Uncertainty treatment in forced response calculation of mistuned bladed disk

Mistuning, imperfections in cyclical symmetry of bladed disks is an inevitable and perilous occurrence due to many factors including manufacturing tolerances and in-service wear and tear. It can cause some unpredictable phenomena such as mode splitting, mode localization and dramatic difference in forced vibration response. In this paper first, a method is presented which calculates the forced vibration response of a mistuned system based on an exact relationship between tuned and mistuned systems. Then, the genetic algorithm is used for solving an optimization problem to find the worst-case response of bladed-disk assembly. The second part tries to find methods to reduce the system worst-case response. Intentional mistuning which breaks the nominal symmetry of a tuned bladed disk and rearranging the bladed-disk assembly are introduced and used to reduce the system worst-case response. Finally, a two degree of freedom per blade simplified model with 56 blades is used to demonstrate the capabilities of the techniques in reducing the worst response of the bladed-disk system.

[1]  B. Henderson-Sellers,et al.  Mathematics and Computers in Simulation , 1995 .

[2]  D. J. Ewins,et al.  Vibration Characteristics of Bladed Disc Assemblies , 1973 .

[3]  Lawrence. Davis,et al.  Handbook Of Genetic Algorithms , 1990 .

[4]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[5]  J. H. Griffin,et al.  Model Development and Statistical Investigation of Turbine Blade Mistuning , 1984 .

[6]  R. C. F. Dye,et al.  Vibration Amplitudes of Compressor Blades Resulting From Scatter in Blade Natural Frequencies , 1969 .

[7]  John Holland,et al.  Adaptation in Natural and Artificial Sys-tems: An Introductory Analysis with Applications to Biology , 1975 .

[8]  Hong Hee Yoo,et al.  Vibration localization of simplified mistuned cyclic structures undertaking external harmonic force , 2003 .

[9]  J. R. Torres-Lapasió,et al.  A hybrid genetic algorithm with local search: I. Discrete variables: optimisation of complementary mobile phases , 2001 .

[10]  S. Wu,et al.  Steady-state genetic algorithms for discrete optimization of trusses , 1995 .

[11]  Jan Zeman,et al.  Applying genetic algorithms to selected topics commonly encountered in engineering practice , 2000 .

[12]  Kumara Sastry,et al.  Efficient Atomic Cluster Optimization Using A Hybrid Extended Compact Genetic Algorithm With Seeded , 2001 .

[13]  Saeed Ziaei-Rad,et al.  Inverse design of supersonic diffuser with flexible walls using a Genetic Algorithm , 2006 .

[14]  D. J. Ewins,et al.  Analysis of the Worst Mistuning Patterns in Bladed Disk Assemblies , 2003 .

[15]  Benjamin Shapiro,et al.  Symmetry Approach to Extension of Flutter Boundaries via Mistuning , 1998 .

[16]  A. Sinha.  Computation of the Statistics of Forced Response of a Mistuned Bladed Disk Assembly via Polynomial Chaos , 2006 .

[17]  Christine M. Anderson-Cook,et al.  A Genetic Algorithm with Memory for Mixed Discrete-Continuous Design Optimization , 2002 .

[18]  Mario A. Rotea,et al.  Efficient algorithms for mistuning analysis , 2002 .

[19]  Takuji Nishimura,et al.  Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator , 1998, TOMC.

[20]  D. J. Ewins,et al.  Resonant Vibration Levels of a Mistuned Bladed Disk , 1984 .

[21]  Jeffrey A. Joines,et al.  Manufacturing Cell Design: An Integer Programming Model Employing Genetic Algorithms , 1996 .

[22]  K. Schittkowski.  NLPQL: A fortran subroutine solving constrained nonlinear programming problems , 1986 .

[23]  Saeed Ziaei-Rad,et al.  Aerodynamic Design Optimization Using Genetic Algorithm (RESEARCH NOTE) , 2003 .

[24]  E. Petrov.  Optimization of Perturbation Parameters for Forced Vibration Stress Levels of Turbomachinery Blade Assemblies , 1994 .

[25]  Joseph C. Slater,et al.  Forced response of bladed disk assemblies : A survey , 1999 .