Journal of Vibration and Sound

Journal of Vibration and Sound

Frequency response analysis of the bladed disk system with the mistuned in mass and stiffness

Document Type : research article

Authors
1 Department of Mechanical Engineering, Faculty of Engineering, University of Jiroft, Jiroft, Iran
2 Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran,
Abstract
Ideally, bladed disk systems are tuned and all blades are identical but, in practice there always exist small, random differences among the blades. In designing bladed disks, all the blades on each stage are generally assumed to be identical, and this is called a tuned bladed disk. However, due to manufacturing tolerances, variations in material properties and wear in service, each blade on a disk is almost always slightly different to the others. These small differences, collectively called mistuning. It is well known that even a small amount of mistuning can induce a large forced response known as mode localization. In this study a representative model for the bladed disk system is presented and equation of motion derived. Then the response of tuned system was obtained. Afterward, frequency response of mistuned system with genetic algorithm for mistuned blade in mass was studied. Also maximum frequency response of the system for mistuned blade in stiffness was calculated. The result indicated the slightly mistuning in system can increase the response of the system. The worst response of mistuned system is 5.563 times greater than the response of the tuned system. Increase in frequency response of the system is undesirable and should be considered in the initial design of these systems.
Keywords

[1] Wang, Shuai, Geng Yang, Li Ji, Chuanxing Bi, and Changjun Zheng, "Multi-mode vibration attenuation of mistuned bladed disks by frictional tuned mass dampers array", Journal of Sound and Vibration, 2022, Vol.536 p.117176.
[2] Bornassi, S., T. M. Berruti, C. M. Firrone, and G. Battiato, "Vibration parameters identification of turbomachinery rotor blades under transient condition using Blade Tip-Timing measurements", Measurement, 2021, Vol.183, p.109861.
[3] Zhou, Biao, Jingchao Zhao, and Teresa Maria Berruti, "Exploration of blade detuning tests for mistuning identification of blisks", Mechanical Systems and Signal Processing, 2022, Vol.175, p.109118.
[4] Nyssen, Florence, Yann Colaïtis, and Alain Batailly. "Numerical investigation of a mistuned industrial bladed disk dynamics with structural contacts using time and frequency methods." Journal of Sound and Vibration (2022), p.117077.
[5] Rivas-Guerra, Alejandro J., and Marc P. Mignolet, "Maximum amplification of blade response due to mistuning: Localization and mode shape aspects of the worst disks", J. Turbomach, 2003, Vol.125, no.3, pp.442-454.
[6] Shin, Sang Ha, Min Kyoo Kang, and Hong Hee Yoo, "Mistuned coupling stiffness effect on the vibration localization of cyclic systems", Journal of mechanical science and technology, 2008, Vol.22, no.2, pp.269-275.
[7] رئیسی استبرق ا.، ضیایی­راد س.، "یافتن بدترین پاسخ فرکانسی سیستم دیسک پره­دار تحت تأثیر نامیزانی به­کمک الگوریتم ژنتیک"، نشریه علمی- پژوهشی مهندسی مکانیک امیرکبیر، زمستان 1391، سال چهل و چهار  شماره 2، ص 41-50.
[8] Raeisi, E., and S. Ziaei-Rad, "The worst response of mistuned bladed disk system using neural network and genetic algorithm", Meccanica, 2013, Vol.48, no.2, pp.367-379.
[9] Basu, P., and J. H. Griffin, "The effect of limiting aerodynamic and structural coupling in models of mistuned bladed disk vibration", 1986, pp.132-139.
[10] Petrov, E. P., and D. J. Ewins, "Analysis of the worst mistuning patterns in bladed disc assemblies", In Turbo Expo: Power for Land, Sea, and Air, 2001, Vol.78538, p.V004T03A051. American Society of Mechanical Engineers.
[11] Kaiser, Teri, Reed S. Hansen, Nhan Nguyen, Roy W. Hampton, Doug Muzzio, Mladen K. Chargin, Roy Guist, Ken Hamm, and Len Walker. “Experimental/analytical approach to understanding mistuning in a transonic wind tunnel compressor”, 1994, No.NAS 1.15:108833.
[12] Rahimi, Mohammad, and Saeed Ziaei-Rad, "Uncertainty treatment in forced response calculation of mistuned bladed disk", Mathematics and Computers in Simulation, 2010, Vol.80, no.8, pp.1746-1757.
[13] Castanier, Matthew P., and Christophe Pierre, "Using intentional mistuning in the design of turbomachinery rotors", AIAA journal, 2002, Vol.40, no.10, pp.2077-2086.
[14] Hou, Jianfu, and Charles Cross, "Minimizing blade dynamic response in a bladed disk through design optimization", AIAA journal, 2005, Vol.43, no.2, pp.406-412.
[15] Estabragh, E. Raeisi, S. Ziaei-Rad, and M. Rahimi, "Effects of mistuning on dynamic behavior of nonlinear cyclic systems with lump masses and cubic nonlinearity", Mechanics & Industry, 2016, Vol.17, no.4, p.409.
[16] Beirow, Bernd, Felix Figaschewsky, Arnold Kühhorn, and Alfons Bornhorn, "Vibration analysis of an axial turbine blisk with optimized intentional mistuning pattern", Journal of Sound and Vibration, 2019, Vol.442, pp.11-27.
[17] Bai, Bin, Han Li, Wei Zhang, and Yanchao Cui, "Application of extremum response surface method-based improved substructure component modal synthesis in mistuned turbine bladed disk", Journal of Sound and Vibration, 2020, Vol.472, p.115210.
[18] Bai, Bin, Junyi Zhang, Yanchao Cui, and Han Li, "Vibration characteristics investigation of mistuned blisks with receptance substructure component modal synthesis method", Journal of Mechanical Science and Technology, 2020, Vol.34, no.7, pp.2715-2729.
[19] Bai, Bin, and Guangwei Zhu, "Application of improved dynamic substructure finite element model-based state-space techniques in mistuned blisks", International Journal of Aerospace Engineering, 2020.
[20] Kan, Xuanen, and Bo Zhao, "A New Method of Reducing the Vibration Localization of the Multi-packet Whole Mistuned Bladed Disk System Using Bladed Packets", International Journal of Aer