Eventos Anais de eventos
DINAME 2017
XVII International Symposium on Dynamic Problems of Mechanics
Sensibility analysis of the stochastic dynamic response of a rotor
Submission Author:
Gabriel Garoli , SP
Co-Authors:
Gabriel Garoli, Helio Fiori de Castro
Presenter: Gabriel Garoli
doi://10.26678/ABCM.DINAME2017.DIN17-0027
Abstract
In many industries, rotating machines are employed in different tasks, for example: power transmission and electricity generation. Therefore, the knowledge of the behavior of these machineries is important. Researches developed different experimental analysis and models to study rotor systems and its components. An important element of rotor machines is the journal bearing, which connects the moving part, the rotor, with the static part, the support. To insert the journal bearing into the dynamic model of the rotor system, a nonlinear equation can be considered to evaluate the hydrodynamic supporting forces of fluid in the bearing. The response in the time domain of the rotor-bearing system is used to analyze the fluid-induced instability, which increase the amplitude of the vibration of the system and is very harmful to the system. However, features and operating conditions of the rotor systems have uncertainties, which can make the simulation results diverge of the collected data of experiments. To include these uncertainties a stochastic model has to be use. Monte Carlo methods are generally utilized to evaluate the stochastic response, due to its simple implementation and convergence. Nevertheless, the Monte Carlo methods take an extended amount of time to compute the simulations. The stochastic collocation methods is gain field to evaluate the stochastic response. These methods utilize a deterministic solver, as the Monte Carlo methods, so its implementation is simple. However, a small number of predetermined points is used in the simulation. The stochastic response can be approach by the generalized polynomial chaos expansion, which is presented in the equation 1. A series of orthogonal polynomials is used and the weight functions of it is equal to the probabilistic density function of some random distributions. Therefore, only the expansion coefficients need to be determined, so a least square method can be use. The approach by the generalized expansion facilitates the evaluation of the statistical parameters of the response and the sensibility analysis to the input random variables, this last one is presented in equation 2. In this paper the stochastic dynamic response of a rotor system will be evaluated, a nonlinear model will be used to calculate the hydrodynamic supporting forces of the bearing, which will be inserted in the finite element model of the rotor-bearing system as an external force. The stochastic collocation method will be used to evaluate the stochastic response, which will be approach by the generalized polynomial chaos expansion. An input sensibility analysis of the stochastic response will be made. This analysis will provide better understanding of the influence of the random input in the fluid-induced instability.
Keywords
Rotordynamics, Uncertainties propagation, stochastic collocation, Sensitivity analysis
