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This paper aims to establish a piecewise Maxwell stress analytical model of bearingless switched reluctance motor (BSRM) for the full rotor angular positions. The proposed model varies from the existing models, which are only applicable to the partial-overlapping positions of stator and rotor poles. By extending the applicable rotor angular positions, this model provides a basic analytical model for the multi-phase excitation control of BSRM.

The full rotor angular positions are classified into the partial-overlapping positions and the non-overlapping positions. At first, two different air gap subdividing methods are proposed, respectively, for the two-position ranges. Then, different integration paths are selected accordingly. Furthermore, two approximate methods are presented to calculate the average flux density of each air gap subdivision. Finally, considering the mutual coupling between the two perpendicular radial suspension forces, a piecewise Maxwell stress analytical model is derived for the full rotor angular positions of BSRM.

A piecewise Maxwell stress analytical model of BSRM is built for the full rotor angular positions, and applicable to the multi-phase excitation mode of BSRM. For the partial-overlapping positions and the non-overlapping positions, two sets of air gap subdividing methods, integration paths and approximate calculation methods of air gap flux densities are proposed, respectively. The accuracy and reliability of the proposed model are verified by the finite element method.

The piecewise Maxwell stress analytical model of BSRM for the full rotor angular positions is proposed for the first time. The novel air gap subdividing methods, integration paths, approximate calculation methods of air gap flux densities and the coupling between the two radial suspension forces are adopted to improve the modeling accuracy. As the applicable range of rotor angular position is extended, this model overcomes the limitation of the existing models only for single-phase excitation mode and contributes to the accurate control of BSRM multi-phase excitation mode.

Discusses the 27 papers in ISEF 1999 Proceedings on the subject of electromagnetisms. States the groups of papers cover such subjects within the discipline as: induction machines; reluctance motors; PM motors; transformers and reactors; and special problems and applications. Debates all of these in great detail and itemizes each with greater in‐depth discussion of the various technical applications and areas. Concludes that the recommendations made should be adhered to.

This paper aims to propose a novel mathematical model of bearingless switched reluctance motor (BSRM). This model differs from conventional mathematical models in the calculation of torque and suspension forces. Conventional mathematical models neglect the coupling relationship between the α- and β-axes or ignore the magnetic saturation of the Si-Fe material. This study considers these issues simultaneously. Additionally, considering the air-gap edge effect, the fringing coefficient is used to establish a high-precision mathematical model.

An innovative mathematical model of BSRM based on the Maxwell stress method was established by selecting an appropriate integration path. The fringing coefficient of the air-gap was computed based on the finite element analysis results at the aligned position of the stator and rotor poles. Using the least squares fitting method, the piecewise fitted magnetization curve of the Si-Fe material was utilized to calculate flux density.

The appropriate integration path of the Maxwell stress method was selected, which considered the coupling relationship of the suspension forces in the α- and β-axes and was closer to the actual situation. The fringing coefficient of the air-gap improved the calculation accuracy of air-gap flux density. The magnetomotive force was consumed by the magnetic resistance of the stator and rotor poles considering the magnetic saturation.

A novel mathematical model of BSRM is proposed. Different from conventional mathematical models, the proposed model can effectively solve the coupling relationship of the suspension forces in the α- and β-axes. Additionally, this model is consistent with the actual situation of motor as it includes a reasonable calculation of the air-gap flux density, considering the air-gap edge effect and magnetic saturation.

This paper aims to develop a new 3D analytical model in cylindrical coordinates to study radial flux eddy current couplers (RFECC) while considering the magnetic edge and 3D curvature effects, and the field reaction due to the induced currents.

The analytical model is developed by combining two formulations. A magnetic scalar potential formulation in the air and the magnets regions and a current density formulation in the conductive region. The magnetic field and eddy currents expressions are obtained by solving the 3D Maxwell equations in 3D cylindrical coordinates with the variable separation method. The torque expression is derived from the field solution using the Maxwell stress tensor. In addition to 3D magnetic edge effects, the proposed model takes into account the reaction field effect due to the induced currents in the conducting part. To show the accuracy of the developed 3D analytical model, its results are compared to those from the 3D finite element simulation.

The obtained results prove the accuracy of the new developed 3D analytical model. The comparison of the 3D analytical model with the 2D simulation proves the strong magnetic edge effects impact (in the axial direction) in these devices which must be considered in the modelling. The new analytical model allows the magnetic edge effects consideration without any correction factor and also presents a good compromise between precision and computation time.

The proposed 3D analytical model presents a considerably reduced computation time compared to 3D finite element simulation which makes it efficient as an accurate design and optimization tool for radial flux eddy current devices.

A new analytical model in 3D cylindrical coordinates has been developed to find the electromagnetic torque in radial flux eddy current couplers. This model considers the magnetic edge effects, the 3D curvature effects and the field reaction (without correction factors) while improving the computation time.

This paper aims to reviewed analytical methodologies, i.e. lumped parameter magnetic equivalent circuit (LPMEC), magnetic co-energy (MCE), Laplace equations (LE), Maxwell stress tensor (MST) method and sub-domain modelling for design of segmented PM(SPM) consequent pole flux switching machine (SPMCPFSM). Electric machines, especially flux switching machines (FSMs), are accurately modeled using numerical-based finite element analysis (FEA) tools; however, despite of expensive hardware setup, repeated iterative process, complex stator design and permanent magnet (PM) non-linear behavior increases computational time and complexity.

This paper reviews various alternate analytical methodologies for electromagnetic performance calculation. In above-mentioned analytical methodologies, no-load phase flux linkage is performed using LPMEC, magnetic co-energy for cogging torque, LE for magnetic flux density (MFD) components, i.e. radial and tangential and MST for instantaneous torque. Sub-domain model solves electromagnetic performance, i.e. MFD and torque behaviour.

The reviewed analytical methodologies are validated with globally accepted FEA using JMAG Commercial FEA Package v. 18.1 which shows good agreement with accuracy. In comparison of analytical methodologies, analysis reveals that sub-domain model not only get rid of multiples techniques for validation purpose but also provide better results by accounting influence of all machine parts which helps to reduce computational complexity, computational time and drive storage with overall accuracy of ∼99%. Furthermore, authors are confident to recommend sub-domain model for initial design stage of SPMCPFSM when higher accuracy and low computational cost are primal requirements.

The model is developed for high-speed brushless AC applications.

The SPMCPFSM enhances electromagnetic performance owing to segmented PMs configuration which makes it different than conventional designs. Moreover, developed analytical methodologies for SPMCPFSM reduce computational time compared with that of FEA.

This paper proposes a new visco‐elastoplastic constitutive model for asphalt concretes able to reproduce the non linear time‐dependent behaviour of such materials.The constitutive model has been developed with the aim of making it fit specific experimental features previously observed. Moreover the proposed formulation will be demonstrated to be fully consistent with general thermodynamic requirements. Apart from a rigorous analytical formulation; a corresponding rheological sketch of the model is also given. From this representation, it can be shown that the model is essentially a combination of a generalized Maxwell model and a hardening visco‐plastic element.

The purpose of this paper is to compare the influence of relative density (RD) and strain rates on failure mechanism and specific energy absorption (SEA) of polyamide lattices ranging from bending to stretch-dominated structures using selective laser sintering (SLS).

Three bending and two stretch-dominated unit cells were selected based on the Maxwell stability criterion. Lattices were designed with three RD and fabricated by SLS technique using PA12 material. Quasi-static compression tests with three strain rates were carried out using Taguchi's L9 experiments. The lattice compressive behaviour was verified with the Gibson–Ashby analytical model.

It has been observed that RD and strain rates played a vital role in lattice compressive properties by controlling failure mechanisms, resulting in distinct post-yielding responses as fluctuating and stable hardening in the plateau region. Analysis of variance (ANOVA) displayed the significant impact of RD and emphasised dissimilar influences of strain rate that vary to cell topology. Bending-dominated lattices showed better compressive properties than stretch-dominated lattices. The interesting observation is that stretch-dominated lattices with over-stiff topology exhibited less compressive properties contrary to the Maxwell stability criterion, whereas strain rate has less influence on the SEA of face-centered and body-centered cubic unit cells with vertical and horizontal struts (FBCCXYZ).

This comparative study is expected to provide new prospects for designing end-user parts that undergo various impact conditions like automotive bumpers and evolving techniques like hybrid and functionally graded lattices.

To the best of the authors' knowledge, this is the first work that relates the strain rate with compressive properties and also highlights the lattice behaviour transformation from ductile to brittle while the increase of RD and strain rate analytically using the Gibson–Ashby analytical model.

In this chapter, the authors consider the role of time for research in occupational stress and well-being. First, temporal issues in studying occupational health longitudinally, focusing in particular on the role of time lags and their implications for observed results (e.g., effect detectability), analyses (e.g., handling unequal durations between measurement occasions), and interpretation (e.g., result generalizability, theoretical revision) were discussed. Then, time-based assumptions when modeling lagged effects in occupational health research, providing a focused review of how research has handled (or ignored) these assumptions in the past, and the relative benefits and drawbacks of these approaches were discussed. Finally, recommendations for readers, an accessible tutorial (including example data and code), and discussion of a new structural equation modeling technique, continuous time structural equation modeling, that can “handle” time in longitudinal studies of occupational health were provided.

The purpose of this study is to calculate the normal force of a two degree of freedom direct drive induction motor considering coupling effects based on an analytical model. Compared with the traditional single degree of freedom motor, normal force characteristics of two-degree-of-freedom direct drive induction motor (2DOFDDIM) is affected by coupling effect when the machine is in a helical motion. To theoretically explain the influence mechanism of coupling effect, this paper conducts a quantitative analysis of the influence of coupling effect on normal force based on the established analytical model of normal force considering coupling effect.

Firstly, the normal forces generated by 2DOFDDIM in linear motion, rotary motion and helical motion are investigated and compared to prove the effect of the coupling effect on the normal force. During this study, several coupling factors are established to modify the calculation equations of the normal force. Then, based on the multilayer theoretical method and Maxwell stress method, a novel normal force calculation model of 2DOFDDIM is established taking the coupling effect into account, which can easily calculate the normal force of 2DOFDDIM under different motions conditions. Finally, the calculation results are verified by the results of 3D finite element model, which proves the correctness of the established calculating model.

The coupling effect produced by the helical motion of 2DOFDDIM affects the normal force.

In this paper, the analytical model of the normal force of 2DOFDDIM considering the coupling effect is established, which provides a fast calculation for the design of the motor.

Introduces the fourth and final chapter of the ISEF 1999 Proceedings by stating electric and magnetic fields are influenced, in a reciprocal way, by thermal and mechanical fields. Looks at the coupling of fields in a device or a system as a prescribed effect. Points out that there are 12 contributions included ‐ covering magnetic levitation or induction heating, superconducting devices and possible effects to the human body due to electric impressed fields.