进展,贺朝霞.弧齿锥齿轮齿面的高精度修形方法[J].华南理工大学学报(自然科学版),2014,42(4):91-96.SU Jinzhan,HE Chaoxia.High-precision modification of tooth surface for spiral bevel gears[J].Journal of south China University of Technology(Natural Science Edition),2014,42(4):91-96.
[12]ARTONI A,BRACCI A,GABICCINI M.Optimization of the loaded contact pattern in hypoid gears by automatic topography modification[J].Journal of Mechanical Design,2009,131:0110081-0110089.
[13]吴勇军,王建军,韩勤锴,等.基于接触有限元分析的斜齿轮齿廓修形与实验[J].航空动力学报,2011,26(2):409-415.WU Yongjun,WANG Jianjun,HAN Qinkai,et al.Tooth profile modification of helical gears and experimental study based on finite element contact analysis[J].Journal of Aerospace Power,2011,26(2):409-415.
[14]唐进元,刘艳平.直齿面齿轮加载啮合有限元仿真分析[J].机械工程学报,2012,48(5):124-131.TANG Jinyuan,LIU Yanping,Loaded meshing simulation of face-gear drive with spur involute pinion based on finite element analysis[J].Journal of Mechanical Engineering,2012,48(5):124-131.
[15]严宏志,艾伍轶,周腾飞,等.相对位置误差对双重螺旋法加工齿轮副接触性能的影响[J].机械科学与技术,2018,3(3):364-371.YAN Hongzhi,AI Wuyi,ZHOU Tengfei,et al.Influence of contact performance of spiral bevel gears generated by duplex helical method with relative position errors[J].Mechanical Science and Technology for Aerospace Engineering,2018,37(3):364-371.
[16]苏进展,方宗德.弧齿锥齿轮误差敏感性优化设计[J].航空动力学报,2012,27(1):183-189.SU Jinzhan,FANG Zongde.Optimization design of the error sensitivity for spiral bevel gears[J].Journal of Aerospace Power,2012,27(1):183-189.
[17]曹雪梅,孙宁,邓效忠.直齿锥齿轮低安装误差敏感性设计与实验验证[J].航空,2016,31(1):227-232.CAO Xuemei,Sun Ning,DENG Xiaozhong.Design for straight bevel gear based on low installation error sensitivity and experience tests[J].Journal of Aerospace Power,2016,31(1):227-232.
[2]STADTFELD H J.Guidelines for modern bevel gear grinding[J].Gear Technology,2008,8:42-53.
[3]SIMON V.Head-cutter for optimal tooth modifications in spiral bevel gears[J].Mechanism and Machine Theory,2009,44(7):1420-1435.
[4]聂少武,邓效忠,李天兴,等.基于圆弧刀廓的端面滚切锥齿轮啮合接触分析[J].航空动力学报,2012,27(6):1424-1431.NIE Shaowu,DENG Xiaozhong,Li Tianxing,et al.Tooth meshing contact analysis for bevel gears by face hobbing method based on arc blade profile[J].Journal of Aerospace Power,2012,27(6):1424-1431.
[5]姜宏阳,刘志辉,肖似蹼.基于修根刀具的螺旋锥齿轮齿面优化[J].机械设计,2016(7):8-11.JIANG Hongyang,LIU Zhihui,XIAO Sipu.Tooth surface optimization of spiral bevel gear based on the toprem tools[J].Journal of Machine Design,2016(7):8-11.
[6]杨宏斌,张广杰,梁桂明.弧齿锥齿轮的修形设计与加工[J].机械传动,2008,32(5):93-95.YANG Hongbin,ZHANG Guangjie,Liang Guiming.The modification design and manufacture of spiral bevel gear[J].Journal of Mechanical Transmission,2008,32(5):93-95.
[7]ZHANG Yu,YAN Hongzhi,ZENG Tao,et al.Tooth surface geometry optimization of spiral bevel and hypoid gears generated by duplex helical method with circular profile blade[J].Journal of Central South University,2016,23(3):544-554.
[8]ARTONI A,GABICCINI M,KOLIVAND M.Ease-off based compensation of tooth surface deviations for spiral bevel and hypoid gears:Only the pinion needs corrections[J].Mechanism&Machine Theory,2013,61(1):84-101.
[9]曾韬.螺旋锥齿轮设计与加工[M].哈尔滨:哈尔滨工业大学出版社,1989:240-243.ZENG Tao.Design and manufacture of spiral bevel gears[M].Harbin:Harbin Institute of Technology Press,1989:240-243.
[10]李剑敏,吴跃成,宣海枫,等.基于齿面网格节点变形量的齿廓修形计算方法[J].中国机械工程,2017,28(3):294-299.LI Jianmin,WU Yuechen,XUAN Haifeng,et al.Calculation method of tooth profile modification based on mesh node deformations[J].China Mechanical Engineering,2017,28(3):294-299.
[11]苏进展,贺朝霞.弧齿锥齿轮齿面的高精度修形方法[J].华南理工大学学报(自然科学版),2014,42(4):91-96.SU Jinzhan,HE Chaoxia.High-precision modification of tooth surface for spiral bevel gears[J].Journal of south China University of Technology(Natural Science Edition),2014,42(4):91-96.
[12]ARTONI A,BRACCI A,GABICCINI M.Optimization of the loaded contact pattern in hypoid gears by automatic topography modification[J].Journal of Mechanical Design,2009,131:0110081-0110089.
[13]吴勇军,王建军,韩勤锴,等.基于接触有限元分析的斜齿轮齿廓修形与实验[J].航空动力学报,2011,26(2):409-415.WU Yongjun,WANG Jianjun,HAN Qinkai,et al.Tooth profile modification of helical gears and experimental study based on finite element contact analysis[J].Journal of Aerospace Power,2011,26(2):409-415.
[14]唐进元,刘艳平.直齿面齿轮加载啮合有限元仿真分析[J].机械工程学报,2012,48(5):124-131.TANG Jinyuan,LIU Yanping,Loaded meshing simulation of face-gear drive with spur involute pinion based on finite element analysis[J].Journal of Mechanical Engineering,2012,48(5):124-131.
[15]严宏志,艾伍轶,周腾飞,等.相对位置误差对双重螺旋法加工齿轮副接触性能的影响[J].机械科学与技术,2018,3(3):364-371.YAN Hongzhi,AI Wuyi,ZHOU Tengfei,et al.Influence of contact performance of spiral bevel gears generated by duplex helical method with relative position errors[J].Mechanical Science and Technology for Aerospace Engineering,2018,37(3):364-371.
[16]苏进展,方宗德.弧齿锥齿轮误差敏感性优化设计[J].航空动力学报,2012,27(1):183-189.SU Jinzhan,FANG Zongde.Optimization design of the error sensitivity for spiral bevel gears[J].Journal of Aerospace Power,2012,27(1):183-189.
[17]曹雪梅,孙宁,邓效忠.直齿锥齿轮低安装误差敏感性设计与实验验证[J].航空,2016,31(1):227-232.CAO Xuemei,Sun Ning,DENG Xiaozhong.Design for straight bevel gear based on low installation error sensitivity and experience tests[J].Journal of Aerospace Power,2016,31(1):227-232.