齿轮乏油传动的摩擦学研究
摘要
为了实现齿轮传动的绿色制造、提高齿轮的传动性能,本文针对齿轮传动的乏油现象,在乏油工况、乏油机理、乏油磨损、改善乏油的供油方法及其载运齿轮传动工程应用等方面进行了摩擦学研究。论文主要创新工作如下：
(1)基于齿轮的啮合过程分析了表征齿轮副工况的两个基本要素——相对运动与载荷。为便于研究齿轮传动设计参数对两理论齿廓相对运动的影响,推导了采用传动比、理论啮合线长度与曲率半径表示的相对滑动率的计算公式；通过随机函数模拟齿轮的制造误差,采用弹簧模型建立了考虑制造误差的啮合刚度与齿间载荷分配率的计算方法。以SS8机车齿轮为例的计算表明：综合误差使得双齿轮副啮合刚度大小在无误差值的啮合刚度值下方波动,但不会超过单齿轮副的啮合刚度值；综合误差使得齿间载荷分配率沿着无制造误差的载荷分配率曲线而上下波动。
(2)从供需关系入手进行了齿轮副乏油的研究,提出了齿轮副的乏油机理：接触区有效供油量不足实际的需求量将导致乏油；并进一步提出了有效供应量是受齿轮的自供油能力与外设供油能力影响的判据。首先,基于弹流润滑理论与散热原理分别推导了齿轮传动的润滑供油需求量与冷却需求量的计算公式；然后,从载荷与速度两方面出发研究了齿轮基本参数对齿轮自供油能力的影响；最后,基于供油效率研究了供油方位与齿轮的设计结构等对外设供油能力的影响,为高速、重载下改善齿轮乏油传动提供了有效的措施。
(3)针对现有磨损计算的理论依据不充分的问题,提出了高副摩擦功原理的磨损计算模型,该模型从能量的角度高度概括地反映了滑动高副摩擦磨损的规律,理论依据可靠,且计算简单实用,适应于高副摩擦磨损的动态仿真分析；并开发了使用方便、计算全面、结果可靠的齿廓磨损仿真软件,以SS8型机车牵引齿轮为例进行了仿真计算与分析,提出了齿轮耐磨设计与维护的相关措施。
(4)针对高速、重载立式齿轮传动在传统润滑供油方法下容易造成供油量不足而导致乏油的情况,提出了具有自主知识产权的齿轮径向自吸流体润滑方法,并以螺杆泵为供油动力源进行了供油能力的理论分析以及实验研究,计算表明：螺杆泵工作容积主要受齿轮转速与齿轮载荷的限制,冷却散热对螺杆泵工作容积的影响与转速无关,螺杆泵工作容积应该按啮合线上最大供油量进行设计；通过实验验证了供油不足将导致乏油的理论分析。
本文具有明显的理论价值、实用价值,对于基于绿色制造的齿轮摩擦学设计具有明显的指导意义。
In order to advance the green manufacturing of gear transmission and improve the transmission performances of gear, a series studies on gear working condition, starved-oil mechanism, wear, oil supply and engineering application of gear in transportation tool are carried in this paper against the starved-oil phenomenon of gear transmission.
(1) To describe the working condition of gear pair, two basic factors, i.e. relative motion and load, are analyzed based on the gear engagement process. The relative sliding ratio expression, which is described by trasmission ratio, theoretical action line length and curvature radius, is developed for a convenient research on the influences of gear design parameters on the relative motion of two theoretical tooth profiles. Also, the manufacturing error of gear is simulated by means of a random function and the computation methods of the tooth engagement stiffness and the ratio of load distribution between theeth are both established based on a spring model after considering the manufacturing error. Taking SS8 locomotive gear as an example, the relative computation results show that the double tooth engagement stiffness value of the gear with comprhensive manufacturing error fluctuates between double tooth eagagement stiffness value and single tooth engagement stiffness value of the gear without comprhensive manufacturing error while the ratio of load distribution between teeth also fluctuates along that value of gear without comprhensive manufacturing error.
(2) After the study on starved-oil phenomenon of gear pair is completed based on supply-demand relationship, starved-oil mechanism of gear pair is suggested that the starved-oil phenomenon will happen when the effective oil supply quantity is less than practical demend quantity; furtherly, it is pointed that the effective oil supply quantity is decided by the gear self-oil-supply ability and peripheral-oil-supply ability. Firstly, the computation expressions of the lubrication oil supply quantity and cooling oil supply quantity are both deduced respectively based on elastic dynamic lubrication theory and cooling principle. The influences of gear basic parameters are studied on the gear self-oil-supply ability are discussed respectively from two different aspects of load and speed. The influences of gear sturucture and relative location on peripheral-oil-supply ability are also discussed based on the supply efficiency. Some relative effective approaches are provided against starved-oil phenomenon of high speed gear or heavy load gear.
(3) A computation model of higher pair friction work principle is suggested against the insufficient theoretical evidence usually used for current wear computation. That model can very resumptively express the friction wear law of sliding higher pair from the point of the energy view, and is suitable to the dynamic friction wear simulation of higher pair because of reliable theory evidence, simplification and practicality. A mathematical simulation software of tooth profile wear with convenience, overall factors and reliable results is developed. The wear of SS8 locomotive traction gear is computated and analyzed as an example. As a result, some measures relevant to the maintenance and design against gear wear are suggested.
(4) A method of gear radial self-inhall liquid lubrication with self-owned intellectual property rights is introduced for the upright gear transmission with high speed and heavy load which is prone to starved-oil lubrication due to insufficient oil supply quantity under traditional oil supply mode. Some theoretical and experiment researches on oil supply of gear by means of screw pump, which is taken as an impetus, is made. It indicates after computating that the working cubage of screw pump is confined to both rotating speed and load while the influence of cooling on the working cubage has nothing to do with the rotating speed, and the working cubage should be designed according to maximum oil supply quantity along the action line of gear transmission, also the theory, the insufficient oil supply quantity will result in the starved oil state, is verified by experiment.
Therefore, this paper manifests obvious theoritical value, practical value, and distinct guiding significance for tribology design of gear tansmission based on green manufacturing.
(1)基于齿轮的啮合过程分析了表征齿轮副工况的两个基本要素——相对运动与载荷。为便于研究齿轮传动设计参数对两理论齿廓相对运动的影响,推导了采用传动比、理论啮合线长度与曲率半径表示的相对滑动率的计算公式；通过随机函数模拟齿轮的制造误差,采用弹簧模型建立了考虑制造误差的啮合刚度与齿间载荷分配率的计算方法。以SS8机车齿轮为例的计算表明：综合误差使得双齿轮副啮合刚度大小在无误差值的啮合刚度值下方波动,但不会超过单齿轮副的啮合刚度值；综合误差使得齿间载荷分配率沿着无制造误差的载荷分配率曲线而上下波动。
(2)从供需关系入手进行了齿轮副乏油的研究,提出了齿轮副的乏油机理：接触区有效供油量不足实际的需求量将导致乏油；并进一步提出了有效供应量是受齿轮的自供油能力与外设供油能力影响的判据。首先,基于弹流润滑理论与散热原理分别推导了齿轮传动的润滑供油需求量与冷却需求量的计算公式；然后,从载荷与速度两方面出发研究了齿轮基本参数对齿轮自供油能力的影响；最后,基于供油效率研究了供油方位与齿轮的设计结构等对外设供油能力的影响,为高速、重载下改善齿轮乏油传动提供了有效的措施。
(3)针对现有磨损计算的理论依据不充分的问题,提出了高副摩擦功原理的磨损计算模型,该模型从能量的角度高度概括地反映了滑动高副摩擦磨损的规律,理论依据可靠,且计算简单实用,适应于高副摩擦磨损的动态仿真分析；并开发了使用方便、计算全面、结果可靠的齿廓磨损仿真软件,以SS8型机车牵引齿轮为例进行了仿真计算与分析,提出了齿轮耐磨设计与维护的相关措施。
(4)针对高速、重载立式齿轮传动在传统润滑供油方法下容易造成供油量不足而导致乏油的情况,提出了具有自主知识产权的齿轮径向自吸流体润滑方法,并以螺杆泵为供油动力源进行了供油能力的理论分析以及实验研究,计算表明：螺杆泵工作容积主要受齿轮转速与齿轮载荷的限制,冷却散热对螺杆泵工作容积的影响与转速无关,螺杆泵工作容积应该按啮合线上最大供油量进行设计；通过实验验证了供油不足将导致乏油的理论分析。
本文具有明显的理论价值、实用价值,对于基于绿色制造的齿轮摩擦学设计具有明显的指导意义。
In order to advance the green manufacturing of gear transmission and improve the transmission performances of gear, a series studies on gear working condition, starved-oil mechanism, wear, oil supply and engineering application of gear in transportation tool are carried in this paper against the starved-oil phenomenon of gear transmission.
(1) To describe the working condition of gear pair, two basic factors, i.e. relative motion and load, are analyzed based on the gear engagement process. The relative sliding ratio expression, which is described by trasmission ratio, theoretical action line length and curvature radius, is developed for a convenient research on the influences of gear design parameters on the relative motion of two theoretical tooth profiles. Also, the manufacturing error of gear is simulated by means of a random function and the computation methods of the tooth engagement stiffness and the ratio of load distribution between theeth are both established based on a spring model after considering the manufacturing error. Taking SS8 locomotive gear as an example, the relative computation results show that the double tooth engagement stiffness value of the gear with comprhensive manufacturing error fluctuates between double tooth eagagement stiffness value and single tooth engagement stiffness value of the gear without comprhensive manufacturing error while the ratio of load distribution between teeth also fluctuates along that value of gear without comprhensive manufacturing error.
(2) After the study on starved-oil phenomenon of gear pair is completed based on supply-demand relationship, starved-oil mechanism of gear pair is suggested that the starved-oil phenomenon will happen when the effective oil supply quantity is less than practical demend quantity; furtherly, it is pointed that the effective oil supply quantity is decided by the gear self-oil-supply ability and peripheral-oil-supply ability. Firstly, the computation expressions of the lubrication oil supply quantity and cooling oil supply quantity are both deduced respectively based on elastic dynamic lubrication theory and cooling principle. The influences of gear basic parameters are studied on the gear self-oil-supply ability are discussed respectively from two different aspects of load and speed. The influences of gear sturucture and relative location on peripheral-oil-supply ability are also discussed based on the supply efficiency. Some relative effective approaches are provided against starved-oil phenomenon of high speed gear or heavy load gear.
(3) A computation model of higher pair friction work principle is suggested against the insufficient theoretical evidence usually used for current wear computation. That model can very resumptively express the friction wear law of sliding higher pair from the point of the energy view, and is suitable to the dynamic friction wear simulation of higher pair because of reliable theory evidence, simplification and practicality. A mathematical simulation software of tooth profile wear with convenience, overall factors and reliable results is developed. The wear of SS8 locomotive traction gear is computated and analyzed as an example. As a result, some measures relevant to the maintenance and design against gear wear are suggested.
(4) A method of gear radial self-inhall liquid lubrication with self-owned intellectual property rights is introduced for the upright gear transmission with high speed and heavy load which is prone to starved-oil lubrication due to insufficient oil supply quantity under traditional oil supply mode. Some theoretical and experiment researches on oil supply of gear by means of screw pump, which is taken as an impetus, is made. It indicates after computating that the working cubage of screw pump is confined to both rotating speed and load while the influence of cooling on the working cubage has nothing to do with the rotating speed, and the working cubage should be designed according to maximum oil supply quantity along the action line of gear transmission, also the theory, the insufficient oil supply quantity will result in the starved oil state, is verified by experiment.
Therefore, this paper manifests obvious theoritical value, practical value, and distinct guiding significance for tribology design of gear tansmission based on green manufacturing.
引文
[1]刘友梅,陈国胜.我国高速列车转向架润滑技术.中国铁道科学,2004,25(5)：1-5
[2]Bhushan B. Introduction to tribology. New York:John Wiley & Sons.2002
[3]Zhang Yicheng, Liu Xiling. Study on information description method for joining dynamic collaboration of small and medium-sized mechanical manufacturing enterprise. In: Henry Zhang, eds. Proceedings of 2004 international conference on management science and engineering. Wuhan-Sydney:Orient Academic Forum,2004.477-482
[4]Zhang Yicheng, Li Fang. Evolvement and feature-based matching approach of BOM in computer aided production management system. In:Li M., eds. Proceedings of the First International Conference on Computer Science & Education. Xiamen:Xiamen University Press,2006.243-245
[5]Ertel A M. Hydrodynamic Lubrication Based on New Principles. Akad Nauk SSSR Prikadnaya Math Mekh 1939,3(2):41-52.
[7]Bo Jacobson. Thin film lubrication of real surfaces. Tribology International,2000, (33): 205-210
[8]Xiaoling Liu, Peiran Yang Analysis of the thermal lastohydrodynamic lubrication of a finite line contact. Tribology International,2002, (35) 137-144
[9]章易程,梅雪松,陶涛,等.直齿轮啮合弹性流体动力润滑的非稳态效应的研究.机械工程学报,2000,36(1)：32-35
[10]Ping Yang, Peiran Yang. Analysis on the thermal elastohydrodynamic lubrication of tapered rollers in opposite orientation. Tribology International,2007,(40):1627-1637
[11]Youqiang Wang, Hongqi Li, Jingwei Tong, et al. Transient thermoelastohydro-dynamic lubrication analysis of an involute spur gear. Tribology International, 2004,(37):773-782
[12]Wedeven L D, Evans D, Cameron A. Optical analysis of ball bearing starvation. ASME Journal of Lubrication Technology,1971,93:349-363
[13]温诗铸,杨沛然.弹性流体动力润滑.清华大学出版社,1992
[14]Castle P, Dowson D. A theoretical analysis of the starved elastohydrodynamic lubrication problem for cylinders in line contact, Elastohydrodynamic Lubrication Symposium, Inst. Mech. Eng.1972:35-72
[15]Kaludj ercic A. Thermohydrodynamic effects in line contacts:[Doctorate thesis]. London:University of London,1979
[16]杨沛然,崔金磊,兼田桢宏.线接触弹性流体动力润滑的供油条件分析.摩擦学学报.2006,26(3)：242-246
[17]尹昌磊,杨沛然.椭圆接触弹性流体动力润滑的供油条件分析.摩擦学学报.2007,27(2)：147-151
[18]Damiens B, Venner C H, Cann P M E, etal. Starved lubrication of elliptical EHD contacts. ASME Journal of Tribology,2004,126:105-111.
[19]Chevalier F, Lubrecht A A, Cann PM E,et al. Film thickness in starved EHL point contacts. ASME Journal of tribology,1998,120:126-133.
[20]Lubrecht T, Mazuyer D, Cann P. Starved elastohydrodynamic lubrication theory: application to emulsions and greases. Different Faces of Tribology,2001, (4):717-728
[21]Cann P M E, Damiens B, Lubrecht A A. The transition between fully flooded and starved regimes in EHL. Tribology International.2004,37 (10):859-864
[22]Damiens B, Venner C H, Cann P, etal. Starved lubrication of elliptical EHD contacts. ASME Journal of Tribology,2004,126:105-111.
[23]Merieux J S, Hurley S, Lubrecht A A, et al. Shear-degradation of grease and base oil availability in starved EHL lubrication. Tribology and Interface Engineering Series.2000, 38:581-588
[24]王延忠,彭伟.点接触乏油弹流润滑数值分析.军民两用技术与产品.2007,(10)：42-45
[25]谭洪恩,杨沛然,尹昌磊.特殊供油条件下点接触弹流润滑乏油分析.摩擦学学报.2007,27(4)：357-361
[26]谭洪恩,杨沛然.点接触弹流润滑供油条件退化的乏油分析.润滑与密封.2007,32(4)： 50-54
[27]温诗铸,朱东.等温弹流问题的直接迭代解.润滑与密封.1995,年第4期：
[28]闫玉涛,孙志礼,张云凤.椭圆接触乏油弹流润滑影响因素分析.润滑与密封.2008,33(9)：12-14
[28]谭洪恩,杨沛然.不同卷吸速度方向下的椭圆接触弹流乏油分析.煤矿机械.2008,29(1)：85-87
[30]Changlei Yin, PeiranYang,HongenTan. Thermal elastohydrodynamic lubrication of starved elliptical contacts. Tribology International,2009,(42):964-974
[31]吴玉启.螺旋锥齿轮乏油润滑相关研究： 北京：北京航空航天大学硕士论文,2007
[32]Ton L, Denis M, Philippa C. Starved elastohydrodynamic lubrication theory: Application to emulsions and greases. Different Faces of Tribology.2001,4(2):717-728,
[33]牛永生,强新伟.乏油问题对牵引曲线上升斜率的影响.润滑与密封.2004,165(5)： 27-29
[34]Goksem P G, Hargreaves R A. The effect of viscous shear heating on both film thickness and rolling traction in an EHL line contact-Part Ⅱ:Starved conditions. ASME Trans. J. Lubr. Technol.1978,100(2):353-358.
[35]Luis Magalhaes, Ramiro Martins. Influence of tooth profile and oil formulation on gear power loss. Tribology International,2010,(43):1861-1871
[36]Anandan N, Pandey R K, Jagga C R. An efficient numerical analysis of starved thermohydrodynamically lubricated rolling line contacts. Tribology International,2008, (41):940-946
[37]Venner C H, Berger G, Lugt P M. Waviness deformation in starved EHL circular contacts. ASME Journal of Tribology,2004,126:248-257
[38]齿轮手册编委会.齿轮手册.北京：机械工业出版社,2002
[39]吕先起,吕传毅.高速齿轮的缺油计算.机械设计与研究.1996,(4)：7-10
[40]吕先起,尹世霞.高速齿轮的润滑方法.山东工业大学学报,1996,26(2)：185-188
[41]杨沛然,崔金磊,兼田桢宏.线接触弹性流体动力润滑的供油条件分析.摩擦学学报.2006,26(3)：242-246
[42]王延忠,王涛,周元子.航空螺旋锥齿轮乏油润滑过程分析.润滑与密封.2008,33(10)：4-7
[43]Hohn B R, Michaelis K. Minimised gear lubrication by a minimum oil/air flow rate. Wear,2009,266:461-467
[44]Fujita K, Obata F, Matsuo K. Instantaneous behavior of lubricating oil supplied onto the tooth flanks and its influence on the scoring resistance of spur gears. ASME Pap.1975
[45]胡邦喜.设备润滑基础(第二版).北京：冶金工业出版社,2002
[46]史晓辉.油雾润滑装置研发及油雾润滑效果分析：[硕士学位论文].沈阳：东北大学,2008
[47]会田俊夫.齿车の润滑.日本润滑学会,1975
[48]格利布B B.数值法解摩擦学技术问题.孟献堂,译.北京：机械工业出版社,1989.
[49]Dhanasekarana S, Gnanamoorthy R. Gear tooth wear in sintered spur gears under dry running conditions. Wear,265,(1):81-87
[50]Huseyin I, Hayrettin D. Relation between wear and tooth width modification in spur gears. Wear,2007,(262):390-394
[51]Amarnath M, Sujatha C, Swarnamani S. Experimental studies on the effects of reduction in gear tooth stiffness and lubricant film thickness in a spur geared system. Tribology International,2009(42):340-352
[52]Hohn B R, Michaelis K, Vollmer T. Thermal rating of gear drives:balance between power loss and heat dissipation. AGMA Technical Paper,1996.
[53]Martins R, Seabra J. Friction coefficient in FZG gears lubricated with industrial gear oils:biodegradable ester vs. mineral oil. Tribology International,2006,39(6):512-21.
[54]Hohn B R, Michaelis K. Influence of oil temperature on gear failures. Tribology International,2004(37):103-109
[55]孙红,常小芳.材料副的硬度对齿轮磨损寿命的影响.沈阳工业大学学报,2003,2：98-100
[56]韩致信,石文瑞,彭国义,等.齿轮系统振动加剧齿轮磨损毁坏的机理分析.机械传动,2006,2：47-49
[57]冯伟,谢小鹏,廖钱生,等.齿轮点蚀破坏中磨损与振动关系的试验研究.润滑与密封,2007,32(11)：69-77
[58]林晨岚.基于摩擦功原理的齿轮副磨损动态仿真：[硕士学位论文].长沙：中南大学,2010
[59]唐琴,章易程,林晨岚,等.凸轮磨损的研究综述与思考.机械传动,2010,34(8)： 95-98
[60]Glodez S, Winter H, Stuwe HP, A fracture mechanics model for the wear of gear flanks by pitting. Wear,1997,(208):177-183
[61]王淑仁,闫玉涛,殷伟俐,等.齿轮啮合摩擦疲劳磨损的计算模型.东北大学学报,2008,29(8)：1164-1167
[62]潘尔顺,王殊轶,杨文通,等.渐开线圆柱齿轮啮合过程中磨损的计算机仿真.上海交通大学学报,2000,34(3)：415-418
[63]Wojnarowski J, Onishchenko V. Tooth wear effects on spur gear dynamics. Mechanism and Machine Theory,2003(38):161-178
[64]Huali D, Ahmet Kahraman. Interactions between nonlinear spur gear dynamics and surface wear. Journal of Sound and Vibration,2007(307):662-679
[65]韩翔.圆柱齿轮传动磨损可靠性优化设计.机械传动,2003,27(5)：24-25
[66]Anders F, Soren A. Simulation of mild wear in spur gears. Wear,1997 (207):16-23
[67]Anders F, Soren A. Simulation of mild wear in helical gears. Wear,2000 (241): 123-128
[68]Park D, Kahraman A. A surface wear model for hypoid gear pairs. Wear,2009 (267): 1595-1604
[69]Yuksel C, Kahraman A. Dynamic tooth loads of planetary gear sets having tooth profile wear. Mechanism and Machine Theory,2004(39):695-715
[70]何荣国,江亲瑜,姚一富.渐开线斜齿圆柱齿轮磨损的数值仿真.润滑与密封,2007,32(3)：88-91
[71]Sharif K J, Evans H P. Prediction of the wear pattern in worm gears. Wear,2006, (261): 666-673
[72]谢友柏.摩擦学设计主要是摩擦学系统的设计.中国机械工程,1999,10(9)：968-973
[73]章易程,李蔚,陈昭莲,等.渐开线外齿轮副相对滑动率的研究.机械设计,2001,18(7)：27-29
[74]章易程,李蔚,聂昌平.渐开线内齿轮副相对滑动率的研究.机械传动,2000,25(2)： 25-27
[75]卢立新,阙师鹏,蔡莹,等.齿轮几何参数对齿轮传动弹流润滑性能的影响.机械传动,1998,22(1)：24-27
[76]杨沛然,郭峰,王静,等.反常弹性流体动力润滑现象的热粘度楔润滑机理研究.青岛理工大学学报.2006,27(6)：1-6
[77]王优强,杨沛然.渐开线直齿圆柱齿轮非稳态热弹流润滑分析.机械工程与学报, 2004,40(9)：10-15
[78]朱孝录,鄂中凯.齿轮承载能力分析.北京：高等教育出版社,1992
[79]Tuplin W A. Gear load capacity. Sir Isaac Pitman & Sans, Ltd.,1962
[80]Michalec, G W.精密齿轮传动装置—理论与实践.楠波,成电,译, 北京：国防工业出版社,1978
[81]仙波正庄.齿轮的误差与强度.张范孚,译,北京： 机械工业出版社,1982
[82]赵叔东.韶山8型电力机车.北京：中国铁道出版社,2007
[83]温诗铸,黄平.摩擦学原理.北京：清华大学出版社,2002
[84]章易程,梅雪松,陶涛,等.直齿轮啮合弹性流体动力润滑的非稳态效应的研究.机械工程学报,2000,36(1)：32～35
[85]章易程,田红旗.渐开线齿轮传动供油能力的研究.润滑与密封,2006,(8)：52-54
[86]Castle P, Dowson D. A theoretical analysis of the Starved elastohydrodynamic lubrication problem for cylinders in line contact, elastohydrodynamic lubrication Symposium, Inst. Mech. Eng.1972:Paper C35/72
[87]ISO/TR 14179-1. Gears thermal capacity part1:Rating gear drives with thermal equilibrium at 95℃ sump temperature. London:International Standard Organization,2001
[88]魏延刚,何卫东,李力行,等.准高速机车牵引齿轮副的侧隙计算与分析.大连铁道学院学报,1995,16(4)：36-39
[89]杨学华.机械设计中齿轮传动侧隙的解决方法.昆明理工大学学报(理工版),2007,(32)5：9-13
[90]顾永泉.机械密封实用技术.北京：机械工业出版社,2001
[91]谢友柏.摩擦学的三个公理.摩擦学学报,2001,202(117)：208.15
[92]江亲瑜,董美云,葛宰林,等.数值仿真技术及其在磨损研究中的应用.大连铁道学院学报,1997,18(2)：41-44
[93]桂长林.Archard的磨损设计计算模型及其应用方法.润滑与密封,1990,(1)：12-21
[94]刘峰壁.直齿圆柱齿轮磨损过程仿真.机械科学与技术.2004,23(1)：55-59
[95]王淑仁,闫玉涛,丁津原,等.渐开线直齿圆柱齿轮啮合磨损试验研究.东北大学学报(自然科学版),2004,25(2)：146-149
[96]Flodin A, Andersson S. Simulation of mild wear in spur gears. Wear,1997, 207(2):16-23
[97]赵源,高万振,李健,等.磨损研究及其方向.材料保护.2004,37(7)：18-34
[98]章易程,田红旗,唐进元,等.基于摩擦功原理的高副滑动磨损的研究.中国机械工程,2010,21(3)：344-347
[99]章易程,李蔚,编著.计算机辅助应用技术基础.北京：国防工业出版社,2005
[100]王淑仁,闫玉涛,丁津原.渐开线直齿圆柱齿轮啮合磨损试验研究.东北大学学报(自然科学版),2004,25(4)：146-149.
[101]中华人民共和国铁道部.SS8型电力机车大修规程.北京：中国铁道出版社,2004
[102]李方,章易程.机车传动齿轮箱开裂现状分析与设计对策.铁道科学与工程学报,2005,2(2)：76-80
[103]章易程,李汉良,田红旗,等.齿轮径向自吸流体润滑方法的供油分析.润滑与密封,2010,35(2)：19-22
[104]章易程.齿轮径向自吸流体润滑方法.中发明专利,CN101586657,2009-11-25
[105]章维一,侯丽雅.润滑理论中卷汲速度的概念辨异及结果分析.中国机械工程,2001,12(11)：1239-1241
[106]林洪义编著.回转式容积泵理论与设计.北京：兵器工业出版社,1995
[107]王世杰,李勤.潜油螺杆泵采油技术及系统设计.北京：冶金工业出版社,2006
[2]Bhushan B. Introduction to tribology. New York:John Wiley & Sons.2002
[3]Zhang Yicheng, Liu Xiling. Study on information description method for joining dynamic collaboration of small and medium-sized mechanical manufacturing enterprise. In: Henry Zhang, eds. Proceedings of 2004 international conference on management science and engineering. Wuhan-Sydney:Orient Academic Forum,2004.477-482
[4]Zhang Yicheng, Li Fang. Evolvement and feature-based matching approach of BOM in computer aided production management system. In:Li M., eds. Proceedings of the First International Conference on Computer Science & Education. Xiamen:Xiamen University Press,2006.243-245
[5]Ertel A M. Hydrodynamic Lubrication Based on New Principles. Akad Nauk SSSR Prikadnaya Math Mekh 1939,3(2):41-52.
[7]Bo Jacobson. Thin film lubrication of real surfaces. Tribology International,2000, (33): 205-210
[8]Xiaoling Liu, Peiran Yang Analysis of the thermal lastohydrodynamic lubrication of a finite line contact. Tribology International,2002, (35) 137-144
[9]章易程,梅雪松,陶涛,等.直齿轮啮合弹性流体动力润滑的非稳态效应的研究.机械工程学报,2000,36(1)：32-35
[10]Ping Yang, Peiran Yang. Analysis on the thermal elastohydrodynamic lubrication of tapered rollers in opposite orientation. Tribology International,2007,(40):1627-1637
[11]Youqiang Wang, Hongqi Li, Jingwei Tong, et al. Transient thermoelastohydro-dynamic lubrication analysis of an involute spur gear. Tribology International, 2004,(37):773-782
[12]Wedeven L D, Evans D, Cameron A. Optical analysis of ball bearing starvation. ASME Journal of Lubrication Technology,1971,93:349-363
[13]温诗铸,杨沛然.弹性流体动力润滑.清华大学出版社,1992
[14]Castle P, Dowson D. A theoretical analysis of the starved elastohydrodynamic lubrication problem for cylinders in line contact, Elastohydrodynamic Lubrication Symposium, Inst. Mech. Eng.1972:35-72
[15]Kaludj ercic A. Thermohydrodynamic effects in line contacts:[Doctorate thesis]. London:University of London,1979
[16]杨沛然,崔金磊,兼田桢宏.线接触弹性流体动力润滑的供油条件分析.摩擦学学报.2006,26(3)：242-246
[17]尹昌磊,杨沛然.椭圆接触弹性流体动力润滑的供油条件分析.摩擦学学报.2007,27(2)：147-151
[18]Damiens B, Venner C H, Cann P M E, etal. Starved lubrication of elliptical EHD contacts. ASME Journal of Tribology,2004,126:105-111.
[19]Chevalier F, Lubrecht A A, Cann PM E,et al. Film thickness in starved EHL point contacts. ASME Journal of tribology,1998,120:126-133.
[20]Lubrecht T, Mazuyer D, Cann P. Starved elastohydrodynamic lubrication theory: application to emulsions and greases. Different Faces of Tribology,2001, (4):717-728
[21]Cann P M E, Damiens B, Lubrecht A A. The transition between fully flooded and starved regimes in EHL. Tribology International.2004,37 (10):859-864
[22]Damiens B, Venner C H, Cann P, etal. Starved lubrication of elliptical EHD contacts. ASME Journal of Tribology,2004,126:105-111.
[23]Merieux J S, Hurley S, Lubrecht A A, et al. Shear-degradation of grease and base oil availability in starved EHL lubrication. Tribology and Interface Engineering Series.2000, 38:581-588
[24]王延忠,彭伟.点接触乏油弹流润滑数值分析.军民两用技术与产品.2007,(10)：42-45
[25]谭洪恩,杨沛然,尹昌磊.特殊供油条件下点接触弹流润滑乏油分析.摩擦学学报.2007,27(4)：357-361
[26]谭洪恩,杨沛然.点接触弹流润滑供油条件退化的乏油分析.润滑与密封.2007,32(4)： 50-54
[27]温诗铸,朱东.等温弹流问题的直接迭代解.润滑与密封.1995,年第4期：
[28]闫玉涛,孙志礼,张云凤.椭圆接触乏油弹流润滑影响因素分析.润滑与密封.2008,33(9)：12-14
[28]谭洪恩,杨沛然.不同卷吸速度方向下的椭圆接触弹流乏油分析.煤矿机械.2008,29(1)：85-87
[30]Changlei Yin, PeiranYang,HongenTan. Thermal elastohydrodynamic lubrication of starved elliptical contacts. Tribology International,2009,(42):964-974
[31]吴玉启.螺旋锥齿轮乏油润滑相关研究： 北京：北京航空航天大学硕士论文,2007
[32]Ton L, Denis M, Philippa C. Starved elastohydrodynamic lubrication theory: Application to emulsions and greases. Different Faces of Tribology.2001,4(2):717-728,
[33]牛永生,强新伟.乏油问题对牵引曲线上升斜率的影响.润滑与密封.2004,165(5)： 27-29
[34]Goksem P G, Hargreaves R A. The effect of viscous shear heating on both film thickness and rolling traction in an EHL line contact-Part Ⅱ:Starved conditions. ASME Trans. J. Lubr. Technol.1978,100(2):353-358.
[35]Luis Magalhaes, Ramiro Martins. Influence of tooth profile and oil formulation on gear power loss. Tribology International,2010,(43):1861-1871
[36]Anandan N, Pandey R K, Jagga C R. An efficient numerical analysis of starved thermohydrodynamically lubricated rolling line contacts. Tribology International,2008, (41):940-946
[37]Venner C H, Berger G, Lugt P M. Waviness deformation in starved EHL circular contacts. ASME Journal of Tribology,2004,126:248-257
[38]齿轮手册编委会.齿轮手册.北京：机械工业出版社,2002
[39]吕先起,吕传毅.高速齿轮的缺油计算.机械设计与研究.1996,(4)：7-10
[40]吕先起,尹世霞.高速齿轮的润滑方法.山东工业大学学报,1996,26(2)：185-188
[41]杨沛然,崔金磊,兼田桢宏.线接触弹性流体动力润滑的供油条件分析.摩擦学学报.2006,26(3)：242-246
[42]王延忠,王涛,周元子.航空螺旋锥齿轮乏油润滑过程分析.润滑与密封.2008,33(10)：4-7
[43]Hohn B R, Michaelis K. Minimised gear lubrication by a minimum oil/air flow rate. Wear,2009,266:461-467
[44]Fujita K, Obata F, Matsuo K. Instantaneous behavior of lubricating oil supplied onto the tooth flanks and its influence on the scoring resistance of spur gears. ASME Pap.1975
[45]胡邦喜.设备润滑基础(第二版).北京：冶金工业出版社,2002
[46]史晓辉.油雾润滑装置研发及油雾润滑效果分析：[硕士学位论文].沈阳：东北大学,2008
[47]会田俊夫.齿车の润滑.日本润滑学会,1975
[48]格利布B B.数值法解摩擦学技术问题.孟献堂,译.北京：机械工业出版社,1989.
[49]Dhanasekarana S, Gnanamoorthy R. Gear tooth wear in sintered spur gears under dry running conditions. Wear,265,(1):81-87
[50]Huseyin I, Hayrettin D. Relation between wear and tooth width modification in spur gears. Wear,2007,(262):390-394
[51]Amarnath M, Sujatha C, Swarnamani S. Experimental studies on the effects of reduction in gear tooth stiffness and lubricant film thickness in a spur geared system. Tribology International,2009(42):340-352
[52]Hohn B R, Michaelis K, Vollmer T. Thermal rating of gear drives:balance between power loss and heat dissipation. AGMA Technical Paper,1996.
[53]Martins R, Seabra J. Friction coefficient in FZG gears lubricated with industrial gear oils:biodegradable ester vs. mineral oil. Tribology International,2006,39(6):512-21.
[54]Hohn B R, Michaelis K. Influence of oil temperature on gear failures. Tribology International,2004(37):103-109
[55]孙红,常小芳.材料副的硬度对齿轮磨损寿命的影响.沈阳工业大学学报,2003,2：98-100
[56]韩致信,石文瑞,彭国义,等.齿轮系统振动加剧齿轮磨损毁坏的机理分析.机械传动,2006,2：47-49
[57]冯伟,谢小鹏,廖钱生,等.齿轮点蚀破坏中磨损与振动关系的试验研究.润滑与密封,2007,32(11)：69-77
[58]林晨岚.基于摩擦功原理的齿轮副磨损动态仿真：[硕士学位论文].长沙：中南大学,2010
[59]唐琴,章易程,林晨岚,等.凸轮磨损的研究综述与思考.机械传动,2010,34(8)： 95-98
[60]Glodez S, Winter H, Stuwe HP, A fracture mechanics model for the wear of gear flanks by pitting. Wear,1997,(208):177-183
[61]王淑仁,闫玉涛,殷伟俐,等.齿轮啮合摩擦疲劳磨损的计算模型.东北大学学报,2008,29(8)：1164-1167
[62]潘尔顺,王殊轶,杨文通,等.渐开线圆柱齿轮啮合过程中磨损的计算机仿真.上海交通大学学报,2000,34(3)：415-418
[63]Wojnarowski J, Onishchenko V. Tooth wear effects on spur gear dynamics. Mechanism and Machine Theory,2003(38):161-178
[64]Huali D, Ahmet Kahraman. Interactions between nonlinear spur gear dynamics and surface wear. Journal of Sound and Vibration,2007(307):662-679
[65]韩翔.圆柱齿轮传动磨损可靠性优化设计.机械传动,2003,27(5)：24-25
[66]Anders F, Soren A. Simulation of mild wear in spur gears. Wear,1997 (207):16-23
[67]Anders F, Soren A. Simulation of mild wear in helical gears. Wear,2000 (241): 123-128
[68]Park D, Kahraman A. A surface wear model for hypoid gear pairs. Wear,2009 (267): 1595-1604
[69]Yuksel C, Kahraman A. Dynamic tooth loads of planetary gear sets having tooth profile wear. Mechanism and Machine Theory,2004(39):695-715
[70]何荣国,江亲瑜,姚一富.渐开线斜齿圆柱齿轮磨损的数值仿真.润滑与密封,2007,32(3)：88-91
[71]Sharif K J, Evans H P. Prediction of the wear pattern in worm gears. Wear,2006, (261): 666-673
[72]谢友柏.摩擦学设计主要是摩擦学系统的设计.中国机械工程,1999,10(9)：968-973
[73]章易程,李蔚,陈昭莲,等.渐开线外齿轮副相对滑动率的研究.机械设计,2001,18(7)：27-29
[74]章易程,李蔚,聂昌平.渐开线内齿轮副相对滑动率的研究.机械传动,2000,25(2)： 25-27
[75]卢立新,阙师鹏,蔡莹,等.齿轮几何参数对齿轮传动弹流润滑性能的影响.机械传动,1998,22(1)：24-27
[76]杨沛然,郭峰,王静,等.反常弹性流体动力润滑现象的热粘度楔润滑机理研究.青岛理工大学学报.2006,27(6)：1-6
[77]王优强,杨沛然.渐开线直齿圆柱齿轮非稳态热弹流润滑分析.机械工程与学报, 2004,40(9)：10-15
[78]朱孝录,鄂中凯.齿轮承载能力分析.北京：高等教育出版社,1992
[79]Tuplin W A. Gear load capacity. Sir Isaac Pitman & Sans, Ltd.,1962
[80]Michalec, G W.精密齿轮传动装置—理论与实践.楠波,成电,译, 北京：国防工业出版社,1978
[81]仙波正庄.齿轮的误差与强度.张范孚,译,北京： 机械工业出版社,1982
[82]赵叔东.韶山8型电力机车.北京：中国铁道出版社,2007
[83]温诗铸,黄平.摩擦学原理.北京：清华大学出版社,2002
[84]章易程,梅雪松,陶涛,等.直齿轮啮合弹性流体动力润滑的非稳态效应的研究.机械工程学报,2000,36(1)：32～35
[85]章易程,田红旗.渐开线齿轮传动供油能力的研究.润滑与密封,2006,(8)：52-54
[86]Castle P, Dowson D. A theoretical analysis of the Starved elastohydrodynamic lubrication problem for cylinders in line contact, elastohydrodynamic lubrication Symposium, Inst. Mech. Eng.1972:Paper C35/72
[87]ISO/TR 14179-1. Gears thermal capacity part1:Rating gear drives with thermal equilibrium at 95℃ sump temperature. London:International Standard Organization,2001
[88]魏延刚,何卫东,李力行,等.准高速机车牵引齿轮副的侧隙计算与分析.大连铁道学院学报,1995,16(4)：36-39
[89]杨学华.机械设计中齿轮传动侧隙的解决方法.昆明理工大学学报(理工版),2007,(32)5：9-13
[90]顾永泉.机械密封实用技术.北京：机械工业出版社,2001
[91]谢友柏.摩擦学的三个公理.摩擦学学报,2001,202(117)：208.15
[92]江亲瑜,董美云,葛宰林,等.数值仿真技术及其在磨损研究中的应用.大连铁道学院学报,1997,18(2)：41-44
[93]桂长林.Archard的磨损设计计算模型及其应用方法.润滑与密封,1990,(1)：12-21
[94]刘峰壁.直齿圆柱齿轮磨损过程仿真.机械科学与技术.2004,23(1)：55-59
[95]王淑仁,闫玉涛,丁津原,等.渐开线直齿圆柱齿轮啮合磨损试验研究.东北大学学报(自然科学版),2004,25(2)：146-149
[96]Flodin A, Andersson S. Simulation of mild wear in spur gears. Wear,1997, 207(2):16-23
[97]赵源,高万振,李健,等.磨损研究及其方向.材料保护.2004,37(7)：18-34
[98]章易程,田红旗,唐进元,等.基于摩擦功原理的高副滑动磨损的研究.中国机械工程,2010,21(3)：344-347
[99]章易程,李蔚,编著.计算机辅助应用技术基础.北京：国防工业出版社,2005
[100]王淑仁,闫玉涛,丁津原.渐开线直齿圆柱齿轮啮合磨损试验研究.东北大学学报(自然科学版),2004,25(4)：146-149.
[101]中华人民共和国铁道部.SS8型电力机车大修规程.北京：中国铁道出版社,2004
[102]李方,章易程.机车传动齿轮箱开裂现状分析与设计对策.铁道科学与工程学报,2005,2(2)：76-80
[103]章易程,李汉良,田红旗,等.齿轮径向自吸流体润滑方法的供油分析.润滑与密封,2010,35(2)：19-22
[104]章易程.齿轮径向自吸流体润滑方法.中发明专利,CN101586657,2009-11-25
[105]章维一,侯丽雅.润滑理论中卷汲速度的概念辨异及结果分析.中国机械工程,2001,12(11)：1239-1241
[106]林洪义编著.回转式容积泵理论与设计.北京：兵器工业出版社,1995
[107]王世杰,李勤.潜油螺杆泵采油技术及系统设计.北京：冶金工业出版社,2006