Permanent magnet AC (PMAC) motor drives are finding expanded use in high-performance applications where torque smoothness is essential. This paper reviews a wide range of motor- and controller-based design techniques that have been described in the literature for minimizing the generation of cogging and ripple torques in both sinusoidal and trapezoidal PMAC motor drives. Sinusoidal PMAC drives generally show the greatest potential for pulsating torque minimization using well-known motor design techniques such as skewing and fractional slot pitch windings. In contrast, trapezoidal PMAC drives pose more difficult trade-offs in both the motor and controller design which may require compromises in drive simplicity: and cost to improve torque smoothness. Controller-based techniques for minimizing pulsating torque typically involve the use of active cancellation algorithms which depend on either accurate tuning or adaptive control schemes for effectiveness. In the end, successful suppression of pulsating torque ultimately relies on an orchestrated systems approach to all aspects of the PMAC machine and controller design which often requires a carefully selected combination of minimization techniques.

Pulsating torque minimization techniques for permanent magnet AC motor drives-a review

An elastic-plastic finite element model for the frictionless contact of a deformable sphere pressed by a rigid flat is presented. The evolution of the elastic-plastic contact with increasing interference is analyzed revealing three distinct stages that range from fully elastic through elastic-plastic to fully plastic contact interface. The model provides dimensionless expressions for the contact load, contact area, and mean contact pressure, covering a large range of interference values from yielding inception to fully plastic regime of the spherical contact zone. Comparison with previous elastic-plastic models that were based on some arbitrary assumptions is made showing large differences. ©2002 ASME

Elastic-Plastic Contact Analysis of a Sphere and a Rigid Flat

This dissertation focuses on efficiently forming reduced-order models for large, linear dynamic systems. Projections onto unions of Krylov subspaces lead to a class of reduced-order models known as rational interpolants. The cornerstone of this dissertation is a collection of theory relating Krylov projection to rational interpolation. Based on this theoretical framework, three algorithms for model reduction are proposed. The first
algorithm, dual rational Arnoldi, is a numerically reliable approach involving orthogonal projection matrices. The second, rational Lanczos, is an efficient generalization of existing Lanczos-based methods. The third, rational power Krylov, avoids orthogonalization and is suited for parallel or approximate computations. The performance of the three algorithms is compared via a combination of theory and examples. Independent of the precise algorithm, a host of supporting tools are also develop ed to form a complete model-reduction package. Techniques for choosing the matching frequencies, estimating the modeling error, insuring the model's stability, treating multiple-input multiple-output systems, implementing parallelism, and avoiding a need for exact factors of large matrix
pencils are all examined to various degrees

https://tel.archives-ouvertes.fr/tel-01711328/document

Krylov Projection Methods for Model Reduction

https://orbilu.uni.lu/bitstream/10993/14191/2/iga_final.pdf

Isogeometric analysis: an overview and computer implementation aspects

This review is devoted to some inverse problems arising in the context of linear elasticity, namely the identification of distributions of elastic moduli, model parameters or buried objects such as cracks. These inverse problems are considered mainly for three-dimensional elastic media under equilibrium or dynamical conditions, and also for thin elastic plates. The main goal is to overview some recent results, in an effort to bridge the gap between studies of a mathematical nature and problems defined from engineering practice. Accordingly, emphasis is given to formulations and solution techniques which are well suited to general-purpose numerical methods for solving elasticity problems on complex configurations, in particular the finite element method and the boundary element method. An underlying thread of the discussion is the fact that useful tools for the formulation, analysis and solution of inverse problems arising in linear elasticity, namely the reciprocity gap and the error in constitutive equation, stem from variational and virtual work principles, i.e., fundamental principles governing the mechanics of deformable solid continua. In addition, the virtual work principle is shown to be instrumental for establishing computationally efficient formulae for parameter or geometrical sensitivity, based on the adjoint solution method. Sensitivity formulae are presented for various situations, especially in connection with contact mechanics, cavity and crack shape perturbations, thus enriching the already extensive known repertoire of such results. Finally, the concept of topological derivative and its implementation for the identification of cavities or inclusions are expounded.

/pdf/inverse-problems-in-elasticity-1dpbui74d3.pdf

Inverse problems in elasticity

This chapter introduces the finite element method (FEM) as a tool for solution of classical electromagnetic problems. Although we discuss the main points in the application of the finite element method to electromagnetic design, including formulation and implementation, those who seek deeper understanding of the finite element method should consult some of the works listed in the bibliography section.

Introduction to the Finite Element Method

PREFACE MATHEMATICAL PRELIMINARIES Introduction The Vector Notation Vector Derivation The Gradient The Divergence The Rotational Second-Order Operators Application of Operators to More than One Function Expressions in Cylindrical and Spherical Coordinates MAXWELL EQUATIONS, ELECTROSTATICS, MAGNETOSTATICS, AND MAGNETODYNAMIC FIELDS Introduction The EM Quantities Local Form of the Equations The Anisotropy The Approximation of Maxwell's Equations The Integral Form of Maxwell's Equations Electrostatic Fields Magnetostatic Fields Magnetodynamic Fields BRIEF PRESENTATION OF THE FINITE ELEMENT METHOD Introduction The Galerkin Method - Basic Concepts A First-Order Finite Element Program Generalization of the Finite Element Method Numerical Integration Some 2D Finite Elements Coupling Different Finite Elements Calculation of Some Terms in the Field Equation A Simplified 2D Second-Order Finite Element Program THE FINITE ELEMENT METHOD APPLIED TO 2D ELECTROMAGNETIC CASES Introduction Some Static Cases Application to 2D Eddy Current Problems Axi-Symmetric Application Advantages and Limitation of 2D Formulations Non-Linear Applications Geometric Repetition of Domains Thermal Problems Voltage-Fed Electromagnetic Devices Static Examples Dynamic Examples COUPLING OF FIELD AND ELECTRICAL CIRCUIT EQUATIONS Introduction Electromagnetic Equations Equations for Different Conductor Configurations Connections Between Electromagnetic Devices and External Feeding Circuits Examples MOVEMENT MODELING FOR ELECTRICAL MACHINES Introduction The Macro-Element The Moving Band The Skew Effect in Electrical Machines Using 2D Simulation Examples INTERACTION BETWEEN ELECTROMAGNETIC AND MECHANICAL FORCES Introduction Methods Based on Direct Formulations Methods Based on the Force Density Electrical Machine Vibrations Originated by Magnetic Forces Example of Coupling Between the Field and Circuit Equations, Including Mechanical Transients IRON LOSSES Introduction Eddy Current Losses Hysteresis Anomalous or Excess Losses Total Iron Losses The Jiles-Atherton Model The Inverse Jiles-Atherton Model Including Iron Losses in Finite Element Calculations BIBLIOGRAPHY INDEX

Electromagnetic Modeling by Finite Element Methods

This introduction to electromagnetics emphasizes the computation of electromagnetic fields and the development of theoretical relations. Beginning with the idea that Maxwell's equations are primary, the authors avoid the lengthy discussions of electro - and magneto - statics that are customary in texts on electromagnetism. After a chapter, therefore, on the basics of vector calculus, the discussion begins with the electromagnetic field and Maxwell's equations; the two following chapters then present the special cases of electrostatic and magnetostatic phenomena. Dynamics is introduced in chapter 5, and electromagnetic induction in chapter 6. The discussion of wave propagation and high-frequency fields emphasizes such practical matters as propagation in lossy dielectrics, waveguides, and resonators. The remaining four chapters discuss computational techniques; the finite element method, Galerkin's residual approach, software implementation, and recent developments in computer techniques.

Electromagnetics and calculation of fields

A modified Jiles-Atherton model presenting the magnetic induction as an independent variable is proposed in order to be directly used in time-stepping finite-element calculations applied to the magnetic vector potential formulation. This model is implemented in the field calculation procedure by introducing a differential reluctivity. The calculated results are validated by experiences performed in an Epstein's frame.

An inverse Jiles-Atherton model to take into account hysteresis in time-stepping finite-element calculations

In this paper, we present a new vector hysteresis model, which is derived from the original Jiles-Atherton scalar one. The model presents the magnetic vector induction as the independent variable. A modified Langevin equation is used to represent the anhysteretic vector magnetization, and some model aspects are discussed. A comparison between measured and calculated curves for an anisotropic soft magnetic material is performed to validate the model.

João P. A. Bastos

Papers

Introduction to the Finite Element Method

Electromagnetic Modeling by Finite Element Methods

Electromagnetics and calculation of fields

An inverse Jiles-Atherton model to take into account hysteresis in time-stepping finite-element calculations

Inverse Jiles-Atherton vector hysteresis model