This paper presents a novel method for identifying the dynamic parameters of a gas bearing, whose force coefficients are strong functions of frequency. The method is based on the analysis of the phase diagram with the model assuming a mass-damper-spring system with time-dependent force coefficients. Usually, it is necessary a controlled mechanism to find the transfer function, this condition limits the application of the method. On the other hand, estimation of the damping and stiffness parameters under real loading is very cumbersome and requires a special care on identifying the excitation forces. One of the main difficulties is the isolation of noise and those vibration signals with an unidentified source. In this work, the excitation force was taken from the unbalance loading of a rotor test. Therefore, there is no need for a special test rig. The dynamic parameters can be estimated analyzing data from the actual rotor mounted on the gas bearings. Identifying the parameters that cause gas bearing instabilities is a big challenge. The gas properties are very sensitive to temperature and pressure changes, and, as a consequence the bearing rotor-dynamic coefficients change drastically and the rotor behaves chaotically, which means that the dynamic parameters are nonlinear. In this research a methodology based on the phase diagram construction to identify nonlinear instabilities of gas bearings is presented. The results show the method capability to estimate the dynamic coefficients by the analysis of the energy variation.
Among nonparametric methods, the phase diagram or phase space is in use to identify nonlinearities in dynamic systems. The identification is conducted through the analysis of the energy variations. The energy variations can be represented as a three dimensional function E(x,v,t). In this way the phase diagram can be related to the frequency and the dynamic parameters of the system. According to Taken’s theorem, a dynamic system can be obtained by reconstructing the phase diagram. Then, using this method, the damping and stiffness coefficients are estimated.