# Influence of Compression Rings on the Dynamic Characteristics and Sealing Capacity of the Combustion Chamber in Diesel Engines

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Mathematical Model of the Compression Ring

#### 2.1.1. Lubrication Oil Properties

^{8}Pa and $6.31\times {10}^{-5}$ Pa$\xb7$s. ${\beta}_{o}$ and ${\alpha}_{o}$ are the thermo-viscosity coefficient and atmospheric piezo-viscosity, respectively.

#### 2.1.2. Kinematic Piston Model

#### 2.1.3. Compression Ring Kinematics

#### 2.1.4. Gas Blow-By Model

#### 2.1.5. Compression Ring Deformation Model

#### 2.1.6. Piston Skirt Deformation Model

#### 2.2. Numerical Methodology

^{®}software was implemented to solve the model equations proposed in Section 2.1. For the simulations, the characteristics of a single-cylinder diesel engine were used as a reference. The technical specifications of the engine are listed in Table 2. The simulation was executed at a rotation velocity of 3600 rpm and a torque of 9 Nm since this is the engine’s main operating condition (maximum efficiency operating zone).

#### 2.3. Experimental Validation

## 3. Results and Discussions

#### 3.1. Analysis of the Reference Conditions

#### 3.2. Analysis of the Influence of Ring Gap

#### 3.3. Analysis of the Variation of the Mass of Compression Rings

#### 3.4. Analysis of the Variation of the Twist Angle of Compression Rings

#### 3.5. Analysis of the Variation of Blow-By Gas

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

Nomenclature | |

$\mathrm{ICE}$ | Internal combustion engine |

FEA | Finite element analysis |

$T$ | Temperature |

$P$ | Pressure |

${c}_{p}$ | Model constant |

$a$ | Acceleration |

$L$ | Longitude |

$F$ | Force |

${m}_{r}$ | Piston mass |

${P}_{h}$ | Hydrodynamic pressure |

$\tau $ | Viscous shear stress |

$A$ | Area |

${\varphi}_{x},{\varphi}_{y}$ | Pressure flow factors |

${\varphi}_{s}$ | Shear flow factor |

$h$ | Thickness of the lubrication film |

$Z$ | Piezo-viscosity index |

${S}_{o}$ | Thermo-viscosity index |

$\zeta $ | Coefficient of asperity shear strength |

${P}_{a}$ | Asperity contact pressure |

${\sigma}_{s}$ | Surface roughness |

${\beta}_{a}$ | Average asperity radius of curvature |

$\xi $ | Asperity distribution |

$\lambda $ | The stribeck’s lubricant film ratio |

$E\prime $ | Equivalent Young’s modulus of elasticity |

${F}_{5/2}$ | Statistical function of lubricant film ratio |

$E$ | Modulus of elasticity |

$\vartheta $ | Poisson’s ratio |

${e}_{t}$ | Eccentricities of piston at the top of the skirt |

${e}_{b}$ | Eccentricities of piston at the bottom of the skirt |

${c}_{cp}$ | Clearance between the cylinder liner and piston skirt |

${L}_{ps}$ | Longitude of piston skirt |

$\delta $ | Piston skirt deformation |

${\tau}_{o}$ | Limiting Eyring shear stress |

${A}_{e}$ | Effective asperity contact area |

${F}_{2}$ | Statistical function of the Stribeck’s lubricant film ratio |

${P}_{k}$ | Specific pressure of the piston ring on the cylinder wall |

$D$ | Diameter of the ring |

$b$ | Width of the ring |

${\sigma}_{b}$ | Bending stress |

${\varphi}_{sr}$ | Shear factor due to local roughness |

$f$ | Ring gap |

${L}_{rp}$ | Length of the ring |

${T}_{t}$ | Stiffness torsion |

${D}_{i}$ | Inner diameter |

${D}_{o}$ | Outer diameter |

$\dot{m}$ | Mass flow |

${\varphi}_{ss}$ | Shear factor due to sliding velocity |

$R$ | Gas constant |

${n}_{g}$ | Dynamic viscosity of the gas |

${S}_{n}$ | Sutherland’s number |

${a}_{g}$ | Ring gap area |

${c}_{d}$ | Discharge coefficient |

${f}_{m}$ | Compressibility factor |

${\gamma}_{s}$ | Ratio of the specific heats |

${I}_{r}$ | Second moment of inertia of the area |

${A}_{r}$ | Cross-sectional area |

${R}_{r}$ | Radius of curvature of the ring |

$\phi $ | Angular position of the ring |

${C}_{ij}$ | Elastic compliance matrix |

$u$ | Radial direction |

$w$ | Axial direction |

${\varphi}_{sp}$ | Shear factor due to mean pressure |

$\delta $ | Distance between the wrist pin and axis of the piston |

Greek Letters | |

$\rho $ | Density |

$\beta $ | Coefficient of thermal expansion |

$\eta $ | Viscosity |

${\eta}_{\infty}$ | Model constant |

${\alpha}_{o}$ | Atmospheric piezo-viscosity coefficient |

${\beta}_{o}$ | Thermo-viscosity coefficient |

$\alpha $ | Displacement angle of the connecting rod |

$\omega $ | Angular velocity |

$\theta $ | Displacement angle of the crankshaft |

$\psi $ | Ring twist angle |

Subscripts | |

$o$ | Environmental conditions |

$atm$ | Atmospheric |

$p$ | Piston |

$r$ | Connecting rod |

c | Crankshaft |

$g$ | Combustion gases |

## References

- Amador, G.; Duarte, J.F.; Rincon, A.; Fontalvo, A.; Bula, A.; Padilla, R.V.; Orozco, W. Characteristics of Auto-Ignition in Internal Combustion Engines Operated with Gaseous Fuels of Variable Methane Number. J. Energy Resour. Technol. Trans. ASME
**2017**, 139. [Google Scholar] [CrossRef] - Ochoa, G.V.; Isaza-Roldan, C.; Duarte Forero, J. Economic and Exergo-Advance Analysis of a Waste Heat Recovery System Based on Regenerative Organic Rankine Cycle under Organic Fluids with Low Global Warming Potential. Energies
**2020**, 13, 1317. [Google Scholar] [CrossRef][Green Version] - Pavlovic, J.; Ciuffo, B.; Fontaras, G.; Valverde, V.; Marotta, A. How much difference in type-approval CO
_{2}emissions from passenger cars in Europe can be expected from changing to the new test procedure (NEDC vs. WLTP)? Transp. Res. Part A Policy Pract.**2018**, 111, 136–147. [Google Scholar] [CrossRef] - Orozco, W.; Acuña, N.; Duarte, J. Characterization of Emissions in Low Displacement Diesel Engines Using Biodiesel and Energy Recovery System. Int. Rev. Mech. Eng.
**2019**, 13, 420–426. [Google Scholar] [CrossRef] - Duarte, J.; Garcia, J.; Jiménez, J.; Sanjuan, M.E.; Bula, A.; González, J. Auto-Ignition Control in Spark-Ignition Engines Using Internal Model Control Structure. J. Energy Resour. Technol. Trans. ASME
**2017**, 139. [Google Scholar] [CrossRef] - Allen, C.M.; Gosala, D.B.; Shaver, G.M.; McCarthy, J. Comparative study of diesel engine cylinder deactivation transition strategies. Int. J. Engine Res.
**2019**, 20, 570–580. [Google Scholar] [CrossRef] - Oglieve, C.J.; Mohammadpour, M.; Rahnejat, H. Optimisation of the vehicle transmission and the gear-shifting strategy for the minimum fuel consumption and the minimum nitrogen oxide emissions. Proc. Inst. Mech. Eng. Part D J. Automob. Eng.
**2017**, 231, 883–899. [Google Scholar] [CrossRef][Green Version] - Duarte, J.; Amador, G.; Garcia, J.; Fontalvo, A.; Vasquez Padilla, R.; Sanjuan, M.; Gonzalez Quiroga, A. Auto-ignition control in turbocharged internal combustion engines operating with gaseous fuels. Energy
**2014**, 71, 137–147. [Google Scholar] [CrossRef] - Turnbull, R.; Mohammadpour, M.; Rahmani, R.; Rahnejat, H.; Offner, G. Coupled elastodynamics of piston compression ring subject to sweep excitation. Proc. Inst. Mech. Eng. Part K J. Multi-Body Dyn.
**2017**, 231, 469–479. [Google Scholar] [CrossRef][Green Version] - Morris, N.; Mohammadpour, M.; Rahmani, R.; Rahnejat, H. Optimisation of the piston compression ring for improved energy efficiency of high performance race engines. Proc. Inst. Mech. Eng. Part D J. Automob. Eng.
**2017**, 231, 1806–1817. [Google Scholar] [CrossRef][Green Version] - Baker, C.; Theodossiades, S.; Rahmani, R.; Rahnejat, H.; Fitzsimons, B. On the Transient Three-Dimensional Tribodynamics of Internal Combustion Engine Top Compression Ring. J. Eng. Gas Turbines Power
**2017**, 139. [Google Scholar] [CrossRef] - Hallouin, B.; Lasseux, D.; Senger, G. Gas flow through a bore-piston ring contact. Int. J. Engine Res.
**2020**. [Google Scholar] [CrossRef] - Namazian, M.; Heywood, J.B. Flow in the Piston-Cylinder-Ring Crevices of a Spark-Ignition Engine: Effect on Hydrocarbon Emissions, Efficiency and Power; SAE Technical Papers; Society of Automotive Engineers: Warrendale, PA, USA, 1982. [Google Scholar]
- Furuhama, S.; Tada, T. On the Flow of Gas through the Piston-Rings: 2nd Report, the Character of Gas Leakage. Bull. JSME
**1961**, 4, 691–698. [Google Scholar] [CrossRef] - Tomanik, E.; Sobrinho, R.M.S.; Zecchinelli, R. Influence Of Top Ring End Gap Types At Blow-By Of Internal Combustion Engines. SAE Tech. Pap.
**1993**. [Google Scholar] [CrossRef] - Wannatong, K.; Chanchaona, S.; Sanitjai, S. Simulation algorithm for piston ring dynamics. Simul. Model. Pract. Theory
**2008**, 16, 127–146. [Google Scholar] [CrossRef] - Keribar, R.; Dursunkaya, Z.; Flemming, M.F. An Integrated Model of Ring Pack Performance. J. Eng. Gas Turbines Power
**1991**, 113, 382–389. [Google Scholar] [CrossRef] - Przesmitzki, S.; Tian, T. An Experimental Study of the Time Scales and Controlling Factors Affecting Drastic Blow-by Increases during Transient Load Changes in SI Engines. SAE Tech. Pap.
**2008**. [Google Scholar] [CrossRef] - Iijima, N.; Miyamoto, T.; Takiguchi, M.; Kai, R.; Sato, M. An Experimental Study on Phenomena of Piston Ring Collapse. SAE Tech. Pap.
**2002**. [Google Scholar] [CrossRef] - Tian, T. Dynamic behaviours of piston rings and their practical impact. Part 2: Oil transport, friction and wear of ring/liner interface and the effects of piston and ring dynamics. Proc. Inst. Mech. Eng. Part J J. Eng. Tribol.
**2002**, 216, 229–248. [Google Scholar] [CrossRef] - Dowson, D.; Higginson, G.R. A Numerical Solution to the Elasto-Hydrodynamic Problem. J. Mech. Eng. Sci.
**1959**, 1, 6–15. [Google Scholar] [CrossRef] - Yang, P.; Cui, J.; Jin, Z.M.; Dowson, D. Transient elastohydrodynamic analysis of elliptical contacts. Part 2: Thermal and Newtonian lubricant solution. Proc. Inst. Mech. Eng. Part J J. Eng. Tribol.
**2005**, 219, 187–200. [Google Scholar] [CrossRef] - Roelands, C.J.A.; Winer, W.O.; Wright, W.A. Correlational Aspects of the Viscosity-Temperature-Pressure Relationship of Lubricating Oils (Dr In dissertation at Technical University of Delft, 1966). J. Lubr. Technol.
**1971**, 93, 209–210. [Google Scholar] [CrossRef][Green Version] - Houpert, L. New Results of Traction Force Calculations in Elastohydrodynamic Contacts. J. Tribol.
**1985**, 107, 241–245. [Google Scholar] [CrossRef] - Perera, M.S.M.; Theodossiades, S.; Rahnejat, H. Elasto-multi-body dynamics of internal combustion engines with tribological conjunctions. Proc. Inst. Mech. Eng. Part K J. Multi-Body Dyn.
**2010**, 224, 261–277. [Google Scholar] [CrossRef][Green Version] - Consuegra, F.; Bula, A.; Guillín, W.; Sánchez, J.; Duarte Forero, J. Instantaneous in-Cylinder Volume Considering Deformation and Clearance due to Lubricating Film in Reciprocating Internal Combustion Engines. Energies
**2019**, 12, 1437. [Google Scholar] [CrossRef][Green Version] - Patir, N.; Cheng, H.S. Application of Average Flow Model to Lubrication between Rough Sliding Surfaces. J. Lubr. Technol.
**1979**, 101, 220–229. [Google Scholar] [CrossRef] - Patir, N.; Cheng, H.S. An Average Flow Model for Determining Effects of Three-Dimensional Roughness on Partial Hydrodynamic Lubrication. J. Lubr. Technol.
**1978**, 100, 12–17. [Google Scholar] [CrossRef] - 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. Tribol. Interface Eng. Ser.
**2005**, 48, 725–737. [Google Scholar] - Makartchouk, A. Diesel Engine Engineering: Thermodynamics, Dynamics, Design, and Control; CRC Press: Boca Raton, FL, USA, 2002; Volume 143. [Google Scholar]
- Tian, T.; Noordzij, L.B.; Wong, V.W.; Heywood, J.B. Modeling Piston-Ring Dynamics, Blowby, and Ring-Twist Effects. J. Eng. Gas Turbines Power
**1998**, 120, 843–854. [Google Scholar] [CrossRef] - Lyubarskyy, P.; Bartel, D. 2D CFD-model of the piston assembly in a diesel engine for the analysis of piston ring dynamics, mass transport and friction. Tribol. Int.
**2016**, 104, 352–368. [Google Scholar] [CrossRef] - Rahmani, R.; Theodossiades, S.; Rahnejat, H.; Fitzsimons, B. 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.
**2012**, 226, 284–305. [Google Scholar] [CrossRef][Green Version] - Lang, T.E. Vibration of Thin Circular Rings, Part 1; Jet Propulsion Laboratory: Pasadena, CA, USA, 1962.
- Sutherland, L.W. The viscosity of gases and molecular force. Philos. Mag.
**1893**, 36, 507–531. [Google Scholar] [CrossRef][Green Version] - Theaker, M.; Rahmani, R.; Rahnejat, H. Prediction of Ring-Bore Conformance and Contact Condition and Experimental Validation. In Proceedings of the ASME 2012 Internal Combustion Engine Division Spring Technical Conference, Piemonte, Italy, 6–9 May 2012; pp. 885–892. [Google Scholar]
- Zhu, D.; Hu, Y.-Z.; Cheng, H.S.; Arai, T.; Hamai, K. A Numerical Analysis for Piston Skirts in Mixed Lubrication: Part II—Deformation Considerations. J. Tribol.
**1993**, 115, 125–133. [Google Scholar] [CrossRef] - Cantore, G.; Giacopini, M.; Rosi, R.; Strozzi, A.; Pelloni, P.; Forte, C.; Achiluzzi, M.; Bianchi, G.M.; Ceschini, L.; Morri, A. Validation of a combined CFD/FEM methodology for the evaluation of thermal load acting on aluminum alloy pistons through hardness measurements in internal combustion engines. Metall. Sci. Tecnol.
**2011**, 29, 16–25. [Google Scholar] - Richardson, D.E. Comparison of Measured and Theoretical Inter-Ring Gas Pressure on a Diesel Engine; SAE Technical Papers; SAE International: Warrendale, PA, USA, 1996. [Google Scholar]
- Dursunkaya, Z.; Keribar, R.; Richardson, D.E. Experimental and Numerical Investigation of Inter-Ring Gas Pressures and Blowby in a Diesel Engine. SAE Tech. Pap.
**1993**. [Google Scholar] [CrossRef] - Nikolakopoulos, P.G. Simulation of deposits effect on cylinder liner and influence on new and worn compression ring of a turbocharged DI engine. Simul. Model. Pract. Theory
**2021**, 106, 102195. [Google Scholar] [CrossRef] - Delprete, C.; Selmani, E.; Bisha, A. Gas escape to crankcase: Impact of system parameters on sealing behavior of a piston cylinder ring pack. Int. J. Energy Environ. Eng.
**2019**, 10, 207–220. [Google Scholar] [CrossRef][Green Version] - Selmani, E.; Bisha, A. Engine Speed and Load on the Sealing Capacity of a Piston Ring-Pack. Eur. J. Eng. Res. Sci.
**2020**, 5, 304–313. [Google Scholar] [CrossRef] - Cheng, C.; Schock, H.; Richardson, D. The dynamics of second ring flutter and collapse in modern diesel engines. J. Eng. Gas Turbines Power
**2015**, 137. [Google Scholar] [CrossRef] - Tian, T. Dynamic behaviours of piston rings and their practical impact. Part 1: Ring flutter and ring collapse and their effects on gas flow and oil transport. Proc. Inst. Mech. Eng. Part J J. Eng. Tribol.
**2002**, 216, 209–228. [Google Scholar] [CrossRef] - Kurbet, S.N.; Kumar, R.K. A finite element study of piston tilt effects on piston ring dynamics in internal combustion engines. Proc. Inst. Mech. Eng. Part K J. Multi-Body Dyn.
**2004**, 218, 107–117. [Google Scholar] [CrossRef]

**Figure 9.**Experimental validation of the simulation results in the (

**a**) combustion chamber and (

**b**) in locations 1 and 2.

**Figure 13.**Pressure in the combustion chamber for (

**a**) modification 1, (

**b**) modification 2 and (

**c**) modification 3.

**Figure 14.**Relative position of the piston rings for (

**a**) modification 1, (

**b**) modification 2 and (

**c**) modification 3.

**Figure 15.**Flow of combustion gases in the piston grooves for (

**a**) modification 1, (

**b**) modification 2, and (

**c**) modification 3.

**Figure 18.**Relative position of piston rings for modifications 5 and 6, (

**a**) positive twist angle and (

**b**) negative twist angle.

Modification | Parameter | First Ring | Second Ring |
---|---|---|---|

1 | Gap | −25% ${G}_{1}$ | +25% ${G}_{2}$ |

2 | +25% ${G}_{1}$ | ${G}_{2}$ | |

3 | −25% ${G}_{1}$ | −25% ${G}_{2}$ | |

4 | Mass | +50% ${m}_{1}$ | +50% ${m}_{2}$ |

5 | Twist angle | Positive | Positive |

6 | Negative | Negative |

Model | SK-MDF300 |
---|---|

Manufacturer | SOKAN |

Bore × stroke | 78 mm × 62.57 mm |

Engine type | 1 cylinder |

Maximum power | 4.6 hp at 3600 rpm |

Cycle | 4 Strokes |

Injection system | Direct injection |

Displaced volume | 299 CC |

Compression ratio | 20:1 |

Intake system | Naturally Aspirated |

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**MDPI and ACS Style**

Hernández-Comas, B.; Maestre-Cambronel, D.; Pardo-García, C.; Fonseca-Vigoya, M.D.S.; Pabón-León, J. Influence of Compression Rings on the Dynamic Characteristics and Sealing Capacity of the Combustion Chamber in Diesel Engines. *Lubricants* **2021**, *9*, 25.
https://doi.org/10.3390/lubricants9030025

**AMA Style**

Hernández-Comas B, Maestre-Cambronel D, Pardo-García C, Fonseca-Vigoya MDS, Pabón-León J. Influence of Compression Rings on the Dynamic Characteristics and Sealing Capacity of the Combustion Chamber in Diesel Engines. *Lubricants*. 2021; 9(3):25.
https://doi.org/10.3390/lubricants9030025

**Chicago/Turabian Style**

Hernández-Comas, Brando, Daniel Maestre-Cambronel, Carlos Pardo-García, Marlen Del Socorro Fonseca-Vigoya, and Jhon Pabón-León. 2021. "Influence of Compression Rings on the Dynamic Characteristics and Sealing Capacity of the Combustion Chamber in Diesel Engines" *Lubricants* 9, no. 3: 25.
https://doi.org/10.3390/lubricants9030025