叶轮的超速预加载与安定性分析
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摘要
叶轮是离心压缩机中最关键的旋转部件,自身结构、工作条件均十分复杂,其工作状态直接影响到整个机组的安全。随着压缩机各种设计参数的不断提高,叶轮的运转条件和自身的力学特性也变得更为复杂。对旋转叶轮进行深入的力学分析,为叶轮设计提供依据,确保叶轮运行的安全性,对于研发具有我国自主知识产权的重大工业装备具有重要的理论意义和工程实用价值。
本文对旋转叶轮的力学特性进行了深入的研究,包括如下两个方面:
(1)综合考虑计算精度、规模和效率,采用自适应有限元方法,对离心压缩机叶轮原始模型与修正模型进行了精细的弹塑性分析。在此基础上,数值模拟了超速预加载工艺过程,分析了超速预加载工艺过程中叶轮的von Mises应力和等效塑性应变的演化历程,通过与无超速预加载历史叶轮在正常工作下的应力水平做对比,揭示了超速预加载工艺的力学机理。分析了叶轮关键部位应力对有限元网格的敏感性问题,介绍了如何得到对网格不敏感的结构热点应力及相应的强度判别准则,进而正确使用有限元计算结果估计叶轮疲劳寿命。
(2)提出了将叶轮加载至发生塑性变形再卸载形成的残余应力作为自平衡应力场的方法。根据极限分析与安定分析的两个下限定理,建立了求解极限荷载和安定荷载的数学规划,并进行求解。通过对简单结构进行安定分析验证了方法的正确性。最后,对复杂的叶轮结构进行了安定性分析,得到了叶轮工作时的安定条件。利用数学规划列式,我们还进一步证明了,如果对于结构的所有点,弹性包络都是在荷载乘子取最大(最小)值时达到,则结构的极限荷载和安定荷载相等。
Rotating bladed-disk are the core rotating component of the centrifugal compressors.Its structure and work condition are both complicated and its work status directly affects the safety of the whole compressor unit.With the advance of the design parameters for compressor,the work condition and static character of the rotating bladed-disk become more critical.A detailed and reliable strength analysis provides designers a solid foundation, ensures the safety of compressor operation and is of great significance of theory and engineering value for design and production of important industrial equipment with self-owned intellectual property right.
The present paper studies several important mechanical performances of the rotating bladed-disk as follows:
(1) Making a comprehensive consideration of the computational accuracy,model size and efficiency,we apply the adaptive finite element method to carry out refined static elastic-plastic strength analysis for the rotating bladed-disk.The over-speed preloading techniques process is simulated;the evolution of von Mises stress and equivalent plastic strain with time is studied.The contrast of stress levels between the over-speed preloading disk and the no over-speed preloading disk in normal working condition reveals the mechanism of the over-speed preloading techniques.The concept of structural hot spot stress is introduced which is not sensitive to the mesh-size,and the method how to get the structural hot spot stress is discussed.With the comprehension of these problems,we can use the result of the finite element calculation to predict its fatigue life.
(2) The residual stress obtained by loading the rotating bladed-disk into plastic deformation and unloading is proposed as the self-equilibrium stress basis.Based on the lower-bound theorem of limit analysis and lower-bound theorem of shakedown analysis,we developed the mathematical formulation of limit load and shakedown load,and solved with mathematical programming.The shakedown analyses of two simple structures are studied to verify the correctness of our method.The shakedown analysis of rotating bladed-disk is carried out.On the basis of mathematical programming formulation,we further prove that safety load factor and shakedown load factor is equal if the elastic envelop for every point in the structure is simultaneously attained at the maximum(or minimum) load factors.
本文对旋转叶轮的力学特性进行了深入的研究,包括如下两个方面:
(1)综合考虑计算精度、规模和效率,采用自适应有限元方法,对离心压缩机叶轮原始模型与修正模型进行了精细的弹塑性分析。在此基础上,数值模拟了超速预加载工艺过程,分析了超速预加载工艺过程中叶轮的von Mises应力和等效塑性应变的演化历程,通过与无超速预加载历史叶轮在正常工作下的应力水平做对比,揭示了超速预加载工艺的力学机理。分析了叶轮关键部位应力对有限元网格的敏感性问题,介绍了如何得到对网格不敏感的结构热点应力及相应的强度判别准则,进而正确使用有限元计算结果估计叶轮疲劳寿命。
(2)提出了将叶轮加载至发生塑性变形再卸载形成的残余应力作为自平衡应力场的方法。根据极限分析与安定分析的两个下限定理,建立了求解极限荷载和安定荷载的数学规划,并进行求解。通过对简单结构进行安定分析验证了方法的正确性。最后,对复杂的叶轮结构进行了安定性分析,得到了叶轮工作时的安定条件。利用数学规划列式,我们还进一步证明了,如果对于结构的所有点,弹性包络都是在荷载乘子取最大(最小)值时达到,则结构的极限荷载和安定荷载相等。
Rotating bladed-disk are the core rotating component of the centrifugal compressors.Its structure and work condition are both complicated and its work status directly affects the safety of the whole compressor unit.With the advance of the design parameters for compressor,the work condition and static character of the rotating bladed-disk become more critical.A detailed and reliable strength analysis provides designers a solid foundation, ensures the safety of compressor operation and is of great significance of theory and engineering value for design and production of important industrial equipment with self-owned intellectual property right.
The present paper studies several important mechanical performances of the rotating bladed-disk as follows:
(1) Making a comprehensive consideration of the computational accuracy,model size and efficiency,we apply the adaptive finite element method to carry out refined static elastic-plastic strength analysis for the rotating bladed-disk.The over-speed preloading techniques process is simulated;the evolution of von Mises stress and equivalent plastic strain with time is studied.The contrast of stress levels between the over-speed preloading disk and the no over-speed preloading disk in normal working condition reveals the mechanism of the over-speed preloading techniques.The concept of structural hot spot stress is introduced which is not sensitive to the mesh-size,and the method how to get the structural hot spot stress is discussed.With the comprehension of these problems,we can use the result of the finite element calculation to predict its fatigue life.
(2) The residual stress obtained by loading the rotating bladed-disk into plastic deformation and unloading is proposed as the self-equilibrium stress basis.Based on the lower-bound theorem of limit analysis and lower-bound theorem of shakedown analysis,we developed the mathematical formulation of limit load and shakedown load,and solved with mathematical programming.The shakedown analyses of two simple structures are studied to verify the correctness of our method.The shakedown analysis of rotating bladed-disk is carried out.On the basis of mathematical programming formulation,we further prove that safety load factor and shakedown load factor is equal if the elastic envelop for every point in the structure is simultaneously attained at the maximum(or minimum) load factors.
引文
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[39]Hany F Abdalla,Mohammad M Megahed,Maher Y.A Younan.A simplified technique for shakedown limit load determination[J].Nuclear Engineering and Design,2007,237:1231-1240.
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[2]大连理工大学工业装备结构分析国家重点实验室.研究报告:压缩机叶轮可靠性研究报告[R],2007.
[3]孙阳,邵国建.结构安定性分析方法综述与展望[J].山西建筑,2005,31(21):1-3.
[4]董兴平,邵国建.结构安定性问题研究综述[J].安徽建筑工业学院学报(自然科学版),2004,12(5):86-89.
[5]廖爱华.增压器的非线性力学分析[D].大连:大连理工大学,2007.
[6]朱宝山,侯炳麟,张蓉蓉.超速叶轮的弹塑性分析[J].北方交通大学学报,1998,22(1):51-55.
[7]侯炳麟,朱宝山.超速叶轮残余变形分析[J].内燃机学报,2000,18(1):84-87.
[8]王德润,钱正芳.超应力技术用于碟式分离机转鼓及其机理的研究[J].流体工程,1986,4:25-30.
[9]吴荣仁.增压器叶轮超速自增强技术[J].化工机械,2000,27(3):149-151.
[10]应用力学系.预应力叶轮弹塑性应力分析[J].西安交通大学学报,1997,11(2):49-58.
[11]盛德恩.高速旋转零件的预应力处理[J].机械制造,1994,32(7):9-11.
[12]唐觉明.基于SolidWorks技术的鼓风机叶轮设计的研究[J].东华大学学报(自然科学版),2006,32(3):75-79.
[13]冯汝坤.结构塑性安定性理论的若干进展及应用[J].河北工业科技,2005,22(6):365-369.
[14]冯西桥,刘信声.影响弹塑性结构安定性的各种因素[J].力学进展,1993,23(2):214-222.
[15]Feng Xiqiao,Liu Xinsheng.On shakedown of three-dimensional elastoplastic strain-hardening structures[J].International Journal of Plasticity,1996,12:1241-1256.
[16]冯西桥,刘信声.不同应变强化模型下结构安定性的研究[J].力学学报,1994,26(6):719-727.
[17]原园,徐颖强,吕国志.应变强化模型的安定准则研究[J].固体力学学报,2007,28(3):229-234.
[18]FENG X Q,YU S W.Damage and shakedown analysis of structures with strain-hardening [J].Int J Plasticity,1995,11(2):247-259.
[19]王勖成,绍敏.有限单元法基本原理和数值方法(第2版)[M].北京:清华大学出版社,2003.
[20]罗伯特.D.库克,戴维.S.马尔库斯,迈克尔.E.普利沙,等.有限元分析的概念与应用(第4版)[M].西安:西安交通大学出版社,2007.
[21]ANSYS基础与应用教程[M].北京:科学出版社,2006.
[22]黄祖瑗.弹塑性有限元法在机械工程中的应用[J].计算结构力学及其应用,1986,3(3):77-82.
[23]吴昌华,吴泓,陆玉珍.增压器压气机叶轮的三维弹塑性精细分析[J].大连铁道学院学报,2004,25(4):21-25.
[24]王辉明,马希龄,赵文.自适应有限元方法及其在ANSYS软件中的应用[J].新疆大学学报(自然科学版),2003,20(1):84-87.
[25]黄晓东,杜群贵,叶邦彦.三维实体有限元自适应网格规划生成[J].计算机辅助设计与图形学学报,2005,17(7):1446-1451.
[26]史述昭.弹性力学及有限元[M].北京:水利电力出版社,1990.
[27]Recommendations for Fatigue Design of Welded Joints and Components.International Institute of Welding,doc[S].XIII-1965-03/XV-1127-03.Paris,France,2003.
[28]H T Kang,P Dong,J K Hong.Fatigue analysis of spot welds using a mesh-insensitive structural stress approach[J].International Journal of Fatigue,2007,29:1523-1530.
[29]P Dong.A structural stress definition and numerical implementation for fatigue analysis of welded joints[J].International Journal of Fatigue,2001,23:865-876.
[30]钱令希,王志必.结构极限分析和安定分析—温度参数法[J].计算结构力学及其应用,1989,6(1):113-121.
[31]王春玲.塑性力学[M].北京:中国建材工业出版社,2005.
[32]张明焕,杨海元.结构安定分析方法研究[J].应用力学学报,1994,11(4):83-90.
[33]王仁,黄文彬,黄筑平.塑性力学引论[M].北京:北京大学出版社,1982.
[34]陈钢,刘应华.结构塑性极限与安定分析理论及工程方法[M].北京:科学出版社,2006.
[35]王仁,熊祝华,黄文彬.塑性力学基础[M].北京:科学出版社,1982.
[36]钱令希,王志必.板、壳极限分析和安定分析—温度参数法[J].力学学报,1989,21:118-124.
[37]陆明万,张远高,张丕辛.理想塑性结构极限与安定分析的数值方法[J].应用力学学报,1994,11(4):19-24.
[38]王健,程耿东.多工况应力约束下连续体结构拓扑优化设计[J].机械强度,2003,25(1):55-57.
[39]Hany F Abdalla,Mohammad M Megahed,Maher Y.A Younan.A simplified technique for shakedown limit load determination[J].Nuclear Engineering and Design,2007,237:1231-1240.
[40]R S Ponter,K F Couter.Shakedown state simulation techniques based on linear elastic solutions[J].Comput.Method.Appl.Eng,1997,140:259-279.
[41]Chen H F,Ponter A R.Shakedown and limit analyses for 3-D structures using the linear matching method[J].The International journal of pressure vessels and piping,2001,78(6):443-451.
[42]徐芝纶.弹性力学[M].高等教育出版社水利电力出版社,2006.
[43]徐秉业,刘信声.应用弹塑性力学[M].北京:清华大学出版社,1995.
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