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In electrical discharge machining (EDM) process, the debris removed from electrode material strongly affects the machining efficiency and accuracy, especially for the deep small hole machining process. In case of Ti alloy, the debris movement and removal process in gap flow between electrodes for small hole EDM process is studied in this paper. Based on the solid-liquid two-phase flow equation, the mathematical model on the gap flow field with flushing and self-adaptive disturbation is developed. In our 3D simulation process, the count of debris increases with number of EDM discharge cycles, and the disturbation generated by the movement of self-adaptive tool in the gap flow is considered. The methods of smoothing and remeshing are also applied in the modeling process to enable a movable tool. Under different depth, flushing velocity, and tool diameter, the distribution of velocity field, pressure field of gap flow, and debris movement are analyzed. The statistical study of debris distribution under different machining conditions is also carried out. Finally, a series of experiments are conducted on a self-made machine to verify the 3D simulation model. The experiment results show the burn mark at hole bottom and the tapered wall, which corresponds well with the simulating conclusion.

Titanium (Ti) alloy is an excellent candidate for aerospace, biomedical applications and ocean development owing to the high specific strength and excellent corrosion resistance. In a traditional hole drilling the high tensile strength and low thermal conductivity of Ti alloy can result in a large machining force, high machining temperature, high tool wear, and poor accuracy, especially for deep small hole machining.

EDM could remove the material by spark erosion, which produces the local high temperature to melt and vaporize the material at the workpiece surface. During EDM process [

There are many researchers studying the debris removal mechanism in EDM process for deep small hole. Koenig et al. built a mathematical model of bottom gap flow field with flushing and calculated the pressure and velocity field [

For above available results, most researchers only developed the single discharge machining models. Actually, the debris is continuously generated in EDM process. Besides, the flow disturbation generated by the movement is not considered. So the debris movement process for multicycle discharge with tool movement in EDM is not fully understood.

This paper develops a mathematical model that considers tool movement in solid-liquid two-phase gap flow field and a 3D model to simulate the tool movement and debris generation when the tool electrode conducts self-adaptive movement. Besides, the debris is generated continuously in the gap between the tool and workpiece. Such simulation is much closer to the real machining process.

EDM as a nontraditional machining method uses the electrothermal effect of pulsed spark discharge between tool and workpiece to remove the material in dielectric fluid. When the distance between the electrodes is reduced to 10^{2} ^{4°}C and a very high pressure in a local minimal area [

As the process going on, a certain amount of material will be removed and the debris will be generated continuously. The accumulative debris can influence the break down process and machining efficiency. During the small hole machining process, the debris is regularly swept away from the machining region by flow of flushing. However, in a deep small hole machining, the flushing effect on debris at the bottom of the hole becomes weak. In addition to the flushing, the tool motion could facilitate the debris removal. As the operation progresses, the servo mechanism controls tool to make self-adaptive movement and maintains a proper gap. Meanwhile the servo movement of tool generates the disturbation to the gap flow. When the tool moves up, a negative pressure zone forms at the bottom and fresh dielectric is drawn into the gap, which lowers the concentration of debris, as shown in Figure

Schematics of tool movement model.

In solid-liquid two-phase flow field, the drag force of particles

The particle is considered to be spherical.

The particle reflects back when colliding with the wall or other particles.

The ambient temperature and machining region temperature are considered as a constant, no heat exchanges.

The fluid field is considered to be infinite, inviscid, and uncompressible.

There is no friction con the inner wall of hole.

Figure

Schematics of interelectrode gap.

Naviers-Stokes equation can be simplified as follows:

Considering the impact of flushing on fluid velocity, the fluid velocity

From the equations above, we deduce that when the depth of gap (

Figure

The schematics of 2D boundary conditions and 3D meshed model.

Boundary conditions

3D model

3D meshed model

The boundary conditions are shown in Figure

This paper assumes simulation cycle and discharge cycle at 0.02 s and 20

Continuous discharge simulating parameters.

Parameter | Description |
---|---|

Dielectric fluid | Deionized water |

Tool | Copper |

Workpiece | TC4 |

Tool velocity | 0.01 m/s |

Polarity | Positive |

Diameter (mm) | 1, 2 |

Flushing vel. (m/s) | 0, 2, 5 |

Depth (mm) | 0.5, 2.0, 3.5, 5.0 |

Without flushing, the simulation results of 1 mm tool diameter are shown in Figures

Gap flow field with 0.5 mm deep hole.

After half a period

After one period

Gap flow field with 2 mm deep hole.

After half a period

After one period

In ordinary EDM machining, the flushing is introduced to bring fresh dielectric fluid into the gap and lower the debris concentration. In order to conduct the impact of flushing on the debris distribution, the flushing is applied in simulation model. In the model with flushing, a dielectric tube aimed at the gap between tool and workpiece induces the flow through the machining gap. Figures

Schematics of gap flow field with flushing at 2 m/s and 0.5 mm deep hole.

Velocity field

Pressure field

Debris distribution

Schematics of gap flow field with flushing at 5 m/s and 0.5 mm deep hole.

Velocity field

Pressure field

Debris distribution

Schematics of gap flow field with flushing at 2 m/s and 2 mm deep hole.

Velocity field

Pressure field

Debris distribution

Schematics of gap flow field with flushing at 5 m/s and 2 mm deep hole.

Velocity field

Pressure field

Debris distribution

Schematics of gap flow field with flushing at 2 m/s and 3.5 mm deep hole.

Velocity field

Pressure field

Debris distribution

Schematics of gap flow field with flushing at 5 m/s and 3.5 mm deep hole.

Velocity field

Pressure field

Debris distribution

Schematics of gap flow field with flushing at 2 m/s and 0.5 mm deep hole.

Velocity field

Pressure field

Debris distribution

Schematics of gap flow field with flushing at 5 m/s and 0.5 mm deep hole.

Velocity field

Pressure field

Debris distribution

Figure

Figure

Figure

Figure

As shown from Figures

Compared with Figures

Figures

Schematics of gap flow field with flushing at 2 m/s and 2 mm deep hole.

Velocity field

Pressure field

Debris distribution

Schematics of gap flow field with flushing at 5 m/s and 2 mm deep hole.

Velocity field

Pressure field

Debris distribution

Schematics of gap flow field with flushing at 2 m/s and 3.5 mm deep hole.

Velocity field

Pressure field

Debris distribution

Schematics of gap flow field with flushing at 5 m/s and 3.5 mm deep hole.

Velocity field

Pressure field

Debris distribution

Schematics of gap flow field with flushing at 2 m/s and 5 mm deep hole.

Velocity field

Pressure field

Debris distribution

Schematics of gap flow field with flushing at 5 m/s and 5 mm deep hole.

Velocity field

Pressure field

Debris distribution

Figure

Figures

Comparing 3.5 mm deep hole with 5 mm, as shown in Figures

Combining the above analysis, one conclusion could be drawn that, for the 2 mm tool diameter, the flushing fluid contains less resistance than those of 1 mm tool diameter, which results in the fluid with higher velocity. Finally, more debris is taken away by the flushing fluid. On the contrary, in situation with lower fluid velocity, the flushing fluid with insufficient drag force could hardly bring the debris out of bottom gap. Such phenomenon could be deduced for deep hole with micro- or smaller diameter.

In order to obtain the debris distribution in machining region, the coordinate of each debris is exported for statistics. For the convenience of analysis, the machining region is divided into 5 zones, as shown in Figure

Schematics of debris domain (moves from the top to the bottom).

Zone view

Bird view

Figure

Impact of depths on the debris distribution.

With the constant of tool diameter and fluid velocity in 5 m/s, the debris distribution is similar to that of fluid velocity in 2 m/s, except the debris distribution in S4 zone, just as shown in Figure

Figure

Impact of diameters on the debris distribution.

Figure

Comparing Figure

A conclusion can also be made that, in the case of a shallow hole, a larger diameter is conducive to remove more debris, whereas in a deeper hole, the tool diameter has little impact on the debris distribution, and debris can hardly be removed.

Figure

Debris statistical distribution of Cu and Ti in different conditions.

Impact of flushing velocities

Impact of tool diameters

Figure

The experiment is carried out on a self-made EDM machine. The detailed parameters applied are listed in Table

Continuous discharge simulating parameters.

Parameter | Description |
---|---|

Maintaining voltage ( |
15 V |

Peak current ( |
0.8 A |

Dielectric fluid | Deionized water |

Tool material | Red copper |

Workpiece material | TC4 |

Tool velocity | 0.01 m/s |

Tool diameter | 2 mm |

Depth (mm) | 0.5, 2.0, 3.5, 5.0 |

Flushing velocity (m/s) | 0, 2 |

The cross section image of machined holes without flushing.

0.5 mm deep hole

2 mm deep hole

The cross section image of machined holes with flushing.

0.5 mm deep hole

2 mm deep hole

3.5 mm deep hole

5 mm deep hole

Figures

Figure

For 3.5 mm deep hole, the burn mark appears at the lower right corner of the hole, which illustrates that most debris accumulates at the lower right corner under the influence of flushing, as shown in Figure

When processing 5 mm deep hole with 2 mm tool diameter, as shown in Figure

This paper researches the effect law of machining parameters to the gap flow field and debris movement. Besides the disturbation induced by self-adaptive movement on the gap flow is considered. Based on the solid-liquid two-phase flow, a mathematical model of fluid in gap flow field and debris movement is derived. The methods of smoothing and remeshing are also considered. The real situation of continuous discharging and debris generating is taken into account, a simulation model of the small hole gap flow field in EDM and debris distribution was established, 3D model simulates the influence of tool movement, machining depth, flushing velocity, and tool diameter on interelectrode gap flow field, and debris distribution was analyzed; furthermore, the mathematical model was verified by the experimental results. The conclusions are listed as follows:

During the machining, the self-adaptive movement of tool can generate disturbance to the machining region, which is positive for the debris removal. However, in the case of deep hole machining, the impact of flushing is of limited effect.

The depth of the hole, flushing velocity and tool diameter influence the gap flow field and debris distribution. Normally, with the increasing depth of machining hole, the fluid velocity declines at the bottom gap, and the debris is not easily removed. With the increase of flushing velocity, the fluid at the bottom takes more debris away. A large diameter is beneficial for reducing the resistance of fluid and debris removal. But when the depth of the machined hole increases to a certain degree, whose depth to diameter exceeds 3, the impact of flushing velocity and tool diameter on debris removal reduces obviously, which results in a lot of debris at the bottom. The side flushing is of limited effect.

During the small deep hole machining process, the cross section appearance of side walls as well as positions of the burn mark is in accordance with the simulating results of debris distribution and movement, which proves the effectiveness of mathematical model and simulation model.

The authors declare that they have no conflicts of interest.

The financial support by National Natural Science Foundation of China under Grant no. 51405058, Program for Liaoning Excellent Talents in University under Grant no. LR2015012, and Talent Special Foundation of Dalian City under Grant no. 2016RQ054 is acknowledged.