On nonlinear dynamics behavior and control of a new model of a magnetically levitated vibrating system, excited by an unbalanced DC motor of limited power supply

We analyze new results on a magnetically levitated body (a block including a magnet whose bottom pole is set in such a way as to repel the upper pole of a magnetic base) excited by a non-ideal energy source (an unbalanced electric motor of limited power supply). These new results are related to the jump phenomena and increase of power required of such sources near resonance are manifestations of a non-ideal system and they are referred as the Sommerfeld effect, which emulates an energy sink. In this work, we also discuss control strategies to be applied to this system, in resonance conditions, in order to decrease its vibration amplitude and avoiding this apparent energy sink.

Investment recovery period in electric motor of higher efficiency in pumping for irrigation

Neste trabalho, ajustou-se um modelo matemático para quantificar o efeito do rendimento do motor elétrico sobre os custos de um sistema de bombeamento para irrigação na estrutura tarifária de energia elétrica convencional e horo-sazonal verde, bem como calcular o tempo de recuperação do capital investido no equipamento de maior rendimento. em seguida, o mesmo foi aplicado a um sistema de irrigação tipo pivô central em duas opções de rendimento do motor elétrico: 92,6% (linha padrão) e 94,3% (linha alto rendimento), sendo que o custo de aquisição do primeiro correspondeu a 70% do segundo. A potência do motor elétrico era de 100 cv. Os resultados mostraram que o modelo permitiu avaliar se um motor de alto rendimento era viável economicamente em relação ao motor-padrão em cada estrutura tarifária. Nas duas estruturas tarifárias, o motor de alto rendimento não foi viável. Na tarifa horo-sazonal verde, somente seria viável se seu rendimento fosse 4,46% superior ao do motor-padrão. Na tarifa convencional, somente seria viável se o ganho de rendimento superasse 2,71%.

LEARNING A COMPLEX MOTOR SKILL FROM VIDEO and POINT-LIGHT DEMONSTRATIONS

The aim of this Study was to compare the learning process of a highly complex ballet skill following demonstrations of point light and video models 16 participants divided into point light and video groups (ns = 8) performed 160 trials of a pirouette equally distributed in blocks of 20 trials alternating periods of demonstration and practice with a retention test a day later Measures of head and trunk oscillation coordination d1 parity from the model and movement time difference showed similarities between video and point light groups ballet experts evaluations indicated superiority of performance in the video over the point light group Results are discussed in terms of the task requirements of dissociation between head and trunk rotations focusing on the hypothesis of sufficiency and higher relevance of information contained in biological motion models applied to learning of complex motor skills

Influence of design parameters on linear induction motor end effect

In this paper, a factor referred to as k(f) for linear induction motor end effect analysis is presented. The mathematical model takes into account the longitudinal entry end effect. The entry end effect produces considerable distortion in magnetic field distribution. It is shown how this influence is derived from the machine-developed force that is calculated through the application of the I-D theory. The k(f) factor establishes the relationship between the longitudinal end effect and machine parameters, mainly the number of magnetic poles, secondary resistivity, and frequency.

On the stabilising effect of gyroscopic moments in an automotive turbocharger

Automotive turbochargers, which operate at very high speeds, exceeding 180,000 r/min, exhibit two strong sub-harmonic modes of vibrations due to oil-whirl instability. These are a conical mode and an in-phase whirl mode. The gyroscopic effects can be very important in such a rotor system. This article presents a theoretical investigation into these effects on the conical whirl instability of a turbocharger induced by the angular (tilting) motion of a rigid rotor. A simplified linear model is used to analyse the rotor-bearing system by investigating the effects of the gyroscopic moment on the internal moments. A gyroscopic coefficient, defined by the geometry of the rotor, is shown to govern the stability of the conical whirl motion. A threshold value of 1/2 is determined for this coefficient to suppress the conical whirl. This value remains unaffected if the rotor is asymmetric and is supported by floating ring bearings, which is the case in a practical turbocharger.

Desempenho motor no esporte: das restrições do iniciante ao experiente

A set of constraints on the performance of motor skills is a determinant factor of success in many sport modalities that require from the athlete continuous adaptation to changes in the game context. Taking into account Newell's model of organism (or performer), task and environmental constraints in the acquisition of motor skills (NEWELL, 1986), the focus of this study is the set of changes that take place in motor behavior from the beginner to the high level athlete. In specific, the focus is toward changes in sports settings in which the ball is the center of the game, responsible for the relationship among athletes of the same team as well as between opponents, as in volleyball. The ball, in its trajectory, carries on a set of constraints to the player's behavior. To be able of imposing constraints on the opponent's behavior is so important as to know how to deal with a ball sent to you by the opponent in an unpredictable trajectory.

Effect of a frictional force on the Fermi-Ulam model

The dynamical properties of a classical particle bouncing between two rigid walls, in the presence of a drag force, are studied for the case where one wall is fixed and the other one moves periodically in time. The system is described in terms of a two-dimensional nonlinear map obtained by solution of the relevant differential equations. It is shown that the structure of the KAM curves and the chaotic sea is destroyed as the drag force is introduced. At high energy, the velocity of the particle decreases linearly with increasing iteration number, but with a small superimposed sinusoidal modulation. If the motion passes near enough to a fixed point, the particle approaches it exponentially as the iteration number evolves, with a speed of approach that depends on the strength of the drag force. For a simplified version of the model it is shown that, at low energies corresponding to the region of the chaotic sea in the non-dissipative model, the particle wanders in a chaotic transient that depends on the strength of the drag coefficient. However, the KAM islands survive in the presence of dissipation. It is confirmed that the fixed points and periodic orbits go over smoothly into the orbits of the well-known (non-dissipative) Fermi-Ulam model as the drag force goes to zero.

Dissipative area-preserving one-dimensional Fermi accelerator model

The influence of dissipation on the simplified Fermi-Ulam accelerator model (SFUM) is investigated. The model is described in terms of a two-dimensional nonlinear mapping obtained from differential equations. It is shown that a dissipative SFUM possesses regions of phase space characterized by the property of area preservation.

Fermi acceleration on the annular billiard: a simplified version

A simplified version of a time-dependent annular billiard is studied. The dynamics is described using nonlinear maps and we consider two different configurations for the billiard, namely (i) concentric and (ii) eccentric cases. For the concentric case and for a null angular momentum, we confirm that the results for the Fermi-Ulam model are recovered and the particle does not experience the phenomenon of Fermi acceleration. However, on the eccentric case the particle demonstrates unlimited energy gain and Fermi acceleration is therefore observed.

On Lugre Friction Model to Mitigate Nonideal Vibrations

In this paper, a nonideal mechanical system with the LuGre friction damping model is considered. The mechanical model of the system is an oscillator not necessarily linear connected with an unbalanced motor of excitation with limited power supply. The control of motion and the attenuation of the Sommerfeld effect of the considered nonideal system are analyzed in this paper The mathematical model of the system is represented by coupled non-linear differential equations. The identification of some interesting nonlinear phenomenon in the transient and steady state motion of the system during the passage through resonance (using applied voltages at dc motor as control parameter) is investigated in detail using numerical simulation. [DOI: 10.1115/1.3124783]

Non-uniform drag force on the Fermi accelerator model

Some dynamical properties of a particle suffering the action of a generic drag force are obtained for a dissipative Fermi Acceleration model. The dissipation is introduced via a viscous drag force, like a gas, and is assumed to be proportional to a power of the velocity: F alpha -nu(gamma). The dynamics is described by a two-dimensional nonlinear area-contracting mapping obtained via the solution of Newton's second law of motion. We prove analytically that the decay of high energy is given by a continued fraction which recovers the following expressions: (i) linear for gamma = 1; (ii) exponential for gamma = 2; and (iii) second-degree polynomial type for gamma = 1.5. Our results are discussed for both the complete version and the simplified version. The procedure used in the present paper can be extended to many different kinds of system, including a class of billiards problems.

A Short Note on Transverse Vibrations of a Shaft Carrying Two (or One) Disk Excited by a Nonideal Motor

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Método experimental para determinação das capacitancias parasitas do motor de indução trifásico acionado por inversor MLP

A proposta deste trabalho é apresentar uma nova metodologia para determinação experimental das capacitancias parasitas do motor de indução trifásico de rotor em gaiola. As capacitancias parasitas fazem parte do circuito equivalente do motor para estudos de interferência eletromagnética causada no motor de indução em modo comum quando ele for acionado por inversor controlado por modulação por largura de pulsos (MLP). Os procedimentos propostos para o desenvolvimento deste novo método consistem em: a) determinação dos parâmetros do circuito equivalente do motor de indução trifásico, em regime permanente, através de ensaio em laboratório; b) estabelecer configurações de ligações entre o inversor MLP e o motor para medições das grandezas de interesse que são as seguintes: tensões de modo comum e de eixo, correntes de fuga e de eixo, através de circuito de medição desenvolvido para este fim; c) calcular os valores das capacitancias parasitas entre estator e carcaça do motor; estator e rotor; rotor e carcaça e de rolamento utilizando a expressão matemática da definição de capacitancia; d) utilizar o software Pspice para simular o sistema motor de indução trifásico, alimentado por inversor MLP, com os circuitos equivalentes em baixas e altas frequências; e) obter as formas de onda características do fenômeno de modo comum.

On an approximate analytical solution to a nonlinear vibrating problem, excited by a nonideal motor

This paper analyzes through Multiple Scales Method a response of a simplified nonideal and nonlinear vibrating system. Here, one verifies the interactions between the dynamics of the DC motor (excitation) and the dynamics of the foundation (spring, damper, and mass). We remarked that we consider cubic nonlinearity (spring) and quadratic nonlinearity (DC motor) of the same order of magnitude according to experimental results. Both analytical and numerical results that we have obtained had good agreement.

Design of a simplified neuro-fuzzy system based on CMAC Architectures

This work presents the design of a fuzzy controller with simplified architecture that use an artificial neural network working as the aggregation operator for several active fuzzy rules. The simplified architecture of the fuzzy controller is used to minimize the time processing used in the closed loop system operation, the basic procedures of fuzzification are simplified to maximum while all the inference procedures are computed in a private way. As consequence, this simplified architecture allows a fast and easy configuration of the simplified fuzzy controller. The structuring of the fuzzy rules that define the control actions is previously computed using an artificial neural network based on CMAC Cerebellar Model Articulation Controller. The operational limits are standardized and all the control actions are previously calculated and stored in memory. For applications, results and conclusions several configurations of this fuzzy controller are considered.