Molecular Dynamics Investigation on Micro-Friction Behavior of Cylinder Liner-Piston Ring Assembly

In the vicinity of the top dead center of a diesel engine, the piston rings operate in a low-speed, high-load, and high-temperature environment, which is detrimental to the formation of an effective lubrication oil film. Consequently, it presents significant challenges for predicting the tribological characteristics of the piston ring-cylinder liner friction (PRCL) assembly. This study explores the micro-friction behavior of PRCL assemblies near the top dead center in engines using the molecular dynamics approach. The tribological characteristics of the PRCL, especially the microscopic wear mechanisms, were analyzed under various operating conditions such as ring sliding speed, ring back load, operating temperature, and lubricant supply amount. The liner surface morphology, liner wear, and lubricant film distribution were used to evaluate the tribological characteristics. It was determined that the lubricant supply amount has the most significant impact on the micro-friction behavior of the PRCL assembly.


Introduction
Lubrication models are a valuable resource for investigating lubrication regimes, characterizing tribological behavior, and addressing wear issues. Historically, these models [1][2][3][4][5] have largely been constructed using the Reynolds equation or its variants, and their effectiveness has been demonstrated under a range of operating conditions. However, when the lubricant film is extremely thin or even absent, these models are prone to inaccurate predictions of tribological properties, largely due to the limitations of the Reynolds equation and its variants under extreme conditions [6]. As a result, alternative approaches have been employed to reveal the lubrication mechanisms of friction pairs under extreme conditions, which are fundamentally different from traditional lubrication models.
Molecular dynamics (MD) is a widely applied tool for investigating the microscopic motion of particles, utilizing Newton's equations of motion. It has been used to address lubrication problems in various materials [7][8][9][10], such as metals [11], ceramics [12], organics [13] and has been particularly effective in uncovering the mechanisms of micro-friction under extreme operating conditions, such as low speed, high temperature, and heavy load [14][15][16][17][18][19]. Song and Zhao [20] explained the significant reduction in wear of PTFE under 500 K water lubrication conditions by analyzing the radius distribution function and the velocity variation in the thickness direction. Zhu et al. [21] conducted non-equilibrium MD studies to investigate the effects of different gap widths and shear rates on the microstructure and lubricating effect of water molecules in TiO 2 nanogaps. Shi et al. [22] examined the influence of a water film on the plastic deformation of the copper film during nanoindentation by varying the loading rate and the indentation speed. Shi et al. [23] revealed the mechanism behind the traction of the power transmission system through their consideration of the effects of sliding velocity and molecular structure. Pan and Gao [24] utilized MD simulations to investigate the bulk compressibility and density distributions of pentaerythritol tetra heptanoate lubricant at varying temperatures. Xia et al. [25] applied MD to study the effect of temperature on the aggregation of organic additives in base oils. Wu et al. [26] performed a study on the rheological properties of graphenepoly α-olefin (PAO) nanofluids at various temperatures, including viscosity, density, mean square displacement, and diffusion coefficient. They established a correlation between the viscosity of the base oil and the percentage of graphene nanoparticles. Ren et al. [27] investigated the effect of aqueous layer lubrication on the AFM-based single-crystal copper nano-scratching process and determined that the aqueous layer had a positive effect on the surface quality. Lu et al. [28] created a non-equilibrium MD simulation to calculate the traction coefficient and establish a correlation between the traction coefficient and the pressure-viscosity coefficient. Lin and Kedzierski [29] conducted comprehensive MD simulations of the density-pressure and viscosity-pressure properties of pentaerythritol tetra hexanoate, employing three force fields (OPLS, LOPLS, and DREIDING), and concluded that LOPLS was the most precise force field for pentaerythritol tetra hexanoate under varying pressures. A non-equilibrium MD simulation of the flow behavior of 2,2,4-trimethyl hexane at different pressures and strain rates was performed using the AIREBO-M potential of Cunha et al. [30]. Jiang et al. [31] performed MD simulations to analyze the tribological properties of dimethyl carbonatediesel blends in various base oils. They discovered that the benzene ring structures and long chains of trimellitic acid esters and alkylated naphthalenes exhibit high adsorption energy for Fe(110) at varying pressures. Zheng et al. [32] conducted a comprehensive investigation of the dynamic contact between two surface boundaries in a friction system, examining the effects of a mixture of C4-alkanes and mixtures of nanoparticles as lubricants. They concluded that the nanoparticles functioned as ball bearings between the contact surfaces, resulting in a shift from sliding to rolling friction mode. Gkagkas et al. [33] proposed a novel modeling approach to simulate the mesoscopic phenomena associated with the lubrication of the piston ring-cylinder liner assembly. They identified two lubrication regimes for varying loads, namely an elastohydrodynamic lubrication regime at low loads and a velocity-independent low friction regime at high loads. Zhang et al. [34] investigated the effect of graphene on the lubrication performance of Si 3 N 4 -GCr 15 friction pairs under increasing pressure and shear rate. Liu et al. [35] proposed a method for obtaining the pressureviscosity coefficient of the 1-decene trimer, a typical base oil. They calculated the effect of pressure on the lubricating performance of molecular oil films in the closed state and the effect of ultimate shear stress in the sliding state. Washizu et al. [36] also studied the effect of pressure on the lubricating performance of molecular oil films, providing insight into the mechanisms of lubrication in different states.
The lubricant supply amount is the other another critical operational factor that influences the lubrication regime of friction pairs. Researchers [37][38][39][40] have employed various methods to control the lubricant supply in their models, including specifying the film thickness or flow rate of the lubricant at the inlet point. In MD simulations, the impact of lubricant supply amount on micro-friction properties has been studied by adjusting the number of lubricant molecules. For instance, Li et al. [41] discovered that water molecules can stabilize graphene by promoting the movement of water molecules and releasing stress, while graphene enhances the rolling bearing of water molecules. Yeon et al. [42] employed the ReaxFF potential in their MD simulations and found that the amount of interfacial water impacts the tribochemical reactions at the sliding interface of hydroxylated amorphous silica and oxidized silicon. Additionally, Chen et al. [43] found that for moderate water molecule concentrations, water diffuses into the DLC film during sliding, reducing the interfacial density of the carbon network. Rullich [44] performed MD simulations of two water-lubricated sliding plates and found that the friction coefficient decreases as the water amount between the plates increases.
The piston rings in a diesel engine operate under highload, high-temperature, and low-speed conditions near the top dead center, which makes it difficult to form a stable lubrication oil film. As a result, research on predicting the tribological characteristics of the PRCL assembly near the top dead center has been a difficult area of investigation. There have been inconsistencies between the predicted tribological characteristics based on lubrication models and experimental observations [45][46][47]. The operating conditions in the PRCL assembly near the top dead center are demanding, with low speeds, high loads, elevated temperatures, and a lack of oil, thereby constituting a boundary lubrication regime [48,49]. To investigate the tribological behavior of the PRCL assembly, MD simulations were conducted to examine its tribological characteristics under varying operating conditions, specifically near the top dead center. This study focuses on the wear problem of the PRCL friction system near the top dead center, and surface morphology, wear amount, and lubricant film distribution are adopted to reveal its micro-wear mechanism.

Model and Method
The following statements emphasize the key aspects of analyzing the micro-friction behavior of the PRCL friction pair using MD: 1. In this study, a nanoscale geometric model was employed to capture the micro-friction behavior of the PRCL assembly near the top dead center, despite its macroscopic nature. 2. To facilitate the utilization of existing and well-established potential functions for describing atomic interactions, the material composition of the PRCL was simplified in this study.

Geometric Models
A PRCL tribosystem has been geometrically modeled and is depicted in Fig. 1. It consists of three parts: the cylinder liner, lubricant, and piston ring. The liner is made of cast iron, simplified as iron crystals in the model. The ring, which is chromium-plated on the surface, is represented by chromium crystals. The liner and ring are constructed in the large-scale atomic/molecular massively parallel simulator (LAMMPS) [50] using the command flow, with dimensions of approximately 50.0 Å(x) × 150.0 Å(y) × 1 00.0 Å(z) and 50.0 Å(x) × 50.0 Å(y) × 80.0 Å(z), respectively. The liner model is divided into three parts from bottom to top: the rigid layer, thermostatic layer, and Newtonian layer, with a z-direction height of 20 Å for the thermostatic and Newtonian layers. The interface roughness of the PRCL assembly is set to a cosine wave, described by the mathematical expression: where A is the amplitude of the cosine wave, ω 1 and ω 2 are the frequencies of the cosine wave in the x and y directions, respectively, and k is the mid-plane position of the cosine wave in the z-direction. In this study, A is set to be 15 Å, ω 1 and ω 2 are set to π/25, and k is determined by the interface position in the absolute coordinate system. The lubricant primarily consists of a PAO base oil, the composition of which can be found in the literature [51]. The PAO has a Newtonian kinematic viscosity of 4.324 ± 0.148 and 1.413 ± 0.035 at 40°C and 100°C, respectively [52]. The PAO base oil molecules are filled into a box with dimensions of 50 Å(x) × 150.0 Å(y) × H Å(z) (H = 10, 20, 30, 40, 50) using the Amorphous Cell module of the Materials Studio software [53]. The lubricant model is then converted to a data file and imported into LAMMPS, where it is merged with the geometric model of the PRCL assembly.

Simulation Procedure
In this study, MD simulations were performed using the LAMMPS software. Before the simulation, various parameters such as boundary conditions, timestep, potentials, and ensemble were specified. Periodic boundary conditions were used with a timestep of 1 fs. A specific force field was chosen based on its applicability, validation in previous studies, and scalability and computational efficiency. The objective was to select a force field that accurately describes the interactions and behaviors in the study, ensuring reliable and reproducible simulation results for the research purposes. The interaction between Fe atoms was described by the embedded-atom-method (EAM) potential developed by Mendelev et al. [54], while the interaction between Cr-Cr atoms was described by a modified EAM potential from the literature [55]. The consistent valence force-field (CVFF) potential was used for the lubricant, and the relevant parameters can be found in the literature [52]. The interactions between atoms of different components (cylinder liner, lubricant, and piston ring) were described using the Lennard-Jones (L-J) potential, whose parameters were calculated using the Lorentz-Berthelot rules [56,57].
where ε is the depth of the potential well, σ is the distance where the interaction between atoms is equal to zero, and the subscripts i and j represent the different atoms. The corresponding parameters, ε and σ, can be sourced from the literature [58]. Additionally, unbounded interactions with a cutoff distance of 10 Å [26] have been considered in the analysis.
The geometric model is initially optimized through energy minimization to remove any excessive local stresses. The conjugate gradient method is utilized for this purpose and the tolerance for energy and force error is set to 1 × 10 -15 , with a maximum number of 5000 calculation steps. The simulation process is controlled by the constant-volume and -energy (NVE) ensemble, with temperature regulation achieved through a Langevin thermostat set at T (T = 300, 400, 500, 600, 700, 800 K). An external load, in the form of gas pressure, is applied to the PRCL tribosystem, causing atoms in the lubricant to exert a force of 3.92 × 10 -4 kcal/(mol Å), and atoms in the ring to exert a force of F (F = 1 × 10 -4 , 3 × 10 -4 , 6 × 10 -4 , 9 × 10 -4 , 1.2 × 10 -3 kcal/(mol Å)). These applied forces are directed along the negative z-axis. During the loading process, the piston ring may require a relaxation period of 200,000 to 420,000 steps to achieve a stable position in the z-direction, depending on the magnitude of the applied load. Finally, the micro-friction of the PRCL tribosystem is performed by imparting a velocity of V (V = 0.03, 0.3, 3, 30 m/s), to the ring along the positive y-axis.
The study of the micro-friction of the PRCL tribosystem was performed by altering various operating conditions, such as velocity (V), temperature (T), force (F), and lubricant height (H). The tribological properties of the system were evaluated based on the surface topography, wear amount, and lubricant film thickness in the lubricated region, as determined by visualization utilizing Ovito software [59] and high-throughput filtering of atom positions in the model using Python. The results of this study provide valuable insights into the tribological characteristics of the PRCL tribosystem, particularly near the top dead center, under varying operating conditions.

Results and Discussion
In this study, we aim to investigate the effect of operation conditions on the micro-friction of the PRCL tribosystem by analyzing four representative positions of the two surfaces in relative terms. The four positions, each characterized by a ring displacement of 0, 16, 28, and 50 Å, were chosen to provide a comprehensive evaluation of the micro-friction phenomenon. The positions are shown in Fig. 2 and are described as follows: (a) the ring displacement S = 0 Å, the

Effect of Sliding Velocity
In diesel engines, the sliding velocity of the ring relative to the liner typically ranges from a few tens of m/s to 0 m/s [60]. This study investigates the effect of four different sliding velocities on the micro-friction of the PRCL tribosystem: 0.03, 0.3, 3, and 30 m/s. The focus of this investigation is the area of the liner surface that is scratched by the ring, i.e., the region where the x coordinate falls between 0 and 50 Å and the y coordinate is between 10 and 60 Å. The simulation results of the liner surface morphology for different ring sliding velocities are shown in Fig. 3. As depicted in the figure, the surface morphology remains relatively unchanged when S = 0 Å, as the applied load and relaxation time are uniform throughout the simulation systems. As the ring displacement increases from 0 to 26 Å, the contact area between the two surfaces increases and the roughness peaks undergo significant deformation. This deformation becomes more pronounced as the velocity increases. At a ring displacement of 50 Å, the roughness peaks of the two surfaces are no longer in contact and it is evident that the liner surface has developed distinct plough grooves, suggesting that the dominant mechanism of liner surface wear is plastic deformation. The ring surfaces, made of high-hardness chromium, do not show signs of wear in this study.
The wear of the liner surface was further analyzed by identifying the number of Fe atoms that exhibited displacements exceeding 5.73 Å from their initial positions. When their displacement relative to the original position exceeded this threshold, which is approximately double the lattice constant of iron, it was considered as wear. [61,62]. Figure 4 displays the changes in the wear amount as a function of ring displacement for different sliding velocities. As the ring displacement increases, the wear amount follows an S-shaped pattern. The wear process of the liner surface can be roughly divided into three stages. In the first stage (0 < S < 15), the liner surface experiences initial wear and the amount of wear remains constant, indicating that the wear amount is independent of the sliding velocity until the roughness peaks make contact. In the second stage (15 < S < 35) the wear rate rapidly increases as the roughness peaks of the liner and ring surfaces come into contact and then separate the wear rate in this stage shows an increase followed by a decrease. For velocities between 0.03 and 3 m/s, the difference in wear amount is not significant, but when the velocity increases to 30 m/s, the wear amount increases significantly, due to the direct contact between the roughness peaks as the lubricant does not completely separate the surfaces. In the third stage (35 < S < 50), the wear rate slowly increases as a small number of atoms continue to deviate from their initial positions under the influence of interatomic collisions from the previous stage. Overall, the difference in the liner surface wear is small at low speeds (< 3 m/s) and increases significantly at high speeds (30 m/s).
The thickness of the lubricant film is a crucial aspect that affects the lubrication regime and friction properties of the lower pair. To visualize the distribution of lubricant between the piston ring and cylinder liner, hydrogen atoms in the PAO molecules were not displayed in this study. This approach allowed for a clearer representation of the spatial arrangement and interactions of the lubricant with the contacting surfaces. The distribution of the lubricant film between the ring and liner is shown in Fig. 5. At the initial position (S = 0 Å), the surfaces are separated by the lubricant. However, as the ring moves along the positive direction of the y-axis, the roughness peaks of both surfaces come into contact, resulting in local rupture of the lubricant film. It is observed that the breakage of the lubricant film is higher at low speed (0.03 m/s) compared to high speed (0.3-30 m/s), which is consistent with the changes in the Stribeck curve [17][18][19]. Furthermore, the repair capacity of the lubricant is lower at low speed as compared to high speed. These results highlight that the load-carrying and repair capacity of the lubricant significantly reduces at low speeds, particularly near the top dead center.

Effect of Temperature
In Sect. 3.1, the calculations were performed at a room temperature of 300 K. However, in diesel engines, the liner surface temperature near the top dead center is influenced by the gas temperature, which can be several hundred degrees Celsius higher. To investigate the effect of temperature on the micro-friction of the PRCL tribosystem, this study used  Fig. 6. At the initial position (S = 0 Å), the roughness peaks do not contact each other and the liner surface morphology does not change significantly with increasing temperature. As the roughness peaks come into contact (S > 18 Å), the liner surface experiences significant deformation, and the higher the atomic temperature of the thermostatic layer, the greater the liner deformation. This is due to two main factors: the softening of the metal with increasing temperature, as described by the material's constitutive equations, and the decreased viscosity and thinner lubricant film at higher temperatures, which are evident from the lubricant viscous-temperature characteristic equation.
When the roughness peaks separate (S = 50 Å), grooves are visible on the liner surface, and their depth is proportional to the temperature. The results in Fig. 6 indicate that the wear mechanism of the liner surface at different temperatures is mainly plastic deformation. Figure 7 shows the changes in the wear amount with ring displacement for different temperatures. As the ring displacement changes from 0 to 50 Å, the wear amount displays an S-shaped growth trend. The three stages of the wear process for different temperatures are similar to those described in Sect. 3.1. When the ring displacement is 0 Å, there is no notable increase in the wear amount of the liner surface at low temperatures (300 ~ 600 K). However, when the temperature rises to above 600 K, revealing that under high-temperature conditions, the wear mechanism of the liner surface is not just limited to plastic deformation, but also encompasses thermal wear. Figure 8 presents the simulation results of the distribution of the lubricant film between the ring and liner in the PRCL tribosystem. The lubricant effectively separates the ring and liner, with only a small number of small holes appearing in the film when the temperature exceeds 500 K. Despite the occasional breakdown of the film as the ring moves, its coherence is maintained. Nonetheless, at higher temperatures, the damage to the film increases and its ability to support loads and repair itself decreases, especially near the top dead center. The coherence of the lubricant film is lost when the temperature exceeds 800 K and the ring displacement is 50 Å, causing the film to split into two parts. However, when

Effect of Applied Load
In diesel engines, the ring back is subjected to high gas pressure, typically ranging from several to tens of MPa [60]. This study investigated the impact of five different applied loads, of 1 × 10 -4 , 3 × 10 -4 , 6 × 10 -4 , 9 × 10 -4 and 1.2 × 10 -3 kcal/ The results of the liner surface morphology for different applied loads are shown in Fig. 9. At the initial position (S = 0 Å), the roughness peaks remain largely unchanged as the applied load increases. As the ring moves, when a lighter load (< 3 × 10 -4 kcal/(mol Å)) is applied, no visible grooves appear on the liner surface. However, with increasing load (> 3 × 10 -4 kcal/(mol Å)), the roughness peaks come into contact, causing significant plastic deformation and increasing the contact area. This leads to a reduction in the valley area of the liner surface, as atoms are worn away by the roughness peaks. The results in Fig. 9 indicate that light loads do not cause significant wear, while heavy loads cause significant plastic deformation, furrows on the liner surface, and a filling of the valley areas with atoms pushed down from the roughness peak. Figure 10 shows the changes in the wear amount with ring displacement for different applied loads. As can be seen in Fig. 10, the trends of the wear amount growth are different for different applied loads. When the applied load is low, the wear process of the liner surface occurs in a single stage and shows a linear progression that increases gradually. This is due to the minimal contact friction between the liner and the ring during the ring's sliding movement, with thermal wear due to high temperatures being the primary cause of wear on the liner surface. Conversely, when heavy loads are applied to the ring atoms, the wear amount displays an S-shaped growth trend as the ring displacement changes from 0 to 50 Å. The three stages of the wear process for different applied forces correspond to the three stages described in Sect. 3.1. As the applied force increases, the extent of the first stage narrows and its endpoint shifts from S = 15 Å to S = 10 Å, while the endpoint of the second stage remains unchanged at a ring displacement of 35 Å. At high applied loads, it becomes challenging for the lubricant to bear the full external load, leading to the roughness peaks taking on some of the load. This results in a closer distance between the tribosystem surfaces and a thinner lubricant film (as shown in Fig. 11). Increased contact between the surface roughness peaks and greater contact depth increases the likelihood of wear. As previously stated, changes in load bring about changes in the wear mechanism. For light loads, the tribosystem is dominated by thermal wear, while at high loads, the wear mechanism of the tribosystem encompasses  Fig. 11 Simulated results of the lubricant film distribution for the different applied loads. The horizontal axis represents the applied load (1 × 10 -4 , 3 × 10 -4 , 6 × 10 -4 , 9 × 10 -4 , and 1.2 × 10 -3 kcal/(mol Å)), while the vertical axis represents the displacement of the ring (0, 18, 26, and 50 Å). The first row of images is the lubricant film at x ∈ [0, 50] and y ∈ [10,60]; the second row of images is the lubricant film at x ∈ [0, 50] and y ∈ [28,78]; the third row of images is the lubricant film at x ∈ [0, 50] and y ∈ [36,86]; the fourth row of images is the lubricant film at x ∈ [0, 50] and y ∈ [60,110]. The simulation conditions are V = 0.3 m/s, T = 800 K, and H = 50 Å not only thermal wear but also plastic deformation, with the latter becoming the dominant mechanism as the load increases. Figure 11 illustrates the distribution of the lubricant film between the ring and liner. The film effectively protects the surfaces of the tribosystem from direct contact under light loads, as evidenced by its intact state in the initial position. This confirms that the thermal wear of the liner surface is caused by high temperature (800 K). As the load increases, the ability of the lubricant to carry the external load decreases, leading to the breakdown and thinning of the film. When the applied load is 1 × 10 -4 kcal/(mol Å), the lubricant film remains intact throughout the movement of the piston ring, indicating that the wear mechanism of the liner surface is primarily thermal. At a higher load of 3 × 10 -4 kcal/(mol Å), the lubricant film locally breaks down, leading to limited surface contact, but remains continuous. The wear mechanism is still primarily thermal with some two-body wear. However, at a higher load of 6 × 10 -4 kcal/ (mol Å) or more, the lubricant film seriously ruptures and loses continuity, leaving the tribosystem to rely on the roughness peaks for support. At this point, plastic deformation becomes the dominant wear mechanism with some thermal wear. Changes in load have a substantial impact on the wear mechanism of the PRCL tribosystem.

Effect of the Lubricant Supply Amount
In the context of a diesel engine's piston ring and liner friction system, the lubricant is either thrown onto the liner wall by the rotating crankshaft or delivered through an oil supply system. Variations in crankshaft speed or the oil supply system's control parameters can alter the lubricant thickness on the liner wall. This study aims to examine the impact of five different lubricant film thicknesses (0, 10, 20, 30, and 40 Å) on the micro-friction of the PRCL tribosystem. The results of the liner surface morphology for different lubricant film thicknesses are shown in Fig. 12. Initially, as the lubricant film decreases, the roughness peaks on the liner surface are not significantly affected. The movement of the piston ring smoothens the peaks, resulting in visible ploughing grooves. However, the depth and width of the groove increase with a decrease in lubricant film thickness. In the absence of lubricant, direct contact between the two surfaces leads to severe plastic deformation as the ring slides, even causing the disappearance of the valley area on the liner surface. When lubricated, the reduction in the valley area on the cylinder liner surface is not a monotonic trend with decreasing lubricant film thickness. The change in the valley area is closely linked to the position of the ring, which has a concave-convex working surface, as shown in Fig. 13a. This results in an uneven lubricant film thickness distribution between the two surfaces, causing varying pressure distribution on the ring surface and resulting in changes in ring attitude, either leaning forward or backward, as shown in Fig. 13b, c. When the Fig. 12 Simulated results of the liner surface morphology for the different lubricant supply amounts. The horizontal axis represents the lubricant film thicknesses (0, 10, 20, 30, and 40 Å), while the vertical axis represents the displacement of the ring (0, 18, 26, and 50 Å). Each subfigure represents the liner surface at x ∈ [0, 50] and y ∈ [10, 60] of the absolute coordinate system in Fig. 1. The simulation conditions are V = 0.3 m/s, T = 800 K, F = 6 × 10 -4 kcal/(mol Å) lubricant film is relatively thick (30 to 40 Å), the piston ring tilts backward, raising the roughness peak near the leading edge and lowering the roughness peak at the trailing edge. The increased roughness peaks near the trailing edge (as shown in the red semi-circular areas in Fig. 13a) increase wear on the liner surface at the edge and decrease wear on the liner surface in the middle. The severe plastic deformation caused by cutting and squeezing between the two surfaces leads to a greater reduction in the valley area of the liner surface at the edge. On the other hand, when the lubricant film is thin (10 to 20 Å), the piston ring tilts forward, lowering the roughness peak near the leading edge and raising the roughness peak at the trailing edge. This increases wear on the liner surface in the middle and decreases wear on the liner surface at the edge, resulting in a less reduction of the valley area at the edge of the liner surface. Figure 14 illustrates the correlation between the wear amount and ring displacement for varying lubricant film thicknesses. As depicted in the figure, a decrease in lubricant film thickness leads to an increase in wear on the liner surface, yet the progression of wear amount varies with different lubricant film thicknesses. In the dry friction state (H = 0 Å), the wear process of the liner surface transpires in two phases: initial wear and rapid wear. The initial wear phase is brief, lasting only for ring displacements less than 5 Å. Beyond 5 Å of ring displacement, the liner surface enters the rapid wear stage, leading to a sharp increase in wear amount. This is because the roughness peaks on the two surfaces are misaligned at the starting position, creating a larger actual contact area and a smaller initial deformation, causing minimal wear in the initial stage. However, with direct surface-to-surface contact in the absence of lubrication, the wear on the cylinder  liner surface increases rapidly with the movement of the piston rings. In the lubricated state (H ≠ 0 Å), the wear amount follows an S-shaped growth pattern as the ring displacement ranges from 0 to 50 Å. The three stages of the wear process for different lubrication conditions align with those described in Sect. 3.1. As demonstrated in Fig. 14, plastic deformation remains the dominant factor in the wear mechanism on the liner surface, with a minor contribution from thermal wear, regardless of lubricant thickness. Figure 15 displays the distribution of the lubricant film between the ring and liner for different lubricants supplied. It's worth noting that there is no need to delve into the results for the dry friction condition (H = 0 Å). To compare the distribution of the lubricant film, the results from Sect. 3.3, with a lubricant film thickness of 50 Å (F = 6 × 10 -4 kcal/ (mol Å)), have been included in Fig. 15. When the lubricant film thickness is 50 Å (H = 50 Å), the film remains largely intact and can effectively separate the two surfaces at S = 0 Å. However, as the thickness of the lubricant film decreases, localized breakage occurs at the initial position and the degree of breakage increases as the film becomes thinner. As the ring moves, the already damaged lubricant film tears further, losing its ability to protect both surfaces. Combined with the results from Fig. 14, it becomes clear that the lubricant supply plays a crucial role in determining the tribological characteristics of the PRCL tribosystem, influencing it to a greater extent than other factors.

Conclusion
This study established a geometrical model of the PRCL assembly and carried out simulations using molecular dynamics methods. The focus was on the impact of operating conditions such as the sliding velocity of the ring, ring back load, operating temperature, and lubricant supply amount on the tribological property of the assembly at the microscale. Friction characteristics, including the liner surface morphology, the wear amount, and the distribution of lubricant film thickness, were used to evaluate the microfriction behavior, with the following main conclusions: 1. The micro-wear of the PRCL tribosystem is primarily dominated by plastic deformation and has a minor amount of thermal wear. 2. High temperature worsens the lubrication state of the piston ring-cylinder liner through the dual effects of softening the metal and reducing the viscosity of the lubricant. Therefore, near the top dead center, the PRCL tribosystem exhibits the boundary lubrication regime. 3. The change in lubricant supply amount has the most significant impact on tribological characteristics compared to changes in other operating conditions in the micro-friction of the PRCL assembly.
This study found the change patterns of micro-friction characteristic parameters, and by utilizing this model, further cross-scale modeling can be established that maps the Fig. 15 Simulated results of the distribution of lubricant film for the different lubricant film thicknesses. The horizontal axis indicates the lubricant film thicknesses (10, 20, 30, 40 and 50 Å), while the vertical axis shows the ring displacements (0, 18, 26, and 50 Å). The first row of images is the lubricant film at x ∈ [0, 50] and y ∈ [10,60]; the second row of images is the lubricant film at x ∈ [0, 50] and y ∈ [28,78]; the third row of images is the lubricant film at x ∈ [0, 50] and y ∈ [36,86]; the fourth row of images is the lubricant film at x ∈ [0, 50] and y ∈ [60,110]. The simulation conditions are V = 0.3 m/s, T = 800 K, F = 6 × 10 -4 kcal/ (mol Å)