Molecular Dynamics Simulations of Lubricant Supply in Porous Polyimide Bearing Retainers

Abstract

Space bearing retainers are widely made of a porous, oil-impregnated material due to the unmaintainability of spacecraft. Porous polyimide (PI) material with a certain micropore structure can be used as a lubricant storage and migration channel to realize the lubricant circulation supply in the bearing system. In this work, molecular dynamics simulations are adopted to model the lubricant outflow process from the pore of the PI material. Coarse-grained models are constructed to investigate the lubricant migration behaviors with different rotation speeds, rotation radii, and pore sizes. The results show that a lubricant within the pore fails to outflow due to the capillary effect in a static state. However, for the rotating pores, if the centrifugal forces resulting from rotation exceed the capillary forces, the lubricants will begin to flow out. Furthermore, the lubricant in the large pore is easier to outflow due to the smaller capillary force, which is the main mechanism of lubricant outflow from the pores.

1. Introduction

The Control Moment Gyro (CMG) and flywheel are the core actuators for spacecraft attitude control, employing rolling bearings as rotating supports to ensure high-precision continuous rotation [1,2]. However, due to the constraint of the harsh space environment, the lubricant supply mode of space bearings cannot be replenished promptly, as is the case with terrestrial bearings. Researchers found that an oil-impregnated, porous polyimide material is capable of providing lubrication to space bearings. Due to the pore structure, porous polyimide materials are infused with a lubricant to obtain oil-impregnated retainers. During bearing operation, the oil-impregnated retainers can transport the lubricant stored in the pores to the contact surfaces, thereby lubricating the bearing [3,4]. When the bearing stops operating, the lubricant on the surface of the internal components of the bearing can be recycled into the pores, preventing the contamination and loss of the lubricant [5,6,7]. However, a current challenge in space bearing operations is that porous polyimide may sometimes experience inadequate lubricant supply, compromising the lubrication performance of the space bearings [8].

To address the issue of inadequate lubricant supply in porous material, researchers have proposed some measurements such as enlarging the pore size in the polyimide to enhance lubricant storage by forming technology [9], pore-foaming agent [10,11], and laser [12,13]. However, while enhancing lubricant supply, these methods cannot ensure a stable lubricant outflow. To further improve the lubricant supply performance of porous polyimide, the factors influencing the release behavior of lubricant from the porous materials were studied in-depth. Wang et al. [14] observed that the temperature rise triggers a thermal expansion effect, causing the lubricant within the pores to outflow. Ruan et al. [15] discovered that the lubricant supply induced by a temperature rise is attributed to not only thermal expansion but also the lubricant viscosity–temperature behavior, thereby enhancing its fluidity and facilitating migration to the contact interface. Furthermore, MacNeill et al. [16] believe that the centrifugal effect and compressive forces experienced by porous polyimide constitute the primary mechanisms for the lubricant supply. Bertrand et al. [17] further emphasize that under the impetus of centrifugal effects, only approximately half of the lubricant is capable of migrating to the surface for sufficient lubrication. Additionally, upon the commencement of bearing rotation, centrifugal effects inevitably lead to the expulsion of lubricant from the pores. However, Marchetti et al. [18] maintain that centrifugal effects can elicit lubricant supply only when the rotation speed of the retainer exceeds a certain threshold. In summary, despite the various research efforts devoted to understanding lubricant supply in porous polyimide, research is still predominantly reliant on experimental observation. Constrained by the pore size scale of porous polyimide, experimental methods face significant challenges in observing the internal flow behavior of lubricant. Consequently, the precise mechanisms underlying the lubricant supply within porous polyimide remain inadequately elucidated, thereby constraining the optimization of performance and the application potential of porous materials.

To further understand the lubricant supply mechanism of a bearing system, it is crucial to investigate the lubricant supply behavior during bearing operation. The bearing operation process comprises two stages: the start-up phase and the stable rotation phase. Our recent research focused on the lubricant supply behavior during the start-up phase [19]; nonetheless, this paper investigates the lubricant supply behavior during the stable operation phase via coarse-grained molecular dynamics simulations and theoretical analyses. By considering the variations in pore sizes, rotate speeds, and rotation radii, a study of the lubricant supply process is conducted to clarify the lubricant supply mechanism. The results reveal that an increase in pore size augments the lubricant outflow, which is consistent with the previous research [20]. Larger rotation speeds and radii of gyration can promote lubricant supply rate. Based on this, a further analysis of the capillary and centrifugal forces acting on the lubricant is undertaken, which clarifies the lubricant supply mechanism.

2. Model

The behavior of the lubricant supply was simulated using poly-α-olefin (PAO) lubricant and polyimide (PI). Poly-α-olefin (PAO) lubricant was bought from Naco Lubrication Co., Ltd. (Shanghai, China), with a dynamic viscosity of 6.962 mPa·s and a density of 0.799 g/cm³. Polyimide (PI) was commercially obtained from Luoyang LYC bearing Co., Ltd. (Luoyang, China) with a density of 1.41 g/cm³. The chemical structures are shown in Figure 1.

Herein, n denotes the degree of polymerization, whereas m indicates the length of the side chain. For the PAO model constructed in this paper, the degree of polymerization is specified as 3, with a side chain length of 6. Meanwhile, the PI model possesses a degree of polymerization of 5.

The all-atom models of the previously mentioned materials were constructed using Material Studio 8.0 (Accelrys, San Diego, CA, USA). Following this, geometric optimization and energy minimization procedures were performed using the Forcite module. In the structural optimization process, the conjugate gradient (CG) algorithm was employed with a fine level of precision. This algorithm used a cutoff energy of 10⁻⁶ kcal/mol and a cutoff force of 10⁻⁴ nN, ensuring a high degree of accuracy in the optimization calculations. For the energy minimization, the Universal force field was selected with a fine level of precision to accurately describe the interactions between the atoms. The optimized all-atom structure, as shown in Figure 2, features carbon atoms represented by gray spheres, hydrogen atoms by white spheres, oxygen atoms by red spheres, and nitrogen atoms by blue spheres.

Given the enormous number of atoms present in polymer molecules, all-atom simulations, while offering insights into their microscopic intricacies, inherently limit the scale of the simulation systems. Coarse-grained (CG) simulation simplifies the representation of particles by grouping the selected atoms into beads, which can enhance the spatial and temporal scales of the simulation and improve the calculation efficiency. However, this approach can lead to a loss of microscopic details between atoms and reduce the accuracy of the potential functions. Therefore, model validation is conducted prior to the simulation to ensure that the coarse-graining method does not alter the physicochemical properties of the material. Specifically, based on the CG method suggested by Marrink [21,22], the all-atom models of PAO and PI in Figure 2 were coarse-grained using Material Studio. The coarse-graining approach for PAO involves mapping four carbon atoms and their attached hydrogen atoms into a single particle, which enables the classification of PAO molecules into three types of particles: C₄H₇, C₄H₈, and C₄H₉, as illustrated in Figure 3a. In this way, a PAO molecule consisting of 98 atoms can be reduced to eight particles, resulting in a 91% decrease in the number of particles. The coarse-graining approach for PI is based on the phenyl ring structure within the PI monomer, defining mapping regions that categorize PI molecules into three types of particles: C₆, C₆O, and C₂O₂N, as shown in Figure 3b. By coarse-graining the PI molecules, a single PI molecule consisting of 36 atoms can be reduced to six particles, resulting in an 83% decrease in the number of particles.

Based on the coarse-grained molecules of PAO and PI, a lubricant supply system consisting of a nanopore and two Fe slabs was constructed, as illustrated in Figure 4. The nanopore is constructed from coarse-grained long-chain molecules of PI, featuring a pore length (h_p) of 40 nm with a long cylindrical channel extending in the z-direction, a wall thickness (l_s) of 2 nm, and a pore diameter designated as D, ranging from 10 to 30 nm. The interior of this nanopore is fully filled with coarse-grained molecules of PAO. Based on the densities of PI and PAO, oil-filled nanopores of varying sizes are created, containing different amounts of PI chains and PAO particles, as shown in

Table 1. Quantity of PI chains and PAO particles present in nanopore models with varying sizes.

D (nm)	10	20	30
PI chains	3340	13,763	30,211
PAO particles	2518	4230	5992

. The Fe slabs are established to simulate other components of the bearing at both ends of the nanopore along the z-direction. The l_x × l_y × h_s nm³ Fe slabs possess a body-centered cubic (bcc) structure with a lattice constant equal to 2.86 Å. The length (l_x) and width (l_y) of the plates are determined by the pore diameter (D) of the PI, while the thickness (h_s) of the plates is 2 nm.

In coarse-graining, the interactions are divided into bonded interaction and nonbonded interaction. For the nonbonded interactions, since the coarse-grained particles in this study are mapped from elements such as carbon, hydrogen, oxygen, and nitrogen, which are connected by covalent bonds, rendering the particles electrically neutral, electrostatic interactions between particles can be neglected. As a result, only the van der Waals forces are considered in the description of nonbonded interactions, and these forces are described by Lennard-Jones (LJ) potential using the lj/gromacs pair style, as expressed in Equation (1) [23].

$$E_{\mathrm{LJ}}=4\epsilon \left[{\left({\displaystyle \frac{\sigma }{r_{ij}}}\right)}^{12}-{\left({\displaystyle \frac{\sigma }{r_{ij}}}\right)}^6\right]+S_{\mathrm{LJ}}r<r_c$$

(1)

where ε represents the well depth, r_ij is the distance between particle i and particle j, and σ is the effective minimum distance, respectively. The values of ɛ and σ reflecting the molecular interaction strength are determined based on the MARTINI force field. The well depth ɛ reflects the strength of the interaction between particles, which depends on the type of coarse-grained particles, as shown in

Table 2. Potential well depth of coarse-grained particles (Unit: kJ/mol).

Type	C4H7	C4H8	C4H9	C6	C6O	C2O2N
C4H7	3.4	3.4	3.4	3.4	2.6	2.6
C4H8	3.4	3.4	3.4	3.4	2.6	2.6
C4H9	3.4	3.4	3.4	3.4	2.6	2.6
C6	3.4	3.4	3.4	3.4	2.6	2.6
C6O	2.6	2.6	2.6	2.6	4.2	4.2
C2O2N	2.6	2.6	2.6	2.6	4.2	4.2

. Assuming that all types of coarse-grained particles have the same size, the minimum effective distance σ is specified as 0.47 nm.

Different from the all-atom system, to ensure that the energy in the coarse-grained system smoothly decreases to zero near the cutoff radius, a smoothing term S(r) is added to the LJ potential, the expression of which is given by Equation (2) [23].

$$\left\{\begin{array}{l}S\left(r\right)=C\begin{array}{cc}& \end{array}{r}_{ij}<r_0\\ S\left(r\right)={\displaystyle \frac{A}{3}}{\left(r_{ij}-r_0\right)}^3+{\displaystyle \frac{B}{4}}{\left(r_{ij}-r_0\right)}^4+C\begin{array}{cc}& \end{array}{r}_0<r_{ij}<r_{\mathrm{c}}\end{array}\right.$$

(2)

where the cutoff radius is divided into two segments: the inner cutoff radius r₀ = 0.9 nm (approximately 2σ) and the outer radius r_c = 1.2 nm (approximately 2.5σ). The coefficients A, B, and C are computed to perform the shifting and smoothing.

Bonded interaction includes bond interaction and angle interaction. The bond interaction between adjacent particles, characterized by the harmonic potential, is detailed in Equation (3) [24].

$$V_{\mathrm{bond}}={\displaystyle \frac{1}{2}}{K}_{\mathrm{bond}}{\left(r-r_{\mathrm{bond}}\right)}^2$$

(3)

where the equilibrium bond distance r_bond = 0.47 nm, and the constant of harmonic bond potential K_bond = 1250 kJ/mol/nm⁻².

The angle interaction, characterized by the cosine square bond angle potential, is detailed in Equation (4) [25].

$$V_{\mathrm{angle}}={\displaystyle \frac{1}{2}}{K}_{\mathrm{angle}}{\left(\cos \beta -\cos {\beta }_0\right)}^2$$

(4)

where the constant of cosine square bond angle potential K_angle = 25 kJ/mol/rad⁻², and the equilibrium bond angle β₀ is measured in the coarse-grained model shown in Figure 5. The specific values of β₀ are listed in

Table 3. Values of equilibrium angles for coarse-grained PAO and PI.

Materials	PAO			PI
Type	Small	Middle	Big
β0(°)	66	117	172	180

.

The simulations of the lubricant supply are performed using LAMMPS packages [26]. The lubricant supply model is placed into a simulation box of 100 × 100 × 100 nm³ (x × y × z), and non-periodic boundary conditions are applied to the box boundaries. During relaxation, the lubricant temperature remains stable at 298.15 K, controlled by a Langevin thermostat. Assisted by the NVE ensemble, the lubricant particles undergo Brownian dynamics for 1 ns, ultimately reaching a state of equilibrium. The model that has attained an equilibrium state is considered to represent the pore structure located at the radius r within the porous polyimide retainer, as shown in Figure 6a. The models rotate at a rotation speed ω, with the axial orientation of the pores within the PI consistently perpendicular to the axis of rotation, as depicted in Figure 6b. Consequently, the PAO molecules within the pore experience an axial centrifugal force, leading to a centrifugal effect within the pore, as illustrated in Figure 6c. During simulations, the lubricant temperature remains at 298.15 K using the Nosé–Hoover thermostat. The motion equations are solved using the velocity-Verlet algorithm, employing a time-step of 2 fs.

Before simulating the lubricant supply behavior in porous polyimide, model verification was conducted. The density, viscosity, surface tension, and contact angle of the lubricant were calculated. The lubricant density, surface tension, and viscosity obtained from MD simulation are 0.806 kg/cm³, 26.103 mN/m, and 6.228 mPa·s, respectively, which correspond well with the experimental data (0.799 kg/cm³, 24.254 mN/m, and 6.962 mPa·s). When the lubricant reached equilibrium, the contact angle was measured to be 17.62°, which agrees well with the experiments (18°) [27]. These results demonstrate the reliability of the values obtained from a molecular dynamics simulation for modeling lubricant supply behavior.

3. Results and Discussion

During the stable operation of the bearing, the lubricant in the pores will be subjected to the centrifugal force generated by the rotation. The centrifugal force is calculated using Equation (5):

$$F=m_{i}r{\omega }^2$$

(5)

where m_i is the mass of the particle, corresponding to a PAO particle with a mass of 9.31 × 10⁻²⁶ kg; r is the rotation radius; and ω is the rotation speed. Exemplified by the model at a rotation radius of 150 mm undergoing rotation at a speed of 10,000 rpm, the centrifugal force experienced by the PAO particles within the pore is calculated to be 1.53 × 10⁻¹¹ nN, which is too small to be susceptible to intermolecular forces, thereby precluding an accurate simulation of the lubricant supply behavior. Owing to the scale constraints, it is challenging for molecular models to directly consider the centrifugal effects in macroscopic models. Nevertheless, in molecular dynamics simulations, the influence of force on atoms is ultimately reflected in their velocities, which are determined by solving Newton’s equations of motion. Consequently, this paper adopts an equivalent approach that enables centrifugal effects to be considered in the molecular models. Specifically, under the premise of ensuring that the linear velocity of the simulation matches that of the actual operating conditions, the rotation speed is increased by reducing the rotation radius. Given that the pore size of the model ranges from 10 nm to 30 nm, the rotation radii are uniformly set at 30 nm to ensure consistency in the centrifugal linear velocity of the lubricant for different pore sizes under the same operating conditions. Although this equivalent approach may exaggerate the centrifugal effect to some extent, making lubricant supply easier in simulations than in actual working conditions, it provides a minimum threshold condition for achieving lubricant supply and can help assess the centrifugal effect on the molecular models.

3.1. Rotation Speed

This section investigated the lubricant supply at various rotation speeds. As the average rotation speed of a typical space bearing can reach 5000 rpm, the rotation processes at, below, and above the average rotation speed were chosen to consider the impact of rotation speed on lubricant supply. Therefore, the rotation speeds were set as 1000, 5000, and 10,000 rpm, respectively. A lubricant supply model with a pore diameter of 30 nm was constructed, and the rotation radius was set as 150 mm.

Table 4. The centrifugal force acting on the PAO molecule at different rotation speeds.

Rotation Speed ω (rpm)	1000	5000	10,000
Centrifugal force before equivalent F (nN)	1.53 × 10−13	3.83 × 10−12	1.53 × 10−11
Centrifugal force after equivalent F’ (nN)	7.65 × 10−7	1.91 × 10−5	7.65 × 10−5

shows the centrifugal force acting on the PAO molecules at different rotation speeds. An observable trend is that the centrifugal force experienced by the lubricant intensifies with the increase in rotation speed. Compared to the centrifugal force before the equivalence, the centrifugal force increased by six to seven orders of magnitude after the equivalence approach was applied. In response to the different centrifugal forces, the density distributions of the lubricants are shown in Figure 7. The white dotted line indicates the size and location of the nanopores. For the rotation of 1000 rpm, the lubricant surface on both sides of the pore presents a concave shape, with the curvature of the concavity at each end being virtually identical. This indicates that the lubricant undergoes the capillary effect, consistent with the findings reported in ref [28]. As the rotation speed rises to 5000 rpm, the curvature of the lubricant surface near the axis of rotation increases, leading to the lubricant migrating towards the pore’s end that is farther away from the axis of rotation and subsequently exiting the pore. When the rotation speed reaches 10,000 rpm, the flow of the lubricant becomes even more pronounced.

The lubricant flowing out of the pore is distributed on the surface of the Fe plate to form an oil film. To quantify the phenomenon, the number of PAO particles outside the pore (n_o) is counted. Therefore, the lubricant supply rate can be obtained by Equation (6).

$$Q={\displaystyle \frac{n_{\mathrm{o}}}{n^{*}}}\times 100\%$$

(6)

where Q is the lubricant supply rate, and n* is the total number of lubricant particles. Consequently, the lubricant supply rate at different rotation speeds is obtained, as shown in Figure 8. For the low rotation speed (ω ≤ 1000 rpm), the lubricant supply rate remains at zero, indicating that the centrifugal effect generated by the low rotation speed fails to cause the lubricant within the pore to flow out. As the rotation speed increases to 5000 rpm, the lubricant supply rate rises from the instant of 1.44 ns. And when the rotation speed further increases to 10,000 rpm, the supply rate starts to rise even earlier, from 0.16 ns, indicating that the lubricant supply from the pore is faster and greater as the rotation speed increases.

3.2. Rotation Radius

This section investigated the lubricant supply at various rotation radii. A lubricant supply model with a pore diameter of 30 nm was employed, and the rotation speed was set as 10,000 rpm. The rotation radius was set as 10, 50, 100, and 150 mm, respectively. The change in rotation radii is mainly aimed at studying the lubricant supply effect of porous, oil-impregnated retainers with different sizes.

Table 5. Centrifugal force acting on PAO molecules at different rotation radii.

Rotation Radii r (mm)	10	50	100	150
Centrifugal force before equivalent F (nN)	1.02 × 10−12	5.1 × 10−12	1.02 × 10−11	1.53 × 10−11
Centrifugal force after equivalent F’ (nN)	3.4 × 10−7	8.48 × 10−6	3.47 × 10−5	7.65 × 10−5

shows the centrifugal force acting on the PAO molecules at different rotation radii. The centrifugal force exerted on the lubricant intensifies with the increase in rotation radii. Compared to the centrifugal force before the equivalence, the centrifugal force for the same rotation radii increased by five to seven orders of magnitude after the equivalence approach was applied. The density distributions of the lubricants at different rotation radii are shown in Figure 9. Under the conditions of uniform pore size and rotation speed, for the low rotation radius (r ≤ 10 mm), the lubricant surface on both sides of the pore presents a concave shape, with the curvature of the concavity at each end being virtually identical. This indicates that the centrifugal force generated by rotation at a small rotation radius is unable to cause the lubricant within the pore to migrate. As the rotation radius increases to 50 mm, the curvature of the lubricant surface near the axis of rotation increases, while the curvature of the lubricant surface farther from the axis of rotation decreases, indicating that the lubricant within the pore migrates to the far end of pore, driven by the centrifugal force. Upon the increase in the rotation radius above 100 mm, the varying curvature of the lubricant surface becomes even more pronounced, with the lubricant overflowing the pore wall.

The lubricant supply rate at different rotation radii is obtained using Equation (6), as shown in Figure 10. For the low rotation radius (r = 10 mm), the lubricant supply rate remains at zero, indicating that the centrifugal effect generated by the small rotation radius fails to cause the lubricant within the pore to flow out. As the rotation radius increases to 50 mm, the lubricant supply rate rises from 3.26 ns. As the rotation radii further increase to 100 mm and 150 mm, the lubricant supply rates begin to rise from 0.55 and 0.18 ns, respectively, exhibiting a more pronounced augmentation over time. This indicates that the lubricant supply from the pore becomes more rapid and sufficient as the rotation radius increases.

3.3. Pore Size

This section investigated the lubricant supply at various pore sizes. The pore size distribution of porous polyimide generally resides at the nanometer level. Therefore, lubricant supply models with diameters ranging from 10 nm to 30 nm were developed, sharing a uniform rotation radius of 100 mm and a constant rotation speed of 10,000 rpm. The centrifugal force acting on the PAO molecules at different pore sizes is uniformly 3.47 × 10⁻⁵ nN. The lubricant density distributions at different pore sizes are shown in Figure 11. Under the conditions of uniform rotation radius and rotation speed, for the low pore size (D = 10 nm), the lubricant surface on both sides of the pore presents a concave shape, with the curvature near the axis being greater than that far away. This indicates that while the lubricant migrates, it does not outflow. As the pore size increases to 20 nm, the curvature of the lubricant surface near the axis of rotation increases, while the curvature of the lubricant surface farther from the axis of rotation decreases, indicating that the lubricant within the pore migrates to the far end of the pore. Upon an increase in pore size to 30 nm, the intensification of lubricant migration occurs, resulting in the coverage of the Fe plate surface with lubricant.

The quantity of PAO particles exiting the pore at different pore sizes is counted, as shown in Figure 12. At the small pore (D = 10 mm), the quantity of PAO particles exiting the pore remains at zero. As the pore size increases to 20 nm and 30 nm, PAO particles begin to appear outside the pore from 2.56 ns and 0.58 ns, respectively, indicating that the lubricant supply from the pore is faster and greater as the pore size increases.

3.4. Mechanism of Lubricant Supply

During the stable operation of the bearing, the lubricant within the pore will migrate out of the pore due to the centrifugal force along the axial direction of the pore. An increase in either the rotation radii or the rotation speed can enhance the centrifugal effect, yet not all conditions guarantee lubricant supply. Consequently, the lubricant supply characteristics were investigated at various rotation radii and pore sizes, with the rotation speed fixed at 10,000 rpm, as shown in Figure 13. It can be observed that the operating conditions within the red dashed box are able to achieve the lubricant supply.

To clarify the mechanism of lubricant supply, the forces acting on the lubricant during stable rotation are analyzed. The concave shape of the lubricant within the pore indicates that the lubricant is influenced by the capillary effect. Consequently, the axial component of capillary force F_v subjected by the lubricant particles in a static model with different pore sizes is statistically analyzed based on the results of the molecular simulation, as shown in Figure 14. It can be observed that the force acting upon the lubricant particles tends to stabilize during the simulation period, with the capillary force being greater for smaller pore sizes.

Table 6. The average simulated values of axial capillary force for various pore sizes.

Pore Diameter D (nm)	10	20	30
Axial capillary force Fv (nN)	2.89 × 10−4	1.48 × 10−5	1.14 × 10−6

presents the average values of simulated axial capillary force for various pore sizes.

The relationship between centrifugal force and axial capillary force at different rotation radii is shown in Figure 15. Corresponding to the lubricant supply characteristics depicted in Figure 13, when the centrifugal force is lower than the axial capillary force of the corresponding pore size, the lubricant fails to exit the pore. Conversely, when the centrifugal force surpasses the axial capillary force, the lubricant within the pore migrates to the far end of the pore and flows out, thereby achieving lubricant supply. Hence, the lubricant supply effect of oil-impregnated, porous retainers can be predicted based on the relationship between the centrifugal force and the axial capillary force, considering varying pore sizes, rotation speeds, and rotation radii.

4. Conclusions

In summary, molecular dynamics simulations are conducted to study the lubricant supply mechanism within the porous polyimide retainers of a bearing during its stable rotation. Coarse-grained molecular dynamics models are developed to simulate a broad range of lubricant outflow processes under various rotation speeds, rotation radii, and pore sizes. The main findings can be obtained as follows:

• The capillary effect keeps the lubricant in the pore at rest. As the pore size increases, the capillary force acting on the lubricant decreases. When the pore begins to rotate, the lubricant may exit the pore due to the centrifugal effect generated by the rotation.
• For the same pore size, the centrifugal force generated by low speed and small rotation radius is small, resulting in the lubricant surface remaining concave. As the rotation speed or the rotation radius increases, the centrifugal force acting on the lubricant also increases. When the centrifugal force increases beyond a certain threshold, the lubricant will exit the pore.
• During stable rotation, the lubricant supply behavior is jointly influenced by both the centrifugal effect and the capillary effect. As the rotation speed of the pore increases, the centrifugal force may surpass the capillary force, thereby causing the lubricant to exit the pore.

The above findings reveal that the centrifugal effect generated during rotation overcoming the capillary effect is the main mechanism for lubricant supply in porous polyimide retainers. However, due to the complexity of the pore structure within porous polyimide and the variability of the space environment, future research can focus on the influence of factors such as the roughness inside the pores and the spatial temperature changes on the fluidity of the lubricant during the lubricant supply process.