TY - JOUR AU1 - Lu, Yanjun AU2 - Liu, Cheng AU3 - Zhang, Yongfang AU4 - Wang, Jiahui AU5 - Yao, Kangrui AU6 - Du, Yafeng AU7 - Müller, Norbert AB - Introduction Compression ring-cylinder liner system in internal combustion engine usually acts as a seal between the combustion chamber and the crankcase [1–4]. In generally, the tribological properties of the compression ring-cylinder liner system affect greatly the seal performance and energy efficiency of the engine because the surface materials of cylinder liner and compression ring wear out during the operation [5, 6]. Under this case, the tribological properties of the compression ring-cylinder liner system have been paid special attention to improve the seal performance and energy efficiency maximally. Jeng et al. [7, 8] proposed a one-dimensional lubrication model to investigate the tribological performance of the compression ring-cylinder liner system under both the fully flooded and starved lubrication conditions, and this model was also extended to predict the performance of the piston ring pack. Usman et al. [9] and Livanois et al. [10] evaluated the tribological performance of the compression ring-cylinder liner system for various oil viscosities, engine speeds, and loads. In their studies, significant influence of oil viscosity, engine speed, and load on the tribological performance was observed. In recently, for the purpose of improving the tribological performance of the compression ring-cylinder liner system, Zhang et al. [11] optimized the face shape of the compression ring by using the inverse method. Etsion and his research group [12, 13] textured micro dimples on the compression ring, and a parametric analysis was conducted to obtain the optimal dimple parameters for maximum friction reduction. In these works, a dominant hydrodynamic lubrication regime was considered. However, besides the hydrodynamic lubrication regime, a mixed lubrication regime is typically encountered at piston top and bottom dead centers [14, 15]. Hence, the asperity contact in the mixed lubrication regime needs to be further considered [16]. By considering the asperity contact behaviors in the mixed lubrication regime, Rahmani et al. [17] studied the influence of liner temperature on the frictional characteristics and engine emissions of the compression ring-cylinder liner system. Morris et al. [18] investigated the influence of the axial profiles and surface roughness of compression ring on the performance of the compression ring-cylinder liner system. The reasonable axial profile and surface roughness of compression ring were chosen to obtain superior frictional performance. Meng et al. [19] and Yin et al. [20] evaluated the frictional properties of the compression ring-cylinder liner system with dimple texturing under the mixed lubrication regime. A great improving of the mixed lubrication performance was observed for the compression ring-cylinder liner system with dimple texturing. However, the analyses in these works were mainly focused on the compression ring-cylinder liner system with ideal circular cylinder liner. In actuality, the cylinder liner is usually deformed because of the large load and inevitable manufacturing errors [21]. For the deformed cylinder liner, Dunaevsky et al. [22] provided a method to model the profile of the deformed cylinder liner based on the Fourier transform. Based on the method of Dunaevsky et al. [22], Hu et al. [23] and Mishra et al. [24] investigated the mixed lubrication performance of the compression ring-cylinder liner system with a deformed cylinder liner. Usman et al. [25] evaluated the sensitivity of mixed lubrication performance to the magnitude of cylinder liner deformation under warm-up engine condition. Their works indicated that the cylinder liner deformation affects greatly the frictional performance of the compression ring-cylinder liner system. However, a pure fully flooded lubrication condition was assumed in their works. Due to the scraping effect of the oil ring, insufficient amount of oil film will be transported/supplied to the compression ring-cylinder liner system, and the lubrication condition of compression ring-cylinder liner system will change from the fully flooded lubrication to starved lubrication when the compression ring reaches near the middle of the strokes [26]. Meng et al. [27] and Tian et al. [28] investigated the frictional performance of the compression ring-cylinder liner system with consideration of the starved lubrication condition in the engine cycle, and the start position of lubrication zone was determined by solving the flow conservation equations. In their work, the starved lubrication performance of the compression ring-cylinder liner system was analyzed with also focus on the ideal circular cylinder liner. Moreover, the above-mentioned studies have been conducted for the conventional internal combustion engines under standard operation condition. However, in modern design of internal combustion engines, some advanced technologies, such as cylinder deactivation (CDA), variable valve actuation (VVA), turbo-charging system, and stop-start management [29, 30], have been widely adopted to reduce the emissions and improve the fuel economy [31]. In these technologies, the CDA is usually adopted in multi-cylinder engines, and can output a desired power by varying the number of active cylinders [32, 33]. Although the CDA shows potential for improving fuel economy, it also promotes certain undesired side-effects in some engine conjunctions because the working condition changes greatly (ex. cylinder pressure, cylinder liner temperature, and etc.) [34, 35]. In order to evaluate the side effects of the CDA on the tribological performance of the compression ring-cylinder liner system, a mixed lubrication model was proposed by Rahmani and his coworkers [34, 36], and the minimum oil film thickness, friction, and power loss were evaluated for the compression ring-cylinder liner system under the CDA. It was showed that the CDA affects greatly the frictional performance of the compression ring-cylinder liner system, and a significant increase in power loss was observed for the compression ring-cylinder liner system under the CDA. However, the fully flooded lubrication condition and ideal circular cylinder liner were assumed in their works. On the basis of the aforementioned studies, the analyses on the tribological performance of the compression ring-cylinder liner system are mainly conducted for the conventional engines (i.e., no use of the CDA), or focused on the engines under the CDA with assumptions of ideal circular cylinder liner and fixed fully flooded lubrication condition. In this study, the tribological performance of the compression ring-cylinder liner system under the CDA is analyzed with consideration of the cylinder liner deformation and the transition between the fully flooded lubrication and starved lubrication. In the analysis, an oil transport model coupled with JFO (Jacobson-Floberg-Olsson) conservative cavitation algorithm is proposed to predict the transient lubrication condition (i.e., fully flooded/starved). A mixed lubrication model is employed to evaluate the frictional properties of the compression ring-cylinder liner system under the mixed lubrication regime. On this basis, the influence of cylinder liner deformation and oil supply on the frictional performance is evaluated, and the tribological performance of the compression ring-cylinder liner system is also compared between the CDA and standard operation condition. Method Governing equation Fig 1 shows the schematic diagram of the compression ring-cylinder liner system. In order to evaluate the tribological performance of the compression ring-cylinder liner system under the CDA accurately, the surface roughness and oil film cavitation phenomenon (i.e., rupture and reformulation of oil film) are considered, and an average Reynolds equation coupled with mass conservative JFO cavitation algorithm [37] is adopted to calculate the pressure distribution of the oil film. In the average Reynolds equation, the side-leakage Couette flow of the oil film in the circumferential direction is not considered [34]. This is justified by assuming that there is no relative motion in the circumferential direction. Therefore, the average Reynolds equation coupled with JFO cavitation algorithm can be written as [37]: (1) where x and y are the axial and circumferential coordinates, p is the pressure of oil film, μ is the oil viscosity, ρ is the oil density, h is the oil film thickness, is the comprehensive surface roughness, σ1 is the surface roughness of compression ring, σ2 is the surface roughness of cylinder liner, t is the time, θc is the oil film saturation, U is the relative speed of compression ring [14]. ϕx and ϕy are the pressure flow factors, ϕs is the shear flow factor, ϕc is the contact factor. The flow factors defined by Patir et al. [38, 39] and Wu et al. [40] are used with an assumption of Gaussian distributed asperity heights, and their expressions are given in Appendix A of S1 File. It should be noted that the cylinder liner is cross-hatched/honed, and the surface asperity heights are usually not Gaussian distributed. However, according to the engine testing results of Gore et al. [41], after the initial running-in period, a plateau surface can be achieved, and the asperity heights of the cylinder liner surface are closely to a Gaussian distribution. In this study, the cylinder liner after its initial running-in period is considered. Therefore, the assumption of Gaussian distributed asperity heights of the cylinder liner surface is considered to be acceptable and reasonable [36, 42, 43, 44]. A calculation on the flow factors of non-Gaussian cylinder liner surface can refer to a study conducted by Leighton et al [45]. Download: PPT PowerPoint slide PNG larger image TIFF original image Fig 1. Schematic diagram of the compression ring-cylinder liner system. https://doi.org/10.1371/journal.pone.0204179.g001 The oil film saturation θc is given as [46]: (2) where pc is the cavitation pressure. It is worth noting that the cavitation region and cavitation boundary (i.e., rupture and reformulation boundaries) can be distinguished and addressed based on the value of saturation of oil film θc in the simulation. More detailed information about the mass conservative JFO cavitation algorithm can refer to the other representative works [46, 47]. Expression of oil film thickness For solving the average Reynolds equation, it is necessary to describe the oil film thickness between the compression ring and cylinder liner reasonably. In this study, a barrel-shaped compression ring is considered because it is most commonly used in the gasoline engines [11, 14, 27]. Meanwhile, according to a large number of research results [21–25], the cylinder liner in the fired engine condition is usually out-of-roundness because of the cylinder liner deformation caused by the thermal load, mechanical load, manufacturing error, and load difference between thrust and anti-thrust sides. Thus, the oil film thickness between the barrel-shaped compression ring and deformed cylinder liner can be expressed as: (3) where h0 is the minimum oil film thickness between the compression ring and cylinder liner, hring is the gap between the compression ring and cylinder liner caused by the axial profile of barrel-shaped compression ring, and it can be described by a parabolic equation [11]. hliner is the gap between the compression ring and cylinder liner caused by the cylinder liner deformation and compression ring conformability. The expressions of hring and hliner can be written as follows [11, 25, 27]: (4) (5) where δ is the crown height of compression ring, b is the axial width of compression ring. ΔR is the variation of cylinder liner radius from its inscribed circle, Un is the elastic deformation of compression ring, and they will be discussed in the next section. Cylinder liner deformation and compression ring conformability According to the work of Ma et al. [48], the cylinder liner deformation varies the radius of cylinder liner, and the variation of cylinder liner radius from its ideal circular shape ΔRcir at an axial cross-section can be expressed by using a Fourier series. (6) where N is the maximum order of the Fourier series, φ is the circumferential position, n is the order of the Fourier series, An and Bn are the Fourier coefficients for the order n. The order n is defined as a non-negative integer. Different values of order n mean different types of cylinder liner deformation [22]. Generally, the cylinder liner deformation can be modeled accurately by using the Fourier series with first few orders. Fig 2 shows the types of cylinder liner deformation for the first five orders. Download: PPT PowerPoint slide PNG larger image TIFF original image Fig 2. Types of cylinder liner deformation for the first five orders. https://doi.org/10.1371/journal.pone.0204179.g002 Under the working conditions, the deformed cylinder liner mainly exhibits an oval shape (i.e., n = 2) and a four-lobe shape (n = 4) [49]. However, as mentioned in the works of Rahmani et al. [50] and Usman et al [51], the compression ring also elastically deforms to accommodate the radial radius variation of cylinder liner when the cylinder liner is deformed, and the elastic deformation of compression ring can completely accommodate the radial radius variation of the deformed cylinder liner with n = 2 [52]. This means that the gap between the compression ring and cylinder liner caused by the cylinder liner deformation after considering the compression ring elastic deformation is mainly the outcome of the cylinder liner deformation with n = 4 [51]. Therefore, n = 4 is chosen to model the measured variation of cylinder liner radius from its ideal circular shape ΔRcir. In order to facilitate the calculation, the expression of ΔRcir can be rewritten as [50]: (7) with (8) where φn is the circumferential position of the maximum deformation of cylinder liner, Δc is the maximum variation of cylinder liner radius from its ideal circular shape, and they are shown in Fig 3. In practice, the variation of Δc is usually very small in the axial direction for the cylinder liner deformation with n = 4 [53]. Therefore, a constant value of Δc is assumed in the simulation of cylinder liner deformation in this and other previous studies [22, 25, 49–52]. Furthermore, according to the works of Usman et al. [42], the value of Δc is set to 15 μm in the current study. Download: PPT PowerPoint slide PNG larger image TIFF original image Fig 3. Schematic diagram of the deformed cylinder liner with n = 4. https://doi.org/10.1371/journal.pone.0204179.g003 Hence, the variation of cylinder liner radius from its inscribed circle ΔR can be expressed as follow [25]: (9) where ΔRmin is the minimum variation of cylinder liner radius from its ideal circular shape. It should be noted that the compression ring also elastically deforms to accommodate the variation in cylinder liner radius when the cylinder liner is deformed (i.e., the conformability of compression ring) [48, 50]. The elastic deformation of compression ring caused by the compression ring conformability is expressed as Un, and can be written as [25]: (10) where ar is the radial thickness of compression ring, r is the nominal radius of cylinder liner, E1 is the elasticity modulus of compression ring. Ft is the tension force of compression ring, Fbp is the backpressure force of compression ring, and their expressions are given as follows [27, 50]: (11) (12) where g is the end gap of compression ring. pg is the cylinder pressure, which is change with the crank angle. α is the ratio of compression ring backpressure to cylinder pressure. In practice, the determination of the compression ring backpressure is very complicated, and it is closely related to the dynamic behaviors of the compression ring and the gas flow in the ring pack. In this study, according to the works of Yin et al. [54] and Meng et al. [27], a constant value of α = 0.7 is assumed to approximately describe the relationship between the compression ring backpressure and cylinder pressure (i.e., the backpressure of compression ring is assumed to be equal to 70% of cylinder pressure) because the compression ring is always in contact with the lower surface of the compression ring groove during the movement [54]. Oil transport model and pressure boundary condition Under engine condition, insufficient oil film is usually supplied to the compression ring-cylinder liner system to provide a hydrodynamic support force because a large amount of oil film has been scraped by the oil control ring [8]. In this case, the starved lubrication and fully flooded lubrication conditions can be encountered simultaneously in an engine cycle because of the time-varying clearance between the compression ring and cylinder liner [48]. In generally, the starved/fully flood lubrication can be distinguished by the axial width of lubrication zone bw, as shown in Fig 4. If bw