Search results for: Second critical rotor speed

Authors: Prabhakar Sathujoda

Abstract:

Vibration analysis of a misaligned rotor coupling bearing system has been carried out while decelerating through its critical speed. The finite element method (FEM) is used to model the rotor system and simulate flexural vibrations. A flexible coupling with a frictionless joint is considered in the present work. The continuous wavelet transform is used to extract the misalignment features from the simulated time response. Subcritical speeds at one-half, one-third, and one-fourth the critical speed have appeared in the wavelet transformed vibration response of a misaligned rotor coupling bearing system. These features are also verified through a parametric study.

Keywords: Continuous wavelet transform, flexible coupling, rotor system, sub critical speed.

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Authors: Hoda Molavi, Sima Hoseinpoor, Hossein Bahmanyar

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A Rotary Disc Contactor with inner diameter of 9.1cm and maximum operating height of 40cm has been used to investigate break up phenomenon. Water-Toluene, Water as continuous phase and Toluene as dispersed phase, was selected as chemical system in the experiments. The mentioned chemical system has high interfacial tension so it was possible to form big drops which permit accurate investigation on break up phenomenon as well as the first and second critical rotor speeds. In this study, Break up phenomenon has been studied as a function of mother drop size, rotor speed and continuous phase height. Further more; the effects of mother drop size and continuous phase height on the first and second critical rotor speeds were investigated. Finally, two modified correlations were proposed to estimate the first and second critical speeds.

Keywords: Breakage, First critical rotor speed, Rotary disccontactor, Second critical rotor speed

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Authors: Rajesh Kumar, Roopali Dogra, Puneet Aggarwal

Abstract:

In recent advancements in electric machine and drives, wound rotor motor is extensively used. The merit of using wound rotor induction motor is to control speed/torque characteristics by inserting external resistance. Wound rotor induction motor can be used in the cases such as (a) low inrush current, (b) load requiring high starting torque, (c) lower starting current is required, (d) loads having high inertia, and (e) gradual built up of torque. Examples include conveyers, cranes, pumps, elevators, and compressors. This paper includes speed control of wound induction motor using MATLAB/Simulink for rotor resistance and slip power recovery method. The characteristics of these speed control methods are hence analyzed.

Keywords: Wound rotor induction motor, MATLAB/Simulink, rotor resistance method, slip power recovery method.

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Authors: Van Thang Nguyen, Amelie Danlos, Richard Paridaens, Farid Bakir

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This article presents a study of the effect of a contra-rotating component on the efficiency of centrifugal compressors. A contra-rotating centrifugal compressor (CRCC) is constructed using two independent rotors, rotating in the opposite direction and replacing the single rotor of a conventional centrifugal compressor (REF). To respect the geometrical parameters of the REF one, two rotors of the CRCC are designed, based on a single rotor geometry, using the hub and shroud length ratio parameter of the meridional contour. Firstly, the first rotor is designed by choosing a value of length ratio. Then, the second rotor is calculated to be adapted to the fluid flow of the first rotor according aerodynamics principles. In this study, four values of length ratios 0.3, 0.4, 0.5, and 0.6 are used to create four configurations CF1, CF2, CF3, and CF4 respectively. For comparison purpose, the circumferential velocity at the outlet of the REF and the CRCC are preserved, which means that the single rotor of the REF and the second rotor of the CRCC rotate with the same speed of 16000rpm. The speed of the first rotor in this case is chosen to be equal to the speed of the second rotor. The CFD simulation is conducted to compare the performance of the CRCC and the REF with the same boundary conditions. The results show that the configuration with a higher length ratio gives higher pressure rise. However, its efficiency is lower. An investigation over the entire operating range shows that the CF1 is the best configuration in this case. In addition, the CRCC can improve the pressure rise as well as the efficiency by changing the speed of each rotor independently. The results of changing the first rotor speed show with a 130% speed increase, the pressure ratio rises of 8.7% while the efficiency remains stable at the flow rate of the design operating point.

Keywords: Centrifugal compressor, contra-rotating, interaction rotor, vacuum.

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Authors: B. X. Tchomeni, A. A. Alugongo, L. M. Masu

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This paper presents a 4-DOF nonlinear model of a cracked de Laval rotor-stator system derived based on Energy Principles. The model has been used to simulate coupled torsionallateral response of the faulty system with multiple parametric excitations; rotor-stator-rub, a breathing transverse crack, eccentric mass and an axial force. Nonlinearity of a “breathing” crack is incorporated in the model using a simple hinge mechanism suitable for a shallow crack. Response of the system while passing via its critical speed with intermittent rotor-stator rub is analyzed. Effects of eccentricity with phase and acceleration are investigated. Features of crack, rub and eccentricity in vibration response are explored for condition monitoring. The presence of a crack and rub are observable in the power spectrum despite excitations by an axial force and rotor unbalance. Obtained results are consistent with existing literature and could be adopted into rotor condition monitoring strategies.

Keywords: Axial force, Crack, Nonlinear, Rotor-Stator, Rub.

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Authors: Ben Hamed M., Sbita L

Abstract:

This paper presents a new method for the implementation of a direct rotor flux control (DRFOC) of induction motor (IM) drives. It is based on the rotor flux components regulation. The d and q axis rotor flux components feed proportional integral (PI) controllers. The outputs of which are the target stator voltages (vdsref and vqsref). While, the synchronous speed is depicted at the output of rotor speed controller. In order to accomplish variable speed operation, conventional PI like controller is commonly used. These controllers provide limited good performances over a wide range of operations even under ideal field oriented conditions. An alternate approach is to use the so called fuzzy logic controller. The overall investigated system is implemented using dSpace system based on digital signal processor (DSP). Simulation and experimental results have been presented for a one kw IM drives to confirm the validity of the proposed algorithms.

Keywords: DRFOC, fuzzy logic, variable speed drives, control, IM and real time.

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Authors: M. Najafi

Abstract:

In the present paper, a large turbo-generator shaft train including a heavy-duty gas turbine engine, a coupling, and a generator is established. The method of analysis is based on finite element simplified model for lateral and torsional vibration calculation. The basic elements of rotor are the shafts and the disks which are represented as circular cross section flexible beams and rigid body elements, respectively. For more accurate results, the gyroscopic effect and bearing dynamics coefficients and function of rotation are taken into account, and for the influence of shear effect, rotor has been modeled in the form of Timoshenko beam. Lateral critical speeds, critical speed map, damped mode shapes, Campbell diagram, zones of instability, amplitudes, phase angles response due to synchronous forces of excitation and amplification factor are calculated. Also, in the present paper, the effect of imbalanced rotor and effects of changing in internal force and temperature are studied.

Keywords: Rotor dynamic analysis, Finite element method, shaft train, Campbell diagram.

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Authors: A. Larabi, M. S. Boucherit

Abstract:

In this paper, we show that the association of the PI regulators for the speed and stator currents with a control strategy using the linearization by state feedback for an induction machine without speed sensor, and with an adaptation of the rotor resistance. The rotor speed is estimated by using the model reference adaptive system approach (MRAS). This method consists of using two models: The first is the reference model and the second is an adjustable one in which two components of the stator flux, obtained from the measurement of the currents and stator voltages are estimated. The estimated rotor speed is then obtained by canceling the difference between stator-flux of the reference model and those of the adjustable one. Satisfactory results of simulation are obtained and discussed in this paper to highlight the proposed approach.

Keywords: Asynchronous actuator, PI Regulator, adaptivemethod with reference model, Vector control.

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Authors: R. Gunabalan, V. Subbiah

Abstract:

This paper describes the speed sensorless vector control method of the parallel connected induction motor drive fed by a single inverter. Speed and rotor fluxes of the induction motor are estimated by natural observer with load torque adaptation and adaptive rotor flux observer. The performance parameters speed and rotor fluxes are estimated from the measured terminal voltages and currents. Fourth order induction motor model is used and speed is considered as a parameter. The performance of the natural observer is similar to the conventional observer. The speed of an induction motor is estimated by MATLAB simulation under different speed and load conditions. Estimated values along with other measured states are used for closed loop control. The simulation results show that the natural observer is also effective for parallel connected induction motor drive.

Keywords: natural observer, adaptive observer, sensorless control

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Authors: Ali A. Mehna, Mohmed A. Ali, Ali S. Zayed

Abstract:

A numbers of important developments have led to an increasing attractiveness for very high speed electrical machines (either motor or generator). Specifically the increasing switching speed of power electronics, high energy magnets, high strength retaining materials, better high speed bearings and improvements in design analysis are the primary drivers in a move to higher speed. The design challenges come in the mechanical design both in terms of strength and resonant modes and in the electromagnetic design particularly in respect of iron losses and ac losses in the various conducting parts including the rotor. This paper describes detailed design work which has been done on a 50,000 rpm, 50kW permanent magnet( PM) synchronous machine. It describes work on electromagnetic and rotor eddy current losses using a variety of methods including both 2D finite element analysis

Keywords: High speed, PM motor, rotor and stator losses, finiteelement analysis

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Authors: Chun-Yao Lee, Yi-Xing Shen, Jung-Cheng Cheng, Yi-Yin Li, Chih-Wen Chang

Abstract:

This paper proposes the method combining artificial neural network (ANN) with particle swarm optimization (PSO) to implement the maximum power point tracking (MPPT) by controlling the rotor speed of the wind generator. First, the measurements of wind speed, rotor speed of wind power generator and output power of wind power generator are applied to train artificial neural network and to estimate the wind speed. Second, the method mentioned above is applied to estimate and control the optimal rotor speed of the wind turbine so as to output the maximum power. Finally, the result reveals that the control system discussed in this paper extracts the maximum output power of wind generator within the short duration even in the conditions of wind speed and load impedance variation.

Keywords: Maximum power point tracking, artificial neuralnetwork, particle swarm optimization.

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Authors: Youcef Bekakra, Djilani Ben attous

Abstract:

In this paper, a field oriented control (FOC) induction motor drive is presented. In order to eliminate the speed sensor, an adaptation algorithm for tuning the rotor speed is proposed. Based on the Model Reference Adaptive System (MRAS) scheme, the rotor speed is tuned to obtain an exact FOC induction motor drive. The reference and adjustable models, developed in stationary stator reference frame, are used in the MRAS scheme to estimate induction rotor speed from measured terminal voltages and currents. The Integral Proportional (IP) gains speed controller are tuned by a modern approach that is the Particle Swarm Optimization (PSO) algorithm in order to optimize the parameters of the IP controller. The use of PSO as an optimization algorithm makes the drive robust, with faster dynamic response, higher accuracy and insensitive to load variation. The proposed algorithm has been tested by numerical simulation, showing the capability of driving load.

Keywords: Induction motor drive, field oriented control, model reference adaptive system (MRAS), particle swarm optimization (PSO).

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Authors: A. Chellil, A. Nour, S. Lecheb, H. Mechakra, A. Bouderba, H. Kebir

Abstract:

In this paper, a coupled damage effect in the instability of a composite rotor is presented, under dynamic loading response in the harmonic analysis condition. The analysis of the stress which operates the rotor is done. Calculations of different energies and the virtual work of the aerodynamic loads from the rotor blade are developed. The use of the composite material for the rotor offers a good stability. Numerical calculations on the model developed prove that the damage effect has a negative effect on the stability of the rotor. The study of the composite rotor in transient system allowed determining the vibratory responses due to various excitations.

Keywords: Rotor, composite, damage, finite element, numerical.

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Authors: Grouz Faten, Sbita Lassaâd

Abstract:

In this paper, Speed Sensorless Indirect Field Oriented Control (IFOC) of a Permanent Magnet Synchronous machine (PMSM) is studied. The closed loop scheme of the drive system utilizes fuzzy speed and current controllers. Due to the well known drawbacks of the speed sensor, an algorithm is proposed in this paper to eliminate it. In fact, based on the model of the PMSM, the stator currents and rotor speed are estimated simultaneously using adaptive Luenberger observer for currents and MRAS (Model Reference Adaptive System) observer for rotor speed. To overcome the sensivity of this algorithm against parameter variation, adaptive for on line stator resistance tuning is proposed. The validity of the proposed method is verified by an extensive simulation work.

Keywords: PMSM, Indirect Field Oriented Control, fuzzy speed and currents controllers, Adaptive Luenberger observer, MRAS.

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Authors: Hussain H. Al-Kayiem, Goh Jin Ming

Abstract:

The common practice of operating S-rotor is in an open environment; however there are times when the rotor is installed in a bounded environment and there might be changes in the performance of the rotor. This paper presents the changes in the performance of S-rotor when operated in bounded flows. The investigation was conducted experimentally to compare the performance of the rotors in bounded environment against open environment. Three different rotors models were designed, fabricated and subjected to experimental measurements. All of the three models were having 600 mm height and 300 mm Diameter. They were tested in three different flow environments; namely: partially bounded environment, fully bounded environment and open environment. Rotors were found to have better starting up capabilities when operated in bounded environment. Apart from that, all rotors manage to achieve higher Power and Torque Coefficients at a higher Tip Speed Ratio as compared to the open environment.

Keywords: Bounded Flows, Savonius Rotor, Wind Turbine, Wind energy, VAWT

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Authors: Chun-Yao Lee , Yi-Xing Shen , Jung-Cheng Cheng , Chih-Wen Chang, Yi-Yin Li

Abstract:

This paper proposes the method combining artificial neural network with particle swarm optimization (PSO) to implement the maximum power point tracking (MPPT) by controlling the rotor speed of the wind generator. With the measurements of wind speed, rotor speed of wind generator and output power, the artificial neural network can be trained and the wind speed can be estimated. The proposed control system in this paper provides a manner for searching the maximum output power of wind generator even under the conditions of varying wind speed and load impedance.

Keywords: maximum power point tracking, artificial neural network, particle swarm optimization.

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Authors: Abdul Rashid Husain, Mohamad Noh Ahmad, Abdul Halim Mohd. Yatim

Abstract:

In this paper, application of Sliding Mode Control (SMC) technique for an Active Magnetic Bearing (AMB) system with varying rotor speed is considered. The gyroscopic effect and mass imbalance inherited in the system is proportional to rotor speed in which this nonlinearity effect causes high system instability as the rotor speed increases. Transformation of the AMB dynamic model into regular system shows that these gyroscopic effect and imbalance lie in the mismatched part of the system. A H2-based sliding surface is designed which bound the mismatched parts. The solution of the surface parameter is obtained using Linear Matrix Inequality (LMI). The performance of the controller applied to the AMB model is demonstrated through simulation works under various system conditions.

Keywords: Active magnetic bearing, sliding mode control, linear matrix inequality, mismatched uncertainty and imbalance.

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Authors: M. Raciti Castelli, G. Grandi, E. Benini

Abstract:

This paper presents a numerical analysis of the performance of a three-bladed Darrieus vertical-axis wind turbine based on the DU91-W2-250 airfoil. A complete campaign of 2-D simulations, performed for several values of tip speed ratio and based on RANS unsteady calculations, has been performed to obtain the rotor torque and power curves. Rotor performances have been compared with the results of a previous work based on the use of the NACA 0021 airfoil. Both the power coefficient and the torque coefficient have been determined as a function of the tip speed ratio. The flow field around rotor blades has also been analyzed. As a final result, the performance of the DU airfoil based rotor appears to be lower than the one based on the NACA 0021 blade section. This behavior could be due to the higher stall characteristics of the NACA profile, being the separation zone at the trailing edge more extended for the DU airfoil.

Keywords: CFD, vertical axis wind turbine, DU91-W2-250, NACA 0021

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Authors: S. Grouni, R. Ibtiouen, M. Kidouche, O. Touhami

Abstract:

Induction machine models used for steady-state and transient analysis require machine parameters that are usually considered design parameters or data. The knowledge of induction machine parameters is very important for Indirect Field Oriented Control (IFOC). A mismatched set of parameters will degrade the response of speed and torque control. This paper presents an improvement approach on rotor time constant adaptation in IFOC for Induction Machines (IM). Our approach tends to improve the estimation accuracy of the fundamental model for flux estimation. Based on the reduced order of the IM model, the rotor fluxes and rotor time constant are estimated using only the stator currents and voltages. This reduced order model offers many advantages for real time identification parameters of the IM.

Keywords: Indirect Field Oriented Control (IFOC), InductionMachine (IM), Rotor Time Constant, Parameters ApproachAdaptation. Optimum rotor flux.

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Authors: G. R. Arab Markadeh, J. Soltani, N. R. Abjadi, M. Hajian

Abstract:

In this paper, a direct torque control - space vector modulation (DTC-SVM) scheme is presented for a six-phase speed and voltage sensorless induction motor (IM) drive. The decoupled torque and stator flux control is achieved based on IM stator flux field orientation. The rotor speed is detected by on-line estimating of the rotor angular slip speed and stator vector flux speed. In addition, a simple method is introduced to estimate the stator resistance. Moreover in this control scheme the voltage sensors are eliminated and actual motor phase voltages are approximated by using PWM inverter switching times and the dc link voltage. Finally, some simulation and experimental results are presented to verify the effectiveness and capability of the proposed control scheme.

Keywords: Stator FOC, Multiphase motors, sensorless.

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Authors: M. Raciti Castelli, S. De Betta, E. Benini

Abstract:

This paper presents a means for reducing the torque variation during the revolution of a vertical-axis water turbine (VAWaterT) by increasing the blade number. For this purpose, twodimensional CFD analyses have been performed on a straight-bladed Darrieus-type rotor. After describing the computational model and the relative validation procedure, a complete campaign of simulations, based on full RANS unsteady calculations, is proposed for a three, four and five-bladed rotor architectures, characterized by a NACA 0025 airfoil. For each proposed rotor configuration, flow field characteristics are investigated at several values of tip speed ratio, allowing a quantification of the influence of blade number on flow geometric features and dynamic quantities, such as rotor torque and power. Finally, torque and power curves are compared for the three analyzed architectures, achieving a quantification of the effect of blade number on overall rotor performance.

Keywords: Vertical-Axis Water Turbine, rotor solidity, CFD, NACA 0025

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Authors: Abdul Rashid Husain, Mohamad Noh Ahmad, Abdul Halim Mohd. Yatim

Abstract:

In this paper, stabilization of an Active Magnetic Bearing (AMB) system with varying rotor speed using Sliding Mode Control (SMC) technique is considered. The gyroscopic effect inherited in the system is proportional to rotor speed in which this nonlinearity effect causes high system instability as the rotor speed increases. Also, transformation of the AMB dynamic model into a new class of uncertain system shows that this gyroscopic effect lies in the mismatched part of the system matrix. Moreover, the current gain parameter is allowed to be varied in a known bound as an uncertainty in the input matrix. SMC design method is proposed in which the sufficient condition that guarantees the global exponential stability of the reduced-order system is represented in Linear Matrix Inequality (LMI). Then, a new chattering-free control law is established such that the system states are driven to reach the switching surface and stay on it thereafter. The performance of the controller applied to the AMB model is demonstrated through simulation works under various system conditions.

Keywords: Active Magnetic Bearing (AMB), Sliding ModeControl (SMC), Linear Matrix Inequality (LMI), mismatcheduncertainty.

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Authors: G. Bedon, M. Raciti Castelli, E. Benini

Abstract:

The present study aims to evaluating the effect of rotor solidity - in terms of chord length for a given rotor diameter - on the performances of a small vertical axis Darrieus wind turbine. The proposed work focuses on both power production and rotor power coefficient, considering also the structural constraints deriving from the centrifugal forces due to rotor angular velocity. Also the smoothness of the resulting power curves have been investigated, in order to evaluate the controllability of the corresponding rotor architectures.

Keywords: Vertical axis wind turbine, Darrieus, solidity, Blade Element-Momentum

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Authors: M. Raciti Castelli, E. Benini

Abstract:

This paper presents a numerical investigation of the unsteady flow around an American 19th century vertical-axis windmill: the Stevens & Jolly rotor, patented on April 16, 1895. The computational approach used is based on solving the complete transient Reynolds-Averaged Navier-Stokes (t-RANS) equations: a full campaign of numerical simulation has been performed using the k-ω SST turbulence model. Flow field characteristics have been investigated for several values of tip speed ratio and for a constant unperturbed free-stream wind velocity of 6 m/s, enabling the study of some unsteady flow phenomena in the rotor wake. Finally, the global power generated from the windmill has been determined for each simulated angular velocity, allowing the calculation of the rotor power-curve.

Keywords: CFD, vertical-axis rotor, windmill.

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Authors: Marco Raciti Castelli, Stefano De Betta, Ernesto Benini

Abstract:

This paper presents a mean for reducing the torque variation during the revolution of a vertical-axis wind turbine (VAWT) by increasing the blade number. For this purpose, twodimensional CDF analysis have been performed on a straight-bladed Darreius-type rotor. After describing the computational model, a complete campaign of simulations based on full RANS unsteady calculations is proposed for a three, four and five-bladed rotor architecture characterized by a NACA 0025 airfoil. For each proposed rotor configuration, flow field characteristics are investigated at several values of tip speed ratio, allowing a quantification of the influence of blade number on flow geometric features and dynamic quantities, such as rotor torque and power. Finally, torque and power curves are compared for the analyzed architectures, achieving a quantification of the effect of blade number on overall rotor performance.

Keywords: CFD, VAWT, NACA 0021, blade number

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Authors: Mehdi Nafar, Mohammad Reza Mansouri

Abstract:

The present research presents a direct active and reactive power control (DPC) of a wind energy conversion system (WECS) for the maximum power point tracking (MPPT) based on a doubly fed induction generator (DFIG) connected to electric power grid. The control strategy of the Rotor Side Converter (RSC) is targeted in extracting a maximum of power under fluctuating wind speed. A fuzzy logic speed controller (FLC) has been used to ensure the MPPT. The Grid Side Converter is directed in a way to ensure sinusoidal current in the grid side and a smooth DC voltage. To reduce fluctuations, rotor torque and voltage use of multilevel inverters is a good way to remove the rotor harmony.

Keywords: DFIG, power quality improvement, wind energy conversion system, WECS, fuzzy logic, RSC, GSC, inverter.

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Authors: Abdolamir Nekoubin

Abstract:

The line start permanent magnet motor (LSPMM) combines a permanent magnet rotor for a better motor efficiency during synchronous running with an induction motor squirrel cage rotor to permit the motor starting by direct coupling to power source. In this paper effect of the rotor structure on a line start synchronous permanent magnet motor (LSPMM) is analyzed. LSPMM motor with three different structures for rotor is designed by using RMxprt software; efficiency and line current of LSPMM motor for different structures in full-load condition have been presented. The results indicate that with correct choosing of rotor structure, maximum efficiency can be found.

Keywords: Permanent magnets, LSPMM motor, rotor.

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Authors: Tayfun Gundogdu, Guven Komurgoz

Abstract:

This paper presents design, analysis and comparison of the different rotor type permanent magnet machines. The presented machines are designed as having same geometrical dimensions and same materials for comparison. The main machine parameters of interior and exterior rotor type machines including eddy current effect, torque-speed characteristics and magnetic analysis are investigated using MAXWELL program. With this program, the components of the permanent magnet machines can be calculated with high accuracy. Six types of Permanent machines are compared with respect to their topology, size, magnetic field, air gap flux, voltage, torque, loss and efficiency. The analysis results demonstrate the effectiveness of the proposed machines design methodology. We believe that, this study will be a helpful resource in terms of examination and comparison of the basic structure and magnetic features of the PM (Permanent magnet) machines which have different rotor structure.

Keywords: Motor design, Permanent Magnet, Finite-Elementmethod.

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Authors: S. Lecheb, A. Nour, A. Chellil, H. Mechakra, N. Hamad, H. Kebir

Abstract:

This study concerned the dynamic behavior of the wind turbine rotor. Before all we have studied the loads applied to the rotor, which allows the knowledge their effect on the fatigue, also studied the rotor with longitudinal crack in order to determine stress, strain and displacement. Firstly we compared the first six modes shapes between cracking and uncracking of HAWT rotor. Secondly we show show evolution of first six natural frequencies with longitudinal crack propagation. Finally we conclude that the residual change in the natural frequencies can be used as in shaft crack diagnosis predictive maintenance.

Keywords: Wind turbine rotor, natural frequencies, longitudinal crack growth, life time.

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Authors: B. X. Tchomeni, A. A. Alugongo, T. B. Tengen

Abstract:

In this paper, de Laval rotor system has been characterized by a hinge model and its transient response numerically treated for a dynamic solution. The effect of the ensuing non-linear disturbances namely rub and breathing crack is numerically simulated. Subsequently, three analysis methods: Orbit Analysis, Fast Fourier Transform (FFT), and Wavelet Transform (WT) are employed to extract features of the vibration signal of the faulty system. An analysis of the system response orbits clearly indicates the perturbations due to the rotor-to-stator contact. The sensitivities of WT to the variation in system speed have been investigated by Continuous Wavelet Transform (CWT). The analysis reveals that features of crack, rubs and unbalance in vibration response can be useful for condition monitoring. WT reveals its ability to detect nonlinear signal, and obtained results provide a useful tool method for detecting machinery faults.

Keywords: Continuous wavelet, crack, discrete wavelet, high acceleration, low acceleration, nonlinear, rotor-stator, rub.

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