Passive vibration control in rotor dynamics: Optimization of composed support using viscoelastic materials

One of the major reasons for inserting damping into bearings is that rotating machines are often requested in critical functioning conditions having sometimes to function under dynamic instability or close to critical speeds. Hydrodynamic and magnetic bearings have usually been used for this purpose, but they present limitations regarding costs and operation, rendering the use of viscoelastic supports a feasible solution for vibration control in rotating machines. Most papers in the area use simple analytic or single degree of freedom models for the rotor as well as classic mechanical models of linear viscoelasticity for the support – like Maxwell, Kelvin−Voigt, Zenner, four-element, GHM models and even frequency independent models – but they lack the accuracy of fractional models in a large range of frequency and temperature regarding the same number of coefficients. Even in those works, the need to consider the addition of degrees of freedom to the support is evident. However, so far no paper has been published focusing on a methodology to determine the optimal constructive form for any viscoelastic support in which the rotor is discretized by finite elements associated to an accurate model for characterizing the viscoelastic material. In general, the support is meant to be a simple isolation system, and the fact the stiffness matrix is complex and frequency-temperature dependent – due to its viscoelastic properties – forces the traditional methods to require an extremely long computing time, thus rendering them too time consuming in an optimization environment. The present work presents a robust methodology based mainly on generalized equivalent parameters (GEP) – for an optimal design of viscoelastic supports for rotating machinery - aiming at minimizing the unbalance frequency response of the system using a hybrid optimization technique (genetic algorithms and Nelder–Mead method). The rotor is modeled based on the finite element method using Timoshenko’s thick beam formulation, and the viscoelastic material is modeled based on four-parameter fractional derivatives. The insertion of supports – a two-degree-of-freedom isolation system - into rotor’s motion equations is performed in two different ways: (1) by adding degrees of freedom and (2) by using the GEP technique. The results show that both techniques are consistent, but the GEP technique proves to be less time consuming, regarding computing time. In the presented simulations it is possible to obse