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This paper deals with modelling the effect of wear on the dynamics of the shrouded bladed disk with frictional contacts at the shrouds and the contact interface evolution. Prediction of fretting wear commonly occurring at the contacts of turbomachinery components, and its impact on the dynamics is increasingly researched due to the components subjected to their structural limits for performance and operating at high loading conditions. Over a lifetime, the fretting wear at these contacts could alter the global dynamic response of these bladed disks from the designed operating point and could lead to high vibration amplitudes. This study implements a coupled static/dynamic harmonic balance method (HBM) with wear energy approach and an adaptive wear logic to study the impact on the steady-state nonlinear dynamic response. Firstly, the methodology is applied to a cantilever beam with a contact patch and then to a shrouded bladed disk with shroud contacts using cyclic symmetry boundary conditions. The novelty of the paper is to show the effect of wear on the dynamics with the changing contact pre-load using a coupled approach. A wear acceleration $v_{w,max}$ parameter is defined, and the impact of the choice of this parameter is discussed in detail on the computation time and the accuracy of results. The test cases demonstrate the impact of wear on the dynamic nonlinear response curves and the contact interface evolution for various scenarios., Comment: 29 pages, submitted to International Journal of Non-linear mechanics

Real applications in structural mechanics, where the dynamic behavior is linear, are rare. Usually, structures are made of components assembled together by means of joints whose behavior maybe highly nonlinear. Depending on the amount of excitation, joints can dramatically change the dynamic behavior of the whole system, and the modelling of this type of constraint is therefore crucial for a correct prediction of the amount of vibration. The solution of the nonlinear equilibrium equations by means of the Harmonic Balance Method (HBM) is widely accepted as an effective approach to calculate the steady state forced response in the frequency domain, in spite of Direct Time Integration (DTI). The state of the art contact element used to model the friction forces at the joint interfaces is a nodal contact element, where the local contact compliance is modelled by means of linear springs and Coulomb law is used to govern the friction phenomena. In the literature, when the HBM is applied to vibrating systems with joint interfaces and the state-of-the-art contact model is used, an uncoupled approach is mostly employed: the static governing equations are solved in advance to compute the pre-stress effects and then the dynamic governing equations are solved to predict the vibration amplitude of the system. As a result, the HBM steady-state solution may lead to a poor correlation with the DTI solution, where static and dynamic loads are accounted for simultaneously. In this paper, the HBM performances are investigated by comparing the uncoupled approach to a fully coupled static/dynamic approach. In order to highlight the main differences between the two approaches, a lumped parameter system, characterized by a single friction contact, is considered in order to show the different levels of accuracy that the proposed approaches can provide for different configurations.