# Viscous Loss Analysis of the Flooded Electro-Hydrostatic Actuator Motor under Laminar and Turbulent Flow States

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Method for Judging Cooling Fluid Flow State

^{2}/s).

_{c}. The expression of K can be defined as:

^{3}), and $\overrightarrow{U}$ is the velocity vector. The expression of $\overrightarrow{U}$ can be expressed as

^{3}).

^{−1}. Figure 2 reflects the relationship between $K/M$ and $y/h$ at different values of $h/{R}_{s}$, in which $M$ is a constant value at a certain rotation speed, and it can be expressed as $M=Re\frac{{R}_{r}}{2\left({R}_{r}+{R}_{s}\right)}$. As can be seen from Figure 2, the value of $K$ increases with increasing $y/h$ for a given $h/{R}_{s}$ less than 0.3 and the maximum value of $K$ is reached when $y/h=1.0$. Therefore, the expression for the maximum value of $K$ can be written as

## 3. Theoretical Analysis of Air Gap Viscous Loss

#### 3.1. Calculation Method of Viscous Loss in Laminar State

#### 3.2. Calculation Method of Viscous Loss in Turbulent State

^{−6}based on the CFD simulation results, and the theoretical results and CFD simulation results are shown in Figure 7. Above all, the expression of the viscous loss of the motor under different flow conditions can be rewritten as

## 4. Experimental Results

## 5. Discussion

_{c}obtained by the experimental data. Using this method, the critical speed of the wet EHA motor’s internal gap fluid flow state was 3500 rpm, while the criterion rotation speed was 4570 rpm obtained by using the Taylor criterion. Then the lumped parameter models of the viscous loss under laminar and turbulent state were analyzed by using Newton’s internal friction theorem and the conservation of momentum theory, respectively. To verify the accuracy of the fluid flow state judgment criteria and the proposed lumped parameter model, a motor viscosity loss experiment was designed. There was a 10% error between experimental results and theoretical results, which verified the correctness of the method.

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

^{2}) and it can be written as

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**Figure 5.**CFD simulation model. (

**a**) Geometry of the air gap. (

**b**) Radial grid of air gap. (

**c**) Axial grid of air gap.

**Figure 6.**Comparison chart of theoretical results based on laminar flow theory and CFD simulation results under laminar state and turbulent state.

**Figure 7.**Comparison chart of theoretical results and CFD simulation results under laminar state and turbulent state.

**Figure 9.**Comparison of theoretical calculation and experimental test of motor loss. (

**a**) Motor rotor torque loss diagram. (

**b**) Motor power loss diagram.

Parameters | Value | Unit |
---|---|---|

Radius of the rotor ${R}_{r}$ | $2.35\times {10}^{-2}$ | m |

Radius of the stator ${R}_{s}$ | $2.3\times {10}^{-2}$ | m |

Length of the air gap L | $1.67\times {10}^{-1}$ | m |

Density of the oil $\rho $ | $839.3$ | kg/m^{3} |

Dynamic viscosity of the oil $\mu $ | $1.16\times {10}^{-2}$ | N s/m^{2} |

Kinematic viscosity of the oil $\nu $ | $1.38\times {10}^{-5}$ | m^{2}/s |

Simulation Settings | Setup | |
---|---|---|

General | Solver Type | Pressure-Based |

Velocity Formulation | Absolute | |

Time | Steady | |

Models | Viscous | Laminar/Standard k-epsilon and Standard Wall Functions |

Boundary | End Face 1 | Symmetry |

End Face 2 | Symmetry | |

Rotor | Moving Wall (Rotation Speed can be set) | |

Stator | Wall (No Slip) | |

Method | Schema | SIMPLEC |

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## Share and Cite

**MDPI and ACS Style**

Li, Y.; Jiao, Z.; Yu, T.; Shang, Y.
Viscous Loss Analysis of the Flooded Electro-Hydrostatic Actuator Motor under Laminar and Turbulent Flow States. *Processes* **2020**, *8*, 975.
https://doi.org/10.3390/pr8080975

**AMA Style**

Li Y, Jiao Z, Yu T, Shang Y.
Viscous Loss Analysis of the Flooded Electro-Hydrostatic Actuator Motor under Laminar and Turbulent Flow States. *Processes*. 2020; 8(8):975.
https://doi.org/10.3390/pr8080975

**Chicago/Turabian Style**

Li, Yanpeng, Zongxia Jiao, Tian Yu, and Yaoxing Shang.
2020. "Viscous Loss Analysis of the Flooded Electro-Hydrostatic Actuator Motor under Laminar and Turbulent Flow States" *Processes* 8, no. 8: 975.
https://doi.org/10.3390/pr8080975