柔性销轴式人字齿星型轮系均载特性
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摘要
为研究人字齿星型轮系各路功率分流载荷分配机理,提高齿轮箱承载能力,采用节点有限元法建立柔性销轴式齿轮涡扇发动机人字齿星型轮系动力学模型.研究当量啮合误差下星型轮系动态均载性能,分析误差激励、销轴结构、工况参数对系统均载特性的影响.结果表明:齿轮偏心误差使中心齿轮振动轨迹偏离原点,是造成不均载的主要原因;系统均载系数随误差增加呈线性增加,且制造误差的影响大于安装误差;柔性销可以明显改善系统均载性能,在4种星轮柔性销轴中Montestruc改进的柔性销均载性能最佳;系统的均载系数随输入转速增加呈增大趋势,共振会导致系统的均载性能急剧下降;均载性能随系统承载功率增大而变好,且功率变小,柔性销对系统的均载性能改善的优势更加明显.
To study the load distribution mechanism of power-split transmission and improve the carrying capacity of the gear box for herringbone star gear transmission system,a dynamics model for the geared turbofan( GTF) engine with a flexible pin was established based on finite element method. The dynamic load sharing characteristic of the system was studied in equivalent meshing error,and the influence of the error incentives,structure of pins,and working condition on load sharing characteristic was analyzed. The results show that the vibration track of the center gears deviates from the origin resulted by the eccentricity error,which is the primary cause for the inequality of load distribution. The load sharing coefficient of the system increases linearly with the error,and the influence of manufacturing errors is larger than assembling errors. The flexible pin can significantly improve the load sharing performance,and the flexible pin improved by Montestruc has best load sharing performance among the four kinds of pins. The load sharing coefficient declines with the increase of input speed,the resonance would lead to a sharp drop of loading sharing performance. The load sharing performance is improved with the increase of the input power,and the advantage of flexible pin is more prominent when the input power becomes lower.
To study the load distribution mechanism of power-split transmission and improve the carrying capacity of the gear box for herringbone star gear transmission system,a dynamics model for the geared turbofan( GTF) engine with a flexible pin was established based on finite element method. The dynamic load sharing characteristic of the system was studied in equivalent meshing error,and the influence of the error incentives,structure of pins,and working condition on load sharing characteristic was analyzed. The results show that the vibration track of the center gears deviates from the origin resulted by the eccentricity error,which is the primary cause for the inequality of load distribution. The load sharing coefficient of the system increases linearly with the error,and the influence of manufacturing errors is larger than assembling errors. The flexible pin can significantly improve the load sharing performance,and the flexible pin improved by Montestruc has best load sharing performance among the four kinds of pins. The load sharing coefficient declines with the increase of input speed,the resonance would lead to a sharp drop of loading sharing performance. The load sharing performance is improved with the increase of the input power,and the advantage of flexible pin is more prominent when the input power becomes lower.
引文
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[14]HICKS R J.Load equalizing means for planetary pinions:U.S.Patent 3,303,713[P].1967-2-14.
[15]FOX G P,JALLAT E.Epicyclic gear system:U.S.Patent 6,994,651[P].2006-2-7.
[16]STRINGER D B.Geared rotor dynamic methodologies for advancing prognostic modeling capabilities in rotary-wing transmission systems[D].Virginia:University of Virginia,2008.
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[19]CHEN Z G,SHAO Y M,LIM T C.Non-linear dynamic simulation of gear response under the idling condition[J].International Journal of Automotive Technology,2012,13(4):541-552.Doi:10.1007/s12239-012-0052-1.
[20]PARKER R G,LIN J.Mesh phasing relationships in planetary and epicyclic gears[J].Journal of Mechanical Design,2004,126(2):525-534.Doi:/10.1115/1.1667892.
[21]焦万铭,杨珏,马飞,等.变速器行星齿轮机构等强度优化设计[J].农业机械学报,2015,46(1):359-364.Doi:10.6041/j.issn.1000-1298.2015.01.050.JIAO Wanming,YANG Jue,MA Fei,et al.Equal strength optimal design of planetary gear transmission[J].Transactions of the Chinese Society for Agricultural Machinery,2015,46(1):359-364.Doi:10.6041/j.issn.1000-1298.2015.01.050.
[2]KAHRAMAN A.Load sharing characteristics of planetary transmissions[J].Mechanism and Machine Theory,1994,29(8):1151-1165.Doi:10.1016/0094-114x(94)90006-x.
[3]BODAS A,KAHRAMAN A.Influence of carrier and gear manufacturing errors on the static load sharing behavior of planetary gear sets[J].JSME International Journal Series C,Mechanical Systems,Machine Elements and Manufacturing,2004,47(3):908-915.Doi:10.1299/jsmeimpt.ii.01.202.633.
[4]SINGH A.Application of a system level model to study the planetary load sharing behavior[J].Journal of Mechanical Design,2005,127(3):469-476.Doi:10.1115/1.1864115.
[5]袁擎宇,朱如鹏,朱自冰,等.两级星型齿轮传动静力学均载分析[J].机械科学与技术,2004,23(7):789-792.Doi:10.3321/j.issn:1003-8728.2004.07.011.YUAN Qingyu,ZHU Rupeng,ZHU Zibing,et al.Analysis of static load sharing in a 2-stage star gearing system[J].Mechanical Science and Technology,2004,23(7):789-792.Doi:10.3321/j.issn:1003-8728.2004.07.011.
[6]MONTESTRUC A N.Influence of planet pin stiffness on load sharing in planetary gear drives[J].Journal of Mechanical Design,2011,133(1):014501.Doi:10.1115/1.4 002971.
[7]ZHU C C,XU X Y,LIU H J,et al.Research on dynamical characteristics of wind turbine gearboxes with flexible pins[J].Renewable Energy,2014,68(7):724-732.Doi:10.1016/j.renene.2014.02.047.
[8]谭援强,胡聪芳,张跃春,等.封闭差动行星齿轮箱动态均载性能试验研究[J].机械工程学报,2016,52(9):28-35.Doi:10.3901/JME.2016.09.028.TAN Yuanqiang,HU Congfang,ZHANG Yuechun,et al.Testing research on dynamic load sharing performance of encased differential planetary gearbox[J].Journal of Mechanical Engineering,2016,52(9):28-35.Doi:10.3901/JME.2016.09.028.
[9]杜进辅,方宗德,王宝宾,等.基于变形协调的行星轮系均载特性研究[J].航空动力学报,2012,27(5):1166-1171.DU Jinfu,FANG Zongde,WNAG Baobin,et al.Study on load sharing behavior of planetary gear train based on deformation compatibility[J].Journal of Aerospace Power,2012,27(5):1166-1171.
[10]刘辉,蔡仲昌,项昌乐.两级行星齿轮传动非线性啮合力频率耦合与动态特性研究[J].振动与冲击,2015,34(19):13-23.Doi:10.13465/j.cnki.jvs.2015.19.003.LIU Hui,CAI Zhongchang,XIANG Changle.Frequency coupling and dynamic characteristics of nonlinear meshing force for two-stage planetary gears[J].Journal of Vibration and Shock,2015,34(19):13-23.Doi:10.13465/j.cn ki.jvs.2015.19.003.
[11]朱伟林,巫世晶,王晓笋,等.安装误差对变刚度系数的复合行星轮系均载特性的影响分析[J].振动与冲击,2016,35(12):77-85.Doi:10.13465/j.cnki.jvs.2016.12.012.ZHU Weilin,WU Shijing,WANG Xiaosun,et al.Influence of position errors on the load-sharing characteristics of compound planetary gear sets considering the variable stiffness coefficient[J].Journal of Vibration and Shock,2016,35(12):77-85.Doi:10.13465/j.cnki.jvs.2016.12.012.
[12]REN F,QIN D T,LIM T C,et al.Study on dynamic characteristics and load sharing of a herringbone planetary gear with manufacturing errors[J].International Journal of Precision Engineering and Manufacturing,2014,15(9):1925-1934.Doi:10.1007/s12541-014-0547-y.
[13]魏静,张爱强,秦大同,等.考虑结构柔性的行星轮系耦合振动特性研究[J].机械工程学报,2017,53(1):1-12.Doi:10.3901/JME.2017.01.001.WEI Jing,ZHANG Aiqiang,QIN Datong,et al.Coupling vibration analysis for planetary gear system considering flexible structure[J].Journal of Mechanical Engineering,2017,53(1):1-12.Doi:10.3901/JME.2017.01.001.
[14]HICKS R J.Load equalizing means for planetary pinions:U.S.Patent 3,303,713[P].1967-2-14.
[15]FOX G P,JALLAT E.Epicyclic gear system:U.S.Patent 6,994,651[P].2006-2-7.
[16]STRINGER D B.Geared rotor dynamic methodologies for advancing prognostic modeling capabilities in rotary-wing transmission systems[D].Virginia:University of Virginia,2008.
[17]HUEBNER K H,DEWHIRST D L,SMITH D E,et al.The finite element method for engineers[M].New York:John Wiley&Sons,2008.
[18]常乐浩.平行轴齿轮传动系统动力学通用建模方法与动态激励影响规律研究[D].西安:西北工业大学,2014.CHANG Lehao.A generalized dynamic model for parallel shaft gear transmissions and the influences of dynamic excitations[D].Xi'an:Northwest Polytechnical University,2014.
[19]CHEN Z G,SHAO Y M,LIM T C.Non-linear dynamic simulation of gear response under the idling condition[J].International Journal of Automotive Technology,2012,13(4):541-552.Doi:10.1007/s12239-012-0052-1.
[20]PARKER R G,LIN J.Mesh phasing relationships in planetary and epicyclic gears[J].Journal of Mechanical Design,2004,126(2):525-534.Doi:/10.1115/1.1667892.
[21]焦万铭,杨珏,马飞,等.变速器行星齿轮机构等强度优化设计[J].农业机械学报,2015,46(1):359-364.Doi:10.6041/j.issn.1000-1298.2015.01.050.JIAO Wanming,YANG Jue,MA Fei,et al.Equal strength optimal design of planetary gear transmission[J].Transactions of the Chinese Society for Agricultural Machinery,2015,46(1):359-364.Doi:10.6041/j.issn.1000-1298.2015.01.050.