Modeling the Fatigue Wear of the Cylinder Liner in Internal Combustion Engines During the Break-In Period and Its Impact on Piston Ring Lubrication

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Article Modeling the Fatigue Wear of the Cylinder Liner in Internal Combustion Engines during the Break-In Period and Its Impact on Piston Ring Lubrication

Chongjie Gu *, Renze Wang and Tian Tian

Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA; [email protected] (R.W.); [email protected] (T.T.) * Correspondence: [email protected]

Received: 18 September 2019; Accepted: 8 October 2019; Published: 11 October 2019

Abstract: In internal combustion engines, a significant portion of the total fuel energy is consumed to overcome the mechanical friction between the cylinder liner and the piston rings. The engine work loss through friction gradually reduces during the engine break-in period, as the result of liner surface topography changes caused by wear. This work is the first step toward the development of a physics-based liner wear model to predict the evolution of liner roughness and ring pack lubrication during the break-in period. Two major mechanisms are involved in the wear model: plastic deformation and asperity fatigue. The two mechanisms are simulated through a set of submodels, including elastoplastic asperity contact, crack initiation, and crack propagation within the contact stress field. Compared to experimental measurements, the calculated friction evolution of different liner surface finishes during break-in exhibits the same trend and a comparable magnitude. Moreover, the simulation results indicate that the liner wear rate or duration of break-in depends greatly on the roughness, which may provide guidance for surface roughness design and manufacturing processes.

Keywords: liner wear; friction; surface roughness; internal combustion engine

1. Introduction With the goal of pollution control and reduction of greenhouse gas emissions, it is always important to improve the efficiency of internal combustion engines. A major source of engine friction is the contact system of piston rings and cylinder liners. On average, for an internal combustion engine, around 10% of the total fuel energy is dissipated to heat because of mechanical friction. About 20% of the friction loss is caused by the contact between piston rings and liners [1]. Friction loss and other performance factors, such as engine oil consumption and certain emission parameters, usually experience rapid changes (mostly reduction) before they are stabilized for the rest of the engine life. This initial running period is called the break-in period. There are a number of practical reasons to study the break-in mechanisms. First, shortening the length of the break-in period can reduce the harmful emissions. Particularly for some heavy-duty engines, the manufacturers are required to finish engine break-in before delivering the engines. Thus, the break-in is directly related to the cost of the engines. Second, the ability to predict the changes during the break-in period allows one to predict engine friction over most of its lifetime. For the ring–liner system, it is considered that the biggest change during the break-in period is the roughness of the plateau part. A critical manufacturing step in the manufacturing process of liners is called the plateau honing process. The process includes two stages: rough honing, creating the valley part with grooves; and fine honing, leading to much less plateau roughness compared with the valleys [2,3]. As the plateau part created by the honing process is gradually worn during the break-in

Lubricants 2019, 7, 89; doi:10.3390/lubricants7100089 www.mdpi.com/journal/lubricants Lubricants 2019, 7, 89 2 of 16 period, engine lubrication conditions evolve accordingly. Therefore, it is crucial to study and simulate the break-in wear of the liner surface with the goal of understanding engine lubrication change and generating better liner roughness design. The two-body asperity fatigue wear model presented here is physics-based and is comprised of different submodels. First, surface plastic flattening was considered as the mechanism responsible for changes of the surface during the initial contact, which was modeled with an asperity contact model and a simple flattening process. Then, the asperity fatigue wear was considered as the dominant process for change of the surface during the rest of the break-in period. As the successive mechanism, asperity fatigue wear is studied, starting with the theory of delamination, which was first proposed by Suh [4]. Two submodels are discussed to complete the simulation of fatigue wear: crack initiation and crack propagation. Because fatigue wear happens at the asperity level and near the surface, surface and subsurface cracks are modeled separately because of their different initiation positions and growth driving forces. Many previous physics-based models were developed to simulate the fatigue wear process. The Lundberg–Palmgren model is a representative work of early fatigue wear [5]. Lundberg and Palmgren proposed the first mathematical model for predicting contact fatigue life. The later studies by Tallian added more physics-based understandings. The proposed models were based on crack propagation and elastic–plastic properties of materials [6,7]. Kudish and Burris improved the previous models by considering the effects of normal stress, the size of the contact, and the friction coefficient [8]. There are a number of published works for modeling of engine break-in wear [9–11]. However, without engaging detailed mechanisms of break-in wear, these models mainly focus on how to model the wear process in a mathematical way. In this work, the fatigue wear theory was for the first time applied tothe liner roughness during break-in. The rest of the content is organized as follows. First, submodels of asperity wear mechanisms and the simulation procedure are introduced in the methodology part. Second, simulation results for break-in wear and engine friction are presented in the results section. Comparison between simulation results and experimental measurements is also made in the results section to evaluate the effectiveness of the wear model.

2. Methodology

2.1. Asperity Contact Owing to the design convention, the ring surface is significantly smoother than the liner surface. The deformation of asperities on the liner surface can be approximated as a flattening process, with a fast change for the plateau roughness. This plastic flattening process is significant, especially during the first several engine cycles. Although this process is short in duration, the change of surface topology significantly affects the behavior of the asperity contact. Therefore, it is essential to consider this mechanism, and to integrate it into the entire two-body break-in wear simulation. This asperity contact model is computationally efficient under several assumptions. First, the contact occurs between a smooth surface and a rough surface, with the smooth surface considered as a rigid body. In the ring liner contact system, the ring is smoother and harder than the liner. Second, the interactions among asperities are neglected, so the deformation of each asperity only depends on the contact situation between the ring and the asperity. This assumption is sufficient for a sparse contact pattern, where the real contact area only consists of a small portion of the nominal contact area. The final assumption is that all asperities have spherical summits that have contact with the ring. The surface topography is measured by confocal microscopy, which is one kind of surface measurement method based on an optical technique [12]. Based on the work of Zhao et al. [13], the contact model for each single spherical asperity can be mathematically expressed as:

4E h 1/2 Ac = πRh; Pa = ( ) (1) 3π R Lubricants 2019, 7, 89 3 of 16 Lubricants 2019, 7, x FOR PEER REVIEW 3 of 16

!3 !2 h h1 hh1 lnh 2 lnh Ac 𝐴= π=𝜋𝑅ℎRh[1 [12−2− ++33 − ];] ;𝑃Pa=𝐻−𝐻= H H(1−𝑘(1 k)) − (2)(2) − h h hh − − lnh lnh 2 − 1 2 − 1 2 − 1 A𝐴c ==2𝜋𝑅ℎ;2πRh; Pa 𝑃 ==𝐻H (3)(3) 𝐴 𝑃 In Equations (1)–(3), (1)–(3), Ac is is thethe realreal contactcontact area,area, Pa is is thethe meanmean contactcontact pressure.pressure. R is the radius curvature ofof thethe asperity asperity tips, tips,H His is the the hardness hardness of theof the material, material, and an k isd thek is mean the mean contact contact pressure pressure factor, factor,such that such the that initial the yieldinginitial yielding occurs occu if thers mean if the nominalmean nominal pressure pressure exceeds exceedskH. For kH a liner. For a made liner ofmade cast ofiron, cast k iron, is usually k is usually taken aroundtaken around 0.4. The 0.4. determining The determining parameter parameter in the modelin the model is the interferenceis the interference depth depthh, which h, iswhich the asperity is the tipasperity height tip reduction height afterreduct contact.ion after Figure contact.1 shows Figure the geometric 1 shows propertiesthe geometric and propertiesasperity deformation and asperity of deformation the contact model. of the contact model. The contact pattern for each asperity always falls into one of the the three three contact categories: elastic, elastic, elastoplastic contact, and fully plasti plastic.c. These These three three categories categories are are identi identiﬁedfied by by two two critical critical interference interference depths: ℎ =( 3πkH)2𝑅 and ℎ =( 3πH )2 𝑅. When ℎ ≤ ℎ , the contact is purely elastic, as the maximum depths: h = R and h = R. When h h , the contact is purely elastic, as the maximum 1 4E 2 2E ≤ 1 normal pressure within the contact area is smaller than the material hardness. Further penetration to the contact leads to the elastoplastic condition as as a transition from the elastic contact to fully plastic contact, with only the center part of the contact re regiongion reaching plasticity. As the interference depth further exceeds hℎ2,, thethe contactcontact becomesbecomes fullyfully plastic.plastic. EquationsEquations (1)–(3) correspond to the analytical expressions of the real contact area and mean contactcontact pressure forfor thethe threethree conditions,conditions, respectively.respectively. Based on thethe asperityasperity contactcontact model model discussed discussed above, above, average average clearance clearance between between the the ring ring and and the therough rough liner liner surface surface under under a given a given pressure pressure can be can solved be solved iteratively. iteratively. The summation The summation of contact of contact forces forcesover all over individual all individual asperities asperities equals equals the total the load total of load solid-to-solid of solid-to-solid contact. contact.

Figure 1. AsperityAsperity contact model. 2.2. Asperity Plastic Flattening 2.2. Asperity Plastic Flattening The asperities that have elastic contact with the ring will recover their original shape right after The asperities that have elastic contact with the ring will recover their original shape right after the ring leaves. However, part of the contact becomes plastic and a permanent flattening effect occurs. the ring leaves. However, part of the contact becomes plastic and a permanent flattening effect occurs. The detailed asperity plastic deformation is not trivial. The fractal nature of the asperities in The detailed asperity plastic deformation is not trivial. The fractal nature of the asperities in contact leads to various plastic deformation patterns at finer scales. Here the peaks of the asperities are contact leads to various plastic deformation patterns at finer scales. Here the peaks of the asperities simplified as spherical. We adopted the model proposed by Sören and Söderberg [14]. The geometry are simplified as spherical. We adopted the model proposed by Sören and Söderberg [14]. The of the asperity after experiencing a plastic contact has an elastic spring on the top of the flattened peak. geometry of the asperity after experiencing a plastic contact has an elastic spring on the top of the The amount of elastic spring at the center of the contact asperity is modeled by Johnson [15]: flattened peak. The amount of elastic spring at the center of the contact asperity is modeled by Johnson [15]: r H A u = 2 1 v2 c (4) el − E π 𝐻 𝐴 𝑢 =2(1−𝑣) (4) 𝐸 𝜋 where v is the Poisson ratio, H is the material hardness, E is the elastic modulus, and Ac is the real contact area. where 𝑣 is the Poisson ratio, 𝐻 is the material hardness, 𝐸 is the elastic modulus, and 𝐴 is the real contact area.

2.3. Asperity Fatigue

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Lubricants 2019, 7, x FOR PEER REVIEW 4 of 16 2.3. Asperity Fatigue Among all the mechanical wear mechanisms, surface plastic deformation, fatigue wear, and Among all the mechanical wear mechanisms, surface plastic deformation, fatigue wear, and abrasive wear are the most essential ones leading to the surface topology change. Delamination abrasive wear are the most essential ones leading to the surface topology change. Delamination theory theory considers fatigue as the core mechanism in the wear process and it is widely supported by considers fatigue as the core mechanism in the wear process and it is widely supported by evidence for evidence for wear of metals and some other solid materials [16]. wear of metals and some other solid materials [16]. In the delamination theory, propagation of the subsurface cracks under cyclic loading leads to In the delamination theory, propagation of the subsurface cracks under cyclic loading leads to surface material fracture in the shape of flat sheets. In this work, the asperity fatigue model also surface material fracture in the shape of ﬂat sheets. In this work, the asperity fatigue model also considers the propagation of surface cracks. considers the propagation of surface cracks. As illustrated in Figure 2, according to the principal normal stress, the subsurface under each As illustrated in Figure2, according to the principal normal stress, the subsurface under each contact can be divided into the tensile region and compressive region. Both surface cracks and contact can be divided into the tensile region and compressive region. Both surface cracks and subsurface cracks are initiated from the material defects. However, the types of stresses leading to subsurface cracks are initiated from the material defects. However, the types of stresses leading to crack initiation are different. Surface crack initiation is caused by the surface tensile stress, as the crack initiation are diﬀerent. Surface crack initiation is caused by the surface tensile stress, as the bond bond at the surface defect is weaker than the tensile stress. at the surface defect is weaker than the tensile stress.

Figure 2. Crack initiation. Surface Surface cracks initiate from th thee edge of the contact region where the surface tensiletensile stressstress reachesreaches maximum.maximum. SubsurfaceSubsurface crackscracks initiateinitiate fromfrom thethe maximummaximum shearshear stressstress region.region.

Therefore, surface cracks always initiate at the edge of the contact region at which the surface Therefore, surface cracks always initiate at the edge of the contact region at which the surface tensile stress is maximum. The stress responsible for the subsurface crack initiation is shear stress. tensile stress is maximum. The stress responsible for the subsurface crack initiation is shear stress. This is because subsurface cracks initiate in the compressive region, where the maximum principal This is because subsurface cracks initiate in the compressive region, where the maximum principal stress isis negative. The only source for crack initiation is the shear component. As a result, the initiation position forfor subsurfacesubsurface crackscracks isis thethe maximummaximum shearshear stressstress position.position. After the initiation of surfacesurface andand subsurfacesubsurface cracks, propagation of cracks ultimately leads to fracture ofof contact contact asperities. asperities. Similar Similar to initiation to initiation of cracks, of crackscracks, in cracks the tensile in the region tensile and compressiveregion and regioncompressive have di regionﬀerent have propagation different modes propagation and driving modes forces. and driving For a surface forces. crack, For a both surface fracture crack, mode both 1 andfracture fracture mode mode 1 and 2 fracture contribute mode to propagation, 2 contribute asto tensilepropagation, stress andas tensile shear stress stress and exist shear simultaneously stress exist insimultaneously the tensile region. in the Thetensile driving region. force The for driving surface force crack for propagation surface crack is thepropagation tensile circumferential is the tensile stress σθθ near the crack tip, with the corresponding propagation direction being perpendicular to the circumferential stress 𝜎 near the crack tip, with the corresponding propagation direction being maximum σθθ direction. For a subsurface crack located in the compressive region, the driving force is perpendicular to the maximum 𝜎 direction. For a subsurface crack located in the compressive theregion, shear the stress driving at the force crack is the tip, shear while stress the crack at the propagates crack tip, while to the the direction crack propagates of maximum to the shear direction stress τmax. The crack initiation and propagation mechanisms are summarized in Table1. of maximum shear stress 𝜏. The crack initiation and propagation mechanisms are summarized in TableThe 1. crack propagation is calculated by the Paris-Erdogan law [18] under the assumption of small yieldThe around crack cracks. propagation Kudish is and calculated Burris presentedby the Paris an-Erdogan eﬃcient methodlaw [18] tounder calculate the assumption the stress intensity of small factors K and K under each contact asperity [8]. An asymptotic solution is presented to solve K and yield around1 cracks.2 Kudish and Burris presented an efficient method to calculate the stress intensity1 K2 in an explicit way. factors 𝐾 and 𝐾 under each contact asperity [8]. An asymptotic solution is presented to solve 𝐾 and 𝐾 in an explicit way.

Table 1. Crack initiation and propagation mechanisms. As surface cracks and subsurface cracks are located in different regions under contact asperities, the mechanisms for initiation and propagation are different

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Table 1. Crack initiation and propagation mechanisms. As surface cracks and subsurface cracks are located in diﬀerent regions under contact asperities, the mechanisms for initiation and propagation are diﬀerent

Fatigue Properties Surface Crack Subsurface Crack

Damage force surface tensile σxx = shear τxy |y 0 Initiation position edge of the contact region location with maximum τxy Propagation mode mode 1 and mode 2 combined mode 2 only tensile circumferential stress: shear stress at crack tip: 2 1 θ θ 3 τ = 1 [K 2sin2θ + 2K K sin2θ + Driving force σθθ= cos( )(K1cos K2sin(θ))[17] 1 1 2 √2πr 2 2 − 2 2 √2πr 2 2 K1, K2: stress intensity factors for mode 1 and mode 1 K 4 3sin θ ]ˆ0.5[17] 2 − Propagation direction perpendicular to σθθmax along τmax

2.4. Systematic Modeling Procedures Based on submodels introduced in the previous sections, a ﬁnal asperity fatigue wear model for the liner surface in the break-in period is developed. This wear model includes the following essential steps: asperity contact, surface plastic deformation, crack initiation, crack propagation, and asperity fracture. These steps are applied for every sliding cycle iteratively. The ﬂowchart in Figure3 shows the algorithm of this fatigue wear model, which integrates all these critical mechanisms in the fatigue Lubricantswear process. 2019, 7, x FOR PEER REVIEW 6 of 16

Figure 3. Algorithm of the asperity fatigue wear model. Figure 3. Algorithm of the asperity fatigue wear model. In Figure3, the asperity fatigue wear algorithm needs two inputs: rough liner surface S, represented 2.5. Tested Surfaces by a matrix; and an external nominal pressure P. First, the algorithm finds the clearance H between the linerTo base investigate altitude andthe effect the flat of ring liner surface, surface according roughness to on the break-in asperity wear, contact simulations model with are the conducted given liner basedroughness on the measurement five different and liner pressure. surface finishes. All asperities As shown in contact in FigureA(n) are4, GG21, numerically 09, and defined 07 are aligned once the alongclearance the horizonal is determined, line with including one-step each honing asperity’s from radius smooth of curvatureto rough. RG21,(n), average28, and 30 normal are plateau- pressure honedP(n), andwith real the contact same radiustoolingr(n). sets Using but different the information plateau for ratios, each asperity,meaning the the algorithm fine honing performs cuts to the differentsurface plasticdepths flatteningcompared calculation, with the rough obtaining honing updated [19,20]. surface S and a new clearance H. As the first

Figure 4. Different liner surface finishes.

2.6. Hydrodynami, Contact and Friction Correlations In order to investigate the effect of break-in fatigue wear on engine lubrication, liner surface finishes before and after wear simulation are utilized to calculate friction. As the piston ring slides to different positions on the liner, the mean clearance also changes, leading to the change of hydrodynamic pressure. To obtain the correlations between the ring liner clearance and hydrodynamic pressure, a deterministic model is applied. According to this model, the dependency of the average hydrodynamic pressure on the ring-liner clearance can be expressed by the following equation [21]:

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Lubricants 2019, 7, 89 6 of 16 step into the fatigue part, each asperity is identified based on whether it is an asperity coming into contact for the first time. If it is a new contact asperity, surface cracks Cs and subsurface cracks Csub are assigned to the corresponding initiation positions. Otherwise, if an asperity is already in contact, the lengths of the cracks are updated based on the Paris-Erdogan law. In the following step, the algorithm checks for each asperity based on whether the surface cracks meet with the subsurface cracks. If these cracks meet with each other, the asperity is fractured, resulting in a new surface topography. This new surface is then used as the input surface of the next cycle. After a specific number of sliding cycles, this fatigue wear algorithm providesFigure 3. a Algorithm simulated of surfaces the asperity roughness fatigue wear after model. wear.

2.5.2.5. Tested SurfacesSurfaces ToTo investigateinvestigate thethe eeffectffect ofof linerliner surfacesurface roughnessroughness onon break-in wear, simulationssimulations areare conductedconducted basedbased onon thethe fivefive didifferentfferent linerliner surfacesurface finishes.finishes. AsAs shownshown inin FigureFigure4 4,, GG21, GG21, 09, 09, and and 07 07 are are aligned aligned alongalong thethe horizonal horizonal line line with with one-step one-step honing honing from from smooth smooth to rough. to rough. G21, G21, 28, and 28, 30and are 30 plateau-honed are plateau- withhoned the with same the tooling same sets tooling but di ffsetserent but plateau different ratios, plateau meaning ratios, the finemeaning honing the cuts fine to dihoningfferent cuts depths to compareddifferent depths with the compared rough honing with the [19 rough,20]. honing [19,20].

Figure 4. DiDifferentﬀerent liner surface ﬁnishes.finishes.

2.6. Hydrodynami, Contact and Friction Correlations 2.6. Hydrodynami, Contact and Friction Correlations In order to investigate the effect of break-in fatigue wear on engine lubrication, liner surface finishes In order to investigate the effect of break-in fatigue wear on engine lubrication, liner surface before and after wear simulation are utilized to calculate friction. As the piston ring slides to different finishes before and after wear simulation are utilized to calculate friction. As the piston ring slides to positions on the liner, the mean clearance also changes, leading to the change of hydrodynamic pressure. different positions on the liner, the mean clearance also changes, leading to the change of To obtain the correlations between the ring liner clearance and hydrodynamic pressure, a deterministic hydrodynamic pressure. To obtain the correlations between the ring liner clearance and model is applied. According to this model, the dependency of the average hydrodynamic pressure on hydrodynamic pressure, a deterministic model is applied. According to this model, the dependency the ring-liner clearance can be expressed by the following equation [21]: of the average hydrodynamic pressure on the ring-liner clearance can be expressed by the following equation [21]: K µV h − h Phydro = Ph( ) (5) µ0V0 σp

In Equation (5), µ0 and V0 are the reference viscosity and reference sliding speed, while µ and V are the corresponding real parameters. Ph and Kh are constants. They depend on the liner finish and ring profile. These two constants can be obtained through least squares fit using simulation results. Here, h/σp is the ratio of average clearance and the standard deviation of plateau roughness. Similarly, the hydrodynamic shear stress can be correlated with the ratio h/σp through the following analytical expression, with Ci (i = 1, 2, 3) as constants [21]: !! µV h fhydro = C1 + C2exp C3 (6) h σp

The total pressure is the sum of the contact pressure and hydrodynamic pressure. The contact pressure also depends on clearance, which can be determined by the contact model introduced in Lubricants 2019, 7, 89 7 of 16

Section 2.1. So as to integrate the contact correlation into the friction model of the entire engine cycle, an analytical expression is also developed [22]:

!Z h Pc = K0E0A Ω (7) − σp

Here, K0, A, Ω, and Z are constants for a speciﬁc surface, obtained by running the asperity model described earlier. E0 is the equivalent elastic modulus of the two contact surfaces, which is computed as [22]: 2 E0 = (8) 1 v 2 1 v 2 − 1 + − 2 E1 E2 where v1, v2, E1, and E2 are the Poisson ratio and elastic modulus of the two contact materials.

3. Results Both wear coefficient and friction change from the simulation are evaluated. For the tested surfaces, wear rate has relatively large magnitude at the beginning but gradually decreases to a constant. In addition, the simulation results also indicate that the constant wear rate for the steady state is proportional to external load if the external load is solely supported by the asperity contact. Therefore, the wear rate predicted with the fatigue mechanism employed here fits the Archard law [23]. Friction for the entire engine cycle is calculated based on existing friction correlations [21]. Different liner surface finishes are tested and compared with engine experimental results. Different cast iron liner finishes are utilized for both simulation and floating liner engine testing. The effectiveness of the asperity fatigue model is verified by the comparison between simulation results and experimental results, which show similar trends for engine friction change after break-in wear. The experimental friction measurements are obtained from floating liner engines (FLE). The detailed experimental setup was adequately described by Westerfield [19]. The design of the FLE was originally provided by Takiguchi [24,25]. The FLE is a specialized internal combustion engine that allows measurement of friction contributions from the piston assembly while the engine is in operation.

3.1. Results of Liner Wear during Break-In Period In this section, liner wear break-in simulation results are presented based on the asperity fatigue wear model. Liner surfaces with different finishes are tested to investigate the impact of roughness, denoted as GG07, GG09, GG21, GG28, and GG30, shown in Figure4 with the Daimler liner finish classification [20]. The surfaces used here as the inputs of the wear model are generated numerically based on the real optical measurements [26]. For each surface, the external nominal pressure varies from 1 MPa to 4 MPa in order to also study the effect of pressure on fatigue wear. Figure5 shows break-in wear as a function of time (number of sliding cycles) for all 5 liner finishes. Wear is evaluated by the average height reduction over the entire surface. According to the results of liner wear simulation, the wear rate of the liner is relatively large at the beginning, but gradually reduces to a steady value for all different nominal stresses. Moreover, the steady-state wear rate is proportional to normal pressure, as indicated in Figure6. The vertical axis is the steady-state wear rate, which is evaluated by the average surface height reduction over each thousand running cycles. For the wear of metallic materials, Archard’s law is a widely used correlation that quantitatively describes sliding wear and external parameters; the volume of wear debris for metal sliding is proportional to the product of normal load and sliding distance, but inversely proportional to the material hardness [23,27]:

PL V = k (9) 3H In Equation (9), V is the volume of wear debris, and P, L, and H are external normal pressure, sliding distance, and material hardness, respectively. Here, k is the wear coeﬃcient, which is a constant Lubricants 2019, 7, x FOR PEER REVIEW 8 of 16

Figure 5 shows break-in wear as a function of time (number of sliding cycles) for all 5 liner finishes. Wear is evaluated by the average height reduction over the entire surface. According to the results of liner wear simulation, the wear rate of the liner is relatively large at the beginning, but gradually reduces to a steady value for all different nominal stresses. Moreover, the steady-state wear rate is proportional to normal pressure, as indicated in Figure 6. The vertical axis is the steady-state wear rate, which is evaluated by the average surface height reduction over each thousand running cycles. For the wear of metallic materials, Archard’s law is a widely used correlation that quantitatively describes sliding wear and external parameters; the volume of wear debris for metal sliding is proportional to the product of normal load and sliding distance, but inversely proportional to the material hardness [23;27]: 𝑃𝐿 𝑉=𝑘 (9) 3𝐻 Lubricants 2019, 7, 89 8 of 16 In Equation (9), V is the volume of wear debris, and P, L, and H are external normal pressure, sliding distance, and material hardness, respectively. Here, k is the wear coefficient, which is a forconstant a certain for a material certain material with a specific with a specific surface su finish.rface finish. As one As important one important mechanism mechanism in metal in metal wear, asperitywear, asperity fatigue fatigue wear obeyswear obeys Archard’s Archard’s law. Therefore,law. Therefore, it is reasonableit is reasonable and and essential essential to calculateto calculate the wearthe wear coeffi coefficientcient of surfaces of surfaces with with diff differenterent finishes, finishes, which which is conventionallyis conventionally used used as as a parametera parameter to evaluateto evaluate wear wear resistance resistance of aof surface. a surface.

(a) (b)

Lubricants 2019, 7, x FOR PEER REVIEW 9 of 16 (c) (d)

(e)

FigureFigure 5.5. SimulationSimulation resultsresults ofof break-inbreak-in wearwear asas aa functionfunction ofof slidingsliding cycles.cycles. WearWear lossloss isis evaluatedevaluated byby thethe average average surface surface height height reduction. reduction. ((aa)–()–(ee)) areare thethe calculationcalculation resultsresults forfor GG07,GG07, GG09,GG09, GG21,GG21, GG28GG28 andand GG30,GG30, respectively.respectively.

Figure 6. The steady-state wear rate is proportional.

Corresponding to the constant slope in Figure 6, the wear coefficient based on Equation (6) is presented in Table 2. It is essential to point out that the wear coefficients of GG21, GG28, and GG30 liner finishes have approximately the same value, indicating the steady-state wear rates of these surfaces are very close. The reason may be found from their manufacturing procedures. As illustrated in Section 2.5, the only difference among GG21, GG28, and GG30 finishes is the height of the fine finish. Although the plateau ratios are different for these three surfaces because of the fine finish, plateau regions have the same roughness level. Additionally, the size and shape of contact asperities are statistically the same for the three finishes. Therefore, it is reasonable that their wear coefficients are so close. Furthermore, the results here imply that the steady-state asperity fatigue wear rate largely depends on the roughness level of the plateau region resulting from fine honing.

Table 2. Steady-state wear coefficients of different liners.

Surface Finish GG07 GG09 GG21 GG28 GG30 Wear Coefficient (×𝟏𝟎𝟖) 1.14 1.22 1.51 1.53 1.50

3.2. Further Investigations on the Effect of Surface Roughness In the previous section, simulation results show that the wear rate of a surface depends greatly on its roughness level, especially the size and shape of contact asperities. In order to seek more

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(e)

Figure 5. Simulation results of break-in wear as a function of sliding cycles. Wear loss is evaluated by

Lubricantsthe average2019, 7, 89 surface height reduction. (a)–(e) are the calculation results for GG07, GG09, GG21, GG289 of 16 and GG30, respectively.

Figure 6. The steady-state wear rate is proportional.

Corresponding to the constant slope in Figure 66,, thethe wearwear coecoefficientfficient based on Equation (6) is presented inin TableTable2 .2. It It is is essential essential to to point point out out that that the the wear wear coe fficoefficientscients of GG21, of GG21, GG28, GG28, and GG30and GG30 liner linerfinishes finishes have approximatelyhave approximately the same the value, same indicating value, indicating the steady-state the steady-state wear rates wear of these rates surfaces of these are verysurfaces close. are The very reason close. may The bereason found may from be their found manufacturing from their manufacturing procedures. As procedures. illustrated As in Sectionillustrated 2.5, inthe Section only di ff2.5,erence the amongonly difference GG21, GG28, among and GG21, GG30 GG2 finishes8, and is the GG30 height finishes of the fineis the finish. height Although of the fine the plateaufinish. Although ratios are the diff erentplateau for ratios these threeare different surfaces fo becauser these ofthree the finesurfaces finish, because plateau of regions the fine have finish, the plateausame roughness regions have level. the Additionally, same roughness the size level. and Additionally, shape of contact the size asperities and shape are statistically of contact asperities the same arefor thestatistically three finishes. the same Therefore, for the three it is reasonable finishes. Theref that theirore, wearit is reasonable coefficients that are their so close. wear Furthermore, coefficients arethe resultsso close. here Furthermore, imply that the the steady-state results here asperity imply fatigue that the wear steady-state rate largely asperity depends fatigue on the roughnesswear rate largelylevel of depends the plateau on regionthe roughness resulting level from of fine the honing.plateau region resulting from fine honing.

TableTable 2. Steady-state wear coefficients coeﬃcients of different diﬀerent liners.

SurfaceSurface Finish Finish GG07GG07 GG09GG09 GG21GG21 GG28 GG28 GG30 GG30 𝟖 WearWear Coe Coefficientfficient ( 10 (×𝟏𝟎8) 1.14) 1.14 1.221.22 1.511.51 1.53 1.53 1.50 1.50 × − 3.2. Further Investigations on the Effect of Surface Roughness 3.2. Further Investigations on the Effect of Surface Roughness In the previous section, simulation results show that the wear rate of a surface depends greatly In the previous section, simulation results show that the wear rate of a surface depends greatly on its roughness level, especially the size and shape of contact asperities. In order to seek more on its roughness level, especially the size and shape of contact asperities. In order to seek more detailed underlying correlations, additional simulations are conducted for break-in fatigue wear. In the following, the sizes of the asperities are varied artificially to examine the effect on the break-in behavior. As inputs of the wear model, the roughness matrix representing a rough liner surface has specific resolutions in the sliding direction and circumferential direction, dx and dy. In this section, dx and dy are stretched by a factor of 0.5, 2, 4, and 8 to modify the size and slope of liner surface asperities. A larger stretched scale indicates flatter asperities. Other simulation parameters remain the same as previous simulations. The steady-state wear rate under different stretched scales and normal pressures is summarized in Figure7. With a constant normal pressure, the steady-state wear rate first increases, then decreases as the size of the asperities increases. The maximum steady state wear rate for all normal pressures occurs with the stretched scale factor of 2. This interesting result indicates that an optimal asperity flatness can be achieved if the designer of the liner surfaces wants to minimize the break-in period. Figure8 qualitatively explains why the optimal asperity flatness and size exist. LubricantsLubricants 2019 2019, 7, x, 7FOR, x FOR PEER PEER REVIEW REVIEW 10 of10 16of 16 detaileddetailed underlying underlying correlations, correlations, additional additional simula simulationstions are are conducted conducted for for break-in break-in fatigue fatigue wear. wear. In In thethe following, following, the the sizes sizes of theof the asperities asperities are are varied varied artificially artificially to examineto examine the the effect effect on onthe the break-in break-in behavior.behavior. As Asinputs inputs of theof the wear wear model, model, the the roughness roughness matrix matrix representing representing a rough a rough liner liner surface surface has has specific specific resolutions in the sliding direction and circumferential direction, dx and dy. In this section, dx and dy resolutions in the sliding direction and circumferential direction, dx and dy. In this section, dx and dy areare stretched stretched by bya factor a factor of 0.5,of 0.5, 2, 4,2, and4, and 8 to 8 modifyto modify the the size size and and slope slope of linerof liner surface surface asperities. asperities. A A largerlarger stretched stretched scale scale indicates indicates flatter flatter asperities. asperities. Other Other simulation simulation paramete parameters remainrs remain the the same same as as previousprevious simulations. simulations. TheThe steady-state steady-state wear wear rate rate under under different different stre stretchedtched scales scales and and normal normal pressures pressures is summarized is summarized in Figurein Figure 7. With 7. With a constant a constant normal normal pressure, pressure, the the steady-state steady-state wear wear rate rate first first increases, increases, then then decreases decreases as theas the size size of theof the asperities asperities incr increases.eases. The The maximum maximum steady steady state state wear wear rate rate for for all allnormal normal pressures pressures occursoccurs with with the the stretched stretched scale scale fact factor orof 2.of This2. This interesting interesting result result indicates indicates that that an anoptimal optimal asperity asperity flatness can be achieved if the designer of the liner surfaces wants to minimize the break-in period. Lubricantsflatness2019 can, 7, 89be achieved if the designer of the liner surfaces wants to minimize the break-in10 period. of 16 FigureFigure 8 qualitatively 8 qualitatively explains explains why why the the optimal optimal asperity asperity flatness flatness and and size size exist. exist.

FigureFigureFigure 7. 7. Steady-state Steady-state7. Steady-state wear wear wear rate rate rate for for forsurfaces surfaces surfaces with with with different diﬀ differenterent stretched stretched stretched scales. scales.

Figure 8. Asperities with different flatness under the same nominal pressure. FigureFigure 8. Asperities 8. Asperities with with different different flatness flatness under under the the same same nominal nominal pressure. pressure. As shown in Figure8, the original surface is modified with a stretch factor of 0.5 and 2, keeping the As Asshown shown in Figurein Figure 8, the8, the original original surface surface is modi is modifiedfied with with a stretch a stretch factor factor of 0.5of 0.5 and and 2, keeping2, keeping height of the asperities constant. In this simple analysis, it is assumed that all asperities have the same thethe height height of theof the asperities asperities constant. constant. In thisIn this simple simple analysis, analysis, it is it assumedis assumed that that all allasperities asperities have have the the shape. Because asperities with a stretch factor of 0.5 have the smallest radius of curvature, according to samesame shape. shape. Because Because asperities asperities with with a stretcha stretch factor factor of of0.5 0.5 have have the the smallest smallest radius radius of ofcurvature, curvature, Equations (1)–(3), the overlapping volume of this liner surface and the ring are the smallest, resulting accordingaccording to toEquations Equations (1)–(3), (1)–(3), the the overlapping overlapping vo lumevolume of ofthis this liner liner surface surface and and the the ring ring are are the the in a low steady-state wear rate. As the asperities are continuously stretched, the overlapping volume smallest,smallest, resulting resulting in ain low a low steady-state steady-state wear wear rate. rate. As Asthe the asperities asperities are are continuously continuously stretched, stretched, the the also increases since the average contact pressure is reduced. However, because of the reduction of overlappingoverlapping volume volume also also increases increases since since the the averag average contacte contact pressure pressure is reduced.is reduced. However, However, because because contact pressure on each asperity, the speed of crack propagation for both surface and subsurface of theof the reduction reduction of contactof contact pressure pressure on oneach each asperi asperity, ty,the the speed speed of crackof crack propagation propagation for for both both surface surface cracks decreases. The two influencing factors, overlapping volume and crack propagation speed, are andand subsurface subsurface cracks cracks decreases. decreases. The The two two infl influencinguencing factors, factors, overla overlappingpping volume volume and and crack crack indeed competitive, as asperities are artificially enlarged with increasing stretch scale factor. If the propagationpropagation speed, speed, are are indeed indeed competitive, competitive, as asasperi asperitiesties are are artificially artificially en largedenlarged with with increasing increasing effect of the crack propagation rate reduction takes the dominant position, the steady-state wear rate stretchstretch scale scale factor. factor. If the If the effect effect of theof the crack crack prop propagationagation rate rate reduction reduction take takes thes the dominant dominant position, position, decreases. This is the reason why the maximum wear rate occurs at a certain asperity flatness level. thethe steady-state steady-state wear wear rate rate decrease decreases. Thiss. This is the is the reason reason why why the the maximum maximum wear wear rate rate occurs occurs at a at certain a certain One extreme case can help to understand this trend—when the liner surface is ideally smooth with

only a single ﬂat asperity, the contact pressure on this asperity is equal to the external nominal pressure. The external nominal pressure on the liner is usually far below the normal range of pressure leading to fatigue wear, resulting in the wear rate being almost zero.

3.3. Calculated Friction Change and Comparison with Experimental Results The evolution of engine lubrication is studied and compared with experimental results through the friction under one complete cycle and the Stribeck curve. Plots of engine cycle friction can reflect friction variation within each engine cycle. The correlation between piston position and friction level is evaluated through various crank angles. The Stribeck curve is presented to illustrate how the friction coefficient evolves as the sliding speed changes. The theoretical calculation of friction is performed by both the model of hydrodynamic pressure and the model of dry contact. The wear process of different liner finishes is simulated by the asperity fatigue wear model, with friction curves plotted for surfaces Lubricants 2019, 7, 89 11 of 16

before wear and after wear. The break-in FLE experiments were conducted at 80 ◦C with an engine speed of 400 rpm. The lubricant is a special high-temperature, high-shear (HTHS) oil with a viscosity of 1.4 mPa s · The correlations of hydrodynamic pressure, hydrodynamic shear stress, and contact pressure introduced in Section 2.6 are utilized to obtain the friction curves for the entire engine cycle. The cycle model is a modified version of the published one [28] and the major modification is the replacement of the hydrodynamic lubrication submodel with the correlation based on the results of the deterministic model, as described earlier [21]. As the ring liner clearance depends on the ring sliding speed, the frictionLubricants also 2019 varies, 7, x FOR for PEER each REVIEW engine cycle, with the minimum friction value occurring during mid-stroke12 of 16 at low engine speed. Since the sliding speed is close to zero at the top dead center (TDC) and the bottom deadFigure center 11. The (BDC), engine diff erentcycle enginefriction speeds curves have of GG07 similar are friction also obtained magnitudes in Figure at the two12. Unlike positions. GG30, When for theGG07, clearance the boundary reaches lubrication this smallest dominates value, neither throughout contact the pressure whole cycle nor hydrodynamic across all engine pressure speeds. show This obviousdomination change did afternot change wear. Themuch simulated after 5 h contactof operation. pressure Two and factors hydrodynamic may contribute pressure to this of difference the GG30 surfacewith GG30. finish First, are plottedthe combination in Figure 9of as the functions range of of engine the ring speed liner and clearance. the lubricant The wear viscosity simulation does not of GG30allow isthe performed ring to escape using the the boundary-lubrication asperity fatigue wear-dominated model, with regime. a simulated Second, duration the average of five asperity hours, enginesize of speedGG07 ofis larger 400 rpm, than and for external GG30, nominalresulting pressure in a lower of 2asperity MPa. For fatigue simplicity, wear thisrate, nominal as mentioned pressure in isthe solely previous supported section. by Therefore, the asperity the contactsurface intopolo the weargy change model. for Therefore, GG07 is also the slower, wear rate resulting should in be a consideredless remarkable as the friction upper bounddrop for estimation GG07 after from wear the than model for because GG30. partThe ofexperimental the ring load measurements is supported byalso the support hydrodynamic this difference pressure between in reality. GG07 and GG30.

FigureFigure 9.9. Hydrodynamic pressures and contact pressures ofof GG30,GG30, beforebefore wearwear andand afterafter 55 hh runningrunning underunder anan externalexternal loadload ofof 22 MPa.MPa.

As shown in Figure9, compared with the original surface, the surface after wear simulation has approximately the same hydrodynamic pressure, but the contact pressure is reduced because the asperities are ﬂattened and gradually fractured. This can be further revealed in Figure 10, which contains the height distribution curves for the liner surface before and after wear simulation. The clearance here in Figure9 is deﬁned as the distance between the ring surface and the peak of the plateau. With a worn plateau, the contact pressure reduces after wear. When the ring liner clearance is

Figure 10. Liner surface height distributions before and after wear simulation.

Lubricants 2019, 7, x FOR PEER REVIEW 12 of 16

Figure 11. The engine cycle friction curves of GG07 are also obtained in Figure 12. Unlike GG30, for GG07, the boundary lubrication dominates throughout the whole cycle across all engine speeds. This domination did not change much after 5 h of operation. Two factors may contribute to this difference with GG30. First, the combination of the range of engine speed and the lubricant viscosity does not allow the ring to escape the boundary-lubrication-dominated regime. Second, the average asperity size of GG07 is larger than for GG30, resulting in a lower asperity fatigue wear rate, as mentioned in the previous section. Therefore, the surface topology change for GG07 is also slower, resulting in a less remarkable friction drop for GG07 after wear than for GG30. The experimental measurements also support this difference between GG07 and GG30.

Lubricants 2019, 7, 89 12 of 16 small, the contact pressure changes little because only high asperities are fractured after 5 h break-in wear. A small clearance exists for low sliding conditions, especially when the piston moves to the top Figure 9. Hydrodynamic pressures and contact pressures of GG30, before wear and after 5 h running dead center or the bottom dead center. Range 1, range 2, and range 3 correspond to the ring liner under an external load of 2 MPa. clearance range when the engine speed is 100 rpm, 500 rpm, and 1000 rpm, respectively.

FigureFigure 10. 10.Liner Liner surfacesurface height height distributions distributions before before and and after after wear wear simulation. simulation.

The pressure change shown in Figure9 is consistent with the friction curves in Figure 11, in which the friction does not change much after wear near TDC and BDC. On the other hand, in the mid-stroke region, the ring may have different sliding velocities with different engine speeds. When the engine speed is 100 rpm, the contact pressure has a slight drop. This leads to the friction reduction after wear at mid-stroke in Figure 11b; here, contact pressure is always the dominant factor, much more so than the hydrodynamic pressure. When the engine speed reaches 1000 rpm, the contact pressure is much lower than hydrodynamic pressure at the mid-stroke, for both conditions before and after wear. Therefore, as shown in Figure 11f, the friction curves become almost overlapped in the middle. Compared with the friction measurements obtained experimentally, the relatively important trend between hydrodynamic pressure and contact pressure agrees well, as shown in Figure 11. The engine cycle friction curves of GG07 are also obtained in Figure 12. Unlike GG30, for GG07, the boundary lubrication dominates throughout the whole cycle across all engine speeds. This domination did not change much after 5 h of operation. Two factors may contribute to this difference with GG30. First, the combination of the range of engine speed and the lubricant viscosity does not allow the ring to escape the boundary-lubrication-dominated regime. Second, the average asperity size of GG07 is larger than for GG30, resulting in a lower asperity fatigue wear rate, as mentioned in the previous section. Therefore, the surface topology change for GG07 is also slower, resulting in a less remarkable friction drop for GG07 after wear than for GG30. The experimental measurements also support this difference between GG07 and GG30. One important mismatch between simulation and experiment is the magnitude of friction drop in GG30. Especially for the engine speed of 100 rpm, the friction drop in the mid-stroke region is larger than the predicted result. As hydrodynamic friction is not dominant at low engine speeds, this indicates that the predicted contact pressure drop is smaller than in experimental measurements. Therefore, the break-in wear rate is also underestimated. One reason for the underestimation of fatigue wear rate comes from the assumption of low yield when calculating crack propagation. However, the plastic regions around cracks are not always small compared with crack lengths. With the extended plastic regions, cracks can propagate faster than predicted in this fatigue model, leading to higher wear rate and more dramatic friction drop. The other possible error source is the assumption that asperity fatigue wear is uniform over the entire liner surface, while in reality asperity contact is different along the stroke during break-in. Lubricants 2019, 7, 89 13 of 16 Lubricants 20192019,, 77,, xx FORFOR PEERPEER REVIEW REVIEW 1313 of of16 16

((aa)) (b(b) )

((cc)) (d(d) )

((ee)) (f()f )

Figure 11. Experimental measurements and simulation results of friction change for the surface of FigureFigure 11. 11.Experimental Experimental measurementsmeasurements and simulation results of friction change change for for the the surface surface of of GG30: (a) experimental measurements, 100 rpm; (b) simulation results, 100 rpm; (c) experimental GG30:GG30: (a(a)) experimentalexperimental measurements,measurements, 100100 rpm;rpm; (b) simulationsimulation results, 100 100 rpm; rpm; ( (cc)) experimental experimental measurements, 500 rpm; (d) simulation results, 500 rpm; (e) experimental measurements, 1000 rpm; measurements,measurements, 500 500 rpm;rpm; ((dd)) simulationsimulation results,results, 500500 rpm;rpm; (e) experimental measurements, measurements, 1000 1000 rpm; rpm; and (f) simulation results, 1000 rpm. andand ( f()f) simulation simulation results, results, 1000 1000 rpm. rpm.

(a) (b) (a) (b)

Lubricants 2019, 7, x FOR PEER REVIEW 14 of 16

Lubricants 2019, 7, 89 (e) (f) 14 of 16 Lubricants 2019, 7, x FOR PEER REVIEW 14 of 16 Figure 12. Experimental measurements and simulation results of friction change for surface GG07: (a) experimental measurements, 100 rpm; (b) simulation results, 100 rpm; (c) experimental measurements, 500 rpm; (d) simulation results, 500 rpm; (e) experimental measurements, 1000 rpm; and (f) simulation results, 1000 rpm.

One important mismatch between simulation and experiment is the magnitude of friction drop in GG30. Especially for the engine speed of 100 rpm, the friction drop in the mid-stroke region is larger than the predicted result. As hydrodynamic friction is not dominant at low engine speeds, this indicates that the predicted contact pressure drop is smaller than in experimental measurements.

Therefore, the break-in wear rate is also underestimated. One reason for the underestimation of (e) (f) fatigue wear rate comes from the assumption of low yield when calculating crack propagation. However,FigureFigure 12. the12. ExperimentalplasticExperimental regions measurements measurementsaround cracks and are andsimulation not simulation always results smallresults of friction compared of change friction with for change surfacecrack lengths. forGG07: surface (a With) theGG07: extendedexperimental (a) experimental plastic measurements, regions, measurements, cracks 100 can rpm; propagate 100 (b rpm;) simulation fa (bster) simulation than results, predicted results, 100 in 100 thisrpm; rpm; fatigue (c) ( c)experimental experimentalmodel, leading to highermeasurements,measurements, wear rate 500 500 and rpm; rpm; more (d(d) dramatic) simulationsimulation friction results,results, drop 500 . rpm; The other ( (ee)) experimental experimental possible error measurements, measurements, source is the 1000 assumption 1000 rpm; rpm; thatand andasperity (f ()f simulation) simulation fatigue results, wearresults, is 1000 1000uniform rpm. rpm. over the entire liner surface, while in reality asperity contact is different along the stroke during break-in. BesidesOneBesides important the the engine engine mismatch cyclecycle friction frictionbetween plots, simulation the the Stribe Stribeck andck ex curveperiment curve reflecting reflecting is the themagnitude the friction friction coefficientof friction coefficient dropas a as ain functionfunction GG30. ofEspeciallyof slidingsliding speedfor the is engine also plotted speed ofin in 100Fi Figuregure rpm, 13.13 the .When When friction the the dropsliding sliding in speedth speede mid-stroke is islow low (boundary (boundaryregion is lubrication),largerlubrication), than frictionthe friction predicted is is mainly mainly result. caused caused As hydrodynamic by by solidsolid contact.contact. friction As As the theis not sliding sliding dominant speed speed atincreases, increases, low engine hydrodynamic hydrodynamic speeds, this frictionindicatesfriction gradually gradually that the makes predictedmakes a a more more contact significant significant pressure contribution,contribution, drop is smaller so so that that than it it changes changes in experimental into into mixed mixed measurements. friction. friction. If the If the speedTherefore,speed keeps keeps the increasing, increasing, break-in the thewear two two rate surfaces surfaces is also areare unde separatedseparestimated.rated further further One and and reason hydrodynamic hydrodynamic for the underestimation force force becomes becomes the of the onlyfatigueonly friction friction wear source. source.rate comes Because Because from of of thethethe increaseincreaseassumption of the of shearlow yieldrate, rate, the thewhen friction friction calculating increases increases crack again. again. propagation. For For GG07, GG07, becauseHowever,because the the the surface surface plastic is is rougher,regions rougher, around it it needs needs cracks aa largerlarger are sliding not always velocity velocity small to to entercompared enter the the hydrodynamic hydrodynamicwith crack lengths. lubrication lubrication With condition,thecondition, extended which which plastic is is beyond beyondregions, the the cracks range range can of of propagate engineengine speed.speed. faster than predicted in this fatigue model, leading to higher wear rate and more dramatic friction drop. The other possible error source is the assumption that asperity fatigue wear is uniform over the entire liner surface, while in reality asperity contact is different along the stroke during break-in. Besides the engine cycle friction plots, the Stribeck curve reflecting the friction coefficient as a function of sliding speed is also plotted in Figure 13. When the sliding speed is low (boundary lubrication), friction is mainly caused by solid contact. As the sliding speed increases, hydrodynamic friction gradually makes a more significant contribution, so that it changes into mixed friction. If the speed keeps increasing, the two surfaces are separated further and hydrodynamic force becomes the only friction source. Because of the increase of the shear rate, the friction increases again. For GG07, because the surface is rougher, it needs a larger sliding velocity to enter the hydrodynamic lubrication condition, which is beyond the range of engine speed.

Lubricants 2019, 7, x FOR PEER REVIEW 15 of 16 (a) (b)

(a) (b)

FigureFigure 13. 13.Stribeck Stribeck curves curves for for experimental experimental measurements measurements and and simulation simulation results: results: (a) simulation (a) simulation results, GG30;results, (b )GG30; simulation (b) simulation results, GG07; results, (c) experimentalGG07; (c) experimental measurements, measurements, GG30; and GG30; (d) experimental and (d) measurements,experimental measurements, GG07. GG07.

4. Conclusions In this paper, an asperity fatigue liner wear model during the break-in period in internal combustion engines is established. Two mechanisms leading to liner topography change are studied: asperity plastic deformation and fatigue. Simulation results agree with Archard’s wear law, showing that for a specific liner surface finish, the steady-state wear rate is proportional to the external nominal load that is solely supported by the asperity contact. Simulations also indicate that the maximum steady-state wear rate can be obtained for a specific surface roughness level. This could be applied in the future for liner surface roughness design to minimize the break-in time. The engine friction change due to the break-in liner wear calculated by the presented wear model shows the same trend as—and comparable magnitude with—the experimental measurements. Such agreements show the adequacy and potential of the present model for break-in wear. On the other hand, the model involving current considerations and parameters underestimates the magnitude of the friction change in the mixed lubrication regime. Additionally, the contribution of the asperity contact decreases during the break-in, which is neglected in the current calculation. Improving part of the fatigue model and adapting the changes of the asperity contact during break-in will allow more accurate prediction of the liner break-in duration and asymptotic friction of the ring pack.

Author Contributions: conceptualization, C.G. and T.T.; methodology, C.G.; data processing, C.G and R.W.; writing—original draft preparation, C.G.; writing—review and editing, C.G., T.T. and R.W.; supervision, T.T.; project administration, C.G. and T.T.; funding acquisition, T.T.

Funding: This work was sponsored by the Consortium on Lubrication in Internal Combustion Engines in the Sloan Automotive Laboratory, Massachusetts Institute of Technology, with additional support by Argonne National Laboratory and the US Department of Energy. The consortium members were Daimler, Mahle, MTU, PSA, Renault, Shell, Toyota, Volkswagen, Volvo Truck, and Weichai Power.

Conflicts of Interest: the authors declare no conflict of interest.

Reference

1. Schmidt, T.T.; Gaertner, F.F.; Kreye, H. New developments in cold spray based on higher gas and particle temperatures. J. Therm. Spray Technol. 2006, 15, 488–494. 2. Sabri, L.; Mezghani, S.; El Mansori, M.; Zahouani, H. Multiscale Study of Finish-Honing Process in Mass Production of Cylinder Liner. Wear 2010, 271, 509–513. 3. Lawrence, D. An Accurate and Robust Method for the Honing Angle Evaluation of Cylinder Liner Surface Using Machine Vision. Int. J. Adv. Manuf. Technol. 2011.

Lubricants 2019, 7, 89 15 of 16

4. Conclusions In this paper, an asperity fatigue liner wear model during the break-in period in internal combustion engines is established. Two mechanisms leading to liner topography change are studied: asperity plastic deformation and fatigue. Simulation results agree with Archard’s wear law, showing that for a specific liner surface finish, the steady-state wear rate is proportional to the external nominal load that is solely supported by the asperity contact. Simulations also indicate that the maximum steady-state wear rate can be obtained for a specific surface roughness level. This could be applied in the future for liner surface roughness design to minimize the break-in time. The engine friction change due to the break-in liner wear calculated by the presented wear model shows the same trend as—and comparable magnitude with—the experimental measurements. Such agreements show the adequacy and potential of the present model for break-in wear. On the other hand, the model involving current considerations and parameters underestimates the magnitude of the friction change in the mixed lubrication regime. Additionally, the contribution of the asperity contact decreases during the break-in, which is neglected in the current calculation. Improving part of the fatigue model and adapting the changes of the asperity contact during break-in will allow more accurate prediction of the liner break-in duration and asymptotic friction of the ring pack.

Author Contributions: Conceptualization, C.G. and T.T.; methodology, C.G.; data processing, C.G and R.W.; writing—original draft preparation, C.G.; writing—review and editing, C.G., T.T. and R.W.; supervision, T.T.; project administration, C.G. and T.T.; funding acquisition, T.T. Funding: This work was sponsored by the Consortium on Lubrication in Internal Combustion Engines in the Sloan Automotive Laboratory, Massachusetts Institute of Technology, with additional support by Argonne National Laboratory and the US Department of Energy. The consortium members were Daimler, Mahle, MTU, PSA, Renault, Shell, Toyota, Volkswagen, Volvo Truck, and Weichai Power. Conﬂicts of Interest: The authors declare no conﬂict of interest.

References

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