典型一次性机械零件设计及其应用研究
摘要
一般常用的机械系统、设备或装置都是长期运行、反复使用的，本文称之为“常规机械”。而在某些特殊场合中，有一类机械只使用一次后就被放弃不用，这类机械被称为“一次性机械”。一次性机械中的机械零件可以笼统地称为“一次性机械零件”。一次性机械零件的设计理论和方法与常规机械零件设计方法应当有所不同，然而，由于目前并未对一次性机械零件与常规机械零件给予明确的区分，所以一次性机械零件的设计仍然沿用常规机械零件的设计思想和方法，这就导致将常规机械设计准则中用于一次性机械零件设计时，不可避免的出现设计结果冗余，造成整体设计指标下降，有时甚至无法满足设计要求。虽然采用试验样机法在一定程度上能够完成一次性机械的研制，但是该方法的研制周期较长、效率较低、成本过高，不能满足日益增加的研制任务要求。因此，有必要深入研究一次性机械零件的设计理论和方法，以便为一次性机械设计理论体系的建立打下基础。
在归纳总结常规机械零件设计准则和方法的基础上，本文将一次性机械中承受循环载荷次数少的机械零件定义为一次性机械零件，明确了一次性机械零件不同于常规机械零件的基本特征，提出了在一次性机械零件设计时应该遵循的基本原则，并通过与常规机械零件设计方法的对比计算，阐明了一次性机械零件概念提出的意义。
在提出了一次性机械零件概念的基础上，本文研究了一次性机械零件与常规机械零件的区分界限。首先，基于疲劳理论，根据机械零件失效形式的不同，将一次性机械零件划分为两类分别进行研究。特别针对发生弹性失效的情况，以常用齿轮钢40Cr为试验材料，深入研究了40Cr在较高循环应力水平下的低周疲劳失效和棘轮失效行为。根据实验结果，定义了产生0.2%的总塑性应变时所对应的循环载荷作用次数为疲劳弹性失效寿命，并用疲劳弹性失效替代疲劳断裂作为高应力作用下的一次性机械零件疲劳失效的判断依据，修正了材料在高应力作用下的疲劳失效寿命模型。为了满足一次性机械零件的高可靠性要求，在40Cr的疲劳特性研究中，根据试验结果，确定了疲劳弹性失效寿命的概率分布类型为三参数Weibull分布，并采用灰色估计和最大相关系数优化法进行了参数估计，在参数估计中依据最可靠原则来确定疲劳概型参数，在提高材料许用应力范围的同时保证一次性机械零件高可靠性要求。
本文还以直齿渐开线圆柱齿轮零件为例研究了典型一次性机械零件的设计方法。在研究过程中，规划了一次性齿轮零件的研究内容，继承和改进了常规齿轮零件设计准则和方法，使之适用于一次性齿轮零件的设计。建立了小模数直齿渐开线圆柱齿轮的低周疲劳强度设计模型。该模型由两个子模型组成，首先建立了基于啮合过程的齿轮接触有限元仿真模型，利用该模型研究了较高载荷下齿轮的齿间载荷分布特征，分析了主要安装误差对齿轮应力状态的影响，获取齿根处应力应变信息。然后，基于FS模型和临界平面理论，利用有限元模型得到的应力应变信息，进行了齿根弯曲强度设计。为验证该疲劳强度设计模型的准确性，研制了小模数齿轮对称疲劳试验机。以40Cr小模数齿轮为试验对象，验证了所建立的疲劳强度设计模型的有效性。
开展了某型号箭用舵机减速器的研制工作，该减速器采用谐波传动形式，减速比300，具有输出80Nm扭矩的能力，总重量约1000g。在研制过程中，采用一次性机械零件设计方法，运用所建立的疲劳强度设计模型，对直筒形柔轮的进行了疲劳强度设计，最后，通过专用测试台测试了所研制的谐波减速器性能，结果表明各项指标均满足要求。
This paper calls the long-term and repeated machines as “general machines”. Insome special occasions, there is a kind of machines used only once before beingabandoned. Such kind of machines are called as "disposable machines”. Mechanicalelements in the disposable machines can be loosely called as “diposable mechanicalelements (DME)”. It could be foreseeable that the design method and theory ofDME should be different from general mechanical elements. However, until now theDME have not been distinguished from general mechanical elements, so the designof DME still follows design methods and theories of the general mechanicalelements, although it will be inevitable to obtain redundant design results. Even attimes, the design tasks can not be completed. A test prototype method is commonlyused in the design of DME now. However, the method with long period is inefficientand high cost, which can not meet the heavy design tasks. Therefore, it is necessaryto focus on the research of design methods and criteria of DME, which will build thefoundation of the design theory system of DME.
Based on the summary of design methods and criteria of general mechanicalelements, this paper provides the definition of DME, that is the elementsundertaking fewer cyclic loading numbers in the disposable machinery. The basicproperties and principles of DME design is explicitly provided. Furthermore, thesignificance of DME design theory is clarified by the contrast calculation betweenthe DME design theory and general mechanical design theory.
Distinguish boundaries of DME and general mechanical elements areconcerned in this paper. Firstly, according to the fatigue theory and failure types ofmechanical elements, the DME are divided into two categories. In particular, for theelements with elastic failures, steel40Cr is selected as test materials to research thelow cycle fatigue and ratcheting behaviors of metals under high level cyclic stresses.On the basis of the test results, the fatigue elastic failure life (FEFL) is defined asthe cyclic numbers when the plastic strain reach0.2%. The fatigue elastic failurewas used to replace the fatigue fracture as the failure criteria of metals under highlevel cyclic stresses. The failure models of materials under high level stresses aremodified. To meet the high reliability requirements of DME, three-parameterWeibull distribution is used to evaluate the material fatigue elastic failure life data.The gray theory and maximum correlation coefficient method are selected toestimate the parameters of three-parameter Weibull distribution. In the parameterestimation process, the most reliable principle is used. By this way, allowancestresses range are improved and the reliabilities of DME are certified at the same time.
This paper used straight involute gears as the typical DME to research thedesign method of DME. The research content is firstly determined. The generalmechanical design criteria and methods are partly accepted and improved to besuitable for the design of DME. A low cycle fatigue strength design model ofstraight involute cylinder gear with small modulus is built. The model consists oftwo parts. The first part is a gear contact finite element model based on the meshprocess. According to the model, load distribution properties under high level loadand installation errors are researched. In addition, the deddendum stress informationcould be obtained from the model. The second part is a fatigue strength designmodel based on the FS model and critical plane theory. The stress informationobtained from the finite elements model are used in the second model for thestrength design. A fatigue test machine which could be used for the gearsymmetrical fatigue test is developed. By using this machine, fatigue tests on thesmall modulus gears manufactured by40Cr steel are conducted. Experiment resultsshow that the fatigue strength design model provided in the paper is effective. Forthis reason, the DME design theory is proved to be feasible.
Certain type rocket steering reducer is developed based on the DME designtheory. The harmonic reducer type is selected. The reducer ratio is300and theoutput torque is up to80Nm. The weight of the reducer is about1000g. In the designprocess, the fatigue strength of straight shape flexsplines are researched by using theDME design methods combined with the fatigue strength design model built in thepapaer. Finally, the performance test of the reducer is conducted on a special testmachine. The test result shows that the performance of the reducer meets thespecification requirements.
在归纳总结常规机械零件设计准则和方法的基础上，本文将一次性机械中承受循环载荷次数少的机械零件定义为一次性机械零件，明确了一次性机械零件不同于常规机械零件的基本特征，提出了在一次性机械零件设计时应该遵循的基本原则，并通过与常规机械零件设计方法的对比计算，阐明了一次性机械零件概念提出的意义。
在提出了一次性机械零件概念的基础上，本文研究了一次性机械零件与常规机械零件的区分界限。首先，基于疲劳理论，根据机械零件失效形式的不同，将一次性机械零件划分为两类分别进行研究。特别针对发生弹性失效的情况，以常用齿轮钢40Cr为试验材料，深入研究了40Cr在较高循环应力水平下的低周疲劳失效和棘轮失效行为。根据实验结果，定义了产生0.2%的总塑性应变时所对应的循环载荷作用次数为疲劳弹性失效寿命，并用疲劳弹性失效替代疲劳断裂作为高应力作用下的一次性机械零件疲劳失效的判断依据，修正了材料在高应力作用下的疲劳失效寿命模型。为了满足一次性机械零件的高可靠性要求，在40Cr的疲劳特性研究中，根据试验结果，确定了疲劳弹性失效寿命的概率分布类型为三参数Weibull分布，并采用灰色估计和最大相关系数优化法进行了参数估计，在参数估计中依据最可靠原则来确定疲劳概型参数，在提高材料许用应力范围的同时保证一次性机械零件高可靠性要求。
本文还以直齿渐开线圆柱齿轮零件为例研究了典型一次性机械零件的设计方法。在研究过程中，规划了一次性齿轮零件的研究内容，继承和改进了常规齿轮零件设计准则和方法，使之适用于一次性齿轮零件的设计。建立了小模数直齿渐开线圆柱齿轮的低周疲劳强度设计模型。该模型由两个子模型组成，首先建立了基于啮合过程的齿轮接触有限元仿真模型，利用该模型研究了较高载荷下齿轮的齿间载荷分布特征，分析了主要安装误差对齿轮应力状态的影响，获取齿根处应力应变信息。然后，基于FS模型和临界平面理论，利用有限元模型得到的应力应变信息，进行了齿根弯曲强度设计。为验证该疲劳强度设计模型的准确性，研制了小模数齿轮对称疲劳试验机。以40Cr小模数齿轮为试验对象，验证了所建立的疲劳强度设计模型的有效性。
开展了某型号箭用舵机减速器的研制工作，该减速器采用谐波传动形式，减速比300，具有输出80Nm扭矩的能力，总重量约1000g。在研制过程中，采用一次性机械零件设计方法，运用所建立的疲劳强度设计模型，对直筒形柔轮的进行了疲劳强度设计，最后，通过专用测试台测试了所研制的谐波减速器性能，结果表明各项指标均满足要求。
This paper calls the long-term and repeated machines as “general machines”. Insome special occasions, there is a kind of machines used only once before beingabandoned. Such kind of machines are called as "disposable machines”. Mechanicalelements in the disposable machines can be loosely called as “diposable mechanicalelements (DME)”. It could be foreseeable that the design method and theory ofDME should be different from general mechanical elements. However, until now theDME have not been distinguished from general mechanical elements, so the designof DME still follows design methods and theories of the general mechanicalelements, although it will be inevitable to obtain redundant design results. Even attimes, the design tasks can not be completed. A test prototype method is commonlyused in the design of DME now. However, the method with long period is inefficientand high cost, which can not meet the heavy design tasks. Therefore, it is necessaryto focus on the research of design methods and criteria of DME, which will build thefoundation of the design theory system of DME.
Based on the summary of design methods and criteria of general mechanicalelements, this paper provides the definition of DME, that is the elementsundertaking fewer cyclic loading numbers in the disposable machinery. The basicproperties and principles of DME design is explicitly provided. Furthermore, thesignificance of DME design theory is clarified by the contrast calculation betweenthe DME design theory and general mechanical design theory.
Distinguish boundaries of DME and general mechanical elements areconcerned in this paper. Firstly, according to the fatigue theory and failure types ofmechanical elements, the DME are divided into two categories. In particular, for theelements with elastic failures, steel40Cr is selected as test materials to research thelow cycle fatigue and ratcheting behaviors of metals under high level cyclic stresses.On the basis of the test results, the fatigue elastic failure life (FEFL) is defined asthe cyclic numbers when the plastic strain reach0.2%. The fatigue elastic failurewas used to replace the fatigue fracture as the failure criteria of metals under highlevel cyclic stresses. The failure models of materials under high level stresses aremodified. To meet the high reliability requirements of DME, three-parameterWeibull distribution is used to evaluate the material fatigue elastic failure life data.The gray theory and maximum correlation coefficient method are selected toestimate the parameters of three-parameter Weibull distribution. In the parameterestimation process, the most reliable principle is used. By this way, allowancestresses range are improved and the reliabilities of DME are certified at the same time.
This paper used straight involute gears as the typical DME to research thedesign method of DME. The research content is firstly determined. The generalmechanical design criteria and methods are partly accepted and improved to besuitable for the design of DME. A low cycle fatigue strength design model ofstraight involute cylinder gear with small modulus is built. The model consists oftwo parts. The first part is a gear contact finite element model based on the meshprocess. According to the model, load distribution properties under high level loadand installation errors are researched. In addition, the deddendum stress informationcould be obtained from the model. The second part is a fatigue strength designmodel based on the FS model and critical plane theory. The stress informationobtained from the finite elements model are used in the second model for thestrength design. A fatigue test machine which could be used for the gearsymmetrical fatigue test is developed. By using this machine, fatigue tests on thesmall modulus gears manufactured by40Cr steel are conducted. Experiment resultsshow that the fatigue strength design model provided in the paper is effective. Forthis reason, the DME design theory is proved to be feasible.
Certain type rocket steering reducer is developed based on the DME designtheory. The harmonic reducer type is selected. The reducer ratio is300and theoutput torque is up to80Nm. The weight of the reducer is about1000g. In the designprocess, the fatigue strength of straight shape flexsplines are researched by using theDME design methods combined with the fatigue strength design model built in thepapaer. Finally, the performance test of the reducer is conducted on a special testmachine. The test result shows that the performance of the reducer meets thespecification requirements.
引文
[1]刘瑞堂.机械零件失效分析[M].哈尔滨：哈尔滨工业大学出版社，2003：18-71.
[2]龙乐豪，王小军，容易.我国一次性运载火箭的发展展望[J].中国科学E辑：技术科学，2009，39（3）：460-463.
[3]沈剑.洛马公司一次性使用的攻击飞行器[J].飞航导弹，2005，（1）：60.
[4]丛敏.一次性多用途炮射无人机[J].飞航导弹，2002，（6）：1.
[5]汪军林，解付强，刘玉浩.导弹电动舵机的研究现状及发展趋势[J].飞航导弹，2008，（3）：42-46.
[6]毛文晋.电动舵机系统的设计与试验研究[D].哈尔滨：哈尔滨工程大学硕士学位论文，2011：1-5.
[7]孙玉环.箭用电动舵机减速装置设计新方法的研究[D].哈尔滨：哈尔滨工业大学硕士学位论文，2005：1.
[8]薛红彦.一次性机械的设计方法的研究[D].哈尔滨：哈尔滨工业大学硕士学位论文，2006：5-10.
[9] Nip K H，Gardner L，Davies C M，et al. Extremely Low Cycle Fatigue Testson Structural Carbon Steel and Stainless Steel[J]. Journal of ConstructionalSteel Research，2010，(66)：96-110.
[10] Shimada K，Komotori J，Shimizu M. Fracture Mode Transition and Damage inExtremely Low Cycle Fatigue[C]. Second International Conference on LowCycle Fatigue and Elasto-Plastic Behavior of Materials，1987，680-686.
[11] Komotori J，Shimizu M. Grain Size Effect in Low Cycle Fatigue of SteelUnder Mean Strain[C]. Proceedings of the7th International Conference onFracture，1989，1213~1220.
[12] Du M L，Li G C，Zhang Y Z，et al. Fracture Behavior of Axisymmetric Barsunder High Triaxial Stress and Large Strain Cyclic Loading[J]. Fatigue andFracture of Engineering Materials and Structures，1992，(15)：1009-1024.
[13] Kuroda M. Extremely Low Cycle Fatigue Life Prediction Based on a NewCumulative Fatigue Damage Model[J]. International Journal of Fatigue，2001，(24)：699-703.
[14] Kunc R， Prebil I. Low Cycle Fatigue Properties of Steel42CrMo4[J].Materials Science Engineering A，2003，345：278-285.
[15] Farfan S，Gonzalez C R，Hernandez T C， et al. High Cycle Fatigue, LowCycle Fatigue and Failure Modes of a Carburized Steel. International Journalof Fatigue，2004，26：673-678.
[16] Miner M A. Cumulative Damage in Fatigue[J]. Journal of Applied Mechanics，1945，(67)：59-64.
[17] Marco S M，Starkey W L. A Concept of Fatigue Damage[J]. Transactions ofthe ASME，1954，(76)：627-632.
[18] Manson S S，Halford G R. Re-examination of Cumulative Fatigue DamageAnalysis-An Engineering Perspective[J]. Engineering Fracture Mechanics，1986，(25)：539-557.
[19] Bui Q T. Cumulative Damage with Interaction Effect Due to Fatigue underTorsion Loading[J]. Experimental Mechanics，1982，(22)：180-187.
[20] Miller K J. Short Crack Problem[J]. Fatigue of Engineering Materials andStructures，1982，5(3)：223-232.
[21] Ma B T，Laird C. Overview of Fatigue Behavior in Copper Single Crystals-II：Population, Size Distribution and Growth Kinetics of Stage I cracks for Testsat Constant Strain Amplitude[J]. Acta Metallurgica et Materialia，1989，(37)：337-348.
[22] Vasek A，Polak J. Low Cycle Fatigue Damage Accumulation in Armci-iron[J].Fatigue of Engineering Materials and Structures，1991，(14)：193-204.
[23] Kujawski D，Ellyin F. A Cumulative Damage Theory of Fatigue CrackInitiation and Propagation[J]. International Journal of Fatigue，1984，(6)：83-88.
[24] Leis B N. A Nonlinear History-Dependent Damage Model for Low CycleFatigue in Low Cycle Fatigue[J]. ASTM STP942，1988：143-159.
[25] Niu X D. Memory Behavior of Stress Amplitude Responses and FatigueDamage Model of a Hot-Rolled Low Carbon Steel in Mechanical Behavior ofMaterials-V[C]. Proceedings of the Fifth International Conference，Oxford，1987：685-690.
[26]许金泉，郭凤明.疲劳损伤演化的机理及损伤演化律[J].机械工程学报：2010，(46)：40-46.
[27] Huang Z Y，Wagner D，Bathias C，Chaboche J L. Cumulative Fatigue Damagein Low Cycle Fatigue and Gigacycle Fatigue for Low Carbon–ManganeseSteel[J]. International Journal of Fatigue，2011，(33)：115-12.
[28] Lemaitre J， Plumtree A. Application of Damage Concepts to PredictCreep-Fatigue Failures[J]. ASME Journal of Engineering Materials andTechnology，1979，(101)：284-292.
[29] Socie D F，Fash J W，Leckie F A. A Continuum Damage Model for FatigueAnalysis of Cast Iron in Advances in Life Prediction Methods[J]. TheAmerican Society of Mechanical Engineers，1983：59-64.
[30] Findley W N. Modified Theory of Fatigue Failure Under Combined Stress[J].Proc Soc Experiment Stress Anal，1956，(14)：35-46.
[31] Brown M W，Miller K J. High Temperature Biaxial Fatigue of Two Steels[J].Fatigue and Fracture of Engineering Materials and Structures，1979，(1)：217-229.
[32] Fatemi A，Socie D F. A Critical Plane Approach to Multiaxial Fatigue Damageincluding Out-of-Phase Loading[J]. Fatigue and Fracture of EngineeringMaterials and Structures，1988，(11)：149-165.
[33] Smith R N，Watson P P，Topper T H. A Stress–Strain Parameter for the Fatigueof Metals[J]. Journal of Materials，1970：(5)：767-778.
[34] Shamsaei N，Gladskyi M，Panasovskyi K，et al. Multiaxial Fatigue of Titaniumincluding Step Loading and Load Path Alteration and Sequence Effects[J].International Journal of Fatigue，2010，(32)：1862-187.
[35] Park J，Nelson D. Evaluation of an Energy Based Approach and a CriticalPlane Approach for Predicting Constant Amplitude Multiaxial Fatigue Life[J].International Journal of Fatigue，2000，22：23-39.
[36] Lagoda T，Macha E，Nieslony A. Fatigue Life Caculation by Means of theCycle Counting and Spectral Methods under Multiaxial Random Loading[J].Fatigue and Fracture of Engineering Materials and Structures，2005，(28)：409-420.
[37] Chen X，Jin D，Kim K S. A Weight Function Critical Plane Approach for LowCycle Fatigue under Variable Amplitude Multiaxial Loading[J]. Fatigue andFracture of Engineering Materials and Structures，2006，(29)：331-339.
[38] Susmel L. A Simple and Efficient Numerical Algorithm to Determin theOrientation of the Critical Plane in Multiaxial Fatigue Problems. InternationalJournal of Fatigue，2010，32：1875-1883.
[39] Susmel L, Tovo R, Benasciutti D. A Novel Engineering Method Based on theCritical Plane Concept to Estimate the Lifetime of Weldments Subjectd toVariable Amplitude Multiaxial Fatigue Loading. Fatigue and Fracture ofEngineering Materials and Structures，2009，(32)：441-459.
[40] Harbour R J，Fatemi A，Mars W V. Fatigue Life Analysis and Predictions inNR and SBR under Variable Amplitude and Multiaxial Loading Conditions[J].International Journal of Fatigue，2008，(30)：1231-1247.
[41] Fatemi A， Shamsaei N. Multiaxial Fatigue: an Overview and SomeApproximation Models for Life Estimation[J]. International Journal ofFatigue，2011.
[42] Shamsaei N，Fatemi A. Effect of hardness on multiaxial fatigue behavior andsome simple approximations for steels[J]. Fatigue and Fracture of EngineeringMaterials and Structures，2009，(32)：631-646.
[43] Bannantine J A，Socie D F. A Variable Amplitude Multiaxial Fatigue LifePrediction Model Fatigue under Biaxial and Multiaxial Loading[J].Mechanical Engineering Publications，1991：35-51.
[44] Wang C H，Brown M W. Life Prediction Techniques for Variable AmplitudeMultiaxial Fatigue-Part One： Theories[J]. ASME Journal of EngineeringMaterials Technology，1996，(118)：367-370.
[45] Hassan T，Kyriakides S. Ratcheting in Cyclic Plasticity Part I：UniaxialBehavior[J]. International Journal of Plasticity，1992，8：91-116.
[46] Hassan T，Corona E，Kyriakides S. Ratcheting in Cyclic Plasticity Part II：Multiaxial Behavior[J]. International Journal of Plasticity，1992，8：117-146.
[47] Yang X J. Low Cycle Fatigue and Cyclic Stress Ratcheting Failure Behavior ofCarbon Steel45under Uniaxial Cyclic Loading[J]. International Journal ofFatigue，2005，27：1124-1132.
[48]罗海波，张娟，康国政.1Cr18Ni9Ti不锈钢单轴棘轮-疲劳交互作用实验研究.塑性力学新进展-2011年全国塑性力学会议论文集，北京，2011，360-365.
[49] Kang G Z，Liu Y J，Li Z. Expedmental Study on Ratcheting Fatigue Interactionof SS304Stainless Steel in Uniaxial Cyclic Stressing[J]. Materials Science andEngineeringA，2006，435-436：396-404.
[50]徐尹杰，蔡力勋，刘宇杰.应力作用下316L不锈钢塑性变形行为研究[J].航空学报，2007，28（3）：567-573.
[51]刘宇杰，康国政，高庆，李钊.调质42CrMO钢的棘轮-疲劳交互作用研究[J].实验室研究与探索，2007，26（11）：185-187，218.
[52]郭严，康国政，刘宇杰，丁俊. LZ50钢真应力控制下单轴棘轮行为的实验研究[J].工程力学，2010，27（9）：216-220，239.
[53]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.
[54]陈奇.基于分形理论的汽车变速箱齿轮接触强度研究[D].合肥：合肥工业大学博士学位论文，2010，44-47.
[55]廖海平，刘启跃.齿轮塑性变形失效的安定极限分析[J].西南交通大学学报，2010，45（5）：676-679,750.
[56] Christopher G，C Robert G P，Sandeep M V. A Frequency Domain FiniteElement Approach for Three-Dimensional Gear Dynamics[J]. Journal ofVibration and Acoustics，2011，133：1-8.
[57] Marcello F，Farhad S S，Gabriele B. Dynamic Optimization of Spur Gears[J].Mechanism and Machine Theory，2011，46：544-557.
[58] Sergio B，Federico T. A Numerical Study on the Fatigue and Rolling ContactFatigue Behaviour of PVD-Coated Steel and Titanium Spur Gears[J].Engineering with Computers，2011，27：127-137.
[59] Hu Y M，Shao Y M，Chen Z G. Transient Meshing Performance of Gears withDifferent Modification Coefficients and Helical Angles Using ExplicitDynamic FEA[J]. Mechanical Systems and Signal Processing，2011，25：1786-1802.
[60]杨生华.齿轮接触有限元分析.计算力学学报，2003，20（2）：189-194.
[61]高小茜.风电齿轮箱轮齿接触有限元分析[M].大连：大连理工大学硕士学位论文，2008，24-28.
[62]曾红，张琳琳，陈燕燕.弧齿锥齿轮齿面接触应力分析[J].机械传动，2012，36（9）：80-82.
[63]李群松，朱颖，谭海林等.变摩擦条件下三维接触问题有限元分析改进[J].中国机械工程，2012，23（16）：1929-1933.
[64]张磊.变速器齿轮承载能力分析方法的研究及应用.长春：吉林大学博士学位论文，2011：30-35,109.
[65] Lenski W J. Advanced Rotorcraft Transmission Programme. NASA ContractorReport，1995：417-419.
[66] Lewicki D G， Ballarini R. Rim Thickness Effects on Gear Crack PropagationLife[J]. International Journal of Fatigue，1997，87：59-86.
[67] Glodez S， Sraml M， Kramberer J.A Computational Model for Determinationof Service Life of Gears[J]. International Journal of Fatigue，2002，24：1013-1020.
[68] Lewicki D G，Spievak L E，Handschuh R F，et al. Consideration of MovingTooth Load in Gear Crack Propagation Predictions[C].The8thInternationalPower Transmission and Gearing Conference，Maryland，2000：1-9.
[69] Podrug S，Jelaska D，Glodez S. Influence of Different Load Models on GearCrack Path Shapes and Fatigue Lives[J]. Fatigue and Fracture of EngineeringMaterials&Structures，2008，31(5)：327-339.
[70] Handschuh R F，Krantz T L，Lerch B A，et al. Investigation of Low CycleBending Fatigue of AISI9310Steel Spur Gears.10th International PowerTransmission and Gearing Conference，2007，1-4.
[71] Krantz T L. The Influence of Roughness on Gear Surface Fatigue[J].Advanced Rotorcraft Transmission Programme，2005，TR3134：1，116，170.
[72]郝瑞贤，谈嘉祯，李威，李元宗.37SiMn2MoV调质齿轮弯曲疲劳强度的试验研究[J].机械传动，2008,32（2）：2,67-68.
[73]祁倩，王永，刘世军等.42CrMo调质及表面淬火渐开线齿轮弯曲疲劳强度试验[J].机械强度，2010,34（9）：69-71.
[74] Lu X，Zheng S L. Strengthening and Damaging under Low Amplitude Loadsbelow the Fatigue Limit[J]. International Journal of Fatigue，2009，31：341-345.
[75] Lu X，Zheng S L. Strengthening of Transmission Gear under Low AmplitudeLoads[J].Materials Science Engineering A，2008，488：55-63.
[76] Lu X. Investigation of the Region of Fatigue Crack Initiation in aTransmission Gear[J]. Materials Science Engineering A，2010，527：1377-1382.
[77]韩志武，吕尤，牛士超等.仿生表面形态对齿轮弯曲疲劳性能的影响[J].吉林大学学报（工学版），2011，41（3）:402-405.
[78]辛洪兵.谐波传动技术及其研究动向[J].北京轻工业学院学报，1999，17（1）：30-36.
[79]阳培.谐波齿轮传动装置及其短筒柔轮分析研究[D].洛阳：机械科学研究总院博士学位论文，2006：83.
[80]刘文芝，张乃仁，张春林，赵永忠.谐波齿轮传动中杯形柔轮的有限元计算与分析[J].机械工程学报，2006,42（4）：52-57.
[81]高海波，李志刚，邓宗全.基于ANSYS的杯形柔轮结构参数对柔轮应力的敏感度分析[J].机械工程学报，2010,46（5）：1-7.
[82]邓聪.基于灵敏度分析方法的谐波减速器柔轮的疲劳强度研究[J].机械传动，2012，36（10）：31-34.
[83]梁锡昌，吕宏展.减速器的分类创新研究[J].机械工程学报，2011,47（7）：1-7.
[84]郦黎伟，范元勋，罗明.谐波传动柔轮扭转刚度的研究[J].机械制造与研究，2012，（3）：6-8.
[85]周惠久，黄明志.在多次重复冲击载荷下钢的断裂抗力的研究.西安交通大学学报，1962，（1）：1-20.
[86] Perez M A. Life Prediction of Different Commercial Dental Implants asInfluence by Uncertainties in Their Fatigue Material Properties and LoadingConditions[J]. Computer Methods and Programs in Biomeddicine，2012，108（3）：1277-1286.
[87] Lopez J G，Verleysen P，Degrieck J. Effect of Fatigue Damage on Static andDynamic Tensile Behaviour of Electro-Discharge Machined Ti-6Al-4V[J].Fatigue&Fracture of Engineering Materials&Structures，2012，35（12）：1120-1132.
[88] Guades E，Aravinthan T. Residual Properties of Square FRP Composite TubesSubjected to Repeated Axial Impact[J]. Composite Structures，2013，95：354-365.
[89]刘鸣放，刘胜新.金属材料力学性能手册[M].北京：机械工业出版社，2011，15-20.
[90]尹士邦.基于载荷谱的航空发动机传动齿轮疲劳寿命研究[D].沈阳：沈阳航空航天大学硕士学位论文，2011,1-5.
[91] Burzic M，Manjgo M，Kozak D，et al.The Effects of Dynamic Load onBehavior of Welded Joint A-387Gr.11Alloyed Steel. Mmetalurgija，2013，52（1）：27-31.
[92] Miner M A. Cumulative Damage in Fatigue[J]. Journal of Applied Mechanics,Transactions ASME，1945，67：159-164.
[93] Mesmacque G，Garcia S，Amrouche A，et al.Sequential Law in MultisxialFatigue，a New Damage Indicator[J]. International Journal of Fatigue，2005，27：461-467.
[94]张恒，张志华.基于极小样本的Weibull分布参数估计方法.船海工程，2010,39（5）：177-180.
[95]吕咸，姚卫星.小样本疲劳寿命分析问题研究进展.力学与实践，2008,30（5）：9-15.
[96]崔卫民，冯振宇，诸德培.高可靠性分析中分布函数统计推断及其影响.机械科学与技术，2000,19（3）：383-404.
[97]凌丹.威布尔分布类型及其在机械可靠性中的应用研究.成都：电子科技大学博士学位论文，2010，20-25.
[98]严晓东，马翔，郑荣跃等.三参数威布尔分布参数估计方法比较.宁波大学学报(理工版)，2005,18（3）：301-305.
[99]蔡季冰，宋海龄，陈永.小样本参数估计算法及其应用.北京理工大学学报，1989，9（1）：92-98.
[100]曹浪，李银军，李献锋.基于小样本Bayes理论的可靠性评估方法.测试测量技术，2010，（10）：25-27.
[101]孙建国，林腾蛟，李润方等.渐开线齿轮动力接触有限元分析及修形影响.机械传动，2008,32（2）：57-59.
[102]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.
[103]Lin T J，Ou H，Li R F. A Finite Element Method for3D Static and DynamicContact/Impact Analysis of Gear Drives.Computer Methods in AppliedMechanics and Engineering，2007,196:1716-1728.
[104]何晓华.20CrMoH齿轮弯曲疲劳强度研究[D].重庆：重庆大学硕士学位论文，2011,9-13.
[105]赵谦.某型电动舵机减速器的研究设计[D].哈尔滨：哈尔滨工业大学，2011，1-5.
[106]王迪.一种新型结构的谐波减速器研究[D].哈尔滨：哈尔滨工业大学，2009，3-5.
[107]付军锋.谐波齿轮传动中柔轮应力的有限元分析[D].西安：西北工业大学，2007，1-5.
[108]潘银良.谐波减速器弹性薄壁构件的疲劳寿命分析[D].重庆：重庆大学硕士学位论文，2011，1-5.
[109]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：哈尔滨工业大学博士学位论文，2008，24-25.
[110]万长森.滚动轴承的分析方法[M].北京：机械工业出版社，1985：31.
[111]黄浩，张鹏顺，温建民.高速圆柱滚子轴承的刚度研究[J].中国机械工程，2001，12（11）,1245-1247.
[2]龙乐豪，王小军，容易.我国一次性运载火箭的发展展望[J].中国科学E辑：技术科学，2009，39（3）：460-463.
[3]沈剑.洛马公司一次性使用的攻击飞行器[J].飞航导弹，2005，（1）：60.
[4]丛敏.一次性多用途炮射无人机[J].飞航导弹，2002，（6）：1.
[5]汪军林，解付强，刘玉浩.导弹电动舵机的研究现状及发展趋势[J].飞航导弹，2008，（3）：42-46.
[6]毛文晋.电动舵机系统的设计与试验研究[D].哈尔滨：哈尔滨工程大学硕士学位论文，2011：1-5.
[7]孙玉环.箭用电动舵机减速装置设计新方法的研究[D].哈尔滨：哈尔滨工业大学硕士学位论文，2005：1.
[8]薛红彦.一次性机械的设计方法的研究[D].哈尔滨：哈尔滨工业大学硕士学位论文，2006：5-10.
[9] Nip K H，Gardner L，Davies C M，et al. Extremely Low Cycle Fatigue Testson Structural Carbon Steel and Stainless Steel[J]. Journal of ConstructionalSteel Research，2010，(66)：96-110.
[10] Shimada K，Komotori J，Shimizu M. Fracture Mode Transition and Damage inExtremely Low Cycle Fatigue[C]. Second International Conference on LowCycle Fatigue and Elasto-Plastic Behavior of Materials，1987，680-686.
[11] Komotori J，Shimizu M. Grain Size Effect in Low Cycle Fatigue of SteelUnder Mean Strain[C]. Proceedings of the7th International Conference onFracture，1989，1213~1220.
[12] Du M L，Li G C，Zhang Y Z，et al. Fracture Behavior of Axisymmetric Barsunder High Triaxial Stress and Large Strain Cyclic Loading[J]. Fatigue andFracture of Engineering Materials and Structures，1992，(15)：1009-1024.
[13] Kuroda M. Extremely Low Cycle Fatigue Life Prediction Based on a NewCumulative Fatigue Damage Model[J]. International Journal of Fatigue，2001，(24)：699-703.
[14] Kunc R， Prebil I. Low Cycle Fatigue Properties of Steel42CrMo4[J].Materials Science Engineering A，2003，345：278-285.
[15] Farfan S，Gonzalez C R，Hernandez T C， et al. High Cycle Fatigue, LowCycle Fatigue and Failure Modes of a Carburized Steel. International Journalof Fatigue，2004，26：673-678.
[16] Miner M A. Cumulative Damage in Fatigue[J]. Journal of Applied Mechanics，1945，(67)：59-64.
[17] Marco S M，Starkey W L. A Concept of Fatigue Damage[J]. Transactions ofthe ASME，1954，(76)：627-632.
[18] Manson S S，Halford G R. Re-examination of Cumulative Fatigue DamageAnalysis-An Engineering Perspective[J]. Engineering Fracture Mechanics，1986，(25)：539-557.
[19] Bui Q T. Cumulative Damage with Interaction Effect Due to Fatigue underTorsion Loading[J]. Experimental Mechanics，1982，(22)：180-187.
[20] Miller K J. Short Crack Problem[J]. Fatigue of Engineering Materials andStructures，1982，5(3)：223-232.
[21] Ma B T，Laird C. Overview of Fatigue Behavior in Copper Single Crystals-II：Population, Size Distribution and Growth Kinetics of Stage I cracks for Testsat Constant Strain Amplitude[J]. Acta Metallurgica et Materialia，1989，(37)：337-348.
[22] Vasek A，Polak J. Low Cycle Fatigue Damage Accumulation in Armci-iron[J].Fatigue of Engineering Materials and Structures，1991，(14)：193-204.
[23] Kujawski D，Ellyin F. A Cumulative Damage Theory of Fatigue CrackInitiation and Propagation[J]. International Journal of Fatigue，1984，(6)：83-88.
[24] Leis B N. A Nonlinear History-Dependent Damage Model for Low CycleFatigue in Low Cycle Fatigue[J]. ASTM STP942，1988：143-159.
[25] Niu X D. Memory Behavior of Stress Amplitude Responses and FatigueDamage Model of a Hot-Rolled Low Carbon Steel in Mechanical Behavior ofMaterials-V[C]. Proceedings of the Fifth International Conference，Oxford，1987：685-690.
[26]许金泉，郭凤明.疲劳损伤演化的机理及损伤演化律[J].机械工程学报：2010，(46)：40-46.
[27] Huang Z Y，Wagner D，Bathias C，Chaboche J L. Cumulative Fatigue Damagein Low Cycle Fatigue and Gigacycle Fatigue for Low Carbon–ManganeseSteel[J]. International Journal of Fatigue，2011，(33)：115-12.
[28] Lemaitre J， Plumtree A. Application of Damage Concepts to PredictCreep-Fatigue Failures[J]. ASME Journal of Engineering Materials andTechnology，1979，(101)：284-292.
[29] Socie D F，Fash J W，Leckie F A. A Continuum Damage Model for FatigueAnalysis of Cast Iron in Advances in Life Prediction Methods[J]. TheAmerican Society of Mechanical Engineers，1983：59-64.
[30] Findley W N. Modified Theory of Fatigue Failure Under Combined Stress[J].Proc Soc Experiment Stress Anal，1956，(14)：35-46.
[31] Brown M W，Miller K J. High Temperature Biaxial Fatigue of Two Steels[J].Fatigue and Fracture of Engineering Materials and Structures，1979，(1)：217-229.
[32] Fatemi A，Socie D F. A Critical Plane Approach to Multiaxial Fatigue Damageincluding Out-of-Phase Loading[J]. Fatigue and Fracture of EngineeringMaterials and Structures，1988，(11)：149-165.
[33] Smith R N，Watson P P，Topper T H. A Stress–Strain Parameter for the Fatigueof Metals[J]. Journal of Materials，1970：(5)：767-778.
[34] Shamsaei N，Gladskyi M，Panasovskyi K，et al. Multiaxial Fatigue of Titaniumincluding Step Loading and Load Path Alteration and Sequence Effects[J].International Journal of Fatigue，2010，(32)：1862-187.
[35] Park J，Nelson D. Evaluation of an Energy Based Approach and a CriticalPlane Approach for Predicting Constant Amplitude Multiaxial Fatigue Life[J].International Journal of Fatigue，2000，22：23-39.
[36] Lagoda T，Macha E，Nieslony A. Fatigue Life Caculation by Means of theCycle Counting and Spectral Methods under Multiaxial Random Loading[J].Fatigue and Fracture of Engineering Materials and Structures，2005，(28)：409-420.
[37] Chen X，Jin D，Kim K S. A Weight Function Critical Plane Approach for LowCycle Fatigue under Variable Amplitude Multiaxial Loading[J]. Fatigue andFracture of Engineering Materials and Structures，2006，(29)：331-339.
[38] Susmel L. A Simple and Efficient Numerical Algorithm to Determin theOrientation of the Critical Plane in Multiaxial Fatigue Problems. InternationalJournal of Fatigue，2010，32：1875-1883.
[39] Susmel L, Tovo R, Benasciutti D. A Novel Engineering Method Based on theCritical Plane Concept to Estimate the Lifetime of Weldments Subjectd toVariable Amplitude Multiaxial Fatigue Loading. Fatigue and Fracture ofEngineering Materials and Structures，2009，(32)：441-459.
[40] Harbour R J，Fatemi A，Mars W V. Fatigue Life Analysis and Predictions inNR and SBR under Variable Amplitude and Multiaxial Loading Conditions[J].International Journal of Fatigue，2008，(30)：1231-1247.
[41] Fatemi A， Shamsaei N. Multiaxial Fatigue: an Overview and SomeApproximation Models for Life Estimation[J]. International Journal ofFatigue，2011.
[42] Shamsaei N，Fatemi A. Effect of hardness on multiaxial fatigue behavior andsome simple approximations for steels[J]. Fatigue and Fracture of EngineeringMaterials and Structures，2009，(32)：631-646.
[43] Bannantine J A，Socie D F. A Variable Amplitude Multiaxial Fatigue LifePrediction Model Fatigue under Biaxial and Multiaxial Loading[J].Mechanical Engineering Publications，1991：35-51.
[44] Wang C H，Brown M W. Life Prediction Techniques for Variable AmplitudeMultiaxial Fatigue-Part One： Theories[J]. ASME Journal of EngineeringMaterials Technology，1996，(118)：367-370.
[45] Hassan T，Kyriakides S. Ratcheting in Cyclic Plasticity Part I：UniaxialBehavior[J]. International Journal of Plasticity，1992，8：91-116.
[46] Hassan T，Corona E，Kyriakides S. Ratcheting in Cyclic Plasticity Part II：Multiaxial Behavior[J]. International Journal of Plasticity，1992，8：117-146.
[47] Yang X J. Low Cycle Fatigue and Cyclic Stress Ratcheting Failure Behavior ofCarbon Steel45under Uniaxial Cyclic Loading[J]. International Journal ofFatigue，2005，27：1124-1132.
[48]罗海波，张娟，康国政.1Cr18Ni9Ti不锈钢单轴棘轮-疲劳交互作用实验研究.塑性力学新进展-2011年全国塑性力学会议论文集，北京，2011，360-365.
[49] Kang G Z，Liu Y J，Li Z. Expedmental Study on Ratcheting Fatigue Interactionof SS304Stainless Steel in Uniaxial Cyclic Stressing[J]. Materials Science andEngineeringA，2006，435-436：396-404.
[50]徐尹杰，蔡力勋，刘宇杰.应力作用下316L不锈钢塑性变形行为研究[J].航空学报，2007，28（3）：567-573.
[51]刘宇杰，康国政，高庆，李钊.调质42CrMO钢的棘轮-疲劳交互作用研究[J].实验室研究与探索，2007，26（11）：185-187，218.
[52]郭严，康国政，刘宇杰，丁俊. LZ50钢真应力控制下单轴棘轮行为的实验研究[J].工程力学，2010，27（9）：216-220，239.
[53]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.
[54]陈奇.基于分形理论的汽车变速箱齿轮接触强度研究[D].合肥：合肥工业大学博士学位论文，2010，44-47.
[55]廖海平，刘启跃.齿轮塑性变形失效的安定极限分析[J].西南交通大学学报，2010，45（5）：676-679,750.
[56] Christopher G，C Robert G P，Sandeep M V. A Frequency Domain FiniteElement Approach for Three-Dimensional Gear Dynamics[J]. Journal ofVibration and Acoustics，2011，133：1-8.
[57] Marcello F，Farhad S S，Gabriele B. Dynamic Optimization of Spur Gears[J].Mechanism and Machine Theory，2011，46：544-557.
[58] Sergio B，Federico T. A Numerical Study on the Fatigue and Rolling ContactFatigue Behaviour of PVD-Coated Steel and Titanium Spur Gears[J].Engineering with Computers，2011，27：127-137.
[59] Hu Y M，Shao Y M，Chen Z G. Transient Meshing Performance of Gears withDifferent Modification Coefficients and Helical Angles Using ExplicitDynamic FEA[J]. Mechanical Systems and Signal Processing，2011，25：1786-1802.
[60]杨生华.齿轮接触有限元分析.计算力学学报，2003，20（2）：189-194.
[61]高小茜.风电齿轮箱轮齿接触有限元分析[M].大连：大连理工大学硕士学位论文，2008，24-28.
[62]曾红，张琳琳，陈燕燕.弧齿锥齿轮齿面接触应力分析[J].机械传动，2012，36（9）：80-82.
[63]李群松，朱颖，谭海林等.变摩擦条件下三维接触问题有限元分析改进[J].中国机械工程，2012，23（16）：1929-1933.
[64]张磊.变速器齿轮承载能力分析方法的研究及应用.长春：吉林大学博士学位论文，2011：30-35,109.
[65] Lenski W J. Advanced Rotorcraft Transmission Programme. NASA ContractorReport，1995：417-419.
[66] Lewicki D G， Ballarini R. Rim Thickness Effects on Gear Crack PropagationLife[J]. International Journal of Fatigue，1997，87：59-86.
[67] Glodez S， Sraml M， Kramberer J.A Computational Model for Determinationof Service Life of Gears[J]. International Journal of Fatigue，2002，24：1013-1020.
[68] Lewicki D G，Spievak L E，Handschuh R F，et al. Consideration of MovingTooth Load in Gear Crack Propagation Predictions[C].The8thInternationalPower Transmission and Gearing Conference，Maryland，2000：1-9.
[69] Podrug S，Jelaska D，Glodez S. Influence of Different Load Models on GearCrack Path Shapes and Fatigue Lives[J]. Fatigue and Fracture of EngineeringMaterials&Structures，2008，31(5)：327-339.
[70] Handschuh R F，Krantz T L，Lerch B A，et al. Investigation of Low CycleBending Fatigue of AISI9310Steel Spur Gears.10th International PowerTransmission and Gearing Conference，2007，1-4.
[71] Krantz T L. The Influence of Roughness on Gear Surface Fatigue[J].Advanced Rotorcraft Transmission Programme，2005，TR3134：1，116，170.
[72]郝瑞贤，谈嘉祯，李威，李元宗.37SiMn2MoV调质齿轮弯曲疲劳强度的试验研究[J].机械传动，2008,32（2）：2,67-68.
[73]祁倩，王永，刘世军等.42CrMo调质及表面淬火渐开线齿轮弯曲疲劳强度试验[J].机械强度，2010,34（9）：69-71.
[74] Lu X，Zheng S L. Strengthening and Damaging under Low Amplitude Loadsbelow the Fatigue Limit[J]. International Journal of Fatigue，2009，31：341-345.
[75] Lu X，Zheng S L. Strengthening of Transmission Gear under Low AmplitudeLoads[J].Materials Science Engineering A，2008，488：55-63.
[76] Lu X. Investigation of the Region of Fatigue Crack Initiation in aTransmission Gear[J]. Materials Science Engineering A，2010，527：1377-1382.
[77]韩志武，吕尤，牛士超等.仿生表面形态对齿轮弯曲疲劳性能的影响[J].吉林大学学报（工学版），2011，41（3）:402-405.
[78]辛洪兵.谐波传动技术及其研究动向[J].北京轻工业学院学报，1999，17（1）：30-36.
[79]阳培.谐波齿轮传动装置及其短筒柔轮分析研究[D].洛阳：机械科学研究总院博士学位论文，2006：83.
[80]刘文芝，张乃仁，张春林，赵永忠.谐波齿轮传动中杯形柔轮的有限元计算与分析[J].机械工程学报，2006,42（4）：52-57.
[81]高海波，李志刚，邓宗全.基于ANSYS的杯形柔轮结构参数对柔轮应力的敏感度分析[J].机械工程学报，2010,46（5）：1-7.
[82]邓聪.基于灵敏度分析方法的谐波减速器柔轮的疲劳强度研究[J].机械传动，2012，36（10）：31-34.
[83]梁锡昌，吕宏展.减速器的分类创新研究[J].机械工程学报，2011,47（7）：1-7.
[84]郦黎伟，范元勋，罗明.谐波传动柔轮扭转刚度的研究[J].机械制造与研究，2012，（3）：6-8.
[85]周惠久，黄明志.在多次重复冲击载荷下钢的断裂抗力的研究.西安交通大学学报，1962，（1）：1-20.
[86] Perez M A. Life Prediction of Different Commercial Dental Implants asInfluence by Uncertainties in Their Fatigue Material Properties and LoadingConditions[J]. Computer Methods and Programs in Biomeddicine，2012，108（3）：1277-1286.
[87] Lopez J G，Verleysen P，Degrieck J. Effect of Fatigue Damage on Static andDynamic Tensile Behaviour of Electro-Discharge Machined Ti-6Al-4V[J].Fatigue&Fracture of Engineering Materials&Structures，2012，35（12）：1120-1132.
[88] Guades E，Aravinthan T. Residual Properties of Square FRP Composite TubesSubjected to Repeated Axial Impact[J]. Composite Structures，2013，95：354-365.
[89]刘鸣放，刘胜新.金属材料力学性能手册[M].北京：机械工业出版社，2011，15-20.
[90]尹士邦.基于载荷谱的航空发动机传动齿轮疲劳寿命研究[D].沈阳：沈阳航空航天大学硕士学位论文，2011,1-5.
[91] Burzic M，Manjgo M，Kozak D，et al.The Effects of Dynamic Load onBehavior of Welded Joint A-387Gr.11Alloyed Steel. Mmetalurgija，2013，52（1）：27-31.
[92] Miner M A. Cumulative Damage in Fatigue[J]. Journal of Applied Mechanics,Transactions ASME，1945，67：159-164.
[93] Mesmacque G，Garcia S，Amrouche A，et al.Sequential Law in MultisxialFatigue，a New Damage Indicator[J]. International Journal of Fatigue，2005，27：461-467.
[94]张恒，张志华.基于极小样本的Weibull分布参数估计方法.船海工程，2010,39（5）：177-180.
[95]吕咸，姚卫星.小样本疲劳寿命分析问题研究进展.力学与实践，2008,30（5）：9-15.
[96]崔卫民，冯振宇，诸德培.高可靠性分析中分布函数统计推断及其影响.机械科学与技术，2000,19（3）：383-404.
[97]凌丹.威布尔分布类型及其在机械可靠性中的应用研究.成都：电子科技大学博士学位论文，2010，20-25.
[98]严晓东，马翔，郑荣跃等.三参数威布尔分布参数估计方法比较.宁波大学学报(理工版)，2005,18（3）：301-305.
[99]蔡季冰，宋海龄，陈永.小样本参数估计算法及其应用.北京理工大学学报，1989，9（1）：92-98.
[100]曹浪，李银军，李献锋.基于小样本Bayes理论的可靠性评估方法.测试测量技术，2010，（10）：25-27.
[101]孙建国，林腾蛟，李润方等.渐开线齿轮动力接触有限元分析及修形影响.机械传动，2008,32（2）：57-59.
[102]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.
[103]Lin T J，Ou H，Li R F. A Finite Element Method for3D Static and DynamicContact/Impact Analysis of Gear Drives.Computer Methods in AppliedMechanics and Engineering，2007,196:1716-1728.
[104]何晓华.20CrMoH齿轮弯曲疲劳强度研究[D].重庆：重庆大学硕士学位论文，2011,9-13.
[105]赵谦.某型电动舵机减速器的研究设计[D].哈尔滨：哈尔滨工业大学，2011，1-5.
[106]王迪.一种新型结构的谐波减速器研究[D].哈尔滨：哈尔滨工业大学，2009，3-5.
[107]付军锋.谐波齿轮传动中柔轮应力的有限元分析[D].西安：西北工业大学，2007，1-5.
[108]潘银良.谐波减速器弹性薄壁构件的疲劳寿命分析[D].重庆：重庆大学硕士学位论文，2011，1-5.
[109]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：哈尔滨工业大学博士学位论文，2008，24-25.
[110]万长森.滚动轴承的分析方法[M].北京：机械工业出版社，1985：31.
[111]黄浩，张鹏顺，温建民.高速圆柱滚子轴承的刚度研究[J].中国机械工程，2001，12（11）,1245-1247.