Stability Analysis of Multiharmonic Nonlinear Vibrations for Large Models of Gas Turbine Engine Structures With Friction and Gaps

An efficient method is proposed for the multiharmonic frequency domain analysis of the stability for nonlinear periodic forced vibrations in gas-turbine engine structures and turbomachines with friction, gaps and other types of nonlinear contact interfaces. The method allows using large-scale finite element models for structural components together with detailed description of nonlinear interactions at contact interfaces between these components. The highly accurate reduced models are applied in the assessment of stability of periodic regimes for large-scale model of gas-turbine structures. An approach is proposed for the highly-accurate calculation of motion of a structure after it is perturbed from the periodic nonlinear forced response. Efficiency of the developed approach is demonstrated on a set of test cases including simple models and large-scale realistic bladed disc models with different types of nonlinearities: friction, gaps and cubic nonlinear springs.

[1]  D. Ewins,et al.  Analytical Formulation of Friction Interface Elements for Analysis of Nonlinear Multi-Harmonic Vibrations of Bladed Discs , 2002 .

[2]  Pierre-Alain Masserey,et al.  Eddy Current Damper for Turbine Blading: Electromagnetic Finite Element Analysis and Measurement Results , 2012 .

[3]  D. Ewins,et al.  The Harmonic Balance Method with arc-length continuation in rotor/stator contact problems , 2001 .

[4]  Sébastien Baguet,et al.  A comparison of stability computational methods for periodic solution of nonlinear problems with application to rotordynamics , 2013 .

[5]  Alain Batailly,et al.  Numerical-experimental comparison in the simulation of rotor/stator interaction through blade-tip/abradable coating contact , 2012 .

[6]  C. H. Menq,et al.  Prediction of Periodic Response of Blades Having 3D Nonlinear Shroud Constraints , 1999 .

[7]  Chia-Hsiang Menq,et al.  Periodic Response of Blades Having Three-Dimensional Nonlinear Shroud Constraints , 2001 .

[8]  Olivier Thomas,et al.  A harmonic-based method for computing the stability of periodic solutions of dynamical systems , 2010 .

[9]  Alper Demir,et al.  A reliable and efficient procedure for oscillator PPV computation, with phase noise macromodeling applications , 2003, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[10]  Evgeny Petrov,et al.  Analysis of Bifurcations in Multiharmonic Analysis of Nonlinear Forced Vibrations of Gas Turbine Engine Structures With Friction and Gaps , 2015 .

[11]  Jun Zhou,et al.  Spectral characteristics and eigenvalues computation of the harmonic state operators in continuous-time periodic systems , 2004, Syst. Control. Lett..

[12]  Fabrizio Bonani,et al.  A frequency-domain approach to the analysis of stability and bifurcations in nonlinear systems described by differential-algebraic equations , 2008 .

[13]  Roman Lewandowski,et al.  Computational formulation for periodic vibration of geometrically nonlinear structures—part 1: Theoretical background , 1997 .

[14]  Bernard Deconinck,et al.  Computing spectra of linear operators using the Floquet-Fourier-Hill method , 2006, J. Comput. Phys..

[15]  Stefano Zucca,et al.  Numerical assessment of friction damping at turbine blade root joints by simultaneous calculation of the static and dynamic contact loads , 2012 .

[16]  G. Floquet,et al.  Sur les équations différentielles linéaires à coefficients périodiques , 1883 .

[17]  John M. Davis,et al.  A unified Floquet theory for discrete, continuous, and hybrid periodic linear systems , 2009, 0901.3841.

[18]  D. J. Ewins,et al.  Analytical Formulation of Friction Interface Elements for Analysis of Nonlinear Multi-Harmonic Vibrations of Bladed Disks , 2003 .

[19]  Evgeny Petrov,et al.  A High-Accuracy Model Reduction for Analysis of Nonlinear Vibrations in Structures With Contact Interfaces , 2010 .

[20]  Gerald Moore,et al.  Floquet Theory as a Computational Tool , 2004, SIAM J. Numer. Anal..

[21]  Mehmet Imregun,et al.  Harmonic Balance Vibration Analysis of Turbine Blades With Friction Dampers , 1997 .

[22]  Luc Masset,et al.  The harmonic balance method for bifurcation analysis of large-scale nonlinear mechanical systems , 2015, 1604.05621.

[23]  Jean-Jacques Sinou,et al.  Stability and vibration analysis of a complex flexible rotor bearing system , 2008 .