# System Characteristics Analysis for Energy Management of Power-Split Hydraulic Hybrids

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## Abstract

**:**

## 1. Introduction

## 2. System Analysis

## 3. Numerical Analysis

#### 3.1. Modeling Approach

#### 3.2. Dynamic System Modeling

#### 3.3. Hydraulic System Modeling

#### 3.4. Thermal Modeling

## 4. Results and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

FTP | Federal test procedure |

HHV | Hydraulic hybrid vehicle |

HP | High pressure |

HST | Hydrostatic transmission |

LP | Low pressure |

UDDS | Urban dynamometer driving schedule |

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**Figure 14.**Empirical loss model for a hydraulic unit for (

**a**) volumetric efficiency and (

**b**) torque efficiency.

Standing Gear Ratio | 1.8 |

Displacement Volume of Unit-1 | 45 cc |

Displacement Volume of Unit-2 | 62 cc |

HP Accumulator Volume | 31.5 L |

LP Accumulator Volume | 31.5 L |

HP Accumulator Precharge Pressure | 90 bar |

LP Accumulator Precharge Pressure | 16 bar |

Maximum System Pressure | 420 bar |

Low-Pressure Setting | 20 bar |

Mode | Engine | Unit-1 | Accumulator | Unit-2 | Driveline | Note |
---|---|---|---|---|---|---|

1 | Idle | Idle | Idle | Idle | Idle | - |

2 | Motoring | Pumping | Charging | Motoring | Driving | Power Additive |

3 | Motoring | Pumping | Idle | Motoring | Driving | |

4 | Motoring | Pumping | Discharging | Motoring | Driving | |

5 | Motoring | Idle | Idle | Idle | Driving | Full Mechanical |

6 | Motoring | Motoring | Charging | Pumping | Driving | Power Recirculation |

7 | Motoring | Motoring | Idle | Pumping | Driving | |

8 | Motoring | Motoring | Discharging | Pumping | Driving | |

9 | Idle | Idle | Charging | Pumping | Braking | - |

Mode | Engine | Unit-1 | Unit-2 | Driveline | Note |
---|---|---|---|---|---|

1 | Idle | Idle | Idle | Idle | - |

2 | Motoring | Pumping | Motoring | Driving | Power Additive |

3 | Motoring | Idle | Idle | Driving | Full Mechanical |

4 | Motoring | Motoring | Pumping | Driving | Power Recirculation |

5 | Idle | Idle | Pumping | Braking | - |

ForcedConvection | Laminar flow: ($Re<2300$) $Nu={\left({3.66}^{3}+{0.7}^{3}+{\left[1.615\sqrt[3]{Re\xb7Pr\xb7{d}_{i}/L}-0.7\right]}^{3}\right)}^{\frac{1}{3}}{\left(\frac{Pr}{P{r}_{w}}\right)}^{0.11}$ Turbulent flow: ($Re>2300$) $Nu=\frac{\frac{\left(Re-1000\right)Pr}{8{\left(1.82\mathrm{log}\left(Re\right)-1.64\right)}^{2}}\left[1+{\left(\frac{{d}_{i}}{L}\right)}^{\frac{2}{3}}\right]}{1+12.7\left(P{r}^{\frac{2}{3}}-1\right)\sqrt{0.125{\left(1.82\mathrm{log}\left(Re\right)-1.64\right)}^{-2}}}{\left(\frac{Pr}{P{r}_{w}}\right)}^{0.11}$ |

FreeConvection | Cylinder shape: $Nu={\left(0.6+0.387{\left[Gr\xb7Pr{\left(1+{\left(\frac{0.559}{Pr}\right)}^{\frac{9}{16}}\right)}^{-\frac{16}{9}}\right]}^{\frac{1}{6}}\right)}^{2}$ Cube shape: $Nu=5.748+0.752{\left(\frac{Pr\xb7Gr}{{\left[1-{\left(\frac{0.492}{Pr}\right)}^{\frac{9}{16}}\right]}^{\frac{16}{9}}}\right)}^{0.252}$ |

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**MDPI and ACS Style**

Kwon, H.; Ivantysynova, M.
System Characteristics Analysis for Energy Management of Power-Split Hydraulic Hybrids. *Energies* **2020**, *13*, 1837.
https://doi.org/10.3390/en13071837

**AMA Style**

Kwon H, Ivantysynova M.
System Characteristics Analysis for Energy Management of Power-Split Hydraulic Hybrids. *Energies*. 2020; 13(7):1837.
https://doi.org/10.3390/en13071837

**Chicago/Turabian Style**

Kwon, Hyukjoon, and Monika Ivantysynova.
2020. "System Characteristics Analysis for Energy Management of Power-Split Hydraulic Hybrids" *Energies* 13, no. 7: 1837.
https://doi.org/10.3390/en13071837