多种载荷下齿轮弯曲强度与齿面摩擦因数的计算方法研究
|
摘要
齿轮是重要的基础件，其设计与制造水平影响到机械装备的性能和可靠性。开展齿轮强度和齿面摩擦的计算与试验研究，对于增大承载能力、提高疲劳寿命、减少摩擦磨损、改善传动性能等具有显著的意义。关于齿轮弯曲强度和齿面摩擦的计算和试验研究较多，以下问题值得探索：多种荷载下齿轮弯曲强度计算的精确建模方法，齿根应力和轮齿变形的数值计算；能够表征齿面多样的摩擦润滑性态及其变化规律的过程模型，齿面关键摩擦参数的普适计算方法；基于啮合理论与摩擦学、接触动力学等交叉的齿面冲击摩擦机理及定量计算等。
基于上述问题的思考并结合作者承担的相关课题，提出了本论文的研究论题。重点研究三个问题：多种荷载下齿轮弯曲强度计算的精确建模方法；齿面摩擦润滑的多态性模型与计算方法；齿面摩擦力与摩擦因数的普适量化计算方法。主要研究内容和创新点如下：
1.对齿轮有限元精确建模与弯曲强度计算方法进行了研究，通过比较研究验证了上述方法的正确性。根据齿轮展成加工原理和坐标系矩阵变换法推导出齿形曲线，基于纯文本数据文件的APDL与MATLAB的混合建模方法，实现了齿轮几何模型的精确建模。基于含误差与变形的计算模型，推导出弯曲强度计算力点的位置判别式，可作为弯曲强度计算力点选取的参考。研究了齿轮弯曲强度有限元计算的多种有效荷载，通过对不同荷载下齿根峰值应力和轮齿变形的比较研究发现：按集中力、线分布力、Hertz接触面分布力、静态接触力的次序，计算结果的精确性不断提高；移动负荷的动载等效分析，较难体现啮合冲击效应。
2.研究了齿间载荷叠加效应、齿高及齿宽方向的载荷分布及轮齿变形和齿根最大拉/压分布规律。研究显示：（1）相邻齿对啮合引起的力叠加效应，在齿轮强度精确计算中不能忽略，啮合力叠加效应对中心齿受压侧的影响大于受拉侧，并使轮齿最大变形进一步增大。（2）均布荷载、三角分布和三次抛物线分布荷载作用下，齿宽方向的齿根峰值应力和接触区域轮齿变形的变化规律，验证了齿端刚度效应和轮齿变形及应力分布的连续性；齿向荷载的不均匀性和齿端刚度效应，使得齿根最大压/拉应力有所增大，接触区域的最大变形略有下降。
3.基于虚拟仪器集成平台，提出了通过无线应变采集卡和路由器传输齿根应变数据的新方法，设计了齿根动应力无线测试台。通过多点平均法消除随机电噪声获取待测数据，将输入端和输出端的转速和转矩取平均值，作为计算模型的加载工况，保证了计算模型力边界与试验条件的一致性。测得的齿根应力变化曲线比较准确地反映了单/双啮区交变、啮合冲击及相邻啮合齿对的影响；测得的最大齿根应力与有限元计算结果及其他研究者的结论比较一致，验证了本文提出的无线测量方法及上述有限元计算模型的正确性。获取了齿面摩擦因数反求需要用到的试验样本数据，即测量应力。
4.提出了齿面摩擦润滑的多态性模型。将啮合传动理论与摩擦学理论相结合，对齿轮传动中的多种摩擦润滑性态（弹流润滑、边界润滑、混合润滑、干摩擦、冲击摩擦等）的形成机理、特征及存在条件等进行了研究。结合齿轮系统的复杂性和传动中出现的摩擦过渡特性，提出了齿轮传动摩擦润滑的多态性概念和过程模型。根据齿面是否出现局部干摩擦，提出将混合润滑分为Ⅰ型（不含局部干摩擦）和Ⅱ型（含局部干摩擦）。最后，研究了混合润滑Ⅰ型的构成模型及其齿面摩擦力/摩擦因数的计算方法。
5.提出了基于齿根计算应力和测量应力的齿面摩擦因数反求方法。研究发现，轮齿在单啮上界点啮合时，齿根非接触区的最大拉/压应力对齿面摩擦具有较高的灵敏性，其中最大拉应力的灵敏度比压应力高出近1倍。在此基础上，提出了以计算应力和测试应力为变量构建优化目标函数，利用隔代映射小种群遗传算法与有限单元程序，反求干摩擦状态下的齿面摩擦因数。根据反求的齿面摩擦因数，研究了齿面摩擦对齿根应力和轮齿变形的影响。
6.提出了将线外啮入冲击阶段分为冲击、刮行和正常啮合三个阶段，基于齿轮啮合原理与数值反推技术，计算含系统误差和轮齿变形的线外啮入冲击几何位置、冲击速度及冲击摩擦因数。主要研究结论：（1）考虑到影响啮入冲击的主要误差项、轮齿变形和齿面载荷均沿啮合作用线方向，提出了在该方向上构建“系统等效误差－轮齿综合变形”计算模型。（2）按统计分布规律将基节偏差、法向侧隙和齿廓修形量沿啮合线合成为系统等效误差；将弯曲、压缩、剪切、接触等变形沿作用线合成为轮齿综合变形；再将系统等效误差与轮齿综合变形进行二次合成，用以判断线外啮入冲击点的初始几何位置。（3）根据轮齿变形－载荷历程曲线按搜索法反推出线外啮入冲击点的轮齿综合变形，据此推算出线外啮入初始点的位置和冲击力；建立线外啮入冲击摩擦模型和计算冲击摩擦因数。
Gear transmission, as a key mechanical part, may affect the performance andreliability of machinery and equipment, which relate to gear design and manufacture.The theoretical and experimental researches on gear strength and friction have asignificant meaning for increasing the carrying capacity, improved fatigue life, andto reduce friction and wear, to improve the transmission performance.
Many researches are devoted to gear bending strength and friction by usingtheoretical and experimental methods. However, there are many intractabilityproblems about exactly calculating or testing the bending strength and friction, andneed to be studied further:(1) Accurate finite element model and numericalsimulation method for calculating root stress and tooth compliance under differentloads;(2) the realistic model for describing the friction and lubrication states andchange rules on the tooth surface, and pervasive calculating methods for toothfriction parameters;(3) Impact friction mechanism and quantitative calculationbased on interdisciplinary such as theory of gear, tribology, contact dynamics.
Above all, the main motivations of the present paper are:(1) Accurate finiteelement model and numerical simulation method for bending strength;(2)polymorphism model and calculating method of gear friction and lubrication;(3)pervasive calculating methods for friction force and coefficient of tooth surface.Main works and innovation points are listed as follows.
1. The research is about the accurate FEM modeling of gear pair and thecalculation method of bending, which are validated by comparative research. Thetooth curve is deduced based on the gear generating method and coordinatetransformation, and the accurate geometrical modeling of gear profile isaccomplished by the co-modeling method of APDL and MATLAB with text data files.Due to the calculation model including error and deformation, the calculationequation of bending strength is deduced, which may be a criterion to determine theselection of calculation points. The effective loads are studied with the FEM of gearbending strength. The peak stress value of dedendum and deformation of gear toothunder varying loads are compared and conclude that the accuracy of calculation isincreased along with the order of concentrated force, line loads, distribution force onHertz contact interface and static contact force. Dynamic characteristic analyses of moving load cannot exhibit the impact effects easily.
2. The additive effects of tooth load, load distribution in the direction of toothdepth and tooth width are exhibited in the research. Moreover, the deformation ofgear tooth and the distribution discipline of maximum pull/press force are deserved.The research shows:(1) the additive effect of adjacent gear tooth meshing cannot beignored in the accurate calculation of gear strength, press sides are more affectedthan pull sides, eventually the maximum deformation of gear tooth is increased.Under the influence of even load, triangular distribution and cubic parabola loaddistribution, the varying disciplines of peak stress of dedendum in the gear widthdirection and tooth deformation in the contact zones are displayed. Moreover, it isvalidated about the gear end stiffness effect, gear tooth deformation and continuationof stress. Overall, the maximum press or pull stress of dedendum is increasedaccording to the irregularity of tooth load and effect of gear end stiffness, whereasthe maximum deformation of contact zones is decreased.
3. Based on the virtual integration platform, a new method of stress is conductedcombined with wireless strain acquisition card and stress data transmitted by router.Further, the wireless test rig of dynamic strain in dedendum is designed. The dataunmeasured is acquired with the elimination of random electrical noise by averagemethod. And the input and output of speeds and torques are averaged to be regard asworking conditions, which can be coordinated with the boundary of calculatingmodel and experimental conditions. The tested variation curve of strain ondedendum reflect the phenomenon of single and double tooth gear meshing, gearmeshing impact and the impact of adjacent gear tooth. The measured maximumstrain on dedendum is coordinated with the results of FEM model and conclusionsderived by other researchers, which means the reliability and correction of methodreferred in the thesis and the FEM model as well as the results deduced. At last, thetest samples, namely measuring stresses, used in the fiction coefficient reverse ofgear tooth are acquired reliable.
4. The polymorphism model of gear friction and lubrication is proposed. Theforming-mechanisms, characteristics and existing conditions of multiple gearfriction and lubrication behaviors (including elastohydrodynamic lubrication,boundary lubrication, mixed lubrication, dry friction, impact friction) in drivingprocess are investigated combining mesh theory with tribology. Then thepolymorphism model is proposed in consideration of the tribology systemcomplexity of gear drive and the friction transient phenomenon of teeth contact. The mixed lubrication can be devided into typeⅠ(not including local dry friction) andtype Ⅱ (including local dry friction). Finally, the composition model of mixedlubricationⅠand calculating method of friction coefficient are studied.
5. The reverse method for coefficient of friction on surfaces on gear teeth isproposed by IP-uGA based on the numerical solution and test value of maximumtooth root stress. The sensibility of the tooth root stress to profile friction force andcoefficient is investigated when loaded on the upper point of single gear engagement.The sensitivity of the maximum tensile stress is twice as much as the maximumcompressive stress. The objective function considering calculating stress, testingstress and friction force as variables is gained and the dry friction coefficient isreversed by the genetic algorithm and FEM program. The effects of tooth surfacefriction on tooth root stress and tooth deformation are studied based on the frictioncoefficient reversed.
6. Corner contact is devided into impact, scrape and normal engagement stages.Combining gear theory with numerical backstepping, the method for modelling andcalculating of impact friction caused by corner contact in gear transmissionconsidering the system error and tooth deformation is proposed. Main conclusionsinclude:(1) The work law of the main system errors, teeth deformation and loads onthe line of action is studied, which influences corner contact. Then the calculationmodel including gear equivalent error—combined deformation is established on theline of action.(2) According to the distributive rule, gear equivalent error issynthesized by base pitch error, normal backlash and tooth profile modification onthe line of action, and combined deformation is synthesized by bending, compressive,shearing and contact compliances. Combining the secondarily equivalent error withthe combined deformation, the position standard of the point situated at cornercontact is established.(3) The combined tooth compliance of the first point lying incorner contact before the normal path is backstepped, on basis of the curve of toothsynthetic compliance&load-history curve. After the impact position and force arecalculated accurately, the impact friction model is estabilshed and the impact frictioncoefficient is calculated.
基于上述问题的思考并结合作者承担的相关课题，提出了本论文的研究论题。重点研究三个问题：多种荷载下齿轮弯曲强度计算的精确建模方法；齿面摩擦润滑的多态性模型与计算方法；齿面摩擦力与摩擦因数的普适量化计算方法。主要研究内容和创新点如下：
1.对齿轮有限元精确建模与弯曲强度计算方法进行了研究，通过比较研究验证了上述方法的正确性。根据齿轮展成加工原理和坐标系矩阵变换法推导出齿形曲线，基于纯文本数据文件的APDL与MATLAB的混合建模方法，实现了齿轮几何模型的精确建模。基于含误差与变形的计算模型，推导出弯曲强度计算力点的位置判别式，可作为弯曲强度计算力点选取的参考。研究了齿轮弯曲强度有限元计算的多种有效荷载，通过对不同荷载下齿根峰值应力和轮齿变形的比较研究发现：按集中力、线分布力、Hertz接触面分布力、静态接触力的次序，计算结果的精确性不断提高；移动负荷的动载等效分析，较难体现啮合冲击效应。
2.研究了齿间载荷叠加效应、齿高及齿宽方向的载荷分布及轮齿变形和齿根最大拉/压分布规律。研究显示：（1）相邻齿对啮合引起的力叠加效应，在齿轮强度精确计算中不能忽略，啮合力叠加效应对中心齿受压侧的影响大于受拉侧，并使轮齿最大变形进一步增大。（2）均布荷载、三角分布和三次抛物线分布荷载作用下，齿宽方向的齿根峰值应力和接触区域轮齿变形的变化规律，验证了齿端刚度效应和轮齿变形及应力分布的连续性；齿向荷载的不均匀性和齿端刚度效应，使得齿根最大压/拉应力有所增大，接触区域的最大变形略有下降。
3.基于虚拟仪器集成平台，提出了通过无线应变采集卡和路由器传输齿根应变数据的新方法，设计了齿根动应力无线测试台。通过多点平均法消除随机电噪声获取待测数据，将输入端和输出端的转速和转矩取平均值，作为计算模型的加载工况，保证了计算模型力边界与试验条件的一致性。测得的齿根应力变化曲线比较准确地反映了单/双啮区交变、啮合冲击及相邻啮合齿对的影响；测得的最大齿根应力与有限元计算结果及其他研究者的结论比较一致，验证了本文提出的无线测量方法及上述有限元计算模型的正确性。获取了齿面摩擦因数反求需要用到的试验样本数据，即测量应力。
4.提出了齿面摩擦润滑的多态性模型。将啮合传动理论与摩擦学理论相结合，对齿轮传动中的多种摩擦润滑性态（弹流润滑、边界润滑、混合润滑、干摩擦、冲击摩擦等）的形成机理、特征及存在条件等进行了研究。结合齿轮系统的复杂性和传动中出现的摩擦过渡特性，提出了齿轮传动摩擦润滑的多态性概念和过程模型。根据齿面是否出现局部干摩擦，提出将混合润滑分为Ⅰ型（不含局部干摩擦）和Ⅱ型（含局部干摩擦）。最后，研究了混合润滑Ⅰ型的构成模型及其齿面摩擦力/摩擦因数的计算方法。
5.提出了基于齿根计算应力和测量应力的齿面摩擦因数反求方法。研究发现，轮齿在单啮上界点啮合时，齿根非接触区的最大拉/压应力对齿面摩擦具有较高的灵敏性，其中最大拉应力的灵敏度比压应力高出近1倍。在此基础上，提出了以计算应力和测试应力为变量构建优化目标函数，利用隔代映射小种群遗传算法与有限单元程序，反求干摩擦状态下的齿面摩擦因数。根据反求的齿面摩擦因数，研究了齿面摩擦对齿根应力和轮齿变形的影响。
6.提出了将线外啮入冲击阶段分为冲击、刮行和正常啮合三个阶段，基于齿轮啮合原理与数值反推技术，计算含系统误差和轮齿变形的线外啮入冲击几何位置、冲击速度及冲击摩擦因数。主要研究结论：（1）考虑到影响啮入冲击的主要误差项、轮齿变形和齿面载荷均沿啮合作用线方向，提出了在该方向上构建“系统等效误差－轮齿综合变形”计算模型。（2）按统计分布规律将基节偏差、法向侧隙和齿廓修形量沿啮合线合成为系统等效误差；将弯曲、压缩、剪切、接触等变形沿作用线合成为轮齿综合变形；再将系统等效误差与轮齿综合变形进行二次合成，用以判断线外啮入冲击点的初始几何位置。（3）根据轮齿变形－载荷历程曲线按搜索法反推出线外啮入冲击点的轮齿综合变形，据此推算出线外啮入初始点的位置和冲击力；建立线外啮入冲击摩擦模型和计算冲击摩擦因数。
Gear transmission, as a key mechanical part, may affect the performance andreliability of machinery and equipment, which relate to gear design and manufacture.The theoretical and experimental researches on gear strength and friction have asignificant meaning for increasing the carrying capacity, improved fatigue life, andto reduce friction and wear, to improve the transmission performance.
Many researches are devoted to gear bending strength and friction by usingtheoretical and experimental methods. However, there are many intractabilityproblems about exactly calculating or testing the bending strength and friction, andneed to be studied further:(1) Accurate finite element model and numericalsimulation method for calculating root stress and tooth compliance under differentloads;(2) the realistic model for describing the friction and lubrication states andchange rules on the tooth surface, and pervasive calculating methods for toothfriction parameters;(3) Impact friction mechanism and quantitative calculationbased on interdisciplinary such as theory of gear, tribology, contact dynamics.
Above all, the main motivations of the present paper are:(1) Accurate finiteelement model and numerical simulation method for bending strength;(2)polymorphism model and calculating method of gear friction and lubrication;(3)pervasive calculating methods for friction force and coefficient of tooth surface.Main works and innovation points are listed as follows.
1. The research is about the accurate FEM modeling of gear pair and thecalculation method of bending, which are validated by comparative research. Thetooth curve is deduced based on the gear generating method and coordinatetransformation, and the accurate geometrical modeling of gear profile isaccomplished by the co-modeling method of APDL and MATLAB with text data files.Due to the calculation model including error and deformation, the calculationequation of bending strength is deduced, which may be a criterion to determine theselection of calculation points. The effective loads are studied with the FEM of gearbending strength. The peak stress value of dedendum and deformation of gear toothunder varying loads are compared and conclude that the accuracy of calculation isincreased along with the order of concentrated force, line loads, distribution force onHertz contact interface and static contact force. Dynamic characteristic analyses of moving load cannot exhibit the impact effects easily.
2. The additive effects of tooth load, load distribution in the direction of toothdepth and tooth width are exhibited in the research. Moreover, the deformation ofgear tooth and the distribution discipline of maximum pull/press force are deserved.The research shows:(1) the additive effect of adjacent gear tooth meshing cannot beignored in the accurate calculation of gear strength, press sides are more affectedthan pull sides, eventually the maximum deformation of gear tooth is increased.Under the influence of even load, triangular distribution and cubic parabola loaddistribution, the varying disciplines of peak stress of dedendum in the gear widthdirection and tooth deformation in the contact zones are displayed. Moreover, it isvalidated about the gear end stiffness effect, gear tooth deformation and continuationof stress. Overall, the maximum press or pull stress of dedendum is increasedaccording to the irregularity of tooth load and effect of gear end stiffness, whereasthe maximum deformation of contact zones is decreased.
3. Based on the virtual integration platform, a new method of stress is conductedcombined with wireless strain acquisition card and stress data transmitted by router.Further, the wireless test rig of dynamic strain in dedendum is designed. The dataunmeasured is acquired with the elimination of random electrical noise by averagemethod. And the input and output of speeds and torques are averaged to be regard asworking conditions, which can be coordinated with the boundary of calculatingmodel and experimental conditions. The tested variation curve of strain ondedendum reflect the phenomenon of single and double tooth gear meshing, gearmeshing impact and the impact of adjacent gear tooth. The measured maximumstrain on dedendum is coordinated with the results of FEM model and conclusionsderived by other researchers, which means the reliability and correction of methodreferred in the thesis and the FEM model as well as the results deduced. At last, thetest samples, namely measuring stresses, used in the fiction coefficient reverse ofgear tooth are acquired reliable.
4. The polymorphism model of gear friction and lubrication is proposed. Theforming-mechanisms, characteristics and existing conditions of multiple gearfriction and lubrication behaviors (including elastohydrodynamic lubrication,boundary lubrication, mixed lubrication, dry friction, impact friction) in drivingprocess are investigated combining mesh theory with tribology. Then thepolymorphism model is proposed in consideration of the tribology systemcomplexity of gear drive and the friction transient phenomenon of teeth contact. The mixed lubrication can be devided into typeⅠ(not including local dry friction) andtype Ⅱ (including local dry friction). Finally, the composition model of mixedlubricationⅠand calculating method of friction coefficient are studied.
5. The reverse method for coefficient of friction on surfaces on gear teeth isproposed by IP-uGA based on the numerical solution and test value of maximumtooth root stress. The sensibility of the tooth root stress to profile friction force andcoefficient is investigated when loaded on the upper point of single gear engagement.The sensitivity of the maximum tensile stress is twice as much as the maximumcompressive stress. The objective function considering calculating stress, testingstress and friction force as variables is gained and the dry friction coefficient isreversed by the genetic algorithm and FEM program. The effects of tooth surfacefriction on tooth root stress and tooth deformation are studied based on the frictioncoefficient reversed.
6. Corner contact is devided into impact, scrape and normal engagement stages.Combining gear theory with numerical backstepping, the method for modelling andcalculating of impact friction caused by corner contact in gear transmissionconsidering the system error and tooth deformation is proposed. Main conclusionsinclude:(1) The work law of the main system errors, teeth deformation and loads onthe line of action is studied, which influences corner contact. Then the calculationmodel including gear equivalent error—combined deformation is established on theline of action.(2) According to the distributive rule, gear equivalent error issynthesized by base pitch error, normal backlash and tooth profile modification onthe line of action, and combined deformation is synthesized by bending, compressive,shearing and contact compliances. Combining the secondarily equivalent error withthe combined deformation, the position standard of the point situated at cornercontact is established.(3) The combined tooth compliance of the first point lying incorner contact before the normal path is backstepped, on basis of the curve of toothsynthetic compliance&load-history curve. After the impact position and force arecalculated accurately, the impact friction model is estabilshed and the impact frictioncoefficient is calculated.
引文
[1]国家自然科学基金委员会工程与材料科学部.机械工程学科发展战略研究（2011-2020）.北京：科学出版社，2010
[2]谢友柏，张嗣伟.摩擦学科学及工程应用现状与发展战略研究—摩擦学在工业节能、降耗、减排中的地位与作用的调查.北京：高等教育出版社，2009
[3]中国机械工程学会.中国机械工程技术路线图.北京：中国科学技术出版社，2011
[4]Lewis W. Investigation of the strength of gear teeth. In: Proceedings ofEngineering Club, Philadelphia, PA,1893,16-23
[5]Rand R V, Peterson R E. Load and stress cycle in gear teeth. MechanicalEngineering,1929,51(9):653-662
[6]Walker H. Gear tooth deflection and profile modification (Part1).The Engineer,1938,166(4318):409-412
[7]Walker H. Gear tooth deflection and profile modification (Part2).The Engineer,1938,166(4319):434-436
[8]Walker H. Gear tooth deflection and profile modification (Part3).The Engineer,1940,170(4414):102-104
[9]Weber C. The deformation of loaded gears and the effect on their load-carryingcapacity. London: British Scientific and Industrial Research,1949
[10]Merritt H E. Gear tooth stresses and rating formula. Proceedings of theInstitution of Mechanical Engineers,1952,166(1):196-216
[11]Niemann. Maschinen elemente Bd.Ⅱ. Berlin: Springer,1960
[12]Wellauer E J, Seireg A. Bending strength of gear teeth by cantilever plate theory.ASME Journal of Engineering for Industry,1960,82(3):213-220
[13]Cornell R W. Compliance and stress sensitivity of spur gear teeth. ASMEJournal of Mechanical Design,1981,103(4):447-459
[14]Tavikoli M S, Houser D R. Optimum profile modifications for the minimizationof static transmission errors of spur gears. ASME Journal of Mechanisms,Transmissions, and Automation in Design,1986,108(3):86-94
[15]Lin H H, Huston R L, Coy J J. On dynamic loads in parallel shaft transmissions:Part I—modeling and analysis. ASME Journal of Mechanisms, Transmissions,and Automation in Design,1988,110(2):221-225
[16]颜海燕.考虑线外啮合的齿轮动力学研究：[中南大学硕士学位论文].长沙：中南大学，2002
[17]Dolan T J，Broghammer E I. A photoelastic study of the stresses in gear toothfillets. University of Illinois Station Bulletin,1942,39(31):1-42
[18]吴继泽,王统.齿根过渡曲线与齿根应力.北京：国防工业出版社，1989
[19]Shotter B A. New approach to gear tooth root stresses. ASME Journal ofEngineering for Industry,1974，96(1)：11-18
[20]程乃士,孙大乐.齿轮应力和位移分析的保角映射法.机械传动，1992，16(1)：40-46
[21]Terauchi Y, Nagamura K. Study on deflection of spur gear teeth. Bull. JSME,1981,24(188)：1682-1688
[22]Baronet C N, Tordion G V. Exact stress distribution in standard gear teeth andgeometry factor. ASME Journal of Engineering for Industry,1973,95(4):1159-1163
[23]Premilhat A, Tordion G V. An improved determination of the elastic complianceof a spur gear tooth acted on by a concentrated load. ASME Journal ofEngineering for Industry,1974,96(2),382-384
[24]Cardou A, Tordion G V. Numerical implementation of complex potentials forgear tooth stress analysis. ASME Journal of Engineering for Industry,1981,103(4):460-465
[25]程乃士,刘温.计算机求解渐开线齿轮齿廓的保角映射函数.应用数学和力学,1988,9(11):1037-1043
[26]许立忠.保角映射法精确求解渐开线直齿轮轮齿挠度.机械工程学报，1996，32(2)：14-18
[27]Zienkiewicz O C, Taylor R L. The finite element method, fifth edition. London:Butterworth Heinemann,2000
[28]李润方，陈大良.斜齿轮三维有摩擦接触应力分析及前后处理方法.齿轮，1990，14(1)：29-34
[29]杜平安，梁锡昌.齿轮传动的现代设计方法.机械，1994，21(1)：43-45
[30]Wilcox L, Colman W. Application of finite elements to the analysis of gear toothstress. ASME Journal Engineering for Industry,1973,95(4)：1139-1148
[31]Chabert G, Dang T T, Mathis R. An evaluation of stresses and deflection of spurgear teeth under strain.ASME Journal of Engineering for Industry,1974,96(1):85-93
[32]魏任之,张永忠,史兴虹.关于直齿圆柱齿轮轮齿受载变形量的计算.齿轮，1980,(4):1-8
[33]Chang S H, Huston R L, Coy J J. A finite element stress analysis of spur gearsincluding fillet radii and rim thickness effects. ASME Journal of Mechanisms,Transmissions, and Automation in Design,1983,105(3):327-330
[34]Von Eiff H, Hirschmann K H, Lechner G. Influence of gear tooth geometry ontooth stress of external and internal gears. ASME Journal of Mechanical Design,1990,112(4):575-583
[35]Andrews J D. A finite element analysis of bending stresses included in externaland internal involutes spur gear. Journal of Strain Analysis,1991,26(3):153-163
[36]Huseyin Filiz I，Eyercioglu O. Evaluation of gear tooth stresses by finite elementmethod. ASME Journal of Engineering for Industry,1995,117(5):232-239
[37]Simon V. FEM stress analysis in hypoid gears.Mechanism and MachineTheory,2000,35(9):1197-1220
[38]Alexander L K，Shekhtman Y V. Direct gear design: bending stress minimization.Gear Technology,2003(9/10):44-47
[39]唐进元,周长江，吴运新.齿轮弯曲强度有限元分析精确建模的探讨.机械科学与技术，2004，23（10）：1146-1149，1248
[40]Conry T F, Seireg A. Mathematical programming technique for the evaluation ofload distribution and optimal modification for gear systems. ASME Journal ofEngineering for Industry,1973,95(11).1115-1122
[41]Coy J J, Hu-Chih Chao C. A method of selecting grid size to account for Hertzdeformation in finite element analysis of spur gears. Journal of MechanicalDesign,1982,104(10):759-765
[42]李润方,汤庆平，陈大良.啮合轮齿接触有限元分析网格自动生成方法.重庆大学学报，1992，15(3):11-14
[43]Refaat M H, Meguid S A. On the contact stress analysis of spur gears usingvariational inequalities. Computers and Structures,1995,57(5):871-882
[44]方宗德,杨宏斌.用规划法的齿轮有摩擦三维连续弹性接触分析.机械工程学报，1999，35(6):98-101
[45]Lee K. Analysis of the dynamic contact between rotating spur gears by finiteelement and multi-body dynamics. Proceedings Institution of MechanicalEngineers, Part C,2001,215:423-434
[46]Li S T. Finite element analyses for contact strength and bending strength of apair of spur gears with machining errors, assembly errors and toothmodifications. Mechanism and Machine Theory,2007,42(1):88-114
[47]Wallance D B, Seireg A. Computer simulation of dynamic stress, deformation,and fracture of gear teeth. Journal of Engineering for Industry,1973,95(11)：1108-1114
[48]Ostiguy L, Constantinescu I. Dynamic response of spur gear teeth. In:Proceedings of the International Modal Analysis Conference&Exhibit,Orlando, FL，1984:286-291
[49]Ramamurti V, Nayak H Vijayendra, Sujatha C. Static and dynamic analysis ofspur and bevel gears using FEM. Mechanism and Machine Theory,1998,33(8):1177-1193
[50]Wu J S, Chen C H. Torsional vibration analysis of gear-branched system byfinite element method. Journal of Sound and Vibration,2001,240(1):159-182
[51]Howard I, Jia S G, Wang J D. The dynamic modeling of a spur gear in meshincluding friction and a crack. Mechanical Systems and Signal Processing,2001,15(5):831-853
[52]Mackaldener M, Olssom M. Analysis of crack propagation during tooth interiorfatigue fracture. Engineering Fracture Mechanics,2002,69(18):2147-2162
[53]Sfakiotakis V G, Anifantis N K. Finite element modeling of spur gearingfractures. Finite Elements in Analysis and Design,2002,39(2):79-92
[54]Aui Ural, Gerd Heber, Paul A, et al. Three-dimensional, parallel, finite elementsimulation of fatigue crack growth in a spiral bevel pinion gear. EngineeringFracture Mechanics,2005,72(8):1148-1170
[55]Glode S, Winter H, Stüwe H P. A fracture mechanics model for the wear of gearflanks by pitting. Wear,1997,208(1-2):177-183
[56]Glode S, Ren Z, Fla ker J. Surface fatigue of gear teeth flanks. Computers andStructures,1999,73(1-5):475-483
[57]Jesper Brauer, S ren Andersson. Simulation of wear in gears with flankinterference-a mixed FE and analytical approach. Wear,2003,254(11-12):1216-1232
[58]Mao K. Gear tooth contact analysis and its application in the reduction of fatiguewear. Wear,2007,262(11-12):1281-1288
[59]Ciavarella Michele, Demelio Giuseppe. Numerical methods for optimization ofspecific sliding, stress concentration and fatigue life of gears. InternationalJournal of Fatigue,1999,21(5):465-474
[60]Yang F, Su D, Gentle C R. Finite element modeling and load share analysis forinvolute worm gears with localized tooth contact. Journal of MechanicalEngineering Science,2001,215(7):805-816
[61]龙慧,张光辉，罗文军.旋转齿轮瞬时接触应力和温度的分析模拟.机械工程学报，2004,40(8):24-29
[62]Argyris J, Fuentes Alfonso, Litvin Faydor L. Computerized integrated approachfor design and stress analysis of spiral bevel gears.Computer Methods inApplied Mechanics and Engineering,2002,191(11-12):1057-1095
[63]Litvin Faydor L, Fuentes Alfonso, Hayasaka Kenichi. Design, manufacture,stress analysis, and experimental tests of a low-noise endurance spiral bevelgears. Mechanism and Machine Theory,2006,41(1):83-118
[64]Kumar V Senthil, Muni D V, Muthuveerrappan G. Optimization of asymmetricspur gear drives to improve the bending load capacity. Mechanism and MachineTheory,2008,43(7)：829-858
[65]赵清澄.光测力学教程.北京：高等教育出版社，1996
[66]Timoshenko S P, Baud R V. Strength of gear teeth. Mechanical Engineering,1926,48(11)：1108-1115
[67]Heywood R B, Sopwith D G. Loads and stresses in screw threads and projections.In: Applied Mechanics Division of the Institution of Mechanical Engineers,London,1948,58-65
[68]Kelly B W, Pedersen R. The beam strength of modern gear tooth design. In: SAEEarthmoving Industry Conference, Peoria Ⅲ,1957,245-268
[69]Jacobson M A. Bending stresses in spur gear teeth: proposed new design factorsbased on a photo-elastic investigation. Proceedings of the Institution ofMechanical Engineers,1955,169(31):587-609
[70]Baxter M L, King C B, Coleman W. Three dimensional photo-elastic analysis inthe hypoid gear pair. In: JSME Semi-international Symposium, Tokyo，1967,357-345
[71]方宗德,蒋孝煜.齿轮轮齿受载变形的激光散斑测量及计算.齿轮，1984，8(5)：19-25
[72]薛春玉,郭懋林，严勇等.某直升机螺旋伞齿轮三维光弹性应力分析.哈尔滨工业大学学报，1995，27(5)：23-25
[73]许洪斌，张光辉，加藤正名.分阶式双渐开线齿轮的光弹试验与弯曲强度试验研究.机械工程学报,2000，36(8)：39-42
[74]Wang, Ming-Jong. A new photoelastic investigation of the dynamic bendingstress of spur gears. ASME Journal of Mechanical Design,2003,125(6):365-372
[75]Vasilios A. Spitas, Theodore N. Costopoulos, Christos A. Spitas. Optimum geartooth geometry for minimum fillet stress using BEM and experimentalverification with photoelasticity. Journal of Mechanical Design,2006,128(9):1159-1164
[76]Gregory R W, Harris S L, Munro R G. Dynamic behaviour of spur gears. Proc.Instn. Mech. Engrs.,1963-64,178(8):207-217
[77]Winter H, Hirt M. The measurement of actual strain at gear teeth, influence offillet radius on stresses and tooth strength. SAME Journal of Engineering forIndustry,1974,96(1):33-50
[78]连小珉,蒋孝煜.齿根动应力测量.齿轮,1987,11(1):33-37(43)
[79]M. Hotait, A. Kahraman. Experiments on root stresses of helical gears with leadcrown and misalignments. ASME Journal of Mechanical Design,2008,130(7):074502-5
[80]王成,方宗德,谷建功等.人字齿轮承载接触分析与试验.航空动力学报,2010,25(3):718-722
[81]Miche`le Guingand, Jean-Pierre de Vaujany, Colin-Yann Jacquin. Quasi-staticanalysis of a face gear under torque. Computer Methods in Applied Mechanicsand Engineering,2005,194(39-41):4301-4318
[82]Litvin F L, Fuentes A, Hayasaka K. Design, manufacture, stress analysis,and experimental tests of low-noise high endurance spiral bevel gears.Mechanism and Machine Theory,2006,41(1):83-118
[83]Pascal Ziegler, Peter Eberhard. Simulative and experimental investigation ofimpacts on gear wheels. Computer Methods in Applied Mechanics andEngineering,2008,197(51-52):4653-4662
[84]Hotait, M. A. Kahraman, A. Nishino, T. An Investigation of Root Stresses ofHypoid Gears with Misalignments. ASME Journal of Mechanical Design,2011,133(7):071006-9
[85]Yong-jun Wu, Jian-jun Wang, Qin-kai Han. Static/dynamic contact FEA andexperimental study for tooth profile modification of helical gears. Journal ofMechanical Science and Technology,2012,26(5):1409-1417
[86]葛世荣，朱华.摩擦学复杂系统及其问题的量化研究方法.摩擦学报，2002，22（5）：405-408
[87]国家自然科学基金委员会工程与材料科学部.机械与制造科学.北京：科学出版社，2006
[88]周仲荣.摩擦学发展前沿.北京：科学出版社，2006
[89]谢友柏.摩擦学科学与工程前沿.北京：高度教育出版社，2005
[90]秦大同.机械传动科学技术的发展历史与研究进展.机械工程学报，2003，39（12）：37-42
[91]Masatoshi Yoshizaki, Chotaro Naruse, Ryozo Nemoto, et al. Study on frictionalloss of spur gears(concerning the influence of tooth form, load, tooth surfaceroughness, and lubricating oil). Tribology Transactions,1991,34(1)：138-146
[92]Shoji Haizuka, Takaaki Kikusaki, Chotaro Naruse. Studies on friction loss ofspur gears. JSME International Journal, Series C,1999,42(4)：1041-1049
[93]姚建初，陈义保，周济等.齿轮传动啮合效率计算方法的研究.机械工程学报，2001，37（11）：18-21
[94]Michlin Y, Myunster V. Determination of power losses in gear transmissionswith rolling and sliding friction incorporated. Mechanism and Machine Theory,2002,37(2)：167-174
[95]Xu F R. Effect of the sliding friction between teeth on the bending fatigue stresson the tooth root of the great gear in the machine tool increasing speed gearing.Journal. of University of Shanghai for Science and Technology,2000,22(2)：119-125
[96]Lehtovaara Arto. Numerical model for the calculation of subsurface stresses inline contact of real rough surface. Tribologia,2003,22(2)：20-31
[97]高创宽，周谋，亓秀梅.齿面摩擦力对齿轮接触应力的影响.机械强度，2003，25（6）：642-645
[98]Vijayarangan S, Ganesan N. Static contact stress analysis of a spur gear toothusing the finite element method, including frictional effects. Computers&Structures,1994,51(6)：765-770
[99]Tian Y T, Li C X, Tong W, et al. A finite-element-based study of the loaddistribution of a heavily loaded spur gear system with effects of transmissionshafts and gear blanks. ASME Journal. of Mechanical Design.2003,125(9)：625-631
[100]Blake J W, Draper C F. Further development of a predictive pitting model forgears: improvements in the life prediction analysis. Tribology Transactions,1994,37(2)：237-244
[101]Fla ker J, Fajdiga G, Glode S, et al. Numerical simulation of surface pittingdue to contact loading. International Journal of Fatigue,2001,23(7)：599-605
[102]Lewicki D G, Handschuh R F, Spievak L E, et al. Consideration of movingtooth load in gear crack propagation predictions. ASME Journal of MechanicalDesign,2001,123(3)：118-124
[103]Velex P, Cahouet V. Experimental and numerical investigations on theinfluence of tooth friction in spur and helical gear dynamics. Journal ofMechanical Design,2000,122(12)：515-522
[104]王三民，沈允文，董海军.含摩擦和间隙直齿轮副的混沌与分叉研究.机械工程学报，2002,38(9):8-11
[105]Aziz S M A，Seireg A. A parametric study of frictional noise in gears. Wear,1994,176(1)：25-28
[106]姚文席,王东，张志强.渐开线直齿轮的摩擦激励及振动阻尼分析.振动、测试与诊断，2000,20(3):206-210
[107]Velex P, Sainsot P. An analytical study of tooth friction excitations in errorlessspur and helical gears. Mechanism and Machine Theory,2002,37(7)：641-658
[108]陈光雄，周仲荣.摩擦系数影响摩擦噪声发生的机理研究.中国机械工程，2003，14（9）：766-769
[109]谢友柏.摩擦学的三个公理.摩擦学学报，2001，21（3）：161-166
[110]葛世荣，朱华.摩擦学的分形.北京：机械工业出版社，2005
[111]林子光，徐大耐等.齿轮传动的润滑.北京：机械工业出版社，1980
[112]Dowson D. Boundary Lubrication—An Appraisal of World Literature. NewYork: ASME Press, Chapter Ⅱ,1969
[113]温诗铸，雒建斌.纳米薄膜润滑研究.清华大学学报，2001，41（4/5）：63-68
[114]McEwen E. The effect of variation of viscosity with pressure on the loadcarrying capacity of oil film between gear teeth. Journal of Institute ofPetroleum,1952,38(3):646-656
[115]Adkins R W, Radzimovsky, E I. Lubrication phenomena in spur gear. ASMEJournal of Basic Engineering,1965,87(3):655-665
[116]Dowson D, Higginson G R. Elasto-hydrodynamic lubrication(SI Edition).Oxford: Pergamon Press,1977
[117]Vichard J P. Transient effects in the lubrication of Hertzian contacts. Journal ofMechanical Engineering Science,1971,13(3):173-189
[118]Wang K L, Cheng H S. A numerical solution to the dynamic load, filmthickness and surface temperatures in spur gears. ASME Journal of MechanicalDesign,1981,103(4):177-195
[119]Petrousevitch A I. The investigation of oil film thickness in lubricated ball-racerolling contact. Wear,1972,19(4):369-389
[120]Wada S, Tsukijihara M. Elastohydrodynamic squeeze problem of two rotatingcylinders(Part1). Bulletin JSME,1981,24(190):937-942
[121]Wada S, Tsukijihara M. Elastohydrodynamic squeeze problem of two rotatingcylinders(Part2). Bulletin JSME,1981,24(192):1072-1077
[122]杨沛然.非稳态热弹性流体动力润滑研究：[清华大学博士论文]，北京：清华大学，1989
[123]Larsson R. Transient non-Newtonian elastohydrodynamic lubrication analysisof an involute spur. Wear,1997,207(11):67-73
[124]卢立新，蔡莹，张和豪.渐开线直齿圆柱齿轮传动瞬态弹流润滑研究.润滑与密封，1999，（5）：5-7
[125]汪久根.时变性对圆柱齿轮弹流润滑的影响.机械设计与研究，2003，19（2）：30-31
[126]王优强，黄丙习，佟景伟等.渐开线直齿轮牛顿流体非稳态热弹流润滑分析.计算力学学报，2005，22（5）：568-573
[127]赵春华，严新平.数学方法在油液监测中的应用.武汉理工大学学报（交通科学与工程版），2004，28（3）：326-333
[128]戴振东，薛群基，王珉.试论摩擦学研究中的科学方法问题.南京航空航天大学学报，1998，30（2）：235-240
[129]温诗铸，黄平.摩擦学原理（第二版）.北京：清华大学出版社，2003
[130]Akin L S. Interdisciplinary lubrication theory for gears with particularemphasis on the scuffing mode of failure. In: Soviet Atomic Energy,1972,Vol.72:6-31
[131]Hamrock B J, Dowson D. Isothermal EHL of point contacts, part Ⅲ－fullflooded results. ASME Journal of Lubrication Technology,1977,99(2)：264-276
[132]Hamrock B J, Dowson D. Elasto-hydrodynamic lubrication of ellipticalcontacts for materials of low elastic modulus,2－starved conjunction. ASMEJournal of Lubrication Technology,1979,101(1)：92-98
[133]Li D F, Kauzlarich J J, Jamison W E. Surface roughness effects on fatigue inpartial EHD lubrication. ASME Journal of Lubrication Technology,1976,98(4):530-537
[134]Buckingham. Analytical mechanics of gears. New York: Dover Press,1949
[135]齿轮手册编委会.齿轮手册（第2版）.北京：机械工业出版社，2006
[136]Christensen H. Stochastic models for hydrodynamic lubrication of roughsurfaces. Proceedings of the Institution of Mechanical Engineers-Part Ⅰ,1970,184(55)：1013-1026
[137]Martin K F. A review of friction predictions in gear teeth. Wear,1978,49(2)：201-238
[138]雒建斌，刘珊，潘国顺等.纳米级混合润滑研究.机械工程学报，2003，39（2）：1-7
[139]孔繁荣.混合润滑的实验技术和特性研究：[清华大学博士论文]，北京：清华大学，1993
[140]Wu S F, Cheng H S. A friction model of partial-EHL contacts and itsapplication to power loss in spur gears. Tribology Transactions,1991,34(3)：398-407
[141]Jiang X, Cheng H S, Hua D Y. A theoretical analysis of mixed lubrication bymacro micro approach: part I-results in a gear surface contact. TribologyTransactions,2000，43(4)：689-699
[142]Kelley B W, Lemanski A J. Lubrication of involute gearing. ProceedingsInstitution of Mechanical Engineers,1967,182(3)：173-184
[143]Martin K F. The efficiency of involute spur gears. ASME Journal ofMechanical Design,1980,105(4)：160-167
[144]Gohar R. Elastohydrodynamics. West Sussex: Ellis Horwood Limited,1988
[145]Vaishya M, Houser D R. Modeling and analysis of sliding friction in geardynamics.In: ASME2000Design Engineering Technical Conferences andComputers and Information in Engineering Conference, Baltimore,2000,601-610
[146]Tallian T E. Pressure and traction rippling in elasto-hydrodynamic contact ofrough surface. In: Trans. ASME,1973,73:18-26
[147]Cameron A, Cordon A N，Symm G T. Contact temperatures in rolling/slidingsurface.In: Proc. Roy. Soc. Lond.,1965, Part A,286-321
[148]Vaishya M, Singh R. Sliding friction-induced non-linearity and parametriceffects in gear dynamics. Journal of Sound and Vibration,2001,248(4)：671-694
[149]Rayiko M V, Dmytrychenko N F. Some aspects of boundary lubrication in thelocal contact of friction surfaces.1988,126(1)：69-78
[150]Britton R D, Elcoate C D, Alanou M P, et al. Effect of surface finish on geartooth friction. ASME Journal of Tribology,2000,122(1)：354-360
[151]S Akbarzadeh, M M Khonsari. Thermoelastohydrodynamic Analysis of SpurGears with Consideration of Surface Roughness. Tribology Letters，2008,32(2)：129-141
[152]Chinmaya Kar, Mohanty, A.R. Determination of time-varying contact length,friction force, torque and forces at the bearings in a helical gear system. Journalof Sound and Vibration,2008,309(1-2)：307-319
[153]王黎钦，刘明霞，古乐.计算机在摩擦实验测试中的应用.哈尔滨工程大学学报，2000，21（2）：81-84
[154]Kleemola, Jaakko, Lehtovaara, A.Experimental evaluation of friction betweencontacting discs for the simulation of gear contact. Tribology Test,2007,13(1)：13-20
[155]Johson K L, Cameron R S. Behavior of elastohydrodynamic oil films at highrolling contact pressures. Proceedings Institution of Mechanical Engineers,1967,182(14):307-319
[156]McCool J I. Evaluating the Tevaarwerk-Johnson elastic/plastic traction modelon the presence of lateral sliding and spin. Tribology Transactions.1990,33(1)：122-130
[157]张钢，李鸣鸣，王中宇等.齿轮润滑摩擦特性模拟试验台的研制.洛阳工学院学报，1997，18（4）：25-29
[158]Gurskii, B.E. Chichinadze, A.V. Thermal friction problem and its development.Journal of Friction and Wear,2007,28(4)：395-400
[159]Voitik R M, Heerdt L. Wear and frictional evaluation of gear lubricants bybench test. JASL Lubrication Engineering,1984,40(12)：719-724
[160]赵建平，杜鸿家.齿面摩擦规律的模拟试验研究.润滑与密封，1994，（2）：6-11
[161]陈文华.仪表齿轮齿面摩擦系数的测定.仪表技术与传感器，1996，（11）：33-36
[162]林子光，李修仁，刘维民等.摩擦过渡的实验研究.润滑与密封，2001，（4）：16-17，20
[163]Smith F W. Rolling contact lubrication-The application of elastohydrodynamictheory. Trans. of ASME,1965,(3):170-176
[164]Benedict G H, Kelley B W. Instantaneous coefficients of gear tooth friction.ASLE Transactions,1961,4(1)：59-70
[165]Oswald F B, Towsend D P, Rebbechi B, et al. Dynamic forces in spurgears-measurement, prediction and code validation. In: Proc.7thASME Int.Power Transmission and Gears Conf., San Diego,1996, Vol.88:9-15
[166]Rebbrchi B, Oswald F B, Townsend D P. Measurement of gear tooth dynamicfriction. In: Proc.7thASME Int. Power Transmission and Gears Conf., SanDiego,1996, Vol.88:355-363
[167]谢如霖.齿轮传动效率、啮合效率和摩擦系数的测试.合肥工业大学学报（自然科学版），1991，14（1）：27-33
[168]Radzimovsy E I, Mirarefi A, Broom W E. Instantaneous efficiency andcoefficient of friction of an involute gear drive. In: Soviet Atomic Energy,1972,72:13-22
[169]Rao A C. Average friction coefficients in gears. Journal MechanicalEngineering Science,1975,17(6)：360-362
[170]Rao A C. Gear friction coefficients and forces. Wear,1979,53(1):87-93
[171]Hori K, Hayashi I, Iwatsuki N. The gravity pendulum method for precisemeasurement of the tooth surface friction coefficient of a pair of mating gears.JSME International Journal, Series C,1999,42(4)：1021-1030
[172]周长江，唐进元，吴运新.齿根应力与轮齿弹性变形的计算方法进展与比较研究.机械传动，2004，28（5）：1-6
[173]Baud S, Velex P. Static and dynamic tooth loading in spur and helical gearedsystems-experiments and model validation. ASME Journal of MechanicalDesign,2002,124(2)：334-346
[174]Bair B W. Computer Aided Design of Elliptical Gears.ASME Journal ofMechanical Design,2002,124(4)：787-793
[175]唐进元，肖利民，文伟军.基于剃前滚刀加工的过渡曲线合成.长沙铁道学院学报，1996，14（2）：27-31
[176]Litvin F L, Donno M D, Peng A, et al. Integrated computer program forsimulation of meshing and contact of gear drives. Computer Methods inApplied Mechanics and Engineering,2000,181(1)：71-85
[177]Mohan L V, Shunmugam M S. CAD approach for simulation of generationmachining and identification of contact lines. International Journal of MachineTools&Manufacture,2004,44(7-8):717-723
[178]饶芳，钟毅芳，张为国等.复杂齿轮自动化及参数化有限元建模.华中科技大学学报（自然科学版），2005，33（10）：7-9
[179]Chang S H, Huston R L,Coy J J. A finite element stress analysis of spur gearsincluding fillet radii and rim thickness effects. ASME Journal of Mechanisms,Transmissions, and Automation in Design,1983,105(3):327-330
[180]Bibel G D, Reddy S K, Savage M. Effects of rim thickness on spur gearbending stress. ASME Journal of Mechanical Design,1994,116(12):1157-1162
[181]Oda S, Nagamura K, Aoki K. Stress analysis of thin rim spur gears by finiteelement method. Bulletin of JSME,1981,24(193):1273-1280
[182]Chong T H, Kubo A. Simple stress formulae for a thin rim spur gear. ASMEJournal of Mechanisms, Transmissions, and Automation in Design,1985,107(3):327-330
[183]周长江，唐进元，钟志华等.齿轮有限元精确建模中边界界定的研究.中国机械工程，2005，16（22）：2044-2049
[184]鲍和云，朱如鹏.两级星型齿轮传动静力学系统基本浮动构件浮动量分析.中南大学学报（自然科学版），2006，37（3）：553-557
[185]刘惟信，高维山，蒋孝煜.齿轮基节误差及轮齿柔度对计算应力的影响.齿轮，1986，10(4)：30-36
[186]庞庆，柏永新.圆柱齿轮加工误差分布规律的研究.机械传动，2004，28（1）：7-9
[187]Kuang J H., Yang Y T. An estimate of mesh stiffness and load sharing ratio of aspur gear pair. In: Proceedings of ASME Journal of12th International PowerTransmission and Gearing Conference, Scottsdale, Arizona,1992,DE-43-1：1-9
[188]周长江，钟志华，唐进元.基于齿轮误差与柔度的弯曲强度计算力点研究.湖南大学学报（自然科学版），2007,34（7）：35-38
[189]Andrzej Kawalec, Jerzy Wiktor. Tooth root strength of spur and helical gearsmanufactured with gear-shaper cutters. ASME Journal of Mechanical Design,2008,130(3):034502-1~5
[190]Shuting Li. Effect of addendum on contact strength, bending strength and basicperformance parameters of a pair of spur gears. Mechanism and MachineTheory,2008,43(12):1557-1584
[191]Vilmos V. Simon. Loaded tooth contact analysis and stresses in spiral bevelgears. In: Proceedings of the ASME2009International Design EngineeringTechnical Conferences&Computers and Information in EngineeringConference, San Diego, California,2009,1-9
[192]Seok-Chul Hwang, Jin-Hwan Lee，et al. Contact stress analysis for a pair ofmating gears. Mathematical and Computer Modelling，2011，doi:10.1016/j.mcm.2011.06.055
[193]José I. Pedrero, Miguel Pleguezuelos, Marta Mu oz. Contact stress calculationof undercut spur and helical gear teeth. Mechanism and Machine Theory,2011,46(11):1633-1646
[194]Vijayarangan S, Ganesan N. A study of dynamic stresses in a spur gear under amoving line load and impact load conditions by a three-dimensional finiteelement method. Journal of Sound and Vibration,1993,162(1):185-189
[195]唐进元，周炜，陈思雨.齿轮传动啮合接触冲击分析.机械工程学报，2011，47（7）：22-30
[196]Pei-Yu Wang, Sih-Ci Fan, Zi-Gui Huang. Spiral bevel gear dynamic contactand tooth impact analysis. ASME Journal of Mechanical Design,2011,133（8）：084501-6
[197]LI S T. Centrifugal load and its effects on bending strength and contact strengthof a high speed thin-walled spur gear with offset web. Mechanism and MachineTheory,2008,43(2)：217-239
[198]JOHNSON K L. Contact mechanics.Lundon: Cambridge University Press,1985
[199]NIEMANN. Maschinen Elemente Bd. II. Springer, Berlin,1960
[200]日本机械学会.齿轮强度设计资料（李茹贞，赵清慧译）.北京：机械工业出版社，1984
[201]Nadolski W, Pielorz A. The influence of variable stiffness of teeth on dynamicloads in single-gears transmission. Archive of Applied Mechanics:1998,68(3-4):185-194
[202]孙月海,毕庆贞，张策等.啮合力移动速度对轮齿变形影响的有限元分析.机械设计,2002(11):15-17
[203]Yoshio, Treauchi, Kazuteru.直齿圆柱齿轮轮齿挠曲计算及其齿廓修缘.齿轮，1983,7(3):37-40
[204]Simon Vilmos. The influence of misalignments on mesh performances ofhypoid gears. Mechanism and Machine Theory,1998,33(11):1277-1291
[205]田涌涛，李从心，佟维等.考虑传动轴变形影响的齿轮载荷分布.上海交通大学学报，2001，35(10)：1526-1530
[206]Ajmi M, Velex P. A model for simulating the quasi-static and dynamicbehavior of solid wide-faced spur and helical gears. Mechanism and MachineTheory,2005,40(2):173-190
[207]Zhang Y, Fang Z. Analysis of tooth contact and load distribution of helicalgears with crossed axes. Mechanism and Machine Theory,1999,34(1):41-57
[208]孙月海,张策,葛楠.含误差的直齿轮的齿廓修形.机械工程学报：2003，39（12）：91-94
[209]G. Niemann. Maschinenelemente, band Ⅱ. Getriebe, Springer Verlag,1965
[210]朱孝录，鄂中凯.齿轮承载能力分析.北京：高等教育出版社，1992
[211]H. Ligata, A. Kahraman, A. Singh, An Experimental Study of the Influence ofManufacturing Errors on the Planetary Gear Stresses and Planet Load Sharing,ASME, Journal of Mechanical Design,2008,130(4):1-9
[212]T.Tobe, M.Kato, K.Inoue. True Stress and Stiffness of Spur Gear Tooth. In:Proceeding of5th World Congress on Theory of Machines and Mechanisms,Montreal: ASME Press,1979,347-359
[213] Winter H.齿轮承载能力计算的进展.齿轮，1986，10（6）：31-43
[214]Dokos S J. Sliding friction under extreme pressures. Journal of AppliedMechanism,1946,13(2):148-156
[215]Kragelskii I V. Friction and wear. London：Butterworths,1965
[216]Kato S, Sato N, Matsubayashi T. Some considerations on characteristics ofstatic friction of machine tool sideways. ASME Journal Lubrication Technology,1972,94(3),234-247
[217]Brockley C, Davis H. The time dependence of static friction. ASME JournalLubrication Technology,1968,90(1),35-41
[218]Oezgueven H N, Houser D R. Mathematical models used in gear dynamics-Areview. Journal of Sound and Vibration,1988,121(3):383-411
[219]Wang J J, Li R F, Peng X H. Survey of nonlinear vibration of gear transmissionsystems. Journal of Applied Mechanics Review,2003,56(3):309-329
[220]Parey A, Tandon N. Spur gear dynamic model including defects-A review. TheShock and Vibration Digest,2003,35(6):465-478
[221]张锁怀，沈允文，董海军.用AOM研究强非线性齿轮系统动力学问题.机械工程学报，2004，40（12）：20-24
[222]Bhushan B. Introduction to tribology. New York: John Wiley&Sons,2002
[223]Jiang X F, Hua D Y, Cheng H S, et al. A mixed elastohydrodynamic lubricationmodel with asperity contact. ASME Journal of Tribology,1999,121(3):481-491
[224]朱华，葛世荣.摩擦学系统的混沌特性.机械工程学报，2004，40（12）：10-13
[225]李华，沈允文，孙智民等.基于A-算符方法的齿轮系统的分岔与混沌.机械工程学报，2002，38（6）：11-15
[226]Singer I L. Friction and energy dissipation at the atomic scale: a review.Journal of Vacuum Science&Technology A,1994,12(5):2605-2616
[227]Ling F F. The possible role of fractal geometry in tribology. TribologyTransactions,1989,32(4):497-505
[228]陈国安，葛世荣.分形理论在摩擦学研究中的作用.摩擦学学报，1998，18（2）：179-185
[229]葛世荣，朱华.摩擦学复杂系统及其问题的量化研究方法.摩擦学学报，2002，22（5）：405-408
[230]朱华，葛世荣.摩擦力和摩擦振动的分形行为研究.摩擦学学报，2004，24（5）：433-437
[231]Booser E R. CRC handbook of lubrication,vol.2theory and design. Florida:CRC Press,1984
[232]Szeri A Z. Fluid film lubrication-theory and design. Cambridge: CambridgeUniversity Press,1998
[233]Bowden F P, Tabor D. Friction and lubrication solids, part Ι]. Oxford:Clarendon Press,1950
[234]Wen-Hwa Chen, Pwu Tsai. Finite element analysis of an involute gear driveconsidering friction effects. ASME Journal of Engineering for Industry,1989,111(2):94-100
[235]Bowden F P, Tabor D. Friction and lubrication solids, part Π. Oxford:Clarendon Press,1964
[236]Stolarski T A. Tribology in machine design. Oxford: Heinemann Newnes,1990
[237]Johnston G J, Wayte R, Spikes H A. The measurement and study of very thinlubricant films in concentrated contacts. Tribology Transaction,1991,34(2):187-194
[238]Luo J B, Wen S Z. Mechanism and characters of thin film lubrication. Sciencein China (Series A),1996,39(12):1312-1322
[239]Johnson K L, Greenwood J A, Poon S Y. Simple theory of asperity contact inelastohydrodynamic lubrication. Wear,1972,19(1):91-108
[240]Gelinck E R M, Schipper D J. Calculation of Stribeck curves for line contacts.Tribology International,2000,33(3-4):175-187
[241]Greenwood J A, Willanson J B P. Contact of normally flat surface[J]. Phil.Trans. Roy. Soc., London, Series A,1966,295:300-319
[242]高创宽.渐开线齿轮传动的混合弹流润滑研究：[太原理工大学博士论文]，太原：太原理工大学，2005
[243]Georges J M, Mazuyer D, Loubet J L, et al. Friction with colloidal lubrication.In：Singer I L, Pollock H M, Eds. Macroscopic and Microscopic Processes,1992,263-286
[244]Buckingham. Analytical mechanics of gears. New York: Dover Press,1949
[245]朱东，温诗铸，郑林庆.弹性流体动力润滑椭圆接触问题的热分析.机械工程学报，1985，21（4）：79-84
[246]周长江，唐进元，钟志华等.齿轮传动齿面摩擦系数计算方法的研究.润滑与密封,2006,10：185-191
[247]S Akbarzadeh, M M Khonsari. Thermoelastohydrodynamic Analysis of SpurGears with Consideration of Surface Roughness. Tribology Letters，2008,32(2)：129-141
[248]Chinmaya Kar, Mohanty, A.R. Determination of time-varying contact length,friction force, torque and forces at the bearings in a helical gear system. Journalof Sound and Vibration,2008,309(1-2)：307-319
[249]G R Liu, X Han. Computational inverse techniques in nondestructive evalution.New York: CRC Press,2003
[250]周长江，钟志华，唐进元.基于齿轮误差与柔度的弯曲强度计算力点研究.湖南大学学报（自然科学版），2007，34（7）：35-38.
[251]Winter H, Gerber H, Muller R. Investigation on the excitation of vibration andnoise at spur and helical gears.In: Proc.1989ASME International PowerTransmission&Gearing Conference, Chicago,1989：765-772
[252]Smith D J. Gears and their vibration. New York：Marcel Dekker,1983
[253]Richardson H H. Static and dynamic load, stress, and deflection cycles in spurgear systems. ScD Thesis, M.I.T.,1958
[254]Munro R G. The dynamic behavior of spur gears. PhD Thesis, CambridgeUniversity,1962
[255]Seireg A, Houser D R. Evaluation of dynamic factors for spur and helical gears.ASME Journal of Engineering for Industry,1970,92(2):504-515
[256]Seager D L. Separation of gear teeth in approach and recess, and the likelihoodof corner contact. ASLE Transactions,1976,19(2):164-170
[257]Tobe T, Kato M. Dynamic loads on spur gear teeth caused by teeth impact.Bulletin of JSME,1973,16(96):1031-1037
[258]Lin H H, Wang J, et al. Effect of extended tooth contact on the modeling ofspur gear transmissions. Gear Technology,1994,(7/8):18-25
[259]肖利民,唐进元.低噪声齿轮设计方法(一).制造技术与机床，1995(5)：30-32
[260]Vedmar L, Henriksson B. A general approach for determining dynamic forcesin spur gears. ASME Journal of Mechanical Design,1998,120(6)：593-598
[261]Kasuba R, Evans J W. An extended model for determining dynamic loads inspur gearing. ASME Journal of Mechanical Design,1981,103(4)：398-409
[262]盛云,武保林.齿轮传动中啮合冲击的计算分析.机械设计,2005，22(7)：41-43
[263]Bahgat B M, Osman M O M, Sankar T S. On the spur-gear dynamic tooth-loadunder consideration of system elasticity and tooth involute profile. Journal ofMechanisms, Transmissions and Automation in Design1983,105(9):302-309
[264]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.机械工程学报,2000,36(6):55-58
[265]Tengjiao Lin, H. Ou, Runfang Li. A finite element method for3D static anddynamic contact/impact analysis of gear drives. Computer Methods in AppliedMechanics and Engineering,2007,196(9–12):1716-1728
[266]Qiang Gao, Makoto Tanabe, Kazue Nishihara. Contact-impact analysis ofgeared rotor systems. Journal of Sound and Vibration,2009,319(1-2):463-475
[267]Pei-Yu Wang, Sih-Ci Fan, Zi-Gui Huang. Spiral bevel gear dynamic contactand tooth impact analysis. ASME Journal of MechanicalDesign,2011,133（8）：084501-6
[268]王优强,畅通.啮入冲击对直齿轮弹流润滑的影响.计算力学学报，2010，27(3)：527-532
[269]Lee C W, Lin H H, Oswald F B, et al. Influence of linear profile modificationand loading conditions on the dynamic tooth load and stress of high-contactratio spur gears. ASME Journal of Mechanical Design,1991,113(4):473-480
[270]Tavikoli M S, Houser D R. Optimum profile modifications for the minimizationof static transmission errors of spur gears. ASME Journal of Mechanisms,Transmissions, and Automation in Design,1986,108(1):86-95
[271]Engel P A. Impact wear of materials. New York：Elsevier Scientific PublishingCompany,1976
[272]КРАГЕЛБСКИЙ И В. Calculation principles of friction and wear. Beijing:China Machine Press,1982.
[273]Lewis A D, Rogers R J Experimental and numerical study of forces duringoblique impact. Sound&Vibration,1988,125(3)：403-412
[2]谢友柏，张嗣伟.摩擦学科学及工程应用现状与发展战略研究—摩擦学在工业节能、降耗、减排中的地位与作用的调查.北京：高等教育出版社，2009
[3]中国机械工程学会.中国机械工程技术路线图.北京：中国科学技术出版社，2011
[4]Lewis W. Investigation of the strength of gear teeth. In: Proceedings ofEngineering Club, Philadelphia, PA,1893,16-23
[5]Rand R V, Peterson R E. Load and stress cycle in gear teeth. MechanicalEngineering,1929,51(9):653-662
[6]Walker H. Gear tooth deflection and profile modification (Part1).The Engineer,1938,166(4318):409-412
[7]Walker H. Gear tooth deflection and profile modification (Part2).The Engineer,1938,166(4319):434-436
[8]Walker H. Gear tooth deflection and profile modification (Part3).The Engineer,1940,170(4414):102-104
[9]Weber C. The deformation of loaded gears and the effect on their load-carryingcapacity. London: British Scientific and Industrial Research,1949
[10]Merritt H E. Gear tooth stresses and rating formula. Proceedings of theInstitution of Mechanical Engineers,1952,166(1):196-216
[11]Niemann. Maschinen elemente Bd.Ⅱ. Berlin: Springer,1960
[12]Wellauer E J, Seireg A. Bending strength of gear teeth by cantilever plate theory.ASME Journal of Engineering for Industry,1960,82(3):213-220
[13]Cornell R W. Compliance and stress sensitivity of spur gear teeth. ASMEJournal of Mechanical Design,1981,103(4):447-459
[14]Tavikoli M S, Houser D R. Optimum profile modifications for the minimizationof static transmission errors of spur gears. ASME Journal of Mechanisms,Transmissions, and Automation in Design,1986,108(3):86-94
[15]Lin H H, Huston R L, Coy J J. On dynamic loads in parallel shaft transmissions:Part I—modeling and analysis. ASME Journal of Mechanisms, Transmissions,and Automation in Design,1988,110(2):221-225
[16]颜海燕.考虑线外啮合的齿轮动力学研究：[中南大学硕士学位论文].长沙：中南大学，2002
[17]Dolan T J，Broghammer E I. A photoelastic study of the stresses in gear toothfillets. University of Illinois Station Bulletin,1942,39(31):1-42
[18]吴继泽,王统.齿根过渡曲线与齿根应力.北京：国防工业出版社，1989
[19]Shotter B A. New approach to gear tooth root stresses. ASME Journal ofEngineering for Industry,1974，96(1)：11-18
[20]程乃士,孙大乐.齿轮应力和位移分析的保角映射法.机械传动，1992，16(1)：40-46
[21]Terauchi Y, Nagamura K. Study on deflection of spur gear teeth. Bull. JSME,1981,24(188)：1682-1688
[22]Baronet C N, Tordion G V. Exact stress distribution in standard gear teeth andgeometry factor. ASME Journal of Engineering for Industry,1973,95(4):1159-1163
[23]Premilhat A, Tordion G V. An improved determination of the elastic complianceof a spur gear tooth acted on by a concentrated load. ASME Journal ofEngineering for Industry,1974,96(2),382-384
[24]Cardou A, Tordion G V. Numerical implementation of complex potentials forgear tooth stress analysis. ASME Journal of Engineering for Industry,1981,103(4):460-465
[25]程乃士,刘温.计算机求解渐开线齿轮齿廓的保角映射函数.应用数学和力学,1988,9(11):1037-1043
[26]许立忠.保角映射法精确求解渐开线直齿轮轮齿挠度.机械工程学报，1996，32(2)：14-18
[27]Zienkiewicz O C, Taylor R L. The finite element method, fifth edition. London:Butterworth Heinemann,2000
[28]李润方，陈大良.斜齿轮三维有摩擦接触应力分析及前后处理方法.齿轮，1990，14(1)：29-34
[29]杜平安，梁锡昌.齿轮传动的现代设计方法.机械，1994，21(1)：43-45
[30]Wilcox L, Colman W. Application of finite elements to the analysis of gear toothstress. ASME Journal Engineering for Industry,1973,95(4)：1139-1148
[31]Chabert G, Dang T T, Mathis R. An evaluation of stresses and deflection of spurgear teeth under strain.ASME Journal of Engineering for Industry,1974,96(1):85-93
[32]魏任之,张永忠,史兴虹.关于直齿圆柱齿轮轮齿受载变形量的计算.齿轮，1980,(4):1-8
[33]Chang S H, Huston R L, Coy J J. A finite element stress analysis of spur gearsincluding fillet radii and rim thickness effects. ASME Journal of Mechanisms,Transmissions, and Automation in Design,1983,105(3):327-330
[34]Von Eiff H, Hirschmann K H, Lechner G. Influence of gear tooth geometry ontooth stress of external and internal gears. ASME Journal of Mechanical Design,1990,112(4):575-583
[35]Andrews J D. A finite element analysis of bending stresses included in externaland internal involutes spur gear. Journal of Strain Analysis,1991,26(3):153-163
[36]Huseyin Filiz I，Eyercioglu O. Evaluation of gear tooth stresses by finite elementmethod. ASME Journal of Engineering for Industry,1995,117(5):232-239
[37]Simon V. FEM stress analysis in hypoid gears.Mechanism and MachineTheory,2000,35(9):1197-1220
[38]Alexander L K，Shekhtman Y V. Direct gear design: bending stress minimization.Gear Technology,2003(9/10):44-47
[39]唐进元,周长江，吴运新.齿轮弯曲强度有限元分析精确建模的探讨.机械科学与技术，2004，23（10）：1146-1149，1248
[40]Conry T F, Seireg A. Mathematical programming technique for the evaluation ofload distribution and optimal modification for gear systems. ASME Journal ofEngineering for Industry,1973,95(11).1115-1122
[41]Coy J J, Hu-Chih Chao C. A method of selecting grid size to account for Hertzdeformation in finite element analysis of spur gears. Journal of MechanicalDesign,1982,104(10):759-765
[42]李润方,汤庆平，陈大良.啮合轮齿接触有限元分析网格自动生成方法.重庆大学学报，1992，15(3):11-14
[43]Refaat M H, Meguid S A. On the contact stress analysis of spur gears usingvariational inequalities. Computers and Structures,1995,57(5):871-882
[44]方宗德,杨宏斌.用规划法的齿轮有摩擦三维连续弹性接触分析.机械工程学报，1999，35(6):98-101
[45]Lee K. Analysis of the dynamic contact between rotating spur gears by finiteelement and multi-body dynamics. Proceedings Institution of MechanicalEngineers, Part C,2001,215:423-434
[46]Li S T. Finite element analyses for contact strength and bending strength of apair of spur gears with machining errors, assembly errors and toothmodifications. Mechanism and Machine Theory,2007,42(1):88-114
[47]Wallance D B, Seireg A. Computer simulation of dynamic stress, deformation,and fracture of gear teeth. Journal of Engineering for Industry,1973,95(11)：1108-1114
[48]Ostiguy L, Constantinescu I. Dynamic response of spur gear teeth. In:Proceedings of the International Modal Analysis Conference&Exhibit,Orlando, FL，1984:286-291
[49]Ramamurti V, Nayak H Vijayendra, Sujatha C. Static and dynamic analysis ofspur and bevel gears using FEM. Mechanism and Machine Theory,1998,33(8):1177-1193
[50]Wu J S, Chen C H. Torsional vibration analysis of gear-branched system byfinite element method. Journal of Sound and Vibration,2001,240(1):159-182
[51]Howard I, Jia S G, Wang J D. The dynamic modeling of a spur gear in meshincluding friction and a crack. Mechanical Systems and Signal Processing,2001,15(5):831-853
[52]Mackaldener M, Olssom M. Analysis of crack propagation during tooth interiorfatigue fracture. Engineering Fracture Mechanics,2002,69(18):2147-2162
[53]Sfakiotakis V G, Anifantis N K. Finite element modeling of spur gearingfractures. Finite Elements in Analysis and Design,2002,39(2):79-92
[54]Aui Ural, Gerd Heber, Paul A, et al. Three-dimensional, parallel, finite elementsimulation of fatigue crack growth in a spiral bevel pinion gear. EngineeringFracture Mechanics,2005,72(8):1148-1170
[55]Glode S, Winter H, Stüwe H P. A fracture mechanics model for the wear of gearflanks by pitting. Wear,1997,208(1-2):177-183
[56]Glode S, Ren Z, Fla ker J. Surface fatigue of gear teeth flanks. Computers andStructures,1999,73(1-5):475-483
[57]Jesper Brauer, S ren Andersson. Simulation of wear in gears with flankinterference-a mixed FE and analytical approach. Wear,2003,254(11-12):1216-1232
[58]Mao K. Gear tooth contact analysis and its application in the reduction of fatiguewear. Wear,2007,262(11-12):1281-1288
[59]Ciavarella Michele, Demelio Giuseppe. Numerical methods for optimization ofspecific sliding, stress concentration and fatigue life of gears. InternationalJournal of Fatigue,1999,21(5):465-474
[60]Yang F, Su D, Gentle C R. Finite element modeling and load share analysis forinvolute worm gears with localized tooth contact. Journal of MechanicalEngineering Science,2001,215(7):805-816
[61]龙慧,张光辉，罗文军.旋转齿轮瞬时接触应力和温度的分析模拟.机械工程学报，2004,40(8):24-29
[62]Argyris J, Fuentes Alfonso, Litvin Faydor L. Computerized integrated approachfor design and stress analysis of spiral bevel gears.Computer Methods inApplied Mechanics and Engineering,2002,191(11-12):1057-1095
[63]Litvin Faydor L, Fuentes Alfonso, Hayasaka Kenichi. Design, manufacture,stress analysis, and experimental tests of a low-noise endurance spiral bevelgears. Mechanism and Machine Theory,2006,41(1):83-118
[64]Kumar V Senthil, Muni D V, Muthuveerrappan G. Optimization of asymmetricspur gear drives to improve the bending load capacity. Mechanism and MachineTheory,2008,43(7)：829-858
[65]赵清澄.光测力学教程.北京：高等教育出版社，1996
[66]Timoshenko S P, Baud R V. Strength of gear teeth. Mechanical Engineering,1926,48(11)：1108-1115
[67]Heywood R B, Sopwith D G. Loads and stresses in screw threads and projections.In: Applied Mechanics Division of the Institution of Mechanical Engineers,London,1948,58-65
[68]Kelly B W, Pedersen R. The beam strength of modern gear tooth design. In: SAEEarthmoving Industry Conference, Peoria Ⅲ,1957,245-268
[69]Jacobson M A. Bending stresses in spur gear teeth: proposed new design factorsbased on a photo-elastic investigation. Proceedings of the Institution ofMechanical Engineers,1955,169(31):587-609
[70]Baxter M L, King C B, Coleman W. Three dimensional photo-elastic analysis inthe hypoid gear pair. In: JSME Semi-international Symposium, Tokyo，1967,357-345
[71]方宗德,蒋孝煜.齿轮轮齿受载变形的激光散斑测量及计算.齿轮，1984，8(5)：19-25
[72]薛春玉,郭懋林，严勇等.某直升机螺旋伞齿轮三维光弹性应力分析.哈尔滨工业大学学报，1995，27(5)：23-25
[73]许洪斌，张光辉，加藤正名.分阶式双渐开线齿轮的光弹试验与弯曲强度试验研究.机械工程学报,2000，36(8)：39-42
[74]Wang, Ming-Jong. A new photoelastic investigation of the dynamic bendingstress of spur gears. ASME Journal of Mechanical Design,2003,125(6):365-372
[75]Vasilios A. Spitas, Theodore N. Costopoulos, Christos A. Spitas. Optimum geartooth geometry for minimum fillet stress using BEM and experimentalverification with photoelasticity. Journal of Mechanical Design,2006,128(9):1159-1164
[76]Gregory R W, Harris S L, Munro R G. Dynamic behaviour of spur gears. Proc.Instn. Mech. Engrs.,1963-64,178(8):207-217
[77]Winter H, Hirt M. The measurement of actual strain at gear teeth, influence offillet radius on stresses and tooth strength. SAME Journal of Engineering forIndustry,1974,96(1):33-50
[78]连小珉,蒋孝煜.齿根动应力测量.齿轮,1987,11(1):33-37(43)
[79]M. Hotait, A. Kahraman. Experiments on root stresses of helical gears with leadcrown and misalignments. ASME Journal of Mechanical Design,2008,130(7):074502-5
[80]王成,方宗德,谷建功等.人字齿轮承载接触分析与试验.航空动力学报,2010,25(3):718-722
[81]Miche`le Guingand, Jean-Pierre de Vaujany, Colin-Yann Jacquin. Quasi-staticanalysis of a face gear under torque. Computer Methods in Applied Mechanicsand Engineering,2005,194(39-41):4301-4318
[82]Litvin F L, Fuentes A, Hayasaka K. Design, manufacture, stress analysis,and experimental tests of low-noise high endurance spiral bevel gears.Mechanism and Machine Theory,2006,41(1):83-118
[83]Pascal Ziegler, Peter Eberhard. Simulative and experimental investigation ofimpacts on gear wheels. Computer Methods in Applied Mechanics andEngineering,2008,197(51-52):4653-4662
[84]Hotait, M. A. Kahraman, A. Nishino, T. An Investigation of Root Stresses ofHypoid Gears with Misalignments. ASME Journal of Mechanical Design,2011,133(7):071006-9
[85]Yong-jun Wu, Jian-jun Wang, Qin-kai Han. Static/dynamic contact FEA andexperimental study for tooth profile modification of helical gears. Journal ofMechanical Science and Technology,2012,26(5):1409-1417
[86]葛世荣，朱华.摩擦学复杂系统及其问题的量化研究方法.摩擦学报，2002，22（5）：405-408
[87]国家自然科学基金委员会工程与材料科学部.机械与制造科学.北京：科学出版社，2006
[88]周仲荣.摩擦学发展前沿.北京：科学出版社，2006
[89]谢友柏.摩擦学科学与工程前沿.北京：高度教育出版社，2005
[90]秦大同.机械传动科学技术的发展历史与研究进展.机械工程学报，2003，39（12）：37-42
[91]Masatoshi Yoshizaki, Chotaro Naruse, Ryozo Nemoto, et al. Study on frictionalloss of spur gears(concerning the influence of tooth form, load, tooth surfaceroughness, and lubricating oil). Tribology Transactions,1991,34(1)：138-146
[92]Shoji Haizuka, Takaaki Kikusaki, Chotaro Naruse. Studies on friction loss ofspur gears. JSME International Journal, Series C,1999,42(4)：1041-1049
[93]姚建初，陈义保，周济等.齿轮传动啮合效率计算方法的研究.机械工程学报，2001，37（11）：18-21
[94]Michlin Y, Myunster V. Determination of power losses in gear transmissionswith rolling and sliding friction incorporated. Mechanism and Machine Theory,2002,37(2)：167-174
[95]Xu F R. Effect of the sliding friction between teeth on the bending fatigue stresson the tooth root of the great gear in the machine tool increasing speed gearing.Journal. of University of Shanghai for Science and Technology,2000,22(2)：119-125
[96]Lehtovaara Arto. Numerical model for the calculation of subsurface stresses inline contact of real rough surface. Tribologia,2003,22(2)：20-31
[97]高创宽，周谋，亓秀梅.齿面摩擦力对齿轮接触应力的影响.机械强度，2003，25（6）：642-645
[98]Vijayarangan S, Ganesan N. Static contact stress analysis of a spur gear toothusing the finite element method, including frictional effects. Computers&Structures,1994,51(6)：765-770
[99]Tian Y T, Li C X, Tong W, et al. A finite-element-based study of the loaddistribution of a heavily loaded spur gear system with effects of transmissionshafts and gear blanks. ASME Journal. of Mechanical Design.2003,125(9)：625-631
[100]Blake J W, Draper C F. Further development of a predictive pitting model forgears: improvements in the life prediction analysis. Tribology Transactions,1994,37(2)：237-244
[101]Fla ker J, Fajdiga G, Glode S, et al. Numerical simulation of surface pittingdue to contact loading. International Journal of Fatigue,2001,23(7)：599-605
[102]Lewicki D G, Handschuh R F, Spievak L E, et al. Consideration of movingtooth load in gear crack propagation predictions. ASME Journal of MechanicalDesign,2001,123(3)：118-124
[103]Velex P, Cahouet V. Experimental and numerical investigations on theinfluence of tooth friction in spur and helical gear dynamics. Journal ofMechanical Design,2000,122(12)：515-522
[104]王三民，沈允文，董海军.含摩擦和间隙直齿轮副的混沌与分叉研究.机械工程学报，2002,38(9):8-11
[105]Aziz S M A，Seireg A. A parametric study of frictional noise in gears. Wear,1994,176(1)：25-28
[106]姚文席,王东，张志强.渐开线直齿轮的摩擦激励及振动阻尼分析.振动、测试与诊断，2000,20(3):206-210
[107]Velex P, Sainsot P. An analytical study of tooth friction excitations in errorlessspur and helical gears. Mechanism and Machine Theory,2002,37(7)：641-658
[108]陈光雄，周仲荣.摩擦系数影响摩擦噪声发生的机理研究.中国机械工程，2003，14（9）：766-769
[109]谢友柏.摩擦学的三个公理.摩擦学学报，2001，21（3）：161-166
[110]葛世荣，朱华.摩擦学的分形.北京：机械工业出版社，2005
[111]林子光，徐大耐等.齿轮传动的润滑.北京：机械工业出版社，1980
[112]Dowson D. Boundary Lubrication—An Appraisal of World Literature. NewYork: ASME Press, Chapter Ⅱ,1969
[113]温诗铸，雒建斌.纳米薄膜润滑研究.清华大学学报，2001，41（4/5）：63-68
[114]McEwen E. The effect of variation of viscosity with pressure on the loadcarrying capacity of oil film between gear teeth. Journal of Institute ofPetroleum,1952,38(3):646-656
[115]Adkins R W, Radzimovsky, E I. Lubrication phenomena in spur gear. ASMEJournal of Basic Engineering,1965,87(3):655-665
[116]Dowson D, Higginson G R. Elasto-hydrodynamic lubrication(SI Edition).Oxford: Pergamon Press,1977
[117]Vichard J P. Transient effects in the lubrication of Hertzian contacts. Journal ofMechanical Engineering Science,1971,13(3):173-189
[118]Wang K L, Cheng H S. A numerical solution to the dynamic load, filmthickness and surface temperatures in spur gears. ASME Journal of MechanicalDesign,1981,103(4):177-195
[119]Petrousevitch A I. The investigation of oil film thickness in lubricated ball-racerolling contact. Wear,1972,19(4):369-389
[120]Wada S, Tsukijihara M. Elastohydrodynamic squeeze problem of two rotatingcylinders(Part1). Bulletin JSME,1981,24(190):937-942
[121]Wada S, Tsukijihara M. Elastohydrodynamic squeeze problem of two rotatingcylinders(Part2). Bulletin JSME,1981,24(192):1072-1077
[122]杨沛然.非稳态热弹性流体动力润滑研究：[清华大学博士论文]，北京：清华大学，1989
[123]Larsson R. Transient non-Newtonian elastohydrodynamic lubrication analysisof an involute spur. Wear,1997,207(11):67-73
[124]卢立新，蔡莹，张和豪.渐开线直齿圆柱齿轮传动瞬态弹流润滑研究.润滑与密封，1999，（5）：5-7
[125]汪久根.时变性对圆柱齿轮弹流润滑的影响.机械设计与研究，2003，19（2）：30-31
[126]王优强，黄丙习，佟景伟等.渐开线直齿轮牛顿流体非稳态热弹流润滑分析.计算力学学报，2005，22（5）：568-573
[127]赵春华，严新平.数学方法在油液监测中的应用.武汉理工大学学报（交通科学与工程版），2004，28（3）：326-333
[128]戴振东，薛群基，王珉.试论摩擦学研究中的科学方法问题.南京航空航天大学学报，1998，30（2）：235-240
[129]温诗铸，黄平.摩擦学原理（第二版）.北京：清华大学出版社，2003
[130]Akin L S. Interdisciplinary lubrication theory for gears with particularemphasis on the scuffing mode of failure. In: Soviet Atomic Energy,1972,Vol.72:6-31
[131]Hamrock B J, Dowson D. Isothermal EHL of point contacts, part Ⅲ－fullflooded results. ASME Journal of Lubrication Technology,1977,99(2)：264-276
[132]Hamrock B J, Dowson D. Elasto-hydrodynamic lubrication of ellipticalcontacts for materials of low elastic modulus,2－starved conjunction. ASMEJournal of Lubrication Technology,1979,101(1)：92-98
[133]Li D F, Kauzlarich J J, Jamison W E. Surface roughness effects on fatigue inpartial EHD lubrication. ASME Journal of Lubrication Technology,1976,98(4):530-537
[134]Buckingham. Analytical mechanics of gears. New York: Dover Press,1949
[135]齿轮手册编委会.齿轮手册（第2版）.北京：机械工业出版社，2006
[136]Christensen H. Stochastic models for hydrodynamic lubrication of roughsurfaces. Proceedings of the Institution of Mechanical Engineers-Part Ⅰ,1970,184(55)：1013-1026
[137]Martin K F. A review of friction predictions in gear teeth. Wear,1978,49(2)：201-238
[138]雒建斌，刘珊，潘国顺等.纳米级混合润滑研究.机械工程学报，2003，39（2）：1-7
[139]孔繁荣.混合润滑的实验技术和特性研究：[清华大学博士论文]，北京：清华大学，1993
[140]Wu S F, Cheng H S. A friction model of partial-EHL contacts and itsapplication to power loss in spur gears. Tribology Transactions,1991,34(3)：398-407
[141]Jiang X, Cheng H S, Hua D Y. A theoretical analysis of mixed lubrication bymacro micro approach: part I-results in a gear surface contact. TribologyTransactions,2000，43(4)：689-699
[142]Kelley B W, Lemanski A J. Lubrication of involute gearing. ProceedingsInstitution of Mechanical Engineers,1967,182(3)：173-184
[143]Martin K F. The efficiency of involute spur gears. ASME Journal ofMechanical Design,1980,105(4)：160-167
[144]Gohar R. Elastohydrodynamics. West Sussex: Ellis Horwood Limited,1988
[145]Vaishya M, Houser D R. Modeling and analysis of sliding friction in geardynamics.In: ASME2000Design Engineering Technical Conferences andComputers and Information in Engineering Conference, Baltimore,2000,601-610
[146]Tallian T E. Pressure and traction rippling in elasto-hydrodynamic contact ofrough surface. In: Trans. ASME,1973,73:18-26
[147]Cameron A, Cordon A N，Symm G T. Contact temperatures in rolling/slidingsurface.In: Proc. Roy. Soc. Lond.,1965, Part A,286-321
[148]Vaishya M, Singh R. Sliding friction-induced non-linearity and parametriceffects in gear dynamics. Journal of Sound and Vibration,2001,248(4)：671-694
[149]Rayiko M V, Dmytrychenko N F. Some aspects of boundary lubrication in thelocal contact of friction surfaces.1988,126(1)：69-78
[150]Britton R D, Elcoate C D, Alanou M P, et al. Effect of surface finish on geartooth friction. ASME Journal of Tribology,2000,122(1)：354-360
[151]S Akbarzadeh, M M Khonsari. Thermoelastohydrodynamic Analysis of SpurGears with Consideration of Surface Roughness. Tribology Letters，2008,32(2)：129-141
[152]Chinmaya Kar, Mohanty, A.R. Determination of time-varying contact length,friction force, torque and forces at the bearings in a helical gear system. Journalof Sound and Vibration,2008,309(1-2)：307-319
[153]王黎钦，刘明霞，古乐.计算机在摩擦实验测试中的应用.哈尔滨工程大学学报，2000，21（2）：81-84
[154]Kleemola, Jaakko, Lehtovaara, A.Experimental evaluation of friction betweencontacting discs for the simulation of gear contact. Tribology Test,2007,13(1)：13-20
[155]Johson K L, Cameron R S. Behavior of elastohydrodynamic oil films at highrolling contact pressures. Proceedings Institution of Mechanical Engineers,1967,182(14):307-319
[156]McCool J I. Evaluating the Tevaarwerk-Johnson elastic/plastic traction modelon the presence of lateral sliding and spin. Tribology Transactions.1990,33(1)：122-130
[157]张钢，李鸣鸣，王中宇等.齿轮润滑摩擦特性模拟试验台的研制.洛阳工学院学报，1997，18（4）：25-29
[158]Gurskii, B.E. Chichinadze, A.V. Thermal friction problem and its development.Journal of Friction and Wear,2007,28(4)：395-400
[159]Voitik R M, Heerdt L. Wear and frictional evaluation of gear lubricants bybench test. JASL Lubrication Engineering,1984,40(12)：719-724
[160]赵建平，杜鸿家.齿面摩擦规律的模拟试验研究.润滑与密封，1994，（2）：6-11
[161]陈文华.仪表齿轮齿面摩擦系数的测定.仪表技术与传感器，1996，（11）：33-36
[162]林子光，李修仁，刘维民等.摩擦过渡的实验研究.润滑与密封，2001，（4）：16-17，20
[163]Smith F W. Rolling contact lubrication-The application of elastohydrodynamictheory. Trans. of ASME,1965,(3):170-176
[164]Benedict G H, Kelley B W. Instantaneous coefficients of gear tooth friction.ASLE Transactions,1961,4(1)：59-70
[165]Oswald F B, Towsend D P, Rebbechi B, et al. Dynamic forces in spurgears-measurement, prediction and code validation. In: Proc.7thASME Int.Power Transmission and Gears Conf., San Diego,1996, Vol.88:9-15
[166]Rebbrchi B, Oswald F B, Townsend D P. Measurement of gear tooth dynamicfriction. In: Proc.7thASME Int. Power Transmission and Gears Conf., SanDiego,1996, Vol.88:355-363
[167]谢如霖.齿轮传动效率、啮合效率和摩擦系数的测试.合肥工业大学学报（自然科学版），1991，14（1）：27-33
[168]Radzimovsy E I, Mirarefi A, Broom W E. Instantaneous efficiency andcoefficient of friction of an involute gear drive. In: Soviet Atomic Energy,1972,72:13-22
[169]Rao A C. Average friction coefficients in gears. Journal MechanicalEngineering Science,1975,17(6)：360-362
[170]Rao A C. Gear friction coefficients and forces. Wear,1979,53(1):87-93
[171]Hori K, Hayashi I, Iwatsuki N. The gravity pendulum method for precisemeasurement of the tooth surface friction coefficient of a pair of mating gears.JSME International Journal, Series C,1999,42(4)：1021-1030
[172]周长江，唐进元，吴运新.齿根应力与轮齿弹性变形的计算方法进展与比较研究.机械传动，2004，28（5）：1-6
[173]Baud S, Velex P. Static and dynamic tooth loading in spur and helical gearedsystems-experiments and model validation. ASME Journal of MechanicalDesign,2002,124(2)：334-346
[174]Bair B W. Computer Aided Design of Elliptical Gears.ASME Journal ofMechanical Design,2002,124(4)：787-793
[175]唐进元，肖利民，文伟军.基于剃前滚刀加工的过渡曲线合成.长沙铁道学院学报，1996，14（2）：27-31
[176]Litvin F L, Donno M D, Peng A, et al. Integrated computer program forsimulation of meshing and contact of gear drives. Computer Methods inApplied Mechanics and Engineering,2000,181(1)：71-85
[177]Mohan L V, Shunmugam M S. CAD approach for simulation of generationmachining and identification of contact lines. International Journal of MachineTools&Manufacture,2004,44(7-8):717-723
[178]饶芳，钟毅芳，张为国等.复杂齿轮自动化及参数化有限元建模.华中科技大学学报（自然科学版），2005，33（10）：7-9
[179]Chang S H, Huston R L,Coy J J. A finite element stress analysis of spur gearsincluding fillet radii and rim thickness effects. ASME Journal of Mechanisms,Transmissions, and Automation in Design,1983,105(3):327-330
[180]Bibel G D, Reddy S K, Savage M. Effects of rim thickness on spur gearbending stress. ASME Journal of Mechanical Design,1994,116(12):1157-1162
[181]Oda S, Nagamura K, Aoki K. Stress analysis of thin rim spur gears by finiteelement method. Bulletin of JSME,1981,24(193):1273-1280
[182]Chong T H, Kubo A. Simple stress formulae for a thin rim spur gear. ASMEJournal of Mechanisms, Transmissions, and Automation in Design,1985,107(3):327-330
[183]周长江，唐进元，钟志华等.齿轮有限元精确建模中边界界定的研究.中国机械工程，2005，16（22）：2044-2049
[184]鲍和云，朱如鹏.两级星型齿轮传动静力学系统基本浮动构件浮动量分析.中南大学学报（自然科学版），2006，37（3）：553-557
[185]刘惟信，高维山，蒋孝煜.齿轮基节误差及轮齿柔度对计算应力的影响.齿轮，1986，10(4)：30-36
[186]庞庆，柏永新.圆柱齿轮加工误差分布规律的研究.机械传动，2004，28（1）：7-9
[187]Kuang J H., Yang Y T. An estimate of mesh stiffness and load sharing ratio of aspur gear pair. In: Proceedings of ASME Journal of12th International PowerTransmission and Gearing Conference, Scottsdale, Arizona,1992,DE-43-1：1-9
[188]周长江，钟志华，唐进元.基于齿轮误差与柔度的弯曲强度计算力点研究.湖南大学学报（自然科学版），2007,34（7）：35-38
[189]Andrzej Kawalec, Jerzy Wiktor. Tooth root strength of spur and helical gearsmanufactured with gear-shaper cutters. ASME Journal of Mechanical Design,2008,130(3):034502-1~5
[190]Shuting Li. Effect of addendum on contact strength, bending strength and basicperformance parameters of a pair of spur gears. Mechanism and MachineTheory,2008,43(12):1557-1584
[191]Vilmos V. Simon. Loaded tooth contact analysis and stresses in spiral bevelgears. In: Proceedings of the ASME2009International Design EngineeringTechnical Conferences&Computers and Information in EngineeringConference, San Diego, California,2009,1-9
[192]Seok-Chul Hwang, Jin-Hwan Lee，et al. Contact stress analysis for a pair ofmating gears. Mathematical and Computer Modelling，2011，doi:10.1016/j.mcm.2011.06.055
[193]José I. Pedrero, Miguel Pleguezuelos, Marta Mu oz. Contact stress calculationof undercut spur and helical gear teeth. Mechanism and Machine Theory,2011,46(11):1633-1646
[194]Vijayarangan S, Ganesan N. A study of dynamic stresses in a spur gear under amoving line load and impact load conditions by a three-dimensional finiteelement method. Journal of Sound and Vibration,1993,162(1):185-189
[195]唐进元，周炜，陈思雨.齿轮传动啮合接触冲击分析.机械工程学报，2011，47（7）：22-30
[196]Pei-Yu Wang, Sih-Ci Fan, Zi-Gui Huang. Spiral bevel gear dynamic contactand tooth impact analysis. ASME Journal of Mechanical Design,2011,133（8）：084501-6
[197]LI S T. Centrifugal load and its effects on bending strength and contact strengthof a high speed thin-walled spur gear with offset web. Mechanism and MachineTheory,2008,43(2)：217-239
[198]JOHNSON K L. Contact mechanics.Lundon: Cambridge University Press,1985
[199]NIEMANN. Maschinen Elemente Bd. II. Springer, Berlin,1960
[200]日本机械学会.齿轮强度设计资料（李茹贞，赵清慧译）.北京：机械工业出版社，1984
[201]Nadolski W, Pielorz A. The influence of variable stiffness of teeth on dynamicloads in single-gears transmission. Archive of Applied Mechanics:1998,68(3-4):185-194
[202]孙月海,毕庆贞，张策等.啮合力移动速度对轮齿变形影响的有限元分析.机械设计,2002(11):15-17
[203]Yoshio, Treauchi, Kazuteru.直齿圆柱齿轮轮齿挠曲计算及其齿廓修缘.齿轮，1983,7(3):37-40
[204]Simon Vilmos. The influence of misalignments on mesh performances ofhypoid gears. Mechanism and Machine Theory,1998,33(11):1277-1291
[205]田涌涛，李从心，佟维等.考虑传动轴变形影响的齿轮载荷分布.上海交通大学学报，2001，35(10)：1526-1530
[206]Ajmi M, Velex P. A model for simulating the quasi-static and dynamicbehavior of solid wide-faced spur and helical gears. Mechanism and MachineTheory,2005,40(2):173-190
[207]Zhang Y, Fang Z. Analysis of tooth contact and load distribution of helicalgears with crossed axes. Mechanism and Machine Theory,1999,34(1):41-57
[208]孙月海,张策,葛楠.含误差的直齿轮的齿廓修形.机械工程学报：2003，39（12）：91-94
[209]G. Niemann. Maschinenelemente, band Ⅱ. Getriebe, Springer Verlag,1965
[210]朱孝录，鄂中凯.齿轮承载能力分析.北京：高等教育出版社，1992
[211]H. Ligata, A. Kahraman, A. Singh, An Experimental Study of the Influence ofManufacturing Errors on the Planetary Gear Stresses and Planet Load Sharing,ASME, Journal of Mechanical Design,2008,130(4):1-9
[212]T.Tobe, M.Kato, K.Inoue. True Stress and Stiffness of Spur Gear Tooth. In:Proceeding of5th World Congress on Theory of Machines and Mechanisms,Montreal: ASME Press,1979,347-359
[213] Winter H.齿轮承载能力计算的进展.齿轮，1986，10（6）：31-43
[214]Dokos S J. Sliding friction under extreme pressures. Journal of AppliedMechanism,1946,13(2):148-156
[215]Kragelskii I V. Friction and wear. London：Butterworths,1965
[216]Kato S, Sato N, Matsubayashi T. Some considerations on characteristics ofstatic friction of machine tool sideways. ASME Journal Lubrication Technology,1972,94(3),234-247
[217]Brockley C, Davis H. The time dependence of static friction. ASME JournalLubrication Technology,1968,90(1),35-41
[218]Oezgueven H N, Houser D R. Mathematical models used in gear dynamics-Areview. Journal of Sound and Vibration,1988,121(3):383-411
[219]Wang J J, Li R F, Peng X H. Survey of nonlinear vibration of gear transmissionsystems. Journal of Applied Mechanics Review,2003,56(3):309-329
[220]Parey A, Tandon N. Spur gear dynamic model including defects-A review. TheShock and Vibration Digest,2003,35(6):465-478
[221]张锁怀，沈允文，董海军.用AOM研究强非线性齿轮系统动力学问题.机械工程学报，2004，40（12）：20-24
[222]Bhushan B. Introduction to tribology. New York: John Wiley&Sons,2002
[223]Jiang X F, Hua D Y, Cheng H S, et al. A mixed elastohydrodynamic lubricationmodel with asperity contact. ASME Journal of Tribology,1999,121(3):481-491
[224]朱华，葛世荣.摩擦学系统的混沌特性.机械工程学报，2004，40（12）：10-13
[225]李华，沈允文，孙智民等.基于A-算符方法的齿轮系统的分岔与混沌.机械工程学报，2002，38（6）：11-15
[226]Singer I L. Friction and energy dissipation at the atomic scale: a review.Journal of Vacuum Science&Technology A,1994,12(5):2605-2616
[227]Ling F F. The possible role of fractal geometry in tribology. TribologyTransactions,1989,32(4):497-505
[228]陈国安，葛世荣.分形理论在摩擦学研究中的作用.摩擦学学报，1998，18（2）：179-185
[229]葛世荣，朱华.摩擦学复杂系统及其问题的量化研究方法.摩擦学学报，2002，22（5）：405-408
[230]朱华，葛世荣.摩擦力和摩擦振动的分形行为研究.摩擦学学报，2004，24（5）：433-437
[231]Booser E R. CRC handbook of lubrication,vol.2theory and design. Florida:CRC Press,1984
[232]Szeri A Z. Fluid film lubrication-theory and design. Cambridge: CambridgeUniversity Press,1998
[233]Bowden F P, Tabor D. Friction and lubrication solids, part Ι]. Oxford:Clarendon Press,1950
[234]Wen-Hwa Chen, Pwu Tsai. Finite element analysis of an involute gear driveconsidering friction effects. ASME Journal of Engineering for Industry,1989,111(2):94-100
[235]Bowden F P, Tabor D. Friction and lubrication solids, part Π. Oxford:Clarendon Press,1964
[236]Stolarski T A. Tribology in machine design. Oxford: Heinemann Newnes,1990
[237]Johnston G J, Wayte R, Spikes H A. The measurement and study of very thinlubricant films in concentrated contacts. Tribology Transaction,1991,34(2):187-194
[238]Luo J B, Wen S Z. Mechanism and characters of thin film lubrication. Sciencein China (Series A),1996,39(12):1312-1322
[239]Johnson K L, Greenwood J A, Poon S Y. Simple theory of asperity contact inelastohydrodynamic lubrication. Wear,1972,19(1):91-108
[240]Gelinck E R M, Schipper D J. Calculation of Stribeck curves for line contacts.Tribology International,2000,33(3-4):175-187
[241]Greenwood J A, Willanson J B P. Contact of normally flat surface[J]. Phil.Trans. Roy. Soc., London, Series A,1966,295:300-319
[242]高创宽.渐开线齿轮传动的混合弹流润滑研究：[太原理工大学博士论文]，太原：太原理工大学，2005
[243]Georges J M, Mazuyer D, Loubet J L, et al. Friction with colloidal lubrication.In：Singer I L, Pollock H M, Eds. Macroscopic and Microscopic Processes,1992,263-286
[244]Buckingham. Analytical mechanics of gears. New York: Dover Press,1949
[245]朱东，温诗铸，郑林庆.弹性流体动力润滑椭圆接触问题的热分析.机械工程学报，1985，21（4）：79-84
[246]周长江，唐进元，钟志华等.齿轮传动齿面摩擦系数计算方法的研究.润滑与密封,2006,10：185-191
[247]S Akbarzadeh, M M Khonsari. Thermoelastohydrodynamic Analysis of SpurGears with Consideration of Surface Roughness. Tribology Letters，2008,32(2)：129-141
[248]Chinmaya Kar, Mohanty, A.R. Determination of time-varying contact length,friction force, torque and forces at the bearings in a helical gear system. Journalof Sound and Vibration,2008,309(1-2)：307-319
[249]G R Liu, X Han. Computational inverse techniques in nondestructive evalution.New York: CRC Press,2003
[250]周长江，钟志华，唐进元.基于齿轮误差与柔度的弯曲强度计算力点研究.湖南大学学报（自然科学版），2007，34（7）：35-38.
[251]Winter H, Gerber H, Muller R. Investigation on the excitation of vibration andnoise at spur and helical gears.In: Proc.1989ASME International PowerTransmission&Gearing Conference, Chicago,1989：765-772
[252]Smith D J. Gears and their vibration. New York：Marcel Dekker,1983
[253]Richardson H H. Static and dynamic load, stress, and deflection cycles in spurgear systems. ScD Thesis, M.I.T.,1958
[254]Munro R G. The dynamic behavior of spur gears. PhD Thesis, CambridgeUniversity,1962
[255]Seireg A, Houser D R. Evaluation of dynamic factors for spur and helical gears.ASME Journal of Engineering for Industry,1970,92(2):504-515
[256]Seager D L. Separation of gear teeth in approach and recess, and the likelihoodof corner contact. ASLE Transactions,1976,19(2):164-170
[257]Tobe T, Kato M. Dynamic loads on spur gear teeth caused by teeth impact.Bulletin of JSME,1973,16(96):1031-1037
[258]Lin H H, Wang J, et al. Effect of extended tooth contact on the modeling ofspur gear transmissions. Gear Technology,1994,(7/8):18-25
[259]肖利民,唐进元.低噪声齿轮设计方法(一).制造技术与机床，1995(5)：30-32
[260]Vedmar L, Henriksson B. A general approach for determining dynamic forcesin spur gears. ASME Journal of Mechanical Design,1998,120(6)：593-598
[261]Kasuba R, Evans J W. An extended model for determining dynamic loads inspur gearing. ASME Journal of Mechanical Design,1981,103(4)：398-409
[262]盛云,武保林.齿轮传动中啮合冲击的计算分析.机械设计,2005，22(7)：41-43
[263]Bahgat B M, Osman M O M, Sankar T S. On the spur-gear dynamic tooth-loadunder consideration of system elasticity and tooth involute profile. Journal ofMechanisms, Transmissions and Automation in Design1983,105(9):302-309
[264]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.机械工程学报,2000,36(6):55-58
[265]Tengjiao Lin, H. Ou, Runfang Li. A finite element method for3D static anddynamic contact/impact analysis of gear drives. Computer Methods in AppliedMechanics and Engineering,2007,196(9–12):1716-1728
[266]Qiang Gao, Makoto Tanabe, Kazue Nishihara. Contact-impact analysis ofgeared rotor systems. Journal of Sound and Vibration,2009,319(1-2):463-475
[267]Pei-Yu Wang, Sih-Ci Fan, Zi-Gui Huang. Spiral bevel gear dynamic contactand tooth impact analysis. ASME Journal of MechanicalDesign,2011,133（8）：084501-6
[268]王优强,畅通.啮入冲击对直齿轮弹流润滑的影响.计算力学学报，2010，27(3)：527-532
[269]Lee C W, Lin H H, Oswald F B, et al. Influence of linear profile modificationand loading conditions on the dynamic tooth load and stress of high-contactratio spur gears. ASME Journal of Mechanical Design,1991,113(4):473-480
[270]Tavikoli M S, Houser D R. Optimum profile modifications for the minimizationof static transmission errors of spur gears. ASME Journal of Mechanisms,Transmissions, and Automation in Design,1986,108(1):86-95
[271]Engel P A. Impact wear of materials. New York：Elsevier Scientific PublishingCompany,1976
[272]КРАГЕЛБСКИЙ И В. Calculation principles of friction and wear. Beijing:China Machine Press,1982.
[273]Lewis A D, Rogers R J Experimental and numerical study of forces duringoblique impact. Sound&Vibration,1988,125(3)：403-412
© 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 |