SINGLE AND MULTI-STAGE BLADED ROTORS WITH GEOMETRIC MISTUNING: REDUCED ORDER MODELING AND MISTUNING IDENTIFICATION

Open Access
Author:
Bhartiya, Yasharth
Graduate Program:
Mechanical Engineering
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
February 24, 2011
Committee Members:
  • Alok Sinha, Dissertation Advisor
  • Alok Sinha, Committee Chair
  • Asok Ray, Committee Member
  • Eric M Mockensturm, Committee Member
  • Suzanne Michelle Shontz, Committee Member
Keywords:
  • Mistuning Identification
  • Mistuning
  • Reduced Order Modelling
Abstract:
Modified Modal Domain Analysis (MMDA) is a novel method for the development of a reduced-order model of a bladed rotor with geometric mistuning. This method utilizes proper orthogonal decomposition (POD) of Coordinate Measurement Machine (CMM) data on blades’ geometries, and sector analyses using ANSYS and solid modeling. First the algorithm to compute reduced-order mass and stiffness matrices from ANSYS sector analyses is provided. It is also shown that the algorithm can be efficiently used to perform Monte Carlo simulations of mistuning patterns arising out of arrangements of a given set of mistuned blades. Numerical examples dealing with variations in natural frequencies and forced responses are presented for different patterns of geometric mistuning. MMDA is then expanded to use 2nd order Taylor series approximations of perturbations in mass and stiffness matrices (δM and δK) instead of exact δM and δK. It is shown that the reduced order model based on 2nd order approximation is accurate enough to provide results comparable to exact MMDA. It is also shown that with the use of Taylor series expansion the calculation of reduced order matrices is just a block assembling exercise which is computationally inexpensive hence this method is ideally suited for Monte Carlo simulations. As a numerical example 1000 mistuning patterns generated by random values of mistuning parameters are analyzed to support the fact that the technique can be efficiently used for Monte Carlo simulations. It is also shown that although a large number of POD features are present in a mistuned bladed disk assembly, only a few are dominant and inclusion of only the dominant POD features in the bases vectors is sufficient to get accurate results. The algorithm for MMDA is then modified to use the mode shapes from cyclic analysis of actual sectors instead of mode shapes from sectors modified along POD features, hence avoiding the step of creating artificial sector geometries perturbed along POD features. The idea is further extended to be applicable in the case of extremely large mistuning where normal POD approach breaks down and it is shown that explicit inclusion of mode shapes from cyclic analysis of blade with extremely large mistuning in the bases rectifies the problem and provides accurate results. A reduced order model of a multi-stage rotor in which each stage has a different number of blades is developed. It is shown that a reduced order model can be developed on the basis of tuned modes of certain bladed disks which can be easily obtained via sector analyses. Further, it is shown that reduced order model can also be obtained when blades are geometrically mistuned. This algorithm is similar to the modified modal domain analysis. The validity of this algorithm is shown for the finite element model of a two-stage bladed rotor. In addition, the statistical distributions of peak maximum amplitudes and natural frequencies of a two-stage rotor are generated via Monte Carlo simulations for different patterns of geometric mistuning. The Taylor series expansions of deviations in mass and stiffness matrices due to geometric mistuning gives a direct approach for generating the reduced order model from the components of POD features of spatial variations in blades’ geometries. Reversing the process, algorithms for mistuning identification based on MMDA are presented to calculate the geometric mistuning parameters. Two types of the algorithm, one based on modal analysis and the other on the forced responses are presented. The validity of the method is then verified through a mistuned academic rotor.