基于瞬态动力学的气缸盖多轴疲劳寿命预测及研究
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摘要
气缸盖作为柴油机的关键零件之一，在工作过程中承受着螺栓力、燃气压力和热负荷的周期性作用，其应力、应变和变形发生周期性的变化。随着强化程度的不断提高，多轴疲劳寿命问题逐渐成为研究热点。针对这一问题，本文以某V型柴油机为例，以气缸盖的一个整缸作为研究对象，在瞬态动力学问题及多轴疲劳寿命预测理论基础上，建立了气缸盖有限元模型、进行了气缸盖的瞬态动力学分析、开展了气缸盖的多轴疲劳寿命预测研究。在气缸盖的多轴疲劳寿命预测研究中对各种计算方法及影响因素进行了一定的探索，为更准确的预测气缸盖的多轴疲劳寿命提供了支撑。
运用建模软件建立气缸盖、机体、缸套、缸垫、螺栓等零件的三维几何实体模型，然后将其导入专业的网格划分软件中对各个零件进行材料、属性的设置，在保证计算结果准确度的前提下，针对各个零件的结构特点，对结构进行一定的简化，并选择合理的单元类型和单元尺寸进行网格划分。分别在气缸盖与缸垫、气缸盖与螺栓、机体与缸垫等零件之间定义5对接触关系，模拟气缸盖的工作条件，施加约束、螺栓力和燃气压力。完成气缸盖组合结构的有限元模型的建立，为瞬态动力学分析提供了有限元模型。
运用有限元分析软件，采用直接积分法中的完全积分法进行动态响应分析，得到各个节点位移和应力的时间历程，分析气缸盖上各个位置的位移和应力的时间历程，获得气缸盖不同位置的位移和应变时间历程的对比图线。为气缸盖的结构设计及改进提供理论依据，也为气缸盖的多轴疲劳寿命预测提供了数据。
将瞬态动力学分析的计算结果导入疲劳寿命计算软件中，定义材料的属性，编制LDF文件，选择临界平面法中的Brown-Miller法作为多轴疲劳寿命计算方法，预测气缸盖的多轴疲劳寿命，获得气缸盖多轴疲劳寿命分布情况及安全系数图，引入威布尔寿命可靠度计算模型，对气缸盖在给定设计期望寿命值前提下的多轴疲劳寿命值进行可靠度研究。
通过对气缸盖火力面、上部加工表面在不同粗糙度下的多轴疲劳寿命情况进行研究，发现提高气缸盖的表面加工质量是提高多轴疲劳寿命的一种有效措施，后续的分析模型中都考虑了粗糙度因素。研究气缸盖在三种多轴疲劳寿命计算模型下的疲劳寿命的区别，发现Brown-Miller法比正应变模型和剪应变模型更适合于气缸盖的多轴疲劳寿命计算。同时研究气缸盖在传统单轴计算模型下的疲劳寿命，与多轴疲劳寿命计算模型结果对比有待于进一步的试验验证。
Cylinder cover as one of the key parts of the diesel engine, work in the process ofbearing force of the bolts, the gas pressure and the heat load of the periodic function, thestress、Strain and deformation of the occurrence of periodic change. Along with thestrengthening of diesel Engine, multi-axial fatigue life problem gradually becomes theresearch hot spot Aiming at this problem, this paper takes a V diesel engine as an example,one cylinder cover of a whole cylinder as the research object, on the basis of the dynamicproblem and multi-axial fatigue life prediction theory, established the finite element model ofcylinder cover, carried out the dynamic response analysis of cylinder cover and made themulti axial fatigue life prediction. To make some explorations on various calculation methodsand influencing factor in the research of the cylinder multi-axial fatigue life prediction, thiswill provide some support for more accurate prediction of cylinder head of the multi-axialfatigue life.
Application of modeling software made the three-dimensional geometry entity model ofcylinder head, cylinder liner, cylinder pad, body, bolt and other parts, then import them intothe professional grid software and finish the material, attribute set on each part, Under thepremise of ensure the accuracy of the calculation results, make some certain simplification forvarious parts of the structure and choice reasonable unit type and unit size to grid. Defined the5 pairs of contacts between the cylinder head and cylinder gasket, cylinder head bolt, bodyand cylinder pad parts and so on, simulate the working conditions of the cylinder cover,loading the constraint, bolt force and gas pressure. Complete cylinder cover combinationstructure finite element model for transient dynamics.
Using finite element analysis software, make the transient dynamics by direct integralmethod in the integral method, get and analysis each node displacement and stress timehistory on the cylinder cover, get the displacement and strain time history comparison chartbetween different position on the cylinder cover. This will not only provide the theory basisfor the cylinder cover design and improvement, but also provide data for the multi-axialfatigue life prediction.
Let the transient dynamics results into the fatigue life calculation software. Definematerial properties, prepare the LDF file, choose the Brown-Miller method in critical planemethod for multi-axial fatigue life calculation, prediction of multi-axial fatigue life of thecylinder cover, get the multi-axial fatigue life distribution and safety coefficient map of thecylinder cover, introducing the Weibull function life reliability calculation model, make themulti-axial fatigue life reliability research in a given design life expectancy.
Through the cylinder cover fire face, upper surface in different roughness undermulti-axial fatigue life was investigated, found improved cylinder head surface machiningquality is to improve the fatigue life of a measure, The follow-up analysis model taking intoaccount the roughness factor. Study on the cylinder head in three kinds of multi-axial fatiguelife calculation model of fatigue life of distinction, found the Brown-Miller method than thenormal strain model and shear strain model is more suitable for the cylinder cover ofmulti-axial fatigue life calculation. At the same time on the cylinder head in a conventionaluni-axial calculation model of fatigue life, contrasting results need further verification test.
运用建模软件建立气缸盖、机体、缸套、缸垫、螺栓等零件的三维几何实体模型，然后将其导入专业的网格划分软件中对各个零件进行材料、属性的设置，在保证计算结果准确度的前提下，针对各个零件的结构特点，对结构进行一定的简化，并选择合理的单元类型和单元尺寸进行网格划分。分别在气缸盖与缸垫、气缸盖与螺栓、机体与缸垫等零件之间定义5对接触关系，模拟气缸盖的工作条件，施加约束、螺栓力和燃气压力。完成气缸盖组合结构的有限元模型的建立，为瞬态动力学分析提供了有限元模型。
运用有限元分析软件，采用直接积分法中的完全积分法进行动态响应分析，得到各个节点位移和应力的时间历程，分析气缸盖上各个位置的位移和应力的时间历程，获得气缸盖不同位置的位移和应变时间历程的对比图线。为气缸盖的结构设计及改进提供理论依据，也为气缸盖的多轴疲劳寿命预测提供了数据。
将瞬态动力学分析的计算结果导入疲劳寿命计算软件中，定义材料的属性，编制LDF文件，选择临界平面法中的Brown-Miller法作为多轴疲劳寿命计算方法，预测气缸盖的多轴疲劳寿命，获得气缸盖多轴疲劳寿命分布情况及安全系数图，引入威布尔寿命可靠度计算模型，对气缸盖在给定设计期望寿命值前提下的多轴疲劳寿命值进行可靠度研究。
通过对气缸盖火力面、上部加工表面在不同粗糙度下的多轴疲劳寿命情况进行研究，发现提高气缸盖的表面加工质量是提高多轴疲劳寿命的一种有效措施，后续的分析模型中都考虑了粗糙度因素。研究气缸盖在三种多轴疲劳寿命计算模型下的疲劳寿命的区别，发现Brown-Miller法比正应变模型和剪应变模型更适合于气缸盖的多轴疲劳寿命计算。同时研究气缸盖在传统单轴计算模型下的疲劳寿命，与多轴疲劳寿命计算模型结果对比有待于进一步的试验验证。
Cylinder cover as one of the key parts of the diesel engine, work in the process ofbearing force of the bolts, the gas pressure and the heat load of the periodic function, thestress、Strain and deformation of the occurrence of periodic change. Along with thestrengthening of diesel Engine, multi-axial fatigue life problem gradually becomes theresearch hot spot Aiming at this problem, this paper takes a V diesel engine as an example,one cylinder cover of a whole cylinder as the research object, on the basis of the dynamicproblem and multi-axial fatigue life prediction theory, established the finite element model ofcylinder cover, carried out the dynamic response analysis of cylinder cover and made themulti axial fatigue life prediction. To make some explorations on various calculation methodsand influencing factor in the research of the cylinder multi-axial fatigue life prediction, thiswill provide some support for more accurate prediction of cylinder head of the multi-axialfatigue life.
Application of modeling software made the three-dimensional geometry entity model ofcylinder head, cylinder liner, cylinder pad, body, bolt and other parts, then import them intothe professional grid software and finish the material, attribute set on each part, Under thepremise of ensure the accuracy of the calculation results, make some certain simplification forvarious parts of the structure and choice reasonable unit type and unit size to grid. Defined the5 pairs of contacts between the cylinder head and cylinder gasket, cylinder head bolt, bodyand cylinder pad parts and so on, simulate the working conditions of the cylinder cover,loading the constraint, bolt force and gas pressure. Complete cylinder cover combinationstructure finite element model for transient dynamics.
Using finite element analysis software, make the transient dynamics by direct integralmethod in the integral method, get and analysis each node displacement and stress timehistory on the cylinder cover, get the displacement and strain time history comparison chartbetween different position on the cylinder cover. This will not only provide the theory basisfor the cylinder cover design and improvement, but also provide data for the multi-axialfatigue life prediction.
Let the transient dynamics results into the fatigue life calculation software. Definematerial properties, prepare the LDF file, choose the Brown-Miller method in critical planemethod for multi-axial fatigue life calculation, prediction of multi-axial fatigue life of thecylinder cover, get the multi-axial fatigue life distribution and safety coefficient map of thecylinder cover, introducing the Weibull function life reliability calculation model, make themulti-axial fatigue life reliability research in a given design life expectancy.
Through the cylinder cover fire face, upper surface in different roughness undermulti-axial fatigue life was investigated, found improved cylinder head surface machiningquality is to improve the fatigue life of a measure, The follow-up analysis model taking intoaccount the roughness factor. Study on the cylinder head in three kinds of multi-axial fatiguelife calculation model of fatigue life of distinction, found the Brown-Miller method than thenormal strain model and shear strain model is more suitable for the cylinder cover ofmulti-axial fatigue life calculation. At the same time on the cylinder head in a conventionaluni-axial calculation model of fatigue life, contrasting results need further verification test.
引文
[1]陈科，王峰.结构有限元寿命设计法-名义应力法[J].中国重型装备,2010,2:1-3.
[2]钱桂安，王茂廷，王莲.用局部应力应变法进行高周疲劳寿命预测的研究[J].机械强度,2004,26:275-277.
[3]张莉，程靳，李新刚.基于临界平面法的缺口件疲劳寿命预测方法[J].宇航学报，2007,28（4）:824-826.
[4]尚德广，姚卫星，王德俊.一种统一的多轴疲劳损伤参量[J].固体力学学报. 1999,20（3）:201-210.
[5] AVL LIST. Layout FE Analyses of the Head-Block-Gasket Compound for the WD618Engine[R]，2004.
[6] F.Zieher,F.Langmayr et a1.Advanced Thermal Mechanical Fatigue LifeSimulation of Cylinder Heads．2004 ABAQUS Users’Conference.
[7] F.S.Sliva. Fatigue on engine pistons-A compendium of case studies.Engineering Failure Analysis.2006(13):480.
[8]窦慧莉,刘忠长,王鹏程等.重型柴油机四气门气缸盖的设计[J].汽车工程，2006,3:15-17.
[9]高岚.CNG发动机典型零部件强度计算与疲劳可靠性分析[D].大连:大连理工大学，2009.
[10]毛金龙.气缸盖鼻梁区结构改进分析及可靠性寿命计算[D].北京:中国农业大学，2007．
[11]夏春晶,刘玉凤等.气缸盖蠕变-疲劳寿命预测[J].失效分析与预防，2008,2(3)：59-63．
[12]杨英.重载机车柴油机活塞可靠性关键技术的研究与应用[D].大连:大连交通大学，2006．
[13]刘洁.柴油机铝合金气缸盖多场耦合强度分析[D].成都:西南交通大学，2009.
[14]陈飞.多维应力状态下的高温低周疲劳寿命预测[D].大连:大连理工大学，2002．
[15]胡定云,陈泽忠,温世杰等.某柴油机气缸盖疲劳的可靠性预测[J].车用发动机增刊,2008,6：38-44．
[16]陶建忠,佟德辉.6200型柴油机强度的有限元分析[J].农业机械学报,2007,38(11):205-210.
[17]罗成.240D型气缸盖裂纹原因分析及改进方案[J].内燃机车,2009,424(6):40-42.
[18] O.C.Zienkiewicz,K.Morgan. Finite Elements and Approximation[M]. PineridgePress,1993:324-325.
[19] K.J.Bathe. Finite Element Procedures in Engineering Analysis[M].Prentice-Hall, Englewood Cliffs,1992:143-144.
[20] Garnier Thierry, Bonneau Dominique, Grente Christian. Three-dimensionalEHD behavior of the engine block/crankshaft assembly for a four cylinderinline automotive engine[J]. ASME,1999, 4 (121) :721-730.
[21] S.W.Chyuan, C.Y.Chiou. Application and modeling of finite element methodon structural mechanics and thermal analysis[J]. The Sixth InternationalColloquium on Numerical Analysis and Computer Science with Applications,1999,6(17):31-33.
[22] SHung H.Sung,Donald.J.Nefske,Francis. Development of a Engine System Modelfor Prediting Structural Vibration and Radited Noise the Running Engine,SEA 972039.
[23] A.F.Sybert,D.A.Hamilton.Prediction of Radiated Noise from EngineComponents Using BEM and the Rayleigh Integral SAE 971954.
[24] Robert Sontall,Malcolm Trim. Noise and Vibration Technology for the PerkinsV6 HSDI Demonstration Engine[J]. SAE Paper 840259,1997,3(28):315-320.
[25] Shiang-Woei Chyuan. Finite element simulation of a twin-cam 16-valvecylinder structure[J].Finite Elements in Analysis and Design,2000,35(7):199-212.
[26]刘志恩,陈国华等.CUB汽油机缸盖热负荷分析[J].柴油机设计与制造,2003,102(1):10-13.
[27]廖日东,左正兴等.对高速大功率柴油机用气缸盖机械负荷有限元分析边界条件施加方式的探讨[J].兵工学报,2001,1(21):5-10.
[28]张儒华,左正兴.气缸盖中一些关键功能结构的承载机理研究[J].内燃机报,2004,3(22):279-287.
[29]窦慧莉,刘忠长等.重型柴油机四气门气缸盖的设计[J].汽车工程,2006,28（3）:242-245.
[30] Lijie Chen, Yinghua Liu,Pu Yang.Limit analysis of structures containingflaws based on a modified elastic compensation method[J].European Journalof Mechanics A/Solids,2008,5(27):195-209.
[31]奚志明,孙平等.柴油机机体有限元结构分析.拖拉机与农用运输车[J], 2006.33（1）:25.
[32]段敏,王丽娟.CY4102BZQ柴油机缸盖有限元分析[J].辽宁工程技术大学学报，2004,6（23）:47-48.
[33]王凯,赵雨东.小型汽油机缸盖有限元强度分析[J].内燃机,2008,6(28): 1-5.
[34]冯慧华,左正兴.高效柴油机整机结构动态特性有限元分析[J].兵工学报，2006,3(23):294-298.
[35]余熳烨.镁合金汽车发动机缸盖有限元分析[J].机械设计与制造,2010, 10:75-77.
[36]张宏远,马星国.一种发动机活塞的瞬态动力学分析[J].沈阳理工大学学报，2006,3(25):32-34.
[37]徐红梅,郝志勇.基于S变换的内燃机气缸盖振动特性研究[J].内燃机工程，2008，3(29): 68-71.
[38]范仲. CY4102BZQ型柴油机的缸盖结构强度分析与研究[D].天津:天津大学，2003.
[39]戴旭东,王义亮.多缸内燃机缸体瞬态动力分析[J].内燃机学报, 2003,21(3):194-198.
[40]张海潮.F168小汽油机机体振动分析[D].上海:上海交通大学，2008.
[41]阙沛祯.柴油机机体与油底壳组合瞬态响应有限元分析[J].装备制造技术,2010.1:13-15.
[42]张翼,苏铁熊等.150型柴油机气缸盖的有限元强度分析[J].华北工学院学报,2003,24(6):458-460.
[43]吴俊清.某发动机缸盖的动力学仿真研究[J].华北工学院学院,2005,26(1):19-21.
[44]陈少林.柴油机缸盖动态响应分析方法研究[D].太原.中北大学.2011.
[45]杜平安,甘娥忠,于亚婷.有限元法-原理、建模及应用[M].北京:国防工业出版社，2006:52-56.
[46] Wang CH,Brown MW.A path-independent parameter for fatigue underproportional and non-proportional loading. Fatigue Fract. Engng Mater.Struct. 1993,16:1285-1298.
[47] Han C,Chen X,Kim KS. Evaluation of multi-axial fatigue criteria underirregular loading.Int.J.Fatigue,2002,24:913-922.
[48]王雷,王德俊.多轴疲劳研究的新进展,第十一届全国疲劳与断裂学术会议论文集,北京,机械工业出版社,2002,78-81.
[49] Ioannis V,Papadopoulos,Piermaria Davoli. A comparative study of multiaxialhigh-cycle fatigue criteria for metals. Int.J.Fatigue，1997,19：219-235.
[50] Yongming Liu,Sankaran Mahadevan. Multi-axial high-cycle fatigue criterionand life prediction for metals.Int.J.Fatigue,2005,27:790-800.
[51] G.Rashed,R.Ghajar,G.Farrahi. Multi-axial Stress-Strain Modeling andEffect of Additional Hardening due to Nonproportional Loading. Int. J.Fatigue, 2007,21:1153-1161.
[52]朱正宇,何国求，张卫华等.多轴非比例加载高周疲劳寿命进展[J].同济大学学报（自然科学版）.2006,9(34):1221-1225.
[53]张巧丽,陈旭.多轴非比例载荷下低周疲劳寿命估算方法[J].机械强度.2004.26(1):76-79.
[54]尚德广,姚卫星.单轴非线性连续疲劳损伤累积模型的研究[J].航空学报,1998,19(6):647-656.
[55]尚德广,王德俊,姚卫星.多轴非线性连续疲劳损伤累积模型的研究[J].固体力学学报,1999,20(4):325-330.
[56] Fe-safe user manual, Fe-safe 5.0.
[57]任善之.铸造表面粗糙度概况.2007:25-27.
[58]李颖.核主泵叶轮非定常流场及疲劳寿命可靠性分析[D].上海:上海交通大学.2009.
[59]谢里阳,林文强.疲劳剩余寿命分布的当量关系及可靠性计算方法[J].东北大学学报，1995,6:99.
[2]钱桂安，王茂廷，王莲.用局部应力应变法进行高周疲劳寿命预测的研究[J].机械强度,2004,26:275-277.
[3]张莉，程靳，李新刚.基于临界平面法的缺口件疲劳寿命预测方法[J].宇航学报，2007,28（4）:824-826.
[4]尚德广，姚卫星，王德俊.一种统一的多轴疲劳损伤参量[J].固体力学学报. 1999,20（3）:201-210.
[5] AVL LIST. Layout FE Analyses of the Head-Block-Gasket Compound for the WD618Engine[R]，2004.
[6] F.Zieher,F.Langmayr et a1.Advanced Thermal Mechanical Fatigue LifeSimulation of Cylinder Heads．2004 ABAQUS Users’Conference.
[7] F.S.Sliva. Fatigue on engine pistons-A compendium of case studies.Engineering Failure Analysis.2006(13):480.
[8]窦慧莉,刘忠长,王鹏程等.重型柴油机四气门气缸盖的设计[J].汽车工程，2006,3:15-17.
[9]高岚.CNG发动机典型零部件强度计算与疲劳可靠性分析[D].大连:大连理工大学，2009.
[10]毛金龙.气缸盖鼻梁区结构改进分析及可靠性寿命计算[D].北京:中国农业大学，2007．
[11]夏春晶,刘玉凤等.气缸盖蠕变-疲劳寿命预测[J].失效分析与预防，2008,2(3)：59-63．
[12]杨英.重载机车柴油机活塞可靠性关键技术的研究与应用[D].大连:大连交通大学，2006．
[13]刘洁.柴油机铝合金气缸盖多场耦合强度分析[D].成都:西南交通大学，2009.
[14]陈飞.多维应力状态下的高温低周疲劳寿命预测[D].大连:大连理工大学，2002．
[15]胡定云,陈泽忠,温世杰等.某柴油机气缸盖疲劳的可靠性预测[J].车用发动机增刊,2008,6：38-44．
[16]陶建忠,佟德辉.6200型柴油机强度的有限元分析[J].农业机械学报,2007,38(11):205-210.
[17]罗成.240D型气缸盖裂纹原因分析及改进方案[J].内燃机车,2009,424(6):40-42.
[18] O.C.Zienkiewicz,K.Morgan. Finite Elements and Approximation[M]. PineridgePress,1993:324-325.
[19] K.J.Bathe. Finite Element Procedures in Engineering Analysis[M].Prentice-Hall, Englewood Cliffs,1992:143-144.
[20] Garnier Thierry, Bonneau Dominique, Grente Christian. Three-dimensionalEHD behavior of the engine block/crankshaft assembly for a four cylinderinline automotive engine[J]. ASME,1999, 4 (121) :721-730.
[21] S.W.Chyuan, C.Y.Chiou. Application and modeling of finite element methodon structural mechanics and thermal analysis[J]. The Sixth InternationalColloquium on Numerical Analysis and Computer Science with Applications,1999,6(17):31-33.
[22] SHung H.Sung,Donald.J.Nefske,Francis. Development of a Engine System Modelfor Prediting Structural Vibration and Radited Noise the Running Engine,SEA 972039.
[23] A.F.Sybert,D.A.Hamilton.Prediction of Radiated Noise from EngineComponents Using BEM and the Rayleigh Integral SAE 971954.
[24] Robert Sontall,Malcolm Trim. Noise and Vibration Technology for the PerkinsV6 HSDI Demonstration Engine[J]. SAE Paper 840259,1997,3(28):315-320.
[25] Shiang-Woei Chyuan. Finite element simulation of a twin-cam 16-valvecylinder structure[J].Finite Elements in Analysis and Design,2000,35(7):199-212.
[26]刘志恩,陈国华等.CUB汽油机缸盖热负荷分析[J].柴油机设计与制造,2003,102(1):10-13.
[27]廖日东,左正兴等.对高速大功率柴油机用气缸盖机械负荷有限元分析边界条件施加方式的探讨[J].兵工学报,2001,1(21):5-10.
[28]张儒华,左正兴.气缸盖中一些关键功能结构的承载机理研究[J].内燃机报,2004,3(22):279-287.
[29]窦慧莉,刘忠长等.重型柴油机四气门气缸盖的设计[J].汽车工程,2006,28（3）:242-245.
[30] Lijie Chen, Yinghua Liu,Pu Yang.Limit analysis of structures containingflaws based on a modified elastic compensation method[J].European Journalof Mechanics A/Solids,2008,5(27):195-209.
[31]奚志明,孙平等.柴油机机体有限元结构分析.拖拉机与农用运输车[J], 2006.33（1）:25.
[32]段敏,王丽娟.CY4102BZQ柴油机缸盖有限元分析[J].辽宁工程技术大学学报，2004,6（23）:47-48.
[33]王凯,赵雨东.小型汽油机缸盖有限元强度分析[J].内燃机,2008,6(28): 1-5.
[34]冯慧华,左正兴.高效柴油机整机结构动态特性有限元分析[J].兵工学报，2006,3(23):294-298.
[35]余熳烨.镁合金汽车发动机缸盖有限元分析[J].机械设计与制造,2010, 10:75-77.
[36]张宏远,马星国.一种发动机活塞的瞬态动力学分析[J].沈阳理工大学学报，2006,3(25):32-34.
[37]徐红梅,郝志勇.基于S变换的内燃机气缸盖振动特性研究[J].内燃机工程，2008，3(29): 68-71.
[38]范仲. CY4102BZQ型柴油机的缸盖结构强度分析与研究[D].天津:天津大学，2003.
[39]戴旭东,王义亮.多缸内燃机缸体瞬态动力分析[J].内燃机学报, 2003,21(3):194-198.
[40]张海潮.F168小汽油机机体振动分析[D].上海:上海交通大学，2008.
[41]阙沛祯.柴油机机体与油底壳组合瞬态响应有限元分析[J].装备制造技术,2010.1:13-15.
[42]张翼,苏铁熊等.150型柴油机气缸盖的有限元强度分析[J].华北工学院学报,2003,24(6):458-460.
[43]吴俊清.某发动机缸盖的动力学仿真研究[J].华北工学院学院,2005,26(1):19-21.
[44]陈少林.柴油机缸盖动态响应分析方法研究[D].太原.中北大学.2011.
[45]杜平安,甘娥忠,于亚婷.有限元法-原理、建模及应用[M].北京:国防工业出版社，2006:52-56.
[46] Wang CH,Brown MW.A path-independent parameter for fatigue underproportional and non-proportional loading. Fatigue Fract. Engng Mater.Struct. 1993,16:1285-1298.
[47] Han C,Chen X,Kim KS. Evaluation of multi-axial fatigue criteria underirregular loading.Int.J.Fatigue,2002,24:913-922.
[48]王雷,王德俊.多轴疲劳研究的新进展,第十一届全国疲劳与断裂学术会议论文集,北京,机械工业出版社,2002,78-81.
[49] Ioannis V,Papadopoulos,Piermaria Davoli. A comparative study of multiaxialhigh-cycle fatigue criteria for metals. Int.J.Fatigue，1997,19：219-235.
[50] Yongming Liu,Sankaran Mahadevan. Multi-axial high-cycle fatigue criterionand life prediction for metals.Int.J.Fatigue,2005,27:790-800.
[51] G.Rashed,R.Ghajar,G.Farrahi. Multi-axial Stress-Strain Modeling andEffect of Additional Hardening due to Nonproportional Loading. Int. J.Fatigue, 2007,21:1153-1161.
[52]朱正宇,何国求，张卫华等.多轴非比例加载高周疲劳寿命进展[J].同济大学学报（自然科学版）.2006,9(34):1221-1225.
[53]张巧丽,陈旭.多轴非比例载荷下低周疲劳寿命估算方法[J].机械强度.2004.26(1):76-79.
[54]尚德广,姚卫星.单轴非线性连续疲劳损伤累积模型的研究[J].航空学报,1998,19(6):647-656.
[55]尚德广,王德俊,姚卫星.多轴非线性连续疲劳损伤累积模型的研究[J].固体力学学报,1999,20(4):325-330.
[56] Fe-safe user manual, Fe-safe 5.0.
[57]任善之.铸造表面粗糙度概况.2007:25-27.
[58]李颖.核主泵叶轮非定常流场及疲劳寿命可靠性分析[D].上海:上海交通大学.2009.
[59]谢里阳,林文强.疲劳剩余寿命分布的当量关系及可靠性计算方法[J].东北大学学报，1995,6:99.