An improved microslip model for variable normal loads

Abstract

Detuning of gas turbine blades in order to avoid high cycle fatigue failure due to large resonant stresses is often unfeasible. A possible solution is to add an external source of damping, in the form of dry friction devices such as the under-platform damper. The relative movement between the blades causes possible slip between damper and blade surfaces. Due to the nonlinear nature of dry friction, dynamic analysis of structures constrained through frictional contacts is difficult, commercial finite element codes using time step integration are not suitable given the large computation times. For this reason, ad hoc numerical codes have been developed in the frequency domain. Some authors Yang and Menq (J Eng Gas Turbine Power 120:410–417, 1998) [1], Sanliturk et al. (J Eng Gas Turbine Power 123:919–929, 2001) [2], Csaba (Proceeding of ASME Gas turbine and aeroengine congress and exhibition) [3], Panning et al. (Int J Rotating Mach 9:219–228, 2003) [4] prefer a separate routine in order to compute contact forces as a function of input displacements, others Cigeroglu et al. (J Eng Gas Turbine Power 131:022505, 2009) [5], Firrone et al. (Modelling a friction damper: analysis of the experimental data and comparison with numerical results, 2006) [6], Firrone and Zucca (Numerical analysis—theory and application, 2011) [7] include the damper in the FE model of the bladed array. The available numerical models of dampers require a description of the contact conditions, both in the normal and in the tangential directions. The approach proposed here differs from those available in the literature in that the tangential force-displacement behaviour is described by arrays of springs in parallel, but, unlike pre-existing models, it introduces a variable sharing of normal force according to the approach along the normal. It thus modulates the tangential stick-slip capabilities according to normal force and approach and is capable to reproduce the analytical contact description as originally proposed by Cattaneo (Accademia dei Lincei 6:P I; 342–348, P II; 434–436, P III; 474–478, 1938) [8] and Mindlin and Deresiewicz (J Appl Mech 20:327–344, 1953) [9]. The paper shows how the model can be described and tuned in reference to the analytical Cattaneo and Mindlin’s benchmark for a spherical contact. It is proved that parameters tuned for a certain normal load will correctly simulate the tangential behaviour at any other lower normal load and finally that the transitions between cycles at different normal loads is correctly described. The paper further shows an application to a cylindrical contact where the tangential characteristics are derived from purposely taken experimental measurements.