# Effect of Coating and Low Viscosity Oils on Piston Ring Friction under Mixed Regime of Lubrication through Analytical Modelling

## Abstract

**:**

## 1. Introduction

_{2}emissions. An important innovation in this respect is the view of ecological tribology, which aims to minimize the environmental footprint of the Internal Combustion (IC) engine. The reduction of toxic emissions and fuel consumption are the main keys in the development of high-performance engines [1]. A recent study presented by the European Commission has showed that new technologies of road vehicles using automation and electrification may improve pollutant emissions according to the new generation of Euro 6 [2].

_{3}N

_{4}as well as PVD multilayer coating and TiN/CrN layer. The tests were subjected to fired engine conditions using a turbo diesel engine. The nano-HVOF coating liner was shown to perform best regarding fuel consumption. Zabala et al. [27] suggested that the type of lubricant and coating topography have a great effect on friction coefficient in the boundary or mixed regime of lubrication. In this manner, Gore et al. [28] presented how a Nickel-Silicon Carbide wear-resistant coating react in piston ring-liner conjunction using a sliding tribometer. The experimental predictions were compared with an analytical model, which can be used as a tool to predict tribological quantities such as the friction and film thickness with very well accuracy. Dolatabadi et al. [29] also noted the impact of coating on cylinder bore surface. They analysed and discussed the importance of coating materials on the global fuel economy and emission of the engine, through multi-physics modelling of ring dynamics, contact tribology and thermal effects. Zavos and Nikolakopoulos [30,31] explored the effect of ring coating on local displacements into the minimum film thickness and, simultaneously, created a contact model between the ring and liner including surface roughness. The positive role of analytical models and tribometer tests when used as tools to understand the mechanisms of tribofilm formation along the coated surface is dominant. Taylor [32] studied the impact of ring motion with “squeeze” effect using several ring profiles and low viscosity oils. It was found that ring profile and oil viscosity influence asperity friction at dead centres, which can motivate automotive companies. Tomanik et al. [33] tested some real coated specimens of the ring-liner conjunction lubricated with low viscosity oils, which are now used in high-performance IC engines. The study explains in detail the influence of the topography combined with the type of lubricant on engine friction and CO

_{2}emissions.

## 2. Analytical Modelling

#### 2.1. Description of Piston Ring-Liner Contact

#### 2.2. Determination of Load by Lubricant Film

_{inlet}and P

_{outlet}are the gas pressures at the left and right sections of the piston ring.

#### 2.3. Determination of Load Carried by the Asperities

_{s}< 3). The generated load W

_{con}can be described as:

_{s}expresses the usual Stribeck lubricant film ratio. In this study, the statistical function of F

_{5/2}can be predicted by a fifth order polynomial curve as it is referred by Teodorescu et al. [37]. Therefore, for λ

_{s}≤ λ

_{crit}= 2.22:

_{s}> λ

_{crit}= 2.22:

_{crit}is the critical film ratio. In order to improve the calculation of the asperities along the ring profile, where the lubricant film falls below the critical film ratio, it is crucial to predict the real asperities located close to the contact centre, which are represented in critical length b

_{c}of Figure 1. Consequently, the contact area A through expression (7) should be modified, and this conversion should follow the variations of F

_{5/2}. Figure 3 shows the variation of the statistical function F

_{5/2}with the Stribeck film ratio.

_{c}as follows:

#### 2.4. Method of Analytical Solution

_{tot}is given as:

**ε**is considered as: ε = 0.15. This value was used for solution stability and fast convergence.

#### 2.5. Low Viscosity Oils

_{1}and θ

_{2}are the parameters of each oil, and T is the lubricant temperature. Table 2 shows the input parameters for each engine oil with the corresponding dynamic viscosities at 120 °C.

#### 2.6. Ring Friction

_{v}is:

_{s}< 3, the boundary friction f

_{b}can be written as [35]:

_{asp}was assumed constant (a hypothetical case) with the experimental value of 0.22 for all running cases. This value was selected by Gore et al. [28] as well as the lubricant oil SAE 10W40 reacted with a stainless steel piston ring, which has similar properties with this investigation in order to model more realistic contact conditions. For this reason, a detailed analysis for ring coated profiles combined with the low viscosity lubricants should be further investigated in the next work.

_{con}for the studied symmetric parabolic ring. This can be defined as [28]:

_{2}can be also presented by a fifth order polynomial curve (Figure 4). In more details, for λ

_{s}≤ λ

_{crit}= 2.29, this function becomes [37]:

## 3. Results and Discussion

#### 3.1. Input Coated Piston Rings and Cylinder Liner Data for the Analysis

#### 3.2. Analysis of Minimum Film Thickness and Coefficient of Friction

_{asp}. This is a significant parameter for boundary friction calculation. Thus, investigations should be made in future research compared to the experimental measurements.

## 4. Summary and Conclusions

## Funding

## Conflicts of Interest

## Nomenclature

A | nominal contact area |

A_{con} | asperity contact area |

b | ring face-width contact |

b_{c} | critical length along the ring face-width contact |

c | ring curvature or crown height |

Ε | Young’s modulus of elasticity |

Ε* | equivalent Young’s modulus of elasticity $\left(\frac{2}{{E}^{*}}=\frac{1-{\nu}_{r}^{2}}{{E}_{r}}+\frac{1-{\nu}_{l}^{2}}{{E}_{l}}\right)$ |

F | applied ring load |

f_{tot} | total friction |

f_{v} | viscous friction |

f_{b} | boundary friction |

F_{5/2}, F_{2} | statistical functions |

h | lubricant film thickness |

h_{c} | critical film thickness |

h_{o} | minimum film thickness |

h_{s} | ring face-width profile |

k | Vogel parameter for describing lubricant viscosity variation with temperature |

L | ring lateral length |

p_{hyd} | hydrodynamic pressure |

P_{inlet} | inlet pressure at the piston ring conjunction |

P_{out} | outlet pressure at the piston ring conjunction |

r | radius of ring curvature |

M,N | input variables |

T | lubricant temperature |

U | sliding velocity |

W_{tot} | total load carrying capacity |

W_{con} | load share by the asperities |

W_{hyd} | load carried by the lubricant film |

Greek symbols | |

δ | local contact deformation |

ε | step for minimum film thickness loop |

ζ | surface density of asperity peaks |

θ_{1,}θ_{2} | Vogel parameters for lubricant viscosity variation with temperature |

κ | average asperity tip radius |

λ_{s} | Stribeck oil film parameter $\left({\lambda}_{s}=\frac{{h}_{o}}{\sigma}\right)$ |

μ | lubricant dynamic viscosity |

μ_{asp} | coefficient of boundary shear strength |

ν | Poisson ratio |

σ | root mean square roughness value of the studied tribo-pair $\left(\sigma =\sqrt{{\sigma}_{r}^{2}+{\sigma}_{l}^{2}}\right)$ |

τ | viscous shear stress |

τ_{ο} | Eyring shear stress of the lubricant film |

X | parameter for ring balance |

Superscripts | |

n | iteration step |

Subscripts | |

_{asp} | asperity |

_{b} | boundary |

_{c,}_{crit} | critical |

_{con} | contact |

_{hyd} | hydrodynamic |

_{l} | liner |

_{r} | ring |

_{s} | shape |

_{S} | Stribeck |

_{tot} | total |

_{v} | viscous |

## References

- Tung, S.C.; McMillan, M.L. Automotive tribology overview of current advances and challenges for the future. Tribol. Int.
**2004**, 37, 517–536. [Google Scholar] [CrossRef] - Szymanski, P.; Ciuffo, B.; Fontaras, G.; Martini, G.; Pekar, F.; Wozniak, M.; Ozuna, G.; Siczek, K.; Stoeck, T.; Sitnik, L. The future of road transport in Europe. Environmental implications of automated, connected and low-carbon mobility. Combust. Engines
**2021**, 186, 3–10. [Google Scholar] [CrossRef] - Golloch, R.; Kessen, U.; Merker, G.P. Tribological investigations on the piston assembly group of a diesel engine. MTZ Worldw.
**2002**, 63, 21–24. [Google Scholar] [CrossRef] - Senatore, A.; Aleksendric, D. Advances in piston rings modelling and design. Recent Pat. Eng.
**2013**, 7, 51–67. [Google Scholar] [CrossRef] - Livanos, G.A.; Kyrtatos, N.P. Friction model of a marine diesel engine piston assembly. Tribol. Int.
**2007**, 40, 1441–1453. [Google Scholar] [CrossRef] - Delprete, C.; Razavykia, A. Piston ring–liner lubrication and tribological performance evaluation: A review. Proc. Inst. Mech. Eng. Part J J. Eng. Tribol.
**2018**, 232, 193–209. [Google Scholar] [CrossRef] - Mishra, P.C. Modeling the root causes of engine friction loss: Transient elastohydrodynamics of a piston subsystem and cylinder liner lubricated contact. Appl. Math. Model.
**2015**, 39, 2234–2260. [Google Scholar] [CrossRef] - Marui, E.; Endo, H. Effect of reciprocating and unidirectional sliding motion on the friction and wear of copper on steel. Wear
**2001**, 249, 582–591. [Google Scholar] [CrossRef] - Chaudhari, T.; Sutaria, B. Investigation of friction characteristics in segmented piston ring liner assembly of IC engine. Perspect. Sci.
**2016**, 8, 599–602. [Google Scholar] [CrossRef] [Green Version] - Furuhama, S. A Dynamic Theory of Piston-Ring Lubrication: 1st Report, Calculation. Bull. JSME
**1959**, 2, 423–428. [Google Scholar] [CrossRef] - Furuhama, S. A Dynamic Theory of Piston-Ring Lubrication: 2nd Report, Experiment. Bull. JSME
**1960**, 3, 291–297. [Google Scholar] [CrossRef] [Green Version] - Tian, T.; Noordzij, L.; Wong, V.W.; Heywood, J.B. Modeling Piston-Ring Dynamics, Blowby, and Ring-Twist Effects. ASME J. Eng. Gas Turbines Power
**1998**, 120, 843–854. [Google Scholar] [CrossRef] - Patir, N.; Cheng, H.S. Application of average flow model to lubrication between rough sliding surfaces. Trans. ASME
**1979**, 101, 220–229. [Google Scholar] [CrossRef] - Wolff, A. Influence of piston ring pack configuration on blowby and friction losses in a marine two-stroke engine. Combust. Engines
**2017**, 170, 164–170. [Google Scholar] [CrossRef] - Priest, M.; Dowson, D.; Taylor, C.M. Theoretical modelling of cavitation in piston ring lubrication. Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci.
**2000**, 214, 435–447. [Google Scholar] [CrossRef] - Chong, W.W.F.; Howell-Smith, S.; Teodorescu, M.; Vaughan, N.D. The influence of inter-ring pressures on piston-ring/liner tribological conjunction. Proc. Inst. Mech. Eng. Part J J. Eng. Tribol.
**2013**, 227, 154–167. [Google Scholar] [CrossRef] - Nouri, J.M.; Vasilakos, I.; Yan, Y.; Reyes-Aldasoro, C.C. Effect of viscosity and speed on oil cavitation development in a single piston-ring lubricant assembly. Lubricants
**2019**, 7, 88. [Google Scholar] [CrossRef] [Green Version] - Taylor, R.I.; Morgan, N.; Mainwaring, R.; Davenport, T. How much mixed/boundary friction is there in an engine—And where is it? Proc. Inst. Mech. Eng. Part J J. Eng. Tribol.
**2020**, 234, 1563–1579. [Google Scholar] [CrossRef] - Morris, N.; Rahmani, R.; Rahnejat, H.; King, P.D.; Fitzsimons, B. The influence of piston ring geometry and topography on friction. Proc. Inst. Mech. Eng. Part J J. Eng. Tribol.
**2013**, 227, 141–153. [Google Scholar] [CrossRef] [Green Version] - Söderfjäll, M.; Herbst, H.M.; Larsson, R.; Almqvist, A. Influence on friction from piston ring design, cylinder liner roughness and lubricant properties. Tribol. Int.
**2017**, 116, 272–284. [Google Scholar] [CrossRef] - Erdemir, A.; Holmberg, K. Energy consumption due to friction in motored vehicles and low-friction coatings to reduce it. In Coating Technology for Vehicle Applications; Springer: Cham, Switzerland, 2015; pp. 1–23. [Google Scholar]
- Ferreira, R.; Martins, J.; Carvalho, Ó.; Sobral, L.; Carvalho, S.; Silva, F. Tribological solutions for engine piston ring surfaces: An overview on the materials and manufacturing. Mater. Manuf. Process.
**2020**, 35, 498–520. [Google Scholar] [CrossRef] - Friedrich, C.; Berg, G.; Broszeit, E.; Rick, F.; Holland, J. PVD CrxN coatings for tribological application on piston rings. Surf Coat. Technol.
**1997**, 97, 661–668. [Google Scholar] [CrossRef] - Abril, S.O.; García, C.P.; León, J.P. Numerical and Experimental Analysis of the Potential Fuel Savings and Reduction in CO Emissions by Implementing Cylinder Bore Coating Materials Applied to Diesel Engines. Lubricants
**2021**, 9, 19. [Google Scholar] [CrossRef] - Barbezat, G. Advanced thermal spray technology and coating for lightweight engine blocks for the automotive industry. Surf. Coat. Technol.
**2005**, 200, 1990–1993. [Google Scholar] [CrossRef] - Igartua, A.; Fdez-Pérez, X.; Conte, M.; Illarramendi, I. Tribological tests to simulate wear on piston rings. In Critical Component Wear in Heavy Duty Engines; Lakshminarayanan, P.A., Nayak, N.S., Eds.; John Wiley & Sons Ltd.: Singapore, 2011; pp. 167–195. [Google Scholar]
- Zabala, B.; Igartua, A.; Fernández, X.; Priestner, C.; Ofner, H.; Knaus, O.; Abramczuk, M.; Tribotte, P.; Girot, F.; Roman, E.; et al. Friction and wear of a piston ring/cylinder liner at the top dead centre: Experimental study and modelling. Tribol. Int.
**2017**, 106, 23–33. [Google Scholar] [CrossRef] - Gore, M.; Morris, N.; Rahmani, R.; Rahnejat, H.; King, P.D.; Howell-Smith, S. A combined analytical-experimental investigation of friction in cylinder liner inserts under mixed and boundary regimes of lubrication. Lubr. Sci.
**2017**, 29, 293–316. [Google Scholar] [CrossRef] [Green Version] - Dolatabadi, N.; Forder, M.; Morris, N.; Rahmani, R.; Rahnejat, H.; Howell-Smith, S. Influence of advanced cylinder coatings on vehicular fuel economy and emissions in piston compression ring conjunction. Appl. Energy
**2020**, 259, 114129. [Google Scholar] [CrossRef] - Zavos, A.; Nikolakopoulos, P. Thermo-mixed lubrication analysis of coated compression rings with worn cylinder profiles. Ind. Lubr. Tribol.
**2017**, 69, 15–29. [Google Scholar] [CrossRef] - Nikolakopoulos, P.G.; Grigoriadis, K.; Zavos, A. Contact modeling with a finite element model in piston ring—liner conjunction under dry conditions. Int. J. Struct. Integr.
**2019**, 10, 393–414. [Google Scholar] [CrossRef] - Taylor, R.I. Squeeze film lubrication in piston rings and reciprocating contacts. Proc. Inst. Mech. Eng. Part J J. Eng. Tribol.
**2015**, 229, 977–988. [Google Scholar] [CrossRef] - Tomanik, E.; Profito, F.; Sheets, B.; Souza, R. Combined lubricant–surface system approach for potential passenger car CO
_{2}reduction on piston-ring-cylinder bore assembly. Tribol. Int.**2018**, 149, 105514. [Google Scholar] [CrossRef] - Zavos, A.; Nikolakopoulos, P.G. Tribology of new thin compression ring of fired engine under controlled conditions-a combined experimental and numerical study. Tribol. Int.
**2018**, 128, 214–230. [Google Scholar] [CrossRef] - Gohar, R.; Rahnejat, H. Fundamentals of Tribology; Imperial College Press: London, UK, 2008; ISBN 978-1-84816860-2. [Google Scholar]
- Greenwood, J.A.; Tripp, J.H. The contact of two nominally flat rough surfaces. Proc. Inst. Mech. Eng.
**1970**, 185, 625–633. [Google Scholar] [CrossRef] - Teodorescu, M.; Balakrishnan, S.; Rahnejat, H. Integrated tribological analysis within a multi-physics approach to system dynamics. In Tribology and Interface Engineering Series; Elsevier: Amsterdam, The Netherlands, 2005; Volume 48, pp. 725–737. [Google Scholar]
- Vogel, H. The law of the relation between the viscosity of liquids and the temperature. Phys. Z
**1921**, 22, 645–646. [Google Scholar] - Styles, G.; Rahmani, R.; Rahnejat, H.; Fitzsimons, B. In-cycle and life-time friction transience in piston ring–liner conjunction under mixed regime of lubrication. Int. J. Engine Res.
**2014**, 15, 862–876. [Google Scholar] [CrossRef] [Green Version] - Arcoumanis, C.; Ostovar, P.; Mortimer, R. Mixed Lubrication Modelling of Newtonian and Shear Thinning Liquids in a Piston-Ring Configuration. SAE Transactions Pap. No. 972924.
**1997**, 106, 1306–1331. [Google Scholar] - Rahmani, R.; Rahnejat, H.; Fitzsimons, B.; Dowson, D. The effect of cylinder bore operating temperature on frictional loss and engine emissions in piston ring conjunction. Appl. Energy
**2017**, 191, 568–581. [Google Scholar] [CrossRef] [Green Version] - Dowson, D. A central film thickness formula for elasto-hydrodynamic line contacts. In Proceedings of the 5th Leeds-Lyon Symposium, Leeds, UK, 19–22 September 1978. [Google Scholar]
- Tung, S.C.; Gao, H. Tribological Investigation of Piston Ring Coatings Operating in an Alternative Fuel and Engine Oil Blend. Tribol. Trans.
**2002**, 45, 381–389. [Google Scholar] [CrossRef] - Howell-Smith, S.; Rahnejat, H.; King, P.D.; Dowson, D. Reducing in-cylinder parasitic losses through surface modification and coating. Proc. Inst. Mech. Eng. Part D J. Automob. Eng.
**2014**, 228, 391–402. [Google Scholar] [CrossRef] [Green Version] - Zavos, A.; Nikolakopoulos, P.G. The effect of square-shaped pockets position in sliding line contacts under mixed regime of lubrication. Proc. Inst. Mech. Eng. Part J J. Eng. Tribol.
**2019**, 233, 490–506. [Google Scholar] [CrossRef]

**Figure 1.**(

**a**) Overview of 3D piston ring-liner contact, (

**b**) piston ring (black line), lubricant film (dotted green line) and cylinder liner (blue line) with main geometrical parameters.

**Figure 5.**Measurement process of the coated ring surfaces (in this case the electroplated CrN piston ring is presented).

**Figure 6.**Description of area of interest including calculated back gas pressure and sliding velocity for a thin piston ring of small motor engine.

**Figure 7.**Comparison of minimum film thickness and load by asperities for steel ring lubricated with SAE 15W40 and 0W20 at 120 °C.

**Figure 8.**Comparison of Stribeck film ratio and load by lubricant film for steel ring lubricated with SAE 15W40 and 0W20 at 120 °C.

**Figure 9.**Minimum film thickness variation with sliding velocity for (

**a**) SAE 15W40 and (

**b**) SAE 0W20.

**Figure 11.**(

**a**) Variation of load by asperities and (

**b**) variation of load by lubricant film with sliding velocity for SAE 0W20.

Parameter | Cylinder Liner Base Material | Piston Ring Base Material | Ring Coatings | Unit | |
---|---|---|---|---|---|

Material | Aluminium | Steel | CrN | TiN | - |

Young’s modulus of elasticity | 70 | 200 | 400 | 250 | GPa |

Poisson’s ratio | 0.33 | 0.31 | 0.2 | 0.25 | - |

Density | 2980 | 7850 | 5900 | 5200 | Kg m^{−3} |

SAE 15W40 | SAE 0W20 | |
---|---|---|

K (MPA.S) | 0.029 | 0.071 |

θ_{1} (°C) | 1424.3 | 983.2 |

θ_{2} (°C) | 137.2 | 116.2 |

M (120 °C) (PA.S) | 0.0073 | 0.0045 |

Parameter | Piston Ring Uncoated | Piston Ring Coated | Unit | |
---|---|---|---|---|

Material | Steel | CrN | TiN | - |

Ring-face width | 0.5 | 0.5 | 0.5 | mm |

Ring radius of curvature | 40.5 | 40.5 | 40.5 | mm |

Ring lateral length | 40 | 40 | 40 | mm |

Ring surface roughness | 0.40 | 0.25 | 0.31 | μm |

Liner surface roughness | 0.1 | 0.1 | 0.1 | μm |

(RMS) surface finish of contact surfaces | 0.412 | 0.269 | 0.325 | μm |

Equivalent Young’s modulus of elasticity | 115.94 | 132.18 | 121.35 | GPa |

Roughness parameter | 0.0412 | 0.0486 | 0.0220 | - |

Asperity slope | 2.51 × 10^{−5} | 1.16 × 10^{−5} | 5.50 × 10^{−4} | - |

Eyring shear stress | 2 | 2 | 2 | MPa |

Coefficient of boundary shear strength | 0.22 | 0.22 | 0.22 | - |

Lubricant temperature | 120 | 120 | 120 | °C |

Sliding velocity | 0.5–1.16 | 0.5–1.16 | 0.5–1.16 | m/s |

Applied load | 60 | 60 | 60 | N |

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**MDPI and ACS Style**

Zavos, A.
Effect of Coating and Low Viscosity Oils on Piston Ring Friction under Mixed Regime of Lubrication through Analytical Modelling. *Lubricants* **2021**, *9*, 124.
https://doi.org/10.3390/lubricants9120124

**AMA Style**

Zavos A.
Effect of Coating and Low Viscosity Oils on Piston Ring Friction under Mixed Regime of Lubrication through Analytical Modelling. *Lubricants*. 2021; 9(12):124.
https://doi.org/10.3390/lubricants9120124

**Chicago/Turabian Style**

Zavos, Anastasios.
2021. "Effect of Coating and Low Viscosity Oils on Piston Ring Friction under Mixed Regime of Lubrication through Analytical Modelling" *Lubricants* 9, no. 12: 124.
https://doi.org/10.3390/lubricants9120124