The applications of POD method in dual rotor-bearing systems with coupling misalignment

Abstract In this paper, the proper orthogonal decomposition (POD) method is first time apply to the dimension reduction of dual rotor-bearing experiment rig which is similar to an aero-engine rotor. The basic theory of the POD method and the application in dynamical system are introduced. The supporting bearing nonlinearity and the coupling misalignment of high and low pressure rotors are considered, and the dynamical model is established by finite element method based on dual rotor experiment rig. The frequency behaviors of dual rotor-bearing coupling misalignment response are discussed via comparing the numerical and experiment results to verify the efficiency of the model. The POD method is used for dimension reduction of rotor-bearing system, and the dynamical behaviors of the reduced-order model (ROM) are compared with the full order system (FOM) and experiment to verify the higher computational efficiency and accuracy of the POD method. These results in this paper can provide engineering guidance to actual dual rotor-bearing system with coupling misalignment fault.

[1]  Fabrice Thouverez,et al.  Rotor to stator contacts in turbomachines. Review and application , 2013 .

[2]  Jin-Gyun Kim,et al.  Evaluating Mode Selection Methods for Component Mode Synthesis , 2016 .

[3]  H. D. Nelson,et al.  Stability Analysis of Rotor-Bearing Systems Using Component Mode Synthesis , 1980 .

[4]  Karen Willcox,et al.  A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems , 2015, SIAM Rev..

[5]  Karen Willcox,et al.  Nonlinear Model Order Reduction via Lifting Transformations and Proper Orthogonal Decomposition , 2018, AIAA Journal.

[6]  Lei Hou,et al.  Bifurcation analysis of reduced rotor model based on nonlinear transient POD method , 2017 .

[7]  Kuan Lu,et al.  An adaptive proper orthogonal decomposition method for model order reduction of multi-disc rotor system , 2017 .

[8]  Kuan Lu,et al.  A modified nonlinear POD method for order reduction based on transient time series , 2015 .

[9]  T. Chondros,et al.  Analytical Methods in Rotor Dynamics , 1983 .

[10]  Hans Troger,et al.  Dimension Reduction of Dynamical Systems: Methods, Models, Applications , 2005 .

[11]  D. Dessì,et al.  Modal parameter estimation for a wetted plate under flow excitation: A challenging case in using POD , 2019, Journal of Sound and Vibration.

[12]  Qihan Li,et al.  Investigation of the Steady-State Response of a Dual-Rotor System With Inter-Shaft Squeeze Film Damper , 1985 .

[13]  B. Wen,et al.  A dynamic model for simulating rubbing between blade and flexible casing , 2020 .

[14]  Terence R. Smith Low-dimensional Models of Plane Couette Flow using the Proper Orthogonal Decomposition , 2003 .

[15]  Kuan Lu Statistical moment analysis of multi-degree of freedom dynamic system based on polynomial dimensional decomposition method , 2018 .

[16]  Dongxiang Jiang,et al.  Vibration response characteristics of a dual-rotor with unbalance-misalignment coupling faults: Theoretical analysis and experimental study , 2018, Mechanism and Machine Theory.

[17]  Lei Hou,et al.  Nonlinear dynamic analysis of a complex dual rotor-bearing system based on a novel model reduction method , 2019, Applied Mathematical Modelling.

[18]  Louis Jezequel,et al.  Center manifold and multivariable approximants applied to non-linear stability analysis , 2003 .

[19]  Lei Hou,et al.  Nonlinear dynamical behaviors of a complicated dual-rotor aero-engine with rub-impact , 2018 .

[20]  Chen Guo,et al.  Hyper-spherical distance discrimination: A novel data description method for aero-engine rolling bearing fault detection , 2018, Mechanical Systems and Signal Processing.

[21]  Qihan Li,et al.  Investigation of the Steady-State Response of a Dual-Rotor System With Intershaft Squeeze Film Damper , 1986 .

[22]  B. Wen,et al.  Nonlinear vibration and dynamic stability analysis of rotor-blade system with nonlinear supports , 2019, Archive of Applied Mechanics.

[23]  Karen Willcox,et al.  Model Reduction for Large-Scale Systems with High-Dimensional Parametric Input Space , 2008, SIAM J. Sci. Comput..

[24]  Lei Hou,et al.  Review for order reduction based on proper orthogonal decomposition and outlooks of applications in mechanical systems , 2019, Mechanical Systems and Signal Processing.

[25]  Amir Younan,et al.  Model Reduction Methods for Rotor Dynamic Analysis: A Survey and Review , 2010 .

[26]  Rui Yang,et al.  Experiments and Numerical Results for Varying Compliance Contact Resonance in a Rigid Rotor–Ball Bearing System , 2017 .

[27]  Benjamin Peherstorfer,et al.  Projection-based model reduction: Formulations for physics-based machine learning , 2019, Computers & Fluids.

[28]  Zhe Ding,et al.  Considering higher-order effects of residual attachment modes in free-interface component mode synthesis method for non-classically damped systems , 2020 .

[29]  J. Peraire,et al.  Balanced Model Reduction via the Proper Orthogonal Decomposition , 2002 .

[30]  K. Athre,et al.  Unbalance response of a dual rotor system : theory and experiment , 1993 .

[31]  Nicolae Herisanu,et al.  Dynamic Response of a Permanent Magnet Synchronous Generator to a Wind Gust , 2019, Optimal Auxiliary Functions Method for Nonlinear Dynamical Systems.

[32]  B. B. Maharathi,et al.  Dynamic Behaviour Analysis of a Dual-Rotor System Using the Transfer Matrix Method , 2004 .

[33]  Haihua Yu,et al.  Bifurcation analysis for nonlinear multi-degree-of-freedom rotor system with liquid-film lubricated bearings , 2013 .

[34]  Yushu Chen,et al.  Bifurcations and hysteresis of varying compliance vibrations in the primary parametric resonance for a ball bearing , 2015 .

[35]  Sk Bhaumik,et al.  Failure analysis of compressor stator blades of an aeroengine , 2004 .

[36]  R. Temam,et al.  Nonlinear Galerkin methods , 1989 .

[37]  Li Ma,et al.  Stability and Bifurcation in a Delayed Reaction–Diffusion Equation with Dirichlet Boundary Condition , 2016, J. Nonlinear Sci..

[38]  G. Kerschen,et al.  The Method of Proper Orthogonal Decomposition for Dynamical Characterization and Order Reduction of Mechanical Systems: An Overview , 2005 .

[39]  F. Gu,et al.  Response analysis of an accelerating unbalanced rotating system with both random and interval variables , 2020, Journal of Sound and Vibration.

[40]  Chen Gu Sensitivity analysis of fault diagnosis of aero-engine rolling bearing based on vibration signal measured on casing , 2014 .

[41]  Xingyu Tai,et al.  A review on dynamic characteristics of blade–casing rubbing , 2016 .

[42]  Chandramouli Padmanabhan,et al.  A fixed–free interface component mode synthesis method for rotordynamic analysis , 2006 .

[43]  J. Zu,et al.  METHOD OF MULTIPLE SCALES FOR VIBRATION ANALYSIS OF ROTOR SHAFT SYSTEMS WITH NON-LINEAR BEARING PEDESTAL MODEL , 1998 .

[44]  D. H. Hibner,et al.  Dynamic response of viscous-damped multi-shaft jet engines , 1975 .