Specifical features of designing of magneticaly levitated transport systems using permanent magnets

. The purpose of the present research is to find approaches for the implementation of constructive solutions that allow for stable suspension and transverse stabilization of magnetolevitation transport systems based on permanent magnets. In order to achieve this goal, the methods of physical modeling were used. Measurements of the magnitude of magnetic induction were carried out using a certified magnetometer Aktakom ATE-8702. While conducting experiments and creating physical models, NdFeB permanent magnets with dimensions of 21x21x21 mm were used. As a result, the suspension and transverse stabilization design based on permanent magnets has been developed and patented. Within the framework of the research, a mock-up of a suspension device for a magnetolevitation transport system was developed and manufactured. The outcomes obtained can be used in the development of technical units with reduced energy consumption, with a minimum coefficient of friction in the guides (escalators, travelators, elevators, etc.), with reduced vibration (magnetic supports) and with minimal consumption of lubricants


Introduction
At the moment, in various fields of technology, there is increased interest in the practical application of technical levitation, in particular, the most common typemagnetic levitation, i.e. the phenomenon of suspension of a body in a magnetic field that compensates for the gravitational field of the Earth.
One of the promising directions of using magnetic levitation technology is, in particular, high-speed transport on a magnetic suspension. No less relevant is the use of this technology in conveyor systems for transporting open-type cargo, or in the execution of a pipeline system, in lifting and transport systems, in bearing systems, etc. [1] There exist two main types of magnetic systems: electromagnetic systems (EMC/EMS) and electrodynamic systems (EMF/EDS). The description of these systems, as well as the methods of their calculation, are most fully reflected in the sources [2][3][4][5][6].
Permanent magnet (PM) systems have not found wide application due to the complexity of configuring magnetic fields. Besides, to date, there is no available engineering apparatus that allows fully operational implementation of pre-design modeling and configuration of levitation system nodes using permanent magnets. Therefore, existing levitation systems using permanent magnets are hybrid, since the levitation forces created by a permanent magnet are not stable in all degrees of freedom.
The purpose of the scientific research presented in the article is to search for technical solutions that are easy to use and allow for stable suspension and transverse stabilization of transport systems based on permanent magnets.
The outcomes obtained could be applied in the design of a non-volatile system, that is, without the use of electromagnets and superconducting materials, as a result of which it is also possible to achieve a reduction in weight and size indicators, a significant reduction in energy consumption, simplification of the design of components and parts, as well as a reduction in the cost of the design compared to superconducting systems.
The practical significance of the obtained research lies in the possibility of applying the described principles in any systems based on the interaction of permanent magnets and/or assemblies of permanent magnets, including magnetolevitation transport systems.
A comparative analysis of various suspension systems of magnetolevitation devices and systems is provided in Table 1. High High Absent Note: * -difficult due to the high cost of manufacturing extended sections; ** -changes in the properties of systems using permanent magnets at critical temperatures have not been studied and confirmed by experimental studies.
Grounding upon a comparative analysis, it can be concluded that it is advisable to use systems with permanent magnets in non-tensioned lines, for example, conveyors, stopping and parking points, where the main advantage will be the absence or small amount of electricity costs to maintain the levitation gap and acceleration sections. Important characteristics of suspension and lateral stabilization systems are the dependences of suspension forces (lateral stabilization), electrodynamic braking forces, as well as their ratio (levitation quality) on speed. It is known a sharp increase in the braking force with an increase in speed to a peak value, then there is a decline in the braking force. Therefore, it is advisable to use a system with the use of permanent magnets in which there is practically no braking force in the acceleration sections.

The design of the combined suspension and transverse stabilization device
As a result of the experimental and theoretical studies carried out, the design of a combined suspension and transverse stabilization device using exclusively permanent magnets was developed [7].
This design is developed and manufactured based on the creation of magnetic fields of the required shape, providing a stable contactless suspension of the vehicle, which is one of the important tasks of research.
The design includes two magnetic systems in the form of a set of permanent magnets. The first magnetic system consists of two axially magnetized magnets with diagonal poles rigidly connected to each other. The second magnetic system is made in the form of two assemblies of magnets rigidly fixed together. Figure 1 (a) depicts a diagram of the magnetic system of the device, in which the first magnetic system is fixed to the roadway, and the second magnetic system is fixed to the vehicle, Figure 1 (b) shows a diagram of the magnetic system of a magnetolevitation vehicle, in which the first magnetic system is fixed to the vehicle, and the second magnetic system is fixed on the roadbed. The scheme of interaction of the first and second magnetic systems can be illustrated using Fig. 2. The considered system is stable under the condition of finding the extreme point of the pole of the magnet of the first magnetic system 3 (point "A" in Fig. 2), facing towards the second magnetic system 4, in the angle formed by the poles of the same name of the side magnets 7 of the second magnetic system 4, and is located from the top of this angle at a distance providing levitation and stabilizing forces. As soon as the point "A" is removed from the specified position, the system loses stability.
In order to ensure the operability of the system, the following conditions must be met: 1. Permanent magnets 3 and 8 should be opposite poles of the same name to each other; 2. The distance "a" in Fig. 2 should be a 0. It is identified that the geometric dimensions of permanent magnets, as well as the material of permanent magnets, do not affect the performance of the system.
Depending on the specified angle α , the claimed magnetic system can operate in three modes: 1) At α = 90 o , the levitation force is equal to the stabilization force (F l = F st); 2) At α 90 o , the levitation force is less than the stabilization force (F l F st). The system might be applied as a device for additional transverse stabilization of a magnetolevitation vehicle; 3) At α 90 o , the levitation force is greater than the stabilization force (F l F st). The system might be applied as a device for additional transverse stabilization of a magnetolevitation vehicle; Fig. 2. The scheme of interaction of magnetic systems 3the first magnetic system, 4the second magnetic system, 7lateral axial magnetization magnets of the second magnetic system with a normal pole arrangement, 8central axial magnetization magnets of the second magnetic system with a diagonal pole arrangement.
The interaction points of the first and second magnetic systems of a magnetolevitation vehicle can be from two or more, as shown in Fig. 3 (a, b, c).

Fig. 3. Options for the location of interaction points.
The considered magnetic systems can have different versions depending on the location of the fixed track structure, as shown in Fig. 4 (a, b, c, d), but the general principles of magnetic interaction of the inner and outer magnetic parts are preserved.  The principle of operation of the suspension device and transverse stabilization of transport systems is based on the formation of magnetic fields of assemblies of permanent or magnetized magnets, according to the scheme shown in Fig. 6, from which it can be seen that in option "b", axially magnetized magnets with a normal pole arrangement and a central magnet with a diagonal pole arrangement form a magnetic field with a pronounced presence an integral line of equal potential, which is the basis for ensuring the operability of the magnetic system as a whole.
In continuation of the development of this theory, the authors considered the use of a single magnet of a given shape (Fig. 7). In order to obtain the required shape of a permanent magnet, electroerosion treatment was used. The use of this method makes it possible to significantly simplify the design of the node, since this option does not require the use of permanent magnet assemblies. Fig. 6. Permanent magnet processing options and general appearance of the processed permanent magnet. a, b)processing schemes and analogues of permanent magnet assemblies; c)a single processed permanent magnet; d)a single permanent magnet in a holding device.
As the analysis of the advantages and disadvantages of existing magnetolevitation transport systems has shown, the main problem of this type of transport is the significant energy costs for ensuring stable levitation and lateral stabilization during movement and when the train is parked [8,9]. Under the current situation, the most promising research can be attributed to research in the field of magnetolevitation transport systems using permanent magnets. However, the initial investment in the creation of such long-range systems can significantly exceed the cost of creating other transport systems. Taking into account this significant disadvantage, the authors consider options for using levitation and stabilization devices on permanent magnets in systems of small extent: 1. Acceleration / deceleration sections; 2. In-shop transportation lines; 3. Conveyor lines.
The most promising area of research in the field of permanent magnets still remains the study of the possibility of creating conditions for stable interaction of permanent magnet assemblies.
The proposed approach makes it possible to evaluate the critical points of interaction of both single permanent magnets of any shape and magnetic assemblies. This approach makes it possible to determine the geometric characteristics of assemblies at the design development stage and set priority directions for further research [10]. Figure 8 shows a layout of a combined suspension and transverse stabilization device using permanent magnets. Physical modeling has shown a high degree of stability both in the vertical direction F L and in the horizontal direction F art.
The authors of the article consider the following stages of creating assemblies and parts using permanent magnets: 1. Production of prototypes of selected magnetic assemblies.
2. Determination of the actual physical parameters of the permanent magnet assemblies under consideration. In particular, the lines of equal magnetic field potential shown in Fig. 5  (a, b, c) are determined experimentally.
3. Consideration of options for the electroerosion treatment of a single permanent magnet as an alternative to permanent magnet assemblies (Fig. 8). An alternative to physical modeling can be the use of computer modeling methods using specialized computer programs and numerical modeling.

Conclusion.
As a result of the conducted research, the following outcomes were achieved: 1. A comparative analysis of existing magnetolevitation transport systems has been performed and their main characteristics have been evaluated. It has been identified that the most promising direction for improving existing types of systems is the creation of systems using permanent magnets. Such systems can significantly reduce energy consumption and can seriously compete with transport systems with other types of magnetic suspension.
2. A non-volatile combined suspension and transverse stabilization device of a magnetolevitation vehicle using permanent magnets has been developed and manufactured in the form of a mock-up, including after electroerosion treatment to give a given configuration.