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The purpose of this study is to present a novel extended hybrid analytical method (HAM) that leverages a two-dimensional (2-D) coupling between the semi-analytical Maxwell–Fourier analysis and the finite element method (FEM) in Cartesian coordinates.

The proposed model is applied to flat permanent-magnet linear electrical machines with rotor-dual. The magnetic field solution across the entire machine is established by coupling an exact analytical model (AM), designed for regions with relative magnetic permeability equal to unity, with a FEM in ferromagnetic regions. The coupling between AM and FEM occurs bidirectionally (x, y) along the edges separating teeth regions and their adjacent regions through applied boundary conditions.

The developed HAM yields accurate results concerning the magnetic flux density distribution, cogging force and induced voltage under various operating conditions, including magnetic or geometric parameters. A comparison with hybrid finite-difference and hybrid reluctance network methods demonstrates very satisfactory agreement with 2-D FEM.

The original contribution of this paper lies in establishing a direct coupling between the semi-analytical Maxwell–Fourier analysis and the FEM, particularly at the interface between adjacent regions with differing magnetic parameters.

When solving the cogging torque of complex electromagnetic structures, such as consequent pole hybrid excitation synchronous (CPHES) machine, traditional methods have a huge computational complexity. The notable feature of CPHES machine is the symmetric range of field-strengthening and field-weakening, but this type of machine is destined to be equipped with a complex electromagnetic structure. The purpose of this paper is to propose a hybrid analysis method to quickly and accurately solve the cogging torque of complex 3D electromagnetic structure, which is applicable to CPHES machine with different magnetic pole shapings.

In this paper, a hybrid method for calculating the cogging torque of CPHES machine is proposed, which considers three commonly used pole shapings. Firstly, through magnetic field analysis, the complex 3D finite element analysis (FEA) is simplified to 2D field computing. Secondly, the discretization method is used to obtain the distribution of permeance and permeance differential along the circumference of the air-gap, taking into account the effect of slots. Finally, the cogging torque of the whole motor is obtained by using the idea of modular calculation and the symmetry of the rotor structure.

This method is applicable to different pole shapings. The experimental results show that the proposed method is consistent with 3D FEA and experimental measured results, and the average calculation time is reduced from 8 h to 4 min.

This paper proposes a new concept for calculating cogging torque, which is a hybrid calculation of dimension reduction and discretization modules. Based on magnetic field analysis, the 3D problem is simplified into a 2D issue, reducing computational complexity. Based on the symmetry of the machine structure, a modeling method for discretized analytical models is proposed to calculate the cogging torque of the machine.

The purpose of this paper is to propose a new combined finite-discrete element method (FDEM) to analyze the mechanical properties, failure behavior and slope stability of soil rock mixtures (SRM), in which the rocks within the SRM model have shape randomness, size randomness and spatial distribution randomness.

Based on the modeling method of heterogeneous rocks, the SRM numerical model can be built and by adjusting the boundary between soil and rock, an SRM numerical model with any rock content can be obtained. The reliability and robustness of the new modeling method can be verified by uniaxial compression simulation. In addition, this paper investigates the effects of rock topology, rock content, slope height and slope inclination on the stability of SRM slopes.

Investigations of the influences of rock content, slope height and slope inclination of SRM slopes showed that the slope height had little effect on the failure mode. The influences of rock content and slope inclination on the slope failure mode were significant. With increasing rock content and slope dip angle, SRM slopes gradually transitioned from a single shear failure mode to a multi-shear fracture failure mode, and shear fractures showed irregular and bifurcated characteristics in which the cut-off values of rock content and slope inclination were 20% and 80°, respectively.

This paper proposed a new modeling method for SRMs based on FDEM, with rocks having random shapes, sizes and spatial distributions.

This paper aims to numerically examine the impact of gyrotactic microorganisms and radiation on heat transport features of magnetic nanoliquid within a closed cavity. Thermophoresis, chemical reaction and Brownian motion are also considered in flow geometry for the moment of nanoparticles.

Finite element method (FEM) was depleted to numerically approximate the temperature, momentum, concentration and microorganisms concentration of the nanoliquid. The present simulation was unsteady state, and the resulting transformed equations are simulated by FEM-based Mathematica algorithm.

It has been found that isotherm patterns get larger with increasing values of the magnetic field parameter. Additionally, numerical codes for rate of heat transport impedance inside the cavity with an increasing Brownian motion parameter values.

To the best of the authors’ knowledge, the research work carried out in this paper is new, and no part is copied from others’ works.

This paper aims to apply the novel numerical model to analyze the effect of pillar material on the response of compound quartz crystal resonator (QCR) with an array of pillars. The performance of the proposed device compared to conventional QCR method was also investigated.

A finite element method model was developed to analyze the behavior of QCR coupled with an array of pillars. The model was composed of an elastic pillar, a solution and a perfectly matched layer. The validation of the model was performed through a comparison between its predictions and previous experimental measurements. Notably, a good agreement was observed between the predicted results and the experimental data.

The effect of pillar Young’s modulus on the coupled QCR and pillars with a diameter of 20 µm, a center-to-center spacing of 40 µm and a density of 2,500 kg/m³ was investigated. The results indicate that multiple vibration modes can be obtained based on Young’s modulus. Notably, in the case of the QCR–pillar in air, the second vibration mode occurred at a critical Young’s modulus of 0.2 MPa, whereas the first mode was observed at 3.75 Mpa. The vibration phase analysis revealed phase-veering behavior at the critical Young’s modulus, which resulted in a sudden jump-and-drop frequency shift. In addition, the results show that the critical Young’s modulus is dependent on the surrounding environment of the pillar. For instance, the critical Young’s modulus for the first mode of the pillar is approximately 3.75 Mpa in air, whereas it increases to 6.5 Mpa in water.

It was concluded that the performance of coupled QCR–pillar devices significantly depends on the pillar material. Therefore, choosing pillar material at critical Young’s modulus can lead to the maximum frequency shift of coupled QCR–pillar devices. The model developed in this work helps the researchers design pillars to achieve maximum frequency shift in their measurements using coupled QCR–pillar.

To improve the output torque density of the machine and to be better suited for automation applications, this paper aims to propose a double-permanent-magnet enhanced hybrid stepping machine (DPMEHSM) with tangential and radial magnetization.

First, the structure of DPMEHSM is introduced and its operation principle is analyzed by describing the variation in stator poles versus time. Second, based on the similar electrical load and amount of PM, the size equations of the DPMEHSM are designed and the main parameters are presented. Third, the electromagnetic performances including the PM flux linkage distribution, magnetic density distribution, air-gap field, back electromotive force (back-EMF), detent torque, holding torque and output torque of DPMEHSM and stator-PM hybrid stepping machine (SPMHSM) are analyzed based on the finite element method.

The results show that the DPMEHSM has superiority in back-EMF, holding torque and output torque.

This paper proposes a DPMEHSM with tangential and radial magnetization to improve the output torque density.

This study aims to research the time-varying mesh stiffness (TVMS) model for orthogonal face gear drives considering elastohydrodynamic lubrication (EHL) and provide a theoretical basis for understanding the dynamic characteristics of face gear drives.

Considering EHL, a novel model is proposed to calculate the TVMS of orthogonal face gears using the deformation compatibility condition. First, the tooth surface equations of orthogonal face gears are derived according to the tooth surface generation principle. Then, the oil film thickness on the tooth surface of face gears is obtained by solving the governing equations of EHL. Furthermore, the proposed model is used to calculate the TVMS of face gears along the mesh cycle and is verified. Finally, the effects of module, tooth number of shaper cutter and pressure angle on mesh stiffness are analyzed.

The results indicate that when the contact ratio is greater than 1 and less than or equal to 2, the TVMS of face gears exhibits a phenomenon of double-single tooth alternating meshing where sudden changes occur. As the module increases, the overall mesh stiffness of face gears increases, and the magnitude of the sudden change at the moment of single-double tooth alternating meshing gradually increases. As the tooth number of shaper cutter and pressure angle increase, so does the TVMS of face gears. When the effect of oil film is considered, the calculated TVMS of face gears slightly increases overall and the increase in average oil film thickness leads to a rise in the TVMS. This study provides a theoretical basis for understanding the dynamic characteristics of face gear drives.

This study’s originality and value lie in its comprehensive approach, which includes conducting analysis based on loaded tooth contact, considering the influence of elastohydrodynamic lubrication, proposing a novel analytical–finite–element model, calculating TVMS of face gears, verifying the proposed model and analyzing the effects of typical structural parameters and oil film thickness.

The purpose of this study is to model the global dynamic hysteresis properties with an improved Jiles–Atherton (J-A) model through a unified set of parameters.

First, the waveform scaling parameters β, λ_k and λ_c are used to improve the calculation accuracy of hysteresis loops at low magnetic flux density. Second, the Riemann–Liouville (R-L) type fractional derivatives technique is applied to modified static inverse J-A model to compute the dynamic magnetic field considering the skin effect in wideband frequency magnetization conditions.

The proposed model is identified and verified by modeling the hysteresis loops whose maximum magnetic flux densities vary from 0.3 to 1.4 T up to 800 Hz using B30P105 electrical steel. Compared with the conventional J-A model, the global simulation ability of the proposed dynamic model is much improved.

Accurate modeling of the hysteresis properties of electrical steels is essential for analyzing the loss behavior of electrical equipment in finite element analysis (FEA). Nevertheless, the existing inverse Jiles–Atherton (J-A) model can only guarantee the simulation accuracy with higher magnetic flux densities, which cannot guarantee the analysis requirements of considering both low magnetic flux density and high magnetic flux density in FEA. This paper modifies the dynamic J-A model by introducing waveform scaling parameters and the R-L fractional derivative to improve the hysteresis loops’ simulation accuracy from low to high magnetic flux densities with the same set of parameters in a wide frequency range.

This study aimed to analyze the free vibration of a radially graded Ni-Al2O3-based functionally graded (FG) disk with uniform thickness.

Using the energy method, natural frequencies of rotating and non-rotating disks were determined at the limit elastic angular speed. Material properties were estimated using a modified rule of mixture. Both even and uneven porosity variation effects were considered in the material modeling. Finite element analysis validated the analytical approach.

The study explored limit angular speeds and natural frequencies across various grading indices, investigating the impact of porosity types and grading indices on these parameters.

Insights from this research are valuable for researchers and design engineers involved in modeling and fabricating porous FG disks, aiding in more effective design and manufacturing processes.

This study contributes to the field by providing a comprehensive analysis of free vibration behavior in radially graded Ni-Al2O3-based FG disks. The incorporation of material modeling considering both even and uneven porosity variation adds originality to the research. Additionally, the validation through finite element analysis enhances the credibility of the findings.

This study aims to use regression Least-Square Support Vector Machine (LS-SVM) as a probabilistic model to determine the factor of safety (FS) and probability of failure (PF) of anisotropic soil slopes.

This research uses machine learning (ML) techniques to predict soil slope failure. Due to the lack of analytical solutions for measuring FS and PF, it is more convenient to use surrogate models like probabilistic modeling, which is suitable for performing repetitive calculations to compute the effect of uncertainty on the anisotropic soil slope stability. The study first uses the Limit Equilibrium Method (LEM) based on a probabilistic evaluation over the Latin Hypercube Sampling (LHS) technique for two anisotropic soil slope profiles to assess FS and PF. Then, using one of the supervised methods of ML named LS-SVM, the outcomes (FS and PF) were compared to evaluate the efficiency of the LS-SVM method in predicting the stability of such complex soil slope profiles.

This method increases the computational performance of low-probability analysis significantly. The compared results by FS-PF plots show that the proposed method is valuable for analyzing complex slopes under different probabilistic distributions. Accordingly, to obtain a precise estimate of slope stability, all layers must be included in the probabilistic modeling in the LS-SVM method.

Combining LS-SVM and LEM offers a unique and innovative approach to address the anisotropic behavior of soil slope stability analysis. The initiative part of this paper is to evaluate the stability of an anisotropic soil slope based on one ML method, the Least-Square Support Vector Machine (LS-SVM). The soil slope is defined as complex because there are uncertainties in the slope profile characteristics transformed to LS-SVM. Consequently, several input parameters are effective in finding FS and PF as output parameters.