Application of rotor response analysis to fault detection in hydro powerplants.

In this article some considerations obtained during the utilization of rotor response analysis techniques in hydraulic powerplants are discussed. An applied research work was carried out in two hydraulic turbines analysing the rotor response both theoretically and experimentally. A developed mathematical model was used to simulate the rotordynamic behaviour of Francis and Kaplan turbines. The main dynamical effects that appear during the operation of the machines are discussed too. A series of measurements were carried out in the turbines using impact hammers to determine the modal behaviour of the units. The tests were carried out with the machine still and in operation. Some results and the comparison with the theory is presented in this article. The improved theoretical model was used for a sensitivity analysis of the different bearings to the main excitations that fake place during the machine operation. From this analysis, the best measuring points for condition monitoring were determined.

Rotor support stiffness estimation by sensitivity analysis

In the present work, a method for rotor support stiffness estimation via a model updating process using the sensitivity analysis is presented. This method consists in using the eigenvalues sensitivity analysis, relating to the rotor support stiffnesses variation to perform the adjustment of the model based on the minimization of the difference between eigenvalues of reference and eigenvalues obtained via mathematical model from previously adopted support bearing stiffness values. The mathematical model is developed by the finite element method and the method of adjustment should converge employing an iterative process. The performance and robustness of the method have been analyzed through a numerical example.

Analytical method for the design of a machine with aligned and skewed permanent magnets

This work aims to present the design and the evaluation of a standard multi-pole machine with permanent magnets inserted in the rotor by two different geometrical forms: aligned and skewed magnets. The design (new analytical method) was based on a standard 250 W three phase 12-pole induction motor (squirrel cage rotor type), beginning with the original stator constructive data to calculate the magnetic flux density to determine the permanent magnets. In the development of the work, a simple and modular rotor was built reusing the original 12-pole stator (concentrated windings). The machine was evaluated in a laboratory for the purpose of checking the quantity and quality of energy produced with the machine operating as a generator and its start, torque, and performance working as a motor. In conclusion, the modular skewed magnet is an option for electrical machines, for the generation of a reasonable quality, in the context of decentralized generation and a motor with high torque and low energetic consumption.

The effect of actuator and sensor placement on the active control of rotor unbalance

This paper investigates both theoretically and experimentally the effect of the location and number of sensors and magnetic bearing actuators on both global and local vibration reduction along a rotor using a feedforward control scheme. Theoretical approaches developed for the active control of beams have been shown to be useful as simplified models for the rotor scenario. This paper also introduces the time-domain LMS feedforward control strategy, used widely in the active control of sound and vibration, as an alternative control methodology to the frequency-domain feedforward approaches commonly presented in the literature. Results are presented showing that for any case where the same number of actuators and error sensors are used there can be frequencies at which large increases in vibration away from the error sensors can occur. It is also shown that using a larger number of error sensors than actuators results in better global reduction of vibration but decreased local reduction. Overall, the study demonstrated that an analysis of actuator and sensor locations when feedforward control schemes are used is necessary to ensure that harmful increased vibrations do not occur at frequencies away from rotor-bearing natural frequencies or at points along the rotor not monitored by error sensors.

Modal Analysis of a Beam with a Tip Rotor by Using a Fundamental Response

The shape modes of a damped-free beam model with a tip rotor are determined by using a dynamical basis that is generated by a fundamental spatial free response. This is a non-classical distributed model for the displacements in the transverse directions of the beam which turns out to be coupled through boundary conditions due to rotation. Numerical calculations are performed by using the Ritz-Rayleigh method with several approximating basis.

Análise do comportamento dinâmico de um rotor vertical através do método dos elementos finitos

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Projeto estrutural do cubo do rotor de uma turbina hidraúlica tipo Kaplan

Pós-graduação em Engenharia Mecânica - FEG

Técnica de projeto de controlador fuzzy aplicada ao acionamento vetorial de motor de indução

Este trabalho investiga uma estratégia de controle fuzzy Takagi-Sugeno aplicada ao controle de velocidade do motor de indução. A estratégia implementa uma interpolação ponderada entre um conjunto de controladores locais previamente projetados. Ao ocorrer variações nas condições operacionais do motor de indução, os ganhos da lei de controle são ajustados automaticamente, de modo a manter satisfatório o desempenho do sistema de controle. Para o projeto do controlador fuzzy a representação em espaço de estados da planta foi considerada sob a forma de um sistema aumentado, incluindo-se uma nova variável de estado que, nesse caso, foi selecionada como sendo a integral do erro de velocidade. Tal formulação permitiu o projeto de controladores locais com a estrutura PI, através de realimentação completa de estados, com posicionamento de pólos. Como variáveis de operação para o chaveamento fuzzy dos controladores locais, foram selecionados as variáveis velocidade angular do rotor e a componente da corrente de estator responsável pelo torque elétrico do motor. Em seguida, a estabilidade do controlador fuzzy Takagi- Sugeno projetado foi comprovada através do critério de Lyapunov, para isso o problema de estabilidade foi escrito na forma de LMIs. O desempenho do controlador fuzzy Takagi-Sugeno foi avaliado através de estudos de simulação, e seus resultados comparados ao desempenho de um controlador PI convencional, para a regulação da velocidade do rotor. Os resultados obtidos nas simulações mostram que o emprego da estratégia proposta torna o sistema mais robusto a variações paramétricas no sistema de acionamento.

Complex modal analysis of a slender vertical rotor by finite elements method

In this paper, natural frequencies were analyzed (axial, torsional and flexural) and frequency response of a vertical rotor with a hard disk at the edge through the classical modal and complex analysis. The equation that rules the movement was obtained through the Lagrangian formulation. The model considered the effects of bending, torsion and axial deformation of the shaft, besides the gravitational and gyroscopic effects. The finite element method was used to discretize the structure into hollow cylindrical elements with 12 degrees of freedom. Mass, stiffness and gyroscopic matrices were explained consistently. The classical modal analysis, usually applied to stationary structures, does not consider an important characteristic of rotating machinery which are the methods of forward and backward whirl. Initially, through the traditional modal analysis, axial and torsional natural frequencies were obtained in a static shaft, since they do not suffer the influence of gyroscopic effects. Later research was performed by complex modal analysis. This type of tool, based on the use of complex coordinates to describe the dynamic behavior of rotating shaft, allows the decomposition of the system in two submodes, backward and forward. Thus, it is possible to clearly visualize that the orbit and direction of the precessional motion around the line of the rotating shaft is not deformed. A finite element program was developed using MATLAB (TM) and numerical simulations were performed to validate this model. Natural frequencies and directional frequency forced response (dFRF) were obtained using the complex modal analysis for a simple vertical rotor and also for a typical drill string used in the construction of oil wells.

Rotor Failure Diagnosis of Induction Motors by Wavelet Transform and Fourier Transform in Function of the Load

This paper presents two diagnostic methods for the online detection of broken bars in induction motors with squirrel-cage type rotors. The wavelet representation of a function is a new technique. Wavelet transform of a function is the improved version of Fourier transform. Fourier transform is a powerful tool for analyzing the components of a stationary signal. But it is failed for analyzing the non-stationary signal whereas wavelet transform allows the components of a non-stationary signal to be analyzed. In this paper, our main goal is to find out the advantages of wavelet transform compared to Fourier transform in rotor failure diagnosis of induction motors.

Aplicação da teoria de potência conservativa para monitoramento do comportamento do motor de indução trifásico sob distúrbios de qualidade de energia

Pós-graduação em Engenharia Elétrica - FEB

Análise de falhas por fadiga num rotor de hidrogerador vertical via método dos elementos finitos

Pós-graduação em Engenharia Mecânica - FEG

Projeto de controladores robustos para acionamento de um motor de indução trifásico

Pós-graduação em Engenharia Elétrica - FEIS

Complex modal analysis of a vertical rotor through finite element method

Natural frequencies were analyzed (axial, torsional and flexural) and frequency response of a vertical rotor with a hard disk at the edge through the classical and complex modal analysis. The mathematical modeling was based on the theory of Euler-Bernoulli beam. The equation that rules the movement was obtained through the Lagrangian formulation. The model considered the effects of bending, torsion and axial deformation of the shaft, besides the gravitational and gyroscopic effects. The finite element method was used to discretize the structure into hollow cylindrical elements with 12 degrees of freedom. Mass, stiffness and gyroscopic matrices were explained consistently. This type of tool, based on the use of complex coordinates to describe the dynamic behavior of rotating shaft, allows the decomposition of the system in two submodes, backward and forward. Thus, it is possible to clearly visualize that the orbit and direction of the precessional motion around the line of the rotating shaft is not deformed. A finite element program was developed using Matlab ®, and numerical simulations were performed to validate this model.

Percolation transition in quantum Ising and rotor models with sub-Ohmic dissipation

We investigate the influence of sub-Ohmic dissipation on randomly diluted quantum Ising and rotor models. The dissipation causes the quantum dynamics of sufficiently large percolation clusters to freeze completely. As a result, the zero-temperature quantum phase transition across the lattice percolation threshold separates an unusual super-paramagnetic cluster phase from an inhomogeneous ferromagnetic phase. We determine the low-temperature thermodynamic behavior in both phases, which is dominated by large frozen and slowly fluctuating percolation clusters. We relate our results to the smeared transition scenario for disordered quantum phase transitions, and we compare the cases of sub-Ohmic, Ohmic, and super-Ohmic dissipation.