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

Experimental study of EDM characteristics using a 5-DOF controllable magnetic levitation actuator | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Experimental study of EDM characteristics using a 5-DOF controllable magnetic levitation actuator Boran Luan, Xiaoyou Zhang, Fangchao Xu, Guang Yang, Junjie Jin, and 2 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-1637310/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 30 Dec, 2022 Read the published version in The International Journal of Advanced Manufacturing Technology → Version 1 posted 4 You are reading this latest preprint version Abstract The efficiency and accuracy of conventional electrical discharge machining (EDM) is limited by the stability of the voltage between the poles. To improve the efficiency of EDM, this paper proposes 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 inter-pole voltage is improved by the actuator micro-adjustment the electrodes of the EDM machine tool. Firstly, 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. Secondly, the actuator was connected to the spindle of a conventional EDM machine tool, and machining experiments were carried out. The experimental results showed that the EDM machine tool connected to the actuator could control the electrode position more quickly, adjust the discharge state quickly, and increase the number of discharges per unit time. The average machining speed increased from 1.108µm/s to 3.925µm/s, which is 3.54 times faster than conventional EDM. Finally, complex shape machining experiments were 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 could be controlled to depict arbitrary shapes. Electrical discharge machining Magnetic levitation controllable actuator Positioning High-speed machining Experimental study Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 1. 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 finally 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 any conductive materials, and the machining of micro-porous and complex shapes has become an indispensable machining method at this stage [5–6] . Due to the huge 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 inter-pole gap in time [7] , resulting in unstable inter-pole voltage for EDM, which affects the discharge probability, thus limiting the efficiency and accuracy of conventional EDM. Compared with traditional cutting methods, the efficiency of EDM does not have an advantage, so it is necessary to find ways to improve the efficiency of EDM. To improve the efficiency of EDM, research scholars have done a lot of research on improving the efficiency of EDM according to the principle of EDM and discharge mechanism, 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 increase of the electrode speed [8] . Yuhua Huang 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] . M. Y. Tsai et al. investigated a vibration-assisted device for machining titanium alloy samples (Ti-6Al-4V) and found that machining a 10 mm deep groove with vibration-assisted EDM resulted in a 200% reduction in machining time compared to unassisted EDM [10] . Yerui Feng et al. proposed a high response frequency magnetic levitation spindle system (MSSS) EDM technique for high-precision micro-hole machining of zirconium diboride-silicon carbide (ZrB-SiC) ceramics and superalloy Inconel 718, and the experimental results showed that MSSSEDM has higher efficiency and quality compared with conventional EDM [11–12] . Dong Yinghuai et al. designed a small ultrasonic vibration-assisted EDM machine tool to avoid spark concentration and abnormal arcing during machining [13] . Liu Yu et al. investigated the effect of ultrasonic vibration tool electrodes on EDM machining efficiency, and the results showed that the periodic ultrasonic vibration promoted the movement of debris. The machining efficiency was improved compared with the conventional hole EDM [14] . Wenjun Kong et al. proposed a horizontal ultrasonic vibration EDM method to make up for the deficiencies of existing ultrasonic EDM technology. Comparative experimental results showed that machining efficiency, workpiece surface quality, and machining process were improved [15] . Wuyi Ming et al. conducted a study on magnetic field-assisted electrical discharge machining. The results of the study show that an appropriate magnetic field helps to improve energy utilization efficiency and material removal rate (MRR) at similar surface roughness. In particular, the MRR of magnetic materials (SKD11) showed a more significant improvement [16] . Preetkanwal Singh Bains et al. studied magnetic field-assisted EDM of metal matrix composites. The experimental results show that magnetic field-assisted EDM has significant process stability and can achieve high efficiency and quality EDM [17] . Gurpreet Singh et al. applied a combination of magnetic field and ultrasonic vibration to EDM and conducted a series of experiments, which showed that the combined effect of magnetic field and ultrasonic vibration on the machining area improved the machining efficiency of EDM [18] . Zhang Jin et al. proposed a high-speed EDM method combining Lorentz force, electric field force and high-speed electrode rotation, and the experimental results showed that the material removal rate was improved [19] . Chao Xu et al. atomized argon and oxygen as EDM media and compared the material removal during machining, and the experimental results showed that the discharge probability was improved and the machining efficiency was increased by more than 8 times [20] . Thrinadh Jadam et al. added multi-walled carbon nanotubes (MWCNT) at a concentration of 0.5 g/l to kerosene as a dielectric for EDM and conducted experiments by varying the peak discharge current. The experimental results show that the use of MWCNT hybrid dielectric can significantly improve the machining performance compared to conventional EDM [21] . Yi Jiang et al. used air and argon as gas media for EDM (Air-EDM and Ar-EDM, respectively) for the electrical discharge machining of TC4 titanium alloy and Cr12 steel. The experimental results show that the material removal rate of TC4 using Ar-EDM is almost four times higher than that using Air-EDM [22] . Reza Najati Ilkhchi et al. proposed a high-speed flushing system to flush the gap between the workpiece and the electrode and investigated the effect of the flushing system in the form of Reynolds number on the material removal rate. The experimental results showed that the efficiency of EDM increased by 44% as the Reynolds number increased [23] . Hao Ni et al. developed an EDM system that simultaneously uses pump forced flushing, ultrasonic vibration and electrode rotation to drill small deep holes. The results show that the combination of pump flushing with vibration and rotation can improve EDM efficiency [24] . Trias Andromeda et al. designed a PID controller based on a differential evolution algorithm to adjust the gap distance between the workpiece and the electrode in time to maintain the proper gap voltage. Simulation results verified the effectiveness of this controller [25] . Wang Jin et al. investigated the adaptive tool lifting technique, and the experimental results showed that the adaptive tool lifting technique can automatically adjust the tool lifting speed according to the discharge between electrodes. Therefore, the optimal machining parameters can guarantee the discharge machining in any machining. They determine 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 was connected to a conventional EDM machine tool for micro-hole machining experiments, and the machining speed was evaluated. The possibility of creating machining is tried by controlling the movement of electrodes to machine complex-shaped workpieces. 2. 5-dof Controlled Magnetic Levitation Actuator For Edm 2.1 EDM with 5-DOF controllable magnetic levitation actuator To improve the efficiency of EDM, this paper 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 inter-pole detection voltage and the target voltage, i.e. a suitable inter-pole 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 of complex shapes. 2.2 Structure and principle of 5-DOF controllable magnetic levitation actuator Figure 2 shows the structure diagram of the proposed 5-DOF controllable magnetic levitation actuator. Compared with the iron core electromagnet, the air-core coils have more leakage and weaker electromagnetic force, but it is proportional to the coil current, easy to control, and can achieve 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 transducers are installed in the X, Y and Z directions. 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. 3(a) 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 of the lower right direction, and coil 1 and the s-pole of the permanent magnet ring generate an attractive force of 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. Also, as shown in Fig. 3(c), when the electromagnetic forces generated by the upper and lower coils are in the same direction, motion in the Z direction can be controlled. 2.3 5-DOF controllable magnetic levitation actuator physical parameters Figure 4 shows the experimental 5-DOF controllable magnetic levitation actuator with its spindle and air-core coils. An aluminum housing was 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 X and Y directions. Considering the remanent magnetism, coercivity, maximum magnetic energy product and economy, the permanent magnet ring is made of NdFeB, the third generation permanent magnet material. The spindle displacements in the 5-DOF directions were measured by five eddy current displacement transducers (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. 2.4 5-DOF controllable magnetic levitation actuator motion control system Figure 5 is a block diagram of the 5-DOF controllable magnetic levitation actuator control system designed. The controller adopts an integral compensator to eliminate the steady-state error and a voltage regulator to stabilize the control system. Set 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 counter-electromotive force coefficient. Also, to improve the response speed of the coil, a current feedback loop containing a PI controller is adopted. To design the controller simply, the transfer function from the target value of coil current to coil current is approximated to a first delay system. Where T d is the approximate time constant of the first-order delay system. Table 2 − 1 shows the model parameters, and Table 2 – 2 shows the control parameters of the actuator, which are determined by experimental results and numerical simulation. Table 2 − 1 Model parameters X(Y)Z θ (Φ) direction Unit m 0.80 kg L 35.4 mH R 2.6 Ω l 25 mm J 1.1×10 − 3 kg‧m 2 T d 3.9×10 − 3 / k i 4.2 N‧A − 1 k x 367.57 N‧m − 1 k z 170.7 N‧m − 1 k θ 9.19 N‧rad − 1 c x 1 N‧s‧m − 1 c z 1 N‧s‧m − 1 c θ 1 N‧s‧rad − 1 Table 2 2 Control parameters X(Y)Z θ (Φ) direction controller δ x 256.45 δ z 256.50 δ θ 3.07×10 4 a 0x 3.07×10 5 a 0z 1.49×10 5 a 0θ 4.53×10 5 a 1x 873.31 a 1z 1.93×10 3 a 1θ 819.73 b 0x 1.30×10 8 b 0z 6.78×10 9 b 0θ 1.79×10 6 b 1x 3.52×10 6 b 1z 8.5×10 7 b 1θ 3.09×10 4 b 2x 4.01×10 4 b 2z 2.16×10 5 b 2θ 93.14 α x 35 α z 35 α θ 35 ε x 2565 ε z 2565 ε θ 2565 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 2 –3. Table 2 3 Performance evaluation of 5-DOF controllable magnetic levitation actuator Response time Stroke Positioning resolution Band-width X direction 6.7ms 4mm 1µm 101Hz Y direction 6.8ms 4mm 1µm 101Hz Z direction 26.3ms 4mm 1µm 51Hz Φ direction 39.9ms 70mrad 25µrad 42Hz θ direction 16.2ms 70mrad 20µrad 45Hz 3. Edm Control System 3.1 Discharge machining system configuration As shown in Fig. 6 , the 5-DOF controllable magnetic levitation actuator was mounted on an existing EDM machine tool for EDM. In the machining system, the actuator is used for the adjustment mechanism of the inter-pole 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 are provided by the existing EDM machine tool. 3.2 Design of 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 inter-pole voltage is the supply voltage itself. When the distance between the electrode and the processing material is too small or in contact, processing occurs in a short circuit and the inter-pole voltage is zero. The frequency of short circuits increases as the inter-pole gap decreases, while the frequency of open circuits increases as the inter-pole gap increases. Therefore, the change in average inter-pole voltage is roughly 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 inter-pole 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, 5-DOF controllable magnetic levitation actuator is used to adjust the inter-electrode distance so that the inter-pole 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. 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 chapter, as shown in Fig. 7 , the initial position of the electrode was kept in the X and Y directions (radial), while the 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 try the possibility of creative machining. 4. Verification Experiments To Improve The Speed Of Edm EDM is 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 through-hole. In order not to affect the machining, the initial position of the electrode is maintained in the X and Y directions, and no swinging or jumping action of the electrode is performed. the inter-pole 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 µsec, and an off time of 57.6 µsec. 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 has 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. 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 seconds to 128 seconds with the actuator. In conventional EDM, the inter-pole voltage is unstable and the inter-pole 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 inter-pole gap fluctuates a lot and the machining time is long. When the inter-pole voltage is unstable, the inter-pole 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 inter-pole gap fluctuates less and the machining time is shortened. Figure 10 (a) and Fig. 10 (b) show the inter-pole voltage after the hole machining passes through the amplifier and low-pass filter. When using conventional EDM, the voltage between the poles often produces short circuits or open circuits. When using the actuator, the inter-pole 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, improve the probability of discharge, and thus increase the processing efficiency. Figure 11 shows the 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 1.108µm/s. Under the action of the actuator, the average machining speed is 3.925µm/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 3.54 times. Table 4 − 1 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 micro-vibrations, 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. Table 4 − 1 Comparison of processing result index The hole diameter Using conventional EDM Using 5-DOF controllable magnetic levitation actuator maximum 1.074mm 1.108mm minimum 1.064mm 1.088mm average 1.069mm 1.101mm extreme difference 0.01mm 0.02mm 5 Feasibility Experiment Of Complex Shape Machining 5.1 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. And 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. The 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 13 shows the displacement and machining results of the electrode in 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 1.0mm, the shape of the machining is a circle with a center diameter of 1.0mm and a width of 0.5mm. When the circumferential motion diameter is 2.0mm, the machining shape is a circle with a center diameter of 2.0mm and a width of 0.5mm. When the circumferential motion diameter of the electrode is 3.0mm, the machining shape is a circle with a center diameter of 3.0mm and a width of 0.5mm. From the machining results, it can be seen that the center diameter of the circle increases proportionally with the increase of the diameter of the circumferential motion of the electrode. 5.2 Square motion machining of electrode As with the circular motion, the target value of the electrode is set to square for the electrical discharge machining. Figure 14 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. 5.3 Eddy current motion machining of electrode As in the case of circular motion, a combination of harmonic function and slope function is set in the X- 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 30s. Figure 15 shows the machining shape and trajectory of the electrode when the vortex motion of the electrode is used in the electrical discharge machining using the actuator. From the results, the motion of the electrodes is spiral and the amplitude of each axis is consistent with the setting. Also, the distance from the center point to the machining endpoint is consistent with the actual machining results. From the above machining results, it can be seen that by adjusting the target value of the radial direction of the actuator, it is possible to control the various motion trajectories of the electrode and depict arbitrary shapes. Therefore, the actuator can be applied to the processing of complex shapes. 6. 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. Secondly, an EDM control system based on local current feedback and decoupled control elements has 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 tried 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 EDM machine tool in the future. Declarations Acknowledgements The authors would like to thank the fund of National Natural Science Fund of China (Grant No.52005345， No. 52005344), National Key Research and Development Project (No.2020YFC2006701), Scientific research fund project of Liaoning Provincial Department of Education (No. LFGD2020002) , LiaoNing Revitalization Talents Program（No.XLYC1905003）, The Central Government Guides Local Special Funds for Science and Technology Development (Grant No. 2020JH6/10500048). Author contribution Boran Luan: software, drawing, experiments, data collection and processing, reading and summarization of all literature, writing-original draft, writing-review & editing; Xiaoyou Zhang: experiments, supervision, writing-review & editing; Fangchao Xu: writing-review & editing; Guang Yang: writing-review & editing; Junjie Jin: writing-review & editing; Chengcheng Xu: writing-review & editing; Feng Sun: writing-review & editing. Ethics declarations Ethics approval Not applicable. Consent to participate Not applicable. Consent for publication All the co-authors consent to the publication of this work. Competing interests The authors declare no competing interests. Data availability The datasets generated and analyzed during the current study are available upon reasonable request. References Ved Prakash et al. Micro-electrical discharge machining of difficult-to-machine materials: A review[J]. 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Differential evolution for optimization of PID gain in Electrical Discharge Machining control system[J]. Transactions of the Canadian Society for Mechanical Engineering， 2013 , 37(3) : 293-301. Jin Wang and Zhixin Jia. Efficiency improvement in electrical discharge machining (EDM) of constant section cavity based on experimental study and numerical calculations[J]. Production Engineering, 2018 , 12(5) : 567-578. Cite Share Download PDF Status: Published Journal Publication published 30 Dec, 2022 Read the published version in The International Journal of Advanced Manufacturing Technology → Version 1 posted Reviewers agreed at journal 29 May, 2022 Reviewers invited by journal 28 May, 2022 Editor assigned by journal 18 May, 2022 First submitted to journal 09 May, 2022 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-1637310","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":109501874,"identity":"575c93d2-21e7-4fe7-8470-94fea553f7db","order_by":0,"name":"Boran 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Xu","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Chengcheng","middleName":"","lastName":"Xu","suffix":""},{"id":109501880,"identity":"3d2b60d1-9ad2-4474-ad08-edcff216d219","order_by":6,"name":"Sun Feng","email":"","orcid":"","institution":"","correspondingAuthor":false,"prefix":"","firstName":"Sun","middleName":"","lastName":"Feng","suffix":""}],"badges":[],"createdAt":"2022-05-09 08:15:29","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-1637310/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-1637310/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s00170-022-10688-0","type":"published","date":"2022-12-30T18:07:11+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":22475880,"identity":"16b2e5af-2d90-425c-a968-b463e6023a34","added_by":"auto","created_at":"2022-06-09 19:31:09","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":22557,"visible":true,"origin":"","legend":"\u003cp\u003eEDM machine tool with an additional local actuator\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-1637310/v1/1503e9ef606105d1cdb2e82f.png"},{"id":22476083,"identity":"1b5c3e5c-f64b-4b58-afe0-eee9996fb421","added_by":"auto","created_at":"2022-06-09 19:41:09","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":71025,"visible":true,"origin":"","legend":"\u003cp\u003eThe structure diagram of the 5-DOF controlled magnetic levitation actuator\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-1637310/v1/44ccc239896c7c9e29244838.png"},{"id":22476001,"identity":"7bf24a85-7209-454b-93c5-459035cf9dee","added_by":"auto","created_at":"2022-06-09 19:36:09","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":79493,"visible":true,"origin":"","legend":"\u003cp\u003ePrinciple of spindle motion control\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-1637310/v1/32dfd669a3c0f7f19eca6cae.png"},{"id":22475879,"identity":"af50c838-499d-4326-8f50-43265db9bb23","added_by":"auto","created_at":"2022-06-09 19:31:09","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":405806,"visible":true,"origin":"","legend":"\u003cp\u003eExperimental 5-DOF controllable magnetic levitation actuator and its spindle\u003c/p\u003e\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-1637310/v1/3198a39c2597e0e39a709b9d.png"},{"id":22475883,"identity":"e50b5f6a-d024-4ec2-971f-ae244861803f","added_by":"auto","created_at":"2022-06-09 19:31:09","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":27864,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cspan class=\"ql-cursor\"\u003e\u003c/span\u003eController designed\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-1637310/v1/2e699447d409630dbda6c7b7.png"},{"id":22476002,"identity":"df25c694-68b3-41d4-bfa8-133bb85f8a92","added_by":"auto","created_at":"2022-06-09 19:36:09","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":201549,"visible":true,"origin":"","legend":"\u003cp\u003eElectrical discharge machine with 5-DOF controllable magnetic levitation actuator\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-1637310/v1/ff407faced3de4679d1eda27.png"},{"id":22476004,"identity":"a1383996-d045-4e51-904a-2c85d0b92107","added_by":"auto","created_at":"2022-06-09 19:36:09","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":49408,"visible":true,"origin":"","legend":"\u003cp\u003eBlock diagram of EDM control system\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-1637310/v1/384dd7d81f5cc24b65a4ae50.png"},{"id":22475888,"identity":"7d051066-aac7-45b4-ac48-ae6fdc74d116","added_by":"auto","created_at":"2022-06-09 19:31:09","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":484359,"visible":true,"origin":"","legend":"\u003cp\u003eMachined holes\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-1637310/v1/015d70c627d4cae23d232d92.png"},{"id":22475884,"identity":"97c48479-a28b-4a34-8b0c-9b1e11c0cd05","added_by":"auto","created_at":"2022-06-09 19:31:09","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":20132,"visible":true,"origin":"","legend":"\u003cp\u003eFeed displacements of electrode\u003c/p\u003e\u003cp\u003e\u003cbr\u003e\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-1637310/v1/742332532d59725c49dc2a90.png"},{"id":22475891,"identity":"ddf380d3-f9c3-4af2-97ab-82a8316d1cdc","added_by":"auto","created_at":"2022-06-09 19:31:09","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":34467,"visible":true,"origin":"","legend":"\u003cp\u003eInter-pole voltage\u003c/p\u003e","description":"","filename":"10.png","url":"https://assets-eu.researchsquare.com/files/rs-1637310/v1/b557ace5bf22a42ef309cfaf.png"},{"id":22475893,"identity":"b057f6a2-e855-4572-a1c7-b36c9022b0f9","added_by":"auto","created_at":"2022-06-09 19:31:10","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":844156,"visible":true,"origin":"","legend":"\u003cp\u003eComparison diagram of processing effect\u003c/p\u003e","description":"","filename":"11.png","url":"https://assets-eu.researchsquare.com/files/rs-1637310/v1/c61c2de8b17c373fbe13fba2.png"},{"id":22475892,"identity":"75068acd-2f00-4843-84e5-ec530da149a5","added_by":"auto","created_at":"2022-06-09 19:31:09","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":17840,"visible":true,"origin":"","legend":"\u003cp\u003eAverage machining speed\u003c/p\u003e","description":"","filename":"12.png","url":"https://assets-eu.researchsquare.com/files/rs-1637310/v1/c6fba7da278c1adc548b4c8e.png"},{"id":22475886,"identity":"e2eadb45-4600-480b-86c0-6ef46e0fe8c1","added_by":"auto","created_at":"2022-06-09 19:31:09","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":295305,"visible":true,"origin":"","legend":"\u003cp\u003eElectric discharge machining with electrode circular motion\u003c/p\u003e","description":"","filename":"13.png","url":"https://assets-eu.researchsquare.com/files/rs-1637310/v1/4778d08ad735a891c145fdae.png"},{"id":22476084,"identity":"523489a6-c93c-484c-a08c-d0e6dd2cdba4","added_by":"auto","created_at":"2022-06-09 19:41:09","extension":"png","order_by":14,"title":"Figure 14","display":"","copyAsset":false,"role":"figure","size":341674,"visible":true,"origin":"","legend":"\u003cp\u003eElectric discharge machining with electrode square motion\u003c/p\u003e","description":"","filename":"14.png","url":"https://assets-eu.researchsquare.com/files/rs-1637310/v1/6465ccc51d5a879800dc916a.png"},{"id":22475890,"identity":"15fce078-4267-4150-a4a1-8b832921875c","added_by":"auto","created_at":"2022-06-09 19:31:09","extension":"png","order_by":15,"title":"Figure 15","display":"","copyAsset":false,"role":"figure","size":164023,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cspan class=\"ql-cursor\"\u003e\u003c/span\u003eProcessing results of vortex motion\u003c/p\u003e","description":"","filename":"15.png","url":"https://assets-eu.researchsquare.com/files/rs-1637310/v1/a3090511329921a749cf2933.png"},{"id":44715058,"identity":"89c76232-0d78-4cd6-b113-0665b2c84b08","added_by":"auto","created_at":"2023-10-16 18:12:53","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3219912,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-1637310/v1/45050eb8-0603-4db0-8443-2308c506982c.pdf"}],"financialInterests":"","formattedTitle":"Experimental study of EDM characteristics using a 5-DOF controllable magnetic levitation actuator","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eThe 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 finally achieve the desired shape, size and surface topography\u003csup\u003e[1\u0026ndash;2]\u003c/sup\u003e. Compared with conventional machining methods, EDM technology has the advantage of not being limited by the hardness and strength requirements of the workpiece material\u003csup\u003e[3\u0026ndash;4]\u003c/sup\u003e. It is widely used in the machining of difficult materials such as high hardness, high toughness, high brittleness and any conductive materials, and the machining of micro-porous and complex shapes has become an indispensable machining method at this stage\u003csup\u003e[5\u0026ndash;6]\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eDue to the huge 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 inter-pole gap in time\u003csup\u003e[7]\u003c/sup\u003e, resulting in unstable inter-pole voltage for EDM, which affects the discharge probability, thus limiting the efficiency and accuracy of conventional EDM. Compared with traditional cutting methods, the efficiency of EDM does not have an advantage, so it is necessary to find ways to improve the efficiency of EDM.\u003c/p\u003e \u003cp\u003eTo improve the efficiency of EDM, research scholars have done a lot of research on improving the efficiency of EDM according to the principle of EDM and discharge mechanism, 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 increase of the electrode speed\u003csup\u003e[8]\u003c/sup\u003e. Yuhua Huang 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\u003csup\u003e[9]\u003c/sup\u003e. M. Y. Tsai et al. investigated a vibration-assisted device for machining titanium alloy samples (Ti-6Al-4V) and found that machining a 10 mm deep groove with vibration-assisted EDM resulted in a 200% reduction in machining time compared to unassisted EDM\u003csup\u003e[10]\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eYerui Feng et al. proposed a high response frequency magnetic levitation spindle system (MSSS) EDM technique for high-precision micro-hole machining of zirconium diboride-silicon carbide (ZrB-SiC) ceramics and superalloy Inconel 718, and the experimental results showed that MSSSEDM has higher efficiency and quality compared with conventional EDM\u003csup\u003e[11\u0026ndash;12]\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eDong Yinghuai et al. designed a small ultrasonic vibration-assisted EDM machine tool to avoid spark concentration and abnormal arcing during machining\u003csup\u003e[13]\u003c/sup\u003e. Liu Yu et al. investigated the effect of ultrasonic vibration tool electrodes on EDM machining efficiency, and the results showed that the periodic ultrasonic vibration promoted the movement of debris. The machining efficiency was improved compared with the conventional hole EDM\u003csup\u003e[14]\u003c/sup\u003e. Wenjun Kong et al. proposed a horizontal ultrasonic vibration EDM method to make up for the deficiencies of existing ultrasonic EDM technology. Comparative experimental results showed that machining efficiency, workpiece surface quality, and machining process were improved\u003csup\u003e[15]\u003c/sup\u003e. Wuyi Ming et al. conducted a study on magnetic field-assisted electrical discharge machining. The results of the study show that an appropriate magnetic field helps to improve energy utilization efficiency and material removal rate (MRR) at similar surface roughness. In particular, the MRR of magnetic materials (SKD11) showed a more significant improvement\u003csup\u003e[16]\u003c/sup\u003e. Preetkanwal Singh Bains et al. studied magnetic field-assisted EDM of metal matrix composites. The experimental results show that magnetic field-assisted EDM has significant process stability and can achieve high efficiency and quality EDM\u003csup\u003e[17]\u003c/sup\u003e. Gurpreet Singh et al. applied a combination of magnetic field and ultrasonic vibration to EDM and conducted a series of experiments, which showed that the combined effect of magnetic field and ultrasonic vibration on the machining area improved the machining efficiency of EDM\u003csup\u003e[18]\u003c/sup\u003e. Zhang Jin et al. proposed a high-speed EDM method combining Lorentz force, electric field force and high-speed electrode rotation, and the experimental results showed that the material removal rate was improved\u003csup\u003e[19]\u003c/sup\u003e. Chao Xu et al. atomized argon and oxygen as EDM media and compared the material removal during machining, and the experimental results showed that the discharge probability was improved and the machining efficiency was increased by more than 8 times\u003csup\u003e[20]\u003c/sup\u003e. Thrinadh Jadam et al. added multi-walled carbon nanotubes (MWCNT) at a concentration of 0.5 g/l to kerosene as a dielectric for EDM and conducted experiments by varying the peak discharge current. The experimental results show that the use of MWCNT hybrid dielectric can significantly improve the machining performance compared to conventional EDM\u003csup\u003e[21]\u003c/sup\u003e. Yi Jiang et al. used air and argon as gas media for EDM (Air-EDM and Ar-EDM, respectively) for the electrical discharge machining of TC4 titanium alloy and Cr12 steel. The experimental results show that the material removal rate of TC4 using Ar-EDM is almost four times higher than that using Air-EDM\u003csup\u003e[22]\u003c/sup\u003e. Reza Najati Ilkhchi et al. proposed a high-speed flushing system to flush the gap between the workpiece and the electrode and investigated the effect of the flushing system in the form of Reynolds number on the material removal rate. The experimental results showed that the efficiency of EDM increased by 44% as the Reynolds number increased\u003csup\u003e[23]\u003c/sup\u003e. Hao Ni et al. developed an EDM system that simultaneously uses pump forced flushing, ultrasonic vibration and electrode rotation to drill small deep holes. The results show that the combination of pump flushing with vibration and rotation can improve EDM efficiency\u003csup\u003e[24]\u003c/sup\u003e. Trias Andromeda et al. designed a PID controller based on a differential evolution algorithm to adjust the gap distance between the workpiece and the electrode in time to maintain the proper gap voltage. Simulation results verified the effectiveness of this controller\u003csup\u003e[25]\u003c/sup\u003e. Wang Jin et al. investigated the adaptive tool lifting technique, and the experimental results showed that the adaptive tool lifting technique can automatically adjust the tool lifting speed according to the discharge between electrodes. Therefore, the optimal machining parameters can guarantee the discharge machining in any machining. They determine 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\u003csup\u003e[26]\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eTo 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 was connected to a conventional EDM machine tool for micro-hole machining experiments, and the machining speed was evaluated. The possibility of creating machining is tried by controlling the movement of electrodes to machine complex-shaped workpieces.\u003c/p\u003e"},{"header":"2. 5-dof Controlled Magnetic Levitation Actuator For Edm","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e\u003cem\u003e2.1 EDM with 5-DOF controllable magnetic levitation actuator\u003c/em\u003e\u003c/h2\u003e \u003cp\u003eTo improve the efficiency of EDM, this paper combines a conventional EDM machine tool with a 5-DOF controllable magnetic levitation actuator, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. The actuator can adjust the electrode to the most suitable position in real-time in the axial direction according to the relationship between the inter-pole detection voltage and the target voltage, i.e. a suitable inter-pole 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 of complex shapes.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Structure and principle of 5-DOF controllable magnetic levitation actuator\u003c/h2\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e shows the structure diagram of the proposed 5-DOF controllable magnetic levitation actuator. Compared with the iron core electromagnet, the air-core coils have more leakage and weaker electromagnetic force, but it is proportional to the coil current, easy to control, and can achieve 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 transducers are installed in the X, Y and Z directions.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe current direction of the air core coil is shown in Fig.\u0026nbsp;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.\u0026nbsp;3(a) 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 of the lower right direction, and coil 1 and the s-pole of the permanent magnet ring generate an attractive force of 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. Also, as shown in Fig.\u0026nbsp;3(c), when the electromagnetic forces generated by the upper and lower coils are in the same direction, motion in the Z direction can be controlled.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3 5-DOF controllable magnetic levitation actuator physical parameters\u003c/h2\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e4\u003c/span\u003e shows the experimental 5-DOF controllable magnetic levitation actuator with its spindle and air-core coils. An aluminum housing was 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 X and Y directions. Considering the remanent magnetism, coercivity, maximum magnetic energy product and economy, the permanent magnet ring is made of NdFeB, the third generation permanent magnet material. The spindle displacements in the 5-DOF directions were measured by five eddy current displacement transducers (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.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e2.4 5-DOF controllable magnetic levitation actuator motion control system\u003c/h2\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e5\u003c/span\u003e is a block diagram of the 5-DOF controllable magnetic levitation actuator control system designed. The controller adopts an integral compensator to eliminate the steady-state error and a voltage regulator to stabilize the control system. Set the gain \u003cem\u003eδ\u003c/em\u003e of the integrator, the parameters of the denominator of the regulator are \u003cem\u003ea\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003ea\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e and the parameters of the numerator are \u003cem\u003eb\u003c/em\u003e\u003csub\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sub\u003e, \u003cem\u003eb\u003c/em\u003e\u003csub\u003e\u003cem\u003e1\u003c/em\u003e,\u003c/sub\u003e and \u003cem\u003eb\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e. In Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e5\u003c/span\u003e, m is the mass of the spindle shaft, \u003cem\u003ec\u003c/em\u003e is the damping coefficient, \u003cem\u003ek\u003c/em\u003e is the stiffness coefficient, \u003cem\u003eL\u003c/em\u003e is the inductance of the coil, \u003cem\u003eR\u003c/em\u003e is the resistance of the coil, \u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e is the current stiffness coefficient, and \u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003ev\u003c/em\u003e\u003c/sub\u003e is the counter-electromotive force coefficient. Also, to improve the response speed of the coil, a current feedback loop containing a PI controller is adopted. To design the controller simply, the transfer function from the target value of coil current to coil current is approximated to a first delay system. Where \u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ed\u003c/em\u003e\u003c/sub\u003e is the approximate time constant of the first-order delay system. Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e2\u003c/span\u003e\u0026thinsp;\u0026minus;\u0026thinsp;1 shows the model parameters, and Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e2\u003c/span\u003e\u0026ndash;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e2\u003c/span\u003e shows the control parameters of the actuator, which are determined by experimental results and numerical simulation.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u0026thinsp;\u0026minus;\u0026thinsp;1 Model parameters\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003eX(Y)Z θ (Φ) direction\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e \u003cp\u003eUnit\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003em\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e0.80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003ekg\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eL\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e35.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003emH\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eR\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e2.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eΩ\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003el\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003emm\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eJ\u003c/em\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e1.1\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003ekg‧m\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eT\u003c/em\u003e\u003csub\u003e\u003cem\u003ed\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e3.9\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e/\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003ei\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e4.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eN‧A\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e367.57\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eN‧m\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e170.7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eN‧m\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003ek\u003c/em\u003e\u003csub\u003e\u003cem\u003eθ\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e9.19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eN‧rad\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003ec\u003c/em\u003e\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eN‧s‧m\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003ec\u003c/em\u003e\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eN‧s‧m\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003ec\u003c/em\u003e\u003csub\u003e\u003cem\u003eθ\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eN‧s‧rad\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e2 Control parameters\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e \u003cp\u003eX(Y)Z θ (Φ) direction controller\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eδ\u003c/em\u003e\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e256.45\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eδ\u003c/em\u003e\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e256.50\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eδ\u003c/em\u003e\u003csub\u003e\u003cem\u003eθ\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3.07\u0026times;10\u003csup\u003e4\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003ea\u003c/em\u003e\u003csub\u003e\u003cem\u003e0x\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3.07\u0026times;10\u003csup\u003e5\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003ea\u003c/em\u003e\u003csub\u003e\u003cem\u003e0z\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.49\u0026times;10\u003csup\u003e5\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003ea\u003c/em\u003e\u003csub\u003e\u003cem\u003e0θ\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4.53\u0026times;10\u003csup\u003e5\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003ea\u003c/em\u003e\u003csub\u003e\u003cem\u003e1x\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e873.31\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003ea\u003c/em\u003e\u003csub\u003e\u003cem\u003e1z\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.93\u0026times;10\u003csup\u003e3\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003ea\u003c/em\u003e\u003csub\u003e\u003cem\u003e1θ\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e819.73\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eb\u003c/em\u003e\u003csub\u003e\u003cem\u003e0x\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.30\u0026times;10\u003csup\u003e8\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eb\u003c/em\u003e\u003csub\u003e\u003cem\u003e0z\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e6.78\u0026times;10\u003csup\u003e9\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eb\u003c/em\u003e\u003csub\u003e\u003cem\u003e0θ\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.79\u0026times;10\u003csup\u003e6\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eb\u003c/em\u003e\u003csub\u003e\u003cem\u003e1x\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3.52\u0026times;10\u003csup\u003e6\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eb\u003c/em\u003e\u003csub\u003e\u003cem\u003e1z\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e8.5\u0026times;10\u003csup\u003e7\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eb\u003c/em\u003e\u003csub\u003e\u003cem\u003e1θ\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3.09\u0026times;10\u003csup\u003e4\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eb\u003c/em\u003e\u003csub\u003e\u003cem\u003e2x\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4.01\u0026times;10\u003csup\u003e4\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eb\u003c/em\u003e\u003csub\u003e\u003cem\u003e2z\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2.16\u0026times;10\u003csup\u003e5\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eb\u003c/em\u003e\u003csub\u003e\u003cem\u003e2θ\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e93.14\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eα\u003c/em\u003e\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e35\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eα\u003c/em\u003e\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e35\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eα\u003c/em\u003e\u003csub\u003e\u003cem\u003eθ\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e35\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eε\u003c/em\u003e\u003csub\u003e\u003cem\u003ex\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2565\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eε\u003c/em\u003e\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2565\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eε\u003c/em\u003e\u003csub\u003e\u003cem\u003eθ\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2565\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eFinally, the performance of the actuator was experimentally evaluated in terms of response time (10 \u0026micro;m 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\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e2\u003c/span\u003e\u0026ndash;3.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e3 Performance evaluation of 5-DOF controllable magnetic levitation actuator\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eResponse time\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eStroke\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003ePositioning resolution\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eBand-width\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eX direction\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e6.7ms\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4mm\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1\u0026micro;m\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e101Hz\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eY direction\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e6.8ms\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4mm\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1\u0026micro;m\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e101Hz\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eZ direction\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e26.3ms\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4mm\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1\u0026micro;m\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e51Hz\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eΦ direction\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e39.9ms\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e70mrad\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e25\u0026micro;rad\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e42Hz\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eθ direction\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e16.2ms\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e70mrad\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e20\u0026micro;rad\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e45Hz\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"3. Edm Control System","content":"\u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Discharge machining system configuration\u003c/h2\u003e \u003cp\u003eAs shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e6\u003c/span\u003e, the 5-DOF controllable magnetic levitation actuator was mounted on an existing EDM machine tool for EDM. In the machining system, the actuator is used for the adjustment mechanism of the inter-pole 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 are provided by the existing EDM machine tool.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Design of control system for discharge machining\u003c/h2\u003e \u003cp\u003eIn EDM, when the distance between the electrode and the processing material is too large, the process is in an open circuit and the inter-pole voltage is the supply voltage itself. When the distance between the electrode and the processing material is too small or in contact, processing occurs in a short circuit and the inter-pole voltage is zero. The frequency of short circuits increases as the inter-pole gap decreases, while the frequency of open circuits increases as the inter-pole gap increases. Therefore, the change in average inter-pole voltage is roughly proportional to the distance between the electrode and the material being machined.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e7\u003c/span\u003e shows the block diagram of the Z-directional EDM control system. During machining, the inter-pole voltage \u003cem\u003eV\u003c/em\u003e is monitored in real-time and, as a feedback signal, the voltage \u003cem\u003eV\u003c/em\u003e needs to be attenuated and averaged through an amplifier and a low-pass filter. The target value \u003cem\u003eZ\u003c/em\u003e\u003csub\u003e\u003cem\u003er\u003c/em\u003e\u003c/sub\u003e for positioning the electrodes in the machining direction is generated by the deviation between the target voltage \u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003er\u003c/em\u003e\u003c/sub\u003e and the feedback voltage \u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003efb\u003c/em\u003e\u003c/sub\u003e. Then, 5-DOF controllable magnetic levitation actuator is used to adjust the inter-electrode distance so that the inter-pole voltage \u003cem\u003eV\u003c/em\u003e remains constant to maintain a stable discharge state.\u003c/p\u003e \u003cp\u003eThe processing controller used in this paper consists of an integrator and a proportioner. Here, \u003cem\u003eγ\u003c/em\u003e and \u003cem\u003eβ\u003c/em\u003e are the parameters of the integrator and proportioner. According to the experiment, the target voltage \u003cem\u003eV\u003c/em\u003e\u003csub\u003e\u003cem\u003er\u003c/em\u003e\u003c/sub\u003e is 1.656 V, the proportional gain \u003cem\u003eβ\u003c/em\u003e is 1.0 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;5\u003c/sup\u003e, and the integral gain \u003cem\u003eγ\u003c/em\u003e is 1.0 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e. In addition, the gain of the amplifier is set to 0.03, and the cutoff frequency of the low-pass filter is 330 Hz.\u003c/p\u003e \u003cp\u003eIn the machining experiments in this chapter, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e7\u003c/span\u003e, the initial position of the electrode was kept in the X and Y directions (radial), while the 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 try the possibility of creative machining.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"4. Verification Experiments To Improve The Speed Of Edm","content":"\u003cp\u003eEDM is 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 through-hole. In order not to affect the machining, the initial position of the electrode is maintained in the X and Y directions, and no swinging or jumping action of the electrode is performed. the inter-pole 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 \u0026micro;sec, and an off time of 57.6 \u0026micro;sec.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e8\u003c/span\u003e 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 has increased by 6%. This is caused by the radial vibration of the electrode due to the electrical noise during the EDM process.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e9\u003c/span\u003e shows the electrode feed during through-hole machining. 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 seconds to 128 seconds with the actuator.\u003c/p\u003e \u003cp\u003eIn conventional EDM, the inter-pole voltage is unstable and the inter-pole 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 inter-pole gap fluctuates a lot and the machining time is long. When the inter-pole voltage is unstable, the inter-pole 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 inter-pole gap fluctuates less and the machining time is shortened.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e10\u003c/span\u003e(a) and Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e10\u003c/span\u003e(b) show the inter-pole voltage after the hole machining passes through the amplifier and low-pass filter. When using conventional EDM, the voltage between the poles often produces short circuits or open circuits. When using the actuator, the inter-pole 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, improve the probability of discharge, and thus increase the processing efficiency.\u003c/p\u003e \u003cp\u003eFigure 11 shows the comparison of the machining effect of 10 holes machined by conventional EDM and the actuator under the same machining conditions.\u003c/p\u003e\u003cp\u003eFigure \u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e12\u003c/span\u003e shows the average machining speed for 10 holes. In conventional EDM, the average machining speed is 1.108\u0026micro;m/s. Under the action of the actuator, the average machining speed is 3.925\u0026micro;m/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 3.54 times.\u003c/p\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e\u0026thinsp;\u0026minus;\u0026thinsp;1 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 micro-vibrations, 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.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003e\u0026thinsp;\u0026minus;\u0026thinsp;1 Comparison of processing result index\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eThe hole diameter\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eUsing conventional EDM\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eUsing 5-DOF controllable magnetic levitation actuator\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003emaximum\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.074mm\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.108mm\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eminimum\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.064mm\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.088mm\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eaverage\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.069mm\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.101mm\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eextreme difference\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.01mm\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.02mm\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e"},{"header":"5 Feasibility Experiment Of Complex Shape Machining","content":"\u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003e5.1 Circular motion processing of electrodes\u003c/h2\u003e \u003cp\u003eUsing 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. And 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. The 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.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e13\u003c/span\u003e shows the displacement and machining results of the electrode in 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 1.0mm, the shape of the machining is a circle with a center diameter of 1.0mm and a width of 0.5mm. When the circumferential motion diameter is 2.0mm, the machining shape is a circle with a center diameter of 2.0mm and a width of 0.5mm. When the circumferential motion diameter of the electrode is 3.0mm, the machining shape is a circle with a center diameter of 3.0mm and a width of 0.5mm. From the machining results, it can be seen that the center diameter of the circle increases proportionally with the increase of the diameter of the circumferential motion of the electrode.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003e5.2 Square motion machining of electrode\u003c/h2\u003e \u003cp\u003eAs with the circular motion, the target value of the electrode is set to square for the electrical discharge machining. Figure\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e14\u003c/span\u003e 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.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003e5.3 Eddy current motion machining of electrode\u003c/h2\u003e \u003cp\u003eAs in the case of circular motion, a combination of harmonic function and slope function is set in the X- 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 30s. Figure\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e15\u003c/span\u003e shows the machining shape and trajectory of the electrode when the vortex motion of the electrode is used in the electrical discharge machining using the actuator. From the results, the motion of the electrodes is spiral and the amplitude of each axis is consistent with the setting. Also, the distance from the center point to the machining endpoint is consistent with the actual machining results. From the above machining results, it can be seen that by adjusting the target value of the radial direction of the actuator, it is possible to control the various motion trajectories of the electrode and depict arbitrary shapes. Therefore, the actuator can be applied to the processing of complex shapes.\u003c/p\u003e \u003c/div\u003e"},{"header":"6. Conclusions","content":"\u003cp\u003eThis 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. Secondly, an EDM control system based on local current feedback and decoupled control elements has 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 tried 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 EDM machine tool in the future.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledgements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors would like to thank the fund of National Natural Science Fund of China (Grant No.52005345，\u0026nbsp;No. 52005344), National Key Research and Development Project (No.2020YFC2006701), Scientific research fund project of Liaoning Provincial Department of Education (No. LFGD2020002) , LiaoNing Revitalization Talents Program（No.XLYC1905003）, The Central Government Guides Local Special Funds for Science and Technology Development (Grant No. 2020JH6/10500048).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor contribution\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eBoran Luan: software, drawing, experiments, data collection and processing, reading and summarization of all literature, writing-original draft, writing-review \u0026amp; editing; Xiaoyou Zhang: experiments, supervision, writing-review \u0026amp; editing; Fangchao Xu: writing-review \u0026amp; editing; Guang Yang: writing-review \u0026amp; editing; Junjie Jin: writing-review \u0026amp; editing; Chengcheng Xu: writing-review \u0026amp; editing; Feng Sun: writing-review \u0026amp; editing.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEthics declarations\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEthics approval\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent to participate\u0026nbsp;\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent for publication\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAll the co-authors consent to the publication of this work.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe datasets generated and analyzed during the current study are available upon reasonable request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eVed Prakash et al. 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Production Engineering, \u003cstrong\u003e2018\u003c/strong\u003e, 12(5) : 567-578.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":true,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"the-international-journal-of-advanced-manufacturing-technology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jamt","sideBox":"Learn more about [The International Journal of Advanced Manufacturing Technology](https://www.springer.com/journal/170)","snPcode":"170","submissionUrl":"https://submission.nature.com/new-submission/170/3","title":"The International Journal of Advanced Manufacturing Technology","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Electrical discharge machining, Magnetic levitation controllable actuator, Positioning, High-speed machining, Experimental study","lastPublishedDoi":"10.21203/rs.3.rs-1637310/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-1637310/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe efficiency and accuracy of conventional electrical discharge machining (EDM) is limited by the stability of the voltage between the poles. To improve the efficiency of EDM, this paper proposes 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 inter-pole voltage is improved by the actuator micro-adjustment the electrodes of the EDM machine tool. Firstly, 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. Secondly, the actuator was connected to the spindle of a conventional EDM machine tool, and machining experiments were carried out. The experimental results showed that the EDM machine tool connected to the actuator could control the electrode position more quickly, adjust the discharge state quickly, and increase the number of discharges per unit time. The average machining speed increased from 1.108\u0026micro;m/s to 3.925\u0026micro;m/s, which is 3.54 times faster than conventional EDM. Finally, complex shape machining experiments were 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 could be controlled to depict arbitrary shapes.\u003c/p\u003e","manuscriptTitle":"Experimental study of EDM characteristics using a 5-DOF controllable magnetic levitation actuator","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2022-06-09 19:31:07","doi":"10.21203/rs.3.rs-1637310/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"reviewerAgreed","content":"","date":"2022-05-29T05:59:33+00:00","index":0,"fulltext":""},{"type":"reviewersInvited","content":"","date":"2022-05-28T21:59:19+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2022-05-18T23:09:29+00:00","index":"","fulltext":""},{"type":"submitted","content":"The International Journal of Advanced Manufacturing Technology","date":"2022-05-09T04:13:48+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"the-international-journal-of-advanced-manufacturing-technology","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jamt","sideBox":"Learn more about [The International Journal of Advanced Manufacturing Technology](https://www.springer.com/journal/170)","snPcode":"170","submissionUrl":"https://submission.nature.com/new-submission/170/3","title":"The International Journal of Advanced Manufacturing Technology","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"45917fd9-d6b9-455e-8b6c-76a155316385","owner":[],"postedDate":"June 9th, 2022","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2023-10-16T18:09:42+00:00","versionOfRecord":{"articleIdentity":"rs-1637310","link":"https://doi.org/10.1007/s00170-022-10688-0","journal":{"identity":"the-international-journal-of-advanced-manufacturing-technology","isVorOnly":false,"title":"The International Journal of Advanced Manufacturing Technology"},"publishedOn":"2022-12-30 18:07:11","publishedOnDateReadable":"December 30th, 2022"},"versionCreatedAt":"2022-06-09 19:31:07","video":"","vorDoi":"10.1007/s00170-022-10688-0","vorDoiUrl":"https://doi.org/10.1007/s00170-022-10688-0","workflowStages":[]},"version":"v1","identity":"rs-1637310","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-1637310","identity":"rs-1637310","version":["v1"]},"buildId":"_2-kVJe1T_tPrBINL-cwx","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}