# Deterministic Simulation of Surface Textures for the Piston Ring/Cylinder Liner System in a Free Piston Linear Engine

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## Abstract

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## 1. Introduction

## 2. Deterministic Mixed Lubrication Model

## 3. Methodology

#### 3.1. Surface Processing

^{®}Imaging Topography software version 9.0 from DigitalSurf. The treatment of the surfaces involved the following steps: (i) surface levelling; (ii) form removal, using a third-degree polynomial fitting; (ii) application of a threshold to remove measurement outliers, eliminating surface height data that fell outside the range of 0.20% to 99.80% according to the Abbot–Firestone curve; (iii) filling in non-measured points; and (iv) application of a robust Gaussian metrological filter with a cut-off of 800 μm to separate surface roughness and waviness.

_{m}/Spq) under steady-state conditions, where h

_{m}is the imposed separation between the reference plane of the piston liner surface roughness and the smooth and rigid theorical surface of the piston’s oil control ring, and Spq is the standard deviation of the roughness in the plateau region of the cylinder liner surface. The variation in the imposed Λ values aimed to use a larger number of points in the regions of thinner films, as described in Table 2, where the variation step increases as the imposed film becomes thicker.

#### 3.2. Outlier Removal

## 4. Results and Discussion

#### 4.1. Original Surface Processing

#### 4.2. Field Results

#### 4.3. Average Results

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Schematics of a free-piston linear engine with opposed pistons. 1—cylinder liner; 2—piston; 3—springs; 4—stator.

**Figure 3.**Stribeck curve describing the correlation between the coefficient of friction and the dimensionless film thickness or lambda ratio ($\Lambda ={h}_{m}/Spq$).

**Figure 5.**Cylinder liner topography; (

**a**) 3D representation of the surface roughness; (

**b**) 2D representation of the surface roughness.

**Figure 6.**Mean plane shift using a Gaussian Mixture Model: (

**a**) top view of the original surface; (

**b**) top view of the shifted original surface; (

**c**) Gaussian Mixture Model used for surface clustering; (

**d**) line profiles comparing original (blue) and shifted condition (red); (

**e**) comparison of height asperity distributions of the original and shifted surfaces.

**Figure 7.**Surfaces for the numerical simulations with different area coverage percentages of the textures: (

**a**) original surface; (

**b**) 5%; (

**c**) 10%; (

**d**) 15%; (

**e**) 20%; (

**f**) 30%; (

**g**) 50%.

**Figure 9.**Field results of the textured surface (50%) for: (

**a**) Λ = 0.5; (

**b**) Λ = 2.5; and (

**c**) Λ = 4.5.

**Figure 10.**Average results of the deterministic simulations: (

**a**) hydrodynamic pressure; (

**b**) hydrodynamic shear stress; (

**c**) asperity contact pressure; (

**d**) asperity contact shear stress; (

**e**) coefficient of friction.

Coverage Area Percentage | Dr (μm) | Ds (μm) | Dd |
---|---|---|---|

Original Untextured Surface | - | - | - |

5% | 100 | 792.66 | 0.03 |

10% | 100 | 560.50 | 0.03 |

15% | 100 | 457.65 | 0.03 |

20% | 100 | 396.33 | 0.03 |

30% | 100 | 323.60 | 0.03 |

50% | 100 | 250.66 | 0.03 |

Λ range | 0.01–0.05 | 0.06–0.10 | 0.10–0.50 | 0.50–1.00 | 1.00–5.00 |

Variation step | 0.01 | 0.02 | 0.05 | 0.10 | 0.25 |

Sliding velocity (U) | 2.82 m∙s^{−1} |

Lubricant dynamic viscosity (μ) | 0.01 Pa∙s |

Lubricant specific mass (ρ) | 0.82 g/cm^{3} |

Young’s Modulus (E) | 120 GPa |

Hardness (H) | 420 HV |

Boundary coefficient of friction (μ_{BL}) | 0.14 |

Parameters | Original Surface | Coverage Area Percentage | |||||
---|---|---|---|---|---|---|---|

5% | 10% | 15% | 20% | 30% | 50% | ||

Spq (μm) | 0.25 | 0.25 | 0.25 | 0.25 | 0.25 | 0.26 | 0.28 |

Ssk (μm) | −2.06 | −2.02 | −1.79 | −1.63 | −1.46 | −1.18 | −0.68 |

Sku (μm) | 7.58 | 7.53 | 6.28 | 5.49 | 4.74 | 3.90 | 2.94 |

Std (deg) | 28.24 | 151.80 | 151.80 | 151.80 | 151.80 | 151.80 | 151.80 |

Spk (μm) | 0.22 | 0.22 | 0.22 | 0.22 | 0.22 | 0.22 | 0.23 |

Sk (μm) | 0.68 | 0.71 | 0.76 | 0.80 | 0.86 | 1.03 | 2.00 |

Svk (μm) | 1.99 | 2.24 | 2.52 | 2.67 | 2.80 | 2.93 | 2.23 |

Smrk1 (%) | 5.61 | 5.35 | 4.95 | 4.61 | 4.28 | 3.46 | 1.19 |

Smrk2 (%) | 71.18 | 69.54 | 67.26 | 65.33 | 63.20 | 58.80 | 57.55 |

Vv (μm^{3}/μm^{2}) | 0.61 | 0.68 | 0.78 | 0.85 | 0.94 | 1.13 | 1.52 |

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## Share and Cite

**MDPI and ACS Style**

Luz, F.K.C.; Profito, F.J.; dos Santos, M.B.; Silva, S.A.N.; Costa, H.L.
Deterministic Simulation of Surface Textures for the Piston Ring/Cylinder Liner System in a Free Piston Linear Engine. *Lubricants* **2024**, *12*, 12.
https://doi.org/10.3390/lubricants12010012

**AMA Style**

Luz FKC, Profito FJ, dos Santos MB, Silva SAN, Costa HL.
Deterministic Simulation of Surface Textures for the Piston Ring/Cylinder Liner System in a Free Piston Linear Engine. *Lubricants*. 2024; 12(1):12.
https://doi.org/10.3390/lubricants12010012

**Chicago/Turabian Style**

Luz, Felipe Kevin Correia, Francisco J. Profito, Marcelo Braga dos Santos, Samuel A. N. Silva, and Henara Lillian Costa.
2024. "Deterministic Simulation of Surface Textures for the Piston Ring/Cylinder Liner System in a Free Piston Linear Engine" *Lubricants* 12, no. 1: 12.
https://doi.org/10.3390/lubricants12010012