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Simulation and modeling of friction for honed and wave-cut cylinder bores of marine engines
Simulation Modelling Practice and Theory 49 (2014) 228–244
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Simulation and modeling of friction for honed and wave-cut cylinder bores of marine engines Anastasios Zavos, Pantelis G. Nikolakopoulos ⇑ Machine Design Laboratory, Dept. of Mechanical Engineering and Aeronautics, University of Patras, Patras 26504, Greece
a r t i c l e
i n f o
Article history: Received 26 July 2014 Received in revised form 11 September 2014 Accepted 2 October 2014
Keywords: Friction Fluid structure interaction Piston ring Navier Stokes Wave-cut Honing
a b s t r a c t A fluid solid interaction model (FSI) developed for two different structural cylinder patterns in order to simulate the frictional performance of piston ring–cylinder liner systems for marine engines. Computational fluid dynamics (CFD) analysis is used to solve the Navier Stokes equations. A fully flooded inlet and outlet conditions are assumed taking into account the piston ring elasticity. Honing and wave-cut cylinder geometries were compared while the pressure distribution along the ring thickness and the lubricant film is determined for each crank angle. The present results demonstrate that the honed cylinder geometry improves the friction results increasing the oil film thickness. Further, the artificially textured piston rings with the honed cylinder liner were investigated. As a result, we propose the operational function between the textured rings with the modified cylinder liners in marine engines. Ó 2014 Elsevier B.V. All rights reserved.
1. Introduction The current trend of shipping technology demand powerful diesel engines. Hence, the continuous growth of fuel prices with the economy crisis leads to reduction of operation costs. As a result, the reduction of the engine load and ship’s speed can create various operational difficulties. Piston rings in large marine diesel engines operate under significant mechanical and thermal loads, such as the combustion pressure changes. The simultaneous friction and wear control of the tribo pair between the piston ring and the cylinder is an important task for the engine reliability. Due to this major problem, different structural modifications are developed on the cylinder bore to achieve smaller friction and fuel consumption. In general, the cylinder conditions improves the operation of piston rings with the oil supply along to the piston ring thickness. Today, honing and wave-cut are the most common patterns on the cylinder bore. MAN B&W and Wartsila companies used these methods reducing the need of purchasing new cylinder liners. The piston ring lubrication conditions have been investigated by many authors under different operational conditions. Wakuri et al. [1] presented a numerical and experimental work about the basic tribological parameters of piston rings. Detailed, the friction forces and the oil film were predicted. The analytical model developed, using the Reynolds equation, while the experimental results have been taken for a four stroke diesel engine. Numerical and experimental friction results clearly presented and discussed. Sutaria et al. [2] developed a numerical model based on the average Reynolds equation that predicts the friction forces for internal combustion engines. Later on, Jeng [3] presented an analytical model about piston ring lubrication conditions. Boundary and fully flooded conditions expressed for a piston ring pack. Results of friction, oil film ⇑ Corresponding author. Tel.: +30 2610969421; fax: +30 2610 997207. E-mail address: [email protected] (P.G. Nikolakopoulos). http://dx.doi.org/10.1016/j.simpat.2014.10.002 1569-190X/Ó 2014 Elsevier B.V. All rights reserved.
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Nomenclature
Model piston–piston ring–cylinder geometry variables Dcyl cylinder diameter (m) Dring piston ring diameter (m) h0 initial distance between the piston ring and the cylinder liner (m) B piston ring thickness (m) Ls stroke length (m) X crankshaft angular velocity (rpm) l fluid dynamic viscosity (Pa s) Ff ring friction force (N) Vp piston velocity (m/s) q fluid density (kg/m3) phyd local hydrodynamic pressure (Pa) E Young modulus of elasticity (GPa) rring piston ring roughness (lm) kCR control ratio rcr crank radius (m) h oil film thickness (m) u crank angle (°) tg the distance from top to the first groove (m) tland the lands between the ring grooves (m) T oil m TTDC TBDC T1,T2 ao pc pa Asmooth A F f s
mean oil temperature (°C) cylinder liner temperature at the top dead center (TDC) (°C) cylinder liner temperature at the bottom dead center (BDC) (°C) numerical parameters for calculating the dynamic viscosity coefficient of friction for the asperity contact combustion gas pressure (Pa) ambient pressure (Pa) area of smooth piston ring (m2) ring surface interfaced the cylinder (m2) Ff dimensionless friction force, p Asmooth a stress tensor
Surface texturing dimple geometry variables N number of dimples rp base radius of dimple (m) Hd dimple depth (m) Bp axial length of texture zone (m) Lut untextured top length (m) Lud untextured down length (m) e dimple depth over diameter ratio: B c texture portion: c ¼ Bp
e ¼ 2rHdp
Honing and wave-cut cylinder liner geometry variables Lh honing length (m) Hh honing depth (m) Lw textured cell length of wave (m) Dw wave diameter (m) Hw wave depth (m)
thickness and power losses presented and discussed for each of the piston rings. Rahmani et al. [4] considered a transient elastohydrodynamic model for a rough compression ring–cylinder liner system. He examined the friction and the oil film behavior of an incomplete circular ring. Additionally, Morris et al. [5], developed a model for the compression piston ring to cylinder liner, when the mixed lubrication conditions was attained. In practical terms, they examined a new and worn ring and the friction behavior is analytically discussed. Furthermore, a one-dimensional wear model of the piston ring– cylinder system was performed by Ma et al. [6]. The friction and the wear were investigated, based on the surface roughness and on the cylinder wall temperature.
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Relevant computational and experimental results about the piston ring–cylinder system for marine engines have been described also by many authors. Wolff [7] developed a simulation model of the system: piston–ring–cylinder (PRC) for a two-stroke marine engine and presented his predictions with experimental results. Hence, his analysis can be useful for the optimization of the piston–ring–cylinder (PRC) system in marine engines. Also, the motion of a ring pack was analyzed by Wolff and Piechna in Ref. [8]. Results of friction with twist or not effects were presented and compared. Moreover, the work of Saburi et al. [9] contains a numerical analysis of the oil film between the piston rings and cylinder liner. The influence of the surface shape of a cylinder liner on piston rings lubrication condition was also examined. In practical terms, concerning the wave-cut cylinder liners, it is expected that the anti-scuffing capacity will be improved by the oil retention capacity of the oil grooves. Elfridsson [10] presented a simulation model for a piston ring in marine engines. In particular, a 3D piston ring model developed using the finite element method while the radial geometry can be expressed by the lathe curve from the industry. This method can be used to perform the operating conditions of the piston ring. Livanos and Kyrtatos [11] developed a friction model for the marine diesel engine piston assembly. The authors considered that the piston rings have a barrel shape face and allowed the piston eccentricities at the top and bottom of the skirt. In detail, the quasi-steady-state conditions were assumed while the external force was balanced by the film load capacity. The structural modifications of the piston–piston ring–cylinder system of large bore slow speed marine diesel engines were described by Lalic et al. in [12]. This work shows that the fully deep honed cylinders improve the problem of high friction and wear in marine engines. The process of honing builds-up a proper hydrodynamic lubrication between the piston rings and cylinder liner. To this end, the honing method is a standard method for large bore of two stroke marine engines since 1997. The study of Maekawa et al. [13] showed with experimental results that the wave-cut surface of cylinder liner has better spread-ability of cylinder oil than honed surface. Also, Zavos and Nikolakopoulos [14] presented a first study, by solving the Navier Stokes equations for pure hydrodynamic conditions between the piston ring and the cylinder. The structural modifications of the cylinder surface, such as honing and wave-cut, were considered and compared. The mechanisms of friction, the pressure distribution and the oil film velocity due to the cylinder patterns are examined, either for smooth top ring or for artificial textured, while the piston ring floats into the piston groove. Moreover, in the work by Bolander and Sadeghi [15] a two-dimensional oil flow model was developed in which a honed pattern of cylinder surface from the measured three dimensional profiles was taken into account. This profile then, was used to generate a surface, which was included in their mixed lubrication model. Detailed studies concerning the surface texturing along to piston rings or cylinder liners have been referred by many authors. Yin et al. [16] developed a mixed lubrication model solving the average Reynolds equation taking into account the asperity contacts function. The effects of micro-dimples on the friction and the lubrication behavior of a cylinder liner–piston ring were investigated. The authors have shown the effects between the surface roughness of non-texturing regions and micro-dimples and the synergistic effects of the multi-micro-dimples. Etsion and Sher [17] provided an experimental work to investigate the effects of partially textured piston rings on the fuel consumption for internal combustion engines. They have shown that the piston rings having a partial surface texturing improve more than 4% the fuel consumption. Kligerman et al. [18] presented a piston ring–cylinder model partially textured, using laser techniques, for piston ring friction reduction. In their work they took into account the Reynolds equations and the radial motion of piston ring. Moreover, the texturing parameters such as dimples depth and textured portion are investigated considering their optimum parameters. Additionally, Ronen et al. [19] presented a study for a piston ring–cylinder system including the generated hydrodynamic effects from the surface texturing. They solved the Reynolds equation and the equation of motion, since the variation of friction force and clearance between the piston ring and cylinder liner was presented. Continuing, a simulation model based on the gas leakage effect on the compression piston ring was proposed by Zavos and Nikolakopoulos [20]. To this end, two different surfaces with texturing, along to the piston ring liner examined, concluding on the structural integrity of the ring of each case. Their model was solved using the Navier Stokes equations for fully flooded conditions, and they took into account the piston ring elasticity. In this paper two structural patterns, the wave-cut and honing, are modeled and simulated, and their effects on the piston ring friction force, under real operational conditions regarding slow speed marine engines are analyzed and discussed. The hydrodynamic simulation model is solved using the Navier Stokes equations, while the fluid structure interaction (FSI) analysis is also used to get more precisely tribological behavior of the cylinder-oil and ring system. According to the knowledge of authors this is a first study by considering the effects of large bore cylinder patterns with artificial textured piston ring surfaces, regarding the prediction of the piston ring friction, the pressure distribution and the oil film distribution of the piston ring.
2. Problem consideration 2.1. Geometrical model of piston ring–cylinder The basic geometrical parameters of the piston ring–cylinder system are presented in Fig. 1. The main engine operation parameters is defined by Wolff in [7] and used here. The rotational speed is X = 105 rpm, the stroke length is defined as Ls = 2.416 m and the cylinder bore is Dcyl = 580 mm. In this study, the two dimensional (2D) simulation model consists of the following parameters:
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Fig. 1. Basic dimensions of the piston ring–cylinder system.
the the the the the
thickness of the top ring is B, piston ring width is noted as W, lands between the ring grooves is tland, distance from top to first piston groove is tg, radial and axial piston–piston ring gap is defined as dgap
Additionally, the numerical parameter ho is the initial distance between the piston ring and cylinder liner. The parameter ho is significant in the simulation model and is used in order to achieve the fully flooded lubrication. In detail, the piston ring floats into the piston groove having an initial value ho = 10 lm, when the crank angle is 0°. Thereafter, the oil thickness h varies as a function of the relative rotation angle of the crankshaft. The piston ring moving wall generates shear forces, exerting motion to the fluid, which flows from the piston ring inlet to the outlet. As the fluid convects, it builds up pressure, which exerts forces on the piston ring wall. Pressure build up is due to the converging geometry, as a result of the ring deformation due to the chamber pressure. In Table 1, the input numerical parameters are given. In summation, the top piston ring dimensions are taken by the Wolff’s work [7]. Actually, the roughness of the top ring is assumed to be rring = 0.044 lm according to the study of Wolff’s [7]. The friction power loss caused by the piston rings makes up a large portion of the power loss in the internal combustion engines. Therefore, an understanding between the piston rings and the cylinder wall is crucial for reducing friction. Hence, designing the profile of the piston ring, of each application, in order to reduce friction losses between the rings and the cylinder is a vital topic in the internal combustion engines. A flat ring profile with surface texturing based on the recent published works by Etsion et al. [17–19] is presented here in combination with textured patterns. Additionally, and from the technological point of view, in the rectangular rings the full ring face sits against the cylinder liner, and such rings have a relatively low contact pressure. Of course, this is a point that needs further investigation comparing the flat and the parabola ring profile in relation with the surface texturing parameters and cylinder modifications, taking into account that in such machines we have to have low friction and to maintain high levels of durability. 2.1.1. Honing and wave-cut cylinder liner geometry In Fig. 2 the basic geometrical parameters of cylinder liner modifications are illustrated. For a fully deep honed cylinder, the parameter Lh is the length of the honing and Hh is the depth of honing. Regarding the wave-cut cylinder liner, the basic geometrical dimensions are the wave diameter Dw, the wave depth, Hw and the textured cell length of wave, Lw. The above cylinder modifications have been defined by many authors, as in references [9,12–18]. The geometrical parameters of the fully deep honed and wave-cut cylinder liners, are taken from Ref. [13], and presented in Table 2. 2.1.2. Piston ring with surface texturing In Fig. 3, the geometry of spherical micro dimples texturing is presented. Each spherical dimple has a base radius rp and BB the textured zone Bp is bounded with two untextured strips of width Lut ¼ Lud ¼ 2 p on each of its sides. The following dimensionless parameters of this analysis were considered:
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the the the the
number of dimples are N, dimple depth is noted as Hd, Hd dimple depth over diameter ratio is e ¼ 2r , p B textured portion is defined as c ¼ Bp :
Here, it is worth to mention that the dimple dimensions were obtained in relation with the current literature [18,19]. Detailed the number of dimples and the central position of texture area were imposed in order to have a partial texturing, as it is provided by Kligerman’s work [18]. In particular, the textured portion parameter was obtained from Ref. [18] where the optimum textured portion c varies from 0.5 to 0.6. Regarding the dimple depth over diameter ratio, e = 0.1, this variable has been taken from the work of Ronen et al. [19], where the optimum value of e varies from 0.1 to 0.18. Hence, the spherical dimple geometry is defined by the above geometrical parameters; the base radius is rp = 80 lm and the dimple depth is Hd = 16 lm. The following dimensionless values assumed: N = 32, c = 0.5, e = 0.1. 3. Governing equations and assumptions The flow is assumed isothermal, while the dynamic viscosity is constant throughout the film thickness. The body forces are considered here, and the assembly of the piston–cylinder is concentric. This study models the top piston ring in fully flooded hydrodynamic lubrication and normal engine conditions. Thus the asperity interaction between the piston ring and cylinder liner near to top dead center (TDC) and bottom dead center (BDC) are neglected. However, reduced engine rotational speeds are likely to maintain thinner oil film enhanced the piston ring and cylinder liner contact. Hence, considered highlight the need for further research in this field. Based on the cavitation phenomenon, significant differences are expected in hydrodynamic pressure profiles, lubricant film thickness, and friction. However, in this study the piston ring operating characteristics associated without cavitation conditions. Therefore, this point will be investigated later on to examine how much significant is the cavitation contribution in the hydrodynamic lift in respect to wave cut and honed geometry, density and position. The conservation equations for unsteady incompressible and isothermal flow with zero gravity and other external body forces are: Mass conservation equation
rV ¼0
ð1Þ
Momentum equation
@V 1 l þ V rV ¼ rp þ r2 V @t q q
ð2Þ
where V is the velocity vector, the static pressure p, the fluid density q and the dynamic viscosity l. Eqs. (1) and (2) are solved with a commercial CFD software, utilizing a finite volume approach. 3.1. Oil flow and boundary conditions A hydrodynamic lubrication model between the piston ring and the cylinder is developed, for a two stroke slow speed marine engine. The main engine dimensions are obtained from Ref. [7]. The piston ring floats into the piston groove and moves according to the piston motion. In this analysis, the piston starts to move upward from bottom dead center (BDC) and for the crank angle 180°. Fig. 4 shows the piston ring–cylinder system conditions. In detail, the piston moves up on expansion as the piston ring floats in the lower level of groove. As expected, the gas pressures of combustion keeps the top ring on the bottom of piston groove. Afterward, when the piston moved down with acceleration, the piston ring is lifted upward. As the ring is lifted, the gas pressure is applied underneath the ring, and the ring slams up hard into the top of its groove. The gas pressures in the cylinder and around from the piston ring varies according to the engine stroke. Fig. 5 shows the boundary conditions on the top piston ring, as the piston moved for each engine stage (compression or expansion). The piston ring moving wall generates shear forces, exerting motion to the fluid, which flows from the piston ring inlet to the outlet.
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Fig. 2. Basic geometrical parameters of cylinder patterns.
Table 2 Design geometrical parameters for cylinder patterns. Patterns
Parameters
Nominal values
Honing
Lh Hh Dw Lw Hw
0.001 m 10, 20, 30 lm 0.001 m 0.002 m 10, 20, 30 lm
Wave-cut
Fig. 3. Piston ring with surface texturing geometry.
The profile of the combustion gas as a function of crank angle rotation is shown in Fig. 6a. The piston moves with a linear velocity in the y axis, expressed by the Eq. (3) and presented in Fig. 6b.
V p ¼ r cr Xðsin u þ
kCR sin 2uÞ 2
ð3Þ
Further, the cylinder remains stationary and the piston ring floats into the piston groove as it is shown in Fig. 5. The flat ring profile is used for this investigation. 3.2. Temperature and lubricant properties The lubricant viscosity is sensitive to the temperature variations. The temperature distribution along the cylinder liner is not uniform and can be estimated using the typical conditions in a two stroke slow marine engines for TDC and BDC. Detailed the temperature variation considered TTDC = 200 °C and TBDC = 80 °C accordingly. Hence, the oil temperature is assumed equal with the cylinder liner temperature. A set of simulations was performed for monograde oil SAE 50 taking the average value of the oil temperature, T oil m ¼ 140 C 3 and the assumed oil density, q = 855 kg/m for each crank angle position. The lubricant dynamic viscosity can be calculated as a function of oil temperature according to the below equation:
l ¼ ao exp
T1 T 2 þ T oil m
! ð4Þ
where ao = 0.06510 m Pa s, T1 = 1078.25 °C, T2 = 95.22 °C are the relevant parameters for lubricant grade SAE 50 and T oil m is the mean value of lubricant oil temperature.
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Fig. 4. Piston ring–cylinder model for hydrodynamic conditions as the piston starts from the bottom dead center (BDC) for crank angle 180°.
Fig. 5. Boundary conditions on the top piston ring for each engine stage.
3.3. Oil film equation The expression of oil film in terms of the gap between piston ring and cylinder wall is:
8 h þ hflat ðtÞ > > < o hðx; y; tÞ ¼ ho þ hflat ðtÞ þ Hpatterns ðx; yÞ > > h þ h ðtÞ þ H Hd ðx2 þ y2 Þ þ H : o
flat
d
r 2p
ð5Þ patterns ðx; yÞ
where hflat(t) is the time nominal thickness between the smooth facing surfaces, Hpatterns(x, y) is the cylinder liner modifications amplitude at coordinate system (x, y), ho is an initial distance between piston ring–cylinder system and Hd
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Fig. 6. (a) Gas pressures versus crank angle and (b) piston linear velocity versus crank angle.
is the spherical dimple depth. For this analysis, the oil film h(x, y, t) across the piston ring profile calculated for smooth facing profiles and presented in Fig. 7. 3.4. Design parameters Basic piston ring material properties for this study were provided by a typical marine engine. Flat profile shape of top ring was examined having the modulus of elasticity, E = 150 GPa, and the poisson’s ratio, m = 0.25. The pressure field is obtained after the numerical solution of the Eq. (2). Since the friction between the piston ring and cylinder liner was obtained entirely from shear stress within the oil, it is expressed by:
Ff ¼
Z
sdA ¼ pDring A
Z
B=2
B=2
p þ 2l
#v y dy #y
Fig. 7. Oil film thickness versus crank angle for smooth facing surfaces.
ð6Þ
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where vy is the lubricant oil velocity in the y axis, Dring = 0.580 m is the piston ring diameter, l is the dynamic viscosity and B is the piston ring thickness. The elastic deformation of the ring is taken into account regarding the friction force calculations [18]. Hence, the stress is expressed as r0 and it is mentioned as the von Mises stress:
1 h
r0 ¼ pffiffiffi ðr1 r2 Þ2 þ ðr2 r3 Þ2 þ ðr3 r1 Þ2
i12
2
ð7Þ
4. Simulation model and meshing requirements A 2D simulation model is developed using CFD. Fig. 8 presents the flow chart structure of the couple field problem. Regarding the fluid field analysis 16,739 tetrahedral elements were used having smooth profiles. In Fig. 9(a) and (b), the fluid–structure meshing details were presented. In particular, when the honing and the wave-cut cylinder liner patterns were modeled, 16,773 total number of elements were used. For this analysis, the radial clearance size between piston ring and cylinder wall is very small, so the use of tetrahedral elements leads to 5511 number of nodes. After the required grid sensitivity tests, 10 divisions were used in the circumferential direction and 500 divisions were used in the axial direction. Using lower number of divisions in the radial direction, the model gave a friction error between 10% and 15%. Thus, using upper number of 10 divisions this error minimized near to 2–3%. On the other hand, increasing the number of divisions in the axial direction from 500 to 600, the error of calculated friction was smaller than 0.5%. Regarding the honed and wave modifications, when the meshing requirements of the clearances were achieved, 10 and 30 divisions were used in the circumferential and axial direction, respectively. The fluid meshing details in the clearance between piston ring and cylinder are presented for each examined case (see Fig. 10). At the same time, when the piston ring with spherical micro dimples examined, the number of fluid elements was 14,572. In practical terms, each micro dimple area is meshed with 25 and 7 divisions in the axial and radial direction, accordingly. Upper and lower number of divisions was examined producing unacceptable errors to pressure term. However, increasing the divisions (upper 7 divisions) in the circumferential direction into the micro dimple area, the friction results have a good agreement with a small error, 2–3%. The fluid meshing detail into the spherical micro dimples is illustrated in Fig. 11. The parameter ho considered to be 10 lm. This parameter evaluated when the pressure error is Errorpres 6 106, and the mesh morphing into the clearance between piston ring and cylinder attained. Hence, the friction force under pure hydrodynamic conditions calculated sufficiently, giving a good agreement compared with the literature. However, using a smaller
Fig. 8. The solution flow chart of the coupled field problem.
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Fig. 9. The adaptive grid for the couple field problem, (a) fluid–structure detail in the clearance between piston ring and cylinder liner and (b) fluid– structure detail between ring and lateral face of the piston ring groove.
Fig. 10. Simulation meshing details for smooth, honed and wave-cut cylinder liners.
parameter ho the pressure error does not get improved while the Arbitrary Lagrangian Eulerian (ALE) formulation failed for ho 6 10 lm. The simulations were performed in a computer with 8 processors (Intel core i7-3770 CPU@ 3.40 GHz) and the typical simulation time considered five minutes for smooth and textured case respectively. When the convergence of pressure field calculations is satisfied, the algorithm moves the nodes of the fluid field taking into account the piston ring displacements, and the solver goes to the next fluid film solution. The fluid nodes in radial clearance between the piston ring and the cylinder liner are moved, including the Arbitrary Lagrangian Eulerian (ALE) formulation. As expected, the generated displacements of the piston ring were created after the mesh morphing. The computational mesh inside the domains can be moved arbitrarily to optimize the shapes of elements, using the ALE technique in the simulations. On the other hand, the mesh on the boundaries and interfaces of the domains can be moved along with the materials, to track precisely the boundaries and the interfaces of the multi-material system. Some steps of the ALE method are presented by the authors in [18]. 4.1. Convergence criteria The convergence of couple field problem confirmed to two steps. Initial, the pressure error expressed by:
Error pres ¼
Pi¼NCFD n
pki pik1 1 106 Pi¼NCFD n k pi i¼1
i¼1
ð8Þ
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Fig. 11. Fluid–structure meshing detail in the spherical micro dimples area.
For greater accuracy, a value of 106 is used for the pressure term. Second, for the structural analysis, the piston ring displacement is performed using a loop defined a critical displacement for each crank angle position. Hence, the critical displacement DScr on the ring in every time step is less/equal than one percent of the maximum displacement DSmax due to the combustion pressure, pc. The time step defined for each crank angle for 600 iterations. The number of iterations occurred using the above meshing requirements and a convergence tolerance of 106. For example, for 100 iterations the pressure error was 103.
5. Validation of Fluid Structure Interaction (FSI) results The present fluid structure interaction (FSI) model is validated by comparing the computational results against already published results. Firstly, some numerical results about the piston ring friction force were presented by Zavos and Nikolakopoulos [18] and compared with Sutaria’s work [2]. The extracted results have shown a good agreement while the gas leakage near to piston ring area varies with the crankshaft position. Simultaneously, a similar flow problem in a lubricated piston ring and cylinder wall was solved, and the predicted friction force compared against the recent literature results. Wakuri0 s [1] and Wolff0 s [8] results are based on the average Reynolds equation and the hydrodynamic lubrication regime. In fact, the solutions have been obtained by a numerical analysis taking into account the basic geometrical dimensions of piston ring–cylinder model, and the piston ring roughness. Thereafter, the gas pressures of combustion are clearly provided using two types of Newtonian oils (SAE 30 and SAE 50) for different oil temperatures. Continuing, the dynamic viscosity of lubricant oils are considered constant along to the cylinder liner, as the piston ring floats into the piston groove without twist effects. Hence, taken the above assumptions for pure hydrodynamic conditions, we decided that the papers of Wakuri et al. [1] and Wolff et al. [8] will encourage our investigation. In the simulation, the results of Fig. 12 (a) are compared with the investigation of Wakuri’s [1] for rotational speed X = 2400 rpm from a four stroke diesel engine, while the results of Fig. 12(b), to the ones of Wolff’s [8] for rotational speed X = 3400 rpm. The maximum differences of friction, compared for both of papers, did not exceed the amount of 10%. Actually, the gas pressures for each rotational speed were applied on a fully piston ring–cylinder model as it is shown in Fig. 5. This justifies a different hydrodynamic pressure near to the piston ring profile taken into account the lubricant oil velocity which influences the friction results, as it is observed between 180° and 270° on Fig. 12(b). Concluding, there is a very good agreement between the values predicted by the current analysis and the respective values mentioned in Ref. [1,8].
6. Results and discussion The extracted results include the fully deep honed and wave-cut cylinder liners with flat piston ring, in a constant crankshaft rotational speed X = 105 rpm. The effects of textured piston ring combined with the proper cylinder pattern is also referred and compared with the smooth case. The friction force, the oil film pressure and the lubricant film thickness on the top piston ring were predicted and presented.
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Fig. 12. Friction force versus crank angle. (a) Validation results of Wakuri paper [1]. (b) Validation results of Wolff’s study [8].
6.1. Friction force of a piston ring Fig. 13 illustrates the dimensionless friction force at a top piston ring lubricated with Newtonian oil SAE 50 and the oil temperature T oil m ¼ 140 C. Mainly the piston ring friction is increased while the viscous shear stress is maximized due to the pure hydrodynamic conditions. As expected, the maximum friction is observed when the piston velocity is maximum and the crank angle is u = 90°. The operation conditions of two stroke marine engine is X = 105 rpm and the oil temperature remains constant for each engine stage and crank angle position. The non-dimensional friction force on the piston ring moving wall is presented in Fig. 14, when the honed and wave-cut cylinder liners are simulated. It was observed that the cylinder patterns reduce substantial the friction force, as the piston ring moves into the piston groove. As presented, the honed cylinder liner improves 25% the friction in relation with the smooth case. At the same time, the wave-cut geometry reduces 7% the friction related to the smooth case. Comparing the honed and wave-cut liners, the shape of honing contributes to a friction reduction of 22%. This is in line with similar results extracted by the authors in [14]. Here, more realistic fully flooded conditions were simulated while the dimensions of honing and wave-cut pattern were obtained from the literature about marine engines. Apparently, a range of depth for honing and wave-cut patterns exists in between, which is identified by the Ref. [13]. As deduced from Fig. 15, the value of depth varies from Hh = Hw = 10, 20, 30 lm for each examined cylinder modification. For honed pattern the dimensionless maximum friction force improved slighter as the depth increases. Thus, the wave-cut liner is more sensitive with the increment of depth. As result, for wave depth Hw = 30 lm, the friction reduction was 4% in relation with the case of depth Hw = 10 lm.
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Fig. 13. Dimensionless friction force of a smooth piston ring and cylinder versus crank shaft angle for rotational speed X = 105 rpm and temperature oil T oil m ¼ 140 C.
Fig. 14. Dimensionless friction force of a smooth piston ring with smooth, honed and wave-cut cylinder liners versus crank shaft angle for rotational speed X = 105 rpm and temperature oil T oil m ¼ 140 C.
6.2. Pressure distribution and oil film thickness of a piston ring Fig. 16 shows the pressure distribution over the piston ring walls as the honed and wave-cut liner performed. The piston moves upward on expansion, the crank angle is u = 90°, and lubricant SAE 50 for temperature T oil m ¼ 140 C is used. It is obvious that the piston ring floats into the piston groove in lower levels under fully flooded lubrication. As it can be seen, the local hydrodynamic pressures in the clearance increased 3.6% with the honed liner (see Fig. 16a). In other case, the wave-cut liner influences moderate the pressure field in the axial direction (see Fig. 16b). Therefore, having honed cylinder liner with depth Hh = 10 lm the maximum pressure was obtained, pmax = 1.64 MPa, while for the case of wave-cut liner the maximum pressure was predicted, 1.58 MPa with the same depth. In practical terms, the deviation of pressure presented detailed in ‘ZOOM A’ and ‘ZOOM B’. The zoomed plots in Fig. 16(a) and (b) corresponds to the pressure distribution depends on the honed and wave-cut geometries. As the fluid intakes in the aforementioned surface modifications a hydrodynamic lift is generated, higher regarding the honed and less regarding the wave cut geometry. Both are compared to the smooth cylinder wall case.
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Fig. 15. Dimensionless maximum friction force of a smooth piston ring for various depth of honing and wave-cut cylinder liners with Hh = Hw = 10, 20, 30 lm.
Fig. 16. Hydrodynamic pressure profiles in Pa on the smooth piston ring at expansion stage for crank angle position u = 90°, (a) with honed cylinder liner Hh = 10 lm and (b) with wave-cut cylinder liner Hw = 10 lm.
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The current phenomenon follows the literature survey indicates that the effect of the geometric features on the generation of hydrodynamic pressure and then on the friction reduction may depends on geometric features dimensions, their density and the certain pattern on the mating surfaces. Regarding the wave cut geometry, the lands between the waves are responsible for the moderate pressure variation compared to the smooth wall case. So, as the wave cut appears it is observed from the color plots that the color alteration in the zoomed areas becomes lesser, compared to the honed geometry. In summation, the contribution of honing shape leads to the maximum pressure built up, due to the wedge effect of the converging surfaces. Hence, this trend reduces the friction results largely in relation with the wave-cut pattern. Regarding the oil film thickness, Fig. 17 illustrates that, the honed and wave-cut cylinder liner increases the oil thickness, as the piston velocity increases under pure hydrodynamic conditions. It is evident that the honing improves mainly 2.1% the oil film distribution in the clearance. Moreover, using the wave-cut liner the lubricant film succeeds a slighter rise of thickness around to 0.55%. Further, as the pressure produced in the clearance between top ring and cylinder liner, the oil supply in the shape of cylinder patterns achieved. 6.3. Comparison of smooth and textured piston ring using the honed cylinder liner In the present work, the piston ring texturing geometry has a spherical shape as it is illustrated in Fig. 3. A texture configuration with 32 micro dimples (N = 32) is examined. The dimple depth and the radius are given by Hd and rp, respectively. Regarding the central position of micro dimples and the piston ring thickness, the basic dimensions of dimple have been identified.
Fig. 17. Oil film thickness on the smooth piston ring with smooth, honed and wave-cut cylinder liners versus crank shaft angle for rotational speed X = 105 rpm and constant depths Hh = Hw = 10 lm.
Fig. 18. Dimensionless maximum friction force of smooth and textured piston ring for various depth of honing Hh = 10, 20, 30 lm.
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Fig. 19. Hydrodynamic pressure profiles in Pa at expansion stage for crank angle position u = 90° with honed cylinder liner Hh = 10 lm, (a) for smooth piston ring and (b) for piston ring with spherical micro dimples N = 32, c = 0.5, e = 0.1.
Fig. 20. Oil film thickness on the smooth and textured piston ring with honed cylinder liner Hh = 10 lm versus crank shaft angle for rotational speed X = 105 rpm .
As follows from Fig. 18, the variation of dimensionless maximum friction force for smooth and textured piston ring when the depth of honed cylinder varies is presented. As observed the friction was improved 12% using N = 32 micro dimples lubricated with the monograde oil SAE 50. In particular, the depths of honed shape influence moderate the friction either for smooth or textured piston ring. For the simulations, the dimple depth Hd was 16 lm and the dimple radius rp was 80 lm.
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Fig. 19 shows the pressure distribution on the top piston ring for smooth and textured cases, as the honed cylinder has a depth Hh = 10 lm. Under constant rotational speed X = 105 rpm, a hydrodynamic local pressure is generated in the gap between the mating surfaces due to the effect of dimples and the wedge effect of the converging surfaces (see Area ‘A’ from Fig. 19b). Local hydrodynamic pressure is maximum at the piston ring central position (see ‘ZOOM D’) when the texturing exists. In this case, the maximum hydrodynamic pressure was increased 4.6% in the clearance when the piston ring treated with the spherical micro dimples. As a result, the lubricant film thickness was increased (Eq. (5)), by considering the texture of the piston ring. Fig. 20, illustrates a comparison of the oil film variation for each engine stage as a function of surface texturing. It is obvious that the film thickness is higher 13% as well as the textured ring and honed liner is taken account into. This phenomenon leads to an increment of the piston ring surface displacements and hence, the friction force is decreased. 7. Conclusions In the present paper a simulation model is presented for piston ring–cylinder system of marine engines. A fluid-structural algorithm solved for pure hydrodynamic conditions, considering the elasticity of the piston ring. For two different types of cylinder pattern (honed and wave-cut liners), some cases of depth variation have been tested, in terms of computing the flow fields by means of a Navier Stokes solver. To this end, the optimal effect of honed cylinder liner with the textured piston rings on the maximum friction force was identified. The following conclusions are drawn: Honing and wave-cut cylinder patterns reduce the friction 7–25% in relation with the smooth case under pure hydrodynamic conditions. Honed cylinder liner achieves a reduction of friction 22% compared with the relevant wave-cut liner. A number of depth variations for each cylinder pattern shown that the friction reduction is moderate. Detailed, the wavecut liner reduces the friction force 4%, as the depth varies between Hw = 10 lm to Hw = 30 lm. Regarding the honed cylinder, the friction is less influenced. Honed and wave-cut liner improves 0.55–2.1% the oil film thickness distribution in the circumferential direction. The contribution of honed cylinder liner with the textured piston rings shown a friction reduction 12% in relation with the smooth flat ring. Maximum produced local hydrodynamic pressures, and the central position of texturing, leads to an oil film increment (13%) along to the piston ring thickness, hence the friction is minimized.
Acknowledgments This work was supported by Grant E.039 from the Research Committee of the University of Patras (Programme K. Karatheodori) and partially by the Greek Secretariat for Research and Technology through the TRIBO-MARINE project, grant Nr. 2595. References [1] Y. Wakuri, T. Hamatake, M. Soejima, T. Kitahara, Piston ring friction in internal combustion engines, Trib. Int. 25 (1992) 299. [2] BM Sutaria, DV Bhatt, KN Mistry, Simulation and modeling of friction force and oil film thickness in piston ring – cylinder liner assembly of an I.C. engine. In: Proceedings of the World Congress on Engineering 2009, vol. II WCE 2009, London, UK, July 1–3, 2009. [3] Y. Jeng, Theoretical analysis of piston-ring lubrication. Part 1 – Fully flooded lubrication, STLE Tribol. Trans. 35 (1992) 696–706. [4] R. Rahmani, S. Theodossiades, H. Rahnejat, B. Fitzsimons, Transient elastohydrodynamic lubrication of rough new or worn piston compression ring conjunction with an out-of-round cylinder bore, Proc. Inst. Mech. Eng., Part J: J. Eng. Tribol. 226 (2012) 284–305. [5] N. Morris, R. Rahmani, H. Rahnejat, P.D. King, B. Fitzsimons, The influence of piston ring geometry and topography on friction, Proc. Inst. Mech. Eng., Part J: J. Eng. Tribol. 227 (2013) 141–153. [6] Z. Ma, N.A. Henein, W. Bryzik, A model for wear and friction in cylinder liners and piston rings, Tribol. Trans. 49 (2006) 315–327. [7] A. Wolff, Simulation based study of the system piston–ring–cylinder of a marine two-stroke engine, Tribol. Trans. 57 (2014) 653–667. Doi: 10.1080/ 10402004.2014.895886. [8] A. Wolff, J. Piechna, Numerical simulation of piston ring pack operation with regard to ring twist effects, Arch. Mech. Eng. 54 (2007) 65–99. [9] S. Saburi, S. Yoshiyuki, Y. Takayuki, Tribology between piston rings and cylinder liners of marine diesel engines, IHI Eng. Rev. 38 (2005) 11–18. [10] Jon Elfridsson, 3D parameterized FEM modeling of a piston ring in a marine diesel engine: a simulation approach using FEM (2010). [11] G.A. Livanos, N.P. Kyrtatos, Friction model of a marine diesel engine piston assembly, Tribol. Int. 40 (2007) 1441–1453. [12] B. Lalic, I. Komar, D. Dobrota, Structural modifications for improving the tribological properties of the cylinder unit in two-stroke slow speed marine diesel engines, Trans. Marit. Sci. 2 (2012) 89–95. [13] K. Maekawa, Y. Akizuki, S. Matsumoto, O. Motomura, K. Ichimaru, Experimental estimation for behavior of cylinder oil on cylinder liner surface, J. MESJ. 35 (2000) 238–244. [14] A.B. Zavos, P.G. Nikolakopoulos, On the Cylinder Honing and Wavecut Effects against Piston Ring Artificial Texturing on the Friction in Marine Engines, in: Proceedings of the 2nd International MARINELIVE Conference on ‘‘All Electric Ship’’, Athens, Greece, February 13–14, 2014. [15] N.W. Bolander, F. Sadeghi, Deterministic modeling of honed cylinder liner friction, Tribol. Trans. 50 (2007) 248–256. [16] BF. Yin, X. Li, Y. Yonghong Fu, W. Yun, Effect of laser textured dimples on the lubrication performance of cylinder liner in diesel engine, Lubr. Sci. 24 (2012) 293–312. [17] I. Etsion, E. Sher, Improving fuel efficiency with laser surface textured piston rings, Tribol. Int. 42 (2009) 542–547. [18] Y. Kligerman, I. Etsion, F. Shinkarenko, Improving tribological performance of piston rings by partial surface texturing, Trans. ASME 127 (2005) 632– 638. [19] A. Ronen, I. Etsion, Y. Kligerman, Friction-reducing surface-texturing in reciprocating automotive components, Tribol. Trans. 44 (2001) 359–366. [20] A.B. Zavos, P.G. Nikolakopoulos, Simulation of piston ring tribology with surface texturing for internal combustion engines, Lubr. Sci. (2014). Doi: 10.1002/ls.1261.
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Simulation Modelling Practice and Theory journal homepage: www.elsevier.com/locate/simpat
Simulation and modeling of friction for honed and wave-cut cylinder bores of marine engines Anastasios Zavos, Pantelis G. Nikolakopoulos ⇑ Machine Design Laboratory, Dept. of Mechanical Engineering and Aeronautics, University of Patras, Patras 26504, Greece
a r t i c l e
i n f o
Article history: Received 26 July 2014 Received in revised form 11 September 2014 Accepted 2 October 2014
Keywords: Friction Fluid structure interaction Piston ring Navier Stokes Wave-cut Honing
a b s t r a c t A fluid solid interaction model (FSI) developed for two different structural cylinder patterns in order to simulate the frictional performance of piston ring–cylinder liner systems for marine engines. Computational fluid dynamics (CFD) analysis is used to solve the Navier Stokes equations. A fully flooded inlet and outlet conditions are assumed taking into account the piston ring elasticity. Honing and wave-cut cylinder geometries were compared while the pressure distribution along the ring thickness and the lubricant film is determined for each crank angle. The present results demonstrate that the honed cylinder geometry improves the friction results increasing the oil film thickness. Further, the artificially textured piston rings with the honed cylinder liner were investigated. As a result, we propose the operational function between the textured rings with the modified cylinder liners in marine engines. Ó 2014 Elsevier B.V. All rights reserved.
1. Introduction The current trend of shipping technology demand powerful diesel engines. Hence, the continuous growth of fuel prices with the economy crisis leads to reduction of operation costs. As a result, the reduction of the engine load and ship’s speed can create various operational difficulties. Piston rings in large marine diesel engines operate under significant mechanical and thermal loads, such as the combustion pressure changes. The simultaneous friction and wear control of the tribo pair between the piston ring and the cylinder is an important task for the engine reliability. Due to this major problem, different structural modifications are developed on the cylinder bore to achieve smaller friction and fuel consumption. In general, the cylinder conditions improves the operation of piston rings with the oil supply along to the piston ring thickness. Today, honing and wave-cut are the most common patterns on the cylinder bore. MAN B&W and Wartsila companies used these methods reducing the need of purchasing new cylinder liners. The piston ring lubrication conditions have been investigated by many authors under different operational conditions. Wakuri et al. [1] presented a numerical and experimental work about the basic tribological parameters of piston rings. Detailed, the friction forces and the oil film were predicted. The analytical model developed, using the Reynolds equation, while the experimental results have been taken for a four stroke diesel engine. Numerical and experimental friction results clearly presented and discussed. Sutaria et al. [2] developed a numerical model based on the average Reynolds equation that predicts the friction forces for internal combustion engines. Later on, Jeng [3] presented an analytical model about piston ring lubrication conditions. Boundary and fully flooded conditions expressed for a piston ring pack. Results of friction, oil film ⇑ Corresponding author. Tel.: +30 2610969421; fax: +30 2610 997207. E-mail address: [email protected] (P.G. Nikolakopoulos). http://dx.doi.org/10.1016/j.simpat.2014.10.002 1569-190X/Ó 2014 Elsevier B.V. All rights reserved.
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Nomenclature
Model piston–piston ring–cylinder geometry variables Dcyl cylinder diameter (m) Dring piston ring diameter (m) h0 initial distance between the piston ring and the cylinder liner (m) B piston ring thickness (m) Ls stroke length (m) X crankshaft angular velocity (rpm) l fluid dynamic viscosity (Pa s) Ff ring friction force (N) Vp piston velocity (m/s) q fluid density (kg/m3) phyd local hydrodynamic pressure (Pa) E Young modulus of elasticity (GPa) rring piston ring roughness (lm) kCR control ratio rcr crank radius (m) h oil film thickness (m) u crank angle (°) tg the distance from top to the first groove (m) tland the lands between the ring grooves (m) T oil m TTDC TBDC T1,T2 ao pc pa Asmooth A F f s
mean oil temperature (°C) cylinder liner temperature at the top dead center (TDC) (°C) cylinder liner temperature at the bottom dead center (BDC) (°C) numerical parameters for calculating the dynamic viscosity coefficient of friction for the asperity contact combustion gas pressure (Pa) ambient pressure (Pa) area of smooth piston ring (m2) ring surface interfaced the cylinder (m2) Ff dimensionless friction force, p Asmooth a stress tensor
Surface texturing dimple geometry variables N number of dimples rp base radius of dimple (m) Hd dimple depth (m) Bp axial length of texture zone (m) Lut untextured top length (m) Lud untextured down length (m) e dimple depth over diameter ratio: B c texture portion: c ¼ Bp
e ¼ 2rHdp
Honing and wave-cut cylinder liner geometry variables Lh honing length (m) Hh honing depth (m) Lw textured cell length of wave (m) Dw wave diameter (m) Hw wave depth (m)
thickness and power losses presented and discussed for each of the piston rings. Rahmani et al. [4] considered a transient elastohydrodynamic model for a rough compression ring–cylinder liner system. He examined the friction and the oil film behavior of an incomplete circular ring. Additionally, Morris et al. [5], developed a model for the compression piston ring to cylinder liner, when the mixed lubrication conditions was attained. In practical terms, they examined a new and worn ring and the friction behavior is analytically discussed. Furthermore, a one-dimensional wear model of the piston ring– cylinder system was performed by Ma et al. [6]. The friction and the wear were investigated, based on the surface roughness and on the cylinder wall temperature.
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Relevant computational and experimental results about the piston ring–cylinder system for marine engines have been described also by many authors. Wolff [7] developed a simulation model of the system: piston–ring–cylinder (PRC) for a two-stroke marine engine and presented his predictions with experimental results. Hence, his analysis can be useful for the optimization of the piston–ring–cylinder (PRC) system in marine engines. Also, the motion of a ring pack was analyzed by Wolff and Piechna in Ref. [8]. Results of friction with twist or not effects were presented and compared. Moreover, the work of Saburi et al. [9] contains a numerical analysis of the oil film between the piston rings and cylinder liner. The influence of the surface shape of a cylinder liner on piston rings lubrication condition was also examined. In practical terms, concerning the wave-cut cylinder liners, it is expected that the anti-scuffing capacity will be improved by the oil retention capacity of the oil grooves. Elfridsson [10] presented a simulation model for a piston ring in marine engines. In particular, a 3D piston ring model developed using the finite element method while the radial geometry can be expressed by the lathe curve from the industry. This method can be used to perform the operating conditions of the piston ring. Livanos and Kyrtatos [11] developed a friction model for the marine diesel engine piston assembly. The authors considered that the piston rings have a barrel shape face and allowed the piston eccentricities at the top and bottom of the skirt. In detail, the quasi-steady-state conditions were assumed while the external force was balanced by the film load capacity. The structural modifications of the piston–piston ring–cylinder system of large bore slow speed marine diesel engines were described by Lalic et al. in [12]. This work shows that the fully deep honed cylinders improve the problem of high friction and wear in marine engines. The process of honing builds-up a proper hydrodynamic lubrication between the piston rings and cylinder liner. To this end, the honing method is a standard method for large bore of two stroke marine engines since 1997. The study of Maekawa et al. [13] showed with experimental results that the wave-cut surface of cylinder liner has better spread-ability of cylinder oil than honed surface. Also, Zavos and Nikolakopoulos [14] presented a first study, by solving the Navier Stokes equations for pure hydrodynamic conditions between the piston ring and the cylinder. The structural modifications of the cylinder surface, such as honing and wave-cut, were considered and compared. The mechanisms of friction, the pressure distribution and the oil film velocity due to the cylinder patterns are examined, either for smooth top ring or for artificial textured, while the piston ring floats into the piston groove. Moreover, in the work by Bolander and Sadeghi [15] a two-dimensional oil flow model was developed in which a honed pattern of cylinder surface from the measured three dimensional profiles was taken into account. This profile then, was used to generate a surface, which was included in their mixed lubrication model. Detailed studies concerning the surface texturing along to piston rings or cylinder liners have been referred by many authors. Yin et al. [16] developed a mixed lubrication model solving the average Reynolds equation taking into account the asperity contacts function. The effects of micro-dimples on the friction and the lubrication behavior of a cylinder liner–piston ring were investigated. The authors have shown the effects between the surface roughness of non-texturing regions and micro-dimples and the synergistic effects of the multi-micro-dimples. Etsion and Sher [17] provided an experimental work to investigate the effects of partially textured piston rings on the fuel consumption for internal combustion engines. They have shown that the piston rings having a partial surface texturing improve more than 4% the fuel consumption. Kligerman et al. [18] presented a piston ring–cylinder model partially textured, using laser techniques, for piston ring friction reduction. In their work they took into account the Reynolds equations and the radial motion of piston ring. Moreover, the texturing parameters such as dimples depth and textured portion are investigated considering their optimum parameters. Additionally, Ronen et al. [19] presented a study for a piston ring–cylinder system including the generated hydrodynamic effects from the surface texturing. They solved the Reynolds equation and the equation of motion, since the variation of friction force and clearance between the piston ring and cylinder liner was presented. Continuing, a simulation model based on the gas leakage effect on the compression piston ring was proposed by Zavos and Nikolakopoulos [20]. To this end, two different surfaces with texturing, along to the piston ring liner examined, concluding on the structural integrity of the ring of each case. Their model was solved using the Navier Stokes equations for fully flooded conditions, and they took into account the piston ring elasticity. In this paper two structural patterns, the wave-cut and honing, are modeled and simulated, and their effects on the piston ring friction force, under real operational conditions regarding slow speed marine engines are analyzed and discussed. The hydrodynamic simulation model is solved using the Navier Stokes equations, while the fluid structure interaction (FSI) analysis is also used to get more precisely tribological behavior of the cylinder-oil and ring system. According to the knowledge of authors this is a first study by considering the effects of large bore cylinder patterns with artificial textured piston ring surfaces, regarding the prediction of the piston ring friction, the pressure distribution and the oil film distribution of the piston ring.
2. Problem consideration 2.1. Geometrical model of piston ring–cylinder The basic geometrical parameters of the piston ring–cylinder system are presented in Fig. 1. The main engine operation parameters is defined by Wolff in [7] and used here. The rotational speed is X = 105 rpm, the stroke length is defined as Ls = 2.416 m and the cylinder bore is Dcyl = 580 mm. In this study, the two dimensional (2D) simulation model consists of the following parameters:
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Fig. 1. Basic dimensions of the piston ring–cylinder system.
the the the the the
thickness of the top ring is B, piston ring width is noted as W, lands between the ring grooves is tland, distance from top to first piston groove is tg, radial and axial piston–piston ring gap is defined as dgap
Additionally, the numerical parameter ho is the initial distance between the piston ring and cylinder liner. The parameter ho is significant in the simulation model and is used in order to achieve the fully flooded lubrication. In detail, the piston ring floats into the piston groove having an initial value ho = 10 lm, when the crank angle is 0°. Thereafter, the oil thickness h varies as a function of the relative rotation angle of the crankshaft. The piston ring moving wall generates shear forces, exerting motion to the fluid, which flows from the piston ring inlet to the outlet. As the fluid convects, it builds up pressure, which exerts forces on the piston ring wall. Pressure build up is due to the converging geometry, as a result of the ring deformation due to the chamber pressure. In Table 1, the input numerical parameters are given. In summation, the top piston ring dimensions are taken by the Wolff’s work [7]. Actually, the roughness of the top ring is assumed to be rring = 0.044 lm according to the study of Wolff’s [7]. The friction power loss caused by the piston rings makes up a large portion of the power loss in the internal combustion engines. Therefore, an understanding between the piston rings and the cylinder wall is crucial for reducing friction. Hence, designing the profile of the piston ring, of each application, in order to reduce friction losses between the rings and the cylinder is a vital topic in the internal combustion engines. A flat ring profile with surface texturing based on the recent published works by Etsion et al. [17–19] is presented here in combination with textured patterns. Additionally, and from the technological point of view, in the rectangular rings the full ring face sits against the cylinder liner, and such rings have a relatively low contact pressure. Of course, this is a point that needs further investigation comparing the flat and the parabola ring profile in relation with the surface texturing parameters and cylinder modifications, taking into account that in such machines we have to have low friction and to maintain high levels of durability. 2.1.1. Honing and wave-cut cylinder liner geometry In Fig. 2 the basic geometrical parameters of cylinder liner modifications are illustrated. For a fully deep honed cylinder, the parameter Lh is the length of the honing and Hh is the depth of honing. Regarding the wave-cut cylinder liner, the basic geometrical dimensions are the wave diameter Dw, the wave depth, Hw and the textured cell length of wave, Lw. The above cylinder modifications have been defined by many authors, as in references [9,12–18]. The geometrical parameters of the fully deep honed and wave-cut cylinder liners, are taken from Ref. [13], and presented in Table 2. 2.1.2. Piston ring with surface texturing In Fig. 3, the geometry of spherical micro dimples texturing is presented. Each spherical dimple has a base radius rp and BB the textured zone Bp is bounded with two untextured strips of width Lut ¼ Lud ¼ 2 p on each of its sides. The following dimensionless parameters of this analysis were considered:
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the the the the
number of dimples are N, dimple depth is noted as Hd, Hd dimple depth over diameter ratio is e ¼ 2r , p B textured portion is defined as c ¼ Bp :
Here, it is worth to mention that the dimple dimensions were obtained in relation with the current literature [18,19]. Detailed the number of dimples and the central position of texture area were imposed in order to have a partial texturing, as it is provided by Kligerman’s work [18]. In particular, the textured portion parameter was obtained from Ref. [18] where the optimum textured portion c varies from 0.5 to 0.6. Regarding the dimple depth over diameter ratio, e = 0.1, this variable has been taken from the work of Ronen et al. [19], where the optimum value of e varies from 0.1 to 0.18. Hence, the spherical dimple geometry is defined by the above geometrical parameters; the base radius is rp = 80 lm and the dimple depth is Hd = 16 lm. The following dimensionless values assumed: N = 32, c = 0.5, e = 0.1. 3. Governing equations and assumptions The flow is assumed isothermal, while the dynamic viscosity is constant throughout the film thickness. The body forces are considered here, and the assembly of the piston–cylinder is concentric. This study models the top piston ring in fully flooded hydrodynamic lubrication and normal engine conditions. Thus the asperity interaction between the piston ring and cylinder liner near to top dead center (TDC) and bottom dead center (BDC) are neglected. However, reduced engine rotational speeds are likely to maintain thinner oil film enhanced the piston ring and cylinder liner contact. Hence, considered highlight the need for further research in this field. Based on the cavitation phenomenon, significant differences are expected in hydrodynamic pressure profiles, lubricant film thickness, and friction. However, in this study the piston ring operating characteristics associated without cavitation conditions. Therefore, this point will be investigated later on to examine how much significant is the cavitation contribution in the hydrodynamic lift in respect to wave cut and honed geometry, density and position. The conservation equations for unsteady incompressible and isothermal flow with zero gravity and other external body forces are: Mass conservation equation
rV ¼0
ð1Þ
Momentum equation
@V 1 l þ V rV ¼ rp þ r2 V @t q q
ð2Þ
where V is the velocity vector, the static pressure p, the fluid density q and the dynamic viscosity l. Eqs. (1) and (2) are solved with a commercial CFD software, utilizing a finite volume approach. 3.1. Oil flow and boundary conditions A hydrodynamic lubrication model between the piston ring and the cylinder is developed, for a two stroke slow speed marine engine. The main engine dimensions are obtained from Ref. [7]. The piston ring floats into the piston groove and moves according to the piston motion. In this analysis, the piston starts to move upward from bottom dead center (BDC) and for the crank angle 180°. Fig. 4 shows the piston ring–cylinder system conditions. In detail, the piston moves up on expansion as the piston ring floats in the lower level of groove. As expected, the gas pressures of combustion keeps the top ring on the bottom of piston groove. Afterward, when the piston moved down with acceleration, the piston ring is lifted upward. As the ring is lifted, the gas pressure is applied underneath the ring, and the ring slams up hard into the top of its groove. The gas pressures in the cylinder and around from the piston ring varies according to the engine stroke. Fig. 5 shows the boundary conditions on the top piston ring, as the piston moved for each engine stage (compression or expansion). The piston ring moving wall generates shear forces, exerting motion to the fluid, which flows from the piston ring inlet to the outlet.
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Fig. 2. Basic geometrical parameters of cylinder patterns.
Table 2 Design geometrical parameters for cylinder patterns. Patterns
Parameters
Nominal values
Honing
Lh Hh Dw Lw Hw
0.001 m 10, 20, 30 lm 0.001 m 0.002 m 10, 20, 30 lm
Wave-cut
Fig. 3. Piston ring with surface texturing geometry.
The profile of the combustion gas as a function of crank angle rotation is shown in Fig. 6a. The piston moves with a linear velocity in the y axis, expressed by the Eq. (3) and presented in Fig. 6b.
V p ¼ r cr Xðsin u þ
kCR sin 2uÞ 2
ð3Þ
Further, the cylinder remains stationary and the piston ring floats into the piston groove as it is shown in Fig. 5. The flat ring profile is used for this investigation. 3.2. Temperature and lubricant properties The lubricant viscosity is sensitive to the temperature variations. The temperature distribution along the cylinder liner is not uniform and can be estimated using the typical conditions in a two stroke slow marine engines for TDC and BDC. Detailed the temperature variation considered TTDC = 200 °C and TBDC = 80 °C accordingly. Hence, the oil temperature is assumed equal with the cylinder liner temperature. A set of simulations was performed for monograde oil SAE 50 taking the average value of the oil temperature, T oil m ¼ 140 C 3 and the assumed oil density, q = 855 kg/m for each crank angle position. The lubricant dynamic viscosity can be calculated as a function of oil temperature according to the below equation:
l ¼ ao exp
T1 T 2 þ T oil m
! ð4Þ
where ao = 0.06510 m Pa s, T1 = 1078.25 °C, T2 = 95.22 °C are the relevant parameters for lubricant grade SAE 50 and T oil m is the mean value of lubricant oil temperature.
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Fig. 4. Piston ring–cylinder model for hydrodynamic conditions as the piston starts from the bottom dead center (BDC) for crank angle 180°.
Fig. 5. Boundary conditions on the top piston ring for each engine stage.
3.3. Oil film equation The expression of oil film in terms of the gap between piston ring and cylinder wall is:
8 h þ hflat ðtÞ > > < o hðx; y; tÞ ¼ ho þ hflat ðtÞ þ Hpatterns ðx; yÞ > > h þ h ðtÞ þ H Hd ðx2 þ y2 Þ þ H : o
flat
d
r 2p
ð5Þ patterns ðx; yÞ
where hflat(t) is the time nominal thickness between the smooth facing surfaces, Hpatterns(x, y) is the cylinder liner modifications amplitude at coordinate system (x, y), ho is an initial distance between piston ring–cylinder system and Hd
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Fig. 6. (a) Gas pressures versus crank angle and (b) piston linear velocity versus crank angle.
is the spherical dimple depth. For this analysis, the oil film h(x, y, t) across the piston ring profile calculated for smooth facing profiles and presented in Fig. 7. 3.4. Design parameters Basic piston ring material properties for this study were provided by a typical marine engine. Flat profile shape of top ring was examined having the modulus of elasticity, E = 150 GPa, and the poisson’s ratio, m = 0.25. The pressure field is obtained after the numerical solution of the Eq. (2). Since the friction between the piston ring and cylinder liner was obtained entirely from shear stress within the oil, it is expressed by:
Ff ¼
Z
sdA ¼ pDring A
Z
B=2
B=2
p þ 2l
#v y dy #y
Fig. 7. Oil film thickness versus crank angle for smooth facing surfaces.
ð6Þ
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where vy is the lubricant oil velocity in the y axis, Dring = 0.580 m is the piston ring diameter, l is the dynamic viscosity and B is the piston ring thickness. The elastic deformation of the ring is taken into account regarding the friction force calculations [18]. Hence, the stress is expressed as r0 and it is mentioned as the von Mises stress:
1 h
r0 ¼ pffiffiffi ðr1 r2 Þ2 þ ðr2 r3 Þ2 þ ðr3 r1 Þ2
i12
2
ð7Þ
4. Simulation model and meshing requirements A 2D simulation model is developed using CFD. Fig. 8 presents the flow chart structure of the couple field problem. Regarding the fluid field analysis 16,739 tetrahedral elements were used having smooth profiles. In Fig. 9(a) and (b), the fluid–structure meshing details were presented. In particular, when the honing and the wave-cut cylinder liner patterns were modeled, 16,773 total number of elements were used. For this analysis, the radial clearance size between piston ring and cylinder wall is very small, so the use of tetrahedral elements leads to 5511 number of nodes. After the required grid sensitivity tests, 10 divisions were used in the circumferential direction and 500 divisions were used in the axial direction. Using lower number of divisions in the radial direction, the model gave a friction error between 10% and 15%. Thus, using upper number of 10 divisions this error minimized near to 2–3%. On the other hand, increasing the number of divisions in the axial direction from 500 to 600, the error of calculated friction was smaller than 0.5%. Regarding the honed and wave modifications, when the meshing requirements of the clearances were achieved, 10 and 30 divisions were used in the circumferential and axial direction, respectively. The fluid meshing details in the clearance between piston ring and cylinder are presented for each examined case (see Fig. 10). At the same time, when the piston ring with spherical micro dimples examined, the number of fluid elements was 14,572. In practical terms, each micro dimple area is meshed with 25 and 7 divisions in the axial and radial direction, accordingly. Upper and lower number of divisions was examined producing unacceptable errors to pressure term. However, increasing the divisions (upper 7 divisions) in the circumferential direction into the micro dimple area, the friction results have a good agreement with a small error, 2–3%. The fluid meshing detail into the spherical micro dimples is illustrated in Fig. 11. The parameter ho considered to be 10 lm. This parameter evaluated when the pressure error is Errorpres 6 106, and the mesh morphing into the clearance between piston ring and cylinder attained. Hence, the friction force under pure hydrodynamic conditions calculated sufficiently, giving a good agreement compared with the literature. However, using a smaller
Fig. 8. The solution flow chart of the coupled field problem.
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Fig. 9. The adaptive grid for the couple field problem, (a) fluid–structure detail in the clearance between piston ring and cylinder liner and (b) fluid– structure detail between ring and lateral face of the piston ring groove.
Fig. 10. Simulation meshing details for smooth, honed and wave-cut cylinder liners.
parameter ho the pressure error does not get improved while the Arbitrary Lagrangian Eulerian (ALE) formulation failed for ho 6 10 lm. The simulations were performed in a computer with 8 processors (Intel core i7-3770 CPU@ 3.40 GHz) and the typical simulation time considered five minutes for smooth and textured case respectively. When the convergence of pressure field calculations is satisfied, the algorithm moves the nodes of the fluid field taking into account the piston ring displacements, and the solver goes to the next fluid film solution. The fluid nodes in radial clearance between the piston ring and the cylinder liner are moved, including the Arbitrary Lagrangian Eulerian (ALE) formulation. As expected, the generated displacements of the piston ring were created after the mesh morphing. The computational mesh inside the domains can be moved arbitrarily to optimize the shapes of elements, using the ALE technique in the simulations. On the other hand, the mesh on the boundaries and interfaces of the domains can be moved along with the materials, to track precisely the boundaries and the interfaces of the multi-material system. Some steps of the ALE method are presented by the authors in [18]. 4.1. Convergence criteria The convergence of couple field problem confirmed to two steps. Initial, the pressure error expressed by:
Error pres ¼
Pi¼NCFD n
pki pik1 1 106 Pi¼NCFD n k pi i¼1
i¼1
ð8Þ
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Fig. 11. Fluid–structure meshing detail in the spherical micro dimples area.
For greater accuracy, a value of 106 is used for the pressure term. Second, for the structural analysis, the piston ring displacement is performed using a loop defined a critical displacement for each crank angle position. Hence, the critical displacement DScr on the ring in every time step is less/equal than one percent of the maximum displacement DSmax due to the combustion pressure, pc. The time step defined for each crank angle for 600 iterations. The number of iterations occurred using the above meshing requirements and a convergence tolerance of 106. For example, for 100 iterations the pressure error was 103.
5. Validation of Fluid Structure Interaction (FSI) results The present fluid structure interaction (FSI) model is validated by comparing the computational results against already published results. Firstly, some numerical results about the piston ring friction force were presented by Zavos and Nikolakopoulos [18] and compared with Sutaria’s work [2]. The extracted results have shown a good agreement while the gas leakage near to piston ring area varies with the crankshaft position. Simultaneously, a similar flow problem in a lubricated piston ring and cylinder wall was solved, and the predicted friction force compared against the recent literature results. Wakuri0 s [1] and Wolff0 s [8] results are based on the average Reynolds equation and the hydrodynamic lubrication regime. In fact, the solutions have been obtained by a numerical analysis taking into account the basic geometrical dimensions of piston ring–cylinder model, and the piston ring roughness. Thereafter, the gas pressures of combustion are clearly provided using two types of Newtonian oils (SAE 30 and SAE 50) for different oil temperatures. Continuing, the dynamic viscosity of lubricant oils are considered constant along to the cylinder liner, as the piston ring floats into the piston groove without twist effects. Hence, taken the above assumptions for pure hydrodynamic conditions, we decided that the papers of Wakuri et al. [1] and Wolff et al. [8] will encourage our investigation. In the simulation, the results of Fig. 12 (a) are compared with the investigation of Wakuri’s [1] for rotational speed X = 2400 rpm from a four stroke diesel engine, while the results of Fig. 12(b), to the ones of Wolff’s [8] for rotational speed X = 3400 rpm. The maximum differences of friction, compared for both of papers, did not exceed the amount of 10%. Actually, the gas pressures for each rotational speed were applied on a fully piston ring–cylinder model as it is shown in Fig. 5. This justifies a different hydrodynamic pressure near to the piston ring profile taken into account the lubricant oil velocity which influences the friction results, as it is observed between 180° and 270° on Fig. 12(b). Concluding, there is a very good agreement between the values predicted by the current analysis and the respective values mentioned in Ref. [1,8].
6. Results and discussion The extracted results include the fully deep honed and wave-cut cylinder liners with flat piston ring, in a constant crankshaft rotational speed X = 105 rpm. The effects of textured piston ring combined with the proper cylinder pattern is also referred and compared with the smooth case. The friction force, the oil film pressure and the lubricant film thickness on the top piston ring were predicted and presented.
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Fig. 12. Friction force versus crank angle. (a) Validation results of Wakuri paper [1]. (b) Validation results of Wolff’s study [8].
6.1. Friction force of a piston ring Fig. 13 illustrates the dimensionless friction force at a top piston ring lubricated with Newtonian oil SAE 50 and the oil temperature T oil m ¼ 140 C. Mainly the piston ring friction is increased while the viscous shear stress is maximized due to the pure hydrodynamic conditions. As expected, the maximum friction is observed when the piston velocity is maximum and the crank angle is u = 90°. The operation conditions of two stroke marine engine is X = 105 rpm and the oil temperature remains constant for each engine stage and crank angle position. The non-dimensional friction force on the piston ring moving wall is presented in Fig. 14, when the honed and wave-cut cylinder liners are simulated. It was observed that the cylinder patterns reduce substantial the friction force, as the piston ring moves into the piston groove. As presented, the honed cylinder liner improves 25% the friction in relation with the smooth case. At the same time, the wave-cut geometry reduces 7% the friction related to the smooth case. Comparing the honed and wave-cut liners, the shape of honing contributes to a friction reduction of 22%. This is in line with similar results extracted by the authors in [14]. Here, more realistic fully flooded conditions were simulated while the dimensions of honing and wave-cut pattern were obtained from the literature about marine engines. Apparently, a range of depth for honing and wave-cut patterns exists in between, which is identified by the Ref. [13]. As deduced from Fig. 15, the value of depth varies from Hh = Hw = 10, 20, 30 lm for each examined cylinder modification. For honed pattern the dimensionless maximum friction force improved slighter as the depth increases. Thus, the wave-cut liner is more sensitive with the increment of depth. As result, for wave depth Hw = 30 lm, the friction reduction was 4% in relation with the case of depth Hw = 10 lm.
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Fig. 13. Dimensionless friction force of a smooth piston ring and cylinder versus crank shaft angle for rotational speed X = 105 rpm and temperature oil T oil m ¼ 140 C.
Fig. 14. Dimensionless friction force of a smooth piston ring with smooth, honed and wave-cut cylinder liners versus crank shaft angle for rotational speed X = 105 rpm and temperature oil T oil m ¼ 140 C.
6.2. Pressure distribution and oil film thickness of a piston ring Fig. 16 shows the pressure distribution over the piston ring walls as the honed and wave-cut liner performed. The piston moves upward on expansion, the crank angle is u = 90°, and lubricant SAE 50 for temperature T oil m ¼ 140 C is used. It is obvious that the piston ring floats into the piston groove in lower levels under fully flooded lubrication. As it can be seen, the local hydrodynamic pressures in the clearance increased 3.6% with the honed liner (see Fig. 16a). In other case, the wave-cut liner influences moderate the pressure field in the axial direction (see Fig. 16b). Therefore, having honed cylinder liner with depth Hh = 10 lm the maximum pressure was obtained, pmax = 1.64 MPa, while for the case of wave-cut liner the maximum pressure was predicted, 1.58 MPa with the same depth. In practical terms, the deviation of pressure presented detailed in ‘ZOOM A’ and ‘ZOOM B’. The zoomed plots in Fig. 16(a) and (b) corresponds to the pressure distribution depends on the honed and wave-cut geometries. As the fluid intakes in the aforementioned surface modifications a hydrodynamic lift is generated, higher regarding the honed and less regarding the wave cut geometry. Both are compared to the smooth cylinder wall case.
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Fig. 15. Dimensionless maximum friction force of a smooth piston ring for various depth of honing and wave-cut cylinder liners with Hh = Hw = 10, 20, 30 lm.
Fig. 16. Hydrodynamic pressure profiles in Pa on the smooth piston ring at expansion stage for crank angle position u = 90°, (a) with honed cylinder liner Hh = 10 lm and (b) with wave-cut cylinder liner Hw = 10 lm.
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The current phenomenon follows the literature survey indicates that the effect of the geometric features on the generation of hydrodynamic pressure and then on the friction reduction may depends on geometric features dimensions, their density and the certain pattern on the mating surfaces. Regarding the wave cut geometry, the lands between the waves are responsible for the moderate pressure variation compared to the smooth wall case. So, as the wave cut appears it is observed from the color plots that the color alteration in the zoomed areas becomes lesser, compared to the honed geometry. In summation, the contribution of honing shape leads to the maximum pressure built up, due to the wedge effect of the converging surfaces. Hence, this trend reduces the friction results largely in relation with the wave-cut pattern. Regarding the oil film thickness, Fig. 17 illustrates that, the honed and wave-cut cylinder liner increases the oil thickness, as the piston velocity increases under pure hydrodynamic conditions. It is evident that the honing improves mainly 2.1% the oil film distribution in the clearance. Moreover, using the wave-cut liner the lubricant film succeeds a slighter rise of thickness around to 0.55%. Further, as the pressure produced in the clearance between top ring and cylinder liner, the oil supply in the shape of cylinder patterns achieved. 6.3. Comparison of smooth and textured piston ring using the honed cylinder liner In the present work, the piston ring texturing geometry has a spherical shape as it is illustrated in Fig. 3. A texture configuration with 32 micro dimples (N = 32) is examined. The dimple depth and the radius are given by Hd and rp, respectively. Regarding the central position of micro dimples and the piston ring thickness, the basic dimensions of dimple have been identified.
Fig. 17. Oil film thickness on the smooth piston ring with smooth, honed and wave-cut cylinder liners versus crank shaft angle for rotational speed X = 105 rpm and constant depths Hh = Hw = 10 lm.
Fig. 18. Dimensionless maximum friction force of smooth and textured piston ring for various depth of honing Hh = 10, 20, 30 lm.
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Fig. 19. Hydrodynamic pressure profiles in Pa at expansion stage for crank angle position u = 90° with honed cylinder liner Hh = 10 lm, (a) for smooth piston ring and (b) for piston ring with spherical micro dimples N = 32, c = 0.5, e = 0.1.
Fig. 20. Oil film thickness on the smooth and textured piston ring with honed cylinder liner Hh = 10 lm versus crank shaft angle for rotational speed X = 105 rpm .
As follows from Fig. 18, the variation of dimensionless maximum friction force for smooth and textured piston ring when the depth of honed cylinder varies is presented. As observed the friction was improved 12% using N = 32 micro dimples lubricated with the monograde oil SAE 50. In particular, the depths of honed shape influence moderate the friction either for smooth or textured piston ring. For the simulations, the dimple depth Hd was 16 lm and the dimple radius rp was 80 lm.
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Fig. 19 shows the pressure distribution on the top piston ring for smooth and textured cases, as the honed cylinder has a depth Hh = 10 lm. Under constant rotational speed X = 105 rpm, a hydrodynamic local pressure is generated in the gap between the mating surfaces due to the effect of dimples and the wedge effect of the converging surfaces (see Area ‘A’ from Fig. 19b). Local hydrodynamic pressure is maximum at the piston ring central position (see ‘ZOOM D’) when the texturing exists. In this case, the maximum hydrodynamic pressure was increased 4.6% in the clearance when the piston ring treated with the spherical micro dimples. As a result, the lubricant film thickness was increased (Eq. (5)), by considering the texture of the piston ring. Fig. 20, illustrates a comparison of the oil film variation for each engine stage as a function of surface texturing. It is obvious that the film thickness is higher 13% as well as the textured ring and honed liner is taken account into. This phenomenon leads to an increment of the piston ring surface displacements and hence, the friction force is decreased. 7. Conclusions In the present paper a simulation model is presented for piston ring–cylinder system of marine engines. A fluid-structural algorithm solved for pure hydrodynamic conditions, considering the elasticity of the piston ring. For two different types of cylinder pattern (honed and wave-cut liners), some cases of depth variation have been tested, in terms of computing the flow fields by means of a Navier Stokes solver. To this end, the optimal effect of honed cylinder liner with the textured piston rings on the maximum friction force was identified. The following conclusions are drawn: Honing and wave-cut cylinder patterns reduce the friction 7–25% in relation with the smooth case under pure hydrodynamic conditions. Honed cylinder liner achieves a reduction of friction 22% compared with the relevant wave-cut liner. A number of depth variations for each cylinder pattern shown that the friction reduction is moderate. Detailed, the wavecut liner reduces the friction force 4%, as the depth varies between Hw = 10 lm to Hw = 30 lm. Regarding the honed cylinder, the friction is less influenced. Honed and wave-cut liner improves 0.55–2.1% the oil film thickness distribution in the circumferential direction. The contribution of honed cylinder liner with the textured piston rings shown a friction reduction 12% in relation with the smooth flat ring. Maximum produced local hydrodynamic pressures, and the central position of texturing, leads to an oil film increment (13%) along to the piston ring thickness, hence the friction is minimized.
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