EDM wire cuting

Study of EDM wire cutting precision 1. Introduction Electrical discharge machining (EDM) is a non-traditional concept of machining which has been widely used to produce dies and molds. It is also used for finishing parts for aerospace and automotive industry and surgical components [1]. This technique has been developed in the late 1940s [2] where the process is based on removing material from a part by means of a series of repeated electrical discharges between tool called the electrode and the work piece in the presence of a dielectric fluid [3]. The electrode is moved toward the work piece until the gap is small enough so that the impressed voltage is great enough to ionize the dielectric [4]. Short duration discharges are generated in a liquid dielectric gap, which separates tool and work piece. The material is removed with the erosive effect of the electrical discharges from tool and work piece [5]. EDM does not make direct contact between the electrode and the work piece where it can eliminate mechanical stresses, chatter and vibration problems during machining. Wire-electro discharge machining (Wire-EDM or WEDM) has become an important nontraditional machining process, widely used in the aerospace, nuclear and automotive industries, for machining difficult-to-machine materials (like titanium, nimonics, zirconium, etc.) with intricate shapes. The selection of optimum machine setting or cutting parameters in WEDM is an important step. Improperly selected parameters may result in serious consequences like short-circuiting of wire and wire breakage, imposing certain limits on the cutting speed and thus reducing productivity. As surface finish and cutting speed are most important parameters in WEDM, various investigations have been carried out by several researchers for improving the surface finish and cutting speed . However, the problem of selection of machine setting parameters is not fully solved, even though the most sophisticated CNC-WEDM machines are presently available. Optimization techniques are required to identify the optimal combination of parameters for achieving required cutting performance in Wire-EDM process. Quite a few researchers have tried to optimize the cutting performance by adopting different optimization techniques. Metal removal rate (MRR) and surface finish were optimized by Scott by explicit enumeration based on signal-to-noise ratio. Further, they split the problem into optimization of MRR with surface finish constraint and optimization of surface finish with MRR as constraint and applied dynamic programming method. Thirty-two non-dominated points thus obtained have been reported. Tarng et al. used a simple weighting method to transform the cutting velocity and 1

surface roughness into a single objective and arrived at the optimal parameters by simulated annealing. In a different attempt, optimizing the process parameters for maximizing MRR taking surface roughness and spark gap as constraints has been carried out by the feasible-direction nonlinear programming method.

A review on current research trends in electrical discharge machining

Guo studied the machining mechanism of wire EDM (WEDM) with ultrasonic vibration of the wire and found that the combined technology of WEDM and ultrasonic facilitates the form of multiple-channel discharge and raise the utilization ratio of the energy that leads to the improvement in cutting rate and surface roughness. High frequency vibration of wire improves the discharge concentration and reduces the probability of rupture wire. Guo concluded that with ultrasonic aid the cutting efficiency of WEDM can be increased by 30% and the roughness of the machined surface reduced from 1.95Ra to 1.7Ra. Furudate and Kunieda conducted studies in dry WEDM. The process reaction force is negligibly small, the vibration of the wire electrode is minute and the gap distance in dry WEDM is narrower than in conventional WEDM using dielectric liquid which enables the dry WEDM to realize high accuracy in finish cutting. No corrosion of the work piece gives an advantage to dry WEDM in manufacturing high precision dies and molds. Wang and Kunieda agreed that WEDM is applicable for finish cut especially for improving the straightness of the machined surface. Traveling tool electrode can remove debris from the working gap even in atmosphere and by utilizing this process as finish-cut the straightness obtained along the work’s thickness direction is better than that machined in water . Kunieda and Furudate found some drawbacks of dry WEDM which include lower MRR (material remove rate)compared to conventional WEDM and streaks generated over the finished surface during the studies in high precision finish cutting by dry EDM. The drawbacks can be resolved by increasing the wire winding speed and decreasing the actual depth of cut. The characteristics of dry EDM list by Kunieda are: (1) Tool electrode wear is negligible for any pulse duration. (2) The processing reaction force is much smaller that in conventional EDM. (3) It is possible to change supplying gas according to different applications. (4) The residual stress is small since the melting resolidification layer is thin. (5) Working gap is narrower than in conventional EDM. (6) The process is possible in vacuum condition as long as there is a gas flow. (7) The machine structure can be made compact since no working basin, fluid tank and fluid circulation system needed. 2

Water with additives, Koenig and Joerres reported that a highly concentrated aqueous glycerine solution has an advantage as compared to hydrocarbon dielectrics when working with long pulse durations and high pulse duty factors and discharge currents, i.e. in the roughing range with high open-circuit voltages and positive polarity tool electrode. Leao and Pashby found that some researchers have studied the feasibility of adding organic compound such as ethylene glycol, polyethylene glycol 200, polyethylene glycol 400, polyethylene glycol 600, dextrose and sucrose to improve the performance of demonized water. The surface of titanium has been modified after EDM using dielectric of urea solution in water . The nitrogen element decomposed from the dielectric that contained urea, migrated to the work piece forming a TiN hard layer which resulting in good wear resistance of the machined surface after EDM. A Study to Achieve a Fine Surface Finish in Wire-EDM Many Wire-EDM machines have adopted the pulse generating circuit using low power for ignition and high power for machining. However it is not suitable for finishing process since the energy generated by the high voltage sub-circuit is too high to obtain a desired fine surface, no matter how short the pulse on time is assigned. For the machine used in this research, the best surface roughness Ra after finishing process is about 0.7μm. In order to obtain good surface roughness, the traditional circuit using low power for ignition is modified for machining as well. With the assistance of Taguchi quality design, ANOVA and F-test, machining voltage, current-limiting resistance, type of pulse generating circuit and capacitance are identified as the significant parameters affecting the surface roughness in finishing process. In addition, it is found that a low conductivity of dielectric should be incorporated for the discharge spark to take place. After analyzing the effect of each relevant factor on surface roughness, appropriate values of all parameter are chosen and a fine surface of roughness Ra equals to 0.22μm is achieved. The improvement is limited because finishing process becomes more difficult due to the occurrence of short circuit attributed to wire deflection and vibration when the energy is gradually lowered.

The Wire-EDMed surface consists of many craters caused by electrical sparks. The larger the electrical discharging energy, the worse the surface quality will be. A large energy will produce a rippled surface, change the structure and physical properties of materials, and result in cracks and residual stresses on the surface.

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In order to obtain a fine surface finish, several investigations using the low conductivity dielectric to reduce the electrolytic current had been reported . By analogy, the AC pulse generator is employed, and it is confirmed by experiments that a fine surface can be achieved. This result is readily understood because the oxidation of work material due to electrolysis when DC pulse generator is applied is suppressed . The white layer can be improved by increasing the slope of the current and pulse-on time . Alternatively, it can be accomplished by reducing the peak current . Practically, using a small energy and AC pulse generating circuit after roughing process can lead to a fine surface finish .

Influence of machining parameters on surface roughness Voltage and resisitance Most related researches of pulse generating circuit for roughing operation pointed out that the dominent factor affecting surface roughness is pulse-on time (Ton), because that surface roughness depends on the size of spark crater. A shallow crater together with a larger diameter leads to a better workpiece surface roughness. To obtain a flat crater, it is important to control the electrical discharging erergy at a smaller level by setting a small pulse-on time (Ton) since most Wire-EDM machines were designed to discharge with the electrical discharging current propotional to the pulseon time. A large discharging energy will cause violent sparks and results in a deeper erosion crater on the surface. Accompanying the cooling process after the spilling of molten metal, residues will remain at the pheriphery of the crater to form a rough surface. In this research, pule-on time in finishing process was set to a constant value of 0.05μs. Hence, the size of a discharing crater depends exclusively on the pulse generating circuit providing a discharging spark. In the designed circuit, a small voltage and a large resistance were used so as to provide a small discharging energy and hence to produce a good surface.

Type of pulse generating system

From the experimental results, it was found that measured surface roughness using DC pulse generating circuit of positive polarity (wire electrode is anode and work material is cathode) is better than that using AC pulse generating circuit. Different from the pulse generating circuit used in roughing process, the polarity remains unchaged for both ignition and machining in this

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research, instead of changing it to negative polarity while machining. To sum up, machining with different polarity results in different sizes of the crater and the surface roughness. The relationship between the erosion rate of the anode or cathode and pulse-on time was schematically illustrated in fig. 4. It is apparent that cathode erosion rate is lower than anode erosion rate while machining with a quite small pulse-on time, such as Ton < 0.5 μs. It is infered that the crater of a single spark produced on the cathode surface will be smaller than that on the anode surface. Hence, the pulse generating circuit for finishing operation in this research adopted DC pulse generating circuit of positive polarity which set wire as the anode. From surface roughness point of view, it is superior to AC pulse generating circuit which is exchanging anode and cathode alternately.

Capacitance As it is easily known from the experimental results, surface quality will be better without using capacitance in the circuit. The waveforms of discharging voltage and current for different capacitance are shown in fig. 5. In these figures, 1 represents the voltage of the pulse, 2 is the total current flowing across the machining gap and capacitance, and 3 is the actual machining current across the gap, which is the upper branch of the total current and is about half of the total current. It can be seen from the discharging current in fig. 5 that the waveform of discharging current in actual machining is flatter when there is no capacitance in the circuit. The waveform with capacitance was sharper, and the larger the capacitance, the larger is the peak current. This can also be verified from the appearance of sparks as they are brighter. It is also noted that there is a pulse-off time of 8μs after discharging for the gap to recover to its initial insulated condition. But the discharging voltage did not approach zero level due to the energy continuously supplied by this extra capacitance. Hence

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discharges of not uniform energy still take place during the pulse off time. Based on these observations, it is inferred that a larger capacitance will result in deeper craters and worsen machined surface roughness. Dielectric

Although the conductivity of dielectric is not a significant factor on Ra, it may however result in unsuccessful discharging in finishing process. Fig. 6 shows the waveforms of discharging voltage and current for different conductivity of the dielectric; where in the figure 1 and 2 stand for discharging voltage and discharging current, respectively. The waveforms of all three figures in fig. 6 are similar. But it can be seen that there is “leaking” current at the stage when ignition voltage is applied, especially for conductivity equals to 30 μS/cm and 45 μS/cm. This leaking current is known as electrolytic current. Applying extra voltage between two electrodes will increase the driving force of chemical reaction and facilitate electrolysis process. This in turn causes the electrolytic current to form due to the flow of electrons and ions. Since electrolytic current is increased proportionally with the increase of conductivity of dielectric as shown in fig. 6, oxidation due to electrolysis will become more serious. The AC pulse generating circuit and DC pulse generating circuit of positive polarity are used in our experiments, hence no electrolysis is encountered. Nevertheless, discharging spark may not be able to take place under the dielectric of high conductivity. Discharging energy decreases with the increase of the resistance, but the electrolytic current still remains at same level under the circumstance of same conductivity as shown in fig. 7. When a large resistance is used, finishing sparks are difficult to occur for the reason that discharging current is smaller than the electrolytic current. Hence, the conductivity of dielectric should be set below about 15 μS/cm to ensure the occurrence of sparks for our machine.

CONCLUSIONS To obtain good surface roughness, the traditional circuit using low power for ignition is

modified for machining as well. With the assistance of Taguchi quality design, ANOVA and Ftest, machining voltage, current-limiting resistance, type of pulse generating circuit and capacitance are identified as the significant parameters affecting the surface roughness in 6

finishing process. A DC pulse generating circuit of positive polarity (wire electrode is set as anode) can achieve a better surface roughness in finishing operation. In addition, it is found that a low conductivity of dielectric should be incorporated for the discharge spark to take place. After analyzing the effect of each relevant factor on surface roughness, appropriate values of all parameter are chosen and a fine surface of roughness Ra equals to 0.22 μm is achieved. The improvement is limited because finishing process becomes more difficult due to the occurrence of short circuit attributed to wire deflection and vibration when the energy is gradually lowered.

An effective-wire-radius compensation scheme for enhancing the precision Using a modified Denavit–Hartenberg (D–H notation), we propose with this study a methodology for generating the wire-radius-compensated NC data equations required to carry out the machining of non-column workpieces on a five-axis wire-cut electrical discharge machine. The modified D–H notation is then employed to derive the machine’s ability matrix and to generate the desired wire location matrices. To ensure the precision of the machining operation, the wire location matrices are modulated by a novel effective-wire-radius compensation scheme. Finally, the NC data equations required to machine the component are derived by equating the ability matrix with the modulated wire location matrix. To validate the proposed methodology, three non-column workpieces with various top and bottom basic curves are machined on a commercial WEDM. The results showthat the components manufactured using the proposed effective-wireradius compensation scheme are more geometrically precise than those produced using the conventional WEDM compensation method.

Generation of NC data equations modulated by effective-wire-radius compensation scheme The value of the electric discharge gap Δ in the WEDM process depends on the machining parameters employed, but typically has a value in the range 0.025 mm to 0.075 mm. Provided that the machining parameters remain unchanged, Δ can be taken as a constant. The NC data values generated for the WEDM machining process indicate the positions at which the wire is to 7

be held by G-code instruction in order to manufacture the designed component. To obtain a high degree of machining precision, the physical radius of the cutting wire must be taken into consideration when generating this NC data. Figure 4 presents a schematic illustration of the proposed compensation method. Note that the thick solid lines in this figure represent the physical wire electrode, while the dashed lines indicate the effective-wire-radius.

The ruled surface of the workpiece shown in Fig. 4 can be represented by the following equation [10]:

Figures 6 (a) and (b) present photographs of workpiece #1 manufactured using the WEDM builtin compensation command and the proposed effective-radius compensation scheme, respectively. Fig. 6 (a) shows that overcutting takes place, resulting in the formation of two cusps in the machined workpiece.

The bottom basic curves wbottom of workpiece #2 manufactured using the built-in compensation command and the proposed effective-wire-radius compensation method, respectively, were found to have radii of 11.04 mm and 11.03 mm. The designed value of this radius is 11.00 mm; hence it is clear that the proposed radius compensation method yields an improvement in the geometrical precision of the machined component.

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These results again demonstrate that the proposed effective-wire-radius compensation method yields a greater geometrical precision than that achieved using the conventional WEDM controller. Analysis of electromagnetic force in wire-EDM This electromagnetic force is caused not only by DC component but also by AC components of the discharge current supplied to the wire. In wire-EDM, four kinds of forces are applied to the wire electrode : discharge reaction force caused by rapid expansion of a dielectric fluid bubble at the discharge spot during discharge duration, electrostatic force when open voltage is applied between the wire and workpiece during ignition delay time, electromagnetic force caused by discharge current flowing through the wire, arc column, and workpiece during discharge duration, and hydrodynamic force generated by the flowof dielectric fluid. These forces cause vibration and deflection of the wire electrode, thereby lowering machining accuracy, speed, and stability . On the other hand, Obara, Han , and Tomura developed programs for WEDM simulation. The simulation is based on the repetition of the following routine; calculation of wire vibration considering the forces applied to the wire, determination of the discharge location considering the gap width between the wire and workpiece, and removal of workpiece at the discharge location. Correct values therefore need to be obtained for these forces applied to the wire for accurate simulation.

Fig. 1 shows the principle of electromagnetic force generated by DC component. It is assumed that a constant current flows through the brass wire along the wire axis toward the front as seen in Fig. 1. When the workpiece is copper, and the atmosphere is air or water, distribution of the magnetic flux density is axisymmetric and counterclockwise around the wire axis as shown in Fig. 1(a), because all the materials are paramagnetic and have significantly small permeability in the same order. The electromagnetic force can be calculated by vector product of current density and magnetic flux density. For this reason, the resultant electromagnetic force applied to the wire is insignificant because of the axisymmetric distribution of the magnetic flux and uniform current density. In contrast, when the workpiece is steel, the magnetic flux is not axisymmetrical around the wire axis as shown in Fig. 1(b) because permeability of the workpiece is significantly larger than the other materials.

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Fig. 2 shows the principle of electromagnetic force generated by AC components. When current in the wire is rising, the magnetic flux density increases counterclockwise, generating an eddy current in the workpiece caused by electromagnetic induction. The direction of eddy current generated by each magnetic flux is determined so that the eddy current cancels the increase in the magnetic flux. Hence, the density of eddy current is highest under the wire, and it flows counterparallel to the current in the wire. Thus, the electromagnetic force caused by increasing current generates repulsive force. In the same way, when the current is falling, an eddy current is generated in the workpiece under the wire in the same direction as the current in the wire.

Calculation of electromagnetic force by electromagnetic field analysis This program can solve the following Poisson’s equation considering electromagnetic induction in the two-dimensional field perpendicular to the wire axis.

Here _ is permeability, Az is Z-component of electromagnetic vector potential, _ is electric potential caused by electromagnetic induction,  is conductivity, and J0 is forced current density. In the case of a steady current flowing through a uniform conductor, the distribution of current density is uniform. Wire movement caused by electromagnetic force Wire movement resulting from the electromagnetic force generated by a consecutive pulse current actually used in WEDM was measured. The wire movement was also calculated using the electromagnetic force which was calculated in the same manner as in the previous section.

To clarify the mechanism of the electromagnetic force applied to the wire electrode in WEDM, was developed a 2D FEM program for electromagnetic field analysis taking into consideration electromagnetic induction. The following results were obtained: (1) It was found that static electromagnetic force is attractive, and amongst the physical properties of workpiece materials, permeability exerts significant influence on static force. However, dynamic electromagnetic force is repulsive, and its magnitude is determined by the conductivity of the workpiece. With steel workpiece, which has large permeability and small conductivity, the resultant electromagnetic force is attractive because the static force is dominant. 10

(2) The wire movements measured in the experiment agreed with the wiremovements analyzed, clarifying the mechanism of the electromagnetic force in WEDM. Moreover, it was found that electromagnetic force should be considered for the accurate simulation of workpiece shapes machined byWEDM.

Fuzzy logic control in wire transport system Wire tension as well as wire feed should be controlled tightly for the geometry and corner accuracy of wire-EDM. In this paper, a closed-loop wire tension control system for MicroWire-EDM is presented to guarantee a smooth wire transport and a constant tension value. In order to keep smooth wire transportation and avoid wire breakage during wire feeding, the reel roller is modified and the clip reel is removed from the wire transport mechanism. A genetic algorithm-based fuzzy logic controller is proposed to investigate the dynamic performance of the closed-loop wire tension control system. Experimental results demonstrate that the developed wire transport system can result in satisfactory transient response, steady-state response and robustness. The proposed genetic algorithm-based fuzzy logic controller can obtain faster transient response and smaller steady-state error than a PI controller.

Wire feed is open-loop controlled by a DCmotor directly coupled to a pair of feeding rollers. Dynamic model of this wire transport system with DC motor drives can be derived from the equivalently simplified schematic in Fig. 2. The dynamic equation of the wire feed control apparatus with the DC motor drive is:

where Tg1 is the output torque of the servo motor, Kt1 is the torque constant of the wire feed motor, Ia1 is the armature current of the motor, J1 is the effective inertia acting on the motor shaft including the motor inertia and the roller inertia, ω is the rotation speed of the servo motor, B1 is the effective friction coefficient including the motor shaft friction and the rollers friction, Td1 is the torque disturbance of the wire feed control apparatus, f stands for the wire tension, and R1 is the radius of the feeding roller.

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Fig. 8 demonstrates the schematic diagram of original and retrofitted wire transport mechanism. Tension is applied to a running wire electrode by turning the wire around the electromagnetic brake once. A wire electrode supply device is composed of a spool, a bobbin and a taper.

Fig. 9(a), the inclination angle of the taper for the original wire electrode supply device is 75◦. Due to the eccentric rotation of the wire reel, the wire electrode vibrates, and wire tension changes periodically. In order to reduce the effect of the eccentric rotation of the wire reel, the wire electrode supply device has been retrofitted by changing the inclination angle of the taper from 75◦ to 45◦ as illustrated in Fig. 9(b). According to some experimental results, a smaller inclination angle of the taper contributes to smaller wire vibration and more stable wire transport. Therefore, the inclination angle of the taper was experimentally designed as 45◦.

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Fig. 11 – Time responses of wire tension with (a) open-loop control, (b) fuzzy logic control and (c) fuzzy logic control with retrofitted wire transport system (brass wire: 0.07mm, wire feed: 5m/min).

Fig. 12 – Time responses of wire tension with (a) openloop control, (b) PI-control and (c) fuzzy logic control with retrofitted wire transport system (tungsten wire:  0.05mm, wire feed: 5m/min).

The original wire transport system equipping with a commercialized wire-EDM machine has been retrofitted to suit for fine wires with a diameter of 80m and below. Genetic synthesis of a fuzzy logic controller for the retrofitted wire transport system of wire-EDM has been described. Comparing with the PI controller, the proposed fuzzy logic controller with retrofitted wire transport mechanism contributes to a faster transient response and a smaller steady-state error under the influence of flushing condition.

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Comparison on linear synchronous motors and conventional rotary motors driven Conventionally, the positioning control of machine tools has been conducted with rotary motors. Either dc or ac motor drives require extra transmission mechanism such as ball screws, gear systems, or belt, etc. These mechanisms transform rotation into linear motion. However, ball screws introduce pitch error, and errors from backlash, wear, friction and even elastic deformation of screw rod itself. Therefore, some positioning inaccuracy and uncertainty are inherited inevitably within the conventional configurations. On the other hand, a directly drive mechanism configured with linear motors seems very promising in motion speed, accuracy and reliability promotion. Because the transformation mechanism is no more needed in direct drive scheme. In recent years, both academics and industries pay intensive attention to the practical application of linear motors to machine tools. Modelling of ac servo motors The throughput torque of a permanent magnet (PM) synchronous servo motor is described as:

Considering the inertial of motor, friction and the load torque to motor, its mechanical equation can be derived as:

where R represents armature’s resistance of motor; id and iq are the armature currents of d-axis and q-axis; vd, and vq are the armature voltages of d-axis and q-axis, respectively. Similarly, Ld and Lq are the armature inductances of d-axis and q-axis. λb, Jm, Bm, Te and Tl represent maximum magnetic flux, inertial of motor, friction coefficient, electromagnetic torque and the torque loading, respectively. Modelling of linear synchronous motors A linear synchronous motor is a linear motor in which the mechanical motion is synchronous with the magnetic field. Mechanical motion is carried out either by the travelling magnetic field or the field excitation system, which may be the source of dc magnetic flux or variable reluctance. And the motor propulsion (thrust force) has two components due to: (1) the travelling magnetic field and the dc current magnetic flux, and (2) the travelling magnetic field and variable d-axis and q-axis (reluctance ferromagnetic components). Assume the armature’s three phases winding are symmetric and distributed in a form of sine wave. Also assume the air gap is uniform and the end effects of motor are negligible. The throughput propulsion of a PM-LSM is described as:

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And its mechanical equation can be derived as,

where idl and iql indicate the armature currents; vdl and vql are the armature voltages for d-axis and q-axis, respectively. Similarly, Ldl and Lql represent the armature inductance of each axis, respectively. λl, τl, M, B, fe and fl represent maximum magnetic flux of PM, poles pitch of linear motor, mass of armature, friction coefficient, electromagnetic propulsion and the disturbance loading, respectively.

Fig. 6. Error comparison on linear segment (CNC code: G01 X1.0

Fig. 8. Circular segment comparison (CNC code: G02 I0.5 for

Y1.0 for low speed): (a) rotary motor with low federate and

both high feedrate and low feedrate tests): (a) rotary motor with

(b) LSM with low feedrate.

high feedrate and (b) LSM with high feedrate.

Fig. 7.Error indexes comparison on linear segments (BS, rotary motor with ball screw drive; LM, linear motor).

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Fig. 10. Comparison on Wire-EDMed slits contouring by: (a) rotary motor drive and (b) LSM direct drive.

Fig.

11. Comparison on Wire-EDMed gears contouring by: (a) rotary motor driven and (b) LSM driven (wire

electrode φ 50m).

A rotary motor with ball-screw table was retrofitted into a sub micro-meter stage. And comparison between conventional drive and linear motor’s (LSM) direct drivewas conducted with submicron feedback. It is evident from Wire-EDM outcomes that direct drive performs much better contouring accuracy in standard segment tests. Because of conventional transmission problems, more uncertainty was introduced into motion control, especially, around changing direction points. In higher feedrate, more than 70% of Wire-EDM accuracy and efficiency can be achieved by direct drive over conventional method. And in machining meso scaled workpiece with thin wire, direct drive presents excellent deviation precision, of ±2.1_m, compared to ±3.5_m of traditional drive. 16

Computational fluid dynamics analysis of working fluid flow and debris movement The demands for fine precision machining have been recently increased along with the miniaturization of mechanical and electronic products. For meeting these demands, the machine control technology, the optimization of machining conditions and the development of finer electrode have been enhanced in wire EDM. In fine wire EDM using thin electrode, better exclusion of debris from the machined kerf becomes more important in order to obtain a stable machining performance, since the area of spark generation is along a line and much smaller than that in conventional wire EDM using thick wire. When much debris stagnates in the gap and the machined kerf, the secondary discharges possibly occur and the discharges easily concentrate on the same location, which leads to unstable machining performance, wire breakage, low machining rate and low shape accuracy. Conventionally, the exclusion of debris is carried out by jet flushing of working fluid from upper and lower nozzles. The purposes are not only flushing away of debris from the spark gap, but also introducing fresh working fluid for dielectric recovery of the gap, and cooling down of electrode and workpiece. As for die sinking EDM, many studies on the fluid flow in the gap and the simulations were done. However, for wire EDM, the flow field of working fluid in the machined kerf and the effect of jet flushing conditions from the nozzles have not yet been made clear sufficiently, since such unsteady flow field is not easy to estimate and a precise in-process observation of working fluid flow in the narrow kerf is very difficult.

Fig. 2. Observed image and PIV analysis results: (a) movie by high-speed camera and (b) flow field by PIV analysis.

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Effect of flow rate of working fluid from nozzles As shown above, it is proven that the analyzed results using the CFD model has high reliability, since they were quantitatively similar to actual flow fields in wire EDM kerf. Therefore, the effects of flow rate of deionized water from nozzles on flow field in the machined kerf were discussed. Analysis conditions are shown in Table 2.

Fig. 4. Comparison of PIV and CFD result.

Fig. 5. Fluid flow in machined kerf.

In actual wire EDM for workpiece of 10 mm in thickness under first cut condition, the process are done usually with applying jet flushing of working fluid from nozzles in order to well exclude debris generated in the discharge gap. The analysis conditions were decided considering first cut conditions. The stand-off distances from nozzle tips to the upper and lower workpiece 18

surfaces are fixed to 2.0 mm, and the diameter of nozzle is 6.0 mm. In the CFD model, circle inlets of 6 mm in diameter are set at the upper and lower boundary surfaces around the wire, and initial flows in the direction parallel to wire running direction are given.The flow fields in the machined kerf were analyzed with varying the flow rates of working fluid from upper and lower nozzles are shown in Fig. 5. As can be seen from the figure, a stagnation area where the flow velocity is nearly zero can be confirmed around the center in any flow rate conditions of jet flushing from nozzles. The area is shown as a dotted triangle. Conclusions The fluid flow and the debris motion in wire EDMed kerf were investigated by CFD simulation comparing with the observation by high-speed video camera. Highly accurate CFD simulation of flow field in wire EDMed kerf could be shown by highly quantitative agreement with the highspeed observation results. The CFD analysis showed that the stagnation area with little flow velocity can be confirmed around the wire under any flow rate conditions of jet flushing from upper and lower nozzles. The exclusion of debris is not efficient in the area, and so jet flushing from upper and lower nozzles is not always effective for debris exclusion in the machined kerf. In addition, debristracking analysis clarified that most debris are excluded out from the same parts of the kerf under any constant flow rate conditions. By using the CFD analysis, better jet flushing conditions of working fluid from the nozzles, such as time changing in flow rate, nozzle shape, flushing position, and flushing direction will be analyzed for more effective debris exclusion and high performance wire EDM.

Corner error simulation of rough cutting in wire EDM Wire EDM is thought to be suitable for processing high accuracy molds and parts, because it is a non-contact machining technique, unlike other cutting machining methods, it can provide higher machining accuracy and good roughness of surface. However, with the high-speed development of the mold industry, the need for precision instruments is steadily increasing, resulting in greater demand for the machining accuracy of the wire EDM technique. Since wire EDM uses a thin and flexible wire as a tool electrode, which is subject to deformation due to reaction forces such as explosive force and the electrostatic force between the wire electrode and workpiece, an unfavorable geometrical error of the machined surface easily occurs (as shown in Fig. 1). 19

Because the simulation of wire EDM is so important, there has been much research in this area. The majority of the new methods use simulations of machining technology in which the machining parameters are generated automatically by optimizing known parameters . Obara and Han simulate the processing phenomenon of wire EDM on the computer by analyzing the vibration of the wire electrode and searching for the discharge locations. Magara describes a research investigation on improvement of machining accuracy of corner parts in finish-cutting of wire EDM, in which the shapes of corner and machining feed at the corner can be simulated by considering changes of removal thickness, however, the vibration of wire electrode is not considered and the simulation only limited in the finish cutting. Although there has been much research about the corner machining for improving the corner accuracy of rough cutting .

Fig. 2. Sketch map of corner machining.

Wire vibration model

Although the wire tension is appended on the wire, since thewire is thin and flexible, it is subject to deformation and vibration due to reaction forces such as explosive force, electromagnetic force, the electrostatic force, etc.

Fig. 4. Wire vibration model in the steady state.

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Fig. 5 shows the change of discharge area during corner cut machining. The angle of the machined corner is P. The little circles represent the movement of the cross section of the wire, and the large circles represent the movement of the machined borderline, whose radius a is half of the machined slit. XOY is the coordinate before the corner is machined, and the two dotted circles represent the wire and machined circle at that time. It is easily known that the discharge area is πah at that time. X’O’Y’ is the coordinate after machining into the corner, and the two solid circles represent the wire and machined circle at that time. The discharge area at that time changes to