**1. Introduction**

One of the main problems in the design of high-speed electrical machines (HS EM) is the task of selecting the bearing assemblies that forms design and determines its application area, allowable load, and efficiency.

The complexity of this task lies in the fact that the high-speed electromagnetic bearing assemblies must meet various criteria, which often contradict each other. So, bearing supports of HS EM should ensure minimum friction losses and maximum resource, wide operating temperature range (which is typical for non-contact bearings, and almost impossible to achieve on the mechanical bearings), but they must have a minimum ductility (maximum stiffness) for sub-critical rotor speeds and rotor dynamics requirements, providing significant mechanical stress and have a minimum weight and overall dimensions (it is ensured well enough mechanical bearing assemblies and is difficult to achieve on a contactless bearing supports).

Therefore, mechanical (ball and roller), hydrostatic and gas bearings, as well as various types of magnetic bearings applied in modern HS EM. The choice of bearings depends on the specific tasks and function of HS EM.

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It is advisable to consider the selection criteria in more detail before analyzing the advantages and disadvantages of various types of bearings.

Bearing stiffness is a value that is characterized by an elastic deformation of the bearing under load. It is expressed as the ratio of the load to the elastic deformation, depending on the type, design and size of the bearing. In simplified form, the bearing stiffness can be defined as follows:

$$k\_{\alpha} = -\frac{F}{\delta'} \tag{1}$$

where *F*—load acting on the bearing; δ—change in the bearing gap under the load; *kx* —bearing stiffness.

Typically, the stiffness is defined in the technical catalogs for the bearing supports.

The so-called stiffness background is used more often rather than bearing stiffness when calculating bearing supports in EM:

$$k\_{\rm it} = \frac{k\_{\rm i}}{LD'} \tag{2}$$

where *L*—bearing length; *D*—bearing diameter.

Also used the damping coefficient attributable to the area of the bearing support:

$$c\_{\rm at} = \frac{c\_s}{LD}.\tag{3}$$

The static load is load acting on the bearing when the rotor is stationary and dynamic load is the load exerted on the bearing with a rotating rotor.

Bearing speed is a technical parameter that determines the maximum speed of the bearing. Bearing speed is measured in mm × rpm/min and defined as follows:

$$DN = D \cdot \mathfrak{n}\_{\prime} \tag{4}$$

where *n*—rotor rotational speed; *D*—bearing diameter.

The main producers of high-speed mechanical bearings are FAG, SKF, GMN and NTR companies.

High-speed bearings of SKF are made in accordance with ISO 683 〈〈Heat-treated steels, alloy steel sand-free-cutting steels—Part 17: Ball and roller bearing steels〉〉 and presented in the N10 series. Under the conditions of the liquid lubrication of the bearings, rotation speed can be achieved 40,000 rpm and can be used at temperatures from −40 to + 150°C.

Rotor rotational speed of HS EM on the FAG bearings with oil lubrication can reach 170,000 rpm. In this mode, the bearings temperature is within the range from −40 to +150°C [1].

GMN Company produces mechanical bearings with speed limit of 75,000 rpm and its temperature limit corresponds to the analogues presented above [2].

Undoubtedly, mechanical bearings have reached significant technical heights. However, they have inherent weaknesses such as limited speed, considerable noise emission and low operating temperature.

HS EM on the mechanical rolling bearings is characterized by thermal deformation; trajectory instability is caused by a change in the rotation angle of the separator with a set of rolling elements and a manufacturing error of the mechanical support rings, as well as limited service life determined by mechanical friction between the dynamic rotating parts. Therefore, for a more promising use in high-speed and high-temperature, EM have a contactless bearing supports: magnetic [active magnetic bearings (AMB), hybrid magnetic bearings (HMB)] or gas [aerodynamic bearings (ADB) or air bearings].
