Harmonics in the Squirrel Cage Induction Motor,Analytic Calculation Part Ⅱ:Synchronous Parasitic Torques,Radial Magnetic Forces

The magnetic field generated in the air gap of the cage asynchronous machine and the harmonics of the magnetomotive forces creating that magnetic field,as well as the synchronous parasitic torques,radial magnetic forces have been discussed in great detail in the literature,but always separately,for a long time.However,systematization of the phenomenon still awaits.Therefore,it is worth summarizing the completeness of the phenomena in a single study–with a new approach at the same time-in order to reveal the relationships between them.The role of rotor slot number is emphasized much more than before.New formulas derived for both synchronous torques and radial magnetic forces are used for further investigation.It will be shown that both phenomena in subject must be treated together.Formulas will be provided to take into account attenuation.Design guide will be provided to avoid dangerous rotor slot numbers.It will be shown that the generation of synchronous torques and radial magnetic forces do not depend–in this new approach-on the slot combination,but on the rotor slot number itself.

Modeling and Analysis of Novel Integrated Radial Hybrid Magnetic Bearing for Magnetic Bearing Reaction Wheel

Conventional ball bearing reaction wheel used to control the attitude of spacecraft can＇t absorb the centrifugal force caused by imbalance of the wheel rotor,and there will be a torque spike at zero speed,which seriously influences the accuracy and stability of spacecraft attitude control.Compared with traditional ball-bearing wheel,noncontact and no lubrication are the remarkable features of the magnetic bearing reaction wheel,and which can solve the high precision problems of wheel.In general,two radial magnetic bearings are needed in magnetic bearing wheel,and the design results in a relatively large axial dimension and smaller momentum-to-mass ratios.In this paper,a new type of magnetic bearing reaction wheel（MBRW） is introduced for satellite attitude control,and a novel integrated radial hybrid magnetic bearing（RHMB） with permanent magnet bias is designed to reduce the mass and minimize the size of the MBRW,etc.The equivalent magnetic circuit model for the RHMB is presented and a solution is found.The stiffness model is also presented,including current stiffness,position negative stiffness,as well as tilting current stiffness,tilting angular position negative stiffness,force and moment equilibrium equations.The design parameters of the RHMB are given according to the requirement of the MBRW with angular momentum of 30 N ？ m ？ s when the rotation speed of rotor reaches to 5 kr/min.The nonlinearity of the RHMB is shown by using the characteristic curves of force-control current-position,current stiffness,position stiffness,moment-control current-angular displacement,tilting current stiffness and tilting angular position stiffness considering all the rotor position within the clearance space and the control current.The proposed research ensures the performance of the radial magnetic bearing with permanent magnet bias,and provides theory basis for design of the magnetic bearing wheel.

Mechanical Characteristics of Radial Magnetic Bearing

This paper is based on the example of a radial magnetic bearing possessed of eight-pole, and derives the calculation formulas of static and dynamic mechanical characteristics of the bearing, in which the shape and curvature of surface, eccentricity and tilt of the journal are taken into account. Variations of the static and dynamic characteristics of the radial magnetic bearing versus static tilt parameters of journal are discussed. The outcomes show that the static tilt of the journal has influence on the mechanical characteristics of radial magnetic bearing, and change the static load capacity between two radial magnetic bearings and exert coupling effect between them. To study the dynamics of a practical rotor-magnetic bearing system, at least six stiffness coefficients in each radial magnetic bearing must be considered in ideal case, and twelve stiffness coefficients must be considered in general case of tilting journal. Such a find can be used for the coupled electromechanical dynamics analysis of rotor system equipped with magnetic bearings.

Convective heat and mass transfer in MHD mixed convection flow of Jeffrey nanofluid over a radially stretching surface with thermal radiation

Mixed convection flow of magnetohydrodynamic(MHD) Jeffrey nanofluid over a radially stretching surface with radiative surface is studied. Radial sheet is considered to be convectively heated. Convective boundary conditions through heat and mass are employed. The governing boundary layer equations are transformed into ordinary differential equations. Convergent series solutions of the resulting problems are derived. Emphasis has been focused on studying the effects of mixed convection, thermal radiation, magnetic field and nanoparticles on the velocity, temperature and concentration fields. Numerical values of the physical parameters involved in the problem are computed for the local Nusselt and Sherwood numbers are computed.

Optimization of rotor shape for constant torque improvement and radial magnetic force minimization

The design of notch and barrier was optimized in order to improve the characteristics of constant torque while minimizing the cogging torque that occurs as a result of teeth and slot structure. The barrier was installed in order to minimize the cogging torque and torque ripple by finite element method (FEM) with a reduced barrier width toward the center of magnetic pole. The position and width of notch, which can offset cogging torque, can be calculated with energy distribution of air-gap using Fourier series. The optimized model demonstrates a 60% decrease in the cogging torque, a 75.3% decrease in the torque ripple and a 3% increase in the operating torque when compared with the basic model.

Radial magnetic field in magnetic confinement device

The intrinsic radial magnetic field（B r） in a tokamak is explored by the solution of the Grad–Shafranov equation in axisymmetric configurations through an expansion of the four terms of the magnetic surfaces. It can be inferred from the simulation results that at the core of the device, the tokamak should possess a three-dimensional magnetic field configuration, which could be reduced to a two-dimensional one when the radial position is greater than 0.6a. The radial magnetic field and the amzimuthal magnetic field have the same order of magnitude at the core of the device. These results can offer a reference for the analysis of the plasma instability, the property of the core plasma, and the magnetic field measurement.

EMF Waveform Optimization using the Permanent Magnet Volume-Integration Method

The emf expression can be derived with the PM volume-integration method,allowing easier optimization and prediction of the emf harmonic content.An analytical expression is developed for predicting the electromotive force(emf)waveforms and flux linkage resulting from the motion of permanent magnets(PM)in the case of two cylinders,where the outer cylinder carries a surface-mounted winding and the inner cylinder carries the PMs.The expressions are based on the PM Volume-Integration Method,which uses a volume integral calculated over the magnet volume,rather than the usual surface integral over the coil surface.The specific case of surface-mounted arc PM with radial magnetization is analyzed.An outer cylinder with infinitely thin winding distribution on its inner surface is considered.The chording factor,slot factor and spread factor are included in the analytical expression.The emf waveform and related harmonics are predicted analytically and validated by comparing with a finite element analysis and with experiment.

Rare earth permanent magnets prepared by hot deformation process

Hot deformation is one of the primary methods for fabricating anisotropic rare earth permanent magnets.Firstly,rapidly quenched powder flakes with a nanocrystal structure are condensed into fully dense isotropic precursors using the hot-pressing process.The prepared isotropic precursors are then hot-deformed to produce high-anisotropy uniaxial bulk rare earth permanent magnets and a highly textured structure is produced via this process.The resulting magnets possess many advantages such as near-net-shape,outstanding corrosion resistance,and ultrafine-grain structure.The influence of the preparation parameters utilized in the hot-pressing and deformation processes on the magnetic properties and microstructure of the permanent magnets are systemically summarized in this report.As a near-net-shape technique,the hot deformation process has notable advantages with regard to the production of irregular shapes,especially for radially oriented ringshaped magnets with high length-diameter ratios or thin walls.The difficulties associated with the fabrication of crack-free,homogeneous,and non-decentered ring-shaped magnets are substantially resolved through an emphasis on mold design,adjustment of deformation parameters,and application of theoretical simulation.Considering the characteristics of hotdeformed magnets which include grain shape and size,anisotropic distribution of intergranular phases,etc.,investigation and improvement of the mechanical and electric properties,in addition to thermal stability,with the objective of improving the application of hot-deformed magnets or ring-shaped magnets,is of practical significance.

Mechanical Characteristics of a Thrust Magnetic Bearing

Static and dynamic mechanical characteristics of a thrust magnetic bearing are studied owing to the inclination of the runner disk. The application refers to a thrust magnetic bearing for a turbo expander/compressor. The static tilt of the runner disk has remarkable influence on the mechanical characteristics of thrust magnetic bearing, it can change the static load distribution between two radial magnetic bearings and will exert violent coupling effect among a thrust magnetic bearing and two radial magnetic bearings. Such a finding can be used for the coupled electromechanical dynamics analysis of rotor system equipped with magnetic bearings.

Calculating magnetic shielding effectiveness for high-power dc comparator by magnetic circuit method

Magnetic shielding is very important in the design of a high-power dc comparator. This paper addressed the application of magnetic circuit method to calculate the magnetic shielding effectiveness of high-power dc comparators when an external radial magnetic field is added. The mathematical relationship between the magnetic shielding effectiveness and the parameters of the magnetic shielding body were obtained. To verify the validity of the calculation method, we developped a procedure to measure the magnetic shielding effectiveness of the magnetic body by measuring the induction voltage of the detection winding instead of the magnetic intensity at a point in the magnetic shielding body, making the manipulation much easier. The result calculated with the magnetic circuit method turns out to be closer to the measured one compared with that calculated with a conventional algorithm proposed by Ren, suggesting that the magnetic circuit method is an applicable tool for estimating the toroidal cavity magnetic shielding effectiveness of a heavy current comparator when a radial magnetic field is added.

Entropy generation under the influence of radial magnetic field and viscous dissipation of generalized Couette flow in an annulus

This paper investigates the combined effect of radial magnetic field and viscous dissipation on entropy generation in horizontal co-axial cylinders of generalized Couette flow.The analytical solutions for velocity and temperature profiles are obtained and utilized to compute the entropy generation,Bejan number as well as the average entropy generation number.The effect of relevant parameters on temperature field,velocity field,entropy generation,average entropy and Bejan number are portrayed graphically and discussed.We isoflux heating near the inner surface of the fixed outer cylinder with higher dominance in the case of isoflux heating.The reverse is seen on the moving inner cylinder.