基于热弹耦合大功率船用齿轮箱动态特性研究
|
摘要
课题来源于国家“十一五”科技支撑计划“高速、重载、精密机械传动系统共性关键技术研究”(2006BAF01B07-01)。为了适应国家重大装备与重点工程的需要,齿轮传动正朝着高速、重载、低噪声、高可靠性的方向发展。以船用减速器、燃气轮机齿轮箱、风力发电齿轮箱为代表的高速、重载机械传动系统是大型机械装备的重要基础件,其性能的优劣直接影响重大机械装备的综合性能和寿命。开展对高速、重载齿轮传动系统共性技术、关键技术的研究与开发,提升机械传动零部件及其相关装备产业的国际竞争能力,具有重要理论意义和工程实用价值。
论文基于齿轮啮合原理、轮齿接触分析、摩擦学和传热学、非线性系统动力学,以理论分析、有限元仿真为手段,对基于热弹耦合的大功率船用齿轮箱系统动态特性进行理论分析和实验研究。
论文的主要研究内容如下:
①建立大功率船用齿轮箱齿轮-转子-轴承-箱体耦合三维精细有限元模型,对系统的固有特性进行分析,得到约束情况下船用齿轮箱前20阶固有频率及振型。
②在考虑热弹耦合的基础上,对齿轮接触状态进行有限元分析,研究在热弹耦合情况下轮齿接触力和变形,得出基于热弹耦合工况下齿轮时变啮合刚度。
③在基于热弹耦合的时变刚度激励、误差激励和啮合冲击激励等内部激励和外部激励的影响下,对船用齿轮箱系统动态响应进行分析,得出系统的振动和结构噪声特征。
④结合非线性动力学方法对系统动态响应的数值特征进行分析,分析其时间历程曲线、功率谱密度、相轨迹、庞加莱截面、最大Lyapunov指数,揭示其非线性动力学规律。
⑤对船用齿轮箱的固有特性、振动和结构噪声进行实验测试,验证理论分析的正确性,归纳总结出了一套针对大型船用齿轮箱动态特性的分析计算方法。
This project,“Research on common and key technologies of high-speed, heavy-duty, precise mechanical transmission system”(2006BAF01B07-01), belongs to the national science & technology pillar program in the Eleventh Five-year Plan Period of China.
Adapting to the needs for the national major equipments and key projects, the gear transmission tends to be high-speed and heavy-duty and bears low noise and high reliability. The high-speed and heavy-duty mechanical transmission system, presented by the marine reducer, gear box of the gas turbine, gear box of the wind power generation, is one of the important basic components of large-scale machineries and equipments. Its quality directly affects the overall performance and longevity.
Therefore, it is of great significance for China's economic and social development to carry out the research and development on the common and key technologies of high-speed and heavy-duty gear transmission system, to improve the technology of major equipments, to upgrade the international competitiveness of the industry of mechanical transmission components and related equipments.
In the thesis, based on the principles of gear meshing, tooth contact analysis, tribology and heat transfer theory, non-linear system dynamics, by means of theoretical analysis and finite element simulation, the dynamic characteristics of the high-power marine gear box system based on thermo-elastic coupling is studied and verified by tests. The major content is as follows:
①A 3-dimensional finite element model of a coupled gear-rotor-bearing-housing system of a heavy duty marine gearbox is developed. The dynamic characteristics is analyzed and the first 20 orders of natural frequency and mode shape of the marine gearbox under constrained condition are obtained
②The finite element analysis is performed to explore the tooth contact force and deformation in the case of thermo-elastic coupling. The time-varying gear mesh stiffness under the thermo-elastic coupling conditions is gained.
③The dynamic response analysis of the marine gear box system is performed under the influence of the internal excitation, i.e. the time-varying stiffness excitation, transmission error excitation and tooth impact excitation external excitation and the external excitation. The feature of the vibration and noise is obtained.
④Methods of nonlinear dynamics are applied to analyze numerical characteristics of system dynamic response, i.e. time course curves, power spectral density, phase traces and Poincare maps, the maximum Lyapunov exponent, to reveal the principles of non-linear dynamics.
⑤The inherent characteristics, structure vibration and noise of the marine gearbox are tested and the results verify the correctness of the theoretical analysis. Methods of analyzing the dynamic characteristics of a large marine gear box are summarized.
论文基于齿轮啮合原理、轮齿接触分析、摩擦学和传热学、非线性系统动力学,以理论分析、有限元仿真为手段,对基于热弹耦合的大功率船用齿轮箱系统动态特性进行理论分析和实验研究。
论文的主要研究内容如下:
①建立大功率船用齿轮箱齿轮-转子-轴承-箱体耦合三维精细有限元模型,对系统的固有特性进行分析,得到约束情况下船用齿轮箱前20阶固有频率及振型。
②在考虑热弹耦合的基础上,对齿轮接触状态进行有限元分析,研究在热弹耦合情况下轮齿接触力和变形,得出基于热弹耦合工况下齿轮时变啮合刚度。
③在基于热弹耦合的时变刚度激励、误差激励和啮合冲击激励等内部激励和外部激励的影响下,对船用齿轮箱系统动态响应进行分析,得出系统的振动和结构噪声特征。
④结合非线性动力学方法对系统动态响应的数值特征进行分析,分析其时间历程曲线、功率谱密度、相轨迹、庞加莱截面、最大Lyapunov指数,揭示其非线性动力学规律。
⑤对船用齿轮箱的固有特性、振动和结构噪声进行实验测试,验证理论分析的正确性,归纳总结出了一套针对大型船用齿轮箱动态特性的分析计算方法。
This project,“Research on common and key technologies of high-speed, heavy-duty, precise mechanical transmission system”(2006BAF01B07-01), belongs to the national science & technology pillar program in the Eleventh Five-year Plan Period of China.
Adapting to the needs for the national major equipments and key projects, the gear transmission tends to be high-speed and heavy-duty and bears low noise and high reliability. The high-speed and heavy-duty mechanical transmission system, presented by the marine reducer, gear box of the gas turbine, gear box of the wind power generation, is one of the important basic components of large-scale machineries and equipments. Its quality directly affects the overall performance and longevity.
Therefore, it is of great significance for China's economic and social development to carry out the research and development on the common and key technologies of high-speed and heavy-duty gear transmission system, to improve the technology of major equipments, to upgrade the international competitiveness of the industry of mechanical transmission components and related equipments.
In the thesis, based on the principles of gear meshing, tooth contact analysis, tribology and heat transfer theory, non-linear system dynamics, by means of theoretical analysis and finite element simulation, the dynamic characteristics of the high-power marine gear box system based on thermo-elastic coupling is studied and verified by tests. The major content is as follows:
①A 3-dimensional finite element model of a coupled gear-rotor-bearing-housing system of a heavy duty marine gearbox is developed. The dynamic characteristics is analyzed and the first 20 orders of natural frequency and mode shape of the marine gearbox under constrained condition are obtained
②The finite element analysis is performed to explore the tooth contact force and deformation in the case of thermo-elastic coupling. The time-varying gear mesh stiffness under the thermo-elastic coupling conditions is gained.
③The dynamic response analysis of the marine gear box system is performed under the influence of the internal excitation, i.e. the time-varying stiffness excitation, transmission error excitation and tooth impact excitation external excitation and the external excitation. The feature of the vibration and noise is obtained.
④Methods of nonlinear dynamics are applied to analyze numerical characteristics of system dynamic response, i.e. time course curves, power spectral density, phase traces and Poincare maps, the maximum Lyapunov exponent, to reveal the principles of non-linear dynamics.
⑤The inherent characteristics, structure vibration and noise of the marine gearbox are tested and the results verify the correctness of the theoretical analysis. Methods of analyzing the dynamic characteristics of a large marine gear box are summarized.
引文
[1]李润方.齿轮系统动力学[M].北京:科学出版社,1997.
[2]李润方,王建军.齿轮系统动力学[M]—振动·冲击·噪声.北京:科学出版社,1997.
[3] H.N.Ozguven.and D.R.Houser.Mathematical Models Used in Gear Dynamics-A Review[J].Journal of Sound and Vibration,1998,121(3):384~411.
[4]唐定国,陈立明.齿轮传动技术的现状和展望[J].机械工程学报. 1993,20(3):35-41.
[5]王建军.齿轮系统非线性振动研究进展[J].力学进展,2005,35(1):37-47.
[6]王建军,李润方.齿轮系统动力学的理论体系[J].中国机械工程,1998,9(12):55-58.
[7]杨宏斌,邓效忠,高建平,方宗德.齿轮非线性振动研究综述[J].中国机械工程,1999,10(7):807-809.
[8] Kahraman,R.Singh.Interactions Between time-Varying Mesh Stiffness and Clearance Non-linearities in a Geared System[J].Journal of Sound and Vibration,1991,146(1):136-156.
[9] P.Velex,M.Matar.A Mathematieal Model for Analyzing the Influence of Shape Deviations and Mounting Errorson Gear Behavior[J].Journal of Sound and Vibration,1996,(191):629-660.
[10] M.Alnabili,A.Rivola.Dynamie Analysis of Spur Gear Pairs:Steady State Responseand Stability of the SDOF Model with Time Varying Meshing Damping[J].Meehanieal Systems and signal Proeessing,1997,(11):375-390.
[11] G.V.Tordion,R.Gouvin.Dynamie Stability of a Two Stage Gear Train under the Influenee of Variable Meshing Stifness[J].ASME Journal of EngineeringforIndustry,1997,(99):785一791.
[12] Barlam D,Zahavi E.The reliability of solutions in contact problems.Comp and Struct[J],1999,70:35-45.
[13] Y.Cai,T.Hayashi.The Linear Approximated Equation of Vibration of A Pair of Spur Gears-Theory and Experiment[J].Journal of Meehanieal Desi,1994,(116):558-564.
[14] Jean-Pierre de Vaujany.Numerical and Experimental Study of the Loaded Transmission Error of a Spiral Bevel Gear[J].ASME J of Mechanical Design, 2007,129(2):195-201.
[15] Gang Liu,Robert G. Parker.Dynamic Modeling and Analysis of Tooth Profile Modification for Multimesh Gear Vibration[J].ASME J of Mechanical Design, 2008,130(12):402-415.
[16] GOSSELIN C. Simulation and experimental measurement of the transmission error of real hypoid gears under load[J]. ASME J of Mechanical Design, 2000,122(1):109-122.
[17]王统,李伟.齿轮轴三维综合弹性变形和齿向修形曲线的研究[J].上海交通大学学报,1993,27(l):64-71.
[18]王统.用有限元法分析估算弹流润滑正齿轮的体积温度[J].润滑与密封,1986,6(3):64-69.
[19]杨生华,王统.齿轮轮齿变形中的接触有限元仿真分析[J].煤矿机械,1999,8:9-11.
[20]朱坚民,周福章,雷静桃.渐开线斜齿圆柱齿轮弹性变形的三维有限元分析[J].农业机械学报,1998,29(4):113-117.
[21]刘国华.考虑反向齿面啮合力的齿轮系统时变啮合刚度的研究[J].天津工业大学学报,2006,25(6):54-57.
[22]吴俊飞.变厚齿轮轮齿啮合综合刚度确定方法研究[J].青岛化工学院学报(自然科学版),2002,23(1):74-76.
[23]卜忠红,刘更.基于线性规划法的齿轮啮合刚度与载荷分布计算的改进方法[J].机械科学与技术,2008,27(11):1035-1037.
[24]唐进元.线外啮合齿轮传动啮合刚度计算[J].青岛化工学院学报(自然科学版),2002,26(4):22-25.
[25]李瑰贤.舰船用齿轮传动啮合刚度及动态性能研究[J].船舶工程,2000,24(5):41-43.
[26]林腾蛟.斜齿轮的齿面载荷及啮合刚度数值分析[J].机械工艺师,2000,17(10):30-31.
[27]许洪斌.分阶式双渐开线齿轮轮齿刚度的研究[J].重庆大学学报(自然科学版),1999,22(1):116-120.
[28]肖来元,易传云.基于本体温度场的齿轮热弹性变形的综合研究[J].武汉城市建设学院学报,1995,12(4):13-16.
[29]陈万吉.耦合热弹性接触问题有限元分析[J].固体力学学报,1981,(3):326~336.
[30] DeWinter and H.Blok.“Fling-Off Cooling of Gear Teeth”.Journal of Engineering for Industry[J],Transactions of the ASME,Vol.96,No.1,pp60-70, Feb.1974.
[31] Blok H. Theoretical study on temperature rise at surface of actual contact under oiliness lubrication conditions[J]. In: Proceeding of the General Discussion on Lubrication & Lubricants, London,1937,A publication of IME,1937:222-235.
[32] Blok H.Thermal Network for Predicting Bulk Temperature in Gear Transmissions.Proc.7th Round Table Discussion[J],Marin Reduction Gears,Fins pong,Sweden(1995):3-25.
[33] J.C.Jaeger.“Moving Sources of Heat and Temperature at Sliding Contacts”[J].Journal of Proceedings Royal Society of New South Wales,1942.
[34] T.Tobe and M.Kato.“A Study on Flash Temperatures on the Spur Gear Teeth”[J].Transactions of the ASME,Journal of Engineering for Industry,February,1974.
[35] Deng G, Kato M. Initial temperature evaluation for flash temperature index of gear tooth[J]. Transaction of the ASME, Journal of Tribology,1995,117(3):476-481.
[36] Y.Terauchi and H.Mori.“Comparison of Theories and Experiemntal Results for SurfaceTemperature of Spur Gear Teeth”[J].Transactions of the ASME,Journal of Engineering for Industry,February,1974.
[37] K.L.Wang and H.S.Cheng.A Numerical Solution to the Dynamic Load,Film Thickness and Surface Temperatures in Spur Gears,Part I Analysis[J].Transactions of the ASME,Journal of Mechanical Design,Vol.103,January 1981.
[38] N.Patir and H.S.Cheng.“Prediction of the Bulk Temperature in Spur Gears Based on Finite Element Temperature Analysis”[J].The ASLE/ASME Lubrication Conference,PREPRINT NO.77-LC-3B-2,USA,1977.
[39] N.Patir.“Estimate of the Bulk Temperature in Spur Gears Based on Finite Element Temperature Analysis”[J].MSc Degree Thesis, Northwestern University,USA.May,1976.
[40] D.P.Townsend and L.S.Akin.“Analytical and Experimental Spur Gear Tooth Temperature as Affected by Operating Variables”[J].Transactions of the ASME, Journal of Mechanical Design, January,1981, 103.
[41] N.Anifantis and A.D.Dimarogonas.Flash and Bulk temperatures of Gear Teeth Due to Friction[J]. Journal of Mechanical Machine Theory,1993, 28(1).
[42] Anifantis N.Flash and Bulk Temperature of a Spur Gear Tooth due to Friction[J].Mech Mach Theory,1993,28(1):159-164.
[43] R.F.Handschuh and T.P.Kicher.“A Method for Thermal Analysis of Spiral Bevel Gears”[J].Transactions of the ASME,Journal of Mechanical Design,Vol.118,December 1996.
[44] Ebubekir Atan. On the prediction of the design criteria for modification of contact stresses due to thermal stresses in the gear mesh[J].Tribology International,2005,38(3):227-233.
[45] Murat Taburdagitan, Metin Akkok. Determination of surface temperature rise with thermo-elastic analysis of spur gears[J].Wear,2006,261(2):656–665
[46]李绍彬.基于热弹变形的圆柱齿轮理想修形曲线[J].中国机械工程,2003,14(14):1175-1179.
[47]龙慧.旋转齿轮瞬时接触应力和温度的分析模拟[J].机械工程学报,2004,40(8):24-29.
[48]赵宁.双圆弧齿轮传动系统失油润滑瞬态热分析[J].计算机仿真,2008,25(7):77-81.
[49]赵宁.基于热弹耦合的双圆弧齿轮接触特性研究[J].机床与液压,2008,36(1):37-40.
[50]刘辉,吴昌林.全工况下斜齿轮轮齿动态温度场的研究[J].华中理工大学学报,1998,26(3):41-43.
[51]邱良恒,辛一行.齿轮本体温度场和热变形修形计算[J].上海交通大学学报,1995,29(2):79-86.
[52]陶燕光,黎上威.高速齿轮热变形修形的实验研究[J].齿轮,1988,12(2):25-28.
[53]朱才朝.环式减速器发热问题分析.重庆大学学报[J]. 2001,24(2):5-8.
[54]李润方,汤庆平.运转过程中轮齿耦合热弹性接触有限元分析[J].齿轮,Vol.13,No.1,1989.
[55]李润方,黎豫生.耦合热弹性接触有限元法及其在齿轮传动中的应用[J].重庆大学学报,1993,(1):96-101.
[56]李润方.关于有摩擦的弹塑性接触问题的有限元分析[J].重庆大学学报,1987,(3):47-53.
[57] Kahaman. Effect of Axial Vibrations on the Dynamic of Helical Gear Pairs[J]. ASME Journal of Vibration andAcoustics, 1993, 115(1):33-38.
[58] Kahaman. Dynamic Analysis of a Multi-Mesh Helical Gear Train[J]. ASME Journal of Mechanical Design, 1994, 116(1):706-712.
[59] Kahaman. Planetary Gear Train Dynamics[J]. ASME Journal of Mechanical Design, 1994 116(1):713-720.
[60] Kahaman.Dynamic Analysis of Geared Rotors by Finite Elements.Proc.Inter[J].Power Transmission and Gearing Conference,1989:375-382.
[61] H.Vinayak,R.Singh.Dynamic analysis of Flexible Gears for High Power Density Transmissions[J].Proc.Inter Gearing’94,1994:105-110.
[62] J.S.Burdess,J.A.Pennell,J.Rosinski.Development of a New Three-dimensional Dynamic Model of Helical Gears[J].Proc.Inter Gearing’94,1994:517-524.
[63] R.L.Robert,P.Papadopoulos.On a Finite Element Method for Dynamic Contact/Impact Problems[J].Int.J.Numer.Meht.Engng.1993,36:2123-2140.
[64] W.H.Chen,J.T.Yen.Three-dimensional Finite Element Analysis of Static and Dynamic Contact Problems with Friction[J].Computer and Structures,1990,35(5):541-552.
[65] Shaofeng Wang,K.Umezawa,H.Houjoh,S.Matsumura.A Analytical Investigation of the Dynamic Behavior of a Helical Gear system[J].ASME Power Transmission and Gearing Conference,1996(88):169-176.
[66] Lida H,Tamura A.Coupled torsional-flexural vibration of shaft in a geared system[J]. In:Proc Conf Vibr Rotation Mesh, Institution of Mechanical Engineers,1984.67-72.
[67] Hochmann D.Friction force excitation in spur and helical involute parallel axis gearing.[D]:The Ohio State Univ,Columbus,OH,1997.
[68] K.Umezawa.Vibration of Power Transmission Helical Gear with Narrow Face-width[J].ASME paper,1984,84-det-159.
[69] K.Umezawa.The developed simulator and the performance diagrams for the vibration of helical gear[J].Proc.Inter.Conf.On Gears,Zhengzhou,China,1988:659~662.
[70] K.Umezawa,Ajima T,Houjoph H,Vibrations of three axis geared systems[J]. Bull JSME,1986,29:950-957.
[71] P.Velex,M.Maatar et al.Some Numerical Methods for the Simulation of Geared Transmission Dynamic Behavior formulation and Assessment[J].ASME Power Transmission and Gearing Conference,1996(88):29-38.
[72] P.Velex,Saada A.A model for the dynamic behavior of multi-stage geared systems[J]. In:Proc 8th Inter Federation theory Mach Mech World Congress,Prague,2,1991.621-625.
[73] Parker R G, Agashe V, Vijayakar S M.Dynamic response of planetary geared system using a finite element/contact mechanics model[J]. ASME Mech Design ,2000,122:305-311.
[74] Haruo Houjoh,Kiyouhicko Umezawa,Shigeki Matsumura.Vibration Analysis for a pair of Helical Gears Mounted on Elastic Shafts[J].ASME Power Transmission and Gearing Conference, Vol.88,1996:501-508.
[75] H.Houjoh,K.Umezawa,S.Matsumura.Vibration Analysis of a Pair of Helical Gears Mounted on Elastic Shafts[J].ASME Power Transmission and Gearing Conference,1996(88):501-508
[76] Bard,D.Remond,D.Play.Dynamic Transmission Error of Cylindrical Gears Comparison of Experimental Measurement and Numerical Calculation[J].ASME Power Transmission and Gearing Conference,1996(88):519-526.
[77]沈允文,李树庭,蔺天存.齿轮系统减振设计的结构灵敏度分析[J].机械工程学报,1996,32(5):13-18.
[78]李树庭,沈允文,蔺天存.航空齿轮的动态设计[J].航空学报,1994,15(8):937-941.
[79]崔博文,沈允文,刘更,段晓革.航空齿轮系统的动态特性分析[J].机械科学与技术1997,16(2):271-274.
[80]孙涛,沈允文,孙智民,刘继岩.行星齿轮传动非线性动力学模型与方程[J].机械工程学报,2002,38(3):6-10.
[81]李润方.齿轮啮合内部动态激励数值模拟[J].机械传动,2001,25(2):1-3.
[82]李润方,韩西,林腾蛟.齿轮系统耦合振动的理论分析与实验研究[J].机械工程学报,2000,36(6):79-81.
[83]王建军,李润方.齿轮系统的转子耦合型振动[J].机械科学与技术,1996,15(2):231-233.
[84]王建军,李润方.齿轮系统参数振动问题研究综述[J].振动与冲击,1997(4):69-73.
[85]朱才朝.两级同轴环式减速机动态特性的研究[J].农业机械学报,2006,37(1):124-128
[86]朱才朝.风力发电齿轮箱系统耦合非线性动态特性的研究[J].机械工程学报,2005,41(8):203-207.
[87]韩西,李润方,林腾蛟,陶泽光.齿轮轴横向弯曲振动结合部参数识别[J].机械设计与研究,2000(2):31-33.
[88]邵忍平,沈允文,孙进才.齿轮减速器系统可变固有特性动力学研究[J].航空学报,200122(1):64-68.
[89]林腾蛟.同轴双输出行星减速器振动分析及噪声预估[J].重庆大学学报(自然与科学版),2007,30(11):1-4.
[90]林腾蛟,李润方,陶泽光.齿轮传动三维间隙非线性冲击-动力接触特性数值仿真[J].机械工程学报,2000,36(6):55-58.
[91]王立华.高速重载齿轮的有限元分析[J].中国机械工程,2003,14(20):1773-1777.
[92]王立华.斜齿圆柱齿轮传动系统的耦合振动分析[J].机械设计与研究,2002,18(5):30-32
[93] K.Nakamura.Tooth Separations and Abnormal Noise on Power-Transmission Gears[J].Bulletin of JSME,1967(10),846-854.
[94] R.J.Comparin,R.Singh.Nonlinear Frequency Response Characteristics of an Impact Pair[J]. Journal of Sound and Vibration,1989,134:259-290.
[95] Kahaman,R.Singh.Non-linear Dynamic of a Spur Gear Pair[J].Journal of Sound and Vibration, 1990,142(1):49-75.
[96] Kahaman,R.Singh.Non-linear Dynamic of a Geared Rotor-bearing System with Multiple Clearances[J].Journal of Sound and Vibration,1991,144(3):469-506.
[97] Raghothama,S.Narayanan.Bifurcation and Chaos in Geared Rotor-bearing System by Incremental harmonic Balance Method[J].Journal of Sound and Vibration,1999,226(3):469-492.
[98] Raghothama A,Narayanan S. Bifurcation and chaos in geared rotor bearing system by incremental harmonic balance method[J]. J sound vib,1999,226(3):469-492.
[99] Al-shyyab.A, Kahraman A.non-linear Dynamic Analysis of A Multi-mesh Gear Train Using Multi-Term Harmonic Balance Method:sub-harmonic Motions[J].Journal of Sound and Vibration,2005,279:417-451.
[100] G.W.Blankenship,A.Kahaman.Steady State forced Response of a Mechanical Oscillator with Combined Parametric Excitation and Clearance type Non-linearity[J].Journal of Sound and Vibration,1995,185(5):742-765.
[101] G.W.Blankenship,R.Singh.Analytical Solution for Modulation Sidebands Associated with a class of Mechanical Oscillators[J].Journal of Sound and Vibration,1995,179(1):13-16.
[102] Kahraman A,Blankenship G W.Interactions between commensurate parametric and forcing excitations in a system with clearance [J]. J Sound Vib,1996,194(3):317-336.
[103] Kahraman A,Blankenship G W. Experiments on nonlinear dynamic behavior of an oscillator with clearance and periodically time-varying parameters[J]. ASME Appl Mech,1997,64:217-226.
[104] C.W.Wong,W.S.Zhang,S.L.Lau,Periodic Forced Vibration of Unsymmertrical Piecewise Linear System by Incremental Harmonic Balance Method[J].Journal of Sound andVibration,1991,149,91-105.
[105] S.L.Lau, W.S.Zhang.Nonlinear Vibrations of Piecewise Linear Systems by Incremental Harmonic Balance Method[J], Journal of Sound and Vibration,1992,59,153-160.
[106] R.J.Comparin,R.Singh.Nonlinear Frequency Response Characteristics of an Impact Pair[J]. Journal of Sound and Vibration,1989,131:177-196.
[107] Blankenship G W, R.Singh.A New Gear Mesh Interface Dynamic Model to Predict Multi-Dimensional Force Couping and Excitation[J].Mesh.Mach.Theory,1995,30(1):43-47.
[108] Kahraman A,Blankenship G W.Dynamice analysis of a multi-mesh helical gear train[J],ASME J.Mech.Des.1994,116:706-712.
[109]孙涛,胡海岩.基于离散博里叶变换与谐波平衡法的行星齿轮系统非线性动力学分析[J].机械工程学报,2002, 38(11) :58-61.
[110]孙智民,季林红,沈允文,常辉兰.齿侧间隙对星型齿轮传动扭振特性的影响研究[J].机械设计,2003,20(2):3-7.
[111]孙智民,沈允文,王三民,李华.星形齿轮传动系统分岔与混沌的研究[J].机械工程学报. 2001, 37(12) :11-15.
[112]张锁怀.用谐波平衡法分析齿轮耦合的转子—轴承系统的动力特性[J].机械工程学报,2000,36(7):18-22.
[113]张锁怀.单级齿轮系统的拍击振动模型[J].机械工程学报,2002,38(12):16-20.
[114]张锁怀.齿轮时变系统的强迫振动[J].中国机械工程,2005,16(8):723-727.
[115]张锁怀.用AOM研究强非线性齿轮系统动力学问题[J].中国机械工程,2005,40(12):20-30.
[116]张锁怀.齿轮耦合的转子—轴承系统非线性动力特性的研究[J].机械工程学报,2001,37(9):53-58.
[117]刘梦军.单级齿轮非线性系统吸引子的数值特性研究[J].机械工程学报,2003,39(10):111-116.
[118]刘梦军.随机外激励下齿轮非线性系统的全局分析[J].中国机械工程,2004,15(13):1182-1185.
[119]陈学森,董海军.含时变啮合刚度的间隙非线性齿轮系统的混沌控制[J].机械科学与技术,2006,25(9):607-610.
[120]李华,沈允文,刘梦军,孙智民.用Lyapunov指数研究单对齿轮间隙非线性系统的动力学行为[J].中国机械工程,2002,13(12):1040-1044.
[121]王三民,沈允文,董海军.含摩擦和间隙直齿轮副的混沌与分又研究[J].机械工程学报,2002,38(9):8-11.
[122]王立华,李润方,林腾蛟等.齿轮系统时变刚度和间隙非线性振动特性研究[J].中国机械工程,2003,14(13):1143-1146.
[123]王玉新.考虑啮合时变刚度和传递误差的齿轮振动分析[J].机械传动,2002,20(1):5-8
[124] Maynard,K.P,1997,Interstitial Processing:The Application of Noise Processing to Gear Fault Detection,International Conference on Condition Monitoring,University of Wales[J],Swansea,UK,12th-16th,April 1999.
[125] Maynard,K.P.Interstitial Processing:The Application of Noise Processing to Gear Fault Detection.Proceedings of the International Conference on Condition Monitoring[J],University of Wales Swansea,U K,12th-16th April 1999,pp.77-86.
[126] Deng G,Kato M. Initial temperature evaluation for flash temperature index of gear tooth[J]. Transaction of the ASME, Journal of Tribology,1995,117(3):476-481.
[127] T.Tobe and M.Kato.“A Study on Flash Temperatures on the Spur Gear Teeth”[J].Transactions of the ASME,Journal of Engineering for Industry,February,1974.
[128] L.D.Mitchell and J.WDaws. Proposed Solution Methodology for the Dynamically Coupled Nonlinear Gear Rotor Mechanics Equation[J]. ASME Vib. Acous. Stress Rehab. Des, 1985, (107):112-116.
[129] L.D.Mitchell and J.W Daws .A Basic Approach to Gearbox Noise Prediction[J]. Traps. Of the SEA,1991:3366-3379.
[130] R.D.Ciskowski,C.A.Brebbia,Boundary Element Methods in Acoustics[M].mputational Mechanics Publications, Southampton Boston, 1991.
[131] Haruo Houjoh et al, Sound Field Assessment by Measurement of Sound Pressure Distribution Close to Machine Noise Source[J], JSME International Journal, Series C, Vol. 40, No. 4, 1997:607-615.
[132]何韫如,宋福堂.齿轮与齿轮箱振动噪声机理分析及控制[J].振动、测试与诊断,1998.18(3).P221-226.
[133]李凯岭.渐开线齿轮不同形式齿廓偏差对齿轮噪声的影响[J].机械工程学报,2008,44(3):234-240.
[134] Chen Lixin,Jung Xiaoyu.Prediction of Vibration and Noise of Gearbox[J]. Chinese Journal of Mechanical Engineering, 1991, 6(4): 257-260.
[135]吴晓如,杨浩广等.强背景噪声下声信号的测量[J].中国科学技术大学学报.1999.29(6). 696-701.
[136]李连进,张维屏.降低齿轮箱噪声的一种途径[J].东北工学院学报, 1989, 10(4):439-444.
[137]刘佳才.低噪声柴油机基本结构参数的选择[J].内燃机学报, 1996, 14(2): 154-159.
[138]朱才朝.三环减速器表面噪声的实验[J].重庆大学学报.2000,23(4):18-21.
[139]邵忍平.齿轮传动振动噪声计算的Kato方法[J].机械,2002,29(3):12-14.
[140]邵忍平.齿轮啮合冲击噪声的定量预估.机械科学与技术[J],2001,20(3):340-344.
[141]陶泽光,官德娟,朵丽霞.齿轮传动噪声的描述和比较[J].昆明理工大学学报.1998.23(6). 53-61.
[142] T. A. Harris. Rolling Bearing Analysis(4th edition) [M]. New York : John Wiley and Sons,Inc. 2001.
[143]陆金铭.扭矩法诊断柴油机动力装置故障[J].振动、测试与诊断,2002,22(2):142~146.
[144]陈忠.滚动轴承及其支承的刚度计算[J].煤矿机械.2006,27(3):387~388.
[145]吕金虎.混沌时间序列分析及其应用[M].武汉:武汉大学出版社,2005.
[146] F Takens. Detecting strange attractors in fluent turbulence[J].Lecture Notes in Mathematics,1981,898:366-381.
[147] H. S. Kim, R. Eykholt, J. D. Salas. Nonlinear dynamics, delay times, and embedding windows [J]. Physica D, 1999, 48–60.
[148] A.Wolf J.B.Swift, H.L.Swinney and J.A.Vastano. Determining Lyapunov exponents from a time series[D]. Physica 16D, 1985, 285~317.
[149] M.T.Rosenstein, J.J.Collins and C.J.De luca. A practical method for calculating largest Lyapunov exponents from small data sets[D], Physica D, 1993, 65: 117-134.
[150]陶泽光.齿轮系统有限元模态分析[J].机械设计与研究,2000,28(3):45-46.
[151]杨成云.中心传动齿轮箱体固有特性研究[J].机械设计与制造工程,2002,31(4):26-28.
[152]王基.某型船用传动齿轮箱振动模态的实验与分析[J].海军工程大学学报,2007,19(2):55-59.
[153]龙慧.高速齿轮传动轮齿的温度模拟及过程参数的敏感性分析[D],重庆:重庆大学,2001.
[154]杨大地,涂光裕.数值分析[M].重庆:重庆大学出版社,1997.
[155]李德葆,陆秋海著.实验模态分析及其应用[M].北京:科学出版社,2001.
[156]沃德·海伦,斯蒂芬·拉门兹,波尔·萨斯著,白化同,郭继忠译.模态分析理论与实验[M].北京:北京理工大学出版社,2000.
[157]李绍彬.高速重载齿轮传动热弹变形及非线性耦合动力学研究[D],重庆:重庆大学,2004.
[158]杨成云.齿轮传动系统耦合振动响应及抗冲击性能研究[D],重庆:重庆大学,2006.
[2]李润方,王建军.齿轮系统动力学[M]—振动·冲击·噪声.北京:科学出版社,1997.
[3] H.N.Ozguven.and D.R.Houser.Mathematical Models Used in Gear Dynamics-A Review[J].Journal of Sound and Vibration,1998,121(3):384~411.
[4]唐定国,陈立明.齿轮传动技术的现状和展望[J].机械工程学报. 1993,20(3):35-41.
[5]王建军.齿轮系统非线性振动研究进展[J].力学进展,2005,35(1):37-47.
[6]王建军,李润方.齿轮系统动力学的理论体系[J].中国机械工程,1998,9(12):55-58.
[7]杨宏斌,邓效忠,高建平,方宗德.齿轮非线性振动研究综述[J].中国机械工程,1999,10(7):807-809.
[8] Kahraman,R.Singh.Interactions Between time-Varying Mesh Stiffness and Clearance Non-linearities in a Geared System[J].Journal of Sound and Vibration,1991,146(1):136-156.
[9] P.Velex,M.Matar.A Mathematieal Model for Analyzing the Influence of Shape Deviations and Mounting Errorson Gear Behavior[J].Journal of Sound and Vibration,1996,(191):629-660.
[10] M.Alnabili,A.Rivola.Dynamie Analysis of Spur Gear Pairs:Steady State Responseand Stability of the SDOF Model with Time Varying Meshing Damping[J].Meehanieal Systems and signal Proeessing,1997,(11):375-390.
[11] G.V.Tordion,R.Gouvin.Dynamie Stability of a Two Stage Gear Train under the Influenee of Variable Meshing Stifness[J].ASME Journal of EngineeringforIndustry,1997,(99):785一791.
[12] Barlam D,Zahavi E.The reliability of solutions in contact problems.Comp and Struct[J],1999,70:35-45.
[13] Y.Cai,T.Hayashi.The Linear Approximated Equation of Vibration of A Pair of Spur Gears-Theory and Experiment[J].Journal of Meehanieal Desi,1994,(116):558-564.
[14] Jean-Pierre de Vaujany.Numerical and Experimental Study of the Loaded Transmission Error of a Spiral Bevel Gear[J].ASME J of Mechanical Design, 2007,129(2):195-201.
[15] Gang Liu,Robert G. Parker.Dynamic Modeling and Analysis of Tooth Profile Modification for Multimesh Gear Vibration[J].ASME J of Mechanical Design, 2008,130(12):402-415.
[16] GOSSELIN C. Simulation and experimental measurement of the transmission error of real hypoid gears under load[J]. ASME J of Mechanical Design, 2000,122(1):109-122.
[17]王统,李伟.齿轮轴三维综合弹性变形和齿向修形曲线的研究[J].上海交通大学学报,1993,27(l):64-71.
[18]王统.用有限元法分析估算弹流润滑正齿轮的体积温度[J].润滑与密封,1986,6(3):64-69.
[19]杨生华,王统.齿轮轮齿变形中的接触有限元仿真分析[J].煤矿机械,1999,8:9-11.
[20]朱坚民,周福章,雷静桃.渐开线斜齿圆柱齿轮弹性变形的三维有限元分析[J].农业机械学报,1998,29(4):113-117.
[21]刘国华.考虑反向齿面啮合力的齿轮系统时变啮合刚度的研究[J].天津工业大学学报,2006,25(6):54-57.
[22]吴俊飞.变厚齿轮轮齿啮合综合刚度确定方法研究[J].青岛化工学院学报(自然科学版),2002,23(1):74-76.
[23]卜忠红,刘更.基于线性规划法的齿轮啮合刚度与载荷分布计算的改进方法[J].机械科学与技术,2008,27(11):1035-1037.
[24]唐进元.线外啮合齿轮传动啮合刚度计算[J].青岛化工学院学报(自然科学版),2002,26(4):22-25.
[25]李瑰贤.舰船用齿轮传动啮合刚度及动态性能研究[J].船舶工程,2000,24(5):41-43.
[26]林腾蛟.斜齿轮的齿面载荷及啮合刚度数值分析[J].机械工艺师,2000,17(10):30-31.
[27]许洪斌.分阶式双渐开线齿轮轮齿刚度的研究[J].重庆大学学报(自然科学版),1999,22(1):116-120.
[28]肖来元,易传云.基于本体温度场的齿轮热弹性变形的综合研究[J].武汉城市建设学院学报,1995,12(4):13-16.
[29]陈万吉.耦合热弹性接触问题有限元分析[J].固体力学学报,1981,(3):326~336.
[30] DeWinter and H.Blok.“Fling-Off Cooling of Gear Teeth”.Journal of Engineering for Industry[J],Transactions of the ASME,Vol.96,No.1,pp60-70, Feb.1974.
[31] Blok H. Theoretical study on temperature rise at surface of actual contact under oiliness lubrication conditions[J]. In: Proceeding of the General Discussion on Lubrication & Lubricants, London,1937,A publication of IME,1937:222-235.
[32] Blok H.Thermal Network for Predicting Bulk Temperature in Gear Transmissions.Proc.7th Round Table Discussion[J],Marin Reduction Gears,Fins pong,Sweden(1995):3-25.
[33] J.C.Jaeger.“Moving Sources of Heat and Temperature at Sliding Contacts”[J].Journal of Proceedings Royal Society of New South Wales,1942.
[34] T.Tobe and M.Kato.“A Study on Flash Temperatures on the Spur Gear Teeth”[J].Transactions of the ASME,Journal of Engineering for Industry,February,1974.
[35] Deng G, Kato M. Initial temperature evaluation for flash temperature index of gear tooth[J]. Transaction of the ASME, Journal of Tribology,1995,117(3):476-481.
[36] Y.Terauchi and H.Mori.“Comparison of Theories and Experiemntal Results for SurfaceTemperature of Spur Gear Teeth”[J].Transactions of the ASME,Journal of Engineering for Industry,February,1974.
[37] K.L.Wang and H.S.Cheng.A Numerical Solution to the Dynamic Load,Film Thickness and Surface Temperatures in Spur Gears,Part I Analysis[J].Transactions of the ASME,Journal of Mechanical Design,Vol.103,January 1981.
[38] N.Patir and H.S.Cheng.“Prediction of the Bulk Temperature in Spur Gears Based on Finite Element Temperature Analysis”[J].The ASLE/ASME Lubrication Conference,PREPRINT NO.77-LC-3B-2,USA,1977.
[39] N.Patir.“Estimate of the Bulk Temperature in Spur Gears Based on Finite Element Temperature Analysis”[J].MSc Degree Thesis, Northwestern University,USA.May,1976.
[40] D.P.Townsend and L.S.Akin.“Analytical and Experimental Spur Gear Tooth Temperature as Affected by Operating Variables”[J].Transactions of the ASME, Journal of Mechanical Design, January,1981, 103.
[41] N.Anifantis and A.D.Dimarogonas.Flash and Bulk temperatures of Gear Teeth Due to Friction[J]. Journal of Mechanical Machine Theory,1993, 28(1).
[42] Anifantis N.Flash and Bulk Temperature of a Spur Gear Tooth due to Friction[J].Mech Mach Theory,1993,28(1):159-164.
[43] R.F.Handschuh and T.P.Kicher.“A Method for Thermal Analysis of Spiral Bevel Gears”[J].Transactions of the ASME,Journal of Mechanical Design,Vol.118,December 1996.
[44] Ebubekir Atan. On the prediction of the design criteria for modification of contact stresses due to thermal stresses in the gear mesh[J].Tribology International,2005,38(3):227-233.
[45] Murat Taburdagitan, Metin Akkok. Determination of surface temperature rise with thermo-elastic analysis of spur gears[J].Wear,2006,261(2):656–665
[46]李绍彬.基于热弹变形的圆柱齿轮理想修形曲线[J].中国机械工程,2003,14(14):1175-1179.
[47]龙慧.旋转齿轮瞬时接触应力和温度的分析模拟[J].机械工程学报,2004,40(8):24-29.
[48]赵宁.双圆弧齿轮传动系统失油润滑瞬态热分析[J].计算机仿真,2008,25(7):77-81.
[49]赵宁.基于热弹耦合的双圆弧齿轮接触特性研究[J].机床与液压,2008,36(1):37-40.
[50]刘辉,吴昌林.全工况下斜齿轮轮齿动态温度场的研究[J].华中理工大学学报,1998,26(3):41-43.
[51]邱良恒,辛一行.齿轮本体温度场和热变形修形计算[J].上海交通大学学报,1995,29(2):79-86.
[52]陶燕光,黎上威.高速齿轮热变形修形的实验研究[J].齿轮,1988,12(2):25-28.
[53]朱才朝.环式减速器发热问题分析.重庆大学学报[J]. 2001,24(2):5-8.
[54]李润方,汤庆平.运转过程中轮齿耦合热弹性接触有限元分析[J].齿轮,Vol.13,No.1,1989.
[55]李润方,黎豫生.耦合热弹性接触有限元法及其在齿轮传动中的应用[J].重庆大学学报,1993,(1):96-101.
[56]李润方.关于有摩擦的弹塑性接触问题的有限元分析[J].重庆大学学报,1987,(3):47-53.
[57] Kahaman. Effect of Axial Vibrations on the Dynamic of Helical Gear Pairs[J]. ASME Journal of Vibration andAcoustics, 1993, 115(1):33-38.
[58] Kahaman. Dynamic Analysis of a Multi-Mesh Helical Gear Train[J]. ASME Journal of Mechanical Design, 1994, 116(1):706-712.
[59] Kahaman. Planetary Gear Train Dynamics[J]. ASME Journal of Mechanical Design, 1994 116(1):713-720.
[60] Kahaman.Dynamic Analysis of Geared Rotors by Finite Elements.Proc.Inter[J].Power Transmission and Gearing Conference,1989:375-382.
[61] H.Vinayak,R.Singh.Dynamic analysis of Flexible Gears for High Power Density Transmissions[J].Proc.Inter Gearing’94,1994:105-110.
[62] J.S.Burdess,J.A.Pennell,J.Rosinski.Development of a New Three-dimensional Dynamic Model of Helical Gears[J].Proc.Inter Gearing’94,1994:517-524.
[63] R.L.Robert,P.Papadopoulos.On a Finite Element Method for Dynamic Contact/Impact Problems[J].Int.J.Numer.Meht.Engng.1993,36:2123-2140.
[64] W.H.Chen,J.T.Yen.Three-dimensional Finite Element Analysis of Static and Dynamic Contact Problems with Friction[J].Computer and Structures,1990,35(5):541-552.
[65] Shaofeng Wang,K.Umezawa,H.Houjoh,S.Matsumura.A Analytical Investigation of the Dynamic Behavior of a Helical Gear system[J].ASME Power Transmission and Gearing Conference,1996(88):169-176.
[66] Lida H,Tamura A.Coupled torsional-flexural vibration of shaft in a geared system[J]. In:Proc Conf Vibr Rotation Mesh, Institution of Mechanical Engineers,1984.67-72.
[67] Hochmann D.Friction force excitation in spur and helical involute parallel axis gearing.[D]:The Ohio State Univ,Columbus,OH,1997.
[68] K.Umezawa.Vibration of Power Transmission Helical Gear with Narrow Face-width[J].ASME paper,1984,84-det-159.
[69] K.Umezawa.The developed simulator and the performance diagrams for the vibration of helical gear[J].Proc.Inter.Conf.On Gears,Zhengzhou,China,1988:659~662.
[70] K.Umezawa,Ajima T,Houjoph H,Vibrations of three axis geared systems[J]. Bull JSME,1986,29:950-957.
[71] P.Velex,M.Maatar et al.Some Numerical Methods for the Simulation of Geared Transmission Dynamic Behavior formulation and Assessment[J].ASME Power Transmission and Gearing Conference,1996(88):29-38.
[72] P.Velex,Saada A.A model for the dynamic behavior of multi-stage geared systems[J]. In:Proc 8th Inter Federation theory Mach Mech World Congress,Prague,2,1991.621-625.
[73] Parker R G, Agashe V, Vijayakar S M.Dynamic response of planetary geared system using a finite element/contact mechanics model[J]. ASME Mech Design ,2000,122:305-311.
[74] Haruo Houjoh,Kiyouhicko Umezawa,Shigeki Matsumura.Vibration Analysis for a pair of Helical Gears Mounted on Elastic Shafts[J].ASME Power Transmission and Gearing Conference, Vol.88,1996:501-508.
[75] H.Houjoh,K.Umezawa,S.Matsumura.Vibration Analysis of a Pair of Helical Gears Mounted on Elastic Shafts[J].ASME Power Transmission and Gearing Conference,1996(88):501-508
[76] Bard,D.Remond,D.Play.Dynamic Transmission Error of Cylindrical Gears Comparison of Experimental Measurement and Numerical Calculation[J].ASME Power Transmission and Gearing Conference,1996(88):519-526.
[77]沈允文,李树庭,蔺天存.齿轮系统减振设计的结构灵敏度分析[J].机械工程学报,1996,32(5):13-18.
[78]李树庭,沈允文,蔺天存.航空齿轮的动态设计[J].航空学报,1994,15(8):937-941.
[79]崔博文,沈允文,刘更,段晓革.航空齿轮系统的动态特性分析[J].机械科学与技术1997,16(2):271-274.
[80]孙涛,沈允文,孙智民,刘继岩.行星齿轮传动非线性动力学模型与方程[J].机械工程学报,2002,38(3):6-10.
[81]李润方.齿轮啮合内部动态激励数值模拟[J].机械传动,2001,25(2):1-3.
[82]李润方,韩西,林腾蛟.齿轮系统耦合振动的理论分析与实验研究[J].机械工程学报,2000,36(6):79-81.
[83]王建军,李润方.齿轮系统的转子耦合型振动[J].机械科学与技术,1996,15(2):231-233.
[84]王建军,李润方.齿轮系统参数振动问题研究综述[J].振动与冲击,1997(4):69-73.
[85]朱才朝.两级同轴环式减速机动态特性的研究[J].农业机械学报,2006,37(1):124-128
[86]朱才朝.风力发电齿轮箱系统耦合非线性动态特性的研究[J].机械工程学报,2005,41(8):203-207.
[87]韩西,李润方,林腾蛟,陶泽光.齿轮轴横向弯曲振动结合部参数识别[J].机械设计与研究,2000(2):31-33.
[88]邵忍平,沈允文,孙进才.齿轮减速器系统可变固有特性动力学研究[J].航空学报,200122(1):64-68.
[89]林腾蛟.同轴双输出行星减速器振动分析及噪声预估[J].重庆大学学报(自然与科学版),2007,30(11):1-4.
[90]林腾蛟,李润方,陶泽光.齿轮传动三维间隙非线性冲击-动力接触特性数值仿真[J].机械工程学报,2000,36(6):55-58.
[91]王立华.高速重载齿轮的有限元分析[J].中国机械工程,2003,14(20):1773-1777.
[92]王立华.斜齿圆柱齿轮传动系统的耦合振动分析[J].机械设计与研究,2002,18(5):30-32
[93] K.Nakamura.Tooth Separations and Abnormal Noise on Power-Transmission Gears[J].Bulletin of JSME,1967(10),846-854.
[94] R.J.Comparin,R.Singh.Nonlinear Frequency Response Characteristics of an Impact Pair[J]. Journal of Sound and Vibration,1989,134:259-290.
[95] Kahaman,R.Singh.Non-linear Dynamic of a Spur Gear Pair[J].Journal of Sound and Vibration, 1990,142(1):49-75.
[96] Kahaman,R.Singh.Non-linear Dynamic of a Geared Rotor-bearing System with Multiple Clearances[J].Journal of Sound and Vibration,1991,144(3):469-506.
[97] Raghothama,S.Narayanan.Bifurcation and Chaos in Geared Rotor-bearing System by Incremental harmonic Balance Method[J].Journal of Sound and Vibration,1999,226(3):469-492.
[98] Raghothama A,Narayanan S. Bifurcation and chaos in geared rotor bearing system by incremental harmonic balance method[J]. J sound vib,1999,226(3):469-492.
[99] Al-shyyab.A, Kahraman A.non-linear Dynamic Analysis of A Multi-mesh Gear Train Using Multi-Term Harmonic Balance Method:sub-harmonic Motions[J].Journal of Sound and Vibration,2005,279:417-451.
[100] G.W.Blankenship,A.Kahaman.Steady State forced Response of a Mechanical Oscillator with Combined Parametric Excitation and Clearance type Non-linearity[J].Journal of Sound and Vibration,1995,185(5):742-765.
[101] G.W.Blankenship,R.Singh.Analytical Solution for Modulation Sidebands Associated with a class of Mechanical Oscillators[J].Journal of Sound and Vibration,1995,179(1):13-16.
[102] Kahraman A,Blankenship G W.Interactions between commensurate parametric and forcing excitations in a system with clearance [J]. J Sound Vib,1996,194(3):317-336.
[103] Kahraman A,Blankenship G W. Experiments on nonlinear dynamic behavior of an oscillator with clearance and periodically time-varying parameters[J]. ASME Appl Mech,1997,64:217-226.
[104] C.W.Wong,W.S.Zhang,S.L.Lau,Periodic Forced Vibration of Unsymmertrical Piecewise Linear System by Incremental Harmonic Balance Method[J].Journal of Sound andVibration,1991,149,91-105.
[105] S.L.Lau, W.S.Zhang.Nonlinear Vibrations of Piecewise Linear Systems by Incremental Harmonic Balance Method[J], Journal of Sound and Vibration,1992,59,153-160.
[106] R.J.Comparin,R.Singh.Nonlinear Frequency Response Characteristics of an Impact Pair[J]. Journal of Sound and Vibration,1989,131:177-196.
[107] Blankenship G W, R.Singh.A New Gear Mesh Interface Dynamic Model to Predict Multi-Dimensional Force Couping and Excitation[J].Mesh.Mach.Theory,1995,30(1):43-47.
[108] Kahraman A,Blankenship G W.Dynamice analysis of a multi-mesh helical gear train[J],ASME J.Mech.Des.1994,116:706-712.
[109]孙涛,胡海岩.基于离散博里叶变换与谐波平衡法的行星齿轮系统非线性动力学分析[J].机械工程学报,2002, 38(11) :58-61.
[110]孙智民,季林红,沈允文,常辉兰.齿侧间隙对星型齿轮传动扭振特性的影响研究[J].机械设计,2003,20(2):3-7.
[111]孙智民,沈允文,王三民,李华.星形齿轮传动系统分岔与混沌的研究[J].机械工程学报. 2001, 37(12) :11-15.
[112]张锁怀.用谐波平衡法分析齿轮耦合的转子—轴承系统的动力特性[J].机械工程学报,2000,36(7):18-22.
[113]张锁怀.单级齿轮系统的拍击振动模型[J].机械工程学报,2002,38(12):16-20.
[114]张锁怀.齿轮时变系统的强迫振动[J].中国机械工程,2005,16(8):723-727.
[115]张锁怀.用AOM研究强非线性齿轮系统动力学问题[J].中国机械工程,2005,40(12):20-30.
[116]张锁怀.齿轮耦合的转子—轴承系统非线性动力特性的研究[J].机械工程学报,2001,37(9):53-58.
[117]刘梦军.单级齿轮非线性系统吸引子的数值特性研究[J].机械工程学报,2003,39(10):111-116.
[118]刘梦军.随机外激励下齿轮非线性系统的全局分析[J].中国机械工程,2004,15(13):1182-1185.
[119]陈学森,董海军.含时变啮合刚度的间隙非线性齿轮系统的混沌控制[J].机械科学与技术,2006,25(9):607-610.
[120]李华,沈允文,刘梦军,孙智民.用Lyapunov指数研究单对齿轮间隙非线性系统的动力学行为[J].中国机械工程,2002,13(12):1040-1044.
[121]王三民,沈允文,董海军.含摩擦和间隙直齿轮副的混沌与分又研究[J].机械工程学报,2002,38(9):8-11.
[122]王立华,李润方,林腾蛟等.齿轮系统时变刚度和间隙非线性振动特性研究[J].中国机械工程,2003,14(13):1143-1146.
[123]王玉新.考虑啮合时变刚度和传递误差的齿轮振动分析[J].机械传动,2002,20(1):5-8
[124] Maynard,K.P,1997,Interstitial Processing:The Application of Noise Processing to Gear Fault Detection,International Conference on Condition Monitoring,University of Wales[J],Swansea,UK,12th-16th,April 1999.
[125] Maynard,K.P.Interstitial Processing:The Application of Noise Processing to Gear Fault Detection.Proceedings of the International Conference on Condition Monitoring[J],University of Wales Swansea,U K,12th-16th April 1999,pp.77-86.
[126] Deng G,Kato M. Initial temperature evaluation for flash temperature index of gear tooth[J]. Transaction of the ASME, Journal of Tribology,1995,117(3):476-481.
[127] T.Tobe and M.Kato.“A Study on Flash Temperatures on the Spur Gear Teeth”[J].Transactions of the ASME,Journal of Engineering for Industry,February,1974.
[128] L.D.Mitchell and J.WDaws. Proposed Solution Methodology for the Dynamically Coupled Nonlinear Gear Rotor Mechanics Equation[J]. ASME Vib. Acous. Stress Rehab. Des, 1985, (107):112-116.
[129] L.D.Mitchell and J.W Daws .A Basic Approach to Gearbox Noise Prediction[J]. Traps. Of the SEA,1991:3366-3379.
[130] R.D.Ciskowski,C.A.Brebbia,Boundary Element Methods in Acoustics[M].mputational Mechanics Publications, Southampton Boston, 1991.
[131] Haruo Houjoh et al, Sound Field Assessment by Measurement of Sound Pressure Distribution Close to Machine Noise Source[J], JSME International Journal, Series C, Vol. 40, No. 4, 1997:607-615.
[132]何韫如,宋福堂.齿轮与齿轮箱振动噪声机理分析及控制[J].振动、测试与诊断,1998.18(3).P221-226.
[133]李凯岭.渐开线齿轮不同形式齿廓偏差对齿轮噪声的影响[J].机械工程学报,2008,44(3):234-240.
[134] Chen Lixin,Jung Xiaoyu.Prediction of Vibration and Noise of Gearbox[J]. Chinese Journal of Mechanical Engineering, 1991, 6(4): 257-260.
[135]吴晓如,杨浩广等.强背景噪声下声信号的测量[J].中国科学技术大学学报.1999.29(6). 696-701.
[136]李连进,张维屏.降低齿轮箱噪声的一种途径[J].东北工学院学报, 1989, 10(4):439-444.
[137]刘佳才.低噪声柴油机基本结构参数的选择[J].内燃机学报, 1996, 14(2): 154-159.
[138]朱才朝.三环减速器表面噪声的实验[J].重庆大学学报.2000,23(4):18-21.
[139]邵忍平.齿轮传动振动噪声计算的Kato方法[J].机械,2002,29(3):12-14.
[140]邵忍平.齿轮啮合冲击噪声的定量预估.机械科学与技术[J],2001,20(3):340-344.
[141]陶泽光,官德娟,朵丽霞.齿轮传动噪声的描述和比较[J].昆明理工大学学报.1998.23(6). 53-61.
[142] T. A. Harris. Rolling Bearing Analysis(4th edition) [M]. New York : John Wiley and Sons,Inc. 2001.
[143]陆金铭.扭矩法诊断柴油机动力装置故障[J].振动、测试与诊断,2002,22(2):142~146.
[144]陈忠.滚动轴承及其支承的刚度计算[J].煤矿机械.2006,27(3):387~388.
[145]吕金虎.混沌时间序列分析及其应用[M].武汉:武汉大学出版社,2005.
[146] F Takens. Detecting strange attractors in fluent turbulence[J].Lecture Notes in Mathematics,1981,898:366-381.
[147] H. S. Kim, R. Eykholt, J. D. Salas. Nonlinear dynamics, delay times, and embedding windows [J]. Physica D, 1999, 48–60.
[148] A.Wolf J.B.Swift, H.L.Swinney and J.A.Vastano. Determining Lyapunov exponents from a time series[D]. Physica 16D, 1985, 285~317.
[149] M.T.Rosenstein, J.J.Collins and C.J.De luca. A practical method for calculating largest Lyapunov exponents from small data sets[D], Physica D, 1993, 65: 117-134.
[150]陶泽光.齿轮系统有限元模态分析[J].机械设计与研究,2000,28(3):45-46.
[151]杨成云.中心传动齿轮箱体固有特性研究[J].机械设计与制造工程,2002,31(4):26-28.
[152]王基.某型船用传动齿轮箱振动模态的实验与分析[J].海军工程大学学报,2007,19(2):55-59.
[153]龙慧.高速齿轮传动轮齿的温度模拟及过程参数的敏感性分析[D],重庆:重庆大学,2001.
[154]杨大地,涂光裕.数值分析[M].重庆:重庆大学出版社,1997.
[155]李德葆,陆秋海著.实验模态分析及其应用[M].北京:科学出版社,2001.
[156]沃德·海伦,斯蒂芬·拉门兹,波尔·萨斯著,白化同,郭继忠译.模态分析理论与实验[M].北京:北京理工大学出版社,2000.
[157]李绍彬.高速重载齿轮传动热弹变形及非线性耦合动力学研究[D],重庆:重庆大学,2004.
[158]杨成云.齿轮传动系统耦合振动响应及抗冲击性能研究[D],重庆:重庆大学,2006.