Effects of pore size on the lubrication properties of porous polyimide retainer material

An oil-impregnated porous polyimide (PI) retainer is used in space rolling bearings to improve the lubrication performance, which depends on the release of lubricant from the pores, and therefore is closely related to the pore size. To study the effect of pore size, in this work, PI materials with different pore sizes were prepared by preheating the retainer tube billet during the limit pressing process, and then the friction tests were conducted with the ball-on-ring mode. The results show that the applied load deforms the pores, allowing the lubricant to be squeezed out from the pore; the centrifugal effect induced by rotation also makes the lubricant migrate out of the pore. Therefore, for the same pore sizes, the friction coefficients decrease with the increasing loads and rotation speeds. In addition, it was found that there exists an optimal pore size for the best lubrication properties of porous PI material. Furthermore, the optimal pore size should be larger for lubricants with high viscosity. The microscopic mechanism for lubricant outflow from pores is clarified by molecular dynamic simulations. The insights gained in this study can guide the preparation of oil-impregnated porous retainers under different working conditions.


Introduction
Much attention has been given to porous polyimide (PI) by researchers [1][2][3][4][5][6] thanks to their potential properties to improve the lubrication performance in space applications. The internal pore structure of PI could be used to store lubricant, thereby acting as an oil reservoir [7]. Based on this feature, in spacecraft, oil-impregnated porous PI materials have been used as bearing retainers to improve lubricant supply [8][9][10] and recycling [11,12].
To improve the lubrication performance of porous retainers, researchers have proposed various measurements such as increasing pore size and porosity of PI materials to carry more lubricant, which can be realized by forming technology [13,14], porefoaming agents [15], and lasers [16][17][18][19]. However, if the pore size and porosity are too large, it is difficult to ensure a long continuous supply of lubricants. Therefore, Ye et al. [20] presented an effective method to shrink surface pores without changing the inside pore structure by laying a thin layer of PI powders on the surface, which effectively prevents the loss of lubricant caused by large pore size. In addition to pore size and porosity, the influence of different working conditions on lubrication performance cannot be ignored either. As an oil reservoir, the lubricant is initially stored in the pore, and then migrates to the surfaces during working conditions. Wang et al. [14] found that the temperature rise makes the lubricant migrate to the surfaces. In addition, the deformation of the pores caused by compression decreases the porosity, forcing the lubricant to outflow to surfaces. Furthermore, in the bearing system, lubricant outflow will also occur due to the centrifugal effect when the bearing is in operation, especially at high speeds [12,14,21,22]. MacNeill [23] found that the centrifugal effect is critical for the lubricant to migrate to surfaces.
At first, it was reported that only approximately half of the lubricant can be supplied to the surface under the centrifugal effect [24]. Subsequently, Marchetti et al. [25,26] quantified the centrifugal effect and proposed that the centrifugal effect enables the lubricant in the pores to be transported to the surfaces only when the rotational speed reaches a certain threshold. Our recent work on the lubricant outflow process further demonstrates that the threshold is a critical linear velocity. When the velocity exceeds the critical linear velocity, the centrifugal effect overcomes the capillary effect to cause lubricant outflow [27]. In summary, the mechanisms of the lubricant outflow have been explored; however, considering different working conditions, how to choose a reasonable pore size to achieve the best lubrication performance is still not clear.
Friction is inevitable between bearing retainers, steel balls, and bearing rings during operation, so understanding the lubrication properties of porous PI retainer materials is important to improve bearing lubrication and friction performance. This paper aims to explore how to choose a reasonable pore size to improve the lubrication performance of porous PI retainer materials based on friction tests and numerical simulations. PI rings with different pore sizes were prepared by preheating the retainer tube billet during the limit pressing process, and then impregnated with PAO4 or PAO10. The lubrication properties of the PI material were investigated by measuring the friction coefficient with consideration of different lubricant viscosities, loads, and rotation speeds, and reasonable pore sizes were further explored. It is found that there is an optimal pore size to minimize the friction coefficient with different working conditions. Furthermore, the microscopic lubrication mechanism of porous PI retainers is clarified using molecular dynamics simulations.

Material and preparation
The PI powders with a density of 1.41 g/cm 3 were used to prepare the porous PI ring. The lubricant poly--olefins (PAO4 and PAO10) were used during experiments, whose densities and dynamic viscosities are listed in Table S1 in the Electronic Supplementary Material (ESM).
The preparation process of the porous PI ring is divided into six steps, as shown in Fig. S1 in the ESM. By adjusting the pressing pressure and sintering time, the porous PI samples with different pore sizes were obtained. The pore size distributions of the prepared PI samples were measured based on the mercury method and given in Fig. S2 in the ESM; it can be found that the pore size concentrates at a certain value with a narrow region. The porosity of the samples (θ) is defined as the ratio of the pore volume over the total volume of the sample and calculated by Eq. (1): where m is the mass of the sample, V is the volume of the sample, and ρ is the density of the PI. According to the measurement, the results of pore sizes and porosities are listed in Table 1. The morphologies of the PI samples were characterized by a scanning electron microscope (SEM; S-4800, Hitachi, Japan). As shown in Fig. 1, the solid samples have no pore, whereas the morphologies of porous samples slightly differed with various pore sizes. Before impregnating the lubricants, according to the requirement of the experiment, all the samples were processed into rings (Φ49.23 mm × 38.13 mm × 14.29 mm) and cleaned with anhydrous ethanol. After drying, porous PI rings were impregnated in PAO4 and PAO10 at 373.15 K and placed in a vacuum oven for 24 h. After long vacuum impregnation, the pores were filled with lubricant until no variation in the weight of the PI ring was observed.

Measurements
Considering the friction between the porous PI retainer and the rolling element in the bearing, the anti-friction property of porous PI was investigated by using a ball-on-ring tribology tester (CETR-III, Bruker, USA). Porous PI rings impregnated with lubricant and without lubricant were tested at room temperature. Figure 2 presents the schematic diagram of the friction test. The upper specimen was a steel ball that was used in the bearing with 7.94 mm in diameter. The lower specimen was the PI rings, which were 14.29 mm in height, 49.23 mm in outer diameter, and 38.13 mm in inner diameter. In this experiment, the upper specimens were loaded to the lower specimen at 1, 2, 3, and 5 N; at the same time, the lower specimens were set to rotate at 1,000, 3,000, and 5,000 r/min. Three repetitions were performed under each experimental condition. The average value of the friction coefficients of the three repeated experiments is calculated to obtain the friction coefficients in each experimental condition, and the standard deviation is used as the error bar. The changes in the surface morphologies of the PI samples before and after the friction test were analyzed by a modular standard optical profilometer (ST400, NANOVEA, USA).

Simulation
The molecular dynamics simulations of lubricant inflow and outflow from porous PI material were performed using LAMMPS software [28]. Lubricant and porous PI were constructed by the coarse-grained (CG) method, which was suggested by Marrink et al. [29,30]. For the lubricant outflow model, the lubricant was distributed in the pore, and two steel slabs were established at both ends of the pore, as shown in Fig. S3(a) in the ESM. For the porous surface lubricant model, the lubricant was distributed between the porous PI surface and steel surface, as shown in Fig. S3(b) in the ESM. The model consisted of an oil reservoir, a nanopore with a diameter of 30-50 nm, and a steel plate. The interaction between CG is described by the Lennard-Jones (LJ) potential. Bond interaction and chain stiffness are described by the harmonic potential and cosine square bond angle potential, respectively. In addition, the lubricant temperature is kept at 298.15 K using a Langevin thermostat during relaxation. Combined with an NVE ensemble,

Oil-impregnated ratio
Before the friction test, the oil-impregnated ratios of porous PI samples with different pore sizes and porosities were measured through the weighing method. By weighing the mass of porous PI before impregnating lubricant and after lubricant saturation, the oil-impregnated ratio (Q) can be calculated by using Eq. (2): where m 0 is the mass of porous PI before impregnating lubricant, and m c is the mass of porous PI after lubricant saturation. Figure 3 shows the oil-impregnated ratios of porous PI samples with different pore sizes and porosities. The results show that the porous PI with higher porosity can impregnate more lubricant, so the higher porosity is, the higher the oil-impregnated ratio is. Besides, in the same porous PI samples, the oil-impregnated ratios of different lubricant viscosities are similar.

Lubricated friction for oil-impregnated porous PI material
Section 3.1.2 studies the lubrication performance of oil-impregnated porous PI material. Before testing, the surface roughness (R a ) of porous PI samples was measured by a modular standard optical profilometer, as shown in Fig. S4 in the ESM. Due to the pore structure, the surface morphology of the porous PI sample fluctuates, and the R a of porous PI samples increases with increasing pore size. The friction coefficients between the ball and PAO4-impregnated porous PI samples with different pore sizes were tested. Referring to the impact force between the retainer pocket and steel ball in space bearing, the loads on the contact surface were set to 1, 2, 3, and 5 N to consider the effect of different loads [31]. By comparing the R a of samples before and after testing at high loads and high rotation speeds with different pore sizes, it is found that there is little wear on the surface, as shown in Fig. S6 in the ESM. Therefore, wear is less likely to occur at low speeds or low loads. Figure 4 shows the friction coefficients for oil-impregnated samples with pore size of 0.631 μm.
As shown in Figs. 4(a)-4(c), the friction coefficients could quickly reach and maintain a stable state, which also explains why the R a does not change much before and after testing. The smooth friction coefficient indicates that there is sufficient lubricant supplied from the pores of the PI samples to lubricate the contacting surfaces. Besides, Fig. 4(d) compares the friction coefficients under different loads and rotation speeds. The friction coefficients under the high load are much lower than those under the low load. It is proven that the lubricant is extruded from the pores due to the deformation of the pores; as the load increases, the lubricant outflow increases, and therefore the friction coefficient decreases at the same rotation speed. At the same load, as the rotation speed increases, the lubricant outflow increases, and the friction coefficient decreases, which demonstrates that the lubricant could also outflow due to the centrifugal effect. Compared with the lubrication performance for the solid PI sample with lubricant spreading on the surface, the oil-impregnated porous PI sample makes the friction coefficient stable at a high rotating speed, which provides a good alternative solution to the continuous lubricant supply in a specific environment such as in space.
www.Springer.com/journal/40544 | Friction To further understand the effect of the pore size, the friction coefficients for the samples with different pore sizes was compared, as shown in Fig. 5. It can be found that the friction coefficients decrease first and then increase with the increasing pore sizes, and therefore, there is an optimal pore size, which will provide a good lubricant supply and result in the lowest friction coefficient. Besides, the optimal pore size increases from 0.801 to 1.171 μm with the increasing rotation speeds. It is indicated that as the rotation speed increases, the contact surfaces need more lubricant to develop lubrication and support the load.
The pore size and porosity are two important factors of porous PI material that influence the lubrication performance. However, in the above discussion, both the pore sizes and porosities of porous PI samples were changed. Due to the preparation process, it is hard to keep the porosity constant while changing the pore size of samples at present. Nearly all the previous studies [14,15,21,22] focused on the effect of porosity by keeping the pore size constant. To further discuss the effect of pore size, according to Table 1, the samples were classified into two groups by similar porosity. Group 1 contained samples #1 and #2, which have an average porosity of about 14%;   | https://mc03.manuscriptcentral.com/friction group 2 only contains sample #3 with a porosity of about 17%; while group 3 contained samples #4 and #5 with a porosity of about 23%. Subsequently, the effect of pore size is discussed at a similar porosity. It can be found in Fig. 5 that with the same level of porosity, the friction coefficient of #2 is lower than that of #1 at the same rotation speed and load. The same phenomenon can also be observed in group 3, but with a smaller variation in friction coefficient except for the condition of 5,000 r/min and 1 N. This may be caused by the pore size of samples in group 3 having exceeded the optimal pore size, and the effect of pore size is not as great as that of the samples in group 1. Therefore, it is indicated that with similar porosity, the friction coefficient is dependent on the pore size. In addition, the samples with large porosity contained more lubricant, implying that the lubrication performance should be better; however, the results showed that the samples with low porosity have relatively low friction coefficient, which implies that the pore size rather than porosity plays a leading role in lubrication performance of porous PI material and has an optimal value. The mechanism will be discussed in Section 3.2.1 based on the molecular dynamics method.
The porous PI sample was also impregnated with PAO10 to investigate the effect of the viscosity of the lubricant on the optimal pore size. The tests were conducted under loads of 1 and 5 N, and the results were presented in Fig. 6. It can be seen that there also exists the lowest value of the friction coefficient for the samples impregnated with PAO10, which means that the samples impregnated with PAO10 also have the optimal pore size. As the rotation speed increases, the optimal pore size increases from 1.171 μm at 1,000 r/min to 1.826 μm at 3,000 and 5,000 r/min. Figure 6 also presents the friction coefficients for the samples impregnated with PAO4. Compared with those of the samples impregnated with PAO4, the optimal pore size of the samples impregnated with PAO10 increases at the same rotation speed, which indicates that when lubricant with a larger viscosity is used, larger pore sizes are needed for the optimal lubricant supply.

Comparison of different lubrication methods
To evaluate the lubrication effect of different lubrication methods, the friction coefficients for PI samples with different lubrication methods are compared at 3,000 r/min, as shown in Fig. 7. The bar represents the amplitude of fluctuations in the friction coefficient. The surface morphology profiles after testing are given in Fig. 8. The detailed results of the lubrication method with the lubricant spreading on the surface of solid PI material are shown and discussed in Figs. S5 and S6 in the ESM. It can be observed that the friction coefficient for the solid PI samples with lubricant spreading on the surface is around 0.07, indicating that lubrication is effectively developed with lubricant spreading on the surface. However, when the load changes from 1 to 5 N, wear grooves still appear for such a lubrication method.
The results indicate that the lubricant will be pushed out of the contact area during friction testing at high load conditions for the lubrication method of spreading lubricant on the surface before testing. However, the oil-impregnated porous PI sample shows a stable friction coefficient with a smaller amplitude of fluctuation. There are no obvious wear grooves on the surfaces despite the pore sizes, especially under a   | https://mc03.manuscriptcentral.com/friction high load, which indicates that oil-impregnated porous PI samples can provide a long continuous supply of lubricant to prevent wear.

Lubricant supply mechanism
The oil-impregnated porous PI sample presents a good lubrication performance, which is due to its special lubricant supply mechanism, as shown Fig. 9(a). The applied load deforms the porous PI sample near the contact area, and the lubricant is extruded from the pores to increase the quantity of lubricant on the contact surface.
Based on the molecular dynamics method, the lubricant outflow was simulated at different rotation speeds, as shown in Fig. S3(a) in the ESM. Due to the limitation of molecular simulation, the pore size could not be established following the test, so the rotation speed setting was improved to equivalently study the effect of centrifugal action. In these simulations, the rotation speeds of the model system are set to 3,000, 5,000, 8,000, and 10,000 r/min. The radius of rotation is set to 150 mm. The number of lubricant particles outside the pore (n) is counted to quantify the lubricant supply. Therefore, the lubricant supply rate can be calculated by Eq. (3): where n * is the original number of lubricant particles in the pore, and e Q is the oil-impregnated ratio. As shown in Fig. 9(b), the lubricant can outflow from the pore with the increasing rotation speeds, which implies that the lubricant supply is more adequate for a higher rotation speed. The simulations show that the lubricant in pores can outflow when the centrifugal effect generated by rotation overcomes the capillary effect, which means that the centrifugal effect due to the high-speed rotation speed is also a key mechanism affecting the lubricant supply in addition to the load, which squeezes the lubricant by deforming the pores.
The samples with larger pore sizes show a better lubricant supply, but this does not mean that the samples with larger pore sizes have lower friction coefficients. The variation in the friction coefficient is mainly due to the fluctuation in the lubricant film thickness. The mechanisms for this phenomenon will be discussed further in Section 3.2.2.

Lubricant bearing capacity
To investigate the reason for the large friction coefficients on the samples with larger pore sizes, the process of pressing lubricant between the steel and the porous surface was simulated by using the molecular dynamics method, as shown in Fig. S3(b) in the ESM. Initially, lubricants are placed between the porous PI surface and the steel surface. Then, let the porous PI surface with different pore sizes move downward 1 nm at a velocity of 5 m/s, which means that the lubricant is loaded by controlling the movement of the porous PI surface. Finally, the porous PI surface stops, and then the simulation lasts for 10 ns. To quantify the bearing capacity of lubricant on the porous surface, the quantity of lubricant is counted for the porous PI surface with pore sizes of 30, 40, and 50 nm, as shown in Fig. 10(a). The lubricant will be pressed into the pore, and the larger the pores, the greater the lubricant is pressed into the pore, indicating that the lubricant on the surface with larger pore size has less bearing capacity. To examine the validity of www.Springer.com/journal/40544 | Friction the phenomenon, the lubricant pressure is calculated for the porous PI surface with pore sizes of 30, 40, and 50 nm, as shown in Fig. 10(b). It can be found that there is a marked pressure peak for all the pore sizes at the pressing stage, and the pressure peak decreases with the increasing pore sizes. For the same lubricant film thickness, the lubricant on the surface with a smaller pore size is more difficult to press into the pore, which means that it can withstand greater loads.
The lubricant supply quantity increases with the increasing pore sizes, which improves the lubrication effect. However, this study shows that if the size of the pore is up to a certain value, the bearing capacity of lubricant on the porous surface will decrease during sliding, which causes the friction coefficient to increase. Therefore, the choice of pore size has a great effect on the lubrication performance of porous PI material.

Conclusions
In this paper, the lubrication properties of porous PI retainer materials were investigated. The PI rings with different pore sizes were prepared by preheating the retainer tube billet during the limit pressing process and then impregnating with PAO4 and PAO10. The friction coefficients were measured on a ball-on-ring tribology tester. The major findings can be summarized as follows: 1) By spreading the lubricant on the surface of solid PI samples, a stable lubrication state can be reached at low rotation speeds (≤ 1,000 r/min). However, the duration of stable lubrication decreases with increasing rotation speeds. It is unable to effectively avoid wear under high rotation speeds and high load conditions by spreading lubricant on the solid PI surface. Compared with the lubrication with lubricant spreading on the solid PI surface, a stable lubrication state can be effectively maintained with the oil-impregnated porous PI samples for a long time whatever the load and speed are.
2) For the same pore size, the friction coefficients for the oil-impregnated porous PI samples decrease with the increasing loads and rotation speeds. This is due to the pore deformation in the noncontact area under the applied load, which makes the lubricant press out of the pore. Besides, the centrifugal effect caused by rotation is also the key factor that makes the lubricant migrate out of the pore.
3) With the increasing pore sizes, the friction coefficient of oil-impregnated samples first decrease and then increase. If the pore size of the samples is too small, it is hard to adequately supply the lubricant to the surface. However, samples with too large pore sizes will reduce the bearing capacity of the lubricant. Therefore, there is an optimal pore size to ensure the lubrication properties of porous PI material. Furthermore, for a porous PI retainer with larger pore size, the lubricant with high viscosity should be selected.