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The purpose of the work is to model disproportions in development of regional economy of Russia and to determine perspectives and recommendations for overcoming them and achieving the balance of the economy. The applied methods are based on Popkova's methodology of calculation of “underdevelopment whirlpools,” which allows conducting dynamic modeling of disproportions in development of regional economy. The research is performed in three consecutive stages. At the first stage, the dynamic model of development of the Russia's regional economy is compiled with the help of the methodology of “underdevelopment whirlpools” in federal districts of the Russian Federation based on GDP per capita. At the second stage, the key factors of emergence of disproportions in development of the Russia's regional economy are determined and models of multiple regression of development of the Russia's regional economy are compiled. At the third stage, target parameters of the determined factors are set for reducing the “underdevelopment whirlpools” in the Russia's regional economy by automatized solution of the optimization task with application of the simplex method and recommendations for overcoming the disproportions in development of the Russia's regional economy are compiled. As a result, it is concluded that regional economy of Russia is not well-balanced, as it has deep structural disproportions. These disproportions are caused by insufficient attention to peculiarities of regional economic systems during development and implementation of regional strategies of state management of economy. For more precise accounting of the influence of the key factors of appearance of disproportions and highly-effective management of them for overcoming the “underdevelopment whirlpools,” the algorithm of overcoming the disproportions in development of the Russia's regional economy is developed by the authors, which envisages various managerial measures depending on peculiarities of each Russian region.

Due to high electromagnetic torque at low speed, vernier machines are suitable for direct-drive applications such as electric vehicles and wind power generators. The purpose of this paper is to present an exact sub-domain model for analytically predicting the open-circuit magnetic field of permanent magnet vernier machine (PMVM) including tooth tips. The entire field domain is divided into five regions, viz. magnets, air gap, slot openings, slots, and flux-modulation pole slots (FMPs). The model accounts for the influence of interaction between PMs, FMPs and slots, and radial/parallel magnetization.

Magnetic field distributions for slot and air-gap, flux linkage, back-EMF and cogging torque waveforms are obtained from the analytical method and validated by finite element analysis (FEA).

It is found that the developed sub-domain model including tooth tips is very accurate and is applicable to PMVM having any combination of slots/FMPs/PMs.

The main contributions include: accurate sub-domain model for PMVM is proposed for open-circuit including tooth-tip which cannot be accounted for in literature; the model accounts the interaction between flux modulation pole (FMP) and slot; developed sub-domain model is accurate and applicable to any slot/FMP/PM combinations; and it has investigated the influence of FMP/slot opening width/height on cogging torque.

An analytical sub-domain model is developed for predicting the armature magnetic field in permanent magnet vernier machine (PMVM) which has either non-overlapping or overlapping windings. The developed model accounts for tooth-tips and flux modulation pole slots (FMPs). The paper aims to discuss these issues.

It is obtained by solving Poisson’s and Laplace’s equations in polar coordinates for each sub-domain, i.e. air gap, slots, slot openings at tooth-tips and FMP slots. Armature reaction field distributions in slots, slot openings FMPs, air-gap and magnet region and winding inductances are obtained from the analytical method and compared by finite element analysis.

It is found that the developed model can be employed to accurately predict the armature field and winding inductance for any combination of slots/FMPs/permanent magnets. In addition, it is observed that the winding inductance is high which results in significant armature reaction and poor power factor in PMVM.

The main contributions include: first, accurate sub-domain model for PMVM is proposed for armature reaction which is not addressed in literature; second, the model accounts the interaction between FMP and slot; and finally, developed sub-domain model is also used for inductance calculation.

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 study aims to extract an analytical model for five-phase fault-tolerant permanent-magnet vernier machines (FTPMVMs) based on the analytical solution of Maxwell’s equations, which has some advantages than the finite element model.

FTPMVMs enhance the torque density by combining the vernier characteristics and the fault-tolerant feature. The principle operation of FTPMVMs is discussed based on the magnetic field modulation due to both permanent magnets and armature current. The analytical solution of the magnetic vector potential in each sub-region is obtained based on the sub-domain technique.

According to the calculated magnetic vector potential, the magnetic flux density, torque, self- and mutual inductance and back-electromotive force are calculated. The FEM is used to validate the results obtained from the proposed analytic model.

Two-dimensional analytical method is used to obtain the electromagnetic model of FTPMVMs.

The purpose of this paper is to analytically predict the on-load field distribution and electromagnetic performance (induced voltage, electromagnetic torque, winding inductances and unbalanced magnetic force) of dual-stator consequent-pole permanent magnet (DSCPPM) machines using subdomain model accounting for tooth-tip effect. The finite element (FE) results are presented to validate the accuracy of this subdomain model.

During the preliminary design and optimization of DSCPPM machines, FE method requires numerous computational resources and can be especially time-consuming. Thus, a subdomain model considering the tooth-tip effect is presented in this paper. The whole field domain is divided into four different types of sub-regions, where the analytical solutions of vector potential in each sub-region can be rapidly calculated. The proposed subdomain model can accurately predict the on-load flux density distributions and electromagnetic performance of DSCPPM machines, which is verified by FE method.

The radial and tangential components of flux densities in each sub-region of DSCPPM machine can be obtained according to the vector potential distribution, which is calculated based on the boundary and interface conditions using variable separation approach. The tooth-tip effect is investigated as well. Moreover, the phase-induced voltage, winding inductances, electromagnetic torque and X-axis/Y-axis components of unbalanced magnetic forces are calculated and compared by FE analysis, where excellent agreements are consistently exhibited.

The on-load field distributions and electromagnetic performance of DSCPPM machines are analytically investigated using subdomain method, which can be beneficial in the process of initial design and optimization for such DSCPPM machines.

This paper aims to propose a semianalytical model of a squirrel-cage induction machine (SCIM), considering local magnetic saturation and eddy-currents induced in the rotor bars.

The regions of the rotor and stator are divided into elementary subdomains (E-SDs) characterized by general solutions at the first harmonic of the magneto-harmonic Maxwell’s equations. These E-SDs are connected in both directions (i.e., along the r- and θ-edges).

The calculation of the magnetic field has been validated for various values of slip and iron permeability. All electromagnetic quantities were compared with those obtained using a two-dimensional finite-element method. The semianalytical results are satisfactory compared with the numerical results, considering both the amplitude and waveform.

Expansion of the recent analytical model (E-SD technique) for the full prediction of the magnetic field in SCIMs, considering the local saturation effect and the eddy-currents induced in the rotor bars.

This study aims to accurately calculate the magnetic field distribution, which is a prerequisite for pre-design and optimization of electromagnetic performance. Accurate calculation of magnetic field distribution is a prerequisite for pre-design and optimization.

This paper proposes an analytical model of permanent magnet machines with segmented Halbach array (SHA-PMMs) to predict the magnetic field distribution and electromagnetic performance. The field problem is divided into four subdomains, i.e. permanent magnet, air-gap, stator slot and slot opening. The Poisson’s equation or Laplace’s equation of magnetic vector potential for each subdomain is solved. The field’s solution is obtained by applying the boundary conditions. The electromagnetic performances, such as magnetic flux density, unbalanced magnetic force, cogging torque and electromagnetic torque, are analytically predicted. Then, the influence of design parameters on the torque is explored by using the analytical model.

The finite element analysis and prototype experiments verify the analytical model’s accuracy. Adjusting the design parameters, e.g. segments per pole and air-gap length, can effectively increase the electromagnetic torque and simultaneously reduce the torque ripple.

The main contribution of this paper is to develop an accurate magnetic field analytical model of the SHA-PMMs. It can precisely describe complex topology, e.g. arbitrary segmented Halbach array and semi-closed slots, etc., and can quickly predict the magnetic field distribution and electromagnetic performance simultaneously.

This paper aims to study microwave pad dyeing process for wool fabric. Influences of various dyeing process conditions including galactomannan dosage, urea dosage, sodium bisulphite dosage, pH value, microwave irradiation power, treating time and cold batching time before microwave fixation on K/S values were analysed. The colour yield, fixation and levelness were compared between microwave fixation and cold batching fixation.

Colour yield (K/S values) was calculated using a Datacolor SF650 colour measuring and matching instrument (10° standard observer, CIE D65 light source Measuring; Datacolor, USA) and was used to determine the depth of the shade of dyed wool fabrics. Levelness of dyeing was evaluated also using the Datacolor SF650 colour measuring and matching instrument by measuring average deviation (S), range (P) of the maximum and the minimum for lightness (L), chroma (C) and hue (h), and balanced colour difference (ΔE) at 20 specified uniform locations on the wool fabrics. The colour difference was calculated as per the equation ΔE=(ΔL2+Δa2+Δb2)1/2 as appearing in the Experimental section. Fixation was determined using a Datacolor SF650 colour measuring and matching instrument by measuring ratio the of K/S for wool fabrics that were rinsed, washed, neutralised and then dried, and wool fabrics that were dried after fixation without washing. The pH of the padding solution was evaluated using a PHSJ-4A PH meter (Datacolor, USA). SEM analysis was done on JEOL JSM-5600LV machine (JEOL Ltd, Japan).

This study is based on application of microwave technology in the processing of silk.

It was found in laboratory experiments that uniform dyeing and deeper colour can be achieved throughout the microwave pad dyeing process for wool by using galactomannan. The novel process could reduce the dyeing time and the energy consumption of the traditional cold pad-batch dyeing process for wool fabric.

In semi-analytical modeling of spoke-type permanent-magnet (PM) machines (STPMM), the saturation effect is usually neglected (i.e. iron parts are considered to be infinitely permeable) and the PM magnetization is assumed tangential (i.e. magnetization pattern is considered to be tangential-parallel). This paper aims to present an improved two-dimensional (2D) subdomain technique for STPMM with the PM magnetization orientation in quasi-Cartesian coordinates by using hyperbolic functions considering non-homogeneous Neumann boundary conditions (BCs) in non-periodic regions and by applying the interfaces conditions (ICs) in both directions (i.e. t- and θ edges ICs).

The polar coordinate system is transformed into a quasi-Cartesian coordinate system. The rotor and stator regions are divided into primary subdomains, and a partial differential equation (PDE) is assigned to each subdomain. In the PM region, the magnetization orientation is considered in the equations. By applying BCs, the general solution of the equations is determined, and by applying the ICs, the corresponding coefficients are determined.

Using the proposed coordinate system, the general solution of PDEs and their coefficients can mathematically be simplified. The magnetic field and non-intrinsic unbalanced magnetic forces (UMF) calculations have been performed for three different values of iron core relative permeability (200, 800 and ∞), as well as different magnetization orientation values (135 and 80 degrees). The semi-analytical model based on the subdomain technique is compared with those obtained by the 2D finite-element analysis (FEA). Results disclose that the PM magnetization angle can affect directly the performance characteristics of the STPMM.

A new model for prediction of electromagnetic performances in the STPMM takes into account magnetization direction, and soft magnetic material relative permeability in a pseudo-Cartesian coordinate system by using subdomain technique is presented.