Reduced Order Modeling of Bladed Disks for Contact Stiffness Identification

Reduced Order Modeling of Bladed Disks for Contact Stiffness Identification

SeunghunBaek,DepartmentofMechanical Engineering,UniversityofMichigan,Ann Arbor,UnitedStates

Bogdan Epureanu,DepartmentofMechanical Engineering,UniversityofMichigan,Ann Arbor,UnitedStates

Abstract

Modeling of contact interfaces is very important in many engineering applications. Modeling of friction contacts in structural dynamics has become a major issue in the design of mechanical parts and structures. In turbomachinery, the friction force at contact interfaces is one of the most common strategies applied to dampen vibrations. To predict the dynamic responses of a structure associated with friction, reliable friction modeling is essential. Structures with frictional contacts between components can be modeled using finite element (FE) analysis. To establish reliable models of bladed disks with friction dampers, it is necessary to obtain the accurate contact parameters. Accurate modeling requires knowledge of contact parameters such as contact stiffness and contact damping, which are not readily available.

The contact stiffness for the mechanical structure must be identified along with their expected ranges of variation in order to use FE models confidently. Contact surfaces can experience slipping and tension release depending on the magnitude of the normal and tangential forces at the contact interface. Due to the nonlinear behavior of the contact, the identification of the contact stiffness and the friction coefficient is not straightforward. Thus, there have been many attempts to estimate the contact parameters correctly through both analytical and experimental methods [1-6]. Often, contact parameters including stiffness and damping are unknown or inaccurate when applied to analytic models. Wang and Sas [7] suggested a method for finding the optimal linear joint stiffness and damping parameters from measured modal parameters (resonant frequency and damping ratio), and Ren and Beards [8] presented a method to extract the optimal linear joint parameters by using experimental frequency response data. Although those techniques are available for the identification of nonlinear joint parameters, they are only applicable to those joints with specific geometric configurations. Moreover, dynamic tests are needed, and they have to be performed on a specialized fixture.

In this study, an efficient methodology to identify the contact stiffness by measuring the forced responses of the system is suggested. A more general method for identifying the contact parameters of a bladed disk system with a friction ring damper is developed based on the system response observations and the estimations. Surrogate measurement data that are obtained through forced responses of a bladed disk with measurement noise are investigated. A ROM is developed to predict the forced response of a bladed disk with a friction ring damper. An optimization problem is stated and solved by finding the minimum residual between the measurement data from the dynamic responses of bladed disks with a friction ring damper and the predictions from the developed ROM.

References

[1] K. L. Johnson, Contact mechanics, Cambridge University Press, London

[2] J. A. Greenwood, J. P. B. Williamson, Contact of nominally flat surfaces, Proc. R. Soc. London 295 (1966) 300-319

[3] A. A. Polycarpou, A. Soom, Boundary and mixed friction in the presence of dynamic normal loads. I. system model, ASME Journal of Tribology 117 (1995) 255-260

[4] Y. Song, C. J. Hartwigsen, L. A. Bergman, A. F. Vakakis, Simulation of dynamics of beam structures with bolted joints using adjust beam elements, Journal of Sound and Vibration 273(1-2) (200) 249-276

[5] L. Gaul, S. Bohlen, Identification of nonlinear structural joint models and implementation in discretized structure models, Proceedings of 11th ASME Conference on Mechanical Vibration and Noise, Boston 5(1987) 213-219

[6] B. S. Heck, A. A .Ferri, Vibration analysis of dry friction damped turbine blades using singular perturbation theory, Journal of Vibration and Acoustics 120(1998) 588-595

[7] J. Wang, P. Sas, A method for identifying parameters of mechanical joints, Journal of Applied Mechanics 57 (1990) 337-342

[8] Y. Ren, C. F. Beards, Identification of effective linear joints using coupling and joint identification techniques, Journal of Vibration and Acoustics 120 (1998) 331-338