Additively Manufactured Compliant Hybrid Gas Thrust Bearing for Supercritical Carbon Dioxide Turbomachinery: Design and Proof of Concept Testing

Super-critical CO₂ Brayton power cycles show great promise as efficient and power-dense solutions for converting renewable solar energy or gas turbine waste-heat sources to electric power [1,2]. Within the sCO₂ power cycle, turbomachinery efficiencies and cost are key elements of interest when assessing the commercial viability of the cycle concept. One approach to improving performance and reducing cost of the system is to support the turbomachinery rotor assembly using process gas lubricated bearings. By eliminating conventional oil-based bearing lube systems and using the process gas as the bearing lubricant, there is potential to simplify mechanical design, reduce bearing windage/power loss [3], reduce part count, and in the case of sCO₂ turbomachinery enable zero-carbon emission-free hermetic machine configurations [4,5]. However, to successfully sustain rotor thrust loads and misalignments indicative of high powered sCO₂ turbomachinery, component bearing technology development is needed. Figure 1 shows a table of some known gas lubricated thrust-bearing concepts.

Fluid-film bearings can generally be categorized into two main types: hydrodynamic and externally pressurized. Furthermore, existing concepts either operate as fixed geometry bearings or flexible/compliant bearings. The simplest fixed geometry hydrodynamic (self-acting) bearing, as shown in Fig. 1(a), uses an interrupted 360 deg thrust face in combination with converging flow geometry on the thrust sector aimed at maximizing pressure generation. Another widely known design uses spiral face grooves (Fig. 1(b)) on a continuous 360-deg thrust face to pump the lubricating fluid to high pressures. To reach higher load capacity, hydrostatic pressurization can be employed to the thrust face (Fig. 1(c)); however, external pressurization with fixed geometries can lead to pneumatic hammer instability [6–9]. Regardless of the film pressurization mechanism, a fundamental limitation of fixed geometry bearings for application into large turbomachinery is the ability to sustain misalignments in the mechanical system. Figure 2 shows typical misalignments and distortions that are present in thrust-bearing systems. Due to the nonlinearity of a lubricating gas film, the clearances in gas bearings do not scale proportionally with machine size. This poses a major challenge when considering machines with increasing size and therefore increasing alignment errors. Additionally, high-performance turbomachinery rotor-bearing systems in the mega-watt power range are required to traverse rotordynamic modes with pitching and yaw rotor motions and therefore necessitate compliance to dynamic misalignment. Also, high speed operation and/or high loading conditions can lead to out-of-plane warping [10,11] of the thrust runner. Therefore, devices designed using fixed geometry bearings are ultrasmall and operate below major rotor modes, making the application to large high-performance turbomachinery difficult.

A major advancement to traditional fixed geometry bearings was the development of the foil bearing. The most common type of foil thrust bearing (Fig. 1(d)) possesses individual thrust sectors comprised of a flexible top foil attached on the leading edge while free on the trailing edge [12]. Furthermore, the top foil is supported underneath by a flexible bump foil that has carefully designed stiffness properties that can vary in both radial and circumferential directions. Other foil bearing designs exist that use multiple 360 deg foil sheets assembled in an axial stack [13] configuration. Regardless of the foil architecture, foil bearings are unique due to the ability to sustain all types of misalignments within reasonable limits. The flexibility of foils allows for local deformations/deflections independent from neighboring regions, making the compliance to complex misalignments and deformations of the thrust runner more manageable when compared to fixed geometry bearings. Additionally, thrust foil bearings have positive damping coefficients [14], generated from the microslip Coulomb friction between foil contact regions and demonstrate superior load capacity compared to spiral groove bearings [15]. With the maturation of foil bearing technology, oil-free operation of high-performance turbomachinery in the kilowatt power range like air cycle machines [16] and microturbines [17] were enabled. Another type of bearing uses a novel approach to creating compliance of a spiral groove thrust face (Fig. 1(e)). The concept uses wire electric discharge machining (EDM) creating four equally spaced beam springs around the circumference of the thrust face support [18]. This allows flexible mounting of the bearing improving the compliance to static and dynamic misalignment compared to the fixed geometry approach. However, the thrust face is a 360-degree rigid body, which makes compliance to out-of-plane warping a challenge.

The last category represents thrust bearings that possess compliance/flexibility in combination with external pressurization. The motivation with this bearing approach is to retain compliance to misalignment while increasing load capacity, when compared to hydrodynamic bearings, through external pressurization. Ream [19,20] developed a flexibly mounted spiral groove thrust bearing with hydrostatic orifice holes for startup. Figure 1(f) shows the concept. It involves a bolted/clamped back to back thrust-bearing arrangement with a spacer in the center. The assembly interfaces with the inside rim of a flexure possessing four tangentially installed spokes. The outer rim of the flexure is held stationary through a hard-mounted bearing carrier. The flexure allows for angular compliance, axial flexibility, and allows for relative movement between the Coulomb friction damper clips. Ream's concept [19,20] is an improvement over fixed geometry spiral groove bearing but requires an assembly of several high precision components and does not possess compliance to out-of-plane thrust runner distortions. Another compliant hybrid bearing concept is the externally pressurized thrust foil bearing. Two references were found discussing the concept [21,22].

The main objective for this work was to develop a gas lubricated bearing suitable for application into large high-powered turbomachinery that demonstrates a notable increase in load-carrying capability. Recognizing the unique challenges associated with integration into large machinery, there is a need for a thrust bearing that can: (1) increase thrust load-carrying capacity using hydrostatics while maintaining dynamic stability, (2) provide compliance not only to misalignment but also to out-of-plane distortions of the thrust runner, (3) provide high levels of precision with a cost-effective scalable design into large machines.

The compliance to misalignment and/or deformation of the thrust runner was a key design consideration when conceptualizing the thrust bearing. Figure 3 shows the high-level concept and the main design elements critical to reliable operation. The concept is comprised of a compliant or flexibly mounted thrust face, which also has hydrostatic pressurization capability. Like radial compliant hybrid gas bearings [1,23,24], the thrust-bearing concept aims to soft-mount the hydrostatic-hydrodynamic (hybrid) gas film to the machine casing using a compliant support. In this configuration, the thrust-bearing support transmits the same forces/moments as the gas film while most of the misalignments in the system are intended to be absorbed by the compliant support. Since deformations and deflections of the thrust runner are absorbed within the support, the gas film thickness is maintained and reliable operation under misalignment is enabled. As shown in Fig. 3, the thrust bearing is required to operate with misalignment and out-of-plane warping of the thrust runner and therefore requires individual thrust pads about the circumference of the thrust face to adapt to nonideal operating clearance geometries. The other design element was the damping of the bearing system. As discussed in the previous section, pneumatic hammer is a concern with externally pressurized gas bearings and becomes more of a risk with increased pressure-flow delivery (high-load capacity requirement). Due to this risk, a hermetic squeeze film damper (HSFD) [3,24] was also envisioned in the bearing support to help render a stable bearing system. Unlike radial bearing systems, thrust bearings do not have axial unbalance forces and therefore do not have to traverse and/or bound rotordynamic critical speeds. Also, axial instabilities in turbomachinery rotor systems are rare compared to lateral instabilities. Therefore, the thrust-bearing support does not necessarily have a stringent requirement for an optimum damping coefficient but needs to possess equivalent damping coefficients that yield an inherently stable bearing system. Without ensuring positive bearing damping with some margin, the rotor-bearing system could be subjected to undesired axial vibrations.

Using the high-level concept in Fig. 3 as the design approach, the next step in the design process was to develop a suitable bearing support spring geometry. There were three main factors evaluated during this design task. The first two factors considered the axial stiffness and rotational stiffness of the thrust pad support. The third factor, design for additive manufacturing, evaluated the manufacturability using direct metal laser melting (DMLM) while adhering to the build geometry constraints associated with the process. Additive manufacturing was selected for the manufacturing process due to the numerous functions required for the bearing concept. Reference [24] shows that using a modular approach with conventionally machined components can lead to hundreds of assembled components rendering a costly and unreliable solution.

Figure 4 shows some of the concepts considered for the thrust pad support architecture. The support geometry was required to provide axial and rotational stiffness to the pad, provide a way to deliver pressurized fluid from a stationary structure to a movable pad, and create internal cavity geometry suitable for a HSFD. The design study down-selected three pad spring architectures (2, 11, and 17) for build trials; shown as cut-up sections in Fig. 4. From these initial studies, concepts 11 and 17 advanced to detailed design for evaluation of stiffness coefficients using a commercially available finite element analysis program. As shown in Fig. 4, concept 17 and 11 resulted in similar axial stiffness coefficients while the rotational stiffness coefficient of concept 17 was shown to be ∼7 times less than concept 11. The axial stiffness was sized to yield an acceptable equivalent damping coefficient, whereas the rotational stiffness provides the compliance necessary to absorb misalignments in the rotor-bearing system while generating safe levels of stress. Another differentiator, due to the diaphragm spring architecture, was the axial space envelope between the two concepts, as concept 17 is significantly more compact in the axial direction. After initial structural analysis, a fluid–structure model of the flexible mounted hybrid gas film using the appropriate degrees-of-freedom needed to be assessed. This was conducted using an in-house thrust-bearing design tool [25]. The design tool combines the compressible Reynolds flow equation with structural force and moment balance equations for a rigid body pad supported through a single discretized linear spring element possessing axial and rotational compliance. The design tool allows prediction of operating clearances, leakage flow, power loss, and the orientation of deflected pads. Detailed explanation of the assumptions and computational methods is described in Ref. [25].

Initially conceptualized by Ertas et al. [26], Figs. 5 and 6 show the detailed design of the final down selected thrust-bearing concept. Figure 5 represents the computer-aided design model and Fig. 6 shows the CT scans used for nondestructive inspection. The engineering of the thrust bearing was comprised of three areas of design. First, the structural design was aimed at creating the pad support spring structure, mechanically coupling the individual pad modules together, and developing design features to mount/install the bearing in a machine casing. The thrust pad interfaces with the bearing housing through forward (FWD) and AFT diaphragm springs. The FWD diaphragm spring is built from the outer circular contour of the thrust pad and then morphs into the pad module support diaphragm. The AFT diaphragm spring grows from the central pad post and interfaces with the outer surface of the pad module. These two springs are responsible for setting the axial and rotational structural stiffness properties for a single pad. Next, to create rigidity between the pad modules inner diameter (ID) and outer diameter (OD); interpad web connections were designed. These web structures morph into OD/ID support pillars, which form a backing cage AFT of the pad modules. The backing cage extracts the thrust reaction force from the pad modules and transmits the reactions to the machine casing.

The second area of design involved integrating the hydrostatic flow circuit into the bearing architecture. The gas entry point into the bearing occurs on the back of the bearing cage through QTY 8 hydrostatic pressure inlets (no. 8 in Fig. 5). The hydrostatic gas flow path then continues through the OD support pillar (no. 5 in Figs. 5 and 6) and interpad web (no. 4 in Figs. 4 and 5) to the annular distribution plenum (no. 15 in in Figs. 5 and 6). The annular plenum distributes the pressurized flow to QTY 12 gas delivery passages (no. 10 in in Figs. 5 and 6). A key challenge with the design of compliant hydrostatic bearing pads is the transfer of pressurized fluid from a stationary reference frame to a movable pad. To accomplish this goal, the design in Figs. 5 and 6 routes the gas delivery passages from the pad module support diaphragm onto the back side of the FWD diaphragm spring. The transition from the stationary frame to the movable pad occurs at the interface between the support diaphragm (no. 14) and the FWD diaphragm spring (no. 12). Once the gas passages have spanned the FWD diaphragm spring they enter the pad labyrinth, which is comprised of several intersecting passages coinciding with the location of QTY 11 orifice restrictions with diameters at 0.018 in. (0.46 mm). Although the bearing was created as a monolithic part, postmachining operations were required to obtain adequate precision of the thrust face and mounting features. The back-side cage surface was finished using a milling operation in combination with a grind operation, whereas the thrust face was established leveraging wire EDM while using the back-side cage surface as the reference surface. This allowed tight control of parallelism between the mounting surface and thrust face, aiding to minimizing static misalignment in the bearing-thrust runner system.

The final design consideration was the engineering of the HSFD for the thrust pad. The HSFD for this bearing possesses two opposing damper cavities separated by a carefully controlled annular restriction clearance. The FWD damper cavity boundary is defined by the FWD diaphragm spring and support diaphragm, whereas the AFT damper cavity is bounded by the AFT diaphragm spring and support diaphragm. The annular clearance is created between the transition bend of the support diaphragm and the central pad post. As the pad experiences vibratory motion, fluid is exchanged between the two damper cavities through the restriction and thereby creates viscous energy dissipation realized as damping. Postbuild cut-ups and CT scans were used to ensure design intent (Fig. 6). Two prototype thrust bearings were taken to final machining as shown in Fig. 6.

The proof-of-concept testing was performed in air and ambient atmospheric conditions. Table 1 shows the test conditions and test parameters achieved during testing along with the bearing details. The test point presented reaches a maximum rotor speed of 10 krpm and uses a bearing inlet pressure of 380 psi (2.62 MPa) for hydrostatics. The objective of the test point was to demonstrate load-carrying capacity of the test bearing using 0.5 mils (12.5 μm) as the film thickness targets. Additionally, the test activity aimed at defining the force deflection curve for the gas film and the flexible bearing support. The test vehicle used for testing is shown in Fig. 7. The test rig is comprised of a straddle-mounted shaft assembly supported at both ends with rolling element bearings hard-mounted in shaft bearing pedestals. The shaft possesses a slave thrust runner for the oil-lubricated thrust bearing (not shown) and a test thrust runner (shown as No. 2 in Fig. 7). The loading system uses three circumferentially placed hydraulic actuators within the thrust housing to load the slave oil-lubricated thrust bearing, which was mounted in an axially movable bearing carrier. This results in axial movement of the test thrust runner toward the test bearing. The test bearing was mounted on a gas delivery housing that provides the pressurized hydrostatic air flow to the back of the test bearing cage. The bearing-housing subassembly was installed on a large load plate interfacing with the thrust housing through three equally spaced load cells. The three load cells were mounted in parallel and therefore the sum of the load cell readings yields the total thrust load on the test thrust bearing. Key measurements acquired during the test were displacement readings for the thrust runner movement with respect to ground (housing probe) and the thrust runner movement with respect to the thrust pad surface (film probe). By measuring the gas film gap and the total thrust runner movement from the housing probe, the gas film stiffness and the bearing support structural stiffness coefficients were calculated. Another important measurement during testing was subsurface thrust pad temperatures. The temperature readings were used to ensure that the load achieved during testing resulted in a thermally stable air film and provided confirmation of safe and reliable operation at the representative test point. The TC locations were chosen to be at the four corners of the instrumented thrust pad. A detailed description of the test rig design and operation can be found in a companion paper [27]. A standard procedure during test rig commissioning typically involves balancing the rotor system residual unbalance to a desired specification. During the balancing procedure, the rotor contacted an off-centered labyrinth seal at high speeds. This stator–rotor interaction created high levels of nonuniform heating on rotor surface in addition to damaging the seal bore. The unintended “rubbing” event (damage pictures shown in the Appendix) generated significant thermomechanical shaft deflection and resulted in a bent shaft. Figure 8 shows the results from measuring in situ shaft runouts using a precision dial gage. Runout readings were taken at 11 different accessible axial locations of the shaft surface and/or thrust runner surfaces. Using these readings, a shaft model was generated and revealed a misaligned thrust runner. The bent shaft limited safe operating speed to 10 krpm, amid several attempts to balance the system. Although the intended maximum speed of 20 krpm was at risk, the decision was made to continue testing the thrust bearing with the bent shaft and misaligned thrust runner. The test point with the severe misalignment would be used to validate and gain confidence on the pad spring design reliability.

The test profile is shown in Fig. 9. Thrust load was gradually increased from 500 lbs (2.2 KN) to 1500 lbs (6.7 KN) over a time span of 40 min. Testing was performed at 380 psi (2.62 MPa) resulting in 0.051 lbm/sec (0.023 kg/s) under loaded conditions. The maximum load capacity of the bearing was not reached; rather the loading was limited by monitoring film probes and limiting clearance closures to ∼0.5 mils (12.5 μm). In combination with monitoring gas film clearance closures, thrust pad temperatures were monitored for stable signatures without the onset of thermal runaway. The first data point of interest was the dynamic acquisition of loads and displacements at maximum load-speed conditions. Figure 10 shows the thrust loads and displacements containing both the static and dynamic signal components acquired at 10 krpm and a thrust load of 1500 lbs (6.7KN). As shown in Fig. 10, the thrust runner reveals a dynamic misalignment of ∼3 mil (75 micron) p–p when looking at the housing probe. The film probe shows dynamic misalignment vibration magnitudes of ∼1 mil (25 μm) p–p. It is important to note that the dynamic motion of the housing and film clearance predominantly revealed frequency content that was synchronous with the 10 krpm rotor speed. This was a notable result, as pneumatic hammer for hydrostatic gas films was a concern for the thrust-bearing system. The lower two plots in Fig. 10 show the thrust load readings acquired from the three load cells and also display the total thrust load signature for the bearing. The dynamic misalignment generates a complex dynamic force waveform with a p-p magnitude of ∼270 lbs (1.2 KN), which is 18% of the static mean thrust load on the bearing system.

The final plots focus on the mean value data readings for the thrust load and displacements. The two probe readings on either side of the thrust pad were averaged for the motion reading and were observed to be within 0.0001 in. (2.54 μm) of one another. Figure 11 was generated to illustrate the reference frames for the different probe readings and how the bearing support structure deflections were extracted. Subfigure (A) from Fig. 11 shows the bearing system with no thrust load and has surface to surface contact between the thrust runner and bearing thrust face. This position established the 0-point reference for the film thickness and the pad position. Reference [27] by Gary et al. describes this procedure in detail. Subfigures (B) and (D) show cases for two different loading conditions (low and high load) with a bearing support stiffness that is infinite (rigid bearing support). For these two cases, the total thrust runner displacement equals the film clearance reading. The last portion of Figs. 11(c) and 11(e) represents the thrust-bearing pad with a flexible bearing support. These two scenarios generate a different housing probe reading with respect to the film clearance reading, as the total thrust runner displacement is a sum of the film clearance and the bearing support deflection. Therefore, the bearing support structural displacement can be found by taking the difference between the total thrust runner displacement and the film clearance probe reading. Figure 11 also shows that high levels of load can lead to the housing probe reading a negative value as the displacement reading passes through the 0-point reference position.

Figure 12 shows the mean value results for the proof of concept testing and the static stiffness coefficients of the bearing system. As indicated earlier, the thrust load was increased from 500 lbs to 1500 lbs (subfigure A) while acquiring the housing probe and film probe signals. As expected with hydrostatic gas films [9], the force deflection characteristics are nonlinear. As the film clearance decreases, the total thrust load increases nonlinearly like a “hardening-spring.” Similarly, the housing probe (the sum of the film clearance closure and bearing support deflection) exhibits a less notable nonlinear trend, as the bearing support stiffness was hypothesized to behave like a linear spring. The bearing support displacement was calculated by taking the difference between film clearance and the housing probe reading. Curve fits were used for the experimentally measured film clearance and the bearing support deflection resulting in a third-order polynomial curve fit for the film clearance and a straight-line curve fit for the bearing support deflection. Both curve fits resulted in R2 values of >0.994. Finally, subfigure B of Fig. 12 presents the stiffness coefficients that were calculated by taking the derivative of the curve fits from subfigure A. The gas film stiffness, as expected, increases as film clearance decreases. For a notional thrust load of 1500 lbs (0.5 mil film clearance), the gas film would generate an axial stiffness of 1 Mlbs/in (175 MN/m), which is comparable to the axial stiffness of a rolling element ball bearing for comparable shaft size. The bearing support stiffness coefficient extracted from experimental data shows a larger stiffness coefficient that is independent of film clearance. This result shows good comparison with finite element analysis yielding a minor difference of 3.2%.

The following work presented rotating test results for a compliant hybrid gas thrust bearing fabricated using additive manufacturing. The design intent was to develop a bearing system that could be used to enable oil-free operation of high-power turbomachinery through the combination of key design elements such as thrust face compliance, external pressurization, and bearing support damping. The additive manufacturing approach proved to be a cost-effective and reliable method for integrating multiple design elements into a relatively complex monolithic part while retaining high levels of precision. The performance of the thrust bearing while operating with a bent shaft, which generated high levels of dynamic thrust runner misalignment, was a notable achievement and hence was key in demonstrating the reliability and robustness of the bearing support design. Bearing unit loading up to 55 psi (0.38 MPa) with relatively low tip speeds was demonstrated and validates the ability to use high pressure for increased load capacity. Considering the test results, the thrust-bearing concept shows initial promise as a scalable and reliable solution for supporting thrust loads in megawatt scale turbomachinery. Further test efforts are required to understand the influence of basic operating parameters on performance [25] to further validate the concept.

The author would like to thank GE for allowing the publication of this material. Thanks to the U.S. Department of Energy for funding the development of the gas thrust bearing. The author also thanks Tom Adcock of GE Research Center for his support in the additive build of the bearing. Thanks to Keith Gary of GE Research Center for supporting test execution. Thanks to Anjali Singh of GE Research Center for her help with NANO CT scans of the bearing.

This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government of any agency thereof. The views and opinions of the authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

• Department of Energy (Award No. DE-EE0007109; Funder ID: 10.13039/100000015).

During commissioning, an unintended rotor–stator rub generated shaft heating and seal damage. Pictures of the shaft and seal after disassembly are shown in Fig. 13. Several balancing trials after the rub event were attempted without success. From these balance trails, 10 krpm was deemed a safe speed to execute testing. The original intent for the maximum test speed was 20 krpm. Figure 14 shows the fast Fourier transform of the 0-peak thrust runner vibration. Note that the primary vibration component in the spectrum is associated with synchronous rotating speed of 5krpm.