# Performance Study of Piezoelectric Injection System Based on Finite Element Simulation

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Finite Element Modeling and Simulation of Droplet Ejection Process

#### 2.1. The Process of Building the Finite Element Model

#### 2.1.1. CAD Model

#### 2.1.2. Theoretical Model

- (i)
- the fluid is an incompressible Newtonian fluid,
- (ii)
- the jetting time is short and the influence of temperature gradient can be ignored.

#### 2.1.3. Generate Meshes and Boundary Conditions

#### 2.2. Finite Element Model

## 3. Experimental Verification

^{−1}. Similarly, the average value of the droplet diameter obtained was 463.2 μm.

^{−1}, with an error of 3.02% from the experimental results, and the droplet diameter predicted by the model is 463.2 μm, with an error of 2.20% from the experimental results, which proves that the finite element model proposed in this paper can predict the jetting velocity and droplet diameter accurately.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Design of the studied piezoelectric ejection system and dimensions of core components (nozzle and needle). (

**a**) Physical drawings, (

**b**) three-dimensional drawings, (

**c**) two-dimensional simplified drawings, (

**d**) two-dimensional drawings of core components.

**Figure 4.**Velocity variation of the virtual probe (point P) in case 7 at different moments: (

**a**) time = 0.0002 s, (

**b**) time = 0.0004 s, (

**c**) time = 0.0006 s, (

**d**) time = 0.0008 s, (

**e**) time = 0.001 s, (

**f**) = 0.0012 s.

**Figure 5.**Results of finite element simulation of droplet diameter at different times in case 7: (

**a**) time = 0.0002 s, (

**b**) time = 0.0004 s, (

**c**) time = 0.0006 s, (

**d**) time = 0.0008 s, (

**e**) time = 0.001 s, (

**f**) = 0.0012 s.

**Figure 7.**Variation in droplet diameter with time, for different cases. (

**a**) variation of droplet diameter with time for different cases, (

**b**) case.1, (

**c**) case.7, (

**d**) case.13, (

**e**) case.19, (

**f**) case.25, (

**g**) case.30.

**Figure 10.**Displacement of the second group of experiments at different moments. (

**a**) initial state of the droplet, (

**b**) the displacement of the 16.73 ms, (

**c**) the displacement of the droplet at 19.93 ms.

**Figure 12.**Experimental and simulation comparison of jetting velocity and droplet diameter for case 27.

Parameter | Fluid Viscosity | Fluid Density | Surface Tension |
---|---|---|---|

Value | 0.02 Pa.s | 1.45 g/cm^{3} | 0.05 N/m |

Data Case No. | Needle Diameter (mm) | Nozzle Diameter (mm) | Nozzle Taper (°) | Needle Speed m s ^{−1} | Jetting Velocity m s ^{−1} | Droplet Diameter (μm) |
---|---|---|---|---|---|---|

N_{A} | N_{B} | N_{C} | N_{D} | |||

1. | 1 | 0.04 | 60 | 0.3 | 4.13 | 320 |

2. | 1 | 0.08 | 75 | 0.4 | 4.21 | 419 |

3. | 1 | 0.12 | 90 | 0.5 | 3.36 | 376 |

4. | 1 | 0.16 | 105 | 0.6 | 2.79 | 326 |

5. | 1 | 0.20 | 120 | 0.7 | 2.34 | 313 |

6. | 1.25 | 0.04 | 75 | 0.7 | 12.80 | 247 |

7. | 1.25 | 0.08 | 90 | 0.3 | 3.52 | 436 |

8. | 1.25 | 0.12 | 105 | 0.4 | 2.86 | 381 |

9. | 1.25 | 0.16 | 120 | 0.5 | 2.36 | 338 |

10. | 1.25 | 0.20 | 60 | 0.6 | 3.78 | 487 |

11. | 1.5 | 0.04 | 90 | 0.6 | 16.13 | 340 |

12. | 1.5 | 0.08 | 105 | 0.7 | 7.78 | 317 |

13. | 1.5 | 0.12 | 120 | 0.3 | 2.13 | 378 |

14. | 1.5 | 0.16 | 60 | 0.4 | 3.58 | 568 |

15. | 1.5 | 0.20 | 75 | 0.5 | 3.35 | 476 |

16. | 1.75 | 0.04 | 105 | 0.5 | 11.00 | 281 |

17. | 1.75 | 0.08 | 120 | 0.6 | 6.69 | 331 |

18. | 1.75 | 0.12 | 60 | 0.7 | 8.96 | 520 |

19. | 1.75 | 0.16 | 75 | 0.3 | 2.85 | 546 |

20. | 1.75 | 0.20 | 90 | 0.4 | 2.83 | 445 |

21. | 2 | 0.04 | 120 | 0.4 | 10.33 | 223 |

22. | 2 | 0.08 | 60 | 0.5 | 11.37 | 614 |

23. | 2 | 0.12 | 75 | 0.6 | 8.21 | 525 |

24. | 2 | 0.16 | 90 | 0.7 | 6.78 | 427 |

25. | 2 | 0.20 | 105 | 0.3 | 2.12 | 461 |

26. | 1 | 0.04 | 60 | 0.7 | 15.25 | 296 |

27. | 1.25 | 0.16 | 75 | 0.5 | 3.53 | 453 |

28. | 1.5 | 0.08 | 90 | 0.3 | 4.08 | 439 |

29. | 1.75 | 0.2 | 105 | 0.6 | 3.76 | 384 |

30. | 2 | 0.12 | 120 | 0.4 | 3.73 | 398 |

Group | Num. | Displacement (m) | Time (s) | Droplet Diameter (μm) | Jetting Velocity (m/s) |
---|---|---|---|---|---|

Group 1 | 1 | 0.055 | 0.01573 | 483 | 3.51 |

2 | 0.066 | 0.01890 | |||

Group 2 | 3 | 0.058 | 0.01673 | 432 | 3.58 |

4 | 0.069 | 0.01993 | |||

Group 3 | 5 | 0.060 | 0.01699 | 466 | 3.69 |

6 | 0.072 | 0.02042 | |||

Group 4 | 7 | 0.073 | 0.01946 | 458 | 3.75 |

8 | 0.085 | 0.02269 | |||

Group 5 | 9 | 0.078 | 0.02251 | 477 | 3.66 |

10 | 0.091 | 0.02630 | |||

Average value | 463.2 | 3.64 |

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**MDPI and ACS Style**

Li, X.; Zhao, Y. Performance Study of Piezoelectric Injection System Based on Finite Element Simulation. *Micromachines* **2023**, *14*, 738.
https://doi.org/10.3390/mi14040738

**AMA Style**

Li X, Zhao Y. Performance Study of Piezoelectric Injection System Based on Finite Element Simulation. *Micromachines*. 2023; 14(4):738.
https://doi.org/10.3390/mi14040738

**Chicago/Turabian Style**

Li, Xin, and Yongsheng Zhao. 2023. "Performance Study of Piezoelectric Injection System Based on Finite Element Simulation" *Micromachines* 14, no. 4: 738.
https://doi.org/10.3390/mi14040738