The Two-Pad: A Novel Gas Foil Bearing for Fuel Cell Vehicles

Reducing costs and improving durability are essential factors for commercializing gas foil bearings, crucial components of fuel cell vehicle air compressors. In this paper, a two-pad gas foil bearing is proposed. By reducing the number of top foils, adopting a symmetrical design, and eliminating the welding step, the cost of processing and assembly is reduced, and the potential source of failure caused by welding is eliminated. The feasibility of the two-pad gas foil bearing was verified through testing on a commercial fuel cell vehicle air compressor. Then, durability testing was performed in accordance with fuel cell vehicle usage requirements, including an accelerated random vibration test equivalent to 6,000 h of on-board operation and a 200,000-cycle start-stop test. These tests simulated the damage caused to the bearings during fuel cell vehicle operation and start-stop periods, respectively. The durability test results indicated that the two-pad gas foil bearing provides good start-stop durability but insufficient durability against on-board random vibration. The failure causes were analyzed, and improvement measures were proposed. Our findings can be utilized to guide the manufacturing of low-cost and highly durable gas foil bearings.


Introduction
Fuel cell vehicles are considered to be a leading contender for next-generation clean energy vehicles due to their high efficiency, zero emissions, and long range [1][2][3][4][5].A fuel cell vehicle air compressor (FCVAC) is one of the most important components of fuel cell vehicles, which provides compressed air to the cathode of the fuel cell.Compared with general air compressors, FCVACs present requirements for oil-free, compactness, high speed, and higher efficiency.These requirements put high pressures on the rolling and plain bearings when using conventional lubricants.Gas foil bearings (GFBs) are plain bearings with gas as the lubrication medium and have been widely utilized in air circulators, high-speed motors, high-speed blowers, high-speed compressors, turbojet engines, gas turbines, and other highspeed equipment [6].Since the lubricant is derived from ambient gas or air, the GFB naturally meets the oil-free requirement.This eliminates the need for complex oil supply systems, making the system very compact.In addition, due to the low viscosity of the gaseous lubricant, it is possible to reach very high speeds with low power loss.Therefore, GFBs are well suited for use in FCVACs.However, it is expensive and challenging to manufacture GFBs [7], which has become an important issue in commercial applications.Additionally, a number of other GFB structures are beginning to receive attention; examples include the use of a wing foil [8], metal mesh [9], or nest compression springs [10] instead of a bump foil and the replacement of the flexible top foil with a rigid air ring [11].Although these bearings have exhibited some positive results under research conditions, they are still not sufficiently mature, and there are few cases of their commercial application.Therefore, it is necessary to further explore low-cost GFBs.
Another challenge in using GFBs for fuel cell vehicles is their durability.For on-board applications, high durability is indispensable.However, more research has been done on the performance of GFBs, and less has focused on their durability [12][13][14][15], and the failure pattern of GFBs under long-term on-board operation is still unclear.Knowledge of this pattern is critical for commercial FCVACs that require both longevity and high safety standards.The start-stop process is an important factor affecting the durability of GFBs.Due to the compliance of the structure, the foil is subject to wear during start-stop operations, and FCVACs will inevitably be exposed to frequent start-stop operations.Heshmat et al. [16] compared the performance changes of PS304, hard chrome, and Korolon coatings during 500 start-stop cycles at 810 °C through testing.Kim and Zimbru [17] presented a 102 mm-diameter hybrid air foil bearing designed for aerospace propulsion applications that can withstand 1,000 startstop cycles.Walton et al. [18] designed a 15 mm-diameter GFB for small rotors, and the life of the bearing and coating exceeded 1,000 start-stop cycles.Dellacorte et al. [19] investigated the tribological properties of a chromium oxidebased coating and showed that the coating had an operating life of up to 20,000 cycles at 25 °C and 500 °C.Dellacorte et al. [20] coated the top foil with a PS304 solid lubricant coating, and tests showed that the bearing life exceeded 30,000 cycles at 25~650 °C.Radil and Dellacorte [21] investigated the sliding contact properties of PS400, a variant of PS304.They designed a test rig and performed 50,000 cyclic load tests.The number of start-stop cycles in the above studies is still an insufficient number compared to the requirement of FCVAC in real-world applications.According to published data, the average life of a vehicle before scrapping is approximately 17 years in the US and 20 years in Europe [22], and the average number of start-stop cycles per day for these vehicles is 5 [23].As such, the number of start-stop cycles required for an FCVAC is at least 36,500 cycles over the average life of a vehicle on the road.Assuming that the instances of start-stop cycles and vehicle life are normally distributed, the actual start-stop cycles required are much larger if the three-sigma limit is considered.To date, few tests have spanned such a high number of start-stop cycles.
Theoretically, the life of GFBs is nearly infinite as long as the rotor can successfully lift off, but only if the rotor can be maintained in a steady state.The relatively low support stiffness of GFBs due to the use of air as the fluid medium means that strong vibrations may bring the high-speed running journals into contact with the bearings, thus causing bearing wear and failure during vehicle travel.In 1993, Peng and Carpino [24] introduced a method for calculating the dynamic coefficients of GFBs, offering a convenient approach to assess their dynamic characteristics.Peng and Carpino [25] found that the GFB can dissipate more energy through Coulomb friction, which provides damping to the GFB to make it more stable.Vleugels et al. [26] conducted a stability comparison between GFBs and rigid gas bearings with similar geometry, revealing that GFBs exhibit greater stability even without additional damping.Lai et al. [27] conducted an experimental study on GFBs with different radial clearances in a high-speed turboexpander and found that too small a clearance would cause thermal runaway of the bearing, while too large a clearance would destabilize the bearing.To enhance stability, Kim and Andres [28] introduced mechanical preload by inserting shims under the bump foils in GFBs.Their experimental results demonstrated the beneficial effect of preload on stability enhancement.Gu et al. [29] explored the impact of flexible supports on the dynamic characteristics of GFB systems, highlighting the potential to optimize dynamic performance through appropriate support stiffness and damping.Kim [30] analyzed four types of GFBs with different bearing shapes and stiffness distributions and found that the threepad GFBs had better stability compared to the single-pad GFBs.
Current research on vibration that cause instability in GFB-rotor systems can be divided into three main categories: (i) Studies on subsynchronous vibration due to nonconservative gas film forces [31][32][33][34][35] (ii) Studies on synchronous and supersynchronous vibration due to rotor rotation [36][37][38][39] (iii) Studies on the system response to harmonic vibration and shock [40][41][42][43][44] Although most vibration studies have focused on these three categories, in the real world, systems are often subjected to random vibrations from the environment, especially in in-vehicle devices, where the forces acting on vehicles traveling over irregular terrain are usually modeled as random vibrations [45].Random vibrations are vibrations that cannot be described by a deterministic function, such as bumps in a vehicle's path and vibrations in an aircraft fuselage due to atmospheric turbulence [46], and random vibrations have been shown to have destructive effects on many devices [45,47].Accelerated endurance tests are often constructed by applying random vibrations to the device to simulate the aging of the device in a natural vibration environment.Therefore, despite its realistic and practical nature, random vibration is not well addressed in the context of GFBs.
Therefore, we propose a low-cost two-pad GFB and investigate its feasibility and durability.The objective of this paper is to (1) propose a low-cost GFB, (2) evaluate the feasibility of the proposed GFB in turbomachinery, and (3) investigate the durability of the proposed GFB in on-board environments.This study presents a low-cost GFBs design and serves as a reference for the durability of GFBs in automotive applications.

Design of the Two-Pad GFB
The GFBs, in this paper, are designed to reduce the cost of processing and assembly techniques.First, welding should be avoided as much as possible.It is difficult to weld on the narrow inner surface of the bearing.In addition, when fixing the foil to the sleeve by welding, both the foil and the sleeve will be deformed by the heat generated by the welding, and thus strains will appear in the foil.If these welds are not properly heat treated, then cracks may develop at these welds [6].Second, the rotor stability of GFBs is poor due to the use of low-viscosity air as the lubrication medium.To solve this problem, multipad GFBs are proposed.By cutting off the continuity between gas foils, multipad GFBs can improve rotor stability [30,48,49].However, the increase in the number of foils also poses processing and assembly problems.Therefore, to reduce the additional costs associated with increasing the number of foils, this paper does not use the three-pad GFB that has received the most 2 International Journal of Energy Research attention [50][51][52][53] but instead uses a two-pad GFB.Third, a symmetrical design has been used in the two-pad GFB to ease the difficulty of assembly.Conventional single-pad or three-pad GFBs can only rotate in one direction.However, during actual assembly, determining the direction of rotation of the rotor and mounting the bearing in the correct direction of rotation is often not as easy as it seems.
Figure 1 shows the structure of the two-pad GFB.The two-pad GFB is designed with a structure of four bump foils and two top foils.It has only two top foils, which is a good way to reduce the cost of coating the top foils.The fourbump foil design provides symmetry to the two-pad GFBs and ensures that the bump foils have free ends to provide friction damping.The sleeve is equipped with two dovetail structures in the horizontal direction and two grooves in the vertical direction.The dovetail structure, originally part of the sleeve, is formed by two cutting grooves inclined on the inner surface of the circumference.During installation, the ends of the top foil are inserted into the gap between the dovetail structure and the sleeve.The depth of the grooves should be appropriate to ensure that there are no large stresses in top foils.This structure is easier to manufacture and assemble and can be implemented without welding seams, eliminating possible failure modes.In the case of bearing damage, it is also easy to replace the foils without replacing the sleeve.The bump foil is designed with a classic folded edge, and the folded edge of the bump foil is inserted into the grooves during installation.The pressure provided by the top foil keeps the bump foil from coming out of the groove.The free end of the bump foil is not inserted into the dovetail structures but is left with a freely retractable distance.This allows the bump foil to provide damping by friction with the top foil and sleeve during expansion and contraction, improving rotor stability.Both the top and bump foils in this paper are made of Inconel X-750 nickel-based alloy.The side of the top foil in contact with the rotor is coated with PTFE, a classic wearresistant coating material that is inexpensive, readily available, and has no patent restrictions.

Feasibility Evaluation of the Two-Pad GFB for FCVACs
Figure 2 shows the structure of the commercial FCVAC in this paper.The rotor of the FCVAC is supported radially by a pair of GFBs and axially by a pair of gas foil thrust bearings.Unlike turbine-driven compressors, the FCVAC is a permanent magnet synchronous motor (PMSM) with a permanent magnet built into the rotor.When the stator placed around the rotor is energized to generate a magnetic field, it drives the rotor to rotate, drawing the air from the impeller 1 side for the first compression.After the primary compression, the air is sent through  3 International Journal of Energy Research a pipe to impeller 2 for the second compression.The commercial FCVAC in this paper has a rated power of 30 kW, a rated speed of 90,000 rpm, and an idling speed of 30,000 rpm.
Table 1 presents the parameters of the FCVAC bearingrotor system in this paper.
To investigate the feasibility of two-pad GFBs for the FCVAC, two tests were designed: a lift-off test to ensure that the rotor can lift off properly under its weight and a rotor stability test as a final evaluation of feasibility.

Lift-off Test.
A lift-off test is performed to ensure that the support force provided by the GFBs can lift the rotor off.The lift-off test bench is shown in Figure 3.The GFB is mounted on the tooling fixture, and a ring for connecting the loading weight and the force sensor is mounted in the vertical direction of the tooling fixture.The loading weight applies a vertical upward pull to the GFB through pulleys to simulate the real situation in which the rotor is pressed against the bearing.When the motor shaft rotates, it applies a torque to the GFB in the same direction of rotation due to friction, causing it to tend to rotate in the same direction.The force sensor and the two-pad GFB are connected by a tensioned elastic cord, providing a tension force that impedes the rotational tendency of the two-pad GFB.This tension force multiplied by the vertical distance from the sensor to the shaft center is the frictional moment applied to the two-pad GFB.
Using one-half of the FCVAC rotor mass (720 g) as the load, the friction torque measured after starting the motor showed a clear trend of increasing and then decreasing with increasing speed.The test was repeated several times until the results were stable, and the relationship between the frictional torque of the bearing and the speed change with time was obtained, as shown in Figure 4.The test results show that the FCVAC rotor using two-pad GFBs can lift off successfully with a lift-off speed of approximately 13 krpm.

Rotor Stability Test.
Rotor stability is the most important basis for evaluating whether GFBs are feasible for FCVACs.The two-pad GFBs were installed in the FCVAC, and the FCVAC was gradually accelerated from idle speed to rated speed.The vertical displacement of the FCVAC rotor was measured using an eddy current displacement sensor, and the test bench and test location are shown in Figure 5.The dynamic balance volume of the FCVAC rotor in this test was less than 0.05 g•mm.
The fast Fourier transform (FFT) is used to process the displacement obtained from the test.The results are shown in Figure 6.Compared to the nominal clearance of 60 μm, the maximum vibration amplitude of the rotor supported by the two-pad GFBs is approximately 20 μm, which is within the safe range, and the subsynchronous harmonics are low, showing good air film stability.Therefore, it is feasible to use two-pad GFBs for FCVAC.

Durability Investigation of the Two-Pad GFB for FCVACs
To investigate whether the proposed two-pad GFBs can meet the durability requirements of FCVAC, durability tests were conducted on FCVAC installed with two-pad GFBs.The durability study of the two-pad GFBs for FCVAC was divided into two parts: an accelerated random vibration test and a start-stop test, which were used to simulate the driving   International Journal of Energy Research process and start-stop process of the fuel cell vehicles, respectively.After the test, durability is evaluated using rotor stability and top foil wear status.Before the test, all tested FCVACs were subjected to a lift-off test and a rotor stability test to ensure that they could operate normally and perform similarly.

Experimental Protocol
4.1.1.Accelerated Random Vibration Test.Random vibration is generally described by the power spectral density [54].Due to the long service life of real equipment, it is impractical to perform durability tests of the same duration in the laboratory.Therefore, accelerated tests are needed.The Miner-Palmgren hypothesis is used to relate exposure time and amplitude according to the US military standard MIL-STD-810.The mathematical expression for this technique is illustrated below in [55] The ratio S 1 /S 2 is commonly known as the exaggeration factor.For factors greater than 1, the test time is shortened; for factors smaller than 1, the test time is extended.In order to stay within the yield limit of the material, the exaggeration factor is generally considered not to exceed a value of 2. The value of m = 7 5 is typically used for random environments.Based on publicly available data [22], we estimate that the fuel cell vehicle will be driven 6,000 h during a typical life cycle.According to the Miner-Palmgren hypothesis, taking the exaggeration factor equal to 1.9, the shortened test time is 1/1 9 7 5 * 6000 ≈ 48 6 h.According to the real vehicle vibration data obtained from our test, the power spectral density of the random vibration test is shown in Figure 7, where Z represents the direction of gravity, Y represents the axial direction of the rotor, and X represents the lateral direction of the rotor.X, Y, and Z represent the direction of travel, the direction of the vehicle's sides, and the vertical direction, respectively.
To simulate the changes in working conditions during the service life of FCVAC, the working conditions were divided into two types: idle speed and rated speed, each accounting for 50% of its service life.During the test, a 24.3 h random vibration test at idle speed was completed in the order of X, Y, and Z directions.Then a 24.3 h random vibration test at rated speed was completed in the order of X, Y, and Z directions.The compressor in the test at rated speed was operating at a compression ratio of 3.25 and a mass flow of 0.178 kg/s.The total random vibration test duration was 145.8 h.Another FCVAC group was prepared to run for the same duration but without inducing random vibration, which was used as a control.

Start-Stop Test.
Based on the FCVAC idle speed, the change in rotor speed during a start-stop cycle is 1 second of uniform acceleration to 30,000 rpm, 5 seconds at 30,000 rpm, followed by 1 second of uniform deceleration to 0 rpm, and 2 seconds at 0 rpm.The number of start-stop cycles for the test was set to 200,000 to meet the maximum possible service life requirement of the GFBs.Compared to the rotor amplitude of 20 μm after normal operation, the maximum vibration amplitude of the rotor affected by random vibration exceeds 40 μm, indicating that the random vibration of this paper's intensity significantly affects the stability of the rotor supported by twopad GFBs.The results also show a significant increase in synchronous and supersynchronous vibrations, which may be caused by the loosening of parts due to random vibrations [56].After 200 k start-stop cycles, the rotor vibration amplitude increased slightly, but the overall amplitude remained within a relatively safe range.The subsynchronous vibration is basically unchanged, indicating that the air film still has good stability after 200 k start-stop cycles.

Top Foil Wear Status.
The condition of the top foils of the two-pad GFBs after the durability test is shown in Figure 9.In this paper, GFB 1 is located on the inlet side, and GFB 2 is located on the outlet side.Compared with the wear of the top foils affected by random vibration, the wear of the top foils in normal operation is significantly lighter, indicating that the random vibration of the intensity tested in this paper has a significant effect on the life of the top foil.The photo also shows that both the upper and lower top foils show axial band wear near the dovetail structure.Defining the side of the GFB with reduced clearance along the rotor rotation direction as the converging wedge and the side with increased clearance as the diverging wedge, the wear of the top foil in   Based on the top foil wear status results, the wear of the top foils shows that the two-pad GFBs can withstand 200,000 start-stop cycles but are not durable enough for 6,000 h of on-board random vibration.To better analyze the causes of failure, we summarized the possible wear-prone areas of the two-pad GFBs after a long operation, as shown in Figure 10.The lower top foil has two high-wear-risk areas and two medium-wear-risk areas, which are located near the dovetail structure and the groove, respectively.The upper top foil has two high-wear-risk areas, both located near the dovetail structure.Additionally, there is a risk of cracking in the converging wedge of the lower top foil.
We propose that the reason why the medium wear risk area arises is related to the lack of support for the top foil near this area.As shown in Figure 11, the medium wear risk area is near the groove, where the top foil in the groove area is slightly depressed due to the lack of support after being subjected to gas pressure, which leads to a slight bulge on both sides of the depressed area.In contrast, the pressure of the top foil on the upper side was lower, and the clearance was larger.Thus, no wear was observed in the vicinity of the upper groove area.A similar phenomenon was reported by Kim and Zimbru [17], where the wear was no longer observed after adding a shim to the area at the notch where the support was lacking.
For the reason why the high wear risk area arises, we believe it is related to the dovetail structure.As shown in Figure 11, the top foil extending from the dovetail structure is not concentric with the circular arc formed by the bump foil, which causes the top foil to bulge and separate from the bump foil after contact with the first bump.This means that this part is more likely to come into contact with the rotor during operation.Now that it is clear that a bulge section of the top foil exists after contact with the bump foil, the remaining question is why the wear is more severe in the converging wedge than in the diverging wedge and the cracks appear in the converging wedge.We think that this is related to foil deformation due to the pressure distribution inside the bearing.Reynolds derived the Reynolds equation from the Navier-Stokes equation in 1886 based on lubrication theory.In the analysis of gas bearings, the thickness of the gas film is much smaller than the radius of the bearing, so it is reasonable to use the Reynolds equation to describe the gas flow in the gas bearing gap.The dimensionless Reynolds equation for a compressible fluid under isothermal conditions can be expressed as where The dimensionless gas film thickness H can be shown as where K is a constant reflecting the structural rigidity of the bumps.It was given by [57] The appropriate boundary conditions for the Reynolds' equation are as follows  The Reynolds equation is discretized by using the finite difference method and then solving.The air pressure distribution of the GFB is shown in Figure 12.Due to the rotor rotation, the air pressure is generally higher on the side of the diverging wedge so that the overhanging top foil shown in Figure 11 is pressurized more tightly against the bump foil than the top foil in the converging wedge.This makes the top foil in the converging wedge more susceptible to wear.
From the above analysis, it is clear that the different curvatures of the bump foil and the top foil are an important cause of wear and cracking.Therefore, the height of a few crests at the free end of the bump foil can be slightly reduced to gradually transition to a normal height to fit the curvature of the top foil.

Conclusions
In conclusion, we propose a novel GFB, featuring a symmetrical configuration with two top foils and four bump foils.Unlike conventional welding techniques, this design employs grooves and dovetail structures to secure the foils.The feasibility of implementing this two-pad GFB in FCVAC was verified through a lift-off test and a rotor stability test.The results indicate that the two-pad GFB exhibits sufficient load-carrying capacity and provides stable rotor performance, making it a feasible option for turbomachines.To assess durability, we designed a comprehensive test comprising 200,000 start-stop cycles and an accelerated random vibration test equivalent to 6,000 hours of on-board operation.The rotor stability remained satisfactory after 200,000 start-stop cycles but significantly deteriorated following the random vibration test.
Notably, regular wear bands and cracks appeared on the surface of the top foils after the durability test.Analysis of the test results revealed that the wear at the bottom position of the GFBs resulted from the lack of support for the top foil at that specific location.Additionally, the wear and cracks near the dovetail structure were attributed to two factors: the local bulging of the top foil due to the difference in local curvature (stemming from the dovetail structure) between the top foil and the bump foil and the pressure distribution within the GFB.
Our study demonstrates the feasibility of this new twopad GFB for utilization in turbomachinery, proves the significant impact of random vibrations on GFBs, and reveals a mechanism for durability failures due to fixed structures.These results can guide manufacturers in producing lowcost and highly durable GFBs.

Figure 1 :Figure 2 :
Figure 1: Structure of two-pad GFB: (a) schematic diagram and (b) explosion image of the upper half side.Rotor

Figure 4 :
Figure 4: Torque and rotation speed versus time.

4. 2 .
Results and Discussion 4.2.1.Rotor Stability.The vibrations on the impeller 2 side of the rotor after the durability test are shown in Figure 8.

Figure 6 :
Figure 6: FFT results of the rotor stability test.

Figure 8 :
Figure 8: FFT results of the durability test: (a) after 145.8 h normal operation, (b) after 145.8 h random vibration, and (c) after 200 k startstop cycles.

Figure 7 :
Figure 7: Power spectral density of random vibration: (a) direction X, (b) direction Y, and (c) direction Z.
a 0.124 mm Bump foil thickness, t b 0.124 mm Bump foil pitch, s 2.00 mm Bump half-length, l 0.63 mm Bearing inner diameter L: Bearing length C: Radial clearance t a : Top foil thickness t b : Bump foil thickness s: Bump foil pitch K: Structural rigidity l: Bump half-length t 1 : Equivalent test time t 2 : In-service time for specified conditions S 1 : Severity RMS at test conditions S 2 : Severity RMS at in-service conditions m: Slope of the S-N curve of the material E: Young's modulus of the material v: Poisson ratio of the material p: Dimensionless gas film pressure H: Dimensionless gas film thickness z: Dimensionless axial coordinate θ: Angular coordinate Λ: Bearing number p: Gas film pressure p a : Environmental pressure H: Gas film thickness z: Axial coordinate μ 0 : Viscosity ω: Angular velocity ε: Eccentricity δ: Foil deformation amount θ 0 : Attitude angle. R: