Transient reliability optimization for turbine disk radial deformation

Abstract

The radial deformation design of turbine disk seriously influences the control of gas turbine high pressure turbine (HPT) blade-tip radial running clearance (BTRRC). To improve the design of BTRRC under continuous operation, the nonlinear dynamic reliability optimization of disk radial deformation was implemented based on extremum response surface method (ERSM), including ERSM-based quadratic function (QF-ERSM) and ERSM-based support vector machine of regression (SR-ERSM). The mathematical models of the two methods were established and the framework of reliability-based dynamic design optimization was developed. The numerical experiments demonstrate that the proposed optimization methods have the promising potential in reducing additional design samples and improving computational efficiency with acceptable precision, in which the SR-ERSM emerges more obviously. Through the case study, we find that disk radial deformation is reduced by about 6.5×10^–5 m; δ=1.31×10^–3 m is optimal for turbine disk radial deformation design and the proposed methods are verified again. The presented efforts provide an effective optimization method for the nonlinear transient design of motion structures for further research, and enrich mechanical reliability design theory.

Keywords

turbine disk / radial deformation / reliability-based transient design optimization / extremum response surface method / support vector machine regression

References

[1] LattimeS B, SteinetzB M. High pressure turbine clearance control system: Current practices and future directions [J]. Journal of Propulsion and Power, 2004, 20: 302-311

[2] AnnetteE N, ChristiphW M, StephanS. Modeling and validation of the thermal effects on gas turbine transients [J]. Journal of Engineering for Gas Turbines and Power, 2005, 127: 564-572

[3] BaiG C, FeiC W. Distributed collaborative response surface method for mechanical dynamic assembly reliability design [J]. Chinese Journal of Mechanical Engineering, 2013, 26: 1160-1168

[4] HuD Y, WangR Q, TaoZ. Probabilistic design for turbine disk at high temperature [J]. Aircraft Engineering and Aerospace Technology, 2011, 83: 199-207

[5] AldersonR G, TaniM A, TreeD J. Three-dimensional optimization of a gas turbine disk and blade attachment [J]. Journal of Aircraft, 1976, 13: 994-999

[6] MeguidS A, KanthP S, CzejanskiA. Finite element analysis of fir-tree region in turbine discs [J]. Finite Element Analysis Design, 2000, 35: 305-317

[7] FarshiB, JahedH, MehrabianA. Optimum design of inhomogeneous nonuniform rotating discs [J]. Computer and Structure, 2004, 82: 773-779

[8] HuangZ J, WangC G, ChenJ. Optimal design of aeroengine turbine disc based on kriging surrogate models [J]. Computer and Structures, 2011, 89: 27-37

[9] ForresterA I J, KeaneA J. Recent advances in surrogate-based optimization [J]. Progress of Aerospace Science, 2009, 45: 50-79

[10] WangG G. Adaptive response surface method using inherited Latin hypercube design points [J]. Journal of Mechanical Design, 2003, 125: 210-220

[11] YeniayO, UnalR, LepschR A. Using dual response surfaces to reduce variability in launch vehicle design: A case study [J]. Reliability Engineering System Safety, 2006, 91: 407-412

[12] MuratE K, HasanB B, AlemdarB. Probabilistic nonlinear analysis of CFR dams by MCS using response surface method [J]. Applied Mathematical Modelling, 2011, 35: 2752-2770

[13] FeiC W, BaiG C. Wavelet correlation feature scale entropy and fuzzy support vector machine approach for aeroengine whole-body vibration fault diagnosis [J]. Shock and Vibration, 2013, 20: 341-349

[14] FeiC W, BaiG C. Nonlinear dynamic probabilistic analysis for turbine casing radial deformation using extremum response surface method based on support vector machine [J]. Journal of Computational and Nonlinear Dynamics, 2013, 8: 041004

[15] GuoZ W, BaiG C. Application of least squares support vector machine for regression to reliability analysis [J]. Chinese Journal of Aeronautics, 2009, 22: 160-166

[16] ZhangC Y, BaiG C. Extremum response surface method of reliability analysis on two-link flexible robot manipulator [J]. Journal of Center South University, 2012, 19: 101-107

[17] FeiC W, BaiG C. Extremum response surface method for casing radial deformation probabilistic analysis [J]. Journal of Aerospace Information System, 2013, 10: 58-63

[18] FeiC W, BaiG C. Distributed collaborative extremum response surface method for mechanical dynamic assembly reliability analysis [J]. Journal of Central South University, 2013, 20: 2414-2422

[19] KimY, MetzgerD. Heat transfer and effectiveness on film cooled turbine blade tip models [J]. ASME Journal of Turbomachinery, 1995, 117: 12-21

[20] KypurosJ A, MelcherkJ. A reduced model for prediction of thermal and rotational effects on turbine tip clearance [R]. NASA/TM-2003-212226, 2003

[21] FeiC W, BaiG C. Extremum selection method of random variable for nonlinear dynamic reliability analysis of turbine blade deformation [J]. Propulsion and Power Research, 2012, 1: 58-63