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In the electromagnetic field simulation of modern servo drives, the computation of higher time and space harmonics is essential to consider appearing torque pulsations, radial forces and ripple torques. The purpose of this paper is to propose a method to cover the effect of saturation on the armature flux density within conformal mapping (CM) by an finite element (FE) re‐parameterization.

Field computation by CM techniques is a time‐effective method to compute the radial and tangential field components, but it generally neglects the effect of saturation.

This paper presents a method to re‐parameterize the CM approach by single FE computations so as to consider saturation in the model over a wide operation range of the electrical drive.

The proposed method is applied to a surface permanent magnet synchronous machine, and compared to numerical results obtained by finite element analysis (FEA).

The paper shows that an accuracy similar to that of FE simulations can be obtained with still the low‐computation time that is the characteristic of analytical models.

The purpose of this paper is to present an improved conformal mapping (ICM) method that simultaneously considers the influence of relative recoil permeability of PMs, the armature reaction, the stator slotting, and the magnetic saturation on determination of the PM operating point in its different parts.

The ICM method is a time-effective method that considers the magnetic saturation by suitable increments in air-gap length under each tooth and also the width of slot openings. In this paper, the analytical and numerical conformal mappings such as the Schwarz-Christoffel (SC) mapping are used for magnetic field analysis due to the permanent magnets and the armature reaction in one slotted air gap. The field solution in the slotted air gap is obtained through the modulation of field solution in one slotless air-gap using the complex air-gap permeance.

The ICM method can consider the magnetic saturation in different electric loadings, and also the variation of PM operating points in its different parts.

The ICM method is applied to one surface mounted permanent magnet (SMPM) motor and is verified by comparing with the corresponding results obtained through finite element method (FEM), and frozen permeability finite element method (FP-FEM).

This paper presents an ICM method with a new technique for saturation effect modeling, which can be used to separate and calculate the on-load components of air-gap field and torque.

The purpose of this paper is to present a new optimal design for integral slot permanent magnet synchronous motors (PMSMs) to shape the air-gap magnetic field in sinusoidal and to reduce the cogging torque, simultaneously.

For obtaining this new optimal design, the influence of different magnetizations of permanent magnets (PMs), including radial, parallel and halbach magnetization is investigated on the performance of one typical PMSM by using the conformal mapping (CM) method. To reduce the cogging torque even more, the technique of slot opening shift is also implemented on the stator slots of analyzed PMSM without reduction in the main performance, including the air-gap magnetic field, the average torque and back-electromotive force (back-EMF).

Finally, an optimal configuration including the Hat-type magnet poles with halbach magnetization on the rotor and shifted slot openings on the stator is obtained through the CM method, which shows the main reduction in cogging torque and the harmonic content of air-gap magnetic field.

The obtained optimal design is completely practical and is validated by comparing with the corresponding results obtained through finite element method.

This paper presents a new optimal design for integral slot PMSMs, which can include different design considerations, such as the reduction of cogging torque and the total harmonic distortion of air-gap magnetic field by using the CM method.

In the optimisation of electrical drives, the required degree of detail in the simulation increases constantly. Especially, the industrial demand on multi‐objective optimisation craves for highly efficient models. The purpose of this paper is to propose a hybrid model for the computation of the air‐gap field of a permanent magnet synchronous motor (PMSM) combining analytic and numeric methods.

The classic conformal mapping (CM) approach is improved by the numeric approximation of the required ansatz‐functions. This approach allows to consider the non‐linear permeability of the applied materials and complex geometries. The non‐linear permeance‐function is described by a one‐dimensional wave varying in time and space.

The permeance‐function has to be derived for different load cases at the actual stage.

A physical motivated modelling allowing for an appropriate interpolation between different load cases is planned in further research.

The proposed approach is applied to a surface mounted PMSM. It is validated by means of a non‐linear finite element analysis.

The hybrid model offers to consider rotors with buried magnets using the CM approach. It is possible to either use analytic or numeric modelling of rotor ansatz‐function, stator current ansatz‐function and permeance‐function with the proposed approach. Non‐linear permeability of iron is modelled by means of a wave representation of the permeance‐function. This can significantly reduce the computational cost in the design and optimisation stage of electrical machines.

The purpose of this paper is to present an improved winding function theory (IWFT) for performance analysis of surface mounted permanent magnet (SMPM) motors, which can precisely and simultaneously consider the impacts of stator slotting, the winding distribution, the magnetic flux density within PMs because of the armature reaction, the PM magnetization angle and the magnetic saturation,.

To obtain this improved analytical model, the conformal mappings (CMs) are introduced to calculate the relative complex permeance of slotted air-gap, which is used to obtain the function of slotted air-gap length. The equivalent magnetizing current model is used to extract the equivalent winding function for each PM pole. For retaining the basic assumption of WFT, the magnetic saturation is also considered by a proper increase in the air-gap length in the front of the stator teeth.

A new hybrid analytical model (HAM) based on WFT is presented in this paper, which can simultaneously and accurately consider the effects of slotting, the magnetic saturation, the variation of PM operating point and the winding distribution. In fact, IWFT removes all the drawbacks of the conventional WFT. Moreover, IWFT is more user-friendly and faster than other analytical and numerical techniques.

The obtained HAM can be used for design, optimization and fault diagnosis in electric machines.

This paper presents a new HAM for accurate modeling the SMPM motors, which includes different considerations of electromagnetic modeling. This new HAM can also be used for modeling the other electric motors.

In this paper, the polygonal-FEM technique is presented in modeling large deformation – large sliding contact on non-conformal meshes. The purpose of this paper is to present a new technique in modeling arbitrary interfaces and discontinuities for non-linear contact problems by capturing discontinuous deformations in elements cut by the contact surface in uniform non-conformal meshes.

The geometry of contact surface is used to produce various polygonal elements at the intersection of the interface with the regular FE mesh, in which the extra degrees-of-freedom are defined along the interface. The contact constraints are imposed between polygonal elements produced along the contact surface through the node-to-surface contact algorithm.

Numerical convergence analysis is carried out to study the convergence rate for various polygonal interpolation functions, including the Wachspress interpolation functions, the metric shape functions, the natural neighbor-based shape functions, and the mean value shape functions. Finally, numerical examples are solved to demonstrate the efficiency of proposed technique in modeling contact problems in large deformations.

A new technique is presented based on the polygonal-FEM technique in modeling arbitrary interfaces and discontinuities for non-linear contact problems by capturing discontinuous deformations in elements cut by the contact surface in uniform non-conformal meshes.

The purpose of this paper is the more exact evaluation of distorted constriction contact resistance between two clamped slabs or thin films, having a bi-dimensional current lines structure.

Mathematical modeling using conformal mappings.

The influence of the tarnish film on the distorted constriction resistance is clarified and three new exact formulas are proposed for the distorted constriction resistance between clamped slabs with rectangular contact spot. Comparisons with early proposed formula for constriction resistance of slab narrowing and with finite element analysis results are presented.

The research is limited to direct current and homogeneous and isotropic media and the results can be extended at alternate current when the skin effect is negligible.

Exact evaluation of 2D constriction contact resistance which appears in macro-scale contacts electrical equipment and in MEMS devices, particularly in crimp contacts.

The proposed formulas are new, original, simple and exact.

A novel method for modelling permanent magnets is investigated based on numerical approximations with rational functions. This study aims to introduce the AAA algorithm and other recently developed, cutting-edge mathematical tools, which provide outstandingly fast and accurate numerical computation of potentials and vector fields.

First, the AAA algorithm is briefly introduced along with its main variants and other advanced mathematical tools involved in the modelling. Then, the analysis of a circular Halbach array with a one-pole pair is carried out by means of the AAA-least squares method, focusing on vector potential and flux density in the bore and validating results by means of classic finite element software. Finally, the investigation is completed by a finite difference analysis.

AAA methods for field analysis prove to be strikingly fast and accurate. Results are in excellent agreement with those provided by the finite element model, and the very good agreement with those from finite differences suggests future improvements. They are also easy programming; the MATLAB code is less than 200 lines. This indicates they can provide an effective tool for rapid analysis.

AAA methods in magnetostatics are novel, but their extension to analogous physical problems seems straightforward. Being a meshless method, it is unlikely that local non-linearities can be considered. An aspect of particular interest, left for future research, is the capability of handling inhomogeneous domains, i.e. solving general interface problems.

The authors use cutting-edge mathematical tools for the modelling of complex physical objects in magnetostatics.

This paper describes a technique for computing characteristic impedance and capacitance of transmission lines using the finite‐element method, which guarantees both upper and lower bounds to the exact solution without any additional programming beyond that required for the initial problem description. The paper also attempts to simplify the essential steps of pre‐processing of data while maintaining flexibility of the method.

The purpose of this paper is to develop a process chain for design and manufacture of endplates of intervertebral disc implants, with specific emphasis on designing footprint profiles and matching endplate geometry.

Existing techniques for acquiring patient‐specific information from CT scan data was and a user‐friendly software solution was developed to facilitate pre‐surgical planning and semi‐automated design. The steps in the process chain were validated experimentally by manufacturing Ti6Al4 V endplates by means of Direct Metal Laser Sintering to match vertebrae of a cadaver and were tested for accuracy of the implant‐to‐bone fitment.

Intervertebral disc endplates were successfully designed and rapid manufactured using a biocompatible material. Accuracy within 0.37 mm was achieved. User‐friendly, semi‐automated design software offers an opportunity for surgeons to become more easily involved in the design process and speeds up the process to more accurately develop a custom‐made implant.

This research is limited to the design and manufacture of the bone‐implant contacting interface. Other design features, such as keels which are commonly used for implant fixation as well as the functionality of the implant joint mechanics were not considered as there may be several feasible design alternatives.

This research may change the way that current intervertebral disc implants are designed and manufactured.

Apart from other areas of application (cranial, maxillofacial, hip, knee, foot) and recent research on customized disc nucleus replacement, very little work has been done to develop patient‐specific implants for the spine. This research was conducted to contribute and provide much needed progress in this area of application.