Research on Mathematical Model of Composite Micromachining of Laser and Electrolysis Based on the Electrolyte Fluid

A new technology of composite micromachining of laser and electrolysis is presented through a combination of technological advantages of laser processing and electrolytic machining.The implication of its method is that laser processing efficiently removes metallic materials and that pulse electrolytic machining removes recast layer and controls shape precisely. Machining accuracy and efficiency can be improved.The impacts that electrolyte fluid effectively cools themicrostructure edge in the lasermachining process and that gas-liquid two-phase flow makes the electrolyte conductivity produce uneven distribution in the electrolytic processing are considered. Some approximate assumptions are proposed on the actual conditions of machining process. The mathematical model of composite micromachining of laser and electrolysis based on the electrolyte fluid is built. The validity of the model can be verified by experimentation. The experimental results show that processing accuracy meets accuracy requirements which are ±0.05mm. Machining efficiency increases more than 20 percent compared to electrolytic processing.


Introduction
Laser processing and electrolytic processing are widely used in manufacturing technology of precision machining of microsystem.Laser micromachining method has the advantages of high efficiency, high precision, and low cost.However, there are still a series of processing defects to be controlled difficultly, such as edge microcrack, heat affected zone, and recast layer [1][2][3][4][5][6][7].Electrolytic micromachining method has the advantages of good surface quality, no heat affected zone, and high machining accuracy.However, there are control problems, such as low machining efficiency, horizontal corrosion, and difficult exclusion of electrolytic products [8][9][10][11][12][13][14].Therefore, it is very necessary to explore a new micromachining method to solve the machining problems of high precision, high efficiency, and high quality of metallic microstructure.
In this paper, a new technology of composite micromachining of laser and electrolysis is presented through a combination of technological advantages of laser processing and electrolytic machining.The implication of its method is that laser processing efficiently removes metallic materials and that pulse electrolytic machining removes recast layer and controls shape precisely.Machining accuracy and efficiency can be improved.It can achieve micron scale machining size and micron scale processing accuracy.It will provide technical support for the micromachining method of microparts in aerospace manufacturing industry with high precision, high efficiency, and low cost.
In order to solve the practical problems, this paper considers the impacts that electrolyte fluid effectively cools the microstructure edge in the laser machining process and that gas-liquid two-phase flow makes the electrolyte conductivity produce uneven distribution in the electrolytic processing.Some approximate assumptions are proposed on the actual conditions of composite micromachining process.The mathematical model of composite micromachining of laser and electrolysis based on the electrolyte fluid is built.The validity of the model is verified by experimentation.

Composite Micromachining Process Model
In order to reduce the attenuation of laser energy by hydrogen bubble and electrolytic product, composite micromachining method adopts time division control of laser and electrolysis.
Negative effects that electrolytic machining has on laser processing can be eliminated.Composite micromachining process model of laser and electrolysis is shown in Figure 1 and its processing sequence is shown in Figure 2. In the time of  1 , green laser processing based on electrolyte fluid can greatly reduce heat affected zone, thermal deformation, and heat damage to keep original structure of materials.Laser beams can still continue to transfer along the original optical path when the electrolyte fluid is scattered around the surface of the workpiece.Therefore, it can improve locality and accuracy by these methods.In the time of  2 , nonlinear characteristic of - curve of current efficiency is strengthened by high frequency microsecond pulse electrolysis power.Electrochemical reaction is limited by side wall insulating tubular electrode on the workpiece area corresponding to the end of electrode.The relative stability of concentration and temperature of electrolyte is maintained by electrolyte system based on PLC.Hydroxide precipitation is not easy to be generated by low concentration of acid composite solution.Pulse electrolytic machining can remove recast layer and control shape precisely by means of these methods.Meanwhile, it makes use of passive film to avoid stray corrosion effectively on the nonprocessing area.So there are these methods that can improve machining stability and precision.In the time of  3 , hydrogen gas bubble and electrolytic processing product can be evacuated from the tubular electrode in order to reduce the attenuation of laser energy.Therefore, composite micromachining can be realized in the time of segmentation with the repeated iteration of laser processing results and electrochemical processing results.
For one thing, there is a part of laser energy that can be used to remove workpiece materials efficiently.The depth of microhole is produced.For another thing, the materials are heated up by another part of laser energy so that their electrochemical dissolution speed can be faster than others.Pulse electrolytic machining removes recast layer and controls shape precisely because of electrochemical anodic dissolution.Machining quality and accuracy can be improved.Time division control can reduce the attenuation of laser energy by hydrogen bubble and electrolytic product.It can eliminate negative effects of laser processing acted on by electrolytic machining.The continuous cooling of materials can greatly reduce thermal effect by electrolyte fluid.It can reduce thermal deformation and heat damage and keep their original structure.Electrolyte fluid can duly discharge electrolytic product, bubble, and Joule heat in machining gap.It can eliminate concentration polarization and equilibrate electrical conductivity.Consequently these means can improve machining efficiency and accuracy.

Mathematical Model of Composite Micromachining of Laser and Electrolysis Based on the Electrolyte Fluid
According to the actual conditions of composite micromachining process, some approximate assumptions are proposed.The mathematical model of composite micromachining of laser and electrolysis based on the electrolyte fluid is built.It is based on the temperature field model of laser processing, electric field model of electrolytic machining, flow field model of electrolyte fluid, and their coupling relationship.It can provide theoretical basis for establishing the experimental system of composite micromachining process.

Mathematical Model of Temperature Field Based on Laser
Processing.In order to study temperature field distribution on the surface of workpiece, the following assumptions are put forward [15,16].
(1) Laser beam in space appears to be on the basic mode of Gaussian distribution.
(2) Workpiece materials are homogeneous mediums with isotropic properties.Physical thermal parameters of materials are constant.(3) Molten metals are removed completely under the action of the rapid expansion of plasma and vapor particles.
(4) Removal of metals by gasification is ignored.
(5) The situation that plasma impacts absorption during laser processing is not considered.
Model of temperature field based on laser processing is shown in Figure 3.
Mathematical model equations of temperature field distribution in the laser micromachining gap is as shown in the following [17,18]: The first boundary condition is as follows.
Temperature on the processing boundary is as shown in the following: The second boundary condition is as follows.
Heat flux density of laser source on the processing boundary is as shown in the following [16,19]: In the formula,  is laser absorption rate of metallic materials,  is peak power of laser pulses,  is radius of laser beam waist,  is  axial distance from the center of heat source, () is attenuation coefficient of laser in the electrolyte, and  is laser transmission length in the electrolyte.
The third boundary condition is as follows.
The interface condition of phase transition is as shown in the following [16,17]: In the formula, ℎ  is convection heat transfer coefficient of electrolyte fluid,  is materials surface temperature after laser processing,  0 is initial temperature which is equal to electrolyte temperature,  is Stefan-Boltzmann constant, and  is thermal radiation rate of metallic materials.Peripheral interface condition of work piece is as shown in the following [16,17]: In the formula, ℎ is natural convection heat transfer coefficient of electrolyte.
The finite element difference method is used to calculate the above formulas.The temperature field distribution of single laser pulse processing can be acquired.Therefore, section profile of laser micromachining can be obtained by the removal of material above the melting temperature.

Mathematical Model of Electric Field Based on Electrolytic
Processing.In order to study the electric field distribution on the surface of workpiece, the following assumptions are put forward [20][21][22][23].
(1) Electric field in machining gap is regarded as electric field in the passive electric conduction medium.
(2) Electrolytic machining has been in a state of balancing process.
(3) Electrolyte is isotropic in the machining process.In other words, the electrical conductivity of electrolyte is the same and constant everywhere.
(4) Anodic electrochemical dissolution obeys Faraday's law.Electric potential distribution is in accord with Laplace equation.
(5) After tubular electrode adsorbs hydrogen and other gases in the machining process, primary battery is formed to produce antielectromotive force.Therefore, voltage drop of electrolyte is regarded as the boundary condition of anode surface to analyse electric field distribution in machining gap.
Model of electric field based on electrolytic processing is shown in Figure 4.  Mathematical model equations of electric potential distribution in electrochemical micromachining gap are as shown in the following: Boundary condition of cathode surface is as shown in the following: Boundary condition of anodic surface is as shown in the following: Electrolytic removal rate of anodic surface is as shown in the following: In the formula,  is voltage between cathode and anode,  is decomposition voltage,   and   are electrolytic removal velocity components,  is actual volume electrochemical equivalent,  is electrical conductivity of electrolyte, and   and   are electric field intensity components.
First of all, removal rates of electrolytic processing on the surface of workpiece can be acquired by the above formulas and boundary conditions.Besides, section profile of electrochemical micromachining is obtained by time integration.

Mathematical Model of Flow Field Based on Electrolyte
Fluid.In order to study flow field distribution in composite micromachining gap, the following assumptions are put forward [24].(1) Electrolyte is continuous incompressible viscous fluid.
(2) The energy dissipation caused by the change of medium temperature can be neglected in the machining process.The flow field is constrained by mass conservation equation and momentum conservation equation.
(3) In the case of high strain rate and larger streamline bending degree, the effects of rotation in mean flow and swirl flow acted on by turbulent flow and low Reynolds number are considered to better deal with the flow.
(4) The influence of gravity is ignored because the machining gap is very small.
Model of flow field based on electrolyte fluid is shown in Figure 5.
Mass conservation equation of incompressible viscous fluid is as shown in the following [25,26]: In the formula,  is electrolyte density and  and V are speed components.
Momentum conservation equation of incompressible viscous fluid is as shown in the following [23]: In the formula,  is pressure,   ,   , and   are viscous stress components, and   and   are mass force components.
The distribution of electrolyte pressure on the surface of workpiece is obtained by the above formulas and boundary conditions.

The Coupled Model of Temperature Field and Flow Field of Laser Processing
Based on Electrolyte Fluid.The comparison of heat conduction of workpiece in the laser machining process is shown in Figure 6.The traditional laser processing must produce heat affected zone and thermal deformation.Laser processing based on electrolyte fluid makes use of electrolyte fluid to effectively cool the edge of microstructure in the machining process.The heat is duly taken away from the ablation zone of microstructure in the first laser pulse interval so that the heat cannot be further conducted to the workpiece.Therefore, thermal deformation and heat damage of materials can be greatly reduced to keep their original structure [27].
In the laser machining process, the changes of convection heat transfer coefficient are caused by pressure changes of electrolyte fluid.It has an influence on laser processing forming.Consequently, the coupling relationship between temperature field and flow field takes convection heat transfer coefficient as a coupling variable, which is shown in the following [16,28]: In the formula, Nu = 0.7212Pr 0.37 Re 0.5 , Pr =   / wat , Re = V wat  ℎ /], V wat = √(2 * )/  ,  wat is thermal conductivity of electrolyte,  is characteristic size of electrolyte fluid, Nu is Nusselt number of electrolyte, Pr is Prandtl number, Re is Reynolds number,  is dynamic viscosity of electrolyte,   is isobaric specific heat of electrolyte, V wat is average velocity of electrolyte fluid,  ℎ is hydraulic diameter of electrolyte fluid, V is kinematic viscosity coefficient of electrolyte fluid,  is electrolyte pressure, and   is electrolyte density.

The Coupled Model of Electric Field and Flow Field of Electrolytic Machining Based on Gas-Liquid Two-Phase Flow.
In the electrolytic machining process, hydrogen gas is produced on the cathode.Electrolytic products, oxygen gas, and other gases are produced because of anodic dissolution.It is not considered that small volume ratio of electrolytic products has an influence on electrical conductivity and density of electrolyte.Therefore, the case can be simplified as gasliquid two-phase flow.Model of gas-liquid two-phase flow in machining gap is shown in Figure 7.The following assumptions are put forward [20,23].
(1) Electrolytic processing has been in a state of equilibrium.Machining gap has reached balance gap.Anodic corrosion rate is equal to cathode feed speed.Heat exchange of electrolyte and tool electrodes has been in balance state.
(2) The surfaces of cathode and anode are equal potential surfaces.Nonlinear mutation of electrode potential approximates to decomposition voltage at the interface of electrodes and solution.The electrical potential gradient is the same in the direction perpendicular to flow speed of electrolyte.
(3) The liquid phase cannot be compressed in the machining gap.The changes of gas phase state obey the ideal gas state equation.There is no mass transfer between two phases.Air bubble is uniform distribution in liquid phase.Phase parameters of cross sections are equal along the flow direction.
The generated gases are uniformly mixed in the electrolyte flowing through the machining gap, which is in the form of small air bubbles.Gas-liquid two-phase flow can be produced.Electrical conductivity of electrolyte decreases with the increase of gas content.At the same time, it produces uneven distribution because of Joule heat generated by machining current.After a certain transient process, electrolyte temperature is in a stable state.That is to say, it is steady state temperature field.In order to simplify the  problem, the effect of temperature on electrical conductivity is neglected.The coupling relationship of electric field and flow field of electrolytic machining based on gas-liquid twophase flow is as shown in the following [20,23]: In the formula,  =     ||/(    || + Δ 0  0 ),  =  0 +   ||,   =  0  2 / 1  1  0 ,   =     ,  =  0 , Δ 0 = ( − )/,  0 is electrical conductivity at the inlet,  is bubble ratio,   is gas state constant of hydrogen gas,  0 is initial temperature of electrolyte,  1 is electrolyte density,  1 is specific heat of electrolyte,   is current efficiency of hydrogen evolution which is equal to electrolytic machining efficiency expressed by ","   is electrochemical equivalent of hydrogen evolution,  is current density, Δ 0 is machining gap of cross section of process ,  is electric field intensity,  0 is flow speed at the inlet of machining gap, and  is pressure.

Experiments of Composite Micromachining Process
According to mathematical model of composite micromachining process, APDL is used to establish the experimental system, which is the abbreviation for "ANSYS parametric design language."Its forming law is analyzed on the basis of temperature cloud chart of laser processing and electric field intensity cloud chart of electrolytic machining.The validity of its mathematical model is verified from the aspects of machining precision and efficiency.

Numerical Simulation Process of Experimental System
of Composite Micromachining Process.Numerical simulation process of experimental system of composite micromachining process is shown in Figure 8. APDL was used to establish its experimental system.Thermal module, FLOTRAN CFD module, and electric module could be called on the platform of ANSYS system to conduct the simulation of its experimental system.The initial boundary of electrolytic machining was achieved by simulation results of laser processing.Final machining profile could be obtained by repeated iteration between the results of laser processing and the results of electrolytic machining.

Experimental Verification of Composite Micromachining
Process.In the process of laser machining, convection heat transfer coefficient was calculated according to pressure of electrolyte fluid.The temperature field distribution on the feed rate of electrochemical machining was 15 um/s.The geometric scale of side wall insulating tubular electrode was that internal diameter was 0.15 mm and external diameter was 0.5 mm.Other process parameters were the same as composite micromachining.Its material removal rate was 66.22 ug/s.The material removal rate of composite micromachining was 32.87% higher than electrochemical machining.Process requirements could be met where machining efficiency increased more than 20 percent compared to electrolytic processing.Therefore, it is the forming law of composite micromachining that microsecond pulse laser processing efficiently removes metallic materials on the machining area and that microsecond pulse electrolytic machining efficiently removes recast layer in the hole wall and controls shape precisely.

Conclusion
The following is a summary of the conclusions.
(1) In this paper, a new technology of composite micromachining of laser and electrolysis is presented through a combination of technological advantages of laser processing and electrolytic machining.The implication of its method is that laser processing efficiently removes metallic materials and that pulse electrolytic machining removes recast layer and controls shape precisely.It can solve the micromachining problems of high precision, high efficiency, and low cost of metallic microstructure in manufacturing technology of microsystem.It will lay the technical foundation for the development of new composite micromachining method of laser and electrolysis.
(2) The effects where electrolyte fluid effectively cools the microstructure edge and gas-liquid two-phase flow makes the electrolyte conductivity produce uneven distribution are considered in the composite micromachining.Some approximate assumptions of its actual conditions are proposed.Based on the temperature field model, electric field model, flow field model, and their coupling relationship, the mathematical model of composite micromachining of laser and electrolysis based on the electrolyte fluid is built.It can provide theoretical basis for establishing the experimental system of composite micromachining process.
(3) According to the mathematical model, the experimental system of composite micromachining process is established.By the experimental verification, the processing accuracy meets accuracy requirements which are ±0.05mm.The machining efficiency increases more than 20 percent compared to electrolytic processing.Therefore, the validity of its mathematical model is demonstrated.
(4) It is the forming law of composite micromachining that microsecond pulse laser processing based on the electrolyte fluid efficiently removes metallic materials on the machining area and that microsecond pulse electrolytic machining efficiently removes recast layer in the hole wall and controls shape precisely.
To sum up, this paper presents a new technology of composite micromachining of laser and electrolysis.The mathematical model of composite micromachining of laser and electrolysis based on the electrolyte fluid is built, of which the validity is demonstrated by experiment.It will lay the

Figure 3 :
Figure 3: Model of temperature field based on laser processing.

Figure 4 :
Figure 4: Model of electric field based on electrolytic processing.

Figure 5 :
Figure 5: Model of flow field based on electrolyte fluid.

Figure 6 :
Figure 6: The comparison of heat conduction of workpiece in the laser machining process.

Figure 7 :
Figure 7: Model of gas-liquid two-phase flow in machining gap.

Figure 8 :
Figure 8: Numerical simulation process of experimental system of composite micromachining process.

Figure 12 :Figure 13 :
Figure 12: Electric field intensity cloud chart of electrochemical machining in the first laser pulse interval and radial electric field strength distribution diagram on the surface of workpiece. :