失谐叶片轮盘的减缩建模及动力响应预测方法
收稿日期: 2014-10-20
修回日期: 2014-11-13
网络出版日期: 2015-03-25
基金资助
国家自然科学基金 (11372128, 51175244); 中央高校基本科研业务费专项资金 (NP2013302, NN2012067); 南京航空航天大学研究生创新基地(实验室)开放基金 (kfjj20130204); 先进航空发动机协同创新中心项目
Reduced-order modelling and dynamic response prediction method for mistuned bladed disks
Received date: 2014-10-20
Revised date: 2014-11-13
Online published: 2015-03-25
Supported by
National Natural Science Foundation of China (11372128, 51175244); The Fundamental Research Funds for the Central Universities (NP2013302, NN2012067); Fundation of Graduate Innovation Center in NUAA (kfjj20130204); Project of Collaborative Innovation Center for Advance Aero-engine
为解决高保真失谐叶盘计算量大的问题,提出了一种新的减缩建模及动力响应预测方法。该方法对叶盘单扇区有限元模型进行圆周对称分析,获取谐调叶盘在局部坐标系下的基本模态特性。同时,运用主节点的概念,仅对少量节点进行模态分析,在大大降低矩阵维度的同时获取准确的失谐模态特性。在动力响应预测分析时,利用失谐固有频率点处响应的基本特性,仅选取危险频段内、危险叶片上的危险节点进行响应分析计算,既极大地提高了运算效率,又能够准确地获取叶盘最大受迫响应幅值。实例分析结果表明:相较于传统的有限元方法,该方法中模态分析的求逆过程矩阵维度从150万下降到384,计算所得的前50阶固有频率的精度保持在0.005%以内,最大响应计算过程运算量下降超过99%时,仅存在-0.35%的误差。
臧朝平 , 段勇亮 , E. P. PETROV . 失谐叶片轮盘的减缩建模及动力响应预测方法[J]. 航空学报, 2015 , 36(10) : 3305 -3315 . DOI: 10.7527/S1000-6893.2015.0025
In order to save the great computation effort for high fidelity mistuned bladed disk, a new reduced-order modelling and dynamic response prediction method for mistuned bladed disks is developed in this paper. Taking full advantage of cyclic symmetry of tuned bladed disk, a sector model is used to provide the primary information about dynamic properties in the local coordinate systems. Just doing model analysis on a small number of nodes utilizing the concept of "active nodes", the dimensions of operation matrices are reduced enormously but the model properties of mistuned structure are preserved with very high accuracy. In the process of dynamic response prediction, the response properties on the natural frequencies can be used for the choice of narrow frequency ranges, dangerous blades and nodes which need to calculate response. The main advantages are its efficiency and accuracy, which allow the high precision maximum forced responses. The results show that compared with traditional finite element method, the inverse matrices in this method are reduced from 1.5 million to 384, but the errors of the first 50 natural frequencies are limited in 0.005%. In addition, the computational complexity of maximum response calculation is lowered by more than 99%, which just produces -0.35% deviation.
Key words： mistuning; bladed disk; reduced-order modelling; dynamic; response prediction; active nodes
[1] Zang C P, Lan H Q. Advances in research vibration problem of mistuned bladed blisk assemblies[J]. Advances in Aeronautical Science and Engineering, 2011, 2(2): 133-142 (in Chinese). 臧朝平, 兰海强. 失谐叶盘结构振动问题研究新进展[J]. 航空工程进展, 2011, 2(2): 133-142.
[2] Wang J J, Li Q H, Zhu Z G. Vibratory localization of mistuned bladed disk assemblies: A review[J]. Advances in Mechanics, 2000, 30(4): 517-528 (in Chinese). 王建军, 李其汉, 朱梓根. 失谐叶片-轮盘结构系统振动局部化问题的研究进展[J]. 力学进展, 2000, 30(4): 517-528.
[3] Wang J J, Li Q H. Methods and applications of reduction modeling for mistuned bladed disk in aero-engine[M]. Beijing: National Defense Industry Press, 2009: 1-3 (in Chinese). 王建军, 李其汉. 航空发动机失谐叶盘振动减缩模型与应用[M]. 北京: 国防工业出版社, 2009: 1-3.
[4] Castanier M P, Pierre C. Modeling and analysis of mistuned bladed disk vibration: Status and emerging directions[J]. Journal of Propulsion and Power, 2006, 22(2): 384-396.
[5] Whitehead D S. Effect of mistuning on the vibration of turbo machine blades induced by wakes[J]. Journal of Mechanical Engineering Science, 1966, 8(1): 15-21.
[6] Wang J J, Yao J Y, Li Q H. Probability characteristics of vibratory mode of bladed disk assemblies with random stiffness mistuning[J]. Journal of Aerospace Power, 2008, 23(2): 256-262 (in Chinese). 王建军, 姚建尧, 李其汉. 刚度随机失谐叶盘结构概率模态特性分析[J]. 航空动力学报, 2008, 23(2): 256-262.
[7] Pierre C. Mode localization and eigenvalue loci veering phenomena in disordered structures[J]. Journal of Sound and Vibration, 1988, 126(3): 485-502.
[8] Ewins D J. Vibration characteristics of bladed disc assemblies[J]. Journal of Mechanical Engineering Science, 1973, 15(3): 165-186.
[9] Kuang J H, Huang B W. Mode localization of a cracked bladed disk[J]. ASME Journal of Engineering for Gas Turbines and Power, 1999, 121(2): 335-341.
[10] Schmidt H I. Mistuned bladed disks, dynamical behavior and computation[C]//Proceedings IFTOMM International Conference on Rotor Dynamic Problems in Power Plants. Zakopane: IFTOMM, 1982: 215-226.
[11] Irretier H. Spectral analysis of mistuned bladed disk assemblies by component mode synthesis[C]//Vibrations of Bladed Disk Assemblies, Proceeding ASME 9th Biennial Conference on Mechanical Vibration and Noise. New York: ASME, 1983: 115-125.
[12] Kruse M J, Pierre C. Dynamic response of an industrial turbo machinery rotor[C]//Proceedings of the 32nd AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit. Reston: AIAA, 1996.
[13] Castanier M P, Ottarsson G, Pierre C. A reduced order modeling technique for mistuned bladed disks[J]. Journal of Vibration and Acoustics, 1997, 119(3): 439-447.
[14] Lim S, Bladh R, Castanier M P. Compact generalized component mode mistuning representation for modeling bladed disk vibration[J]. AIAA Journal, 2007, 45(9): 2285-2298.
[15] Wang P Y, Li L. Reduced order computational method for analysis of mistuning bladed disk dynamics characteristic[J]. Journal of Aerospace Power, 2014, 29(6): 1395-1402 (in Chinese). 王培屹, 李琳. 用于失谐叶盘动力学特性分析的减缩计算方法[J]. 航空动力学报, 2014, 29(6): 1395-1402.
[16] Yang M T, Griffin J H. A reduced-order model of mistuning using a subset of nominal system modes[J]. Journal of Engineering for Gas Turbines and Power, 2001, 123(4): 893-900.
[17] Feiner D M, Griffin J H. A fundamental model of mistuning for a single family of modes[J]. Journal of Turbomachinery, 2002, 124(4): 597-605.
[18] Martel C, Corral R. Asymptotic description of maximum mistuning amplification of bladed disk forced response[J]. Journal of Engineering for Gas Turbines and Power, 2009, 131(2): 601-610.
[19] Petrov E P, Sanliturk K Y, Ewins D J. A new method for dynamic analysis of mistuned bladed disks based on the exact relationship between tuned and mistuned system[J]. Journal of Engineering for Gas Turbines and Power, 2002, 124(3): 586-597.
[20] Lan H Q, Zang C P. Effects of blade stagger angle on forced reponse of bladed disk assmeblies[J]. Journal of Aerospace Power, 2012, 27(11): 2547-2552 (in Chinese). 兰海强, 臧朝平. 叶片安装角对叶盘结构受迫响应特性的影响[J]. 航空动力学报, 2012, 27(11): 2547-2552.
/
| 〈 |
|
〉 |
CJA