Contact interfaces with dry friction are frequently used in turbomachinery. Dry friction damping produced by the sliding surfaces of these interfaces reduces the amplitude of bladed-disk vibration. The relative displacements at these interfaces lead to fretting-wear which reduces the
INTRODUCTIONSources of non-linearity in turbomachinery are multiple. Contact with friction is one of the most important causes of non-linearity in turbomachinery, especially in bladed-disks. Contact with friction must be taken into account to ensure efficient that the vibration of this type of structure can be predicted well. Friction dampers can be added to decrease response to vibration, although this requires numerical tools to evaluate the added damping rate. In bladed disks, contact with friction occurs at the interfaces between the blades and the disk to which they are attached. Fluid is another source of non-linearity. It is possible to simulate the periodic behaviour of coupled fluid-structures by using the frequency method.HBM (Harmonic Balance Method) is the most widely used frequency method. It is based on the expansion of variables in Fourier series and the Galerkin procedure to obtain non-linear algebraic systems. For systems with contact and friction, an alternating frequency time (AFT) procedure is performed to calculate non-linear forces in the time domain and then transform them into the frequency domain.Other approaches are possible, in this paper we study two other methods: the trigonometric collocation method (TCM) and the high dimension harmonic balance method (HDHB). In TCM a non-linear algebraic system is solved in the time domain. In the HDHB method the unknowns are values of displacements with an equal time step and the non-linear algebraic system is solved once again in the time domain. Some authors have called this method the time spectral method (TSM) [1] and it was used in CFD and proved highly efficient.In the first section we present the theory underlying these methods and explain the advantages of each one. Different strategies are possible for solving non-linear algebraic systems the most common of which is Newton-Raphson solver [2]. For very large systems a Jacobian matrix can be ill-conditioned, with problems of convergence in the linear direction search step. For CFD applications, several authors [1,3,4] propose transforming the non-linear algebraic system into a first order differential system and integrating it to obtain the steady state and thus the solution of the non-linear system. The second section sets out the theory of this method and different schemes are tested by using numerical examples.In previous papers [5][6][7] we have shown that steady state in fretting-wear can occur during vibration. To identify steady state we proposed an integration scheme involving the calculation of transient kinetics. A method that allows finding the steady state directly would be very useful. In this paper we propose using a pseudo-time method and integrating wear kinetics in pseudo-time. It is s...