**3. Bearing comparison**

The adequacy of the most reliable types of bearings is studied. To this purpose, the behavior of the following types of bearings is analyzed:


The first two categories include conventional bearings, taken as a reference for performance comparison. The last item includes rolling element bearings entirely manufactured in ceramic material and hybrid bearings, made up of steel rings and ceramic balls, with or without film coatings on the races.

Only supports based on well-established technology are analyzed, while research solutions (still in development), such as squeeze film bearings, hydroinertia gas bearings, ferrofluid bearings, and metal mesh foil bearings, are not considered.

The assessment of compliance of the different bearing types with micro-GT operating conditions, including speed (DN factor), temperature, and loads, requires a proper comparison of literature and technical data.

#### **3.1. Operating speed**

Operative and absolute speed limits of the different bearing solutions are compared in **Figure 2**.

**Figure 2.** Maximum speed factors for different bearings.

The speed limit of rolling element bearings is mainly due to the skidding of the elements on the rings [5]. Among such bearings, high-precision angular contact ball bearings by means of suitable tolerances, osculation, rolling element size, and number can reach the high speed required by micro-GT (DN > 1 × 10<sup>6</sup> mm rpm). The maximum DN reached by high-precision ball bearings is about 3 million mm rpm [6, 7]. Higher DN values can be reached by angular contact bearings by means of specific lubrication systems [8].

(1) steel rolling element bearings, lubricated by grease or oil;

bearings, and metal mesh foil bearings, are not considered.

The first two categories include conventional bearings, taken as a reference for performance comparison. The last item includes rolling element bearings entirely manufactured in ceramic material and hybrid bearings, made up of steel rings and ceramic balls, with or without film

Only supports based on well-established technology are analyzed, while research solutions (still in development), such as squeeze film bearings, hydroinertia gas bearings, ferrofluid

The assessment of compliance of the different bearing types with micro-GT operating conditions, including speed (DN factor), temperature, and loads, requires a proper comparison of

Operative and absolute speed limits of the different bearing solutions are compared in **Figure 2**.

(2) sliding bearings, lubricated by oil;

(3) air (film) bearings; (4) magnetic bearings; (5) ceramic bearings.

6 Bearing Technology

coatings on the races.

literature and technical data.

**Figure 2.** Maximum speed factors for different bearings.

**3.1. Operating speed**

Manufacturer's catalogs (SKF, Schaeffler) show that the use of ceramic balls in place of steel ones can yield an operating speed increase of roughly 20–30%. Such a result is confirmed by the data reported in reference [9], i.e., speed of hybrid bearings can be increased by 20–30% compared with conventional ones. Accordingly, in comparison with steel bearings, a 60% decrease of centrifugal load matched with the 30% load capacity reduction predicted by Hertz theory finally provides a maximum allowable increase in rotation speed of just 32%. It decreases to 10% for all ceramic bearings.

The DN operative limit reported for oil-lubricated slide bearings regards bearings of turbines for power generation plants [10] and for induction motors [11]. In such cases, operative speed is only restricted by strength limits and by the allowable temperature. In microturbine applications, the operative speed of slide bearings is also limited by their stability and suitable bearing geometries are required, e.g., elliptical and pocket bearings, multilobe bearings, tilting pad bearings (listed from least to most stable).

Waumans et al. [12, 13] report that the highest achieved DN-number for a self-acting bearing operated in air is 7.2 × 106 mm rpm. It is reached by an aerodynamic journal bearing stabilized by means of a grooved bush with a wave-shaped geometry as well as a flexible and damped support structure.

As far as foil bearings are concerned, maximum speed is relevant to a Ø8 mm bearing for microturbines operating up to 642,000 rpm (DN = 5,136,000 mm rpm) from results in reference [14].

Among the grooved bearings, the maximum operative DN of a Herringbone grooved journal bearing (HGJB) with enhanced grooved geometry [15] is 2.7 × 106 mm rpm, and it is lower than foil bearing one. In addition, experimental results confirm that grooved hybrid bearings (GHBs) can run satisfactory at speeds in excess of 3.0 × 106 rpm mm. Nevertheless, such DN is assumed as upper speed limit for grooved bearings, as they are prone to destructive whirl instability at ultrahigh speed [16].

Hybrid aerostatic bearings are suitable due to both the aerostatic stabilizing effect at high speeds and the low air consumption, which has extremely small effect on the global efficiency [17]. For a proper operation, they require air supply at high speed, when it is actually available in micro-GT systems. Data relevant to the maximum speed reached by aerostatic bearings refer to reference [18]. The relevant maximum operative speed is also documented in reference [19].

In today's industrial applications, active magnetic bearing (AMB) rotational speeds are in the range of about 180,000 rpm for a grinding spindle, or about 300,000 rpm for small turbo-machinery [20]. The latter value, by assuming D = 15 mm as suggested by **Table 1**, corresponds to DN = 4.5 × 106 mm rpm, which is confirmed by the data suggested by SKF. Anyway, by means of carbon fiber bandages in the rotor, 6.8 × 106 mm rpm can be reached [19]. Such a value is a documented maximum speed for actual applications rather than a maximum theoretical limit, which is unknown as in the case of air foil bearings [21].

#### **3.2. Operating temperature**

**Table 3** lists the maximum operational temperatures of the bearings.


**Table 3.** Maximum operating temperatures for different bearing types.

As far as steel rolling bearings are concerned, in addition to the lubrication system and the lubricant characteristic, steel reaction to heat and dimensional stability influences their endurance at high temperature. Generally, hardness of steel starts to decrease as temperature rises over 200°C. In addition, as steel heats up, phase transformation occurs and the bearing parts expand. The maximum dimensionally stable temperature ranges between 120 and 250°C, depending on steel type (source: NSK). Accordingly, a limit temperature of 180–260°C for rolling element bearings is indicated in reference [21]. Similarly, a 125–150°C operative limit for AISI 52100 bearings that can be specially stabilized up to 200°C and up to 315°C by using tool steel bearing materials is reported in reference [10]. The authors of reference [11] confirm that operative temperature is usually kept below 150°C except for heat-stabilized bearings.

Ceramic bearings behave better than steel rolling bearings at high temperature. Indeed, hardness and strength of silicon nitride do not deteriorate at high temperatures when compared with those of bearing steel. Particularly, the advantage of all ceramic bearings over hybrid bearings consists especially on the major capability of working in dry or underlubricated conditions, at high temperature (<800°C) and corrosive environment [9]. Such a suitability to high temperatures is confirmed in reference [10], which indicates a limit of 650°C for ceramic bearings with vapor phase lubrication or solid lubricants.

Hydrodynamic bearings are the most limited in operating temperature. Indeed, such a limit comes from bearing surface and oil endurance. Soft metal and Babbitt limit upper temperatures are usually in the 125–150°C range [10]. Limit operating temperature of hydrocarbon oils is 93°C [22], while high temperature oils can also reach 150–200°C, e.g., silicon oils. Therefore, oil lubricated slide bearings are ultimately limited in temperature by bearing surface resistance.

Gases can be employed as lubricants over an extremely wide range of temperatures. For gas bearings, operating temperature limits come from shortcomings of solid components (journal and bearing material), not of the lubricant. Electric motors with ceramic windings supported by gas bearings can work for long periods at temperature up to 500°C [23], which is assumed as the limit temperature for aerodynamic bearings.

Foil bearings require the use of a solid lubrication to prevent wear and reduce friction during instances of contact, i.e., at low-speed conditions at start-up and shutdown. Since common lubricants, e.g., graphite and moly-disulfide (MoS<sup>2</sup> ), are limited to 150°C, solid lubrication is often obtained on the shaft and top foil layer by means of thin, soft polymeric film and sacrificial coatings. Innovative coatings, e.g., nanocomposite for journals and CuAl alloy for top foils, can reach temperatures as high as 650°C, which not by chance is also the limit operating temperature indicated for foil bearings in reference [21]. By using wellestablished tribo-solutions like polymer coatings, air bearing operation is roughly limited below 300°C [24].

Ceramic aerostatic bearings can reach a temperature as high as 800°C [23] and, in general, temperatures up to 900°C and speeds up to 65,000 rpm are feasible for externally pressurized gas bearings [25]. Indeed, aerostatic bearings have the highest temperature limit among the bearing analyzed. It is higher than temperature limit of aerodynamic bearings due to the external air supply, since air cools as it expands. In addition, the very low friction losses avoid thermal expansion due to viscous heating.

Among magnetic bearings, a great drawback of passive magnetic bearings (PMBs) comes from high temperature operation requirements of micro-GT systems, as permanent magnet stability is affected by temperature. Maximum practical operating and Curie (demagnetization) temperatures for the major classes of permanent magnet materials are in the ranges of 150–540 and 310–860°C, respectively. On the contrary, AMBs can work in extreme temperature environments (500–600°C) [21].

#### **3.3. Load-carrying capacity and life**

turbo-machinery [20]. The latter value, by assuming D = 15 mm as suggested by **Table 1**,

[19]. Such a value is a documented maximum speed for actual applications rather than a maxi-

As far as steel rolling bearings are concerned, in addition to the lubrication system and the lubricant characteristic, steel reaction to heat and dimensional stability influences their endurance at high temperature. Generally, hardness of steel starts to decrease as temperature rises over 200°C. In addition, as steel heats up, phase transformation occurs and the bearing parts expand. The maximum dimensionally stable temperature ranges between 120 and 250°C, depending on steel type (source: NSK). Accordingly, a limit temperature of 180–260°C for rolling element bearings is indicated in reference [21]. Similarly, a 125–150°C operative limit for AISI 52100 bearings that can be specially stabilized up to 200°C and up to 315°C by using tool steel bearing materials is reported in reference [10]. The authors of reference [11] confirm that operative temperature is usually kept below 150°C except for heat-stabilized

Ceramic bearings behave better than steel rolling bearings at high temperature. Indeed, hardness and strength of silicon nitride do not deteriorate at high temperatures when compared with those of bearing steel. Particularly, the advantage of all ceramic bearings over hybrid

Anyway, by means of carbon fiber bandages in the rotor, 6.8 × 106

**Table 3** lists the maximum operational temperatures of the bearings.

Rolling element 125–315 Ceramic hybrid 350 Ceramic integral 800 Oil sleeve (journal) 125–150 Oil tilting pad 125–150 Hydrostatic 125–150 Magnetic (AMB) 500–600 Magnetic (PMB) 150–300 Aerodynamic, air foil 650 Aerodynamic, rigid/grooved 500 Aerostatic 900

**Table 3.** Maximum operating temperatures for different bearing types.

**Bearing type Max operating temperature (°C)**

mum theoretical limit, which is unknown as in the case of air foil bearings [21].

mm rpm, which is confirmed by the data suggested by SKF.

mm rpm can be reached

corresponds to DN = 4.5 × 106

8 Bearing Technology

**3.2. Operating temperature**

bearings.

The maximum specific loads for the bearing types in analysis are summarized in **Table 4**.


**Table 4.** Maximum service-specific loads for different bearing types.

For rolling element bearings, the "carrying capacity" is the ability of the bearing to carry a given load for a predetermined number of cycles or revolutions [26].

The maximum documented specific load for rolling element bearings operating in gas turbines is reported in reference [21]. **Table 5** reports the durations of bearings in a shaft support system designed by means of catalog high-precision rolling bearings solely. They are computed according to the adjusted basic rating life [27] by using data in **Table 1** and radial as well as thrust loads in **Table 2**. It is assumed that radial load is equally distributed between two sets of high-precision angular contact bearings and only one (locating) set carries the axial load in order to allow the thermal dilatation of the shaft. The solutions with both 2 and 5 matched bearings in the sets (in tandem arrangement) that carry the axial load are not satisfactory compared with the machine life (about 70,000 hours).


**Table 5.** Expected life for sets of angular contact high-precision bearings, carrying half of the rotor weight and, if specified, the axial load.

Dynamic load ratings of steel bearings can also be used for ceramic bearings of the same dimensions [28], since from test results and predicted values service life of ceramic bearings is longer than that of steel bearings, except for heavy loads.

For the remaining bearings, fatigue is not the main concern, and the external load can be treated as static.

Sleeve bearings life is theoretically infinite and extremely long when they are properly maintained. Significant wear may occur only during extended start-up or coast-down periods, as mixed lubrication occurs at low speed. If the frequency of such events is high, hydrostatic jacking is recommended to minimize bearing wear [11].

Load capacity of oil-film bearings is basically a function of speed and oil viscosity so that high temperature plays a role by reducing viscosity. Many specifications limit motor bearing specific pressures to 1.4 MPa, which is often compliant with structural strength. Nevertheless, most journal bearings safely tolerate pressures beyond 2 MPa, as reported in reference [10]. Tilting pad thrust bearings for turbines carry further increase of specific load, and pads are subject to elastic deformation.

Generally, as hydrodynamic and hydrostatic bearings distribute the load over a larger area than rolling element bearings, their load capacity can be higher. Particularly, hydrostatic bearings can support huge loads, higher than hydrodynamic supports, as their pressure distribution is more uniform.

Air (aerostatic and foil) bearings, because of the different film layer, approximately support only a fraction of the load carried by hydraulic bearings with the same dimension. Indeed, specific load capacity of air foil bearings is 0.7 MPa [21], which is roughly one-fifth of the specific load for hydrodynamic bearings (3.5 MPa, on average). Differently, specific load for aerostatic bearings is lower due to a further constraint. Indeed, aerostatic bearings are typically limited to operate at less than 10 atm of pressure (usually 0.69 MPa) for safety reasons and due to the lubricant compressibility, which yields much higher flow rates and pumping power demand for the same pressure in comparison with liquid lubricants [29]. Such value is much lower than supply pressure of hydrostatic bearings, which typically operate at 20–40 atm but can reach 200 atm, when space is not limited and large loads must be supported. Specific load capacity (load per pad area) for aerostatic and hydrostatic bearings is the efficiency multiplied by supply pressure, where the efficiency is typically 25–40%.

For rolling element bearings, the "carrying capacity" is the ability of the bearing to carry a

The maximum documented specific load for rolling element bearings operating in gas turbines is reported in reference [21]. **Table 5** reports the durations of bearings in a shaft support system designed by means of catalog high-precision rolling bearings solely. They are computed according to the adjusted basic rating life [27] by using data in **Table 1** and radial as well as thrust loads in **Table 2**. It is assumed that radial load is equally distributed between two sets of high-precision angular contact bearings and only one (locating) set carries the axial load in order to allow the thermal dilatation of the shaft. The solutions with both 2 and 5 matched bearings in the sets (in tandem arrangement) that carry the axial load are not satis-

Dynamic load ratings of steel bearings can also be used for ceramic bearings of the same dimensions [28], since from test results and predicted values service life of ceramic bearings

**Table 5.** Expected life for sets of angular contact high-precision bearings, carrying half of the rotor weight and, if specified,

One bearing, radial load W 267,960 1,276,000 6,380,200 Two bearings, radial load W and axial load Tref 65 310 1549 Five bearings, radial load W and axial load Tref 451 2150 10,747

 **(h) L10 (h) L50 (h)**

For the remaining bearings, fatigue is not the main concern, and the external load can be

given load for a predetermined number of cycles or revolutions [26].

**Table 4.** Maximum service-specific loads for different bearing types.

**Bearing type Max service-specific load (MPa)**

Rolling element 2 Ceramic hybrid 2 Ceramic integral 2 Oil sleeve 2.1 Oil tilting pad 4.4 Hydrostatic 6 Magnetic (AMB) 0.8 Magnetic (PMB) 0.4 Aerodynamic, air foil 0.7 Aerodynamic, rigid/grooved 0.1–0.2 Aerostatic 0.2

10 Bearing Technology

factory compared with the machine life (about 70,000 hours).

**Set L1**

is longer than that of steel bearings, except for heavy loads.

treated as static.

the axial load.

According to the basic rating life formula [27], for constant duration load-carrying capacity of rolling element bearings drops as speed rises. On the contrary, load capacity of foil bearings is proportional to rotational speed. Hence, foil bearings outperform rolling element bearings at high speeds [30] but require solid lubrication at low speed in order to reduce friction and wear. Particularly, conventional solid lubrication systems, i.e, thin polymer films, enable over 100,000 h of operation before requiring a major overhaul. Beyond the temperature limits of polymer coatings (300°C), innovative coatings (PS304, Korolon) have demonstrated lives in excess of 100,000 h start-stop cycles under moderate loads (0.34 MPa) and high temperatures (ranging between 178 and 650°C) where such solid lubricants become active. However, bearing operating life is cut by over half (roughly 33,000 cycles) at room temperature (25°C), where the coating does not perform as well [24]. For low temperature start-ups, usually under higher loads, life may further decrease [31].

In order to characterize the behavior of foil bearings by means of a suitable map, in reference [32], a modified Sommerfeld number S′ is correlated with the specific power loss. Foil journal bearings must be designed so that they operate in the high speed (or lightly loaded) regime (S′ > 6) of the operating map plotted in **Figure 3** in agreement with the suitable regression proposed by the reference authors. Particularly, the nominal working point should be located in the high-speed (lightly loaded) regime, but significantly far from the shaft strength and thermal limits (specific power loss lower than 155,000 W/m2 ).

**Figure 3.** Performance map of foil bearings and operating points of the reference micro-GT for different journal diameters.

In order to locate in the operating map the nominal working point of a single radial foil bearing supporting the reference microturbine shaft, the data reported in **Table 1** are used together with unit (axial) length to diameter ratio (L/D = 1), load coefficient equal to 2.7 × 10−4 N/(mm3 krpm) (third-generation bearings) and isoviscous behavior assumption. In addition, the total load is approximated by the external one (40 N) as first estimate. By means of such assumptions, the assessment of S′ according to reference [32] suggests that the working conditions are not suitable (S′ = 1.6 < 6). Therefore, the journal diameter must be increased (optimal values range between 25 and 40 mm, as suggested in **Figure 3**). Indeed, transitioning over to oil-free lubrication requires suitable design solutions in that thin shafts are not required anymore to avoid rolling element bearings from operating above their DN threshold. On the contrary, large diameter hollow shafts must be used in order to increase the peripheral speed and, as a consequence, the load capacity of air bearings [31].

As far as the remaining air film bearings are concerned, the different fluid film bearing designs (multilobe and tilting-pad geometries) achieve better stability than plain bearings at the expense of load-carrying capacity. On the contrary, gas-lubricated grooved bearings promise stability with minor reduction of lift [33].

Magnetic bearings have advantageous load-carrying characteristics, whereas load does not drop as speed decreases. Nevertheless, if the electromagnets are unable to support the applied load because they are undersized or malfunctioning, the shaft cannot be levitated and the machine shuts down [34]; therefore, backup bearings are required to protect the rotor against overloads and power loss.

Reasonable specific loads for AMBs range between 0.3 and 1 MPa. Particularly, the maximum specific load value reported in **Table 4** is suggested for AMBs in reference [21] on the basis of the data published in references [35, 36].

For a stacked structure of PMB fabricated using neodymium-iron-boron magnets with a remanence of 1.3 Tesla (42 MGOe magnetic field), the maximum specific load, referred to the axial cross section (LD), is roughly 0.4 MPa and the corresponding axial specific load is 0.6 MPa [37].

Life expectancy of passive bearings is very high, i.e., in excess of 20 years. As AMBs include more components (controllers, coils, and sensors) and a laminated rotor, their life is expected to be shorter but, anyway, AMBs can still last 20–30 years with proper substitutions of failed components.
