**2. Bearings supports types**

#### **2.1. Air bearings (AB)**

It is advisable to consider the selection criteria in more detail before analyzing the advantages

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:

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

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

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

The so-called stiffness background is used more often rather than bearing stiffness when cal-

\_\_\_*<sup>x</sup>*

\_\_\_*<sup>x</sup>*

The static load is load acting on the bearing when the rotor is stationary and dynamic load is

Bearing speed is a technical parameter that determines the maximum speed of the bearing.

*DN* = *D* ⋅ *n*, (4)

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

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

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 tem-

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

be achieved 40,000 rpm and can be used at temperatures from −40 to + 150°C.

perature limit corresponds to the analogues presented above [2].

<sup>δ</sup>, (1)

*LD*, (2)

*LD*. (3)

—bear-

and disadvantages of various types of bearings.

*kx* <sup>=</sup> <sup>−</sup>\_\_*<sup>F</sup>*

*kx*<sup>1</sup> <sup>=</sup> *<sup>k</sup>*

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

*<sup>с</sup><sup>x</sup>*<sup>1</sup> <sup>=</sup> *<sup>с</sup>*

the load exerted on the bearing with a rotating rotor.

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

Bearing speed is measured in mm × rpm/min and defined as follows:

culating bearing supports in EM:

ing stiffness.

78 Bearing Technology

companies.

ing temperature.

AB is a slide bearings (according to Standard ISO 4378-1-2001) in which the lubricating membrane pressure is created by the gas supply system. AB operating principle is based on the injection of air through a system of holes under pressure into the gap between the pin and the bearing. At the same time, the pin is separated by a layer of pressurized air from bearing. They are not used in HS EM due to the fact that the air bearings require additional pressurization system compressor.

#### **2.2. Aerodynamic bearings (ADB)**

Aerodynamic bearings (ADB) is the sliding bearings (according to ISO 4378-1-2001), in which the lubricant membrane pressure, and hence load bearing capacity is created by the surface movement. The operating principle of the ADB is that in the absence of rotation of the pin rests on the inner surface of the bearing, while rotating air or other gas is sucked from the environment, creating an air cushion with increased pressure, thus, lifting the pin and separating it from the bearing (**Figure 1**).

**Figure 1.** Aerodynamic bearing: 1—trunnion; 2—foil.

**Table 1** shows the characteristics of radial ADP made by Russian production (produced by National Research University "Moscow Power Engineering Institute"). **Table 2** shows the axial ADB made by Russian production.

The advantages of ADB is the absence of necessity for a control system (as compared with the electromagnetic bearings), as well as their noncontact (compared to mechanical). The


**Table 1.** Radial ADB made by Russian production.


**Table 2.** Axial ADB made by Russian production.

disadvantage is that ADB provides noncontact rotation of the rotor only with a certain speed (rate surfacing), and up to this frequency ADB acts as a mechanical bearing of a high friction (for example, from **Table 1** it is seen that the bearing frequency surfacing is 2400 rpm with a load capacity of 105 N). Furthermore, using ADB is an increased requirement for the surface treatment of the shaft. Also ADB cannot be operated in the absence of a gas environment, such as a vacuum, which limits their use in cosmic space.

### **2.3. Active magnetic bearings (AMB)**

**Table 1** shows the characteristics of radial ADP made by Russian production (produced by National Research University "Moscow Power Engineering Institute"). **Table 2** shows the

The advantages of ADB is the absence of necessity for a control system (as compared with the electromagnetic bearings), as well as their noncontact (compared to mechanical). The

**(***N***)**

**The static load-bearing capacity** 

**(rpm) Usual scheme Enhanced scheme**

axial ADB made by Russian production.

**diameter of the pin (mm)**

**The axial length (mm)** **The** 

**(rpm)**

**recommended maximum speed** 

FGB11 10.5 13 364,000 2 – 19,000 FGB14 13.5 16 283,000 3 – 14,800 FGB16 15.5 18 247,000 4 – 13,000 FGB20 19.5 24 196,000 7 – 10,000 FGB30 30 34 127,000 15 – 6700 FGB35 35 31 109,000 16 27 5700 FGB40 39 44 98,000 25 42 5100 FGB61 61 70 63,000 63 105 3300 FGB67 67 70 57,000 69 115 3000 FGB74 74 70 52,000 76 127 2700 FGB80 80 70 48,000 82 137 2500 FGB84 84 85 46,000 105 175 2400 FGB103 103 70 37,000 – 177 1900 FGB103l 103 120 37,000 – 303 1900

**Bearing type The nominal** 

80 Bearing Technology

**Type The diameter of** 

**the heel (mm)**

**Table 1.** Radial ADB made by Russian production.

**Table 2.** Axial ADB made by Russian production.

**The outer diameter of the bearing (mm)**

TFGB37 37 43 19 207,000 95 TFGB44 44 49 22 174,000 137 TFGB64 64 74 34 119,000 277 TFGB72 72 82 42 106,000 322 TFGB85 85 95 52 90,000 426 TFGB105 95 116 93 75,000 702 TFGB120 120 132 70 64,000 895

**The inner diameter of the bearing (mm)**

**Rated speed (rpm) Bearing capacity at** 

**rated speed (N)**

**The frequency of surfacing** 

AMB (according to ISO 14839-1-2011) is a rotor maintenance device without mechanical contact by the magnetic attraction forces and uses feedback servo, in which the circuit typically contains sensors, solenoids, power amplifiers, power supplies and the controller (**Figure 2**).

AMBs are widely used in Russian and foreign industry [in Russia are engaged in the development of the 〈〈VNIIEM Corporation〉〉 JSC and 〈〈Pskov engineering company〉〉, among foreign manufacturers can mark SKF, CalnetixTechnologies (USA), the Synchrony (USA) and others.].

The advantages of the AMB are their features such as controllability, contactless operation, providing rotor levitation when power is supplied to the control electromagnets (unlike ADB), the ability to work at high temperatures and in corrosive environments, bearing stiffness control possibility (due to pulse changes the electromagnetic force) and the bearing damping ability and the ability to work in vacuum.

The AMB disadvantages include the complexity of their design, the complexity of their control systems, significant product price and their high weight and overall dimensions. The stiffness of the AMB under normal operating conditions is comparable or slightly higher than the stiffness of the ADB.

**Figure 2.** AMB: 1—rotor position sensor; 2—AMB magnetic core; 3—shaft; 4—ferromagnetic sleeve; 5—AMB winding.

Despite these disadvantages, the AMB are widely used in HS EM. Moreover, the use of AMB in the Russian Federation is rationed by the technical documentation (ISO 14839-1-2011, ISO 14839-2-2011, ISO 14839-3-2013, ISO 14839-4-2014).

Importantly, the AMB are not only electromagnets, in which the shaft is concentrically located but an intellectual complex system consisting of microscopic sensors, signal amplifiers, etc. A more complete design of AMB control systems, as well as their control algorithms is described in Refs. [3, 4].

**Table 3** shows the geometric dimensions of the AMB, produced by 〈〈Pskov Engineering Company〉〉.

To evaluate the effectiveness of the AMB and ADB energy characteristics, it is advisable to make a comparison on the specific speed and static load, which is accepted in the form:

$$F\_{sp} = \frac{F}{DL} \tag{5}$$

ADB and AMB of Russian production are considered when comparing.

From **Table 3**, it is seen that when the static load-bearing capacity is 180 N, the specific speed of AMB is 3,750,000 rpm and the specific static load is 100,000 N/m2 . At the same time at the static load of 175 N, specific speed is 3,864,400 rpm and the specific static load is 24,509 N/m2 . That is, the AMB of Russian production exceeds ADB by the specific static load, and the specific speed of both variants is about the same (AMB's specific speed at 2.4% less than ADB).


Notes: d—diameter of the shaft; D—external diameter; m—mass of the AMB; L—active length; F—static load-bearing capacity; n—permissible speed.

**Table 3.** Standards of 〈〈Pskov engineering company〉〉 for radial AMB.

To eliminate the AMB and ADB disadvantages, hybrid magnetic bearings (HMB) are applied in HS EM. HMB is the bearing that combines AMB design and magnetic bearing at permanent magnets (MB PM) in accordance with ISO 14839-1-2011.

At the same time, as shown in Ref. [5], the concept of the HMB goes far beyond the definition of an ISO and represents a combination of different bearing types in a single product that allows them to combine their design merits and ADB, and AMB, reaching thus the minimum weight and overall dimensions, controllability and stability of the entire HS EM.

There are three main types of structural HMB: gas-magnetic bearing, magnetomechanical and various combinations of MB PM with AMB.

#### **2.4. HMB, as a combination of MB PM and AMB**

Despite these disadvantages, the AMB are widely used in HS EM. Moreover, the use of AMB in the Russian Federation is rationed by the technical documentation (ISO 14839-1-2011, ISO

Importantly, the AMB are not only electromagnets, in which the shaft is concentrically located but an intellectual complex system consisting of microscopic sensors, signal amplifiers, etc. A more complete design of AMB control systems, as well as their control algorithms is described

**Table 3** shows the geometric dimensions of the AMB, produced by 〈〈Pskov Engineering

To evaluate the effectiveness of the AMB and ADB energy characteristics, it is advisable to make a comparison on the specific speed and static load, which is accepted in the form:

From **Table 3**, it is seen that when the static load-bearing capacity is 180 N, the specific

time at the static load of 175 N, specific speed is 3,864,400 rpm and the specific static load

load, and the specific speed of both variants is about the same (AMB's specific speed at

Notes: d—diameter of the shaft; D—external diameter; m—mass of the AMB; L—active length; F—static load-bearing

. That is, the AMB of Russian production exceeds ADB by the specific static

*DL* (5)

 **rpm)** *F* **(N)** *m* **(kg)**

. At the same

14839-2-2011, ISO 14839-3-2013, ISO 14839-4-2014).

*Fsp* <sup>=</sup> \_\_\_*<sup>F</sup>*

*d* **(mm)** *D* **(mm)** *L* **(mm)** *n* **(103**

**Table 3.** Standards of 〈〈Pskov engineering company〉〉 for radial AMB.

ADB and AMB of Russian production are considered when comparing.

speed of AMB is 3,750,000 rpm and the specific static load is 100,000 N/m2

 44 14 252 20 0.07 52 16 190 30 0.12 58 20 150 50 0.18 66 24 125 70 0.3 72 27 110 90 0.4 80 30 95 120 0.52 94 36 75 180 0.84 110 42 63 250 1.32 130 46 54 360 2 148 50 47 450 2.7

in Refs. [3, 4].

82 Bearing Technology

Company〉〉.

is 24,509 N/m2

2.4% less than ADB).

capacity; n—permissible speed.

This type of HMB is the most common and used in practice. Moreover, it is considered the most promising design of HMB. This area has two main ways of development: the permanent magnets are installed in the magnetic AMB (**Figure 3**) to increase the magnetic flux. Separation of the AMB and MB PM, for example, two radial MB PM placed on one shaft, and the rotor axial fixation is provided by axial AMB (**Figure 4**).

A significant pulling force of the electromagnet is required when using the second option, so the first design most widely used in industry. At the same time some technical branches of second design has broad application prospects.

**Figure 3.** Radial-axial HMB, in which PM are used to amplify the magnetic flux.

**Figure 4.** HMB where AMB and MB PM used separately.

#### **2.5. Magnetomechanical HMB**

This HMB class is a combination of mechanical bearings, which serve as the main shaft support and MB PM, which are intended for unloading mechanical bearings. The advantages of this HMB type is the lack of a control system and simplicity of design and the disadvantages is the presence of mechanical bearings friction, and consequently also their low reliability.

For example, it is known that magnetomechanical bearing (MMB) design [6] for the electromechanical battery consists of flywheel and a high-speed electric generator with a vertical shaft. A feature of this design is the use of a ball in HMB made of sapphire, which provides the axial support system. **Table 4** shows the effectiveness of different ball materials and plate in the MMB.

To improve the efficiency of MMB in rotary system of the HS EM the passive vibration damper also entered besides mechanical bearings and MB PM, which is needed for damping vibration energy. A passive vibration damper is an electrically conductive plate installed with a gap relative to the PM. Eddy currents are induced in the copper sleeve with displacements of the PM, which provide damping of vibration energy.

MMB are actively developing due to their simple application design. The major trends in the development of this type of HMB are reduction of friction in the mechanical bearings by the use of coatings and materials, as well as by the maximum discharge of mechanical bearings


**Table 4.** The effectiveness of different ball materials and plate in the MMB.

and levitating shaft vibration reduction. It is obvious that in a number of industries, especially in high-speed systems with short life cycles, the HMB type have broad prospects.

#### **2.6. Gas-magnetic HMB**

This HMB is a combination of ADB and AMB. **Figure 5** shows a design of this HMB type [7].

The advantages of this type of HMB include high stiffness and handling, but they have considerable design complexity of execution, so they are not widely used in the industry. Gasmagnetic HMB are considered in Refs. [8–10] in more detail.

#### **2.7. Electrostatic bearings**

**2.5. Magnetomechanical HMB**

**Figure 4.** HMB where AMB and MB PM used separately.

PM, which provide damping of vibration energy.

low reliability.

84 Bearing Technology

in the MMB.

This HMB class is a combination of mechanical bearings, which serve as the main shaft support and MB PM, which are intended for unloading mechanical bearings. The advantages of this HMB type is the lack of a control system and simplicity of design and the disadvantages is the presence of mechanical bearings friction, and consequently also their

For example, it is known that magnetomechanical bearing (MMB) design [6] for the electromechanical battery consists of flywheel and a high-speed electric generator with a vertical shaft. A feature of this design is the use of a ball in HMB made of sapphire, which provides the axial support system. **Table 4** shows the effectiveness of different ball materials and plate

To improve the efficiency of MMB in rotary system of the HS EM the passive vibration damper also entered besides mechanical bearings and MB PM, which is needed for damping vibration energy. A passive vibration damper is an electrically conductive plate installed with a gap relative to the PM. Eddy currents are induced in the copper sleeve with displacements of the

MMB are actively developing due to their simple application design. The major trends in the development of this type of HMB are reduction of friction in the mechanical bearings by the use of coatings and materials, as well as by the maximum discharge of mechanical bearings

**Ball material Material plate Friction coefficient Friction losses at 50,000 rpm** 

Sapphire Sapphire 0.1 152 Steel Steel 0.42 628 Cast iron Cast iron 0.15 230 Teflon Steel 0.04 63

**Table 4.** The effectiveness of different ball materials and plate in the MMB.

**(MW)**

At low mass of the rotor, as well as to the possibility of providing vacuum in the cavity of the EM, it seems appropriate to use electrostatic poles. Electrostatic support is a noncontact bearing assembly, in which efforts are created by attractive forces between two surfaces having different potentials (**Figure 6**). The created ascensional power in electrostatic supports is insignificant and is accepted in the form:

$$f = \frac{\varepsilon \cdot E^2}{2} \tag{6}$$

where ε—the dielectric constant of the suspended body; *E*—the electric field strength.

The advantage of the electrostatic poles relates primarily to no energy losses due to eddy currents. The electrostatic bearings application allows creating ultra-high-speed, contactless, vacuumed, miniature EM with low noise and heat generation. Electrostatic supports are controlled.

In the Russian Federation industry, the electrostatic support is most widely used as gyro bearings. Basic electrostatic bearing theory is presented in Refs. [11–16].

Additionally, certain industrial application perspectives have bearings, which are based on the Lorentz force, which are defined as follows:

**Figure 5.** Hybrid gas-magnetic shaft suspension of high-speed spindle: 1—front gas-magnetic bearing; 2—rear gas-static bearing; 3—electromagnet.

**Figure 6.** The electrostatic support.

$$f = q(E + \{\upsilon \times B\}).\tag{7}$$

This type of bearings has broad prospects for use in HS EM. For example, the Swiss company Seleroton has developed ultra-high-speed vacuumed motor CM-AMB-400 using this type of bearings (power of 250 W, the rotor speed of 400 000 rpm).

Using the suspension based on the Lorentz forces in the electric motor in conjunction with vacuum allowed to almost completely solve the problems of the rotor friction of the air and the friction in the bearing supports. Overall efficiency of the EM reaches 91–92%.
