航空发动机高速滚动轴承动力学行为研究
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摘要
航空发动机不断向大推重比、长寿命和高可靠性方向发展，对航空发动机高速滚动轴承的转速、载荷等指标提出了越来越苛刻的要求。长期工作在高转速和重载荷情况下的滚动轴承常呈现应力过大、温升过高等特点，发生擦伤、烧伤等失效，严重的还会带来轴承卡死抱轴等严重后果。为此，对高速滚动轴承作了大量的结构及材料方面的改进和创新，然而快速提升的苛刻工况条件已经逼近了现有材料的使用极限。同时，航空发动机在工作过程中的高转速巡航以及多工况转换的特点，使得滚动轴承的动态稳定性问题日益凸显，带来保持架断裂、转子系统失稳等严重后果，在此背景下航空发动机高速滚动轴承的全工况包络设计显得不可或缺。因此，对航空发动机高速滚动轴承进行动态性能分析，研究其高速动力学行为，是面向工况进行轴承结构优化、保证轴承工作可靠性和延长轴承寿命的必不可少的共性基础研究课题。本文围绕航空发动机轴承典型苛刻工况条件，通过建模和仿真展开轴承动态性能研究，为轴承性能优化提供依据，为轴承—转子系统可靠性和稳定性增长研究奠定基础。
论文通过轴承内部零件间的运动和位置关系分析，建立了零件间的相互作用模型，建立了高速球轴承和滚子轴承的完全动力学模型。采用Newtown-Raphson算法和Runge-Kutta算法结合的方法对动力学模型求解，解决了套圈和滚动体之间高频振动对计算效率的影响，同时保证了动力学结果的精度。分析结果为分析不同工况条件下轴承的动力学行为提供了基础数据。建立的动力学模型适用于油润滑和固体润滑轴承计算，可以分析轴承装配、温差及离心作用影响，可以分析球轴承保持架的椭圆兜孔形式以及滚子轴承的母线轮廓修型影响。
针对轴承装配导致的内外圈轴线不对中现象，分析了轴承内外圈偏斜对承载区载荷特性的影响：轴承内外圈偏斜不仅导致承载滚动体发生偏载现象，引起局部接触应力过大，在轴承运转过程中还会因为变刚度振动而影响承载区最大接触应力的波动。随着内外圈偏转角度的增大，轴承接触区内最大接触应力值呈现逐渐上升趋于平稳的状态，而承载区最大接触应力的波动幅度呈现先减小而后小幅增大的趋势。以改善内外圈偏斜对承载区最大接触应力的影响为目的，兼顾承载区应力波动幅度变化，给出了增加滚子数量及滚子母线对数修型的定量依据。
根据建立的高速球轴承和滚子轴承动力学模型，从描述保持架稳定性的保持架质心涡动速度偏差比及反映滚动体整体打滑的保持架滑动率两方面分析了定常工况下高速滚动轴承的动态性能，分析结果可为轴承失效分析提供理论依据。结果表明：转速的增加可以提高保持架的稳定性，但导致滚动体打滑率上升。对于球轴承，控制径向载荷与轴向载荷的比值可以降低轴承滚动体的打滑率并有助于保持架稳定性的提升；对于滚子轴承，径向载荷的增加可以降低滚动体的打滑率，但同时导致保持架稳定性减弱。
针对航空发动机工作中的多工况转换特点，分别就发动机启动、加速和加力三种过渡状态，分析了轴承的瞬态动力学行为。结果表明：保持架的稳定性与初始状态关系较大。轴承启动阶段，外引导保持架受滚动体推动，承受载荷较小，但在较长一段时间内处于不稳定状态；轴承加速和加载阶段，保持架受滚动体和引导套圈共同作用，速度或推力的增加会加剧保持架与套圈引导面及滚动体的碰磨。
基于航空轴承高速、重载、高温的工况特点，建立了考虑配合、工作温度及高速离心载荷的轴承工作游隙计算模型，分析了轴承不同工况的工作游隙及其对轴承性能的影响。模型和分析结果为轴承配合参数设计提供指导。
对建立的动力学计算模型，采用软件集成技术，通过Visual Basic和Matlab混合编程研制了滚动轴承动态性能分析软件。软件功能通过与SHABERTH软件及ADORE软件对典型算例的计算结果对比获得了模型和方法的准确性验证，表明本软件在轴承稳态动力学参数预测及轴承瞬态运动学预测两方面都具有较好的精度。
基于考虑轴承微区接触载荷的疲劳寿命计算方法，建立了以疲劳寿命为目标函数，以保持架滑动率、内外圈沟曲率系数和填球角为约束条件的轴承结构参数优化模型。分析了轴承结构参数对轴承稳定性的影响。研究了轴承内外圈相对转动方式对轴承结构优化的影响。分析结果为航空发动机轴承的延寿方法提供了理论基础。
针对高速轴承-转子系统的动力学耦合特点，建立了轴承-转子系统的耦合动力学分析模型，初步分析了转子对轴承动力学的影响：转子振动引起的滚动体和套圈间接触应力和相对滑动增大将对轴承疲劳寿命及温升产生不良影响，分析结果为进一步研究重载摩擦副接触微区的微观失效行为提供了基础。
To satisfy the trending of aeroengine for high thrust-weight ratio, long life andhigh reliability, high-speed rolling bearings of aeroengine is required more and morerigorous on speed and loads. Due to high contact pressure and temperature rise, kinds ofsurface failures, such as surface scratch and surface burning, even serious consequencessuch as journal sticking the on severe case, occur on rolling bearings that operates onthe high speed and heavy load conditions. Although materials and structures of spindlebearings have been gradually improved to meet requirements of aeroengine, limitationof the materials has come in the applications in critical conditions. In addition,instability of high-speed rolling bearings, which makes the cage fracture and rotorinstability happened, becomes more and more important while the aeroengine workingon different conditions. Therefore, analysis of dynamic properties and behaviors ofhigh-speed rolling bearings are basic to optimize the bearing design and key researchfor improve the reliability and life of bearings. The objects of this dissertation arehigh-speed rolling bearings of aeroengines under typical rigorous working conditions.Dynamic performances of bearings are investigated according to establishment ofdynamic model and simulation. The results provide the checking basis for bearingdesign and theoretical basis to reliability and stability growth of bearing-rotor system inaeroengine.
According to the geometry and kinematic relationship of bearing elements, modelsof interaction between elements were established. Dynamic models of high speedrolling bearings were established and solved by integration method of Runge-Kutta andNewtown-Raphson which is proposed to improve the calculation efficiency and keepingprecision of dynamic results. The results could provide the basis data to analyze thebearing dynamic behavior on different conditions. The dynamic model is applied on oillubricated and solid lubricated bearing. This model can be used to analyze the influenceof assembling, temperature differential and centrifugal force. The effects of ellipticalcage pocket in ball bearing and roller profile modification in roller bearing can beinvestigated by this model.
Aiming at the misalignment between inner ring and outer ring caused byassembling error, effect of tilted misalignment on loading characteristics of rollerbearings was investigated based on the dynamic model of roller bearings. The resultsshown: The deflection between inner and outer rings caused eccentric loads on rollers,generating excessive contact pressure. In addition, the fluctuation of maximum contactpressure during the running process of bearings influenced by deflection between rings.With the increase of deflection angle between inner and outer rings, the maximumcontact stress in loading zone gradually went up and then got stabilized when deflection reached to a certain angle. While during bearing running, the fluctuation range ofmaximum contact stress first gradually decreased and then modestly increased. Forimproving the loading characteristics of roller bearings under the condition of tiltmisalignment, the quantity design basis that increasing the number of roller and usinglogarithmic roller profile modification were proposed.
Based on the dynamic model of rolling bearings, characteristics of rolling bearingsin steady conditions were analyzed from two aspects: deviation ratio of cage whirlspeed and cage sliding ratio. The results have significance for bearing failure analysis.The results shown: increasement of bearing velocity improves the cage stability butmakes cage sliding ratio increased meanwhile. It is available for decrease the cagesliding ratio and improves the cage stability through control the ratio of radial loads toaxial load. Increasement of radial loads on roller bearings decreases the cage slidingratio but makes cage stability become weak.
According to the aeroengine features that switching between several workingconditions, transitional dynamic performance of high speed bearings in starting,accelerating and loading processes were investigated. The results shown: Initial status ofbearing has great influence on cage stability. In starting process, cage motion completeddepends on the push of rolling elements, the force on cage are less. Cage stability isworse in the beginning of bearing starting process. In the accelerating process andloading process, cage motion is influenced by rolling elements and guiding ring. Therub and impact between cage and rolling elements increased with the raising of bearingspeeds and loads.
Based on the features of working condition, including high speed, heavy load andhigh temperature, of rolling bearings in aeroengines, the calculation model of bearingworking clearance, considering the assembling, temperature differential and centrifugalforce, was established. The working clearance and its effcts on bearing performancewere investigated. The model and analysis results can be used to guide the design ofbearing assembling parameters.
Dynamic analysis software of rolling bearings was developed through hybridprogramming of Visual Basic and Matlab. According to the example calculation,accuracy of the dynamic model and software were validated by comparing the resultscalculated by this dissertation to the results calculated by SHABERTH and ADORE.
Base on the calculation method of bearing fatigue life considering the contact loadon micro area, bearing structure optimization model, which the fatigue life as the goalfunction, the cage sliding ratio, race curvature factor and ball filling angle as theconstraint condition, was established. Effect of bearing structure on bearing stabilitywas studied. In addition, effect of rotation modes of bearings, including rotation bysingle and double rings, on bearing performance was investigated. Analysis resultsapplies theory basis for life extension of high speed rolling bearings in aeroengines.
Coupling dynamic model of rolling bearing-rotor system was established to analyze the influence of rotor on dynamic behavior of bearings. The results shown:vibration of rotor makes contact loads and relative sliding of bearing between rollingelement and rings increased, and thus influence on bearing life and temperature rise.The results are basis to analyze the micro-failure behaviors of heavy-load friction pairon micro contact area.
论文通过轴承内部零件间的运动和位置关系分析，建立了零件间的相互作用模型，建立了高速球轴承和滚子轴承的完全动力学模型。采用Newtown-Raphson算法和Runge-Kutta算法结合的方法对动力学模型求解，解决了套圈和滚动体之间高频振动对计算效率的影响，同时保证了动力学结果的精度。分析结果为分析不同工况条件下轴承的动力学行为提供了基础数据。建立的动力学模型适用于油润滑和固体润滑轴承计算，可以分析轴承装配、温差及离心作用影响，可以分析球轴承保持架的椭圆兜孔形式以及滚子轴承的母线轮廓修型影响。
针对轴承装配导致的内外圈轴线不对中现象，分析了轴承内外圈偏斜对承载区载荷特性的影响：轴承内外圈偏斜不仅导致承载滚动体发生偏载现象，引起局部接触应力过大，在轴承运转过程中还会因为变刚度振动而影响承载区最大接触应力的波动。随着内外圈偏转角度的增大，轴承接触区内最大接触应力值呈现逐渐上升趋于平稳的状态，而承载区最大接触应力的波动幅度呈现先减小而后小幅增大的趋势。以改善内外圈偏斜对承载区最大接触应力的影响为目的，兼顾承载区应力波动幅度变化，给出了增加滚子数量及滚子母线对数修型的定量依据。
根据建立的高速球轴承和滚子轴承动力学模型，从描述保持架稳定性的保持架质心涡动速度偏差比及反映滚动体整体打滑的保持架滑动率两方面分析了定常工况下高速滚动轴承的动态性能，分析结果可为轴承失效分析提供理论依据。结果表明：转速的增加可以提高保持架的稳定性，但导致滚动体打滑率上升。对于球轴承，控制径向载荷与轴向载荷的比值可以降低轴承滚动体的打滑率并有助于保持架稳定性的提升；对于滚子轴承，径向载荷的增加可以降低滚动体的打滑率，但同时导致保持架稳定性减弱。
针对航空发动机工作中的多工况转换特点，分别就发动机启动、加速和加力三种过渡状态，分析了轴承的瞬态动力学行为。结果表明：保持架的稳定性与初始状态关系较大。轴承启动阶段，外引导保持架受滚动体推动，承受载荷较小，但在较长一段时间内处于不稳定状态；轴承加速和加载阶段，保持架受滚动体和引导套圈共同作用，速度或推力的增加会加剧保持架与套圈引导面及滚动体的碰磨。
基于航空轴承高速、重载、高温的工况特点，建立了考虑配合、工作温度及高速离心载荷的轴承工作游隙计算模型，分析了轴承不同工况的工作游隙及其对轴承性能的影响。模型和分析结果为轴承配合参数设计提供指导。
对建立的动力学计算模型，采用软件集成技术，通过Visual Basic和Matlab混合编程研制了滚动轴承动态性能分析软件。软件功能通过与SHABERTH软件及ADORE软件对典型算例的计算结果对比获得了模型和方法的准确性验证，表明本软件在轴承稳态动力学参数预测及轴承瞬态运动学预测两方面都具有较好的精度。
基于考虑轴承微区接触载荷的疲劳寿命计算方法，建立了以疲劳寿命为目标函数，以保持架滑动率、内外圈沟曲率系数和填球角为约束条件的轴承结构参数优化模型。分析了轴承结构参数对轴承稳定性的影响。研究了轴承内外圈相对转动方式对轴承结构优化的影响。分析结果为航空发动机轴承的延寿方法提供了理论基础。
针对高速轴承-转子系统的动力学耦合特点，建立了轴承-转子系统的耦合动力学分析模型，初步分析了转子对轴承动力学的影响：转子振动引起的滚动体和套圈间接触应力和相对滑动增大将对轴承疲劳寿命及温升产生不良影响，分析结果为进一步研究重载摩擦副接触微区的微观失效行为提供了基础。
To satisfy the trending of aeroengine for high thrust-weight ratio, long life andhigh reliability, high-speed rolling bearings of aeroengine is required more and morerigorous on speed and loads. Due to high contact pressure and temperature rise, kinds ofsurface failures, such as surface scratch and surface burning, even serious consequencessuch as journal sticking the on severe case, occur on rolling bearings that operates onthe high speed and heavy load conditions. Although materials and structures of spindlebearings have been gradually improved to meet requirements of aeroengine, limitationof the materials has come in the applications in critical conditions. In addition,instability of high-speed rolling bearings, which makes the cage fracture and rotorinstability happened, becomes more and more important while the aeroengine workingon different conditions. Therefore, analysis of dynamic properties and behaviors ofhigh-speed rolling bearings are basic to optimize the bearing design and key researchfor improve the reliability and life of bearings. The objects of this dissertation arehigh-speed rolling bearings of aeroengines under typical rigorous working conditions.Dynamic performances of bearings are investigated according to establishment ofdynamic model and simulation. The results provide the checking basis for bearingdesign and theoretical basis to reliability and stability growth of bearing-rotor system inaeroengine.
According to the geometry and kinematic relationship of bearing elements, modelsof interaction between elements were established. Dynamic models of high speedrolling bearings were established and solved by integration method of Runge-Kutta andNewtown-Raphson which is proposed to improve the calculation efficiency and keepingprecision of dynamic results. The results could provide the basis data to analyze thebearing dynamic behavior on different conditions. The dynamic model is applied on oillubricated and solid lubricated bearing. This model can be used to analyze the influenceof assembling, temperature differential and centrifugal force. The effects of ellipticalcage pocket in ball bearing and roller profile modification in roller bearing can beinvestigated by this model.
Aiming at the misalignment between inner ring and outer ring caused byassembling error, effect of tilted misalignment on loading characteristics of rollerbearings was investigated based on the dynamic model of roller bearings. The resultsshown: The deflection between inner and outer rings caused eccentric loads on rollers,generating excessive contact pressure. In addition, the fluctuation of maximum contactpressure during the running process of bearings influenced by deflection between rings.With the increase of deflection angle between inner and outer rings, the maximumcontact stress in loading zone gradually went up and then got stabilized when deflection reached to a certain angle. While during bearing running, the fluctuation range ofmaximum contact stress first gradually decreased and then modestly increased. Forimproving the loading characteristics of roller bearings under the condition of tiltmisalignment, the quantity design basis that increasing the number of roller and usinglogarithmic roller profile modification were proposed.
Based on the dynamic model of rolling bearings, characteristics of rolling bearingsin steady conditions were analyzed from two aspects: deviation ratio of cage whirlspeed and cage sliding ratio. The results have significance for bearing failure analysis.The results shown: increasement of bearing velocity improves the cage stability butmakes cage sliding ratio increased meanwhile. It is available for decrease the cagesliding ratio and improves the cage stability through control the ratio of radial loads toaxial load. Increasement of radial loads on roller bearings decreases the cage slidingratio but makes cage stability become weak.
According to the aeroengine features that switching between several workingconditions, transitional dynamic performance of high speed bearings in starting,accelerating and loading processes were investigated. The results shown: Initial status ofbearing has great influence on cage stability. In starting process, cage motion completeddepends on the push of rolling elements, the force on cage are less. Cage stability isworse in the beginning of bearing starting process. In the accelerating process andloading process, cage motion is influenced by rolling elements and guiding ring. Therub and impact between cage and rolling elements increased with the raising of bearingspeeds and loads.
Based on the features of working condition, including high speed, heavy load andhigh temperature, of rolling bearings in aeroengines, the calculation model of bearingworking clearance, considering the assembling, temperature differential and centrifugalforce, was established. The working clearance and its effcts on bearing performancewere investigated. The model and analysis results can be used to guide the design ofbearing assembling parameters.
Dynamic analysis software of rolling bearings was developed through hybridprogramming of Visual Basic and Matlab. According to the example calculation,accuracy of the dynamic model and software were validated by comparing the resultscalculated by this dissertation to the results calculated by SHABERTH and ADORE.
Base on the calculation method of bearing fatigue life considering the contact loadon micro area, bearing structure optimization model, which the fatigue life as the goalfunction, the cage sliding ratio, race curvature factor and ball filling angle as theconstraint condition, was established. Effect of bearing structure on bearing stabilitywas studied. In addition, effect of rotation modes of bearings, including rotation bysingle and double rings, on bearing performance was investigated. Analysis resultsapplies theory basis for life extension of high speed rolling bearings in aeroengines.
Coupling dynamic model of rolling bearing-rotor system was established to analyze the influence of rotor on dynamic behavior of bearings. The results shown:vibration of rotor makes contact loads and relative sliding of bearing between rollingelement and rings increased, and thus influence on bearing life and temperature rise.The results are basis to analyze the micro-failure behaviors of heavy-load friction pairon micro contact area.
引文
[1]林左鸣.战斗机发动机的研制现状和发展趋势[J].航空发动机，2006，32（1）：1-8.
[2]姜晓莲，王斌.浅析未来航空发动机技术的发展[J].航空科学技术,2010(2):10~12
[3]林基恕.航空发动机主轴滚动轴承的技术进展[J].燃气涡轮试验与研究，2003，16（4）：52-56.
[4] Wang Liqin，Chen Guanci，Gu Le，et al. Operating Temperature in High-SpeedBall Bearing[J]. Journal of Mechanical Engineering Science，2007，221（3）：353-359.
[5]王道全.双半内圈三点接触球轴承的几何分析[J].轴承，1988，（2）：2-8.
[6] Harris T A. An Analytical Investigation of Cylindrical Roller Bearings HavingAnnular Rollers[J]. Tribology Transaction，1967，10：235-242.
[7]范大鹏，严自强.高速防滑轴承非圆滚道磨削加工技术[J].轴承，1996，（12）：18-33.
[8]王黎钦，陈观慈.航空轴承非圆滚道的预变形加工技术[J].机械工程学报，2005，41（9）：223-227.
[9]王黎钦，崔立，郑德志等.航空发动机高速球轴承动态特性分析[J].航空学报，2007，28（6）：1461-1467.
[10] Hartnett M J. The Analysis of Contact Stresses in Rolling Element Bearings[J].Journal of Lubrication Technology，1979，101：105-109.
[11] Hanson M T，Keer L M. Mechanics of Edge Effects on Frictionless Contacts[J].International Journal of Solids and Structures，1995，32（3）：391-405.
[12] Ju S H， Horng T L， Cha K C. Comparisons of Contact Pressures of CrownedRollers[J]. Journal of Engineering Tribology，2000，214：147-256.
[13]李思成,陈晓阳,陈爱华等.重载下调心滚子轴承接触应力分析及凸形设计[J].轴承，2010，4：1-6.
[14] Gupta P K. Cage Unbalance and Wear in Ball Bearings[J]. Wear，1991，147：93-104.
[15] Gupta P K. Cage Unbalance and Wear in Roller Rearings[J]. Wear，1991，147：105-118.
[16] Masataka Nosaka，Satoshi Takada，Makoto Yoshida，et al. Effect of TiltedMisalignment on Trio-Characteristics of High-Speed Ball Bearings in LiquidHydrogen[J]. Tribology Online，2010，5（2）：71-79.
[17] Sunil Kumar K，Rajiv Tiwari， Prasad P V V N. An Optimum Design of CrownedCylindrical Roller Bearings Using Genetic Algorithms[J]. Journal of MechanicalDesign，2009，131（5）051011：1-14.
[18] Zaretsky E V. Rolling Bearing Steels-A Technical and Historical Perspective[J].Materials Science and Technology，2012，28（1）：58-69.
[19] Harris T A. On the Fatigue Life of M50NiL Rolling Bearings[J]. TribologyTransaction，1992，35（4）：731-737.
[20]曾照明，汤宝寅，王松雁.金属等离子体浸没离子注入改善9Cr18轴承钢表面耐磨性的研究[J].真空科学与技术，2000，20（2）：77-80.
[21] Stewart S，Ahmed R. Rolling Contact Fatigue of Surface Coatings-A Review[J].Wear，2002，253（11-12）：1132-1144.
[22] Averbach B L. Surface-Initiated Spalling Fatigue in M50and M50Nil Bearings[J].Lubrication Engineering，1991，47（10）：837-843.
[23] Trojahn W， Streit E， Chin H A，et al. Progress in Bearing Performance ofAdvanced Nitrogen Alloyed Stainless Steel, Cronidur30[J]. Materialwissenschaftund Werkstofftechnik，1999，30（10）：605-611.
[24] Wert D E. Development of A Carburizing Stainless Steel Alloy[J]. AdvancedMaterials and Processes，1994，145（6）：89-91.
[25] Wang L，Snidle R W，Gu L. Rolling Contact Silicon Nitride Bearing Technolgy:A Review of Recent Research[J]. Wear，2000，246：159-173.
[26]张传伟.陶瓷球轴承固体润滑涂层制备与承载特性分析[D].哈尔滨:哈尔滨工业大学,2009.
[27]王黎钦，李秀娟，古乐等.弹用混合式陶瓷轴承的开发研究[J].推进技术，2001，22（6）：522-525.
[28]万长森.滚动轴承的分析方法[M].北京：机械工业出版社，1987.
[29] Jones A B. Ball Motion and Sliding Friction in Ball Bearings[J]. Journal of BasicEngineer，1959，81：1-12.
[30]陈观慈，王黎钦，古乐等.高速球轴承生热分析[J].航空动力学报，2007，22（1）：163-168.
[31]王黎钦，陈观慈，古乐等.高速圆柱滚子轴承生热研究[J].润滑与密封，2007，32（8）：8-11.
[32] Pete Cento，Don W. Dareing. Ceramic Material in Hybrid Ball Bearings[J].Tribology Transaction，1999，42（4）：707-714.
[33]彭波，王黎钦，崔立等.角接触球轴承分析模型的数值求解[J].南京航空航天大学学报，2009，41（3）：370-374.
[34] Harris T A. Rolling Bearing Analysis[M]. New York：JohnWiley&Sons, Inc.，2001.
[35] Pirvics J. Numerical Analysis Techniques and Design Methodology for RollingElement Bearing Load Support Systems[J]. ASME，1980，（11）：47-85.
[36] Poplawski J V. Slip and Cage Forces in a High-Speed Roller Bearing[J]. Journalof Lubrication Technology，1972，4：143-152.
[37] Kannel J W， Bupara S S. A Simplified Model of Cage Motion in AngularContact Bearings Operating in the EHD Lubrication Regime[J]. Journal ofLubrication Technology，1978，100：395-403.
[38]罗祝三，吴林丰，孙心德.轴向受载的高速球轴承的拟动力学分析[J].航空动力学报，1996，11（3）：257-260.
[39]袁茹，李继庆.高速滚子轴承的拟动态分析计算[J].机械科学与技术，1995，1：65-68.
[40]张铁成，陈国定，李建华.高速滚动轴承的动力学分析[J].机械科学与技术，1997，16（1）：136-139.
[41] Ebert Franz-Josef. An Overview of Performance Characteristics, Experiences andTrends of Aerospace Engine Bearings Technologies[J]. Chinese Journal ofAeronautics，2007，20：378-384.
[42]崔立，王黎钦，郑德志等.航空发动机高速滚子轴承动态特性分析[J].航空学报，2008，29（2）：492-498.
[43]王斌.航空发动机滚动轴承保持架动力学研究[D].沈阳:沈阳航空航天大学,2012.
[44]崔立,时大方,郑建荣等.基于ANSYS/LS-DYNA的保持架动力学分析[J].机械传动.2012,6:78~81
[45] Walters C T. The Dynamics of Ball Bearings[J]. Journal of LubricationTechnology，1971，93：1-10.
[46] Gupta P K. Dynamic of Rolling-Element Bearings. Part Ⅲ: Ball BearingAnalysis[J]. Journal of Lubrication Technology，1979，10（3）：312-318.
[47] Gupta P K. Dynamic of Rolling-Element Bearings. Part Ⅳ: Ball BearingResults[J]. Journal of Lubrication Technology，1979，10（3）：319-326.
[48] Gupta P K， Dill J F， Bandow H E. Dynamics of Rolling-Element BearingsExperimental Validation of the DREB and RAPIDREB Computer Programs[J].Journal of Tribology，1985，107：132-137.
[49] Gupta P K. Dynamic of Rolling-Element Bearings. PartⅠ: Cylindrical RollerBearing Analysis[J]. Journal of Lubrication Technology，1979，10（3）：293-304.
[50] Gupta P K. Dynamic of Rolling-Element Bearings. Part Ⅱ: Cylindrical RollerBearing Results[J]. Journal of Lubrication Technology，1979，10（3）：305-311.
[51] Gupta P K. Modeling of Instabilities Induced by Cage Clearances in BallBearings[J]. Tribology Transaction，1991，31（4）：93-99.
[52] Gupta P K. Modeling of Instabilities Induced by Cage Clearances in CylindricalRoller Bearings[J]. Tribology Transaction，1991，31（4）：1-8.
[53] Meeks C R， Ng K O. The Dynamics of Ball Separators in Ball Bearings. Part1~2: Analysis and Results of Optimization Study[J]. Tribology Transaction，1985，28（3）：277-295.
[54] Meeks C R， Tran L. Ball Bearing Dynamic Analysis Using Computer Methods.Part1: Analysis[J]. Journal of Tribology，1996，118（1）：52-58.
[55] Bai C Q，Xu Q Y. Dynamic Model of Ball Bearings with Internal Clearance andWaviness[J]. Journal of Sound and Vibration，2006，294：23-28.
[56] Liu X H，Deng S E，Teng H F. Dynamic Stability Analysis of Cages inHigh-Speed Oil-Lubricated Angular Contact Ball Bearings[J]. Transactions ofTianjin University，2011，17（1）：20-27.
[57]张铁成，陈国定，李建华.高速滚动轴承动态特性的粗糙效应分析[J].西北工业大学学报，1999，4：643-647.
[58]刘文秀，杨咸启，陈贵.高速滚子轴承保持架碰撞模型与运动分析[J].轴承，2003，9：1-5.
[59]周延泽，王春浩，陆震.高速滚动轴承保持架自由振动特性研究[J].北京航空航天大学学报，2001，27（5）：596-599.
[60] Guangyoung Sun. Auxiliary Bearing Life Prediction Using Hertzian ContactBearing Model[J]. Journal of Vibration and Acoustics，2006，128：203-209.
[61] Weinzapfel N，Sadeghi F. A Discrete Element Approach for Modeling CageFlexibility in Ball Bearing Dynamics Simulations[J]. Journal of Tribology，2009，131（2）：021102.
[62] Ashtekar A，Sadeghi F，Stacke L E. A New Approach to Modeling SurfaceDefects in Bearing Dynamics Simulations[J]. Journal of Tribology，2008，130（4）：041103.
[63]刘春浩.滚动轴承的结构振动问题[J].轴承，2000，5：27-29.
[64]罗继伟.滚动轴承受力分析及其进展[J].轴承，2001，9：28-31.
[65] Harsha S. P. Nonlinear dynamic response of a balanced rotor supported by rollingelement bearings due to radial internal clearance effect[J]. Mechanism andmachine theory,2006,41(6):688-706
[66]韩宝财,唐六丁,邓四二等．多频耦合的航空发动机转子系统动力特性分[J]．振动与冲击，2008,27(8)：25-28．
[67]张耀强,陈建军,唐六丁等．滚动轴承－转子系统非线性参数、强迫联合振动[J]．机械强度，2009，31(6)：871-875．
[68]周海仑,陈果．航空发动机双转子－滚动轴承－机匣耦合系统动力学分析[J]．航空动力学报，2009,24(6)：1284-1291．
[69]陈果．航空发动机整机耦合动力学模型及振动分析[J]．力学学报，2010，42(3)：548-559．
[70] Jones A B. A General Theory for Elastically Constrained Ball and Radial RollerBearings[J]. Journal of Basic Engineering，1960，82：309-320.
[71] Harris T A. Ball Motion in Thrust-Loaded Angular Contact Ball Bearings withCoulomb Friction[J]. Journal of Lubrication Technology，1971，93：17-24.
[72] Harris T A. An Analytical Method to Predict Skidding in Thrust-Loaded AngularContact Ball Bearings[J]. Journal of Lubrication Technology，1971，93：32-38.
[73] Poplawski J V. Slip and Cage Forces in a High-Speed Roller Bearing[J]. Journalof Lubrication Technology，1972，94：143-152.
[74] Crecelius W J， Pirvics J. Computer Program Operation Manual on SHABERTH,A Computer Program for the Analysis of the Steady-State and Transient ThermalPerformance of Shaft Bearing Systems[R]. U.S. Air Force Technical ReportAFAPL-TR-76-90，U.S. Aero Propulsion Laboratory，Wright-Patterson Air ForceBase，Ohio，1976.
[75] Ragen M A. Steady-State and Transient Thermal Analysis of a TransmissionSystems-SKF Computer Program “TRANSIM”[R]. SKF Industries Report No.AT79Y001，1979.
[76] Kleckner R J， Pirvics J. High Speed Cylindrical Roller Bearing Analysis, SKFComputer Program CYBEAN[R]. NASA-CR-159460~159461，1979.
[77] Poplawski J V， Rumbarger J H， Peters S M，et al. Advanced Analysis Packagefor High Speed Multi-Bearing Shaft Systems: COBRA-AHS[R]. Final Report，NASA Contract NAS3-00018，2002.
[78] Gupta P K. Dynamics of Rolling Element Bearings. Part Ⅵ:DREB ComputerProgram Manual[M]. New York：Mechanical Technology Incorporated，1977.
[79] Gupta P K. Interactive Graphic Simulation of Rolling Element Bearings-PhaseⅠ:Low Frequency Phenomenon and RAPIDREB Development[R]. U.S. Air ForceTechnical Report AFWAL-TR-81-4148，1981.
[80] Gupta P K. Advanced Dynamic of Rolling Elements[M]. New York：Springer-Verlag，1984.
[81] Meek C R，Murphy B，Tran L. Development of Ball Bearing Dynamic AnalysisMethods Including Life Prediction Methods for Ceramic or Metal Bearings[R].U.S. Air Force Report WL-TR-96-4019，1994.
[82] Meek C R， Polendo E. Computerized Design and Life Prediction-Bearings[R].U.S. Air Force Report WL-TR-96-4050，1995.
[83] Aramaki H. Rolling Bearing Analysis Program Package “BRAIN”[J]. Motion&Control，1997，3：15-24.
[84] Stacke L-E， Fritzson D， Nordling P. BEAST-A Rolling Bearing SimulationTool[J]. Journal of Muti-body Dynamic，1999，213：63-71.
[85] Ghaisas N， Wassgren C R， Sadeghi F. Cage Instability in Cylindrical RollerBearings[J]. Journal of Tribology，2004，126：681-689.
[86] Houpert L. CAGEDYN: A Contribution to Roller Bearing Dynamics Calculations.PartⅠ: Base Tribology Concepts[J]. Tribology Transaction，2010，53（1）：1-9.
[87] Houpert L. CAGEDYN: A Contribution to Roller Bearing Dynamics Calculations.Part Ⅱ: Description of the Numerical Tool and Its Output[J]. TribologyTransaction，2010，53（1）：10-21.
[88]张志华，邓四二，周彦伟等.高速圆柱滚子轴承保持架动力学分析[J].河南科技大学学报，2006，27（2）：16-22.
[89]唐云冰，高德平，罗贵火.航空发动机高速滚珠轴承力学特性分析与研究[J].航空动力学报，2006，21（2）：354-360.
[90]李媛媛，徐浩.高速机床主轴用陶瓷轴承动态性能研究[J].现代零部件，2004，（8）：54-57.
[91]王黎钦，崔立，郑德志等.高速滚动轴承智能化设计方法研究[J].哈尔滨工业大学学报，2006，38（增刊）：4-7.
[92] Tomoya Sakaguchi，Kazuyoshi Harada. Dynamic Analysis of Cage Behavior in aTapered Roller Bearing[J]. Journal of Tribology，2006，128：604-611.
[93]张风琴，杜辉，邓四二等.基于ADAMS的圆柱滚子轴承仿真分析[J].河南科技大学学报，2009，30（2）：15-18.
[94] Johnson K L. Contact Mechanics [M]. Cambridge：Cambridge University Press，1987.
[95] Kannel J W， Walowit J A. Simplified Analysis for Tractions BetweenRolling-Sliding Elastohydrodynamic Contacts[J]. Journal of LubricationTechnology，1987，93：39-46.
[96] Hamrock B J， Schmid S R， Jacobson B O. Fundamentals of Fluid FilmLubrication[M]. New York：Marcell Dekker Inc.，2004.
[97]孙大成.润滑力学讲义[M].北京：中国友谊出版公司，1991.
[98] Pinkus O， Sterlicht B著，西安交通大学轴承研究小组译.流体动力润滑理论[M].北京：机械工业出版社，1980.
[99] Schlichting H， Gersten K. Boundary-Layer Theory[M]. Berlin：Springer Verlag，2000.
[100] Palmgren A. Ball and roller bearing engineering [M]. Philadelphia: SKFIndustries Inc.,1959.
[101] Harris T，Kotzalas M. Advanced Concepts of Bearing Technology[M]. New York：Taylor&Francis，2006.
[102] Harsha S. P. Non-linear dynamic response of a balanced rotor supported onrolling element bearings[J]. Mechanical Systems and Signal Processing,2005,19(3):551-578．
[103] Kragelsky I V，Alisin V V. Tribology-Lubrication, friction and wear[M]. London：Professional Engineering Publishing Ltd.，2001.
[104]周志澜，马纯民.航空发动机主轴轴承失效分析与预防[M].北京：科学出版社：1998.
[105] Tauqir A， Salam I， Haq A ul，et al. Causes of Fatigue Failure in the MainBearing of an Aero-Engine[J]. Engineering Failure Analysis，2000，7(2)：127-144.
[106] Sakaguchi T， Kaoru U. Dynamic Analysis of Cage Behavior in a CylindricalRoller Bearing[J]. NTN Technical Review，2004，No.71.
[107] Kingsbury E， Walker R. Motions of an Unstable Retainer in an Instrument BallBearing[J]. Joumal of Tribology，1994，16（2）：202-208.
[108]崔立，王黎钦，郑德志等.高速球轴承打滑的临界负荷[J].航空动力学报，2007，22（11）：1971-1976.
[109] Harris T，Kotzalas M. Essential Concepts of Bearing Technology[M]. New York：Taylor&Francis Group，2006.
[110]《航空发动机设计手册》总编委会.航空发动机设计手册，第12册：传动及润滑系统[M].北京：航空工业出版社，2002:21.
[111] Howard G Gibson, James D Moore, Joe C Cody. SSME Bearing and Seal TesterData Compilation, Analysis and Reporting; And Refinement of the CryogenicBearing Analysis Mathematical Model[R]. NASA final reports NAS8-39379，2000.
[112] ISO281/1. International organization for standardization rolling bearings dynamicload ratings and rating life[S]. Switzer Land:1977.
[113]冷钢.复合工况下高速滚动轴承的寿命和可靠性预测[D].哈尔滨：哈尔滨工业大学，2011:12-16.
[114]崔立.航空发动机高速滚动轴承及转子系统的动态性能研究[D].哈尔滨：哈尔滨工业大学，2008：130-136.
[115]李建华，姜维.固体润滑轴承保持架试验分析[J].轴承，2004，9：18-20.
[116] FAG Rolling Bearings. Technology Information No. WL43-1190EA[R].Germany: Weppert GmbH&Co. KG Schweinfurt，1999
[2]姜晓莲，王斌.浅析未来航空发动机技术的发展[J].航空科学技术,2010(2):10~12
[3]林基恕.航空发动机主轴滚动轴承的技术进展[J].燃气涡轮试验与研究，2003，16（4）：52-56.
[4] Wang Liqin，Chen Guanci，Gu Le，et al. Operating Temperature in High-SpeedBall Bearing[J]. Journal of Mechanical Engineering Science，2007，221（3）：353-359.
[5]王道全.双半内圈三点接触球轴承的几何分析[J].轴承，1988，（2）：2-8.
[6] Harris T A. An Analytical Investigation of Cylindrical Roller Bearings HavingAnnular Rollers[J]. Tribology Transaction，1967，10：235-242.
[7]范大鹏，严自强.高速防滑轴承非圆滚道磨削加工技术[J].轴承，1996，（12）：18-33.
[8]王黎钦，陈观慈.航空轴承非圆滚道的预变形加工技术[J].机械工程学报，2005，41（9）：223-227.
[9]王黎钦，崔立，郑德志等.航空发动机高速球轴承动态特性分析[J].航空学报，2007，28（6）：1461-1467.
[10] Hartnett M J. The Analysis of Contact Stresses in Rolling Element Bearings[J].Journal of Lubrication Technology，1979，101：105-109.
[11] Hanson M T，Keer L M. Mechanics of Edge Effects on Frictionless Contacts[J].International Journal of Solids and Structures，1995，32（3）：391-405.
[12] Ju S H， Horng T L， Cha K C. Comparisons of Contact Pressures of CrownedRollers[J]. Journal of Engineering Tribology，2000，214：147-256.
[13]李思成,陈晓阳,陈爱华等.重载下调心滚子轴承接触应力分析及凸形设计[J].轴承，2010，4：1-6.
[14] Gupta P K. Cage Unbalance and Wear in Ball Bearings[J]. Wear，1991，147：93-104.
[15] Gupta P K. Cage Unbalance and Wear in Roller Rearings[J]. Wear，1991，147：105-118.
[16] Masataka Nosaka，Satoshi Takada，Makoto Yoshida，et al. Effect of TiltedMisalignment on Trio-Characteristics of High-Speed Ball Bearings in LiquidHydrogen[J]. Tribology Online，2010，5（2）：71-79.
[17] Sunil Kumar K，Rajiv Tiwari， Prasad P V V N. An Optimum Design of CrownedCylindrical Roller Bearings Using Genetic Algorithms[J]. Journal of MechanicalDesign，2009，131（5）051011：1-14.
[18] Zaretsky E V. Rolling Bearing Steels-A Technical and Historical Perspective[J].Materials Science and Technology，2012，28（1）：58-69.
[19] Harris T A. On the Fatigue Life of M50NiL Rolling Bearings[J]. TribologyTransaction，1992，35（4）：731-737.
[20]曾照明，汤宝寅，王松雁.金属等离子体浸没离子注入改善9Cr18轴承钢表面耐磨性的研究[J].真空科学与技术，2000，20（2）：77-80.
[21] Stewart S，Ahmed R. Rolling Contact Fatigue of Surface Coatings-A Review[J].Wear，2002，253（11-12）：1132-1144.
[22] Averbach B L. Surface-Initiated Spalling Fatigue in M50and M50Nil Bearings[J].Lubrication Engineering，1991，47（10）：837-843.
[23] Trojahn W， Streit E， Chin H A，et al. Progress in Bearing Performance ofAdvanced Nitrogen Alloyed Stainless Steel, Cronidur30[J]. Materialwissenschaftund Werkstofftechnik，1999，30（10）：605-611.
[24] Wert D E. Development of A Carburizing Stainless Steel Alloy[J]. AdvancedMaterials and Processes，1994，145（6）：89-91.
[25] Wang L，Snidle R W，Gu L. Rolling Contact Silicon Nitride Bearing Technolgy:A Review of Recent Research[J]. Wear，2000，246：159-173.
[26]张传伟.陶瓷球轴承固体润滑涂层制备与承载特性分析[D].哈尔滨:哈尔滨工业大学,2009.
[27]王黎钦，李秀娟，古乐等.弹用混合式陶瓷轴承的开发研究[J].推进技术，2001，22（6）：522-525.
[28]万长森.滚动轴承的分析方法[M].北京：机械工业出版社，1987.
[29] Jones A B. Ball Motion and Sliding Friction in Ball Bearings[J]. Journal of BasicEngineer，1959，81：1-12.
[30]陈观慈，王黎钦，古乐等.高速球轴承生热分析[J].航空动力学报，2007，22（1）：163-168.
[31]王黎钦，陈观慈，古乐等.高速圆柱滚子轴承生热研究[J].润滑与密封，2007，32（8）：8-11.
[32] Pete Cento，Don W. Dareing. Ceramic Material in Hybrid Ball Bearings[J].Tribology Transaction，1999，42（4）：707-714.
[33]彭波，王黎钦，崔立等.角接触球轴承分析模型的数值求解[J].南京航空航天大学学报，2009，41（3）：370-374.
[34] Harris T A. Rolling Bearing Analysis[M]. New York：JohnWiley&Sons, Inc.，2001.
[35] Pirvics J. Numerical Analysis Techniques and Design Methodology for RollingElement Bearing Load Support Systems[J]. ASME，1980，（11）：47-85.
[36] Poplawski J V. Slip and Cage Forces in a High-Speed Roller Bearing[J]. Journalof Lubrication Technology，1972，4：143-152.
[37] Kannel J W， Bupara S S. A Simplified Model of Cage Motion in AngularContact Bearings Operating in the EHD Lubrication Regime[J]. Journal ofLubrication Technology，1978，100：395-403.
[38]罗祝三，吴林丰，孙心德.轴向受载的高速球轴承的拟动力学分析[J].航空动力学报，1996，11（3）：257-260.
[39]袁茹，李继庆.高速滚子轴承的拟动态分析计算[J].机械科学与技术，1995，1：65-68.
[40]张铁成，陈国定，李建华.高速滚动轴承的动力学分析[J].机械科学与技术，1997，16（1）：136-139.
[41] Ebert Franz-Josef. An Overview of Performance Characteristics, Experiences andTrends of Aerospace Engine Bearings Technologies[J]. Chinese Journal ofAeronautics，2007，20：378-384.
[42]崔立，王黎钦，郑德志等.航空发动机高速滚子轴承动态特性分析[J].航空学报，2008，29（2）：492-498.
[43]王斌.航空发动机滚动轴承保持架动力学研究[D].沈阳:沈阳航空航天大学,2012.
[44]崔立,时大方,郑建荣等.基于ANSYS/LS-DYNA的保持架动力学分析[J].机械传动.2012,6:78~81
[45] Walters C T. The Dynamics of Ball Bearings[J]. Journal of LubricationTechnology，1971，93：1-10.
[46] Gupta P K. Dynamic of Rolling-Element Bearings. Part Ⅲ: Ball BearingAnalysis[J]. Journal of Lubrication Technology，1979，10（3）：312-318.
[47] Gupta P K. Dynamic of Rolling-Element Bearings. Part Ⅳ: Ball BearingResults[J]. Journal of Lubrication Technology，1979，10（3）：319-326.
[48] Gupta P K， Dill J F， Bandow H E. Dynamics of Rolling-Element BearingsExperimental Validation of the DREB and RAPIDREB Computer Programs[J].Journal of Tribology，1985，107：132-137.
[49] Gupta P K. Dynamic of Rolling-Element Bearings. PartⅠ: Cylindrical RollerBearing Analysis[J]. Journal of Lubrication Technology，1979，10（3）：293-304.
[50] Gupta P K. Dynamic of Rolling-Element Bearings. Part Ⅱ: Cylindrical RollerBearing Results[J]. Journal of Lubrication Technology，1979，10（3）：305-311.
[51] Gupta P K. Modeling of Instabilities Induced by Cage Clearances in BallBearings[J]. Tribology Transaction，1991，31（4）：93-99.
[52] Gupta P K. Modeling of Instabilities Induced by Cage Clearances in CylindricalRoller Bearings[J]. Tribology Transaction，1991，31（4）：1-8.
[53] Meeks C R， Ng K O. The Dynamics of Ball Separators in Ball Bearings. Part1~2: Analysis and Results of Optimization Study[J]. Tribology Transaction，1985，28（3）：277-295.
[54] Meeks C R， Tran L. Ball Bearing Dynamic Analysis Using Computer Methods.Part1: Analysis[J]. Journal of Tribology，1996，118（1）：52-58.
[55] Bai C Q，Xu Q Y. Dynamic Model of Ball Bearings with Internal Clearance andWaviness[J]. Journal of Sound and Vibration，2006，294：23-28.
[56] Liu X H，Deng S E，Teng H F. Dynamic Stability Analysis of Cages inHigh-Speed Oil-Lubricated Angular Contact Ball Bearings[J]. Transactions ofTianjin University，2011，17（1）：20-27.
[57]张铁成，陈国定，李建华.高速滚动轴承动态特性的粗糙效应分析[J].西北工业大学学报，1999，4：643-647.
[58]刘文秀，杨咸启，陈贵.高速滚子轴承保持架碰撞模型与运动分析[J].轴承，2003，9：1-5.
[59]周延泽，王春浩，陆震.高速滚动轴承保持架自由振动特性研究[J].北京航空航天大学学报，2001，27（5）：596-599.
[60] Guangyoung Sun. Auxiliary Bearing Life Prediction Using Hertzian ContactBearing Model[J]. Journal of Vibration and Acoustics，2006，128：203-209.
[61] Weinzapfel N，Sadeghi F. A Discrete Element Approach for Modeling CageFlexibility in Ball Bearing Dynamics Simulations[J]. Journal of Tribology，2009，131（2）：021102.
[62] Ashtekar A，Sadeghi F，Stacke L E. A New Approach to Modeling SurfaceDefects in Bearing Dynamics Simulations[J]. Journal of Tribology，2008，130（4）：041103.
[63]刘春浩.滚动轴承的结构振动问题[J].轴承，2000，5：27-29.
[64]罗继伟.滚动轴承受力分析及其进展[J].轴承，2001，9：28-31.
[65] Harsha S. P. Nonlinear dynamic response of a balanced rotor supported by rollingelement bearings due to radial internal clearance effect[J]. Mechanism andmachine theory,2006,41(6):688-706
[66]韩宝财,唐六丁,邓四二等．多频耦合的航空发动机转子系统动力特性分[J]．振动与冲击，2008,27(8)：25-28．
[67]张耀强,陈建军,唐六丁等．滚动轴承－转子系统非线性参数、强迫联合振动[J]．机械强度，2009，31(6)：871-875．
[68]周海仑,陈果．航空发动机双转子－滚动轴承－机匣耦合系统动力学分析[J]．航空动力学报，2009,24(6)：1284-1291．
[69]陈果．航空发动机整机耦合动力学模型及振动分析[J]．力学学报，2010，42(3)：548-559．
[70] Jones A B. A General Theory for Elastically Constrained Ball and Radial RollerBearings[J]. Journal of Basic Engineering，1960，82：309-320.
[71] Harris T A. Ball Motion in Thrust-Loaded Angular Contact Ball Bearings withCoulomb Friction[J]. Journal of Lubrication Technology，1971，93：17-24.
[72] Harris T A. An Analytical Method to Predict Skidding in Thrust-Loaded AngularContact Ball Bearings[J]. Journal of Lubrication Technology，1971，93：32-38.
[73] Poplawski J V. Slip and Cage Forces in a High-Speed Roller Bearing[J]. Journalof Lubrication Technology，1972，94：143-152.
[74] Crecelius W J， Pirvics J. Computer Program Operation Manual on SHABERTH,A Computer Program for the Analysis of the Steady-State and Transient ThermalPerformance of Shaft Bearing Systems[R]. U.S. Air Force Technical ReportAFAPL-TR-76-90，U.S. Aero Propulsion Laboratory，Wright-Patterson Air ForceBase，Ohio，1976.
[75] Ragen M A. Steady-State and Transient Thermal Analysis of a TransmissionSystems-SKF Computer Program “TRANSIM”[R]. SKF Industries Report No.AT79Y001，1979.
[76] Kleckner R J， Pirvics J. High Speed Cylindrical Roller Bearing Analysis, SKFComputer Program CYBEAN[R]. NASA-CR-159460~159461，1979.
[77] Poplawski J V， Rumbarger J H， Peters S M，et al. Advanced Analysis Packagefor High Speed Multi-Bearing Shaft Systems: COBRA-AHS[R]. Final Report，NASA Contract NAS3-00018，2002.
[78] Gupta P K. Dynamics of Rolling Element Bearings. Part Ⅵ:DREB ComputerProgram Manual[M]. New York：Mechanical Technology Incorporated，1977.
[79] Gupta P K. Interactive Graphic Simulation of Rolling Element Bearings-PhaseⅠ:Low Frequency Phenomenon and RAPIDREB Development[R]. U.S. Air ForceTechnical Report AFWAL-TR-81-4148，1981.
[80] Gupta P K. Advanced Dynamic of Rolling Elements[M]. New York：Springer-Verlag，1984.
[81] Meek C R，Murphy B，Tran L. Development of Ball Bearing Dynamic AnalysisMethods Including Life Prediction Methods for Ceramic or Metal Bearings[R].U.S. Air Force Report WL-TR-96-4019，1994.
[82] Meek C R， Polendo E. Computerized Design and Life Prediction-Bearings[R].U.S. Air Force Report WL-TR-96-4050，1995.
[83] Aramaki H. Rolling Bearing Analysis Program Package “BRAIN”[J]. Motion&Control，1997，3：15-24.
[84] Stacke L-E， Fritzson D， Nordling P. BEAST-A Rolling Bearing SimulationTool[J]. Journal of Muti-body Dynamic，1999，213：63-71.
[85] Ghaisas N， Wassgren C R， Sadeghi F. Cage Instability in Cylindrical RollerBearings[J]. Journal of Tribology，2004，126：681-689.
[86] Houpert L. CAGEDYN: A Contribution to Roller Bearing Dynamics Calculations.PartⅠ: Base Tribology Concepts[J]. Tribology Transaction，2010，53（1）：1-9.
[87] Houpert L. CAGEDYN: A Contribution to Roller Bearing Dynamics Calculations.Part Ⅱ: Description of the Numerical Tool and Its Output[J]. TribologyTransaction，2010，53（1）：10-21.
[88]张志华，邓四二，周彦伟等.高速圆柱滚子轴承保持架动力学分析[J].河南科技大学学报，2006，27（2）：16-22.
[89]唐云冰，高德平，罗贵火.航空发动机高速滚珠轴承力学特性分析与研究[J].航空动力学报，2006，21（2）：354-360.
[90]李媛媛，徐浩.高速机床主轴用陶瓷轴承动态性能研究[J].现代零部件，2004，（8）：54-57.
[91]王黎钦，崔立，郑德志等.高速滚动轴承智能化设计方法研究[J].哈尔滨工业大学学报，2006，38（增刊）：4-7.
[92] Tomoya Sakaguchi，Kazuyoshi Harada. Dynamic Analysis of Cage Behavior in aTapered Roller Bearing[J]. Journal of Tribology，2006，128：604-611.
[93]张风琴，杜辉，邓四二等.基于ADAMS的圆柱滚子轴承仿真分析[J].河南科技大学学报，2009，30（2）：15-18.
[94] Johnson K L. Contact Mechanics [M]. Cambridge：Cambridge University Press，1987.
[95] Kannel J W， Walowit J A. Simplified Analysis for Tractions BetweenRolling-Sliding Elastohydrodynamic Contacts[J]. Journal of LubricationTechnology，1987，93：39-46.
[96] Hamrock B J， Schmid S R， Jacobson B O. Fundamentals of Fluid FilmLubrication[M]. New York：Marcell Dekker Inc.，2004.
[97]孙大成.润滑力学讲义[M].北京：中国友谊出版公司，1991.
[98] Pinkus O， Sterlicht B著，西安交通大学轴承研究小组译.流体动力润滑理论[M].北京：机械工业出版社，1980.
[99] Schlichting H， Gersten K. Boundary-Layer Theory[M]. Berlin：Springer Verlag，2000.
[100] Palmgren A. Ball and roller bearing engineering [M]. Philadelphia: SKFIndustries Inc.,1959.
[101] Harris T，Kotzalas M. Advanced Concepts of Bearing Technology[M]. New York：Taylor&Francis，2006.
[102] Harsha S. P. Non-linear dynamic response of a balanced rotor supported onrolling element bearings[J]. Mechanical Systems and Signal Processing,2005,19(3):551-578．
[103] Kragelsky I V，Alisin V V. Tribology-Lubrication, friction and wear[M]. London：Professional Engineering Publishing Ltd.，2001.
[104]周志澜，马纯民.航空发动机主轴轴承失效分析与预防[M].北京：科学出版社：1998.
[105] Tauqir A， Salam I， Haq A ul，et al. Causes of Fatigue Failure in the MainBearing of an Aero-Engine[J]. Engineering Failure Analysis，2000，7(2)：127-144.
[106] Sakaguchi T， Kaoru U. Dynamic Analysis of Cage Behavior in a CylindricalRoller Bearing[J]. NTN Technical Review，2004，No.71.
[107] Kingsbury E， Walker R. Motions of an Unstable Retainer in an Instrument BallBearing[J]. Joumal of Tribology，1994，16（2）：202-208.
[108]崔立，王黎钦，郑德志等.高速球轴承打滑的临界负荷[J].航空动力学报，2007，22（11）：1971-1976.
[109] Harris T，Kotzalas M. Essential Concepts of Bearing Technology[M]. New York：Taylor&Francis Group，2006.
[110]《航空发动机设计手册》总编委会.航空发动机设计手册，第12册：传动及润滑系统[M].北京：航空工业出版社，2002:21.
[111] Howard G Gibson, James D Moore, Joe C Cody. SSME Bearing and Seal TesterData Compilation, Analysis and Reporting; And Refinement of the CryogenicBearing Analysis Mathematical Model[R]. NASA final reports NAS8-39379，2000.
[112] ISO281/1. International organization for standardization rolling bearings dynamicload ratings and rating life[S]. Switzer Land:1977.
[113]冷钢.复合工况下高速滚动轴承的寿命和可靠性预测[D].哈尔滨：哈尔滨工业大学，2011:12-16.
[114]崔立.航空发动机高速滚动轴承及转子系统的动态性能研究[D].哈尔滨：哈尔滨工业大学，2008：130-136.
[115]李建华，姜维.固体润滑轴承保持架试验分析[J].轴承，2004，9：18-20.
[116] FAG Rolling Bearings. Technology Information No. WL43-1190EA[R].Germany: Weppert GmbH&Co. KG Schweinfurt，1999