提出一种高效的失谐叶盘瞬态强迫响应分析方法，不同于传统的数值积分方法，该方法推导出瞬态强迫响应的解析表达式，能更为高效地预测失谐叶盘的瞬态强迫响应。首先，对叶盘的高保真有限元模型进行减缩建模，在精确地描述叶盘结构的动力学特性的前提下，极大的减少了模型的自由度数目。其次，模拟加速旋转的涡轮叶盘经过复杂流场时叶片表面上的气动载荷，并建立叶盘固有频率和振型随转速变化的数学函数；通过共振分析确定叶盘共振的转速区间并分析引起共振的激励阶次成分。最后，计算了不同旋转加速度和阻尼下叶盘的瞬态强迫响应，并对叶盘的失谐幅值放大因子进行研究。应用本办法对某86个叶片的涡轮叶盘进行了数值分析，结果表明，相同阻尼水平下，叶盘的瞬态强迫响应幅值随旋转加速度增加而降低，失谐幅值放大因子在瞬态条件下大于稳态条件下，最高可达30%。
An efficient novel method different from the traditional numerical integration method is proposed for transient forced response calculation of mistuned bladed disks. Firstly, under the premise of accurate description of the dynamic structure characteristics of the bladed disk, the number of degrees of freedom of the large-scale finite element model of the bladed disk is reduced using the reduced-order modeling. The blade surface aerodynamic loads are then simulated when the accelerated turbine blades pass through a complex flow field, considering the influence of rotation speed on the natural frequency and mode shapes of the mistuned bladed disk. The resonance analysis determines the rotational speed range of the bladed disk resonance and analyzes the excitation order components causing resonance. Finally, the transient forced responses and amplitude amplifications are numerically studied. The effect of the excitation force of different rotation accelerations on the transient amplitude amplification factor is illustrated by a large number of computational results and comparative analyses. The results of a turbine bladed disk composed of 86 blades show that the amplitude of the transient forced response decreases with the increase of the rotation acceleration, and that the transient amplification factor of the mistuned bladed disk is 30% larger than that in the steady state with the same damping.
[1] COWLES B A. High cycle fatigue in aircraft gas turbines-an industry perspective[J]. International Journal of Fracture, 1996, 80(2-3):147-163.
[2] 李其汉, 王延荣, 王建军. 航空发动机叶片高循环疲劳失效研究[J]. 航空发动机, 2003, 29(4):16-18, 41. LI Q H, WANG Y R, WANG J J. Investigation of high cycle fatigue failures for the aero engine blades[J]. Aeroengine, 2003, 29(4):16-18, 41(in Chinese).
[3] 王建军, 于长波, 李其汉. 错频叶盘结构振动模态局部化特性分析[J]. 航空动力学报, 2009, 24(4):788-792. WANG J J, YU C B, LI Q H. Localization characteristics of vibratory mode for bladed disk assemblies[J]. Journal of Aerospace Power, 2009, 24(4):788-792(in Chinese).
[4] SLATER J, MINKIEWICZ G, BLAIR A. Forced response of bladed disk assemblies-A survey[C]//34th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit. Reston:AIAA, 1998:3743.
[5] KRACK M, SALLES L, THOUVEREZ F. Vibration prediction of bladed disks coupled by friction joints[J]. Archives of Computational Methods in Engineering, 2017, 24(3):589-636.
[6] 臧朝平, 段勇亮, PETROV E P. 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. ZANG C P, DUAN Y L, E.P.PETROV. Reduced-order modelling and dynamic response prediction method for mistuned bladed disks[J]. Acta Aeronautica et Astronautica Sinica, 2015, 36(10):3305-3315(in Chinese).
[7] DRESIG H, FIDLIN A. Schwingungen mechanischer Antriebs systeme[M]. Berlin:Springer Berlin Heidelberg, 2014.
[8] MARKERT R, SEIDLER M. Analytically based estimation of the maximum amplitude during passage through resonance[J]. International Journal of Solids and Structures, 2001, 38(10-13):1975-1992.
[9] AYERS J P, FEINER D M, GRIFFIN J H. A reduced-order model for transient analysis of bladed disk forced response[J]. Journal of Turbomachinery, 2006, 128(3):466-473.
[10] YASUTOMO K. Study on transient vibration of mistuned bladed disk passing through resonance[C]//ASME Turbo Expo:Turbine Technical Conference & Exposition.New York:AMSE, 2013.
[11] HARTUNG A. A numerical approach for the resonance passage computation[C]//ASME Turbo Expo:Power for Land, Sea, & Air. New York:AMSE,2010.
[12] HACKENBERG H P, HARTUNG A. An approach for estimating the effect of transient sweep through a resonance[C]//Proceedings of ASME Turbo Expo 2015:Turbine Technical Conference and Exposition. New York:AMSE, 2015
[13] WALLASCHEK J, VON SCHEIDT L P, POHLE L, et al. Transient amplitude amplification of mistunedblisks[J]. Journal of Engineering for Gas Turbines and Power, 2015, 137(11):112502.
[14] BONHAGE M, ADLER J T, KOLHOFF C, et al. Transient amplitude amplification of mistuned structures:An experimental validation[J]. Journal of Sound and Vibration, 2018, 436:236-252.
[15] SIEWERT C, STVER H. Transient forced response analysis of mistuned steam turbine blades during start-up and Coast-down[C]//Proceedings of ASME Turbo Expo 2014:Turbine Technical Conference and Exposition. New York:AMSE, 2014
[16] MICHAEL W. Rotor-stator interactions in a four-stage low-speed axial compressor-part i:Unsteady profile pressures and the effect of clocking[J]. Journal of Turbomachinery, 2004, 126(4):833-845.
[17] MAILACH R, LEHMANN I, VOGELER K. Periodical unsteady flow within a rotor blade row of an axial compressor-part II:Wake-tip clearance vortex interaction[J]. Journal of Turbomachinery, 2008, 130(4):1587-1597
[18] MARCO E, ARMIN M, PETER J. Analysis of rotor-stator-interaction and blade-to-blade measurements in atwo stage axial flow compressor[J]. Journal of Turbomachinery, 2011, 133(1):186-192.
[19] BREARD C, GREEN J S, IMREGUN M. Low-engine-order excitation mechanisms in axial-flow turbomachinery[J]. Journal of Propulsion and Power, 2003, 19(4):704-712.
[20] ZHOU B, MUJEZINOVIC A, COLEMAN A, et al. Forced response prediction for steam turbine last stage blade subject to low engine order excitation[C]//Proceedings of ASME 2011 Turbo Expo:Turbine Technical Conference and Exposition.New York:AMSE, 2012:2447-2453.
[21] STUMMANN S, JESCHKE P, METZLER T. Circumferentially non-uniform flow in the rear stage of a multistage compressor[C]//Proceedings of ASME Turbo Expo 2015:Turbine Technical Conference and Exposition. New York:AMSE, 2015.
[22] TYLER J M, SOFRIN T G. Axial flow compressor noise studies[R]. SAE Technical Papers, 1962:70
[23] FIGASCHEWSKY F, KUEHHORN A, BEIROW B, et al. Analysis of mistuned forced response in an axial high-pressure compressor rig with focus on Tyler-Sofrin modes[J]. The Aeronautical Journal, 2019, 123(1261):356-377.
[24] ZAKER T A. Calculation of the complementary error function of complex argument[J]. Journal of Computational Physics, 1969, 4(3):427-430.
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