Analytical Formulation of Friction Interface Elements for Analysis of Nonlinear Multi-Harmonic Vibrations of Bladed Disks

Abstract

An analytical formulation for the vectors of contact forces and the stiffness matrix of the nonlinear friction contact interface is developed for the analysis of multi-harmonic vibrations in the frequency domain. The contact interface elements provided here an exact description of friction and unilateral contact forces at the interacting surfaces, taking into account the influence of the variable normal load on the friction forces, including the extreme cases of separation of the two surfaces. Initial gaps and interferences at the contact nodes, which affect the normal force, as well as the unilateral action of the normal force at the contact surface, are all included in the model. The accurate calculation of the force vector and the tangent stiffness matrix provides a very reliable and fast convergence of the iteration process used in the search for the amplitudes of nonlinear vibrations of bladed disks. Numerical investigations demonstrate excellent performance with respect to speed, accuracy and stability of computation.

Modelling the nonlinear behaviour of an underplatform damper test rig for turbine applications

“…In more advanced models [16][17][18][19][20], these hypotheses were removed and the damper motion is calculated purely as the result of its interaction with the blades by means of the nonlinear contact forces. To reproduce damper motions, advanced 3D friction contact elements were employed; these account for normal load variation with separation effects and 2D tangential in plane motion [21]. To further improve the accuracy of the contact force calculation, local deformation effects were also taken into account using an explicit FE damper model [22].…”

Qualitative analysis of forced response of blisks with friction ring dampers

“…Pierre et al, 1985), and some have used an iterative procedure in the time domain (e.g. Poudou and Pierre, 2003;Guillen and Pierre, 1999;Petrov and Ewins, 2003). For the latter strategy, it is convenient to add a tangent stiffness to each friction element; doing so, the Coulomb law can be used straightforward to compute at each time step the equilibrium of the contact point.…”

“…This method is found to be efficient and was widely used, in the past, to study friction dampers in bladed disks assemblies or shroud contacts. Some examples have been presented by Wang and Chen (1993), Sanliturk et al (1997) and Yang and Menq (1997) for mono-harmonic vibrations and by Pierre et al (1985), Petrov and Ewins (2003), Nacivet et al (2003), and Guillen and Pierre (1999) for multi-harmonic vibrations.…”

“…These devices were widely studied in the past and numerous methods of design and analysis are found in the literature. The interest reader can find examples based on lumped parameter or equivalent models in works of Griffin (1990), Sinha and Griffin (1983), Ferri and Heck (1998) or Csaba (1998) and, more recently, extended to more complex structures in works by Guillen and Pierre (1999), Nacivet et al (2003) or Petrov and Ewins (2003) among others. The contact interface could be one dimensional, two dimensional or three dimensional (e.g.…”

Effects of mistuning on dynamic behavior of nonlinear cyclic systems with lump masses and cubic nonlinearity

“…Petrov et al [45] formulated friction element under variable normal load conditions. The multiharmonic balance method (MHBM) is utilized for linearization of the nonlinearity to calculate the equivalent forcing vector as well as the tangent stiffness matrix.…”