Eventos Anais de eventos
COBEM 2023
27th International Congress of Mechanical Engineering
Balancing of Rotating Systems without Trial Masses
Submission Author:
Diego Ataíde Couto de Paula , SP
Co-Authors:
Diego Ataíde Couto de Paula, Katia Lucchesi Cavalca Dedini, Diogo Stuani Alves
Presenter: Diego Ataíde Couto de Paula
doi://10.26678/ABCM.COBEM2023.COB2023-0040
Abstract
Rotating machines are used in several industrial activities with great emphasis on energy generation, in which a series of characteristic problems can arise from a rotating system on flexible or rigid supports. In this sense, mathematical models representing the dynamic characteristics of rotors have been developed to simulate their operating conditions. However, a simple consideration of the shaft behavior is not enough for representing the complexity of this type of machinery. Therefore, other components such as bearings must be also considered. Hydrodynamic bearings have lubricating fluid between its rigid parts in order to eliminate dry friction and decrease operating temperatures and wear of the surfaces. In addition to understanding the rotor characteristics, performance improvement and cost reduction are highly desirable. For these, fault detection and identification are paramount. Unbalance is the most common cause of undesirable vibrations in rotating systems. Even small unbalance masses can cause high vibration amplitudes due to its quadratic relationship with the rotating speed, which may be a significant impediment to the safe operation of the machine. Therefore, balancing is essential for any equipment. With this in mind, the objective of this paper is to develop a model-based multi-plane balancing procedure for rotating machines. The proposed methodology has the potential to eliminate the use of trial masses during field balancing tasks, saving precious maintenance time. The procedure relies on optimization techniques to find a solution that minimizes the difference between the theoretical vibrations added by noise (which represents the experimental results) and the vibrations calculated numerically by the mathematical model. In this work, the rotor is supported by hydrodynamic bearings and it is modeled by the finite element method. The bearings are modeled analytically by the short bearing theory, which considers negligible pressure gradient in the circumferential direction. Moreover, this machine element is inserted in the rotating system as parallel springs and dampers by means of the linear equivalent coefficients.The equation of motion is solved in the frequency domain, where the Unbalance Response and optimization techniques are used to solve a Mixed-Integer Nonlinear Programming (MINLP). For this class of optimization problem, special techniques must be used to identify unbalance. The Barrier Method is used to solve the Nonlinear Programming and the Outer Approximation and Branch and Bound methods, with simplex algorithm, are used to solve the resulting Mixed-Integer Linear Programming (MILP). The results present striking balance identification, evidencing that the procedure adopted is indeed promising.
Keywords
rotating machines, balancing, unbalance identification, optimization techniques
