# Non-Structural Damage Verification of the High Pressure Pump Assembly Ball Valve in the Gasoline Direct Injection Vehicle System

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Model Analysis

_{2}. The left side of the valve ball is initially subjected to the preload force F

_{t}of the spring. When the oil pressure p

_{2}at the right end of the valve ball increases to a certain value, exceeding the spring force provided at the left end, and the left end oil pressure is changed to 0 MPa, the valve ball will be opened and the right side high pressure oil will be released to the left side, which acts as a safe unloading valve. The ball valve structural parameters and oil pressure parameters are shown in Table 1. The equivalent calculation is carried out according to the pressure, and the contact area between the valve ball and the valve seat is subjected to an equivalent oil pressure of 5–50 MPa.

^{9}times) will occur as shown in Figure 3. The most critical and most important damage mechanism under complex conditions may be hidden and cannot be directly seen in Figure 3, so further analysis and judgment is needed to reach a conclusion. Firstly, it is necessary to consider whether the valve ball will be structurally damaged from the perspective of static force and fatigue.

## 3. Theoretical Analysis

#### 3.1. Structural Micro-Division

#### 3.2. Equivalent Friction Coefficient Calculation

_{1}and forward pressure N

_{1}. When the horizontal thrust F

_{1}is within the range of 0 ≤ F

_{1}≤ f

_{max}= μ

_{1}N

_{1}(μ

_{1}—maximum static friction between the two materials), the slider has no displacement. However, there is a slight slip Δx between the slider and the horizontal plane. It can be considered that the micro slip range in which the slider does not move is 0 ≤ Δx ≤ Δx

_{max}. It can be also considered that the equivalent friction coefficient f

_{x}satisfies f

_{x}∝Δx [15].

_{x}is the ratio of the value of non-critical equivalent friction to the positive pressure:

_{x}and the micro-slip Δx is experimentally verified and obtained by Dr. Liu [16]. μ

_{x}and Δx are proportional to each other.

_{1}, which can be expressed as:

#### 3.3. Structural Contact Stress Analysis

^{*}is the equivalent elastic modulus, which satisfies:

_{1}and E

_{2}are the elastic modulus values of the valve ball and the valve seat material, respectively. υ

_{1}and υ

_{2}are the Poisson′s ratios of the valve ball and the valve seat material, respectively. E

_{1}= 200 GPa, E

_{2}= 213 GPa. υ

_{1}= 0.3, υ

_{1}= 0.29.

## 4. Simulation Analysis

_{1}′ = 0.01, p

_{2}′ = 0.05, p

_{3}′ = 0.1 and p

_{4}′ = 0.5 data given by the material according to the normal distribution.

_{min}= 0.1 × 50 MPa = 5 MPa. The pulsating form is shown in Figure 9.

_{max}′ = 1107.8 MPa, and the theoretical calculation result is p

_{max}= 1220 MPa. The error between the two is about 9.2%, less than 10%, which verifies the correctness of the theoretical model. The overall equivalent stress distribution is obtained as shown in Figure 11. The maximum equivalent stress is 725.63 MPa. The yield strength of the ball and seat material is σ

_{t}= 1900 MPa, and the tensile yield strength and compressive yield strength of the elastoplastic material are generally considered to be the same, i.e., σ

_{t}= σ

_{c}(σ

_{c}is the compressive yield strength). The von Mises equivalent stress theoretical shear yield strength satisfies τ

_{s}= σ

_{t}/√3, and τ

_{s}≈ 1096 MPa can be calculated [20]. The check is performed with the minimum shear yield strength, which is much larger than the equivalent stress of 725.63 MPa that is theoretically calculated. It can be judged that the ball valve is safe under static conditions.

^{9}times is shown in Figure 12; the maximum is 3.6558, which indicates that the structural ball will not suffer structural fatigue damage under the action of fatigue alone.

## 5. Discussion

## 6. Conclusions

^{9}cycles. It is verified that the traditional structural fatigue is not the cause of the ball failure of the unloading valve.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 13.**Test bench, (1) piezoelectric actuator; (2) fixed disc; (3) cylinder 1; (4) force sensor; (5) cylinder 2; (6) testing object; (7–9) base.

r (Ball radius) | 0.794 mm |

θ (Contact angle) | 27.5° |

p_{1} (Alternating oil pressure) | 0–45 MPa |

p_{2} (High pressure rail constant oil pressure) | 35 MPa |

F_{t} (Spring preload force) | 63 N |

Parameter | p′ = 0.01 | p′ = 0.05 | p′ = 0.10 | p′ = 0.50 |
---|---|---|---|---|

C | 9.15 × 10^{44} | 8.66 × 10^{42} | 1.90 × 10^{41} | 2.79 × 10^{41} |

m | 10.9314 | 10.201 | 9.6618 | 9.5012 |

Cycles (N) | Stress (MPa) | Cycles (N) | Stress (MPa) |
---|---|---|---|

5,000,000 | 1744.08238 | 80,000,000 | 1434.25699 |

10,000,000 | 1661.91273 | 85,000,000 | 1428.03274 |

15,000,000 | 1615.32473 | 90,000,000 | 1422.18528 |

20,000,000 | 1582.92424 | 95,000,000 | 1416.67270 |

25,000,000 | 1558.16337 | 100,000,000 | 1411.45968 |

30,000,000 | 1538.17126 | 200,000,000 | 1342.59599 |

35,000,000 | 1521.43492 | 300,000,000 | 1303.65968 |

40,000,000 | 1507.06016 | 400,000,000 | 1276.62594 |

45,000,000 | 1494.47505 | 500,000,000 | 1255.99123 |

50,000,000 | 1483.29191 | 600,000,000 | 1239.3462 |

55,000,000 | 1473.23605 | 700,000,000 | 1225.42251 |

60,000,000 | 1464.10579 | 800,000,000 | 1213.47126 |

65,000,000 | 1455.74882 | 900,000,000 | 1203.01377 |

70,000,000 | 1448.04730 | 1,000,000,000 | 1193.72581 |

75,000,000 | 1440.90824 |

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**MDPI and ACS Style**

Lu, L.; Xue, Q.; Zhang, M.; Liu, L.; Wu, Z.
Non-Structural Damage Verification of the High Pressure Pump Assembly Ball Valve in the Gasoline Direct Injection Vehicle System. *Processes* **2019**, *7*, 857.
https://doi.org/10.3390/pr7110857

**AMA Style**

Lu L, Xue Q, Zhang M, Liu L, Wu Z.
Non-Structural Damage Verification of the High Pressure Pump Assembly Ball Valve in the Gasoline Direct Injection Vehicle System. *Processes*. 2019; 7(11):857.
https://doi.org/10.3390/pr7110857

**Chicago/Turabian Style**

Lu, Liang, Qilong Xue, Manyi Zhang, Liangliang Liu, and Zhongyu Wu.
2019. "Non-Structural Damage Verification of the High Pressure Pump Assembly Ball Valve in the Gasoline Direct Injection Vehicle System" *Processes* 7, no. 11: 857.
https://doi.org/10.3390/pr7110857