Experimental study of EDM characteristics using a 5-DOF controllable magnetic levitation actuator

The efficiency and accuracy of conventional electrical discharge machining (EDM) are limited by the stability of the voltage between the poles. To improve the efficiency of EDM, this paper presents a machining method that combines a self-developed 5-degree-of-freedom (5-DOF) controllable magnetic levitation actuator with a conventional EDM machine tool. The stability of the interpole voltage is improved by actuator microadjustment of the electrodes of the EDM machine tool. First, an EDM control system with local current feedback and decoupling control elements is designed based on the EDM servo drive principle to improve the response speed and positioning accuracy of the actuator. Second, the actuator is connected to the spindle of a conventional EDM machine tool, and machining experiments are carried out. The experimental results show that the EDM machine tool connected to the actuator can control the electrode position more quickly, adjust the discharge state quickly, and increase the number of discharges per unit time. The average machining speed increases from 1.108 to 3.925 µm/s, which is 3.54 times as fast as conventional EDM. Finally, complex shape machining experiments are carried out, and the machining results showed that by adjusting the target value of the radial direction of the actuator, the various trajectories of the electrode can be controlled to depict arbitrary shapes.


Introduction
The EDM technique uses pulsed spark discharge between the electrode and the workpiece in a certain working medium to remove the material to be machined and ultimately achieve the desired shape, size, and surface topography [1,2]. Compared with conventional machining methods, EDM technology has the advantage of not being limited by the hardness and strength requirements of the workpiece material [3,4].
It is widely used in the machining of difficult materials such as high-hardness, high-toughness, high-brittleness, and conductive materials, and the machining of microporous and complex shapes has become an indispensable machining method at this stage [5,6].
Due to the large inertia of the mechanical transmission system, the conventional EDM using a motor and ball screw actuator is slow to respond and cannot guarantee the ideal interpole gap in time [7], resulting in unstable interpole voltage for EDM, which affects the discharge probability, thus limiting the efficiency and accuracy of conventional EDM. Compared with traditional cutting methods, the EDM does not provide an efficiency advantage, so it is necessary to find ways to improve the efficiency of EDM.
To improve the efficiency of EDM, scholars have performed much research on improving the efficiency of EDM according to the principle of EDM and discharge mechanisms, including increasing the rotation and vibration of the electrode to promote chip removal, adjusting the gap voltage to increase the probability of spark discharge, combining ultrasonic vibration technology in EDM, increasing the magnetic field of the discharge gap, changing the working medium, forcing the flushing fluid, lifting the tool at regular intervals, etc. Liu, J. W. et al. used a high electrode rotation speed (EDM-HS). The experimental results of machining metal matrix composites with electrodes showed that the material removal rate was directly related to the rotational speed of the electrode, and the material removal rate increased with the increasing electrode speed [8]. Huang Y.H. et al. investigated the effect of the rotational speed of the electrode on the machining efficiency. By comparing the experimental results, it was determined that the optimum electrode speed could effectively improve the machining efficiency [9]. Tsai Y.M. et al. investigated a vibration-assisted device for machining titanium alloy samples (Ti-6Al-4 V) and found that machining a 10 mm deep groove with vibration-assisted EDM resulted in a 200% improvement in machining efficiency compared to unassisted EDM [10].
Feng Y.R. et al. proposed a high response frequency magnetic levitation spindle system (MSSS) EDM technique for high-precision microhole machining of zirconium diboride-silicon carbide (ZrB-SiC) ceramics and superalloy Inconel 718, and the experimental results showed that MSSS EDM offers higher efficiency and quality than conventional EDM [11,12]    parameters can guarantee discharge machining in any machining. That group determined the optimal electrode machining time by detecting the voltage and current signals between the electrodes and the workpiece and calculating the normal discharge frequency and abnormal discharge rate. Experimental results showed that the proposed strategy improved the efficiency of EDM [26].
To improve the positioning response speed of the electrode and the machining efficiency of the EDM and to meet the requirements of high-speed and fine discharge machining in this paper, a 5-DOF controllable magnetic levitation actuator is introduced. The actuator is compact and can be connected to a conventional EDM machine tool for EDM, enabling rapid positioning of the electrode and maintaining the proper distance between the workpiece and the electrode. Based on this, a local current feedback controller and decoupling control elements are used to reduce coupling interference and improve the response speed and positioning accuracy of the actuator as much as possible. Finally, the actuator is connected to a conventional EDM machine tool for microhole machining experiments, and the machining speed is evaluated. The possibility of creative machining is investigated by controlling the movement of electrodes to machine complexshaped workpieces.

EDM with a 5-DOF controllable magnetic levitation actuator
To improve the efficiency of EDM, this study combines a conventional EDM machine tool with a 5-DOF controllable magnetic levitation actuator, as shown in Fig. 1. The actuator can adjust the electrode to the most suitable position in real time in the axial direction according to the relationship between the interpole detection voltage and the target voltage: i.e., a suitable interpole gap is always maintained between the electrode and the workpiece to ensure smooth machining. The radial direction allows the electrode to be moved for machining complex shapes. Figure 2 shows the structure diagram of the proposed 5-DOF controllable magnetic levitation actuator. Compared with iron core electromagnets, air-core coils have more leakage and weaker electromagnetic force, but this force is proportional to the coil current, is easy to control, and can achieve a larger stroke. Therefore, to facilitate control and generate larger strokes to meet the needs of machining more shaped workpieces, the actuator mainly consists of two permanent magnet rings on the spindle and eight sets of air-core coils on the stator symmetrical to the center of gravity of the spindle. To concentrate the magnetic flux, a soft iron ring is sandwiched between two oppositely placed permanent magnet rings. The 5-DOF motion of the spindle is controlled by the attractive or repulsive forces between the coils and the permanent magnets. To measure the displacement of the spindle, five displacement sensors are installed in the X, Y, and Z directions. Compared to a previously designed 3-DOF magnetic actuator, more degrees of freedom are provided in the direction of actuator rotation [27]. Compared to a previously designed 5-DOF actuator, the coil structure of Table 1 Model parameters  the actuator has been simplified so that the motion in the Z-direction no longer requires a separate set of coils for individual control, allowing all 5 directions of freedom to be controlled by 8 pairs of coils while increasing the actuator stroke [28]. The current direction of the air core coil is shown in Fig. 3. The coil and the permanent magnet ring generate repulsive and attractive forces, respectively, controlling the rotor movement in the 5-DOF direction. Taking Fig. 3a as an example, coil 1 and the n-pole of the permanent magnet ring at the upper end of the shaft generate a repulsive force in the lower right direction, and coil 1 and the s-pole of the permanent magnet ring generate an attractive force in the upper left direction so that the combined force direction is in the upper right direction. The principle of motion in other directions is similar. When the electromagnetic forces generated by the upper and lower coils are in opposite directions, rotational motion in the X direction can be controlled, as can motion control in the Y direction. Additionally, as shown in Fig. 3c, when the electromagnetic forces generated by the upper and lower coils are in the same direction, motion in the Z direction can be controlled. Figure 4 shows the experimental 5-DOF controllable magnetic levitation actuator with its spindle and air-core coils. An aluminum housing is used to reduce the weight of the actuator, which has a height of 190 mm, a width of 134 mm, and a mass of 8 kg. The material of the air-core coil is copper wire with a wire diameter of 0.7 mm, and the number of turns is 670. The height of the spindle is 148 mm, the diameter is 45 mm, and the mass is 0.8 kg. Both sides of the spindle are made of stainless steel material (SUS304), which is used as the detection material of the displacement sensor in the X and Y directions. Considering the remanent magnetism, coercivity, maximum magnetic energy product, and economy, the permanent magnet ring is made of NdFeB, a third-generation permanent magnet material. The spindle displacements in the 5-DOF directions were measured by five eddy current displacement sensors (PU-09, AEC Corp.) and the actuator was measured by a digital signal processor (DSP; DS1103 PPC Controller Board, dSPACE Corp.) with a sampling rate of 10 kHz. Figure 5 shows a block diagram of the designed 5-DOF controllable magnetic levitation actuator control system. The controller adopts an integral compensator to eliminate the steadystate error and a voltage regulator to stabilize the control system. Upon setting the gain δ of the integrator, the parameters of the denominator of the regulator are a 1 and a 0 and the parameters of the numerator are b 2 , b 1 , and b 0 . In Fig. 5, m is the mass of the spindle shaft, c is the damping coefficient, k is the stiffness coefficient, L is the inductance of the coil, R is the resistance of the coil, k i is the current stiffness coefficient, and k v is the counterelectromotive force coefficient. Additionally, to improve the response speed of the coil, a current feedback loop containing a PI controller is adopted. To ensure a simple controller design, the transfer function from the target value of the coil current to the coil current is approximated as a firstorder delay system, where T d is the approximate time constant. Table 1 shows the model parameters, and Table 2 shows the control parameters of the actuator, which are determined by experimental results and numerical simulation. Finally, the performance of the actuator was experimentally evaluated in terms of response time (10 µm step signal input in the X, Y, and Z directions and 1.0 mrad step signal in the Φ and θ directions), positioning resolution, kinematic travel, and frequency response. The results of the experiments are shown in Table 3.

Discharge machining system configuration
As shown in Fig. 6, the 5-DOF controllable magnetic levitation actuator was mounted on an existing EDM machine tool (EA8PV, Mitsubishi Electric Corp.) for EDM. In the machining system, the actuator is used for the adjustment mechanism of the interpole gap. The gap between the electrodes and the material to be machined is adjusted by the actuator, and the voltage between the electrodes is continuously controlled. The initial setting of the electrodes and the power supply mechanism for the electrodes is provided by the existing EDM machine tool.

Design of the control system for discharge machining
In EDM, when the distance between the electrode and the processing material is too large, the process is in an open circuit, and the interpole voltage is the supply voltage itself. When the distance between the electrode and the processing material is too small or zero (i.e., with the components in contact), processing occurs in a short circuit, and the interpole voltage is zero. The frequency of short circuits increases as the interpole gap decreases, while the frequency of open circuits increases as the interpole gap increases. Therefore, the change in average interpole voltage is approximately proportional to the distance between the electrode and the material being machined. Figure 7 shows the block diagram of the Z-directional EDM control system. During machining, the interpole voltage V is monitored in real time and as a feedback signal, the voltage V needs to be attenuated and averaged through an amplifier and a low-pass filter. The target value Z r for positioning the electrodes in the machining direction is generated by the deviation between the target voltage V r and the feedback voltage V fb . Then, a 5-DOF controllable magnetic levitation actuator is used to adjust the interelectrode distance so that the interpole voltage V remains constant to maintain a stable discharge state.
The processing controller used in this paper consists of an integrator and a proportioner. Here, γ and β are the parameters of the integrator and proportioner, respectively. According to the experiment, the target voltage V r is 1.656 V, the proportional gain β is 1.0 × 10 −5 , and the integral gain γ is 1.0 × 10 −3 . In addition, the gain of the amplifier is set to 0.03, and the cutoff frequency of the low-pass filter is 330 Hz.
In the machining experiments in this section, as shown in Fig. 7, the initial position of the electrode was kept in the X and Y directions (radial), while a hole was machined in the Z direction (axial) to verify the effectiveness of increasing the speed of electrical discharge machining. In addition, electrical discharge machining was performed in the Z direction while the electrode was moved along the XY plane to investigate the possibility of creative machining.

Verification experiments to improve the speed of EDM
EDM was performed in oil treatment fluid (EDF-K, Nippon Oil Corp.) using a pure copper cylindrical electrode with a diameter of 1 mm and machined in the shape of a throughhole. To avoid affecting the machining, the initial position

mm
of the electrode is maintained in the X and Y directions, and no swinging or jumping action of the electrode is performed. The interpole gap in the Z direction (axial) is controlled by the 5-DOF controllable magnetic levitation actuator only. The processing material is stainless steel (SUS304) with a thickness of 0.5 mm. The processing power supply is a transistor circuit with a peak current of 9.0 A, a pulse width of 44.8 μs, and an off time of 57.6 μs. Figure 8 shows the top view of the machined hole measured with a digital microscope (MSO-3080, Panrico Golden Root Co. Ltd.). Using a conventional EDM machine tool, the diameter of the EDM hole is 1.068 mm, while the diameter of the EDM hole using the actuator is 1.132 mm. The diameter of the hole increased by 6%. This is caused by the radial vibration of the electrode due to the electrical noise during the EDM process. Figure 9 shows the electrode feed during through-hole machining. The material removal rate is usually calculated in terms of the volume of the material being processed, and both conventional EDM and 5-DOF magnetic levitation actuators both use the same electrode for discharge machining and the same target machining. The machining depths are both 1 mm through the hole, and the effective machining diameters are both 1 mm, so comparing only the electrode feed rate has the same effect as comparing the material removal volume. In a conventional EDM machine tool, the feed rate is measured by a laser displacement meter (LM10, Panasonic Industrial Equipment SUNX Co., Ltd.) mounted on the machine spindle. When the actuator is used, it is measured by an eddy current sensor. The measurement results showed that the electrode feed waveform was approximately the same for the EDM machine tool and the actuator, but the machining time was reduced from 422 to 128 s with the actuator.
In conventional EDM, the interpole voltage is unstable, the interpole gap needs to be adjusted in the Z-axis direction, and the adjustment method is independently adjusted by the EDM machine tool, so the Z-axis interpole gap fluctuates considerably and the machining time is long. When the interpole voltage is unstable, the interpole gap is fine-tuned by the actuator in the Z-axis direction, which does not need to be adjusted independently by the EDM machine tool, so the Z-axis interpole gap fluctuates less and the machining time is shortened. Figures 10a and b show the interpole voltage through the amplifier and low-pass filter after the hole machining experiments. When using conventional EDM, the voltage between the poles often produces short circuits or open circuits. When using the actuator, the interpole voltage can be quickly restored from a short-circuit or open-circuit condition to a normal discharge condition. The actuator can control the electrode position more quickly, adjust the discharge state quickly, increase the number of discharges per unit time, and improve the probability of discharge; thus increasing the processing efficiency. Figure 11 shows a comparison of the machining effect of 10 holes machined by conventional EDM and the actuator under the same machining conditions. Figure 12 shows the average machining speed for 10 holes. In conventional EDM, the average machining speed is 1.108 μm/s. Under the action of the actuator, the average machining speed is 3.925 μm/s. It can be seen from the processing results that the actuator can quickly adjust the electrode position in the processing process to reach the optimal position, and the average processing speed is increased by a factor of 3.54. Figure 13 shows a comparison of the machining result indicators. The average hole diameter with the actuator is slightly larger than that of conventional EDM, and the extreme difference is also larger than that of conventional EDM, again due to the influence of electrical noise during EDM, which causes the actuator to drive the electrode in the radial direction with microvibrations, resulting in a slight increase in the machined hole diameter. In the future, it will be necessary to reduce the influence of noise during the machining process and to improve the stability of the actuator to reduce the polar difference and the average bore diameter of the machined bore.

Circular motion processing of electrodes
Using the same control system, the electrode gap in the Z-direction was controlled by the 5-DOF controllable magnetic levitation actuator only. The target values in the X-direction and Y-direction were set as sine and cosine waves with a frequency of 0.5 Hz and amplitudes of 0.5, 1.0, and 1.5 mm, respectively, to make the electrodes move in a circular motion. No jumping action of the electrode was performed. The electrode for the electrical discharge machining was a solid copper cylinder with a diameter of 0.5 mm. Discharge machining was carried out in oil treatment fluid (EDF-K, Nippon Oil Corporation), and the thickness of the material to be machined was 0.5 mm stainless steel SUS304. Other machining conditions were kept constant, and the machining time was 30 s. Figure 14 shows the displacement and machining results of the electrode in the X and Y directions when the diameter of the circumferential motion of the electrode is 1.0 mm, 2.0 mm, and 3.0 mm, respectively. When the circumferential motion diameter is 1.0 mm, the shape of the machining is a circle with a center diameter of 1.0 mm and a width of 0.5 mm. When the circumferential motion diameter is 2.0 mm, the machining shape is a circle with a center diameter of 2.0 mm and a width of 0.5 mm. When the circumferential motion diameter of the electrode is 3.0 mm, the machining shape is a circle with a center diameter of 3.0 mm and a width of 0.5 mm. From the machining results, it can be seen that the center diameter of the circle increases proportionally with the increase in the diameter of the circumferential motion of the electrode.

Square motion machining of the electrode
As with the circular motion, the target value of the electrode is set to square for electrical discharge machining. Figure 15 shows the displacement and machining results of the electrode in the X and Y directions when the side lengths of the square motion of the electrode are 1.0, 1.5, and 2.0 mm, respectively. As with the circular motion of the electrode, the machined shape increases proportionally with the increase in the length of the square edge.

Eddy current motion machining of the electrode
As in the case of circular motion, a combination of harmonic function and slope function is set in the X-axis and Y-axis directions to make the electrode move in the shape of an eddy current for electrical discharge machining. The constant of the combined function is set to 0.75 mm, the frequency is set to 0.5 Hz, and the machining time is set to 30 s. Figure 16 shows the machining shape and trajectory of the electrode when the vortex motion of the electrode is used in electrical discharge machining using the actuator. From the result, the movement of the electrode is of vortex type, and there is a certain shape error (the initial point of the machining is not in the center of the initial point of machining slot). The reason for this conclusion is that during the machining process, the electrode starts to move spirally as soon as it touches the workpiece, so when the electrode goes to the next machining point, the initial machining point of the workpiece is not completely machined out of the machining slot. In general, the amplitude of each axis is consistent with the setting, the shape after machining is consistent with the set shape trend and the shape is basically the same. From the above machining results, it can be seen that by adjusting the target value of the radial direction of the actuator, various motion trajectories of the electrode can be controlled to depict an arbitrary shape. Therefore, this actuator can be applied to the processing of complex shapes.

Conclusions
This paper introduces a 5-DOF controllable magnetic levitation actuator that can be directly attached to a conventional EDM machine tool that has been developed to improve the efficiency of EDM. Second, an EDM control system based on local current feedback and decoupled control elements was been designed to improve the response speed and positioning accuracy of the actuator. The actuator was also subjected to EDM, and the effect of the improved machining speed was verified by conventional through-hole machining experiments. The experimental results show that the machining speed of the EDM machine tool connected to the actuator has been increased by a factor of 3.54 compared to conventional EDM. In addition, the application of the developed actuator to the machining of complex shapes was attempted using its 5-DOF control function. The electrodes can perform circular, square, and eddy current movements. The actuator developed will be used in the future for EDM of complex shapes. In addition, the stability of the actuator will be improved, and noise reduction studies will be carried out on the EDM machine tool in the future.