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The purpose of this paper is to introduce a novel cross (+) type yoke with hybrid electromagnets and new reluctance modeling to precisely calculate attraction force is given.

The comparison of attraction force and torque analyses between the proposed formulation and the existing formulation in the literature is comparatively presented. For the correctness of the force and torque values calculated in the model created, the system was created in ANSYS Maxwell and its accuracy was proved by making analyses. The maglev carrier system is inherently unstable from the point of view of control engineering. For that, it needs an active controller to eliminate this instability. For the levitation of the carrier system, it is necessary to design a controller in three axes (z, α and β). I-PD controller was designed for the air gap control of the carrier system in three axes and the controller parameters were determined by the canonical method.

While the new formulation proposed in the modeling of the carrier system has a maximum error of 1.03%, the existing formula in the literature has an error of 16.83% in the levitation distance point.

A novel cross-type hybrid carrier system has been proposed in the literature. With the double integral used in modeling the system, it takes a long time to solve symbolically, and it is difficult to simulate dynamic behavior in control validation. To solve this problem, attraction force and inclination torque values are easily characterized by new formulation and besides the simulations are conducted easily. The experimental setup was manufactured and assembled, and the carrier system was successfully levitated, and reference tracking was performed without overshoot.

This paper aims to introduce an alternative for modeling levitation forces between NdFeB magnets and bulks of high-temperature superconductors (HTS). The presented approach should be evaluated through two different formulations and compared with experimental results.

The T-A and H-ϕ formulations are among the most efficient approaches for modeling superconducting materials. COMSOL Multiphysics was used to apply them to magnetic levitation models and predict the forces involved.The permanent magnet movement is modeled by combining moving meshes and magnetic field identity pairs in both 2D and 3D studies.

It is shown that it is possible to use the homogenization technique for the T-A formulation in 3D models combined with mixed formulation boundaries and moving meshes to simulate the whole device’s geometry.

The case studies are limited to the formulations’ implementation and a brief assessment regarding degrees of freedom. The intent is to make the simulation straightforward rather than establish a benchmark.

The H-ϕ formulation considers the HTS bulk domain as isotropic, whereas the T-A formulation homogenization approach treats it as anisotropic. The originality of the paper lies in contrasting these different modeling approaches while incorporating the external magnetic field movement by means of the Lagrangian–Eulerian method.

This paper aims to study the clearance compatibility of active magnetic bearing (AMB) and gas bearing (GB) to achieve a single-structured hybrid gas-magnetic bearing (HGMB), which uses a single bearing structure to realize both the functions of gas bearing and magnetic bearing.

Because the radial clearance size of the AMB is typically ten times larger than that of the GB, radial clearance compatibility of GB and AMB needs to maximize the radial clearance of GB by adjusting structural parameters. Parametric analysis of structural parameters of GB is explored. Furthermore, a general structural design principle based on static analysis, rotordynamic performance and system stability is established for the single-structured HGMB.

Load capacity is vastly reduced due to the enlarged radial clearance of the GB. A minimum clearance needs to be ensured by increasing the bearing diameter or width to compensate for the reduced load capacity, yet indirectly raising the bearing load. Increased bearing load is conducive to stability, yet it raises the risk of rotor abrasion. In addition, excessively large bearing diameter leads to system instability, and inappropriate bearing width affects critical speeds. A general structural design principle is established and the designed HGMB–rotor processes optimal performances.

A single-structured HGMB is proposed to address the urgent demand for high-speed, cryogenic turboexpanders with frequent starts/stops. This design applies a single-bearing structure to realize the characteristics of both GB and AMB, greatly simplifying the implementation, reducing air friction loss and raising critical speeds. This paper provides a fresh perspective on the development of cryogenic turboexpanders for hydrogen liquefaction. It theoretically validates the feasibility and provides a design guide for a single-structured HGMB system.

An excessive increase in temperature will reduce the lifespan and even burn the coil. The variety of materials in the structure of the electromagnet along with its multi-layer winding creates a complex and heterogeneous thermal structure. There are very few researches that are completely focused on the thermal analysis of electromagnets. The purpose of this paper is to provide an accurate, yet fast and simple method for the thermal analysis of cylindrical electromagnets in both transient and steady-state modes. For this purpose, a thermal equivalent circuit (TEC) is presented based on the nodding approach.

The results of TEC analysis of cylindrical electromagnet, for two orthogonal and orthocyclic winding coil technologies, were compared with the results of the thermal simulation in COMSOL. The authors also built a laboratory model of the cylindrical electromagnet, similar to those analyzed and simulated, and measured the temperature in different parts of it.

The comparison of the results obtained from different methods for the thermal analysis of the cylindrical electromagnet indicates that the proposed TEC has an error of less than 2%. The simplicity and high accuracy of the results are the most important advantages of the proposed TEC.

Comparing the information and results related to winding schemes, indicates that the orthogonal winding has less cost and weight due to the shorter length of the wire used. On the other hand, orthocyclic winding generates lower temperature and has more lifting force, and is simpler to implement. Therefore, in practice, orthocyclic winding technology is usually used.

In this paper, improvements in reducing transmitted accelerations in a full vehicle are obtained by optimizing the gain parameters of an active control in a roughness road profile.

For a classically designed linear quadratic regulator (LQR) control, the vibration attenuation performance will depend on weighting matrices Q and R. A methodology is proposed in this work to determine the optimal elements of these matrices by using a genetic algorithm method to get enhanced controller performance. The active control is implemented in an eight degrees of freedom (8-DOF) vehicle suspension model, subjected to a standard ISO road profile. The control performance is compared against a controlled system with few Q and R parameters, an active system without optimized gain matrices, and an optimized passive system.

The control with 12 optimized parameters for Q and R provided the best vibration attenuation, reducing significantly the Root Mean Square (RMS) accelerations at the driver’s seat and car body.

The research has positive implications in a wide class of active control systems, especially those based on a LQR, which was verified by the multibody dynamic systems tested in the paper.

Better active control gains can be devised to improve performance in vibration attenuation.

The main contribution proposed in this work is the improvement of the Q and R parameters simultaneously, in a full 8-DOF vehicle model, which minimizes the driver’s seat acceleration and, at the same time, guarantees vehicle safety.

This paper aims to present an accurate magnetic equivalent circuit for modeling the cylindrical electromagnet so that by analyzing it, the magnetic flux density in different parts of the electromagnet, as well as its lifting force, can be calculated.

The structure of the electromagnet is divided into parts that can be modeled by lumped element parameters. Mathematical equations for calculating these elements are presented and proved. The axial symmetry of the cylindrical electromagnet made it possible to use planar circuits for its modeling. To increase the accuracy of the proposed equivalent circuit, attention has been paid to the leakage flux as well as the nonlinear behavior of the ferromagnetic core. Also, the curvature of the magnetic flux path is considered in the calculation of the corner permeances of the core.

The magnetic flux density in different parts of the electromagnet was calculated using nodal analysis of the circuit and compared to the results of the finite element method. Also, a test bed was established to measure the lifting force of the electromagnet. Comparing the results shows a difference of less than 3% which indicate the good accuracy of the proposed circuit. In addition, due to the curvature of the flux path, there is a no-flux region in the center of the disk, the extent of which depends on the thickness of the disk and the diameter of the middle leg.

Magnetic equivalent circuit is a new contribution to analyze the cylindrical electromagnet and calculate its lifting force with good accuracy. The circuit lumped elements can be quickly calculated using mathematical equations and software such as MATLAB according to the actual path of the magnetic flux. Compared to other methods, the proposed circuit analyzes the electromagnet in a shorter period of time. This is the most important advantage of the proposed circuit model.