计及齿面摩擦的斜齿轮传动动态特性研究
|
摘要
齿轮是机械系统中重要的传递运动和动力的机械元件，随着传动系统的高速、高效、精密、可靠、低振动、低噪声、轻量化的要求越来越高，齿轮的工作性能对整个传动系统的影响也会越来越大。在航空航天、舰船、机械等行业，齿轮正朝着高速、重载方向发展，其动态特性引起研究人员的广泛关注。由于我国齿轮行业的振动噪声等动态特性不足较发达国家的严重，因此传动系统中尤其斜齿轮的动态特性研究是现阶段工程实际中急需要解决的问题，但在该领域中国内的研究更多的忽略了齿面摩擦对动态特性的影响，国外近年研究表明齿面摩擦对齿轮传动动态特性的影响是不可忽略的。本文主要以斜齿轮传动作为研究对象，分析在考虑齿面摩擦时斜齿轮的动态特性。研究结果对于认识复杂的斜齿轮传动的动态性能、进行动态优化设计具有重要的理论和实际应用价值，也为齿轮传动及其转子系统的动态特性分析提供理论基础，为传动系统的可靠性以及减振降噪分析提供技术支持。
本文首先根据齿轮啮合理论推导出计算斜齿轮时变接触线的改进数值算法，该算法突破了文献计算时变接触线的限制条件，扩大了数值计算斜齿轮时变接触线的适用范围，算法准确、快速、方便实用，为时变摩擦力、时变摩擦转矩以及时变啮合刚度的计算和频响分析、误差分析等动态特性分析奠定基础。分析斜齿轮时变接触线的变化规律并揭示出接触线总长度变化最小的条件：初始时刻当L1(啮合起始时刻接触线上端距离啮合区右端最短距离)和端面齿距相等，且L2(啮合起始时刻接触线上端距离啮合区左端最短距离)和L4(啮合起始时刻接触线下端距离啮合区右端最短距离)相等时，接触线总长度不变。在时变接触线长度算法基础上考虑齿轮的混合弹流润滑状态下的摩擦影响，采用分片直齿轮法构建计算斜齿轮齿面摩擦力以及齿面摩擦转矩的算法。研究结果表明：时变接触线的波动是齿面摩擦力以及齿面摩擦转矩波动的重要原因。在本文所选的参数范围内，当螺旋角为20°时，时变接触线长度的波动、齿面摩擦力的波动和齿面摩擦转矩的波动最小。时变接触线以及齿面摩擦力、摩擦转矩的算法为齿轮的参数优化以及动态特性分析提供了更准确的基础。
以能量最小原理构建了渐开线齿轮时变接触线载荷分布的数学模型，得到了齿轮沿接触线的载荷分布。直齿轮在啮合周期内双齿啮合时载荷分配率在0.33~0.67之间变化。斜齿轮沿接触线的载荷分布较直齿轮平缓，没有载荷突变。在轮齿的变形计算中考虑齿面摩擦力对变形的影响，研究结果表明：齿面摩擦对齿轮的弯曲效应随着齿廓参数的变大其影响也变得较为明显，由于节点的摩擦力方向改变，节点产生了变形突变。在此基础上计算斜齿轮的时变啮合刚度，给出考虑齿面摩擦时斜齿轮的时变啮合刚度曲线，以及时变啮合刚度的变化对振动位移的影响程度，为谐波共振分析以及齿轮传动误差分析提供了较为真实的时变啮合刚度。
考虑齿面摩擦情况下构建斜齿轮动力学方程，分析了主频共振响应、2阶超频共振响应以及1/2阶次频共振响应的动力学频响特性，分析结果表明：齿面摩擦对共振幅值有抑制作用，随着摩擦系数的变大，共振幅值随之降低，共振频率略有增大。在考虑齿面摩擦情况下，动、静态载荷引起的共振幅值较无摩擦时明显的降低，静态载荷较大时发生共振的频率较无摩擦时明显变小；动态载荷、阻尼系数所引起的共振幅值较无摩擦时明显减小，但共振频率变化不大。
采用整体误差理论并考虑齿面摩擦以及时变啮合刚度构建斜齿轮动力学方程。在变转速的情况下，分析载荷、阻尼对齿轮传动误差、最大啮合力以及动载系数的影响。研究结果表明：误差激励对重载齿轮的动态响应的影响较小，对高速齿轮的动态响应的影响较大，阻尼对降低误差激励引起的动态响应的影响效果较为明显。最后在传动误差引起的啮合冲击模型中考虑进齿面摩擦引起的啮合变形，给出基节误差、齿距偏差以及由齿形误差反映的齿轮精度等级对齿轮振动噪声的影响。
Gears are very impoint element for motion and power transmission in mechanicalsystems. The gear dynamics performance have great influence on entire transmissionsystem, with the increasing of performance such as fast, efficient, precise, reliable, lowvibration, low noise and lightweight. With the development of aerospace, machinery,electronics and ship industries, the performance of gear look forward to high-speed,overloaded. The study of dynamic characteristics was extensive concerned by theresearchers. Noise, vibration and dynamic characteristics of the gear are more seriousthan the performance of foreign. So transmission system, especially gear dynamiccharacteristics are an urgent engineering problem to be solved. But, most researchneglect the influence of tooth friction, with the further studies the researcher realize theimportance of tooth friction and can not be ignored in recent years. This paper focuseson the helical gear pair and analyzes the dynamics performance considering the toothfriction. The results have theoretical and practical significance for complex helical geardynamic performance, and also provide a theoretical basis for dynamic performance oftransmission system and technical support in order to reduce vibrations and noise.
An improved numerical algorithm is proposed in order to calculate time-varyingcontact line according to gear meshing theory. The algorithm has broken through thecalculation restrictions of numerical from literature published abroad in recent years andexpands numerical calculation application range of the conference. The algorithm has somany advantages such as accurate, fast, convenient and practical. Analyze the changelaw of time-varying and reveal the minimum fluctuation conditions of the time-varyingcontact line. The results show the fluctuation of contact line is the smallest when thelength of L1(the smallest distance from the top of contact line to the right end surface)is a transverse pitch and L2(the smallest distance from the top of contact line to the leftend surface) equal L4(the shortest distance from the bottle of contact line to the rightend surface). The gear runs stably when the change law satisfies with the minimumfluctuation conditions. An algorithm is given about the calculation of tooth frictionforce and tooth friction torque condiering the friction coefficient of elastohydrodynamiclubrication. The change laws are obtained about tooth friction force and friction torque.The results shown that the fluctuation of time-varying contact line is very importantfactor for the fluctuation of tooth friction force and tooth torque. Within the selectedparameters scope of this article the fluctuation of tooth friction force and friction torqueare small when helix angle is20°. The conclusions will provide theoretical basis todesign gears and dynamic analysis of future work of this paper.
The load distribution model of involute gear was constructed along thetime-varying contact line based on the energy minimization principle. The model wasused to calculate the load distribution along the contact line. The distribution rate is0.33~0.67when spur gear run at double contact zone. The load distribution of helicalgear is smoothly then spur gear. There is no load mutation of helical gear. The contactdeformation was calculated considering the tooth friction force. The analysis resultsshow the bending effect become larger with the increasing profile parameter. There is adeformation motion at pitch point, because the direction is changed of tooth frictionforce at pitch point. According to the above work the time-varying stiffness is calculatedand analyzed considering the tooth friction force. The calculation results providetheorial basis for frequency spectrum analysis and foundation for transmission error anddynamics analysis.
The dynamic function of helical gear was built considering the tooth friction force.Main frequency resonance response,1/2order frequency resonance response and2orderfrequency resonance response were analyzed. The results show the tooth friction canreduce the resonance amplitude. The resonance amplitude will decrease with increasingof friction coefficient, but the resonance frequency will become large. The resonanceamplitude of static load obviously reduces when considering the tooth friction force. Thedynamic load and damping factor can reduce effectively the resonance amplitude, but theinfluence on resonance frequency is not obvious.
In this paper, the integrate error and tooth friction are considered to constructdynamic equation of helical gear pair. The results about the maximum dynamictransmission error, maximum meshing force and maximum dynamic factor are obtainedwith the different speeds. The results show that error excitations are not important forheavy-duty gear. But, error excitations are important element for heavy-duty gear. Thedamping has obviously effect for reducing the dynamic response. Finally, the noise wasanalyzed considering different tooth base error、individual circular pitch error、pitchcumulative error and gear precision when the meshing impact was caused bytransmission error.
本文首先根据齿轮啮合理论推导出计算斜齿轮时变接触线的改进数值算法，该算法突破了文献计算时变接触线的限制条件，扩大了数值计算斜齿轮时变接触线的适用范围，算法准确、快速、方便实用，为时变摩擦力、时变摩擦转矩以及时变啮合刚度的计算和频响分析、误差分析等动态特性分析奠定基础。分析斜齿轮时变接触线的变化规律并揭示出接触线总长度变化最小的条件：初始时刻当L1(啮合起始时刻接触线上端距离啮合区右端最短距离)和端面齿距相等，且L2(啮合起始时刻接触线上端距离啮合区左端最短距离)和L4(啮合起始时刻接触线下端距离啮合区右端最短距离)相等时，接触线总长度不变。在时变接触线长度算法基础上考虑齿轮的混合弹流润滑状态下的摩擦影响，采用分片直齿轮法构建计算斜齿轮齿面摩擦力以及齿面摩擦转矩的算法。研究结果表明：时变接触线的波动是齿面摩擦力以及齿面摩擦转矩波动的重要原因。在本文所选的参数范围内，当螺旋角为20°时，时变接触线长度的波动、齿面摩擦力的波动和齿面摩擦转矩的波动最小。时变接触线以及齿面摩擦力、摩擦转矩的算法为齿轮的参数优化以及动态特性分析提供了更准确的基础。
以能量最小原理构建了渐开线齿轮时变接触线载荷分布的数学模型，得到了齿轮沿接触线的载荷分布。直齿轮在啮合周期内双齿啮合时载荷分配率在0.33~0.67之间变化。斜齿轮沿接触线的载荷分布较直齿轮平缓，没有载荷突变。在轮齿的变形计算中考虑齿面摩擦力对变形的影响，研究结果表明：齿面摩擦对齿轮的弯曲效应随着齿廓参数的变大其影响也变得较为明显，由于节点的摩擦力方向改变，节点产生了变形突变。在此基础上计算斜齿轮的时变啮合刚度，给出考虑齿面摩擦时斜齿轮的时变啮合刚度曲线，以及时变啮合刚度的变化对振动位移的影响程度，为谐波共振分析以及齿轮传动误差分析提供了较为真实的时变啮合刚度。
考虑齿面摩擦情况下构建斜齿轮动力学方程，分析了主频共振响应、2阶超频共振响应以及1/2阶次频共振响应的动力学频响特性，分析结果表明：齿面摩擦对共振幅值有抑制作用，随着摩擦系数的变大，共振幅值随之降低，共振频率略有增大。在考虑齿面摩擦情况下，动、静态载荷引起的共振幅值较无摩擦时明显的降低，静态载荷较大时发生共振的频率较无摩擦时明显变小；动态载荷、阻尼系数所引起的共振幅值较无摩擦时明显减小，但共振频率变化不大。
采用整体误差理论并考虑齿面摩擦以及时变啮合刚度构建斜齿轮动力学方程。在变转速的情况下，分析载荷、阻尼对齿轮传动误差、最大啮合力以及动载系数的影响。研究结果表明：误差激励对重载齿轮的动态响应的影响较小，对高速齿轮的动态响应的影响较大，阻尼对降低误差激励引起的动态响应的影响效果较为明显。最后在传动误差引起的啮合冲击模型中考虑进齿面摩擦引起的啮合变形，给出基节误差、齿距偏差以及由齿形误差反映的齿轮精度等级对齿轮振动噪声的影响。
Gears are very impoint element for motion and power transmission in mechanicalsystems. The gear dynamics performance have great influence on entire transmissionsystem, with the increasing of performance such as fast, efficient, precise, reliable, lowvibration, low noise and lightweight. With the development of aerospace, machinery,electronics and ship industries, the performance of gear look forward to high-speed,overloaded. The study of dynamic characteristics was extensive concerned by theresearchers. Noise, vibration and dynamic characteristics of the gear are more seriousthan the performance of foreign. So transmission system, especially gear dynamiccharacteristics are an urgent engineering problem to be solved. But, most researchneglect the influence of tooth friction, with the further studies the researcher realize theimportance of tooth friction and can not be ignored in recent years. This paper focuseson the helical gear pair and analyzes the dynamics performance considering the toothfriction. The results have theoretical and practical significance for complex helical geardynamic performance, and also provide a theoretical basis for dynamic performance oftransmission system and technical support in order to reduce vibrations and noise.
An improved numerical algorithm is proposed in order to calculate time-varyingcontact line according to gear meshing theory. The algorithm has broken through thecalculation restrictions of numerical from literature published abroad in recent years andexpands numerical calculation application range of the conference. The algorithm has somany advantages such as accurate, fast, convenient and practical. Analyze the changelaw of time-varying and reveal the minimum fluctuation conditions of the time-varyingcontact line. The results show the fluctuation of contact line is the smallest when thelength of L1(the smallest distance from the top of contact line to the right end surface)is a transverse pitch and L2(the smallest distance from the top of contact line to the leftend surface) equal L4(the shortest distance from the bottle of contact line to the rightend surface). The gear runs stably when the change law satisfies with the minimumfluctuation conditions. An algorithm is given about the calculation of tooth frictionforce and tooth friction torque condiering the friction coefficient of elastohydrodynamiclubrication. The change laws are obtained about tooth friction force and friction torque.The results shown that the fluctuation of time-varying contact line is very importantfactor for the fluctuation of tooth friction force and tooth torque. Within the selectedparameters scope of this article the fluctuation of tooth friction force and friction torqueare small when helix angle is20°. The conclusions will provide theoretical basis todesign gears and dynamic analysis of future work of this paper.
The load distribution model of involute gear was constructed along thetime-varying contact line based on the energy minimization principle. The model wasused to calculate the load distribution along the contact line. The distribution rate is0.33~0.67when spur gear run at double contact zone. The load distribution of helicalgear is smoothly then spur gear. There is no load mutation of helical gear. The contactdeformation was calculated considering the tooth friction force. The analysis resultsshow the bending effect become larger with the increasing profile parameter. There is adeformation motion at pitch point, because the direction is changed of tooth frictionforce at pitch point. According to the above work the time-varying stiffness is calculatedand analyzed considering the tooth friction force. The calculation results providetheorial basis for frequency spectrum analysis and foundation for transmission error anddynamics analysis.
The dynamic function of helical gear was built considering the tooth friction force.Main frequency resonance response,1/2order frequency resonance response and2orderfrequency resonance response were analyzed. The results show the tooth friction canreduce the resonance amplitude. The resonance amplitude will decrease with increasingof friction coefficient, but the resonance frequency will become large. The resonanceamplitude of static load obviously reduces when considering the tooth friction force. Thedynamic load and damping factor can reduce effectively the resonance amplitude, but theinfluence on resonance frequency is not obvious.
In this paper, the integrate error and tooth friction are considered to constructdynamic equation of helical gear pair. The results about the maximum dynamictransmission error, maximum meshing force and maximum dynamic factor are obtainedwith the different speeds. The results show that error excitations are not important forheavy-duty gear. But, error excitations are important element for heavy-duty gear. Thedamping has obviously effect for reducing the dynamic response. Finally, the noise wasanalyzed considering different tooth base error、individual circular pitch error、pitchcumulative error and gear precision when the meshing impact was caused bytransmission error.
引文
[1]刘忠明,王长路,张元国.中国齿轮工业的现状、挑战与2030年愿景[J].机械传动,2011,35(12):1-6.
[2]李润方,王建军.齿轮系统动力学[M].北京,科学出版社,1997.
[3]李润方.齿轮传动的刚度分析和修形方法[M].重庆,重庆大学出版社,1998.
[4] H. Endo, R.B. Randall. Enhancement of autoregressive model based gear toothfault detection technique by the use of minimum entropy deconvolution filter[J].Mechanical Systems and Signal Processing,2007,21(2):906-919.
[5]黄中华,张晓建,周玉军.渐开线齿轮啮合碰撞力仿真[J].中南大学学报,2011,42(2):379:383.
[6]林腾蛟,杨妍妮,李润方.弧齿锥齿轮传动内部动态激励数值仿真[J].重庆大学学报,2009,32(6):609:613.
[7] A. Andersson, L. Vedmar. A dynamic model to determine vibrations in involutehelical gears[J]. Journal of Sound and Vibration,2003,260(2):195-212.
[8] S. Baud, P. Velex, Static and dynamic tooth loading in spur and helical gearedsystems-experiments and model validation[J]. Journal of Mechanical Design,2002,124(2):334-346.
[9] Shuting Li.Effects of centrifugal load on tooth contact stresses and bendingstresses of thin-rimmed spur gears with inclined webs [J]. Mechanism andMachine Theory,2013,59:34-47.
[10] Niels L. Pedersen.Improving bending stress in spur gears using asymmetric gearsand shape optimization [J],Mechanism and Machine Theory,2010,45:1707-1720.
[11] Seok-Chul Hwang,Jin-Hwan Lee,Dong-Hyung Lee,Seung-Ho Hana,Kwon-HeeLeeContact stress analysis for a pair of mating gears [J].Mathematical andComputer Modelling,2013,57:40-49.
[12] Tengjiao Lin, Runfang Li. A finite element method for3D static and dynamiccontact/impact analysis of gear drives[J]. Comput. Methods Appl. Mech. Engrg,2007,196(9-12):1716-1728.
[13] Shuting Li. Efect of addendum on contact strength, bending strength and basicperformance parameters of a pair of spur gears[J].Mechanism and MachineTheory,2008,13(12):1543-1556.
[14] Ignacio Gonzalez-Perez, Jose L. Iserte. Alfonso FuentesImplementation of Hertztheory and validation of a finite element model for stress analysis of gear driveswith localized bearing contact[J].Mechanism and Machine Theory2011,46(6):765-783.
[15] Song He, B.S., M.S. EFFECT OF SLIDING FRICTION ON SPUR ANDHELICAL GEAR DYNAMICS AND VIBRO-ACOUSTICS [D]. The Ohio StateUniversity.2008:5.
[16] Monsak Pimsarn, Kazem Kazerounian.Efcient evaluation of spur gear toothmesh load usingpseudo-interference stifness estimation method[J]. Mechanismand Machine Theory,2002,37(8):769-786.
[17]常山,徐振忠,霍肇波等.斜齿圆柱齿轮瞬时啮合刚度及齿廓修形的研究[J].热能动力工程,1997,12(4):270-274.
[18]林腾蛟,李润方,朱才朝等.斜齿轮的齿面载荷及啮合刚度数值分析[J].机械工艺师,2000,10:30-31.
[19] Fakher Chaari, Tahar Fakhfakh, Mohamed Haddar. Analytical modelling of spurgear tooth crack and influence on gearmesh stiffness[J], European Journal ofMechanics A/Solids,2009,28(3):461-468.
[20]唐进元,彭方进,黄云飞.冲击载荷下的齿轮动应力变化规律数值分析[J].振动与冲击,2009,28(8):138-143.
[21]康焱,石照耀,姚文席.渐开线直齿内齿轮的轮齿变形挠度解析[J].机械传动,2008,32(1):5-8.
[22]姚文席.修形渐开线直齿轮的啮合冲击研究[J].北京工业大学学报,2000,15(2):1-5.
[23]周长江,唐进元,钟志华.齿轮传动的线外啮合与冲击摩擦[J].机械工程学报,2008,44(3):75-81.
[24]唐进元,刘欣,戴进.考虑间隙与摩擦时的齿轮传动动力学键合图建模研究[J].机械工程学报,2011,47(9):53-59.
[25]唐进元,周炜,陈思雨.齿轮传动啮合接触冲击分析[J].机械工程学报,2011,47(7):22-30.
[26]刘文,林腾蛟,李润方.冲击谱激励下齿轮系统的动力学性能[J].重庆大学学报,2010,33(1):7-11.
[27]刘文,林腾蛟,李润方.新型少齿差减速器动态特性分析及实验研究[J].振动与冲击,2009,28(7):22-27.
[28]林腾蛟,廖勇军,李润方.齿轮箱动态响应及辐射噪声数值仿真[J].重庆大学学报,2009,32(8):892-896.
[29]邵忍平,孙进才,沈允文等.齿轮啮合冲击噪声的定量预估[J].机械科学与技术,2001,20(3):340-342.
[30] A. Bajer, L. Demkowicz. Dynamic contact impact problems，energy conservation,and Planetary gear trains[J].Comp.Meth.Appl.Mech.Eng.2002,191(37-38):4159-4191.
[31] R.G. Parker, S.M. Vijayakar, T. Imajo. Non-linear dynamic response of a spurgear pair: modelling and experimental comparisons[J]. Journal of Sound andVibration,2000,237(3),435-455.
[32] I. Howard, S. Jia, J. Wang. The dynamic modelling of a spur gear in meshincluding friction and a crack[J]. Mechanical Systems and Signal Processing,2001,15(5):831-853.
[33] R.I. Raja Hamzah, D. Mba. The influence of operating condition on acousticemission (AE) generation during meshing of helical and spur gear[J]. TribologyInternational,2009,42(1):3-14.
[34] Lassaad Walha, Tahar Fakhfakh, Mohamed Haddar. Nonlinear dynamics of atwo-stage gear system with mesh stiffness fluctuation, bearing flexibility andbacklash[J].Mechanism and Machine Theory,2009,44(5):1058-1069.
[35] Yongjun Shen, Shaopu Yang, Xiandong Liu.Nonlinear dynamics of a spur gearpair with time-varying stiffnessand backlash based on incremental harmonicbalance method[J].International Journal of Mechanical Sciences,2006,48(11):1256-1263.
[36] A. Kahmaran. Nonlinear dynamics of a spur gear pair[J]. Journal of Sound andVibration,1990,103(2):447-459.
[37] T. Tsuta. Excitation force analysis of helical gear-pair with tolerance in their toothshape and Pitch，mounted on flexible shaft[C]. MPT'91JSME InternationalConference on Motion and Power Transmission， Hiroshima， Japan，1991,(23-26):72-77.
[38]程爱明,张春林,赵自强.内平动齿轮副多齿接触激励下的非线性振动周期解特性[J].北京理工大学学报,2010,30(4):420-424.
[39]朱才朝,陆波,宋朝省.大功率船用齿轮箱系统耦合非线性动态特性研究[J].机械工程学报,2009,45(9):31-35.
[40] Lim, T. C, Singh, R.Vibration Transmission Through Rolling Element Bearings.Part III: Geared Rotor System Studies [J]. Journal of Sound and Vibration,1991,151(1):31-54.
[41] Yi-Cheng Chen, Chia-Chang Liu. Contact stress analysis of concave conicalinvolute gear pairs with non-parallel axes [J]. Finite Elements in Analysis andDesign,2011,47:443-452.
[42] Zhang Dayi, Liu Shuguo, Liu Baolong.Investigation on bending fatigue failure ofa micro-gear through finite element analysis[J]. Engineering Failure Analysis,2013,31:225-235.
[43] DongWang,Teilin Shi.Finite element simulation and experimental investigation offorming micro-gear with Zr-Cu-Ni-Al bulk metallic glass[J]. Journal of MaterialsProcessing Technology,2010,210:684-688.
[44] R.G Parker. S. M. Vijayakar, T.Imajo. Non-linear dynamic response of a spur gearpair: modeling and experimental comparisons[J]. Journal of Sound and Vibration,2000,237(3):435-455.
[45]林腾蛟,廖勇军,李润方等.双环减速器辐射噪声数值仿真及试验研究[J].振动与冲击,2010,29(3):43-47.
[46]刘文,林腾蛟,李润方等.双环减速器振动特性分析及实验研究[J].中国机械工程,2009,20(10):1192-1196.
[47] P. Velex, P. Sainsot. An analytical study of tooth friction excitations in errorlessspur and helical gears[J]. Mechanism and Machine Theory,2002,37(7):641-658.
[48] L. Vedmar, A. Andersson. A method to determine dynamic loads on spur gearteeth and on benangs[J]. Journal of Sound and Vibration,2003,267(5-6):1065-1084.
[49]王玉新,柳杨.含侧隙齿轮副的动载荷分析[J].机械强度,2003,25(4):373-377.
[50] M. Vaishya, R. Singh, Analysis of periodically varying gear mesh systems withCoulomb friction using Floquet theory[J]. Journal of Sound and Vibration,2001,243(3):525-545.
[51] M. Vaishya, R. Singh, Sliding friction-induced non-linearity and parametriceffects in gear dynamics[J].Journal of Sound and Vibration,2001,248(4):671-694.
[52] M. Vaishya, R. Singh. Strategies for modeling friction in gear dynamics[J].ASME Journal of Mechanical Design,2003,125(2):383-393.
[53] Houser, D.R, Bolze, V.M, Graber, J.M. Static and Dynamic Transmission ErrorMeasurements and Predictions for Spur and Helical Gear Sets[C]. Proceedings of7th ASME International Power Transmission and Gearing Conference. San Diego,1996:365-372.
[54] Borner, J. Houser, D.R. Friction and Bending Moments on Gear NoiseExcitations [J]. SAE Transactions,1996.105(6):1669-1676.
[55] Balasubramaniam Vengudusamy, Alexander Grafl,Franz Novotny-Farkas, WernerSchofmann.Comparison of frictional properties of gear oils in boundary andmixed lubricated rolling-sliding and pure sliding contacts[J].TribologyInternational,2013,62:100-109.
[56] Lassaad Walha, Tahar Fakhfakh, Mohamed Haddar. Nonlinear dynamics of atwo-stage gear system with mesh stiffness fluctuation, bearing flexibility andbacklash [J]. Mechanism and Machine Theory,2009,44(5):1058-1069.
[57] Lundvall, O, Stromberg, N, Klarbring, A. A Flexible Multi-Body Approach forFrictional Contact in Spur Gears[J]. Journal of Sound and Vibration,2004.278(3):479-499.
[58] Houser, D. R., Vaishya M., Sorenson J. D., Vibro-Acoustic Effects of Friction inGears: An Experimental Investigation[J]. SAE Paper,2001:15-16.
[59] Borner, J., Houser, D. R. Friction and Bending Moments as Gear NoiseExcitations[J], SAE Paper,2008:816-961.
[60] Velex, P, Cahouet, V. Experimental and Numerical Investigations on the Influenceof Tooth Friction in Spur and Helical Gear Dynamics[J]. ASME Journal ofMechanical Design,2000,122(4):515-522.
[61] Velex, P, Sainsot. P. An Analytical Study of Tooth Friction Excitations in Spurand Helical Gears [J]. Mechanism and Machine Theory,2002,37:641-658.
[62] Ah-Der Lina, Jao-Hwa Kuang. Dynamic interaction between contact loads andtooth wear of engaged plastic gear pairs[J]. International Journal of MechanicalSciences,2008,50(2):205-213.
[63] Chinmaya Kar, A.R. Mohanty.Determination of time-varying contact length,friction force, torque and forces at the bearings in a helical gear system[J].Journal of Sound and Vibration.2008,309:307-319.
[64] Song He, Sungmin Cho, Rajendra Singh.Prediction of dynamic friction forces inspur gears using alternate sliding friction formulations[J]. Journal of Sound andVibration.2008,309:843-851.
[65] S. Baglioni, F. Cianetti, L. Landi.Influence of the addendum modification on spurgear efficiency[J]. Mechanism and Machine Theory,2012,49:216-233.
[66] M. Kolivand, S. Li, A. Kahraman.Prediction of mechanical gear mesh efficiencyof hypoid gear pairs[J]. Mechanism and Machine Theory2010,45:1568-1582.
[67] Valentin Onishchenko. Tooth wear modeling and prognostication parameters ofengagement of spur gear power transmissions[J]. Mechanism and MachineTheory,2008,43(12):1639-1664.
[68] Duan, C, Singh, R.Super-Harmonics in a Torsional System with Dry Friction PathSubject to Harmonic Excitation under a Mean Torque[J]. Journal of Sound andVibration,2005,285(4-5):803-834.
[69] Hamrock, B. J, Dowson, D. Isothermal Elastohydrodynamic Lubrication of PointContacts, Part III-Fully Flooded Results[J]. Journal of Lubrication Technology,1977,99(2):264-276.
[70] Rebbechi, B. Oswald, F. B., Dynamic Measurements of Gear Tooth Friction andLoad, NASA-Technical Memorandum,1991:103-281.
[71] Vaishya, M., Houser, D. R. Modeling and Measurement of Sliding Friction forGear Analysis, American Gear Manufacturer Association Technical Paper,1999,99:1-12.
[72] Ottewill JR, Neild SA,Wilson RE. An investigation into the effect of tooth profileerrors on gear rattle. Journal of Sound and Vibration,2010(329):3495-506.
[73] A. Fernondez, M. Iglesias, A. de-Juan, P. García, R. Sancibrián, F. Viadero Geartransmission dynamic: Effects of tooth profile deviations and support flexibility.Applied Acoustics,2013:1-12.
[74] Fernandez Del Rincon A, Iglesias M, De Juan A, Viadero F. Defect simulation ina spur gear transmission model. New Trends Mech Sci Anal Des Mech Mach Sci2010(5):191-198.
[75] James R. Ottewill, Simon A. Neild, R. Eddie Wilson.Intermittent gear rattle dueto interactions between forcing and manufacturing errors. Journal of Sound andVibration,2009(321)913-935.
[76] Shyue-Cheng Yang.Mathematical model of a stepped triple circular-arc gear.Mechanism and Machine Theory,2009(44):1019-1031.
[77] Li Ting, Pan Cunyun.On grinding manufacture technique and tooth contact andstress analysis of ring-involute spherical gears. Mechanism and Machine Theory2009(44):1807-1825.
[78] Cai-Wan Chang-Jian.Nonlinear analysis for gear pair system supported by longjournal bearings under nonlinear suspension. Mechanism and Machine Theory,2010(45):569-583.
[79] T.F. Conry, A. Seireg. A mathematical programming technique for the evaluationof load distribution and optimal modifications for gear systems[J], Journal ofEngineering for Industry-Transactions of the ASME,1995,1115-1122.
[80] G. Dalpiaz, A. Fernandez Del Rincon, E. Mucchi, A. Rivola, Experimentalvalidation of a model for the dynamic analysis of gear pumps. Proceedings ofNovem, Saint Raphael, France,2005.
[81] E. Mucchi. Dynamic analysis of external gear pumps by means of non linearmodels and experimental techniques[D]. EnDIF-Engineering Department inFerrara, University a degli Studi di Ferrara, Ferrara, Italy, March2007.
[82] Giorgio Bonori, Francesco Pellicano. Non-smooth dynamics of spur gears withmanufacturing errors[J].Journal of Sound and Vibration,2007,306(1-2):271-283.
[83] Faydor L. Litvin, Galina I. Sheveleva, Daniele Vecchiato. Modified approach fortooth contact analysis of gear drives and automatic determination of guess values[J]. Comput. Methods Appl. Mech. Engrg,2005,194(27-29):2927-2946.
[84] Rui-Tang Tseng, Chung-Biau Tsay.Contact characteristics of cylindrical gearswith curvilinear shaped teeth[J]. Mechanism and Machine Theory,2004,39(9):905-919.
[85] Carlos Henrique Wink a, Alberto Luiz Serpa. Performance assessment of solutionmethods for load distribution problem of gear teeth[J]. Mechanism and MachineTheory,2008,43(1):80-94.
[86] Jerome Bruyere, Jean-Yves Dantan, Regis Bigot, Patrick Martin. Statisticaltolerance analysis of bevel gear by tooth contact analysis and Monte Carlosimulation [J]. Mechanism and Machine Theory,2007,42(10):1326-1351.
[87] A. Kahraman, G.W. Blakenship. Effect of involute tip relief on dynamic responseof spur gear pairs[J]. ASME Journal of Mechanical Design,1999,121(2):313-315.
[88] K. Umezawa, H. Houjoh, S. Matsumura, S. Wang. Investigation of the dynamicbehaviour of a helical gear system-dynamics of gear pairs with biasmodification[C]. Proceedings of the Fourth World Congress on Gearing andPower Transmissions, Paris,1999(3):1981-1990.
[89] Wei-Shiang Wang, Zhang-Hua Fong. Undercutting and contact characteristics oflongitudinal cycloidal spur gears generated by the dual face-hobbing method[J].Mechanism and Machine Theory,2011,46(4):399-411.
[90] K. Mao. Gear tooth contact analysis and its application in the reduction of fatiguewear [J]. Wear,2007,262(11-12):1281-1288.
[91] A.Kubo, S.Kiyono.Vibration excitation of cylindrical involute gears due to toothform errors[J], Bulletin of JSME,1980,23(183):1536-1543.
[92] Chinmaya Kar, A.R. Mohanty. An algorithm for determination of time-varyingfrictional force and torque in a helical gear system[J]. Mechanism and MachineTheory,2007,42(4):482-486.
[93]中华人民共和国航空工业部.HB/Z84.2-1984航空渐开线圆柱齿轮齿面接触疲劳强度计算[S].
[94]冯守卫，张申林等.齿轮接触线长度和重合度系数[J].长安大学学报(自然科学版),2004,24(2):101-103.
[95] HU Z, ZHU D. A full numerical solution to the mixed lubrication pointcontacts[J]. Journal of tribology,2000,122(1):1-9.
[96] DOWSON D, HIGGINSON G R. Elastohydrodynamic lubrication: thefundamental of roller and gear lubrication[M]. Oxford Pergamon Press,1966.
[97] Reese E Jones. A Greenwood-Williamson Model of Smill-scale Friction[J].Journal of Applied Mechanicas,2007,74(1):21-40.
[98] CASTRO M SEABREA J.Coeffcient of friction in mixed film lubrication gearversus twin-disc[J]. Journal of Engineer Tribology,2007,22(13):399-411.
[99] AGMA Standard2001-D04. Fundamental Rating Factors and CalculationMethods for Involute Spur and Helical Gear Teeth, American Gear ManufacturersAssociation, Alexandria, VA,2004.
[100] AGMA Information Sheet908-B89,Geometry Factors for Determining the PittingResistance and Bending Strength of Spur, Helical and Herringbone Gear Teeth,American Gear Manufacturers Association, Alexandria, VA,1989.
[101] ISO Standard6336-2:1996, Calculation of Load Capacity of Spur and HelicalGears-Part2: Calculation of Surface Durability(Pitting),International Organizationfor Standardization, Geneva, Switzerland,1996.
[102] ISO Standard6336-3:1996, Calculation of Load Capacity of Spur and HelicalGears-Part3: Calculation of Tooth Bending Strength, International Organizationfor Standardization, Geneva, Switzerland,1996.
[103] Jose I. Pedrero, Miguel Pleguezuelos, Marta Munoz.Critical stress and loadconditions for pitting calculations of involute spur and helical gear teeth[J].Mechanism and Machine Theory,2011,46(4):425-437.
[104] AGMA Information Sheet908-B89, Geometry Factors for Determining thePitting Resistance and Bending Strength of Spur, Helical and Herringbone GearTeeth, American Gear Manufacturers Association, Alexandria, VA,1989.6.
[105] Jose I. Pedrero, Miguel Pleguezuelos, Marta Munoz.Contact stress calculation ofundercut spur and helical gear teeth[J]. Mechanism and Machine Theory,2011,46(11):1633-1646.
[106] Gang Liu, Roubert G. Parker, Impact of tooth Friction and its Bending Effect onGear Dynamics[J]. Journal of sound and Vibration,2009,320(4-5):1039-1063.
[107]李瑰贤.马亮等.舰船用齿轮传动啮合刚度及动态性能研究[J].船舶工程,2000(5):41-43.
[108]王建平,王玉新.齿轮系统谐波共振的多尺度分析方法[J].机械设计与研究,2005,21(4):43-46.
[109] M.VAISHYA, R.SINGH. ANALYSIS OF PERIODICALLY VARYING GEARMESH SYSTEMS WITH COULOMB FRICTION USING FLOQUENTTHEORY[J]. Journal of sound and Vibration,2001,243(3):525-545.
[110]李瑰贤,于广滨,温建民等.求解齿轮系统非线性动力学微分方程的多尺度法[J].吉林大学学报:工学版,2008,38(1):75-79.
[111]王建平,王玉新.运用多尺度法对齿轮系统组合共振特性的分析[J].西安理工大学学报,2005,21(1):5-10.
[112]石照耀,康焱.齿轮副整体误差及其获取方式[J].天津大学学报,2012,45(2):128-134.
[113]曹麟祥.齿轮全谐波误差分离技术[J].宇航计测技术,2001,21(6):27-32.
[114] P. Velex, M. Ajmi. Dynamic tooth loads and quasi-static transmission errors inhelical gears-Approximate dynamic factor formulate[J].Mechanism and MachineTheory,2007,42(11):1512-1526.
[115]邵忍平,沈允文等.齿轮传动加速度噪声辐射机理研究[J].机械强度,2000,22(4):310-312.
[116]王玉芳,童忠舫.齿轮误差对齿轮加速度噪声的影响[J].振动、测试与诊断,1993,13(4):1-10.
[2]李润方,王建军.齿轮系统动力学[M].北京,科学出版社,1997.
[3]李润方.齿轮传动的刚度分析和修形方法[M].重庆,重庆大学出版社,1998.
[4] H. Endo, R.B. Randall. Enhancement of autoregressive model based gear toothfault detection technique by the use of minimum entropy deconvolution filter[J].Mechanical Systems and Signal Processing,2007,21(2):906-919.
[5]黄中华,张晓建,周玉军.渐开线齿轮啮合碰撞力仿真[J].中南大学学报,2011,42(2):379:383.
[6]林腾蛟,杨妍妮,李润方.弧齿锥齿轮传动内部动态激励数值仿真[J].重庆大学学报,2009,32(6):609:613.
[7] A. Andersson, L. Vedmar. A dynamic model to determine vibrations in involutehelical gears[J]. Journal of Sound and Vibration,2003,260(2):195-212.
[8] S. Baud, P. Velex, Static and dynamic tooth loading in spur and helical gearedsystems-experiments and model validation[J]. Journal of Mechanical Design,2002,124(2):334-346.
[9] Shuting Li.Effects of centrifugal load on tooth contact stresses and bendingstresses of thin-rimmed spur gears with inclined webs [J]. Mechanism andMachine Theory,2013,59:34-47.
[10] Niels L. Pedersen.Improving bending stress in spur gears using asymmetric gearsand shape optimization [J],Mechanism and Machine Theory,2010,45:1707-1720.
[11] Seok-Chul Hwang,Jin-Hwan Lee,Dong-Hyung Lee,Seung-Ho Hana,Kwon-HeeLeeContact stress analysis for a pair of mating gears [J].Mathematical andComputer Modelling,2013,57:40-49.
[12] Tengjiao Lin, Runfang Li. A finite element method for3D static and dynamiccontact/impact analysis of gear drives[J]. Comput. Methods Appl. Mech. Engrg,2007,196(9-12):1716-1728.
[13] Shuting Li. Efect of addendum on contact strength, bending strength and basicperformance parameters of a pair of spur gears[J].Mechanism and MachineTheory,2008,13(12):1543-1556.
[14] Ignacio Gonzalez-Perez, Jose L. Iserte. Alfonso FuentesImplementation of Hertztheory and validation of a finite element model for stress analysis of gear driveswith localized bearing contact[J].Mechanism and Machine Theory2011,46(6):765-783.
[15] Song He, B.S., M.S. EFFECT OF SLIDING FRICTION ON SPUR ANDHELICAL GEAR DYNAMICS AND VIBRO-ACOUSTICS [D]. The Ohio StateUniversity.2008:5.
[16] Monsak Pimsarn, Kazem Kazerounian.Efcient evaluation of spur gear toothmesh load usingpseudo-interference stifness estimation method[J]. Mechanismand Machine Theory,2002,37(8):769-786.
[17]常山,徐振忠,霍肇波等.斜齿圆柱齿轮瞬时啮合刚度及齿廓修形的研究[J].热能动力工程,1997,12(4):270-274.
[18]林腾蛟,李润方,朱才朝等.斜齿轮的齿面载荷及啮合刚度数值分析[J].机械工艺师,2000,10:30-31.
[19] Fakher Chaari, Tahar Fakhfakh, Mohamed Haddar. Analytical modelling of spurgear tooth crack and influence on gearmesh stiffness[J], European Journal ofMechanics A/Solids,2009,28(3):461-468.
[20]唐进元,彭方进,黄云飞.冲击载荷下的齿轮动应力变化规律数值分析[J].振动与冲击,2009,28(8):138-143.
[21]康焱,石照耀,姚文席.渐开线直齿内齿轮的轮齿变形挠度解析[J].机械传动,2008,32(1):5-8.
[22]姚文席.修形渐开线直齿轮的啮合冲击研究[J].北京工业大学学报,2000,15(2):1-5.
[23]周长江,唐进元,钟志华.齿轮传动的线外啮合与冲击摩擦[J].机械工程学报,2008,44(3):75-81.
[24]唐进元,刘欣,戴进.考虑间隙与摩擦时的齿轮传动动力学键合图建模研究[J].机械工程学报,2011,47(9):53-59.
[25]唐进元,周炜,陈思雨.齿轮传动啮合接触冲击分析[J].机械工程学报,2011,47(7):22-30.
[26]刘文,林腾蛟,李润方.冲击谱激励下齿轮系统的动力学性能[J].重庆大学学报,2010,33(1):7-11.
[27]刘文,林腾蛟,李润方.新型少齿差减速器动态特性分析及实验研究[J].振动与冲击,2009,28(7):22-27.
[28]林腾蛟,廖勇军,李润方.齿轮箱动态响应及辐射噪声数值仿真[J].重庆大学学报,2009,32(8):892-896.
[29]邵忍平,孙进才,沈允文等.齿轮啮合冲击噪声的定量预估[J].机械科学与技术,2001,20(3):340-342.
[30] A. Bajer, L. Demkowicz. Dynamic contact impact problems，energy conservation,and Planetary gear trains[J].Comp.Meth.Appl.Mech.Eng.2002,191(37-38):4159-4191.
[31] R.G. Parker, S.M. Vijayakar, T. Imajo. Non-linear dynamic response of a spurgear pair: modelling and experimental comparisons[J]. Journal of Sound andVibration,2000,237(3),435-455.
[32] I. Howard, S. Jia, J. Wang. The dynamic modelling of a spur gear in meshincluding friction and a crack[J]. Mechanical Systems and Signal Processing,2001,15(5):831-853.
[33] R.I. Raja Hamzah, D. Mba. The influence of operating condition on acousticemission (AE) generation during meshing of helical and spur gear[J]. TribologyInternational,2009,42(1):3-14.
[34] Lassaad Walha, Tahar Fakhfakh, Mohamed Haddar. Nonlinear dynamics of atwo-stage gear system with mesh stiffness fluctuation, bearing flexibility andbacklash[J].Mechanism and Machine Theory,2009,44(5):1058-1069.
[35] Yongjun Shen, Shaopu Yang, Xiandong Liu.Nonlinear dynamics of a spur gearpair with time-varying stiffnessand backlash based on incremental harmonicbalance method[J].International Journal of Mechanical Sciences,2006,48(11):1256-1263.
[36] A. Kahmaran. Nonlinear dynamics of a spur gear pair[J]. Journal of Sound andVibration,1990,103(2):447-459.
[37] T. Tsuta. Excitation force analysis of helical gear-pair with tolerance in their toothshape and Pitch，mounted on flexible shaft[C]. MPT'91JSME InternationalConference on Motion and Power Transmission， Hiroshima， Japan，1991,(23-26):72-77.
[38]程爱明,张春林,赵自强.内平动齿轮副多齿接触激励下的非线性振动周期解特性[J].北京理工大学学报,2010,30(4):420-424.
[39]朱才朝,陆波,宋朝省.大功率船用齿轮箱系统耦合非线性动态特性研究[J].机械工程学报,2009,45(9):31-35.
[40] Lim, T. C, Singh, R.Vibration Transmission Through Rolling Element Bearings.Part III: Geared Rotor System Studies [J]. Journal of Sound and Vibration,1991,151(1):31-54.
[41] Yi-Cheng Chen, Chia-Chang Liu. Contact stress analysis of concave conicalinvolute gear pairs with non-parallel axes [J]. Finite Elements in Analysis andDesign,2011,47:443-452.
[42] Zhang Dayi, Liu Shuguo, Liu Baolong.Investigation on bending fatigue failure ofa micro-gear through finite element analysis[J]. Engineering Failure Analysis,2013,31:225-235.
[43] DongWang,Teilin Shi.Finite element simulation and experimental investigation offorming micro-gear with Zr-Cu-Ni-Al bulk metallic glass[J]. Journal of MaterialsProcessing Technology,2010,210:684-688.
[44] R.G Parker. S. M. Vijayakar, T.Imajo. Non-linear dynamic response of a spur gearpair: modeling and experimental comparisons[J]. Journal of Sound and Vibration,2000,237(3):435-455.
[45]林腾蛟,廖勇军,李润方等.双环减速器辐射噪声数值仿真及试验研究[J].振动与冲击,2010,29(3):43-47.
[46]刘文,林腾蛟,李润方等.双环减速器振动特性分析及实验研究[J].中国机械工程,2009,20(10):1192-1196.
[47] P. Velex, P. Sainsot. An analytical study of tooth friction excitations in errorlessspur and helical gears[J]. Mechanism and Machine Theory,2002,37(7):641-658.
[48] L. Vedmar, A. Andersson. A method to determine dynamic loads on spur gearteeth and on benangs[J]. Journal of Sound and Vibration,2003,267(5-6):1065-1084.
[49]王玉新,柳杨.含侧隙齿轮副的动载荷分析[J].机械强度,2003,25(4):373-377.
[50] M. Vaishya, R. Singh, Analysis of periodically varying gear mesh systems withCoulomb friction using Floquet theory[J]. Journal of Sound and Vibration,2001,243(3):525-545.
[51] M. Vaishya, R. Singh, Sliding friction-induced non-linearity and parametriceffects in gear dynamics[J].Journal of Sound and Vibration,2001,248(4):671-694.
[52] M. Vaishya, R. Singh. Strategies for modeling friction in gear dynamics[J].ASME Journal of Mechanical Design,2003,125(2):383-393.
[53] Houser, D.R, Bolze, V.M, Graber, J.M. Static and Dynamic Transmission ErrorMeasurements and Predictions for Spur and Helical Gear Sets[C]. Proceedings of7th ASME International Power Transmission and Gearing Conference. San Diego,1996:365-372.
[54] Borner, J. Houser, D.R. Friction and Bending Moments on Gear NoiseExcitations [J]. SAE Transactions,1996.105(6):1669-1676.
[55] Balasubramaniam Vengudusamy, Alexander Grafl,Franz Novotny-Farkas, WernerSchofmann.Comparison of frictional properties of gear oils in boundary andmixed lubricated rolling-sliding and pure sliding contacts[J].TribologyInternational,2013,62:100-109.
[56] Lassaad Walha, Tahar Fakhfakh, Mohamed Haddar. Nonlinear dynamics of atwo-stage gear system with mesh stiffness fluctuation, bearing flexibility andbacklash [J]. Mechanism and Machine Theory,2009,44(5):1058-1069.
[57] Lundvall, O, Stromberg, N, Klarbring, A. A Flexible Multi-Body Approach forFrictional Contact in Spur Gears[J]. Journal of Sound and Vibration,2004.278(3):479-499.
[58] Houser, D. R., Vaishya M., Sorenson J. D., Vibro-Acoustic Effects of Friction inGears: An Experimental Investigation[J]. SAE Paper,2001:15-16.
[59] Borner, J., Houser, D. R. Friction and Bending Moments as Gear NoiseExcitations[J], SAE Paper,2008:816-961.
[60] Velex, P, Cahouet, V. Experimental and Numerical Investigations on the Influenceof Tooth Friction in Spur and Helical Gear Dynamics[J]. ASME Journal ofMechanical Design,2000,122(4):515-522.
[61] Velex, P, Sainsot. P. An Analytical Study of Tooth Friction Excitations in Spurand Helical Gears [J]. Mechanism and Machine Theory,2002,37:641-658.
[62] Ah-Der Lina, Jao-Hwa Kuang. Dynamic interaction between contact loads andtooth wear of engaged plastic gear pairs[J]. International Journal of MechanicalSciences,2008,50(2):205-213.
[63] Chinmaya Kar, A.R. Mohanty.Determination of time-varying contact length,friction force, torque and forces at the bearings in a helical gear system[J].Journal of Sound and Vibration.2008,309:307-319.
[64] Song He, Sungmin Cho, Rajendra Singh.Prediction of dynamic friction forces inspur gears using alternate sliding friction formulations[J]. Journal of Sound andVibration.2008,309:843-851.
[65] S. Baglioni, F. Cianetti, L. Landi.Influence of the addendum modification on spurgear efficiency[J]. Mechanism and Machine Theory,2012,49:216-233.
[66] M. Kolivand, S. Li, A. Kahraman.Prediction of mechanical gear mesh efficiencyof hypoid gear pairs[J]. Mechanism and Machine Theory2010,45:1568-1582.
[67] Valentin Onishchenko. Tooth wear modeling and prognostication parameters ofengagement of spur gear power transmissions[J]. Mechanism and MachineTheory,2008,43(12):1639-1664.
[68] Duan, C, Singh, R.Super-Harmonics in a Torsional System with Dry Friction PathSubject to Harmonic Excitation under a Mean Torque[J]. Journal of Sound andVibration,2005,285(4-5):803-834.
[69] Hamrock, B. J, Dowson, D. Isothermal Elastohydrodynamic Lubrication of PointContacts, Part III-Fully Flooded Results[J]. Journal of Lubrication Technology,1977,99(2):264-276.
[70] Rebbechi, B. Oswald, F. B., Dynamic Measurements of Gear Tooth Friction andLoad, NASA-Technical Memorandum,1991:103-281.
[71] Vaishya, M., Houser, D. R. Modeling and Measurement of Sliding Friction forGear Analysis, American Gear Manufacturer Association Technical Paper,1999,99:1-12.
[72] Ottewill JR, Neild SA,Wilson RE. An investigation into the effect of tooth profileerrors on gear rattle. Journal of Sound and Vibration,2010(329):3495-506.
[73] A. Fernondez, M. Iglesias, A. de-Juan, P. García, R. Sancibrián, F. Viadero Geartransmission dynamic: Effects of tooth profile deviations and support flexibility.Applied Acoustics,2013:1-12.
[74] Fernandez Del Rincon A, Iglesias M, De Juan A, Viadero F. Defect simulation ina spur gear transmission model. New Trends Mech Sci Anal Des Mech Mach Sci2010(5):191-198.
[75] James R. Ottewill, Simon A. Neild, R. Eddie Wilson.Intermittent gear rattle dueto interactions between forcing and manufacturing errors. Journal of Sound andVibration,2009(321)913-935.
[76] Shyue-Cheng Yang.Mathematical model of a stepped triple circular-arc gear.Mechanism and Machine Theory,2009(44):1019-1031.
[77] Li Ting, Pan Cunyun.On grinding manufacture technique and tooth contact andstress analysis of ring-involute spherical gears. Mechanism and Machine Theory2009(44):1807-1825.
[78] Cai-Wan Chang-Jian.Nonlinear analysis for gear pair system supported by longjournal bearings under nonlinear suspension. Mechanism and Machine Theory,2010(45):569-583.
[79] T.F. Conry, A. Seireg. A mathematical programming technique for the evaluationof load distribution and optimal modifications for gear systems[J], Journal ofEngineering for Industry-Transactions of the ASME,1995,1115-1122.
[80] G. Dalpiaz, A. Fernandez Del Rincon, E. Mucchi, A. Rivola, Experimentalvalidation of a model for the dynamic analysis of gear pumps. Proceedings ofNovem, Saint Raphael, France,2005.
[81] E. Mucchi. Dynamic analysis of external gear pumps by means of non linearmodels and experimental techniques[D]. EnDIF-Engineering Department inFerrara, University a degli Studi di Ferrara, Ferrara, Italy, March2007.
[82] Giorgio Bonori, Francesco Pellicano. Non-smooth dynamics of spur gears withmanufacturing errors[J].Journal of Sound and Vibration,2007,306(1-2):271-283.
[83] Faydor L. Litvin, Galina I. Sheveleva, Daniele Vecchiato. Modified approach fortooth contact analysis of gear drives and automatic determination of guess values[J]. Comput. Methods Appl. Mech. Engrg,2005,194(27-29):2927-2946.
[84] Rui-Tang Tseng, Chung-Biau Tsay.Contact characteristics of cylindrical gearswith curvilinear shaped teeth[J]. Mechanism and Machine Theory,2004,39(9):905-919.
[85] Carlos Henrique Wink a, Alberto Luiz Serpa. Performance assessment of solutionmethods for load distribution problem of gear teeth[J]. Mechanism and MachineTheory,2008,43(1):80-94.
[86] Jerome Bruyere, Jean-Yves Dantan, Regis Bigot, Patrick Martin. Statisticaltolerance analysis of bevel gear by tooth contact analysis and Monte Carlosimulation [J]. Mechanism and Machine Theory,2007,42(10):1326-1351.
[87] A. Kahraman, G.W. Blakenship. Effect of involute tip relief on dynamic responseof spur gear pairs[J]. ASME Journal of Mechanical Design,1999,121(2):313-315.
[88] K. Umezawa, H. Houjoh, S. Matsumura, S. Wang. Investigation of the dynamicbehaviour of a helical gear system-dynamics of gear pairs with biasmodification[C]. Proceedings of the Fourth World Congress on Gearing andPower Transmissions, Paris,1999(3):1981-1990.
[89] Wei-Shiang Wang, Zhang-Hua Fong. Undercutting and contact characteristics oflongitudinal cycloidal spur gears generated by the dual face-hobbing method[J].Mechanism and Machine Theory,2011,46(4):399-411.
[90] K. Mao. Gear tooth contact analysis and its application in the reduction of fatiguewear [J]. Wear,2007,262(11-12):1281-1288.
[91] A.Kubo, S.Kiyono.Vibration excitation of cylindrical involute gears due to toothform errors[J], Bulletin of JSME,1980,23(183):1536-1543.
[92] Chinmaya Kar, A.R. Mohanty. An algorithm for determination of time-varyingfrictional force and torque in a helical gear system[J]. Mechanism and MachineTheory,2007,42(4):482-486.
[93]中华人民共和国航空工业部.HB/Z84.2-1984航空渐开线圆柱齿轮齿面接触疲劳强度计算[S].
[94]冯守卫，张申林等.齿轮接触线长度和重合度系数[J].长安大学学报(自然科学版),2004,24(2):101-103.
[95] HU Z, ZHU D. A full numerical solution to the mixed lubrication pointcontacts[J]. Journal of tribology,2000,122(1):1-9.
[96] DOWSON D, HIGGINSON G R. Elastohydrodynamic lubrication: thefundamental of roller and gear lubrication[M]. Oxford Pergamon Press,1966.
[97] Reese E Jones. A Greenwood-Williamson Model of Smill-scale Friction[J].Journal of Applied Mechanicas,2007,74(1):21-40.
[98] CASTRO M SEABREA J.Coeffcient of friction in mixed film lubrication gearversus twin-disc[J]. Journal of Engineer Tribology,2007,22(13):399-411.
[99] AGMA Standard2001-D04. Fundamental Rating Factors and CalculationMethods for Involute Spur and Helical Gear Teeth, American Gear ManufacturersAssociation, Alexandria, VA,2004.
[100] AGMA Information Sheet908-B89,Geometry Factors for Determining the PittingResistance and Bending Strength of Spur, Helical and Herringbone Gear Teeth,American Gear Manufacturers Association, Alexandria, VA,1989.
[101] ISO Standard6336-2:1996, Calculation of Load Capacity of Spur and HelicalGears-Part2: Calculation of Surface Durability(Pitting),International Organizationfor Standardization, Geneva, Switzerland,1996.
[102] ISO Standard6336-3:1996, Calculation of Load Capacity of Spur and HelicalGears-Part3: Calculation of Tooth Bending Strength, International Organizationfor Standardization, Geneva, Switzerland,1996.
[103] Jose I. Pedrero, Miguel Pleguezuelos, Marta Munoz.Critical stress and loadconditions for pitting calculations of involute spur and helical gear teeth[J].Mechanism and Machine Theory,2011,46(4):425-437.
[104] AGMA Information Sheet908-B89, Geometry Factors for Determining thePitting Resistance and Bending Strength of Spur, Helical and Herringbone GearTeeth, American Gear Manufacturers Association, Alexandria, VA,1989.6.
[105] Jose I. Pedrero, Miguel Pleguezuelos, Marta Munoz.Contact stress calculation ofundercut spur and helical gear teeth[J]. Mechanism and Machine Theory,2011,46(11):1633-1646.
[106] Gang Liu, Roubert G. Parker, Impact of tooth Friction and its Bending Effect onGear Dynamics[J]. Journal of sound and Vibration,2009,320(4-5):1039-1063.
[107]李瑰贤.马亮等.舰船用齿轮传动啮合刚度及动态性能研究[J].船舶工程,2000(5):41-43.
[108]王建平,王玉新.齿轮系统谐波共振的多尺度分析方法[J].机械设计与研究,2005,21(4):43-46.
[109] M.VAISHYA, R.SINGH. ANALYSIS OF PERIODICALLY VARYING GEARMESH SYSTEMS WITH COULOMB FRICTION USING FLOQUENTTHEORY[J]. Journal of sound and Vibration,2001,243(3):525-545.
[110]李瑰贤,于广滨,温建民等.求解齿轮系统非线性动力学微分方程的多尺度法[J].吉林大学学报:工学版,2008,38(1):75-79.
[111]王建平,王玉新.运用多尺度法对齿轮系统组合共振特性的分析[J].西安理工大学学报,2005,21(1):5-10.
[112]石照耀,康焱.齿轮副整体误差及其获取方式[J].天津大学学报,2012,45(2):128-134.
[113]曹麟祥.齿轮全谐波误差分离技术[J].宇航计测技术,2001,21(6):27-32.
[114] P. Velex, M. Ajmi. Dynamic tooth loads and quasi-static transmission errors inhelical gears-Approximate dynamic factor formulate[J].Mechanism and MachineTheory,2007,42(11):1512-1526.
[115]邵忍平,沈允文等.齿轮传动加速度噪声辐射机理研究[J].机械强度,2000,22(4):310-312.
[116]王玉芳,童忠舫.齿轮误差对齿轮加速度噪声的影响[J].振动、测试与诊断,1993,13(4):1-10.
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |