# A Minimal Input Engine Friction Model for Power Loss Prediction

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## Abstract

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## 1. Introduction

## 2. Design Tool Overview

- Geometric (and inertial, if necessary) data of connecting rod-crank mechanism.
- Working conditions in the combustion chamber (motored or fired).
- Geometrical data and lubrication conditions of the component under examination.
- Tribological data of the lubricant and the modeled surfaces
- Parameters necessary to the numerical integration method.

#### 2.1. Modeling and Numerical Methods

- Necessary semianalytical model to define the relationship between external forces acting on the component, and the pressure and thickness present in the lubricant meatus.
- Numerical discretization (1D or 2D) to solve the Reynolds equation associated with the lubricant meatus.
- Numerical methods such as finite differences to solve the Reynolds equation, and algorithms to link equilibrium equations with meatus thickness h.

- crankshaft angular speed $\omega $ is constant;
- lubricant is Newtonian and incompressible;
- oil viscosity and density are constant;
- thermal and elastic deformation of the components are neglected.

#### 2.1.1. Piston Rings

#### 2.1.2. Piston Skirt

#### 2.1.3. Connecting Rod and Main Bearings

## 3. Results

- quantities directly related to the Reynolds equation such as oil film thickness and pressure distribution;
- frictional forces due to viscous shear stresses and the associated power loss (typically obtained as the integral of the frictional force).

#### Sensitivity Analysis of Piston Assembly Power Losses to Uncertain Parameters

## 4. Conclusions

- use of the smallest possible number of inputs to calibrate the models, a necessary feature in the preliminary phase when not all design details are already available;
- use of semianalytical models with simple discretizations that guarantee low computational times;
- ease of use thanks to a graphical interface for data entry, and for the interpretation and export of results;
- proven predictive capabilities thanks to the experimental numerical comparison operated in different operating conditions;
- robustness of the model in the choice of uncertain parameters during the initial design phases of internal combustion engines, which guarantees limited variability in estimated power losses.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 5.**Flowchart of general process of the model solution individually applied to each subsystem (piston rings, piston skirt, journal bearings) analyzed.

**Figure 10.**Example of results on instantaneous power loss and its average value for the second piston ring.

**Figure 11.**Experimental–numerical comparison for piston assembly (piston rings, skirt, and connecting rod bearing) for four different speed values.

**Figure 12.**Experimental–numerical comparison for five main bearings supporting crankshaft for four different speed values.

**Figure 14.**Piston assembly power losses for 15 analyzed cases using Latin hypercube sampling method.

Module | Calculation Time [min] |
---|---|

Piston Rings | 8 |

Piston Skirt | 40 |

Journal Bearing | 10 |

Component | ${\mathit{m}}_{\mathit{f}}$ [W] | ${\mathit{m}}_{\mathit{r}}$ [W μm${}^{-1}$] | ${\mathit{m}}_{\mathit{v}}$ [W mPa${}^{-1}$ s${}^{-1}$] |
---|---|---|---|

Ring 1 | 0.102 | 0.74 | 1.022 |

Ring 2 | 0.065 | −0.397 | 0.857 |

Oil control ring | 0.132 | −0.782 | 1.277 |

Conrod bearing | − | −10.614 | 1.791 |

Piston skirt | − | − | 6.625 |

Case | Oil Viscosity [mPa s] | Surface Rough. μm | Friction Coeff. [−] |
---|---|---|---|

1 | 9.873 | 0.363 | 0.104 |

2 | 9.974 | 0.373 | 0.045 |

3 | 9.181 | 0.393 | 0.075 |

4 | 10.045 | 0.388 | 0.054 |

5 | 9.654 | 0.398 | 0.061 |

6 | 9.120 | 0.376 | 0.122 |

7 | 9.371 | 0.361 | 0.095 |

8 | 9.567 | 0.392 | 0.079 |

9 | 10.291 | 0.397 | 0.127 |

10 | 10.392 | 0.381 | 0.047 |

11 | 9.292 | 0.384 | 0.092 |

12 | 10.407 | 0.388 | 0.084 |

13 | 10.177 | 0.369 | 0.108 |

14 | 9.477 | 0.375 | 0.116 |

15 | 9.802 | 0.366 | 0.067 |

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**MDPI and ACS Style**

Delprete, C.; Gastaldi, C.; Giorio, L.
A Minimal Input Engine Friction Model for Power Loss Prediction. *Lubricants* **2022**, *10*, 94.
https://doi.org/10.3390/lubricants10050094

**AMA Style**

Delprete C, Gastaldi C, Giorio L.
A Minimal Input Engine Friction Model for Power Loss Prediction. *Lubricants*. 2022; 10(5):94.
https://doi.org/10.3390/lubricants10050094

**Chicago/Turabian Style**

Delprete, Cristiana, Chiara Gastaldi, and Lorenzo Giorio.
2022. "A Minimal Input Engine Friction Model for Power Loss Prediction" *Lubricants* 10, no. 5: 94.
https://doi.org/10.3390/lubricants10050094