Eventos Anais de eventos
COBEM 2023
27th International Congress of Mechanical Engineering
Numerical Analysis of Rotordynamic Systems Using Harmonic Balance Method
Submission Author:
Bárbara Nara Teixeira Cunha , MG
Co-Authors:
Bárbara Nara Teixeira Cunha, Aldemir Ap Cavalini Jr, Valder Steffen Jr, Prashant Kambali, C. Nataraj
Presenter: Bárbara Nara Teixeira Cunha
doi://10.26678/ABCM.COBEM2023.COB2023-1736
Abstract
Hence the investigation of techniques to reduce the computational cost for numerical solutions of dynamical systems is in constant development. This research aims to solve the differential equations that describe the behavior of a rotating machine using Harmonic Balance Method (HBM), which determines steady-state vibration amplitudes and phase angles directly by solving nonlinear equations of dynamic systems in the frequency domain. Traditional numerical integration methods in the time domain possess limitations due to the required longer integration times. Thus, depending on the complexity of the model, it may be necessary to simulate the system for an extended period to ensure that we obtain a steady-state solution. The finite element method is used to model the behavior of a rotor system, considering the effects of rotor inertia and gyroscopic moments. This rotary machine under investigation has a flexible horizontal shaft, two rigid discs, and two rolling element bearings. An external force is introduced into the system to simulate non linearity. The initial step of the procedure involves defining an approximate solution for displacements, velocity, and acceleration as a sum of harmonics using the Fourier Series for all degrees of freedom. The unknown coefficients of the harmonic functions are determined by substituting these approximations into the differential equation. Hence, the unknown coefficients constitute a set of nonlinear equations that can be solved using numerical techniques. Once this system of equations has been solved, it is possible to determine the vibration responses in the frequency and time domains. The number of equations that the method needs to solve corresponds to double the number of degrees of freedom of the system, and the Levenberg-Marquardt numerical method is used to solve the resulting nonlinear algebraic equations. The results obtained through the HBM demonstrate that this method solves the differential equations of the movement with similar accuracy, but less computation cost when compared to the conventional time-domain method.
Keywords
Harmonic balance method, frequency domain analysis, rotating machinery, computational cost, Numerical Solutions
