Chapter9 Consideration of Interface Damping in Shrouded Mistuned Turbine Blades F. Schreyer, J. Gross, P. Reuss, M. Junge, and H. Schoenenborn Abstract Running turbines are exposed to high mechanical load. Due to gas excitations the structure can vibrate with high oscillation amplitudes which can damage the turbine blades. Mistuning can additionally lead to high local stresses which must be taken into account in the turbine design process. Introducing damping due to friction in the interface of shrouded turbines can be used to decrease this oscillation amplitudes. The computation of full turbine finite-element models with nonlinear coupling forces causes high computational costs. As a consequence, Component Mode Synthesis methods are used to reduce the number of DOFs of each blade substructure. Mistuning of the blades can now be applied in modal space. Coupling of the mistuned substructures is done by nonlinear interface forces which have to be included in the substructuring formulation. The resulting reduced and mistuned system with nonlinear coupling forces is solved with a Harmonic Balance Method such that the effect of mistuning and interface damping can be studied very efficiently. Keywords Turbine • Mistuning • Interface damping • Component Mode Synthesis • Harmonic Balance Method 9.1 Introduction Calculating the steady state response of turbine blades is an important task during the design process of turbines. To analyze the oscillation of randomly mistuned turbine blades stochastic analysis must be done. In general, this requires many calculations and therefore a very fast numeric routine is desirable. If nonlinear contacts are considered, the calculation is very time expensive. In this contribution a fast approximation for the nonlinear contact on shrouded blades is presented using the Harmonic Balance Method (HBM). Additionally, a Component Mode Synthesis (CMS) to reduce the linear substructures is used to decrease the calculation time to a minimum. A small benchmark model is considered in order to show the approach and illustrate numeric results. In Fig. 9.1 the components as well as the assembly of the used FE-model are shown. This paper is organized as follows. In Sect. 9.2 the reduction and adjacent assembly of the substructures are described in detail. Section 9.3 is addressed to the used mistuning formulation. The coupling method applied to the shroud interfaces is demonstrated in Sect. 9.4. Subsequently, the Harmonic Balance Method is shortly reviewed in Sect. 9.5 and Sect. 9.6 is dedicated to the obtained results. The paper closes with a brief conclusion. F. Schreyer ( ) • J. Gross • P. Reuss Institute of Applied and Experimental Mechanics, University of Stuttgart, Pfaffenwaldring 9, 70550 Stuttgart, Germany e-mail: schreyer@iam.uni-stuttgart.de; gross@iam.uni-stuttgart.de; reuss@iam.uni-stuttgart.de M. Junge • H. Schoenenborn MTU Aero Engines, Muenchen, Germany M. Allen et al. (eds.), Dynamics of Coupled Structures, Volume 1: Proceedings of the 32nd IMAC, A Conference and Exposition on Structural Dynamics, 2014, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-04501-6__9, © The Society for Experimental Mechanics, Inc. 2014 105
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