考虑轴变形影响的零度弧齿锥齿轮传动误差计算研究
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摘要
传动误差是评判弧齿锥齿轮啮合性能的重要指标之一,直接反映弧齿锥齿轮的传动啮合特性,其与轴系结构密切相关.本文主要研究轴系结构与传动误差之间的正向设计计算方法,提出一种基于通用软件工具平台的考虑轴变形影响的弧齿锥齿轮传动误差数值计算方法,并与国际先进弧齿锥齿轮设计软件(KIMoS软件)进行对比,验证本文计算方法.针对两种轴系结构设计方案,应用本文方法分析轴变形对航空发动机弧齿锥齿轮传动误差的影响.分析计算结果表明:支撑形式对齿面接触力的大小影响甚微,但支撑形式与轴的变形对传动误差的影响较大.通过改变轴系的支撑结构可以获得良好的弧齿锥齿轮传动误差曲线.本文工作可为研究轴系结构与零度弧齿锥齿轮传动误差关系提供参考.
Transmission error, to a certain extent, is one of the most important indexes to evaluate the meshing performance of spiral bevel gears, which directly reflects the transmission meshing characteristics of the Spiral Bevel Gears and is closely related to the shafting structure. This paper mainly studies the positive design calculation method between shaft structure and transmission error, and proposes a numerical calculation method of the spiral bevel gear transmission error considering the influence of shaft deformation based on the common software tool platform. It is compared with the international advanced design software(KIMoS software) of spiral bevel gear to verify the calculation method of the paper. The influence of shaft deformation on the transmission error of aero-engine spiral bevel gears is analyzed aiming at two kinds of design schemes for shaft structures in this paper. The analysis results show that the different forms of support have little effect on the contact force of the tooth surface, but the support form and the deformation of the shaft have a greater impact on the transmission error. Good transmission error curve of spiral bevel gears can be obtained by changing the support structure of the shafting system. Therefore, the work of this paper can provide reference for studying the relationship between shafting structure and transmission error of spiral bevel gear.
Transmission error, to a certain extent, is one of the most important indexes to evaluate the meshing performance of spiral bevel gears, which directly reflects the transmission meshing characteristics of the Spiral Bevel Gears and is closely related to the shafting structure. This paper mainly studies the positive design calculation method between shaft structure and transmission error, and proposes a numerical calculation method of the spiral bevel gear transmission error considering the influence of shaft deformation based on the common software tool platform. It is compared with the international advanced design software(KIMoS software) of spiral bevel gear to verify the calculation method of the paper. The influence of shaft deformation on the transmission error of aero-engine spiral bevel gears is analyzed aiming at two kinds of design schemes for shaft structures in this paper. The analysis results show that the different forms of support have little effect on the contact force of the tooth surface, but the support form and the deformation of the shaft have a greater impact on the transmission error. Good transmission error curve of spiral bevel gears can be obtained by changing the support structure of the shafting system. Therefore, the work of this paper can provide reference for studying the relationship between shafting structure and transmission error of spiral bevel gear.
引文
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[15]樊大伟,王殿秋,姚庆芬.弧齿锥齿轮设计中TE值影响因素及控制方法[J].汽车工艺师,2017(5):56 FAN Dawei,WANG Dianqiu,YAO Qingfen.Influencing factors and control methods of te value in spiral bevel gear design[J].Automobile Technologist,2017(5):56
[16]何渠,贺敬良,何畅然,等.弧齿锥齿轮传动仿真分析及修形优化[J].北京信息科技大学学报(自然科学版),2014(6):37 HE Qu,HE Jingliang,HE Changran,et al.Simulation analysis and modification optimization of spiral bevel gear transmission[J].Journal of Beijing University of Information Science and Technology(Natural Science),2014(6):37
[17]LITVIN F L,FUENTES A,HAYASAKA K.Design,manufacture,stress analysis,and experimental tests of low-noise high endurance spiral bevel gears[J] .Mechanism & Machine Theory,2006 ,41(1):83
[18]LITVIN F L,ZHANG Y.Local synthesis and tooth contact analysis of face-milled spiral bevel gears[J] .Forum,1991,1(2):1
[19]GAMEZ-MONTERO P J,CASTILL A R,KHARMASHTA M.Contact problem of a trochoidal-gear pump[J].Interational Journal of Mechanical Sciences,2006,48(12):1471
[20]SIMON V.Influence of tooth errors and misalignments on tooth contact in spiral bevel gears[J] .Mechanism & Machine Theory,2008,43(10):1253
[21]VOGEL O,GRIEWANK A,B?R G.Direct gear tooth contact analysis for hypoid bevel gears[J].Computer Methods in Applied Mechanics & Engineering,2002,191(36):3965
[22]常乐浩,刘更,吴立言.齿轮综合啮合误差计算方法及对系统振动的影响[J].机械工程学报,2015,51(1):123 CHANG Lehao,LIU Geng,WU Liyan.Determination of composite meshing errors and its influence on the vibration of gear system[J].Chinese Journal of Mechanical Engineering,2015,51(1):123
[23]RINCON A F D,VIADERO F,IGLESIAS M,et al.A model for the study of meshing stiffness in spur gear transmissions[J].Mechanism & Machine Theory,2013,61(61):30
[24]丁长安,张雷,周福章,等.线接触弹性接触变形的解析算法[J].摩擦学学报,2001,21(2):135 DING Changan,ZHANG Lei,ZHOU Fuzhang,et al.Theoretical formula for calculation of line-contact elastic contact deformation[J].Tribology,2001,21(2):135
[25]MOHAMAD E N,KOMORI M,MURAKAMI H,et al.Analysis of general characteristics of transmission error of gears with convex modification of tooth flank form considering elastic deformation under load[J].Journal of Mechanical Design,2009,131(6):2751
[26]曾攀.有限元分析及应用(附光盘)[M].北京:清华大学出版社,2004 ZENG Pan.Finite element analysis and application (with CD) [M].Beijing:Tsinghua University Press,2004
[2]汪中厚,李刚,久保爱三.基于数字化真实齿面的螺旋锥齿轮齿面接触分析[J].机械工程学报,2014,50(15):1 WANG Zhonghou,LI Gang,KUBO Aizoh.Tooth contact analysis of spiral bevel gears based on digital real tooth surfaces[J].Chinese Journal of Mechanical Engineering,2014,50(15):1
[3]方宗德,邓效忠,任东锋.考虑边缘接触的弧齿锥齿轮承载接触分析[J].机械工程学报,2002,38(9):69 FANG Zongde,DENG Xiaozhong,REN Dongfeng.Loaded tooth contact analysis of spiral bevel gears considering edge contact[J].Chinese Journal of Mechanical Engineering,2002,38(9):69
[4]方宗德.齿轮轮齿承载接触分析(LTCA)的模型和方法[J].机械传动,1998(2):2 FANG Zongde.Model and method of gear tooth contact analysis (LTCA)[J].Mechanical Transmission,1998(2):2
[5]唐进元,蒲太平.加载螺旋锥齿轮接触轨迹变化规律的研究[J].机械科学与技术,2010,29(4):461 TANG Jinyuan,PU Taiping.A study of contact path variation of a loaded spiral bevel gear[J].Mechanical Science and Technology for Aerospace Engineering,2010,29(4):461
[6]唐进元,蒲太平.基于有限元法的螺旋锥齿轮啮合刚度计算[J].机械工程学报,2011,47(11):23 TANG Jinyuan,PU Taiping.Spiral bevel gear meshing stiffness calculations based on the finite element method[J].Chinese Journal of Mechanical Engineering,2011,47(11):23
[7]唐进元,卢延峰,周超.螺旋锥齿轮齿面接触分析改进算法研究[J].航空动力学报,2009,24(1):189 TANG Jinyuan,LU Yanfeng,ZHOU Chao.Research on improved tooth contact analysis algorithm of spiral bevel gears[J].Journal of Aerospace Power,2009,24(1):189
[8]DING Han,TANG Jinyuan,SHAO Wen,et al.Optimal modification of tooth flank form error considering measurement and compensation of cutter geometric errors for spiral bevel and hypoid gears[J].Mechanism & Machine Theory,2017,118:14
[9]DING Han,TANG Jinyuan,ZHONG Jue,et al.A hybrid modification approach of machine-tool setting considering high tooth contact performance in spiral bevel and hypoid gears[J].Journal of Manufacturing Systems,2016,41:228
[10]DING Han,ZHOU Yuansheng,TANG Jinyuan,et al.A novel operation approach to determine initial contact point for tooth contact analysis with errors of spiral bevel and hypoid gears[J].Mechanism & Machine Theory,2017,109:155
[11]苏进展,方宗德,蔡香伟.弧齿锥齿轮四阶传动误差的设计[J].华南理工大学学报 (自然科学版),2014,42(1):29 SU Jinzhan,FANG Zongde,CAI Xiangwei.Design of fourth-order transmission error of spiral bevel gear[J].Journal of South China University of Technology(Natural Science Edition),2014,42(1):29
[12]彭方进.基于接触动力学的螺旋锥齿轮动态啮合性能有限元分析研究[D].长沙:中南大学,2010 PENG Fangjin.Finite element analysis of dynamic meshing performance of spiral bevel gears based on contact dynamics [D].Changsha:Central South University,2010
[13]唐进元,彭方进.惯性载荷对螺旋锥齿轮动态啮合特性的影响研究[J].振动与冲击,2011,30(3):161 TANG Jinyuan,PENG Fangjin.Influence of inertial load in dynamic meshing analysis of spiral bevel gears[J].Journal of Vibration and Shock,2011,30(3):161
[14]刘光磊,张瑞庭,赵宁,等.安装误差对航空弧齿锥齿轮传动误差曲线的影响分析[J].航空发动机,2012,38(2):32 LIU Guanglei,ZHANG Ruiting,ZHAO Ning,et al.Analysis of influence of installation error on error curve of aeronautical spiral bevel gear transmission[J].Aero Engine,2012,38(2):32
[15]樊大伟,王殿秋,姚庆芬.弧齿锥齿轮设计中TE值影响因素及控制方法[J].汽车工艺师,2017(5):56 FAN Dawei,WANG Dianqiu,YAO Qingfen.Influencing factors and control methods of te value in spiral bevel gear design[J].Automobile Technologist,2017(5):56
[16]何渠,贺敬良,何畅然,等.弧齿锥齿轮传动仿真分析及修形优化[J].北京信息科技大学学报(自然科学版),2014(6):37 HE Qu,HE Jingliang,HE Changran,et al.Simulation analysis and modification optimization of spiral bevel gear transmission[J].Journal of Beijing University of Information Science and Technology(Natural Science),2014(6):37
[17]LITVIN F L,FUENTES A,HAYASAKA K.Design,manufacture,stress analysis,and experimental tests of low-noise high endurance spiral bevel gears[J] .Mechanism & Machine Theory,2006 ,41(1):83
[18]LITVIN F L,ZHANG Y.Local synthesis and tooth contact analysis of face-milled spiral bevel gears[J] .Forum,1991,1(2):1
[19]GAMEZ-MONTERO P J,CASTILL A R,KHARMASHTA M.Contact problem of a trochoidal-gear pump[J].Interational Journal of Mechanical Sciences,2006,48(12):1471
[20]SIMON V.Influence of tooth errors and misalignments on tooth contact in spiral bevel gears[J] .Mechanism & Machine Theory,2008,43(10):1253
[21]VOGEL O,GRIEWANK A,B?R G.Direct gear tooth contact analysis for hypoid bevel gears[J].Computer Methods in Applied Mechanics & Engineering,2002,191(36):3965
[22]常乐浩,刘更,吴立言.齿轮综合啮合误差计算方法及对系统振动的影响[J].机械工程学报,2015,51(1):123 CHANG Lehao,LIU Geng,WU Liyan.Determination of composite meshing errors and its influence on the vibration of gear system[J].Chinese Journal of Mechanical Engineering,2015,51(1):123
[23]RINCON A F D,VIADERO F,IGLESIAS M,et al.A model for the study of meshing stiffness in spur gear transmissions[J].Mechanism & Machine Theory,2013,61(61):30
[24]丁长安,张雷,周福章,等.线接触弹性接触变形的解析算法[J].摩擦学学报,2001,21(2):135 DING Changan,ZHANG Lei,ZHOU Fuzhang,et al.Theoretical formula for calculation of line-contact elastic contact deformation[J].Tribology,2001,21(2):135
[25]MOHAMAD E N,KOMORI M,MURAKAMI H,et al.Analysis of general characteristics of transmission error of gears with convex modification of tooth flank form considering elastic deformation under load[J].Journal of Mechanical Design,2009,131(6):2751
[26]曾攀.有限元分析及应用(附光盘)[M].北京:清华大学出版社,2004 ZENG Pan.Finite element analysis and application (with CD) [M].Beijing:Tsinghua University Press,2004