An Experimental Study on the Influence of Spring Support Structures and Hydrostatic Recess Areas on the Characteristics of Hybrid Tilting Pad Bearings Lubricated by High-Pressure CO₂

Abstract

The purpose of this study is to explore the influence of different spring support structures and hydrostatic recess areas on the characteristics of hybrid tilting pad bearings lubricated by high-pressure CO₂ to promote the development of high-pressure CO₂-lubricated bearings. A high-pressure CO₂ hybrid tilting pad bearing experiment system was designed and built, and performance comparison experiments were carried out under various speed and load conditions. The performance differences of bearings with different spring support structures and hydrostatic recess areas under high-pressure CO₂ lubrication were obtained. The results show that compared with the bearing structure, the bearing stiffness has a more significant effect on the bearing performance. The design of the bearing should consider the matching of stiffness and rotor dynamics.

1. Introduction

With the trend of efficient, compact, and clean development of energy and power systems, the importance of advanced power cycles, such as the supercritical carbon dioxide (S-CO₂) Brayton cycle, has become increasingly prominent. Turbine machinery in such systems needs to operate stably under harsh conditions of high temperature, high pressure, and high speed. Traditional oil-lubricated bearings struggle to meet the stringent requirements for oil-free sealing, high temperature stability, and low maintenance. Gas bearings using air as the lubricating medium are limited by the low density, viscosity, and thermal conductivity of air. Although they offer advantages such as cleanliness, ease of gas sourcing, and low operating costs, their limited heat dissipation performance, insufficient bearing capacity, and low gas film stiffness make them more suitable for specific working conditions, such as high speed and light load, or low temperature and low pressure. Therefore, it is very important to find a new type of gas lubrication medium that can adapt to high-pressure and high-temperature environments with superior performance.

Carbon dioxide (CO₂) is an environmentally friendly medium that is inert and non-toxic. Under high pressure, its density, viscosity, and thermal conductivity are significantly superior to those of air, making high-pressure CO₂ a promising high-performance gas lubrication medium for bearings.

In 2013, Conboy [1] compared the performance of air-lubricated bearings and CO₂-lubricated bearings by theoretical calculation. The results indicated that compared to air-lubricated bearings, CO₂-lubricated bearings have stronger bearing capacity and higher gas film stiffness, and the bearing capacity enhancement effect is more significant at high speeds. Under high pressure, the heat transfer capacity of CO₂ is significantly higher than that of an ideal gas (such as air) [2]. Therefore, CO₂ as a lubricating medium is more suitable for high-load and high-pressure working environments than air.

In 2016, Kim [3] proposed a three-dimensional turbulent THD model for CO₂-lubricated radial bump foil bearings to address the issue of high power loss prediction in foil bearings within the S-CO₂ cycle. In the same year, Dousti et al. [4] solved the problem that the traditional incompressible Reynolds equation is not applicable in the design of S-CO₂-lubricated bearings by innovating the compressible Reynolds equation, allowing the systematic solution of the pressure and density of S-CO₂-lubricated bearings.

In 2017, Wen [5] established a turbulent Reynolds equation considering fluid density and viscosity changes, coupled with a foil deformation model. Based on the finite difference method, the static and dynamic characteristics of CO₂-lubricated radial bearings and thrust foil bearings were calculated.

In 2019, Ertas [6] designed and verified a composite gas bearing with high damping, high carrying capacity, and good flexibility, which solves the key problems of insufficient damping, poor stability, and limited adaptability of traditional gas bearings in high-speed and high-load applications. Li et al. [7] revealed the pressure distribution and bearing characteristics of S-CO₂-lubricated bearings for the first time through CFD.

In 2020, Bi et al. [8] accurately predicted the frequency-dependent dynamic characteristics of S-CO₂ bearings by the full variable perturbation method (ECVP), and solved the problem of rotor stability analysis under compressible turbulent lubrication. Bi et al. [9] also proposed an overall thermal equilibrium analysis method for S-CO₂ tilting pad bearings. This method derives a two-dimensional adiabatic energy equation by introducing real gas effects, variable thermodynamic properties, and turbulence effects, and analyzes the law of bearing performance changing with working conditions. In the same year, Li et al. [10] established a numerical simulation model of the dynamic characteristics of S-CO₂ foil thrust bearings in ANSYS CFX, and calculated the dynamic performance of S-CO₂ foil thrust bearings under different working fluid temperatures, different working fluid pressures, different gas film thicknesses, and different disturbance frequencies.

In 2021, based on the artificial neural network algorithm, Zhang et al. [11] obtained the flow factor expression for determining the flow state, studied the influence of the flow state on the flow field distribution and sealing performance of the S-CO₂ dry gas seal, and proposed a criterion for determining the overall flow state entering the seal gap. The prediction error caused by turbulence in the S-CO₂ dry gas seal is solved, and the accuracy and efficiency of seal design are significantly improved.

In 2022, Mehdi et al. [12] proposed a theoretical model of S-CO₂-lubricated hybrid tilting pad bearings coupled with the compressible turbulent lubrication Reynolds equation, energy equation, and CO₂ physical property equation, and compared the performance of hybrid bearings with pure dynamic pressure bearings. The significant advantages of hybrid bearings over pure dynamic pressure bearings in minimum film thickness, stiffness, and eccentricity are clarified. With an increase in gas supply pressure, the bearing capacity and stiffness coefficient of the bearing are also significantly enhanced. Che et al. [13] coupled the deformation equation of elastic foil and solved the turbulent Reynolds equation with variable density and viscosity, revealing that the sudden change of density and viscosity in the near-critical region has a significant effect on the bearing performance, especially the closer to the critical point, the more significant the effect is.

Han et al. [14] developed a partial derivative method that incorporates structural perturbation to calculate the frequency-dependent dynamic stiffness and damping coefficients of supercritical CO₂ foil bearings. It addresses the lack of methods for predicting dynamic characteristics in such bearings by coupling perturbations in both the compressible turbulent Reynolds equation and the foil structural model.

In 2024, Xiong et al. [15] established a wedge-shaped S-CO₂ fluid lubrication model and used the CFD method to analyze the viscous dissipation, compression heat, temperature, and pressure distribution in the lubricating gas film under different parameters and lubrication conditions. The dominant mechanism of the temperature characteristics of the lubricating gas film under different pressure conditions is clarified. The fluctuation of the load capacity and friction torque near the critical temperature and its influence on the stability of the rotor are revealed, and the influence of the film thickness change on the load capacity and viscous heat loss is revealed.

In the same year, Zhu et al. [16] established the model of S-CO₂ foil hydrodynamic bearings by fitting the physical equation of S-CO₂, based on the heat transfer model and energy equation, and explored the factors affecting the static characteristics of S-CO₂ foil bearings. Compared with air foil bearings, it is proven that S-CO₂ has a higher bearing capacity than air as a lubricating medium.

In 2025, Yi et al. [17] established a thermal elastohydrodynamic mixed lubrication model of S-CO₂ tilting pad bearings, considering the surface topography effect, which solved the problem that ignoring elastic deformation and local temperature rise caused by viscous shear and contact friction may lead to inaccurate prediction of bearing performance.

Although the theoretical research of high-pressure CO₂-lubricated bearings has progressed significantly, based on the authors’ investigation, there are few reports on experimental research for such bearings.

In 2009, Bruckner [18] compared gas foil bearings lubricated with nitrogen, helium, and carbon dioxide under an experimental environment of 42,000 rpm and 4.5 MPa. The experimental results show that the bearing power loss caused by CO₂ under high pressure is more serious than that of He and N₂, which reveals the potential complexity of achieving stable operation at high speed in a high-pressure CO₂ environment. In 2016, Cho et al. [19] developed a 10 kWe-level simple non-regenerative S-CO₂ Brayton test cycle using gas foil radial bearings and gas foil thrust bearings. The experiment was initially operated successfully at 30,000 rpm, a turbine inlet temperature of 83 °C, and a pressure of 8.5 MPa.

In 2017, Ertas et al. [20] systematically quantified the dynamic performance of an integral squeeze film damper (ISFD) in a high-speed S-CO₂ expander, for the first time, through the combination of an experiment and a model, and solved the key problems such as the unclear influence of end seal clearance, unknown cavitation behavior, and the large error of the inertia effect model. In 2021, Colgan et al. [21] developed a simplified numerical model of S-CO₂-lubricated bearings. Through model–experiment closed-loop verification, the stable operation ability of S-CO₂-lubricated hydrodynamic bearings at near-critical points was confirmed.

In 2023, in order to reduce the technical risks associated with oil-free sealed S-CO₂ turbomachinery [22], Ertas et al. [23] designed and developed an experimental rig that could run in a CO₂ environment of 2.76 MPa, with a maximum speed of 27,000 rpm. Through additive manufacturing bearings, modular HSFD dampers, and customized permanent magnet motors, the thrust bearing, rotor stability, and thermal management problems of oil-free sealed S-CO₂ turbomachinery are systematically solved. In the same year, their team [24] carried out thermal design of an experiment platform and its related gas supply circuit. An iterative thermal model and the ASPEN HYSYS model of the flow loop are introduced in detail, and the cooling flow required under the temperature limit of the gas bearing and the motor is calculated.

The significant changes in the viscosity and density of CO₂ under high pressure, which affect bearing characteristics, make experimental research in this area challenging. Although significant theoretical progress has been made, experimental studies reported in the literature remain scarce. Therefore, a high-pressure CO₂ hybrid tilting pad bearing experiment system was designed and built for this study, and bearing performance comparison experiments were carried out under different speeds and load conditions.

Based on the research of our research team [25], a tilting pad bearing with a spring support structure has better performance than an ordinary tilting pad bearing in gas lubrication, which is due to its special structure. It can form a wedge-shaped dynamic pressure gas film and produce elastic deformation to improve the redundancy of rotor misalignment and produce a certain degree of stiffness damping. Therefore, this study utilized tilting pad bearings with different spring support structures for experimental investigation. Through the analysis of the experiment data, the influence of different spring support structures and bearing stiffnesses on the characteristics of the hybrid tilting pad bearings lubricated by high-pressure CO₂ is discussed, and the influence of different hydrostatic recess areas on the bearing characteristics is further studied, which provides an important theoretical reference and experimental basis for the design optimization of high-pressure CO₂-lubricated bearings.

2. Experiment Bearings Description and Stiffness Measurement

The hybrid tilting pad bearing with a spring support structure in this study is shown in Figure 1 and Figure 2. The bearing is mainly composed of tilting pads, spring support structures, and a bearing housing. In this study, two types of single-layer spring tilting pad bearings with different spring supporting structures were used. The structure in Figure 2a comes from Reference [6]. Figure 2b,c are the innovation structures of our research team. The difference between Figure 2a,b is that the former has a pad fulcrum between the pad and the single-layer spring, while in the latter, the pad is directly connected to the single-layer spring. Figure 2c is shown as a double-layer spring tilting pad bearing.

A hydrostatic recess with a depth of 0.1 mm is opened at the inner circle of each tilting pad to provide a static pressure load during the start–stop stage of the rotor, which reduces the wear of the bearing and the rotor during the start–stop stage. The diameter of the gas inlet ports in Figure 1b is 2 mm. The whole bearing is machined from 40CrMo, which has high strength, hardness, toughness, and good wear resistance, making it suitable for heavy-load and impact-load conditions. A babbitt alloy with a thickness of 1 mm is centrifugally cast on the bearing bush. This material has the advantages of a low friction coefficient, adaptability to impact and vibration, and strong fatigue resistance. It can be applied to high-speed conditions, and the lower friction coefficient can effectively reduce the friction between the shaft and the bearing and improve the transmission efficiency. The bearings analyzed in this study are all upper and lower split bearings, which facilitate bearing disassembly and installation. There is no need to disassemble and assemble experiment rig components, such as dry gas seals and rotors, and the bearings are manufactured by wire cutting, creating a flexible spring structure. The basic parameters of the experiment bearings are shown in

Table 1. Basic design parameters of experiment bearings.

Bearing Parameter	Value	Bearing Parameter	Value
Inner diameter	35 mm	Depth of hydrostatic recess	0.1 mm
Outside diameter	95 mm	Axial pad length	28 mm
Number of pads	4	Preload factor	0.375
Pad arc angle	80°	Bearing assembly clearance	0.042 mm

.

In Table 1, the determination of the inner diameter and axial pad length was principally based on the motor’s speed and torque, while also taking into account the convenience of experimental operation. The outer diameter was determined by the combined thickness of the pad and the spring. Considering the good stability of the tilting pad bearing, we selected the commonly used four-pad tilting pad bearing. This study was conducted under no-load or light-load conditions. A positive preload helps ensure a converging fluid film under such operating states [26]. The preload factor in tilting pad bearings under high-speed, light-load conditions typically falls within 0.2 to 0.5 [27]. Therefore, a preload factor of 0.375 and a bearing assembly clearance of 0.042 mm were selected. The relevant parameters of the hydrostatic recess in Table 1 and

Table 2. Experiment bearing specific parameters.

Bearing Type	Bearing Number	Axial Length of Hydrostatic Recess (mm)	Arc Length of Hydrostatic Recess (mm)	Bearing Stiffness (N/m)
Single-layer spring tilting pad bearing 1	Case 1	8	9.2	5.91 × 106
Single-layer spring tilting pad bearing 2	Case 2	8	9.2	3.73 × 106
Double-layer spring tilting pad bearing 1	Case 3	8	9.2	3.62 × 106
Double-layer spring tilting pad bearing 2	Case 4	8	4.6	3.64 × 106

referred to the values in Reference [25].

In order to accurately control the experimental variables, the static stiffness of each bearing was calibrated in this study. The bearing was statically loaded, and the static stiffness of the bearing was calibrated by measuring the change in bearing displacement. The stiffness calibration experiment started at 10 N, increased by 10 N each time, and collected the corresponding data. After increasing to 100 N, it began to unload, reduced by 10 N each time, and collected the corresponding data until 10 N. In order to reduce the error caused by installation, operation, and other factors, three repeated loading and unloading experiments were carried out. The operation of each experiment was completely consistent, and the average values of the three data points were taken. Figure 3 is the fitting curve of the loading data and unloading data of the final selected bearing. It can be seen from the figure that the force on the bearing is almost linear with the deformation caused by the spring. According to the fitting curve, the stiffness of each experiment bearing can be obtained.

Table 2 shows the specific parameters and numbers of the four experiment bearings. Based on the table, Case 1, Case 2, and Case 3 are different spring support structures. Among them, the stiffness of Case 1 is significantly higher than that of Case 2 due to the existence of the tile fulcrum structure. This stiffness difference provides a clear comparison basis for exploring the influence of bearing stiffness on bearing stability in subsequent experiments. The bearing stiffness values of Case 2, Case 3, and Case 4 are very close. This design ensures that the stiffness variables are effectively controlled when comparing the performance of Case 2 and Case 3 (different spring structures), and Case 3 and Case 4 (different hydrostatic recess areas), so that the influence of the spring structures or hydrostatic recess areas on bearing performance can be more clearly separated.

3. Design of High-Pressure CO₂ Hybrid Tilting Pad Bearing Experiment System

In order to explore the system characteristics of high-pressure CO₂-lubricated hybrid tilting pad bearings with different spring support structures and hydrostatic recess areas, a high-pressure CO₂ hybrid tilting pad bearing experiment system was built in this study. The high-pressure CO₂ hybrid tilting pad bearing experiment system is mainly composed of four parts, including a gas supply pressurization system, a dry gas seal control system, a bearing experiment rig, and sensors and a data acquisition system.

CO₂ is pressurized through the gas supply pressurization system to ensure stable pressure. It is then heated via the dry gas seal control system, with the required pressure adjusted before entering the bearing experiment rig. Finally, sensors and the data acquisition system collect signal data under various operating conditions. The signal data is processed to study the static and dynamic characteristics of the bearing. A diagram of CO₂ flow direction is shown in Figure 4.

3.1. CO₂ Supply and Pressurization System

The CO₂ supply pressurization system is mainly composed of a CO₂ (pre-pressurized gas) cylinder, a N₂ (driving gas) cylinder, a CO₂ booster pump, a pressure gauge, and a connecting pipeline. Since the CO₂ out of the CO₂ cylinder is generally 4 MPa, the volume becomes larger, and the pressure will be reduced after the gas is introduced into the bearing experiment platform from the cylinder. Therefore, the CO₂ booster pump is required to continuously supercharge the CO₂ during the experiment to ensure that the gas introduced into the bearing experiment rig reaches the required pressure and the stability of the gas source. The gas source pressure of N₂ can reach 12 MPa, and the property is stable, which is an ideal choice for a driving gas.

3.2. Bearing Experiment Rig

Figure 5 is a schematic diagram of the bearing experiment rig. The rig is mainly composed of a drive system, a sealing cavity, a dry gas sealing system, and a static loading system.

The drive system consists of a high-speed motorized spindle, a frequency converter, and a high-speed coupling. The experiment bearing was installed inside the sealing cavity. Figure 6 shows the internal structure of the sealing cavity. The experiment bearing is installed in the middle of the shaft to facilitate the static loading experiment of the bearing. In addition, in order to simplify the installation and disassembly process, the bearing is processed according to the split structure. In this experiment, pressure in the bearing hydrostatic recesses was supplied through the two gas inlet pipes shown in Figure 6, and the inlet medium was high-pressure CO₂ at 4 MPa. Only two bearing pads located below the bearing were supplied with gas. Throughout the entire experiment process, the hydrostatic recesses maintained a continuous gas supply.

The dry gas seal system is composed of the main seal of the drive end and the main seal of the non-drive end. During the installation, the stationary part of the drive end side is first installed on the sealing cavity. The next step is to install the moving rings on both sides onto the rotor. After that, the pressing parts are installed and locked with the locking nut and the shaft so that all the rotating parts are pressed on the bearing. Subsequently, the rotor with the dry gas seal rotating parts is installed in the stationary part of the drive end. Finally, the non-driven end-side stationary part is installed on the sealing cavity, and the rolling bearing end covers on both sides are tightened to ensure that the rotor position does not float. In a non-ventilated state, the moving ring and the static ring of the dry gas seal are in a fit state. Consequently, the leakage is almost zero, but the rotor cannot rotate at this time. If it is forced to rotate, it will cause damage. When CO₂ is introduced, the gas pushes the push ring and compresses the spring, and the moving ring and the static ring will be separated. At this point, the rotor can rotate smoothly.

The common static loading methods include weight loading, cylinder loading, and other loading methods. However, they are not applicable to the high-pressure sealing experiment environment in this study. Therefore, this study designs an anti-thread loading device, as shown in Figure 5b. The static loading device is composed of a bearing preload hex screw, a bearing loading rod, a static force sensor, and a counterclockwise loading device. By twisting the bottom screw, it fits with the bearing loading rod to achieve the purpose of loading. A maximum static force of 300 N can be applied to meet the requirements of this experiment.

3.3. CO₂ Dry Gas Seal Control System

The CO₂ dry gas seal control system is crucial for the experiment. Its main function is to heat the high-pressure CO₂ from the booster pump to the operating temperature required for the dry gas seal, and to control and adjust the system outlet pressure. Figure 7 is a photo of the CO₂ dry gas seal control system.

3.4. Sensors and Data Acquisition System

Two types of sensors were used in this experiment, including two eddy current sensors, which are used to measure the displacement signals of the bearing in the X and Y directions, and a static force sensor. The eddy current sensor used is a PX series model produced by Hunan Taiwei Dashi Science and Technology Co., Ltd. (Shenzhen, China). It is a non-contact sensor that responds to changes in displacement based on the distance to the measured object, with an output voltage range of 0–5 V and a measurement range of 1 mm. The static force sensor is an SBT673-type column tension and compression sensor produced by Sparton. The layout of the eddy current sensors is shown in Figure 8.

Signal acquisition is an important part of the experiment process to ensure the reliability of the experiment data. In this study, the real-time acquisition of experimental data is completed by a B&K acquisition system, which is composed of an acquisition card and acquisition software. The B&K signal acquisition card has 12 channels, which can realize the simultaneous acquisition of multiple signals. In this experiment, three channels are selected to collect two displacement signals and one static force signal, respectively. The signal acquisition software is B&K PULSE software 18.1.1.9, which can set the sampling frequency and sampling time. The sampling frequency of this experiment is 2560 Hz, and a total of 2048 data points are collected within 0.8 s.

3.5. Rotor System Parameters and Modal Analysis

In this study, MADYN2000 software is used to model the rotor system and analyze the dynamic characteristics. MADYN 2000 is an advanced software designed for dynamic analysis and vibration simulation of rotating machinery.

Figure 9 is a schematic diagram of the experimental rotor structure. The total length of the experiment rotor is 391 mm, the rotor material is 3Cr17NiMo, the density is 7850 Kg/m³, the elastic modulus is 2.07 × 10¹¹ Pa, and the Poisson’s ratio is 0.28. Shaft Section 1 is the shaft section connecting the experimental spindle to the motor shaft. Shaft Section 2 and Section 6 are the shaft sections for installing the double-row back-to-back angular contact ball bearings. Shaft Section 3 and Section 5 are the installation positions of the dry gas seal rotating parts. Shaft Section 4 is the installation position of the experiment bearing.

Firstly, the rotor is divided into 26 shaft segments. A finite element model of the rotor is shown in Figure 10. The rolling bearings are added at nodes 5, 6, 24, and 25, and the dry gas seal rotating parts are added at nodes 13 and 17. The weight of the dry gas seal rotating parts is 0.84 Kg, and the moment of inertia is 0.001 Kg·mm². Figure 11 is a rotor vibration mode diagram.

Since only the forward motion of the rotor is typically considered, Figure 11 indicates that the first-order critical speed of the rotor is 70,954 rpm, and the second-order critical speed of the rotor is 137,141 rpm. As these values significantly exceed the experimental operating speed, the rotor can be regarded as rigid.

4. Experimental Result and Discussion

4.1. Comparison of Experimental Results of Different Types of Bearings

In this section, the experiment was carried out at an environmental pressure of 4 MPa and an ambient temperature of 45 °C. The experiment bearings (Case 1, Case 2, Case 3) with different spring support structures were compared. The displacement signals under different rotational speeds and static loads were collected to analyze the actual performance of the three bearings in the bearing–rotor system.

4.1.1. Comparison of Experimental Results of Different Types of Bearings at Different Speeds

Figure 12 shows the wavelet amplitude diagrams of displacement signals in the vertical direction of the bearing journal with different spring support structures at 3000 rpm and 8000 rpm without load. In order to analyze the wavelet signal more clearly, the peak amplitudes from the wavelet signal diagrams of the three bearings at different speeds are extracted and listed in

Table 3. Peak amplitude of wavelet signal diagram of experiment bearings with different rotational speeds.

	Rotational Speed	3000 rpm	8000 rpm
Bearing Type
Case 1		0.1836 mm	0.1144 mm
Case 2		0.1592 mm	0.1024 mm
Case 3		0.1566 mm	0.0994 mm

. As shown in Figure 12 and Table 3, at the double frequency of 3000 rpm, Case 3 has the smallest amplitude, Case 2 is close to that of Case 3, and Case 1 has the largest amplitude.

The amplitude of the double frequency at 8000 rpm, shown in Figure 12 and Table 3, also shows the same law, which indicates that Case 2 and Case 3 are close to each other in terms of vibration suppression performance, and both are significantly better than Case 1. Although the spring support structures of Case 1, Case 2, and Case 3 are different, the bearing stiffness values of Case 2 and Case 3 are similar and significantly lower than that of Case 1. This further illustrates that under the conditions of this study, the bearing stiffness is the dominant factor affecting the performance of the bearing, and its effect exceeds the influence of the spring support structure itself. At the same time, it also shows that properly changing the bearing stiffness helps to improve the vibration characteristics and structural deformation adaptability, thereby improving the reliability and stability of the system.

Figure 13 shows the axis orbits of the experiment bearings with different structures under speeds of 3000 rpm and 8000 rpm. It can be seen that the axis orbit of Case 1 is the largest, the axis orbits of Case 2 and Case 3 are similar and relatively small. This phenomenon shows that Case 2 and Case 3 have stable support, a good equilibrium state, and low vibration. In contrast, Case 1 exhibits a reduced stability margin, which is characterized by a higher amplitude and a larger and more eccentric axis orbit than the other bearings. These characteristics suggest that Case 1 may present a higher risk of instability, particularly if operational parameters (speed, load) were to be extended beyond the experimental range. From a comparison of the wavelet diagram and axis orbit diagram, it is found that Case 2 and Case 3, with lower bearing stiffnesses, have better stability and reliability than Case 1.

4.1.2. Comparison of Experimental Results for Different Types of Bearings Under Static Load

In this section, the rotational speed was set to 3000 rpm with a static load of 20 N. Figure 14 is a time–frequency diagram of the vertical displacement amplitude of the bearing with different spring support structures when the load is 20 N and the speed is 3000 rpm. It can be seen from the figure that the displacement amplitude of Case 3 is the lowest, and Case 1 is the largest. However, Case 2 is not significantly different from Case 3.

In order to further compare the bearing performance, the peak displacement amplitudes from Figure 14 were extracted and summarized in

Table 4. Peak displacement amplitude of time–frequency diagram.

Bearing Type	Peak Displacement Amplitude
Case 1	0.02893 mm
Case 2	0.02444 mm
Case 3	0.02126 mm

. It can be seen from Table 4 that the displacement amplitude of Case 3 is significantly lower than that of Case 2. This observation can be analyzed together with the data presented in Table 3, where the peak amplitude of Case 3 is slightly less than that of Case 2. The analysis result shows that compared with the single-layer spring structure, the double-layer spring structure has better vibration suppression performance under high-pressure CO₂ conditions.

Figure 15 is an axis orbit diagram of bearings with different spring support structures when the load is 20 N and the speed is 3000 rpm. From the figure, it can be seen that the axis orbit of Case 1 is the largest, and the axis orbit of Case 3 is still the smallest, so the same conclusion can be obtained as in Section 4.1.1.

In summary, optimizing the bearing structure to achieve an appropriate change in stiffness is an effective strategy to improve the performance of tilting pad bearings, as well as the operational stability and damping capacity of the rotor–bearing system. However, if only adjusting the structural design without paying attention to the matching of bearing stiffness and rotor dynamics, it will lead to a limited improvement in overall performance. Therefore, it is necessary to combine structural modification with accurate stiffness design to achieve effective suppression of system vibration.

4.2. The Influence of Hydrostatic Recess Areas on Bearing Performance

The bearings compared in this section are Case 3 and Case 4. It can be seen from Table 2 that both bearings are double-layer spring tilting pad bearings with the same structure and the same axial length of the hydrostatic recess. However, since the arc length of the hydrostatic recess of Case 3 is twice that of Case 4, the corresponding area of the hydrostatic recess of Case 3 is twice that of Case 4. The experiment was also carried out at an ambient pressure of 4 MPa and an ambient temperature of 45 °C.

4.2.1. Comparison of Experimental Results of Bearings with Different Hydrostatic Recess Areas at Different Speeds

In this section, the performance of different types of bearings is analyzed by changing the rotational speed. Figure 16 presents wavelet amplitude diagrams of the displacement signal in the vertical direction of the two bearing journals at different speeds. Figure 17 shows the peak amplitudes of the wavelet signals for the two bearings at different speeds.

It can be seen from Figure 16 and Figure 17 that when the rotational speeds are 3000 rpm, 6000 rpm, and 8000 rpm, the amplitude of Case 3 with a larger hydrostatic recess area is lower.

Figure 18 shows the axis orbits of the two bearings at 3000 rpm, 6000 rpm, and 8000 rpm. It can be seen from the figure that when the rotational speeds are 3000 rpm and 8000 rpm, the axis orbit of Case 3 with a larger hydrostatic recess area is smaller. When the rotation speed is 6000 rpm, the axis orbits of Case 3 and Case 4 are almost the same.

4.2.2. Comparison of Experimental Results of Bearings with Different Hydrostatic Recess Areas Under Different Loads

In this section, the motor speed is set to 3000 rpm, and the performance of different types of bearings is analyzed by changing the static load. Figure 19 is a time–frequency diagram of the vertical displacement amplitude of the bearing with different hydrostatic recess areas under different loads. As shown in the figure, at static loads of 40 N and 60 N, Case 3 with a larger hydrostatic recess area exhibits lower displacement amplitude. This indicates that within the tested rotational speed range, appropriately increasing the hydrostatic recess area can reduce vibration.

Figure 20 is an axis orbit diagram of the two bearings when static loads are 40 N and 60 N. It can be observed that when the static load is 40 N, the axis orbit of Case 3, which has a larger hydrostatic recess area, is only slightly smaller than that of Case 4. When the static load increases to 60 N, the axis orbit of Case 3 remains smaller than that of Case 4, and the difference increases. In summary, increasing the area of the hydrostatic recess makes the displacement amplitude of the bearing in the tested speed range lower.

5. Conclusions

In this study, in order to explore the system characteristics of high-pressure CO₂-lubricated hybrid tilting pad bearings with different spring structures and hydrostatic recess areas, a high-pressure CO₂ hybrid tilting pad bearing experiment system was designed and built, and the structural stiffness of the experiment bearing was measured by the static loading experiment of the bearing.

Through analysis of the displacement signals collected by the experiment, it is found that the performance of Case 2 and Case 3 with lower stiffness was better than that of Case 1 with larger stiffness under a high-pressure CO₂ lubrication environment. Under the same load, the vibration suppression performance of Case 3 with a double-layer spring structure is slightly better than that of Case 2 with a single-layer spring structure. It can be concluded that the bearing stiffness is the dominant factor affecting the bearing performance, and its effect is greater than that of the spring support structure itself. Therefore, when the bearing is improved, not only should the structural design be considered, but also the stiffness of the bearing should be matched with the rotor dynamics; otherwise, the performance gain of the bearing is limited.

The experimental results indicate that within the rotational speed range tested in this study, a bearing with a larger hydrostatic recess area exhibits lower vibration amplitude. Therefore, the area of the hydrostatic recess is an important parameter that needs to be optimized according to the expected working speed range in the design of a high-pressure CO₂ hybrid tilting pad bearing.