Two-dimensional modeling of an aircraft engine structural bladed disk-casing modal interaction

In modern turbo machines such as aircraft jet engines, structural contacts between the casing and bladed disk may occur through a variety of mechanisms: coincidence of vibration modes, thermal deformation of the casing, rotor imbalance due to design uncertainties to name a few. These nonlinear interactions may result in severe damage to both structures and it is important to understand the physical circumstances under which they occur. In this study, we focus on a modal coincidence during which the vibrations of each structure take the form of a k-nodal diameter traveling wave characteristic of axi-symmetric geometries. A realistic two-dimensional model of the casing and bladed disk is introduced in order to predict the occurrence of this very specific interaction phenomenon versus the rotation speed of the engine. The equations of motion are solved using an explicit time integration scheme in conjunction with the Lagrange multiplier method where friction is accounted for. This model is validated from the comparison with an analytical solution. The numerical results show that the structures may experience different kinds of behaviors (namely damped, sustained and divergent motions) mainly depending on the rotational velocity of the bladed disk.

[1]  B. F. Beacher,et al.  The Impact of Forward Swept Rotors on Tip Clearance Flows in Subsonic Axial Compressors , 2004 .

[2]  T. R. Camp.  A Study of Acoustic Resonance in a Low-Speed Multistage Compressor , 1997 .

[3]  D. J. Ewins,et al.  The effects of detuning upon the forced vibrations of bladed disks , 1969 .

[4]  Huijiu Zhou,et al.  Friction and wear behaviour and abradability of abradable seal coating , 1999 .

[5]  P. Raveendranath,et al.  Free vibration of arches using a curved beam element based on a coupled polynomial displacement field , 2000 .

[6]  Agnes Muszynska,et al.  Chaotic responses of unbalanced rotor/bearing/stator systems with looseness or rubs , 1995 .

[7]  Patrick Chabrand,et al.  Complementarity methods for multibody friction contact problems in finite deformations , 2001 .

[8]  R. Taylor,et al.  A simple algorithm for three-dimensional finite element analysis of contact problems , 1993 .

[9]  Wing Kam Liu,et al.  Nonlinear Finite Elements for Continua and Structures , 2000 .

[10]  J. C. Simo,et al.  An augmented lagrangian treatment of contact problems involving friction , 1992 .

[11]  Michel Raous,et al.  Consistent time discretization for a dynamical frictional contact problem and complementarity techniques , 1998 .

[12]  K. Bathe.  Finite Element Procedures , 1995 .

[13]  D. L. Thomas.  Dynamics of rotationally periodic structures , 1979 .

[14]  Chong-Won Lee,et al.  Vibration Analysis of Rotors , 1994 .

[16]  T. Laursen.  Computational Contact and Impact Mechanics , 2003 .

[17]  A. Leissa,et al.  Vibration of shells , 1973 .

[18]  Sunil K. Sinha,et al.  Non-linear dynamic response of a rotating radial Timoshenko beam with periodic pulse loading at the free-end , 2005 .

[19]  R. Taylor,et al.  Lagrange constraints for transient finite element surface contact , 1991 .

[20]  L. Meirovitch.  Analytical Methods in Vibrations , 1967 .

[21]  Dara W. Childs,et al.  Turbomachinery Rotordynamics: Phenomena, Modeling, and Analysis , 1993 .

[22]  Y. S. Choi,et al.  Investigation on the whirling motion of full annular rotor rub , 2002 .

[23]  Mehmet Imregun,et al.  A review of aeroelasticity methods with emphasis on turbomachinery applications , 1996 .

[24]  Ronnie Bladh,et al.  Efficient predictions of the vibratory response of mistuned bladed disks by reduced order modeling , 2001 .

[25]  Patrick Chabrand,et al.  Various numerical methods for solving unilateral contact problems with friction , 1998 .