Updating Bearing Stiffness and Damping Coefficients of a Rotor System
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IGINAL CONTRIBUTION
Updating Bearing Stiffness and Damping Coefficients of a Rotor System M. Chouksey • J. K. Dutt • S. V. Modak
Received: 13 January 2013 / Accepted: 30 August 2013 / Published online: 22 November 2013 Ó The Institution of Engineers (India) 2013
Abstract Finite element (FE) models of structures have been quite useful in both static and dynamic analyses of structures. However, quite often, these models are not reliable enough since predictions based on them may not be found to have acceptable correlation with experimentally obtained data. This paper attempts updating of bearing radial and tilt stiffness as well as damping parameters of a rotor system by using inverse eigen sensitivity method (IESM). Non-proportional viscous damping model has been used in modelling damping coefficients of bearings. The state space form of equations of motion of the system is used in applying the IESM for model updating. The results show that both stiffness and damping coefficients of bearings can be effectively found out by using the IESM. The method is found to update the eigenvalues quite well even under the presence of measurement noise. Keywords Modal analysis Bearing coefficients Model updating Inverse eigen sensitivity method
Introduction Engineering structures, e.g. rotor systems, are generally modeled by finite element method [1] for carrying out
M. Chouksey SGSITS, Indore, India e-mail: [email protected] J. K. Dutt (&) S. V. Modak IIT Delhi, New Delhi, India e-mail: [email protected] S. V. Modak e-mail: [email protected]
analysis to get an understanding of the behaviour of the structure. However, the results predicted by the finite element model may deviate from the experimental results due to the errors in parameters of the finite element model. Model updating methods [2, 3] may be used to update the parameters of the FE model such that the difference between the results of numerical analysis and experiments are minimum. Model updating methods are classified into direct methods and iterative methods. In direct methods, the model is updated in one run, whereas in iterative methods the model is updated in a number of iterations. In direct methods the mass, stiffness and damping matrices are updated such that the updated model reproduce the measured data, however the updated matrices using direct methods generally do not maintain structural connectivity of the system and the corrections predicted are also not physically meaningful. Iterative methods provide flexibility of selecting the updating parameters apart from overcoming the shortcomings of the direct methods. These methods are classified into inverse eigen sensitivity method (IESM) and frequency response sensitivity method (FRSM). In IESM, the rate of eigenvalues and/or eigenvectors with respect to updating parameters are used to define sensitivity matrix whereas in FRSM the sensitivity of the frequency response functions with respect to the updating parameters is used to update the model. This work uses IESM to update stiffness an
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