# An Improved Lubrication Model between Piston Rings and Cylinder Liners with Consideration of Liner Dynamic Deformations

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## Abstract

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## 1. Introduction

_{i}, B

_{i}= amplitude constants; i = order; n = highest order distortion to be considered.

## 2. Simulation and Extraction of Surface Dynamic Deformation

#### 2.1. Establishment of Dynamic Model

_{y}can be expressed as Equation (2) [19]:

_{l}is the equivalent mass of the piston assembly. P

_{c}is the longitudinally acting combustion force and P

_{i}is the inertial force of the moving piston assembly.

#### 2.2. Geometric Extraction and Coordinate Transformation

## 3. Development of Dynamic Deformation Based Lubrication Models

#### 3.1. Governing Equations

#### 3.1.1. Average Reynolds Equation

_{0}is the ambient lubricant temperature, and the lubricant temperature T is calculated based on a series of heat flow balance equations [1,3,24].

#### 3.1.2. Asperity Contact

_{a}was related to the density of asperities μ, the curvature of asperity of radius β, composite surface roughness σ, and composite material modulus E. It was defined as Equation (5):

_{1}and E

_{2}are Young’s modulus of ring and liner, and ν

_{1}and ν

_{2}are their corresponding Poisson’s ratio.

#### 3.1.3. Calculation of the Frictional Force

_{h}can be predicted by an integration of viscous shear stress across the sliding surfaces as Equation (8):

_{a}is caused by contact between the ring surface and cylinder wall,

#### 3.2. The Introduction of Dynamic Deformations into the Oil Film Formation and Distribution Model

_{T}

_{(x)}describes the local film thickness, including surface roughness.

_{T}is given by

_{1}is the ring surface roughness amplitude, and ∆

_{2}is the liner surface roughness amplitude. The nominal film thickness h = h

_{min}(t) + h

_{x}(x), giving

_{x}into account in the film formation model, the nominal film thickness can be improved as

_{x}and circumferential deformation ∆

_{y}.

#### 3.3. The Numerical Solution of Shear Stress Factors

## 4. Results and Discussion

#### 4.1. Friction Responses to Dynamic Deformations of Liner Surface

_{min}and friction forces versus the crank angle with and without considering dynamic deformations can be calculated and are presented in Figure 9, Figure 10 and Figure 11. In order to study the differences in influences of surface dynamic deformations on the oil film distribution and oil shear properties, two improved lubrication models are proposed, which only considers the effect of dynamic deformation on the oil film distribution named improved model 1, and the model considering both the influences on oil film distribution and oil shear properties is named as improved model 2. Figure 10 shows the minimum oil film thickness and friction force curves predicted from improved model 1, which only considers the influence on the oil film distribution. For comparison, Figure 11 presents the curves simulated based on improved model 2, which considers both influences.

_{min}considering the impact of liner dynamic deformation shows significant oscillations throughout the entire operating cycle, especially in the mid-strokes with higher sliding speed. The friction curves of the improved models also manifest some obvious oscillations. This indicates that the lubrication behaviour between the piston rings and liners can indeed be affected by the dynamic deformations of cylinder liners.

#### 4.2. Time-Frequency Analysis

#### 4.3. Experimental Verification

## 5. Conclusions

- (1)
- The minimum oil film thicknesses and friction forces predicted by the improved lubricant model considering the impact of liner dynamic deformation show significant oscillations related with liner modal frequencies, indicating that the lubrication behaviours between the piston rings and liners can indeed be affected by the dynamic deformations of cylinder structures.
- (2)
- Around the combustion TDC, the value of asperity friction predicted by the improved model considering liner deformation is lower than that of the original model, indicating that the dynamic deformation of the liner can help to reduce the asperity friction between the matched surfaces and enhance the operation efficiency and service life of engines.
- (3)
- In the middle of piston strokes, the viscous friction force obtained from the improved model shows an obvious decrease compared to the original model, which suggests that the inclusion of surface deformations can cause changes in the flow shear factors and lead to the observable reduction in viscous friction forces.
- (4)
- Under the condition of low sliding speed and thin oil film, the severe surface deformation caused by the piston slap can always result in a serious instantaneous asperity friction after combustion TDC at the crank angle of 380°–385°. This phenomenon has been confirmed by both wear image analysis and acoustic emission signal analysis. The rationality of the improved model constructed in this paper has also been verified to a great degree of extent.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 5.**Short-time Fourier transform (STFT) of responses to piston slaps under 40 Nm and 1800 rpm: (

**a**) STFT of predicted liner responses; (

**b**) piston side-thrust force, the predicted displacement and the predicted acceleration.

**Figure 6.**Flowchart of the geometric extraction and coordinate transformation. (

**a**) Simulated deformation of cylinder liner in ANSYS; (

**b**) Deformation of liner inner surface in MATLAB; (

**c**) Liner deformation in two-dimensional coordinates; (

**d**) Liner deformation excluding the overall displacement.

**Figure 7.**Rough piston ring and cylinder liner conjunction: (

**a**) without liner deformation; (

**b**) with consideration of liner deformation.

**Figure 9.**Minimum oil film thickness and friction force predicted based on conventional model without considering deformations.

**Figure 10.**Minimum oil film thickness and friction force predicted based on improved model 1 considering dynamic deformation.

**Figure 12.**Comparison of H

_{m}and friction forces based on two improved models and original models.

**Figure 13.**Enlarged view of friction forces predicted by three different models under four operating conditions: (

**a**) 1800 rpm and 40 Nm; (

**b**) 1800 rpm and 10 Nm; (

**c**) 1000 rpm and 40 Nm; (

**d**)1000 rpm and 10 Nm.

**Figure 14.**Measured friction in a single-cylinder engine [13] (major reviesd).

**Figure 15.**The STFT of friction force predicted by the improvel model: (

**a**) STFT of the predicted friction force; (

**b**) The predicted friction force.

**Figure 18.**(

**a**) Installation of acoustic emission (AE) sensor; (

**b**) A photograph of the diesel engine test rig.

**Figure 19.**AE signal of liner under different operating conditions: (

**a**) 1799 rpm–40 Nm; (

**b**) 1799 rpm–40 Nm; (

**c**) 1001 rpm–40 Nm; (

**d**) 1001 rpm–10 Nm.

Symbol | Nomenclature | Value |
---|---|---|

${\sigma}_{1}$ | Cylinder surface roughness | 0.8 $\mathsf{\mu}\mathrm{m}$ |

${\sigma}_{2}$ | Ring surface roughness | 0.4 $\mathsf{\mu}\mathrm{m}$ |

r | Crank radius | 0.057 m |

l | Connecting rod length | 0.19 m |

e_{1} | Piston ring surface height | 0.003 m |

B | The axial height of piston ring | 0.003 m |

$\rho $ | Oil density | 890 Kg/m^{3} |

E_{1} | Liner elastic modulus | 122 × 10^{9} Pa |

E_{2} | Modulus of elasticity of piston rings | 165 × 10^{9} Pa |

${\eta}_{0}$ | Lubricant viscosity at atmospheric pressure and 40 °C | 0.095 Pa.s |

T_{o} | The ambient temperature | 20 °C |

Manufacturer | Quanjiao Power Co., Ltd., PR. China |

Engine type | QCH1125 |

Number of cylinders | One |

Combustion system | Direct injection, toroidal combustion chamber |

Bore/stroke | 125/115 mm |

Displacement volume | 1.093 L |

Compression ratio | 18:1 |

Cylinder liners | Cast iron replaceable wet liner |

Start of fuel injection | 14 ± 2° BTDC |

Rated power | 14.7/2400 kW/r/min |

Piston clearance | 0.5 mm |

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**MDPI and ACS Style**

Li, G.; Gu, F.; Wang, T.; Lu, X.; Zhang, L.; Zhang, C.; Ball, A.
An Improved Lubrication Model between Piston Rings and Cylinder Liners with Consideration of Liner Dynamic Deformations. *Energies* **2017**, *10*, 2122.
https://doi.org/10.3390/en10122122

**AMA Style**

Li G, Gu F, Wang T, Lu X, Zhang L, Zhang C, Ball A.
An Improved Lubrication Model between Piston Rings and Cylinder Liners with Consideration of Liner Dynamic Deformations. *Energies*. 2017; 10(12):2122.
https://doi.org/10.3390/en10122122

**Chicago/Turabian Style**

Li, Guoxing, Fengshou Gu, Tie Wang, Xingchen Lu, Li Zhang, Chunfeng Zhang, and Andrew Ball.
2017. "An Improved Lubrication Model between Piston Rings and Cylinder Liners with Consideration of Liner Dynamic Deformations" *Energies* 10, no. 12: 2122.
https://doi.org/10.3390/en10122122