3D multiphysic simulations of energy field and material process in radial ultrasonic rolling electrochemical micromachining

Minghun WANG, Yongcho SHANG, Chngshun LIU, Jijie WANG,Jinsong ZHENG, Xufeng XU,b

a College of Mechanical Engineering, Zhejiang University of Technology, Hangzhou 310023, Zhejiang, China

b Key Laboratory of Special Purpose Equipment and Advanced Processing Technology of Ministry of Education,Zhejiang University of Technology, Hangzhou 310023, Zhejiang, China

KEYWORDS 3D Multiphysics simulation;Electrochemical micromachining;Energy field;Material process;Micro dimple;Ultrasonic vibration

Abstract The radial ultrasonic rolling electrochemical micromachining (RUR-EMM) combined rolling electrochemical micromachining (R-EMM) and ultrasonic vibration was studied in this paper.The fundamental understanding of the machining process especially the interaction between multiphysics in the interelectrode gap (IEG) was investigated and discussed by the finite element method.The multiphysics coupling model including flow field model,Joule heating model,material dissolution model and vibration model was built.3D multiphysics simulation based on micro dimples process in RUR-EMM and R-EMM was proposed. Simulation results showed that the electrolyte flowed into and out IEG periodically, gas bubbles were easy to squeeze out and the gas void fraction deceased about 16% to 54%, the maximum current density increased by 1.36 times in RUR-EMM than in R-EMM in one vibration period of time.And application of the ultrasonic vibration increased the electrolyte temperature about 1.3–4.4%in IEG.Verification experiments of the micro dimple process denoted better corrosion consistency of array dimples in RUR-EMM,there was no island at the micro dimple bottom which always formed in R-EMM, and an aggregated deviation of less than 8.7% for the micro dimple depth and 4% for the material removal amount between theory and experiment was obtained.

1. Introduction

Electrochemical micromachining (EMM) was a promising machining method in fabricating microstructures on metal surface for its advantages of removing material from ionic level,no heat or mechanical stress and no tool wear.EMM has been applied in automotive, aerospace, electronics, and communications industries for micro textures, micro grooves and micro pin, etc.

Nevertheless, EMM still had some problems with efficient material removal, disposal of byproducts, predicting of machined size. In order to solve these problems, additional energy field was applied in EMM. The assisted ultrasonic to EMM was proved by Kumar et al.and Natsu et al.to be an effective method to improve the efficiency of material removal, the machining accuracy and the surface quality of machined surfaces. Perusich and Alkire studied the effects of ultrasonic cavitation in IEG on the electrochemical oxide film by theoretical and experimental methods,and denoted that the high-speed micro-jet produced by ultrasonic cavitation bubbles was beneficial for discharging the byproducts and destroying the passivation layer on the workpiece surface. Ruszaj et al.and Liu et al.reported that the tool cathode ultrasonic vibration can effectively improve the processed surface quality of the workpiece in EMM. Nicoara˘ et al. found that the ultrasonic field made the anodic polarization curve move to the high current density region in EMM process,which proved that the ultrasonic vibration can effectively promote the substances transmission in IEG. Skoczypiecstudied ultrasonically assisted electrochemical machining (USAECM)by numerical method in 2D model and revealed the pressure and void fraction in IEG changed periodical in the ultrasonic vibration period,which promoted the heat and reactions products to remove out of machining area. However, the verification was not realized due to the cavitation phenomena.Natsu et al.found the replicating accuracy and the material removal rate can be effectively improved by applying ultrasonic vibration on cathode tool in ECM. Mitchell-Smith and Claredenoted the use of ultrasonic during electrochemical jet machining of titanium can increase the feature aspect ratio by increasing depth and reducing the overcut in the same machining parameters, and it also demonstrated the surface roughness can be reduced up to 31%with ultrasonic vibration in ECM. Ghoshal and Bhattacharyyadenoted the vibration of the tool was beneficial for improving the machining stability by promoting the flow of electrolyte in EMM. Wang et al.proved that ultrasonic vibration on cathode enhanced the disposal of byproducts in IEG and increased the aspect ratio of micro structures.Furthermore,micro dimples array was processed by using RUR-EMM, the machining efficiency and machined surface roughness are improved.

For predicting of machined size, the numerical simulation based on finite element method(FEM)was expected to be useful.Smets et al.proposed a more simple and positive method to calculated the temperature distribution during the pulse electrochemical machining through theoretical basisand numerical simulation.Fujisawa et al.analyzed the EMM process through a numerical model, the visual simulation results showed that the joule heat and bubbles in IEG made the material removal of the workpiece uneven which can greatly influence the machining accuracy. Deconinck et al.built a temperature dependent multi-domain model to discuss the temperature variation & electrolyte flow and workpiece shape, and found that the variation temperature can make the workpiece shape asymmetry.Hackert-Oschaetzchen et al.simulated the shape change of jet flow in jet electrochemical machining by using two steps, the jet was formed firstly and then the material removal was simulated by the change of surface topography of workpiece, where the byproducts was ignored. Klocke et al.introduced a multidisciplinary numerical model, which considered the influence of gas and temperature in the flow of electrolyte to make a more precisely simulation of macro ECM processes for aero engine blade manufacture, and a better machining result whose inlet and outlet area were more consistent was obtained. Mayank and Kuniedabuilt a two-phase indirect model to simulate the distribution of the gas volume fraction and then approximated the effective conductivity in IEG by using Bruggemann equation, and found the material removal rate at the outer region of machining area is lower than that of the central area with the axisymmetric tool. Zhu et al.established a threedimensional flow field model to obtain the best flow field in the diffuser electrochemical machining process and found that increasing the flow rate can make the flow field distribution more uniform.Gomez-Gallegos et al.built a 3D multiphysics model to predict the current density, conductivity, flow velocity,temperature in IEG and the workpiece shape development,which was helpful for understanding ECM process, however,the effects of any sludgy or gas bubbles were not considered in the multiphysics model. Chen et al.established a multiphysical coupling model of electric field, two-phase flow field and temperature field and the deviation of predicted machining gap between simulation and experiment is less than 50 μm.Wang et al.analyzed the influence of flow field, electric field and thermal field on the material removal process in airshielding electrochemical micromachining through the multiphysics model, and an aggregated deviation of less than 11.8% between experimental and theoretical results has been observed. Chen et al.developed a multiphysics coupling model to investigate the influence of temperature, gas volume fraction and conductivity in different flow mode on the machining process, results denoted jet flow mode was more suitable for micro groove with masked porous cathode.

Literatures have shown that the benefits of ultrasonic on material dissolution, disposal of byproducts and surface quality in EMM. Numerical simulation was a powerful and helpful tool for prediction of the machining process.However, fundamental understanding of the machining process in EMM, especially the interaction between different physical fields in IEG was still limiting the using of EMM. To investigate their influences on process and better understand the coupling effect between physical fields, the 3D multiphysics coupling model including flow field model,Joule heating model, material dissolution model and vibration model was built in this paper based on the radial ultrasonic rolling electrochemical micromachining (RUR-EMM)(Fig. 1), the distribution of electrolyte fluid, void fraction of gas, current density, temperature in IEG was investigated and their influences on machined micro dimples profile were compared with R-EMM and RUR-EMM.

Fig. 1 Scheme of developed model in RUR-EMM.

2. Model description and research zone

The schematic of the developed model in RUR-EMM is shown in Fig. 1. The ultrasonic transducer with micro-protrusion on its surface is used as cathode and is fixed on the spindle of machine tool (see Fig. 1(a)). The central part of radial ultrasonic vibration transducer is the piezoelectric ceramic which converts electrical signals into radial vibrations, and the part with micro protrusions fits tightly to the piezoelectric ceramic part which can promise all the micro protrusions on the electrode to vibrate radially at the same time. The machine tool spindle brings a rotary motion and the micro-protrusions on the surface of ultrasonic transducer generate radial vibration in RUR-EMM. With the electrolyte as the conductive medium, the material on workpiece (stainless steel) surface opposite the micro-protrusions is eroded to be micro dimples while the power is connected. Meanwhile, the X-directional vibration and Z-directional vibration are generated with the cathode rotating (see Fig. 1(b)). The X-direction vibration can realize the secondary machining to the side wall with the rotation of tool electrode which can reduce the roughness of the side wall and the Z-direction vibration is beneficial for leveling process to the bottom of micro dimple. So the Xdirectional vibration and –Z-directional vibration can make a better surface quality of the bottom and side wall of micro dimple. In order to investigate the variations of the multiphysics in the IEG and their influences on micro dimple process, a one-dimensional liner array is selected as the research zone, as shown in Fig. 1(c).

3. Multiphysics models in IEG

The multiphysical simulation model in this work is developed coupled with the gas-fluild flow, Joule heating effects, electric and vibration, which influences each other and affecting the material removal.The study is based on the following assumptions: 1) The gas density is negligible compared to the flow density.2)The motion of the gas bubbles relative to the liquid is determined by a balance between viscous drag and pressure forces.3)The processed material is homogeneous.4)There are no other sub-reactions and material removal only happens on the workpiece surface.

3.1. Flow field model

There exists liquid,gas and solid in IEG in RUR-EMM,solid can be ignored in study due to the small proportion. The Euler-Euler modeldescribes the dynamics model of each phase according to the momentum balance equation and the continuity equation. In this model,the gas and liquid are considered to be interpenetrating each other. The velocity of each phase is interacting on each other. The continuity equations for the gas–liquid phase can be described as

where uis the oscillation speed of sound waves in the flow field.

The distribution of flow field in IEG can be obtained from Eqs. (6), (7) and (8).

3.2. Joule heating model

In RUR-EMM, the increase of the temperature in IEG is mainly from the joule heat based on electric field and the reaction heat can be ignored compared to joule heat.The relationship between electric field and thermal field is as follows

3.3. Material dissolution model

According to I law of Faraday, the velocity of metal dissolution vcan be obtained as follows,

where M,z and ρ are the atomic weight,valence and density of dissolves metal respectively. F is the Faraday constant.

Substituting of Eq. (13) and Eq. (14) into Eq. (12), the velocity of metal dissolution is,

3.4. Moving mesh model

In RUR-EMM, the boundary of cathode and the profile of workpiece surface are changing with the process continues.This can be described by the moving mesh model,as for nodes in the mesh model, the moving velocity is as follows,

The coupling relationship between multiphysics is shown in Fig. 2.

First, with the ultrasonic vibration, there will be disturbances to the flow field in IEG which will increase the velocity of electrolyte and decrease the gas volume fraction. Then, the ultrasonic vibration can also promote the discharge of electrolyte products especially the bubbles in IEG which will decrease the gas volume fraction and make the electrical conductivity more uniform,so the current density will be larger in the processing. Finally, the larger current density means more violent electrochemical reaction and there is more heat of reaction being produced.So the ultrasonic vibration can also influence the thermal field.

Fig. 2 Coupling relationship between multiphysics.

4. Numerical simulation and discussions

4.1. Mesh model description

The 3D geometric model of research zone in the IEG (as shown in Fig. 1) is established as Fig. 3(a). Micro protrusion with sectional size of 0.5 mm×0.5 mm is applied in this model. Here, the machining gap is defined as the distance between the center point of the micro protrusion bottom and the workpiece surface. In this study, the initial machining gap is 50 μm. The tetrahedron element is used, and the model is divided into 62,194 elements with minimum size of 0.0114 mm and maximum size of 0.0383 mm. The grid quality factor is 0.6612.The grid is dense around the micro protrusion while it is coarse at other region in order to save the computing time.Moving grid auxiliary ensures the dynamic mesh moving smoothly and avoids the distortion.

According to the actual processing situation and consulting the relevant literature,the numerical simulation parameters are shown in Table 1.

4.2. Simulation results and discussions

In this study, based on the parameters listed in Table.1, the machining process for the cathode rotates from θ=3° to θ=-3° to the right of the workpiece is selected (see Fig. 4).Static electrolyte flow is used for processing, that is, the initial electrolyte flow velocity is 0. For comparison, the distribution of electric field, thermal field and the dynamic generationprocess of dimple in R-EMM and RUR-EMM are investigated and discussed respectively.

Table 1 Numerical simulation parameters.

4.2.1. Flow field characteristics in IEG

Fig.5(a)and Fig.5(c)show the cloud chart of flow velocity at T/2 and T during one period of vibration time in RUR-EMM respectively. The electrolyte flows out and flows into the narrow machining gap with the tool moves towards and deviates from the workpiece, the velocity is changing from 0 m/s to 8 m/s. The fluctuation of flow improves the discharge of the byproducts in IEG,the combination of gas bubbles is also prohibited.As for R-EMM,the electrolyte velocity is keeping low during the process which is unfavorable for byproducts removal (Fig. 5(e)).

Fig. 3 3D geometric model.

Fig. 4 Relative position of workpiece and micro protrusion at different stages in process.

Fig. 5 Cloud charts for flow velocity and gas void fraction in RUR-EMM and R-EMM in IEG.

Fig. 5(b) and Fig. 5(d), Fig. 5(f) show the cloud charts of gas void fraction in the IEG at T/2 and T time in RUREMM and in R-EMM. The photographs indicate that the gas void fraction in the narrow machining gap is lower in RUR-EMM than that in R-EMM. Compared to R-EMM,when the ultrasonic vibration is applied, the absolute value of pressure in IEG is increased,under the action of ultrasound,the pressure in IEG increases with the compression of the fluid and the instantaneous energy generated by the collapse of the bubbles, the growing of gas bubbles is forbidden and is washed out of the machining gap resulting lower gas void fraction. In R-EMM, with more material is eroded, bubbles will accumulate on the bottom of the cathode to form a bubble film which will decrease the electrical conductivity and prohibit the material removal.

Fig.6 shows the variation of the electrolyte velocity and gas void fraction for RUR-EMM and R-EMM in one vibration period of time at point A (0, 0, 25 μm). In R-EMM, the pressure and electrolyte velocity keep almost zero and the gas void fraction is about 50%, which are disadvantages for material removal in EMM.Comparing with R-EMM,the electrolyte velocity and gas void fraction in IEG change periodically in RUR-EMM due to the ultrasonic vibration. When cathode moves towards the workpiece at t= ((n+1/4)T,(n+3/4)T),the electrolyte in IEG is squeezed and ejects from the machining gap and reaches its maximum value -7.58 m/s at t=(n+1/2)T.During this time,the pressure is decreasing from 0.87 MPa to-0.87 MPa.Moreover,the gas void fraction changes between 34% and 23%. When cathode moves in direction opposite to workpiece at t=((n-1/4)T,(n+1/4)T),the electrolyte is absorbed and flows into the IEG and reaches its maximum value 7.58 m/s at t=nT. The pressure is increasing from-0.87 MPa to 0.87 MPa and the gas void fraction is changing between 42%and 34%.It shows that the fluctuation of fluid flow decreases the gas void fraction about 16%to 54% and the electrolyte renewal will be enhanced, this will benefit the machining process.

Fig. 6 Variations of velocity and gas volume fraction for REMM and RUR-EMM in one vibration period of time at point A.

4.2.2. The electric field characteristics in IEG

Fig. 7 shows the variation of the current density in RUREMM and R-EMM in one vibration period of time at point A (0, 0, 25 μm). It shows that the current density keeps about 139 A/cmin R-EMM during machining. However, the value of current density is changing between 122 A/cm(t=T/4)and 183 A/cm(t=3 T/4) when the ultrasonic vibration is applied.The maximum current density in RUR-EMM is about 1.36 times as much as in R-EMM in one vibration period of time.

Fig. 7 Variation of current density for R-EMM and RUREMM in one vibration period of time at point A.

The micro dimples generate on the workpiece surface with the cathode rotating and the workpiece moving at the same linear speed.In this study,the initial,middle and last stage are set when the cathode is 3°,0 and-3°to the right of the workpiece respectively, as shown in Fig. 4. Fig. 8 shows the 3D distribution of current density at different stage in RUR-EMM and REMM.At the initial stage(see Fig.8(a)and Fig.8(d)),in both RUR-EMM and R-EMM, the current density is asymmetrically distributed and the peak current density appears in the position of the smallest gap as tool electrode center line has an angle θ=3°with the workpiece vertical line which makes one side of the tool electrode closer to the workpiece surface.In R-EMM, the current density in central area is sunken because some electrolytic byproducts produced in the previous process are not removed immediately. At the middle stage when the tool electrode is vertical to the workpiece surface(see Fig.8(b)and Fig.8(e)),the distribution of current density in RUR-EMM is more uniform while that in R-EMM is uneven. In R-EMM, the electrolytic byproducts such as bubbles and impurities are accumulating in the center of the electrode which leads lower electrical conductivity, so the current density in the center of electrode is lower than other area around it. However, most of electrolytic byproducts are discharged by pulsating flow caused by ultrasonic vibration so that the distribution of current density is more uniform. At the last stage (see Fig. 8(c) and Fig. 8(f)), the current density is a little higher at one side than the other which is because that one side of the tool electrode is closer to the workpiece surface as θ=-3°.

The current density curves along line A(y=0,z=25 μm)at different stage are shown in Fig. 9. And A, B, C represent initial stage,middle stage and last stage in RUR-EMM respectively, A1, B1, C1 also correspond to this order in R-EMM.The distribution of current density is varied with the tool cathode rolling,and the peak current density always appears at the position of minimum machining gap. In the whole machining process, the current density in RUR-EMM is always larger than R-EMM and its variation is smooth which benefitted from the ultrasonic vibration assistant. The peak values of the current density for R-EMM and RUR-EMM are 116.1 A/cmand 123.2 A/cm, 122.8 A/cmand 135.4 A/cm, 67.8 A/cmand 72 A/cmat initial, middle and last stage respectively. The current density remains increasing from initial to middle stage and then decreasing during the process.As shown in Fig. 1, the –Z-directional vibration is enhancing with the cathode tool rolling from initial to middle stage,the flow velocity in IEG is also increasing. Based on thermodynamics Eq.(11), the current density will increase with velocity increasing.Therefore, the ultrasonic vibration promotes the discharge of electrolytic byproducts and the uniformity of conductivity which makes the machining more stable and improves the material removal rate.

Fig. 10 shows the variation of current density with the machining time at point A (0, 0, 25 μm) (Fig. 5(a)). During machining, the current density increases to be the maximum 113.54 A/cmat t=3.1 s for R-EMM and 157.76 A/cmat t=2.7 s for RUR-EMM, and then decreases. The maximal current density increases about 40%when the ultrasonic vibration is applied during machining. Furthermore, the current density increases more quickly to be maximum in RUREMM, which means the material removal speed is enhanced.

4.2.3. The thermal field characteristics in IEG

Fig. 8 Current density distributions in IEG in R-EMM and RUR-EMM.

Fig. 9 Curve of current density at different time along line A(x=0, z=25 μm).

Fig.11 shows the cloud chart of electrolyte temperature distribution at different stage in R-EMM and RUR-EMM. It can be observed that the electrolyte temperature in the central of the micro dimple is higher than other area surrounding. This is because the renewal of the electrolyte at the micro dimple border is sufficient and more heat generated in process is also removed. At the initial stage, the electrolyte temperature is higher at the location of the right than the left of the machined dimple,and it is increasing with the material dissolving in both RUR-EMM and R-EMM.Then,with the cathode tool rolling to the middle stage, the tool electrode is vertical to the workpiece surface, the distribution of temperature is almost symmetric. With more materials is removed, the IEG increases and then the electrolyte temperature decreases. Moreover, at the last stage,the temperature is a little higher at one side than the other as the micro protrusion center line has an angle θ=3° with the workpiece vertical line which makes one side of the tool electrode closer to the workpiece surface, more materials is dissolved and more heat is generated.

Fig. 10 Variation of current density & machining time at point A.

Fig. 11 Temperature distributions in IEG in R-EMM and RUR-EMM.

Fig.12 depicts the electrolyte temperature curves along line A (x=0, z=25 μm) in IEG at different stages. And A, B, C represent initial stage, middle stage and last stage in RUREMM respectively, A1,B1,C1 also correspond to this order in R-EMM The curves indicate the electrolyte temperature that has a trend of increasing first and then decreasing during machining, and the temperature in RUR-EMM is always higher than that of R-EMM.The peak values of the electrolyte temperature for R-RMM and RUR-EMM are 309.9 K and 314 K,323.4 K and 337.6 K,310 K and 315.7 K at initial,middle and last stage respectively. Application of the ultrasonic vibration increases the electrolyte temperature about 1.3%-4.4% in IEG. It is because higher electrical conductivity and current density making the reaction violent with the assistance of ultrasonic vibration. The electrolyte temperature increases 4.3%and 7.5%in R-EMM and RUR-RMM with the cathode rolling from initial stage to middle stage. The reason is with more material is removed, and more heat is generated during machining resulting higher electrolyte temperature in IEG.Nevertheless, from middle stage to last stage, the electrolyte temperature decreases 4.1% and 6.5% in R-RMM and RUR-RMM respectively. This is because the machining gap is increasing with the material erosion, the electrolyte renewal in IEG improves and more heat is taken away from machining gap.

Fig. 12 Curve of temperature at different stage along line A(x=0, z=25 μm).

Fig.13 shows the variation of the electrolyte temperature in IEG during machining. The electrolyte temperature peaks to be 325.4 K at time t=3.1 s in R-EMM and 335.08 K at time 2.9 s. This is in accordance with the variation of current density shown in Fig. 9.

4.2.4. Material erosion process

To better study the machining process in R-EMM and RUREMM, the photographs of machined dimples and the crosssectional profile at different stages are shown in Fig. 14.Fig.14(a)to Fig.14c presents the 3D micro dimple profile generated in R-EMM. At the initial stage, the morphology of the micro pit is deeper on one side than another side because the micro protrusion is inclined with the workpiece in this case,changes the machining gap to be nonuniform (see Fig. 4),resulting uneven current density and material removal speed.With the tool cathode rolling,the material removal is increased and the depth of the micro dimple is increased gradually, the morphology of dimple is finally axisymmetric as shown in Fig. 14(c). Moreover, it is observed from Fig. 14(a) to Fig. 14(c) that the workpiece material near the central area of the dimple is undissolved to form an island because the existed byproducts especially the gas bubble on the central area in IEG is more difficult to remove than the border area.The impedance of the electrolyte is higher and the electric field is continuously suppressed on the central area in IEG which makes its material removal rate lower than area around it.On the other hand, in RUR-EMM, with the ultrasonic vibration was applied,the convex portion in the central area on the bottom of the micro dimple is disappears. It is because the ultrasonic vibration promotes the discharge of electrolytic byproducts, enhances the electrolyte renewal, the current density in the IEG is more uniform along the sweep route.

Fig.13 Variations of electrolyte temperature&machining time.

Comparing the micro dimple profile curves of R-EMM and RUR-EMM, shown in Fig. 15, And A, B, C represent initial stage, middle stage and last stage in RUR-EMM respectively,A1, B1, C1 also correspond to this order in R-EMM. It is found that applying the vibration results in not only a flat bottom surface,but also the deeper micro dimple and larger material removal. The micro dimple’s depth and the area of the cross-sectional profile increase from 66.9 μm to 78.2 μm, and 43175 μmto 48052 μmin R-EMM and in RUR-EMM at the last stage respectively. Thus, it can be concluded that applying ultrasonic vibration in EMM, the material removal amount is increased significantly.

5. Experimental verification

The verifications are done by using the built experimental setup, as shown in Fig. 16. Machining conditions listed in Table.1 are selected. During machining, ultrasonic generator provides vibration on the tool electrode.The movement is controlled by the machine tool system. The detection of electric signal and machining zone observation are realized by oscilloscope and optical microscope respectively. The micro dimple was processed from the initial to last stage and then the dimensions including depth,width and cross-sectional profiles of the machined micro dimples are examined with 3D laser scanning microscope (KEYENCE, VR-5000, Japan).

The morphology and the cross-sectional profile of micro dimples machined in R-EMM and RUR-EMM at middle and last stage are shown in Fig. 17 and Fig. 18 respectively.Fig. 17 indicates the morphologies of the micro pits in REMM and RUR-EMM are deeper on one side than another side because the micro protrusion is inclined with the workpiece from initial to middle stage (t=0–5 s), the machining gap is nonuniform (see Fig. 4), resulting uneven current density and material removal speed. Simulations shown in

Fig. 14 were proved by comparison of the micro-pits crosssectional profiles between simulation and experiments in Fig. 19.

Fig. 19 shows a comparison of the cross-sectional profiles of the dimples produced by R-EMM and RUR-EMM at 5 seconds in the experiment and simulation. The machined micro dimple depth and cross-section area are 46.2 μm and 20118 μmin RUR-EMM compare to 39.5 μm and 22468 μmin R-EMM at middle stage. Compared with the simulation results, the errors of depth and cross-section area are 2.78%, 4.97% and 2.63%, 7.02% for RUR-EMM and R-EMM respectively.

It is observed the workpiece material in the center of the micro dimple is undisolved to form an island in R-EMM(Fig. 18(a)), while the morphology of dimple bottom is flat in RUR-EMM (Fig. 18(b)). The material on the border of dimples is removed ununiform in the machining and the replicating accuracy in R-EMM is worse than in RUR-EMM.Moreover, comparing with the simulation results, the shape of machined islands is irregular. It is because byproducts in the narrow machining gap influence the distribution the electric field,which changes the workpiece surface material erosion regulation.

Fig. 14 Machined dimple profile at different stages in R-EMM and RUR-EMM.

Fig. 15 Sectional micro dimple profiles at different stage.

Fig. 20 shows the cross-sectional profiles of micro dimples generated by R-EMM and RUR-EMM compared to the simulated results. It can be recognized that the experimental shapes of the dimples agree better with the simulations. The machined micro dimple depth and cross-section area are 74.4 μm and 44229 μmin RUR-EMM compare to 64.1 μm and 40188 μmin R-EMM at last stage. The errors of depth and cross-section area between simulation and experiments are 5.1%, 8.64% and 4.81%, 7.43% for RUR-EMM and REMM respectively. Applying ultrasonic vibration, the micro dimple depth increases 8.7%and the material removal amount increases about 4%. A good agreement between simulations and experiments verified the theoretical multiphysic model presented in this study.

6. Conclusions

In this paper, the energy field and material process in RUREMM are studied. The 3D multiphysics coupling model including flow field model,Joule heating model,material dissolution model and vibration model is built. The array micro dimples is selected to be processed based on the proposed model. Simulations results including the distribution for fluid flow, current density, electrolyte temperature and material removal are investigated and compared R-EMM with RUREMM based on finite element method. Some conclusions can be summarized as follows:

Fig. 16 Photo of experimental equipments.

Fig. 17 Machined micro dimples and their profiles in R-EMM and RUR-EMM at middle stage (t=5 s).

Fig. 18 Machined micro dimples and their profiles in R-EMM and RUR-EMM at last stage (t=10 s).

Fig. 19 Profile comparison of micro dimples machined in REMM and RUR-EMM at middle stage (t=5 s).

Fig. 20 Profile comparison of micro dimples machined in REMM and RUR-EMM at last stage (t=10 s).

It is feasible to build the 3D multiphysics coupling model at the complex working conditions. The average deviation is less than 8.7%for the micro dimple depth and 4%for the material removal amount between experimental and theoretical results at the conditions of the vibration frequency 20 kHz,the amplitude 10 μm, the machining gap 50 μm, the tool cathode rotating angular velocity 0.6°/s and the electrolyte conductivity 7.9 S/m.

Energy fields can be forecasted before the real trial. Application of ultrasonic vibration resulting the periodically variation of the fluid flow in IEG, the electrolyte is squeezed out and absorbed into the machining gap, the electrolyte renewal and the byproducts discharge is enhanced. Simulations results for the current density, temperature and velocity distributions provide evidence of the material erosion process and machined micro dimple shape.

Increasing of current density proves the enhancement of ultrasonic vibration on material removal. Distribution of current density and the micro dimple simulated provide evidence for micro dimple machining in the experiments. It denotes the island caused by uneven material removal in R-EMM can be avoided in RUR-EMM and smooth bottom of the micro dimple could be obtained,which benefits from the effects of vibration on energy field in IEG.

Moreover,prediction based on simulations is beneficial for reducing experimental time.

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

The authors would like to thank the financial support of the projects from the National Natural Science Foundation of China(Nos.51975532 and 51475428)and the Zhejiang Provincial Natural Science Foundation (No. LY19E050007).