# Modeling and Fault Simulation of a New Double-Redundancy Electro-Hydraulic Servo Valve Based on AMESim

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## Abstract

**:**

## 1. Introduction

## 2. Working Principles

## 3. DREHSV Modeling

#### 3.1. Torque Motor Modeling

_{g}is the length of each working air gap when the armature is in the middle position, μ

_{0}is the magnetic permeability of air, and A

_{g}is the area of the magnetic pole surface.

_{1}and R

_{3}of the working air gaps 1 and 3 and R

_{2}and R

_{4}of the working air gaps 2 and 4 are the same, assuming that the armature deflects x to the right since the magnetic circuit is symmetric.

_{13}is the synthetic magnetic flux of working air gaps 1 and 3, ϕ

_{24}is the synthetic magnetic flux of working air gaps 2 and 4, and E

_{0}is the polarized magnetomotive force generated by the permanent magnet and is calculated as follows:

_{p}is the length of the element of the permanent magnet, and H

_{mc}is the minimum coercive field. μ

_{p}is the magnetic permeability, B

_{mi}is the minimum induction, and B

_{ri}is the remanent induction of the permanent magnet.

#### 3.2. Armature Assembly Modeling

_{g}). The spring tube deforms while deflecting, causing horizontal movement (x

_{t}). As a result, the matrix form can be used to express the torque tube (τ

_{tube}) and spring tube force (F

_{tube}).

_{1}is the distance between the armature center and the bottom of the spring tube.

_{L}is the resultant hydraulic force on the flapper, f

_{l}is the hydraulic force on the left of the flapper, and f

_{r}is the hydraulic force on the right of the flapper.

_{d}is the electromagnetic torque, b

_{r}is the rotational damping, d

_{2}is the distance between the armature center and the nozzle, m is the armature mass, and b

_{t}is the moving damping.

#### 3.3. Double-System Slide Valve Modeling

_{Q}applied to the spool is shown as follows:

_{P}is the force area of the piston and P

_{L}is the pilot stage differential pressure.

_{r}is shown as follows:

_{v}is the spool displacement and m

_{v}is the total mass of the spool and four pistons.

_{m}between the spool and valve sleeve and the piston and bush is shown as follows:

_{v}

_{1}is the damping coefficient between the spool and valve sleeve, and B

_{v}

_{2}is that between the piston and push.

_{t}is shown as follows:

_{f}is the transient hydrodynamic force damping coefficient.

_{v}is the velocity coefficient, ρ is the hydraulic oil density, and ΔP is the valve port differential pressure.

_{R}of the double-system valve port is shown as follows:

_{R}is the rectangular valve port length.

_{L}through the double-system valve port is shown as follows:

_{d}is the flow coefficient and C

_{d}= 0.707.

_{s}can be calculated as follows:

_{f}is the steady hydrodynamic force stiffness, and K

_{f}= 8C

_{v}C

_{d}L

_{R}ΔPcosθ.

_{L}, the force balance equation of the double-system spool is shown as follows:

_{P}) was calculated as $\frac{\pi}{4}\times \left({17.02}^{2}-{14.93}^{2}\right)=52.445{\mathrm{mm}}^{2}$.

#### 3.4. AMESim Overall Simulation Model

_{v}), and m

_{v}was set to 0.6512 kg. The friction force is important during the movement of the spool, which can be modeled with a simple formulation taking into account Coulomb friction, stiction, viscous friction, and windage. In the DREHSV simulation model, the stiction force and Coulomb friction force were set at 10 N, and the coefficient of viscous friction was 2000 N/(m/s).

## 4. Simulation and Fault Research

#### 4.1. DREHSV Normal Mode

#### 4.2. Pilot Stage Nozzle Clogged

#### 4.3. Power Stage Spool Worn

#### 4.4. Redundant Design Advantage

_{p}) was 62.8 mm, the rod diameter (d

_{r}) was 38.7 mm, and the clearance on the diameter (d

_{c}) was 0.03 mm, as shown in Figure 22.

## 5. Experiment

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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Component | Parameter | Value |
---|---|---|

Air gap | Initial air gap (l_{g}) | 0.3 mm |

Pole area (A_{g}) | 15 mm^{2} | |

Permanent magnet | Length of the element (l_{p}) | 28 mm |

Effective area of the element (A_{p}) | 65 mm^{2} | |

Remanent induction (B_{ri}) | 0.3 T | |

Minimum coercive field (H_{mc}) | −20,000 A/m | |

Minimum induction (B_{mi}) | 0.16 T | |

Coil | Number of turns (N) | 4200 tr |

Internal resistor | 400 Ohm |

Parameter | Value | Parameter | Value |
---|---|---|---|

m | 0.0048 kg | d_{1} | 2.8 mm |

J | 5.3 × 10^{−7} kg·m^{2} | d_{2} | 12.8 mm |

L | 4.5 mm | b_{r} | 0.001 Nm/(rad/s) |

E | 1.2 × 10^{6} bar | b_{t} | 100 N/(m/s) |

Parameter | Value | Parameter | Value |
---|---|---|---|

Spool diameter | 14.18 mm | Critical flow number | 100 |

Rod diameter | 11.3 mm | Underlap corresponding to zero displacement | 0.008 mm |

Width of a slot | 1.95 mm | Rounded corner radius | 0.007 mm |

Depth of a slot | 0.87 mm | Clearance on diameter | 0.006 mm |

Number of Coils | Amplitude | Phase |
---|---|---|

4 | 39.835 Hz | 31.386 Hz |

2 | 17.983 Hz | 22.931 Hz |

1 | 5.497 Hz | 14.871 Hz |

Number of Coils | Maximum Displacement | Required Time |
---|---|---|

4 | 0.798 mm | 0.271 s |

2 | 0.797 mm | 0.278 s |

1 | 0.794 mm | 0.286 s |

Different Wear Parts | Maximum Displacement | Time |
---|---|---|

Unworn | 58.807 mm | 0.296 s |

System 1 worn | 58.431 mm | 0.300 s |

All worn | 58.156 mm | 0.303 s |

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**MDPI and ACS Style**

Liang, Q.; Wang, W.; Zhai, Y.; Sun, Y.; Zhang, W.
Modeling and Fault Simulation of a New Double-Redundancy Electro-Hydraulic Servo Valve Based on AMESim. *Actuators* **2023**, *12*, 417.
https://doi.org/10.3390/act12110417

**AMA Style**

Liang Q, Wang W, Zhai Y, Sun Y, Zhang W.
Modeling and Fault Simulation of a New Double-Redundancy Electro-Hydraulic Servo Valve Based on AMESim. *Actuators*. 2023; 12(11):417.
https://doi.org/10.3390/act12110417

**Chicago/Turabian Style**

Liang, Qiuhui, Wentao Wang, Yifei Zhai, Yanan Sun, and Wei Zhang.
2023. "Modeling and Fault Simulation of a New Double-Redundancy Electro-Hydraulic Servo Valve Based on AMESim" *Actuators* 12, no. 11: 417.
https://doi.org/10.3390/act12110417