# A Novel Approach of Studying the Fluid–Structure–Thermal Interaction of the Piston–Cylinder Interface of Axial Piston Pumps

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## Abstract

**:**

## 1. Introduction

## 2. Modeling

#### 2.1. Film Geometry

#### 2.2. The Reynolds Equation and Energy Equation

#### 2.3. Finite Volume Method

#### 2.4. Fluid–Structure–Thermal Interaction

#### 2.5. Dynamic Model

#### 2.5.1. The Force Exerted on the Piston

#### 2.5.2. The Extra Friction Force

## 3. Results and Discussion

#### 3.1. The Influence of Temperature

#### 3.2. Axial Friction Force

#### 3.3. Leakage of the Piston–Cylinder Interface

#### 3.4. Discussion

## 4. Conclusions

- (1)
- The temperature greatly influences the lubrication performance. The dynamic viscosity will drop by 73% when the temperature rises from 293.15 K to 323.25 K at the pressure of 0.1 MPa. This will lead to the decrease in the film’s load-bearing capacity and the increase in the leakage;
- (2)
- Insufficient film height brings extra friction force, which is related to the pressure in the area;
- (3)
- A dynamic model of the piston–cylinder interface integrated the temperature and elastic deformation effects can accurately predict the friction force.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 5.**Pressure field, elastic deformation, and temperature field: (

**a**) Predicted by the fluid model; (

**b**) predicted by the fluid–structure–thermal interaction model; (

**c**) the elastic deformation of the piston’s surface; (

**d**) the elastic deformation of the bushing’s surface; (

**e**) the temperature distribution of the film; and (

**f**) the dynamic viscosity distribution of the film.

**Figure 6.**(

**a**)Viscosity–pressure and viscosity–temperature relationship; (

**b**) viscosity–pressure relationship at T = 313.15 K; (

**c**) and viscosity–temperature relationship at p = 0.1 MPa.

**Figure 11.**Comparison of the axial friction force exerted on the bushing: (

**a**) Condition 1; (

**b**) Condition 2; and (

**c**) Condition 3.

**Figure 13.**Comparison of the leakage of the piston–cylinder interface: (

**a**) Condition 1; (

**b**) Condition 2; and (

**c**) Condition 3.

Parameters | Symbol | Value |
---|---|---|

Piston outer diameter (mm) [2] | ${D}_{p}$ | 20.700 |

Bushing inner diameter (mm) [2] | ${D}_{b}$ | 20.724 |

Piston height (mm) | ${L}_{p}$ | 54 |

Swash plate inclination (°) | $\beta $ | 17 |

Hydraulic fluid dynamic viscosity at 40 °C (cst) | $\mu $ | 32 |

Friction coefficient | ${\mu}_{ext}$ | 0.02 |

Minimum film height (μm) | ${h}_{min}$ | 2 |

Operating Conditions | Condition 1 | Condition 2 | Condition 3 |
---|---|---|---|

The average temperature of the film (°C) | 53.0 | 54.9 | 55.7 |

Change of the gap height (μm) | 0.95 | 1.01 | 1.20 |

Average dynamic viscosity (Pa⋅s) | 0.020 | 0.019 | 0.019 |

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**MDPI and ACS Style**

Zhou, J.; Li, T.; Wang, D.
A Novel Approach of Studying the Fluid–Structure–Thermal Interaction of the Piston–Cylinder Interface of Axial Piston Pumps. *Appl. Sci.* **2021**, *11*, 8843.
https://doi.org/10.3390/app11198843

**AMA Style**

Zhou J, Li T, Wang D.
A Novel Approach of Studying the Fluid–Structure–Thermal Interaction of the Piston–Cylinder Interface of Axial Piston Pumps. *Applied Sciences*. 2021; 11(19):8843.
https://doi.org/10.3390/app11198843

**Chicago/Turabian Style**

Zhou, Junjie, Tianrui Li, and Dongyun Wang.
2021. "A Novel Approach of Studying the Fluid–Structure–Thermal Interaction of the Piston–Cylinder Interface of Axial Piston Pumps" *Applied Sciences* 11, no. 19: 8843.
https://doi.org/10.3390/app11198843