Electromagnetic Sheet Forming by Uniform Pressure Using Flat Spiral Coil

materials

Article Electromagnetic Sheet Forming by Uniform Pressure Using Flat Spiral Coil

Xiaohui Cui 1,2,3,*, Dongyang Qiu 2, Lina Jiang 4, Hailiang Yu 1,2,3, Zhihao Du 1 and Ang Xiao 1

1 Light alloy research Institute, Central South University, Changsha 410083, China; [email protected] (H.Y.); [email protected] (Z.D.); [email protected] (A.X.) 2 College of Mechanical and Electrical Engineering, Central South University, Changsha 410083, China; [email protected] 3 State Key Laboratory of High Performance Complex Manufacturing, Central South University, Changsha 410083, China 4 Shandong North Binhai Machinery Company, Zibo 255201, China; [email protected] * Correspondence: [email protected]; Tel.: +86-15388028791

Received: 13 May 2019; Accepted: 13 June 2019; Published: 18 June 2019

Abstract: The coil is the most important component in electromagnetic forming. Two important questions in electromagnetic forming are how to obtain the desired magnetic force distribution on the sheet and increase the service life of the coil. A uniform pressure coil is widely used in sheet embossing, bulging, and welding. However, the coil is easy to break, and the manufacturing process is complex. In this paper, a new uniform-pressure coil with a planar structure was designed. A three-dimensional (3D) finite element model was established to analyze the effect of the main process parameters on magnetic force distribution. By comparing the experimental results, it was found that the simulation results have a higher analysis precision. Based on the simulation results, the resistivity of the die, spacing between the left and right parts of the coil, relative position between coil and sheet, and sheet width significantly affect the distribution of magnetic force. Compared with the structure and magnetic force on a traditional uniform pressure coil, the planar uniform pressure coil can produce a uniform magnetic force distribution on the sheet, reduce the manufacturing difficulty, reduce manufacturing cost, and enhance the service life for the coil.

Keywords: electromagnetic sheet forming; uniform pressure; numerical simulation

1. Introduction In electromagnetic forming (EMF), the coil is a key component that converts the electrical energy stored in a capacitor into the kinetic energy required for the deformation of a workpiece. The shape of the coil determines the distribution of electromagnetic force, affecting the forming result of the workpiece. According to the deformed shape of a workpiece, the forming coil can be divided into two types: (1) The forming coil for a tube; (2) the forming coil for a flat sheet. The tube forming coils have a solenoid structure, mainly used to achieve tube bulging and tube compression. For example, Cui et al. [1] found that electromagnetic tube bulging with multidirectional magnetic pressure can decrease the tensile stress and thickness at the easily broken position on a tube. Yu et al. [2] predicted electromagnetic tube compression and evaluated the optimum current frequency using a finite element model (FEM). Compared with electromagnetic tube forming, electromagnetic sheet forming is more complex. Thus, there are many coil structures for sheet deformation. Cui et al. [3] accurately predicted sheet bulging using a flat spiral circular coil. Li et al. [4] obtained the biaxial tensile stress state on a sheet by using flat spiral circular coils. It was found that the forming limit of Ti–6Al–4V sheets increased by

Materials 2019, 12, 1963; doi:10.3390/ma12121963 www.mdpi.com/journal/materials Materials 2019, 12, 1963 2 of 16

24.37% when subjected to electromagnetic sheet bulging compared with the quasi-static condition.

Cui etMaterials al. [5 2019] used, 11, x the FOR electromagnetic PEER REVIEW incremental forming (EMIF) method to produce a large2 of 17 part using a small flat spiral circular coil under the condition of a small discharge energy. Cui et al. [6] placed a flatby spiral 24.37% circular when coil subjected at the sheet-metal to electromagnetic end to generatesheet bulging radial magneticcompared pressure.with the Severalquasi-static steps of quasi-staticcondition. stamping Cui et al. and [5] magnetic-pulse used the electromagnetic forming withincremental radial forceforming improve (EMIF) the method forming to produce depth bya 31% comparedlarge part to quasi-static using a small stamping. flat spiral Cui circular et al. coil [7] usedunder two the flatcondition spiral-waisted of a small coils discharge and a energy. small discharge Cui et al. [6] placed a flat spiral circular coil at the sheet-metal end to generate radial magnetic pressure. energy to manufacture a large-size part after 36 discharging and six stretching steps. Cui et al. [8] Several steps of quasi-static stamping and magnetic-pulse forming with radial force improve the used the spiral circular coil with tower type and multidirectional magnetic pressure to reduce the forming depth by 31% compared to quasi-static stamping. Cui et al. [7] used two flat spiral-waisted cornercoils radius and a of small a cylindrical discharge part.energy Li to et manufacture al. [9] designed a large-size special part specimens after 36 discharging to obtain theand uniaxialsix tensionstretching state by steps. EMF Cui using et al. a single-turn[8] used the coil. spiral Oliveira circular et coil al. [with10] designedtower type a doubleand multidirectional spiral square coil to makemagnetic sheet-free pressure bulging to reduce and the formed corner a radius flat insert of a cavity.cylindrical However, part. Li aet “dead al. [9] spot”designed (region special of low magneticspecimens pressure) to obtain occurred the uniaxial on the sheet,tension corresponding state by EMF using to the a centersingle-turn of winding coil. Oliveira of the et flat al. spiral [10] coil. Therefore,designed traditional a double flat spiral actuators square producecoil to make a non-uniform sheet-free bulging pressure and distribution, formed a flat limiting insert thecavity. types of partsHowever, that can bea “dead formed. spot” (region of low magnetic pressure) occurred on the sheet, corresponding to Thus,the center a new of type winding of actuator of the that flat provided spiral coil. a uniform Therefore, pressure traditional distribution flat actuators on a sheet produce was proposed a non-uniform pressure distribution, limiting the types of parts that can be formed. by Kamal et al. [11]. Figure1a shows the design principle of a uniform-pressure coil. The outer Thus, a new type of actuator that provided a uniform pressure distribution on a sheet was channel is in close contact with the sheet metal, generating the induced current on an outer channel proposed by Kamal et al. [11]. Figure 1a shows the design principle of a uniform-pressure coil. The and sheetouter metalchannel composed is in close ofcontact a closed with circuit the sheet after me coiltal, generating discharge. the Manish induced et al.current [12] usedon an aouter two-step formingchannel process and tosheet manufacture metal composed a good of phone a closed face circuit by using after acoil uniform-pressure discharge. Manish coil. et al. Golowin [12] used et al.a [13] demonstratedtwo-step forming that the process uniform to pressuremanufacture actuator a good can phone form face a sheet by using metal a withuniform-pressure a complex shape coil. and obtainGolowin fine surface et al. [13] features. demonstrated Kinsey that et al. the [14 uniform] established pressure the actuator electromagnetic-mechanically can form a sheet metal with coupled a numericalcomplex model shape to predict and theobtain forming fine pressuresurface andfeat mechanicalures. Kinsey deformation et al. [14] using established a uniform pressurethe actuator.electromagnetic-mechanically Weddeling et al [15] proved coupled the magneticnumerical pulsemodel welding to predict is feasible the forming and applicable pressure byand using the uniformmechanical pressure deformation electromagnetic using a uniform coil. Thibaudeaupressure actuator. et al. [Weddeling16] proposed et al an [15] analytical proved modelthe to magnetic pulse welding is feasible and applicable by using the uniform pressure electromagnetic design the uniform pressure coil. The designed coil can be used for electromagnetic forming and coil. Thibaudeau et al. [16] proposed an analytical model to design the uniform pressure coil. The magneticdesigned pulsed coil welding.can be used Cui for etelectromagnetic al. [17] analyzed forming the distributionand magnetic ofpulsed magnetic welding. force Cui on et aal. sheet [17] and coil usinganalyzed a uniform the distribution pressure of coil.magnetic It was force found on a thatsheet a and uniform coil using pressure a uniform is distributed pressure coil. in It the was region correspondingfound that a to uniform the under-surface pressure is distributed of the coil. in th Thus,e region the corresponding coil undergoes to the a complexunder-surface state of ofthe stress, whichcoil. may Thus, cause the coil coil failure. undergoes Figure a 1complexd shows state that of a bulgestress, appears which may in the cause bottom coil surfacefailure. ofFigure the coil1d [ 18]. Therefore,shows comparedthat a bulge to appears a flat spiral in the coil,bottom the surface uniform-pressure of the coil [18]. coil Therefore, in Figure compared1 has two to maina flat spiral problems: (1) Thecoil, coil the can uniform-pressure easily break, andcoil in (2) Figure the coil 1 has has two a complex main problems: structure. (1) The coil can easily break, and (2) the coil has a complex structure.

FigureFigure 1. Traditional 1. Traditional uniform-pressure uniform-pressure coil. (a ()a Design) Design principle, principle, (b) magnetic (b) magnetic force on force sheet on [17], sheet (c) [17], (c) magneticmagnetic force force onon a coil [17], [17], and and (d ()d failure) failure of ofa coil a coil [18]. [18 ].

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Therefore, a new uniform-pressure coil with a planar structure was designed in this study. A three-dimensional (3D) FEM was established to analyze the effect of the main process parameters on magneticMaterials 2019 force, 12, 1963distribution. Finally, the rationality of the coil design was verified according to3 ofthe 16 experiment of sheet deformation. Therefore, a new uniform-pressure coil with a planar structure was designed in this study. 2. Design Principle of New Uniform-Pressure Coil A three-dimensional (3D) FEM was established to analyze the effect of the main process parameters on magneticTo obtain force a distribution. uniform distribution Finally, the of rationality magnetic offorce the on coil a design sheet, wasit must verified be ensured according that to the inducedexperiment current of sheet directions deformation. on the sheet are the same. Thus, the same current direction should be applied to the coil facing on the sheet region to be deformed. Based on this principle, a uniform-pressure2. Design Principle coil of with New Uniform-Pressureplanar spiral structur Coile was designed, as shown in Figure 2. It was assumedTo obtain that the a uniform coil is loaded distribution with ofa counterclockwise magnetic force on current. a sheet, If it mustthe current be ensured in the that left the half induced of the coilcurrent flows directions in the negative on the sheetdirection are the of same.the Y-axis, Thus, the the induced same current current direction on the sheet should should be applied flow in to the the positivecoil facing direction on the sheetof the region Y-axis. to beTo deformed.make the in Basedduced on current this principle, constitute a uniform-pressure a closed current coil loop, with a conductiveplanar spiral die structure was set wasto contact designed, with as both shown the inends Figure of the2. It sheet, was assumed as shown that in Figure the coil 2b. is loaded with a counterclockwiseTo analyze the current.distribution If the of current magnetic in theforce left on half the of sheet the coil generated flows in by the the negative coil, the direction following of processthe Y-axis, parameters the induced were current analyzed: on the (1) sheet The shouldresistivit flowy of in the the die; positive (2) the direction spacing of between the Y-axis. the Toleft make and rightthe induced parts of current the coil, constitute set to L1; a (3) closed the distance current loop, of the a conductivecenter line between die was setthe to sheet contact and with the left both part the ofends the ofcoil, the set sheet, to L2; as (4) shown the width in Figure of the2b. sheet, set to L3.

FigureFigure 2. DesignDesign principleprinciple for for the the new new uniform-pressure uniform-pressure coil. coil. (a) Coil(a) andCoil sheetand andsheet (b and) induced (b) induced current currentflowing flowing in the sheet in the and sheet die. and die. To analyze the distribution of magnetic force on the sheet generated by the coil, the following 3. FEM process parameters were analyzed: (1) The resistivity of the die; (2) the spacing between the left and rightIn parts this of paper, the coil, the set ANSYS/EMAG to L1; (3) the distance software of was the centerused to line calculate between the the magnetic sheet and force the leftacting part on of thethe coil,sheet, set and to L2; ANSYS/LSDYNA (4) the width of thewas sheet, used set to to predict L3. the sheet deformation process after coil discharge. Figure 3 shows the 3D FEM for electromagnetic forming. The electromagnetic field model consists3. FEM of a far-air region, an air region, a coil, and a sheet. The element types for the far-air region, air region,In this coil, paper, and the sheet ANSYS were/EMAG infin111, software solid97, was solid97, used to and calculate solid97, the respectively. magnetic force The acting far-field on theair representssheet, and the ANSYS boundary/LSDYNA conditions was used of the to predictmagnetic the fi sheeteld, while deformation the near-field process air after is used coil to discharge. transfer theFigure magnetic3 shows field the 3Dgenerated FEM for by electromagnetic the coil to both forming. the sheet The and electromagnetic the die. During field the model electromagnetic consists of a formingfar-air region, process, an airthe region,current a density coil, and was a sheet. loaded The on element the coil. types Both for the the sheets far-air and region, the coils air region, were dividedcoil, and into sheet a werehexahedral infin111, mesh. solid97, The solid97, number and of solid97,nodes and respectively. elements Thefor far-fieldthe sheet air were represents 8505 and the 6400,boundary respectively. conditions The of number the magnetic of nodes field, and while elemen thets near-fieldfor the coil air element is used type to transfer were 4800 the and magnetic 1600, respectively.field generated To bydescribe the coil the to contact both the between sheet and the the sh die.eet and During the die the in electromagnetic electromagnetic forming field analysis, process, thethe contact-region current density between was loaded the onsheet the and coil. die Both was the pr sheetsocessed and by the common coils were nodes. divided For intofurther a hexahedral analysis, mesh. The number of nodes and elements for the sheet were 8505 and 6400, respectively. The number of nodes and elements for the coil element type were 4800 and 1600, respectively. To describe the Materials 2019, 12, 1963 4 of 16

Materials 2019, 11, x FOR PEER REVIEW 4 of 17 contact between the sheet and the die in electromagnetic field analysis, the contact-region between the sheetthree andpaths die were was processeddefined on by the common sheet. Path nodes. 1 and For furtherPath 2 were analysis, used three to analyze paths were the defineddistribution on the of sheet.magnetic Path force 1 and on Path the 2sheet. were Path used 3 to was analyze used theto describe distribution the final of magnetic deformation force onprofile the sheet. of the Path sheet. 3 wasThe usedintersection to describe points the of final Path deformation 1 and Path 2, profile as well of theas Path sheet. 2 and The Path intersection 3, were set points to point of Path A and 1 and B, Pathrespectively. 2, as well as Path 2 and Path 3, were set to point A and B, respectively.

FigureFigure 3.3. Finite-elementFinite-element models:models: (a)) ElectromagneticElectromagnetic ﬁeldfield modelmodel andand ((bb)) coilcoil andand sheet.sheet.

InIn thisthis study,study, 0.50.5 mmmm thicknessthickness 5052-O5052-O aluminumaluminum alloyalloy sheetssheets werewere usedused inin thethe followingfollowing experiments.experiments. TheThe truetrue stress–strainstress–strain for for the the sheet sheet is is shown shown in in Equation Equation (1), 1, and the yield strength ofof thethe sheetsheet waswas 105.8 105.8 MPa. MPa. The The material material properties properties of theof the sheet, sheet, coil, coil, and and steel steel die (made die (made by Q235) by Q235) are given are ingiven Table in1 .Table To consider 1. To consider the e ﬀect the of effect a high of strain a high rate strain on therate forming on the forming process, theprocess, properties the properties of material of werematerial modeled were usingmodeled the using Cowper–Symonds the Cowper–Symonds constitutive constitutive model as shownmodel as in shown Equation in (2).Equation 2.

0.377 σεσs ==+474.6(ε + 0.01866) 0.377 (1) s 474.6( 0.01866) (1) . m ε σ = σ (1 + ( ) ) (2) s Pε σσ=+m s (1 ( ) ) . (2) where σ is the dynamic ﬂow stress, σs is quasi-static stress,P ε is the plastic strain, ε is the strain rate, P = 1 6500 s− , and m = 0.25 is a speciﬁc parameter of aluminum alloy. where σ is the dynamic flow stress, σs is quasi-static stress, ε is the plastic strain, ε is the strain rate, P = 6500 s−1, and m = 0.25 is Tablea specific 1. Materials parameter parameters of aluminum of forming alloy. system.

Density (kg/m3) 2750 Table 1. Materials parameters of forming system. Sheet (5052 aluminum alloy) Elastic modulus (GPa) 68 Density (kg/m3) 2750 Yield strength (MPa) 105.8 Elastic modulus (GPa) 68 Sheet (5052 aluminum alloy) Electrical resistivity (Ω m) 4.93 10 8 Yield strength· (MPa) × 105.8− 8 Coil (Copper) Electrical resistivity (Ω m) 1.7 10 -8 Electrical resistivity· (Ω·m) × 4.93− × 10 Die (Q235Coil (Copper) steel) Electrical Electrical resistivity resistivity (Ω m) (Ω·m) 5 10 1.77 × 10-8 · × − Die (Q235 steel) Electrical resistivity (Ω·m) 5 × 10-7 Figure4a shows the current curves through the coil at 2.5 KV measured using a Rogowski coil. To improveFigure the4a shows operating the lifetimecurrent ofcurves capacitor, through a diode the coil and at resistor 2.5 KV were measured connected using in parallela Rogowski with coil. the capacitorTo improve to inhibitthe operating the reverse lifetime charging of capacitor, of the capacitor. a diode Theand currentresistor datawere were connected recorded in forparallel∆t = with1 µs andthe capacitor loaded into to theinhibit coil the to calculatereverse charging the subsequent of the capacitor. magnetic The ﬁeld current and sheet data deformation. were recorded for Δt = 1 μs and loaded into the coil to calculate the subsequent magnetic field and sheet deformation.

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FigureFigure 4.4. Current through the coil. 4. Eﬀect of Process Parameters on Magnetic Force 4. Effect of Process Parameters on Magnetic Force 4.1. Resistivity of Die 4.1. Resistivity of Die If L1 = 95 mm, L2 = 0 mm, and L3 = 20 mm, Figure5 shows the induced current and magnetic If L1 = 95 mm, L2 = 0 mm, and L3 = 20 mm, Figure 5 shows the induced current and magnetic force on a sheet using the die with a resistivity equal to 5e-7 Ω m. It was found that the induced current force on a sheet using the die with a resistivity equal to 5e-7· Ω·m. It was found that the induced occurs on both the sheet and die after the coil is discharged. It was assumed that the coil is loaded current occurs on both the sheet and die after the coil is discharged. It was assumed that the coil is with clockwise current, as shown in Figure3b. The direction of induced current on the sheet and die loaded with clockwise current, as shown in Figure 3b. The direction of induced current on the sheet was opposite to the direction of current on the coil. Moreover, the induced current formed a current and die was opposite to the direction of current on the coil. Moreover, the induced current formed a loop. Thus, the current with same direction generated on the sheet corresponded to the hollow region current loop. Thus, the current with same direction generated on the sheet corresponded to the of the die. Because the width of the left half of the coil was equal to 27 mm and the width of sheet hollow region of the die. Because the width of the left half of the coil was equal to 27 mm and the L3 was set to 20 mm, the current density in the middle of the sheet was less than those on the two width of sheet L3 was set to 20 mm, the current density in the middle of the sheet was less than those sides of the sheet, as shown in Figure5b. In addition, the current density at the right side of sheet on the two sides of the sheet, as shown in Figure 5b. In addition, the current density at the right side was smaller than that at the left side of the sheet. This is because the right half of the coil can produce of sheet was smaller than that at the left side of the sheet. This is because the right half of the coil can electromagnetic induction on the right side of the sheet. The current direction of the right half of the produce electromagnetic induction on the right side of the sheet. The current direction of the right coil was opposite to that of left half of the coil. This will result in a lower current density at the right half of the coil was opposite to that of left half of the coil. This will result in a lower current density at side of the sheet. Figure5c shows the distribution of magnetic ﬁeld force on the sheet. The direction of the right side of the sheet. Figure 5c shows the distribution of magnetic field force on the sheet. The electromagnetic force was positive along the Z-axis as a whole, but magnetic forces existed along the direction of electromagnetic force was positive along the Z-axis as a whole, but magnetic forces X-axis at both sides of the sheet. Based on the 3D distribution of magnetic force in Figure5c, Figure5d existed along the X-axis at both sides of the sheet. Based on the 3D distribution of magnetic force in shows the magnetic force along Path 1. A uniform magnetic pressure was observed at the location Figure 5c, Figure 5d shows the magnetic force along Path 1. A uniform magnetic pressure was of 35 mm–35 mm away from the sheet center. The length, with a uniform pressure, is equal to the observed− at the location of −35 mm–35 mm away from the sheet center. The length, with a uniform length of the die opening. pressure, is equal to the length of the die opening. If L1 = 95 mm, L2 = 0 mm, and L3 = 20 mm, Figure6 shows the induced current and magnetic force on the sheet using the die with a resistivity of 5e-4 Ω m. After the coil discharge, induced current · can be generated on the sheet, but no induced current is generated on the die. Thus, the induced current on sheet constitutes a current loop, as shown in Figure6a. The current density at the right side of the sheet is much larger than that at the left side of sheet, as shown in Figure6b. Figure6c shows the distribution of electromagnetic force on sheet. A very small magnetic force was generated on the left and middle region of the sheet. Though the magnetic force at the right side of the sheet has a large magnetic force, the direction of magnetic force is not positive along the Z-axis. Therefore, a die with a smaller resistivity should be used to generate a uniform magnetic force on the sheet according to the results shown in Figures5 and6.

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Figure 5. DistributionFigure 5. Distribution of induced of induced current current and and magnetic magnetic force force using using the die the with die resistivity with resistivity equal to equal to 5e-7: (a) Current5e-7: (a) on Current the sheet on the and sheet die, and (die,b) current(b) current in in detailed detailed sheet sheet region, region, (c) 3D (c) magnetic 3D magnetic force on force on the sheet, and (thed) sheet, magnetic and (d force) magnetic along force Path along 1. Path 1. Materials 2019, 11, x FOR PEER REVIEW 7 of 17 If L1 = 95 mm, L2 = 0 mm, and L3 = 20 mm, Figure 6 shows the induced current and magnetic force on the sheet using the die with a resistivity of 5e-4 Ω·m. After the coil discharge, induced current can be generated on the sheet, but no induced current is generated on the die. Thus, the induced current on sheet constitutes a current loop, as shown in Figure 6a. The current density at the right side of the sheet is much larger than that at the left side of sheet, as shown in Figure 6b. Figure 6c shows the distribution of electromagnetic force on sheet. A very small magnetic force was generated on the left and middle region of the sheet. Though the magnetic force at the right side of the sheet has a large magnetic force, the direction of magnetic force is not positive along the Z-axis. Therefore, a die with a smaller resistivity should be used to generate a uniform magnetic force on the sheet according to the results shown in Figures 5 and 6.

Figure 6. DistributionFigure 6. Distribution of induced of induced current current and and magneticmagnetic force force using using the die the with die a withresistivity a resistivity of 5e-4: of 5e-4: (a) Current(a) on Current the sheet, on the (sheet,b) current (b) current in detailedin detailed sheet sheet region, region, and and (c) 3D (c) magnetic 3D magnetic force on force the sheet. on the sheet.

4.2. DistanceBetween the Left and Right Parts of Coil (L1) If L2 = 0 mm, L3 = 20 mm, and the resistivity of die is set to 5e-7, Figure 7 shows the effect of L1 on the current density of the sheet. With the increase in L1, the current density in the middle and side of the sheet increased. The difference in current density on the left and right sides of the sheet decreased.

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4.2. DistanceBetween the Left and Right Parts of Coil (L1) If L2 = 0 mm, L3 = 20 mm, and the resistivity of die is set to 5e-7, Figure7 shows the e ﬀect of L1 on the current density of the sheet. With the increase in L1, the current density in the middle and side of the sheetMaterials increased. 2019, 11, x FOR The PEER diﬀ REVIEWerence in current density on the left and right sides of the sheet decreased.8 of 17

FigureFigure 7. E 7.ﬀ ectEffect of of L1 L1 on on current current density:density: (a ()a )L1 L1 = 30= 30mm, mm, (b) L1 (b )= L160 =mm,60 and mm, (c) and L1 = ( c95) L1mm.= (95d) mm. (d) CurrentCurrent densitydensity with with L1 L1 = =3030 mm, mm, (e) (valuee) value of current of current with L1 with = 60 L1 mm,= 60 and mm, (f) value and (off) current value ofwith current withL1 == 9595 mm. mm.

FigureFigure8 shows 8 shows the distributionthe distribution of magneticof magnetic force force on on Path Path 2 2 alongalong thethe X-axis. Because Because the the width width of the sheetof the is sheet smaller is smaller than the than width the ofwidth the leftof the half left of thehalf coil, of the the coil, two the sides two of sides the sheet of the were sheet subjected were to magneticsubjected force to along magnetic the X-axis. force along Thus, the the X-axis. sheet tendsThus, bethe compressed sheet tends inbe thecompressed width direction. in the width Figure 8b showsdirection. the distribution Figure 8b ofshows magnetic the distribution force on Pathof magn 2 alongetic force the on Z-axis. Path 2 The along larger the Z-axis. the L1, The the larger larger the magneticthe L1, force the generatedlarger the magnetic on Path 2force and generated the diﬀerence on Path in magnetic2 and the forcedifference between in magnetic the left force and right between the left and right sides of the sheet decreased. Thus, the uniformity of magnetic field force sides of the sheet decreased. Thus, the uniformity of magnetic ﬁeld force on the sheet was improved on the sheet was improved with the increase in L2. with the increase in L2.

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Figure 8. Effect of L1 on magnetic force along Path 2: (a) Along the X-axis and (b) along the Z-axis. Figure 8. Effect of L1 on magnetic force along Path 2: (a) Along the X-axis and (b) along the Z-axis. Figure 8. Effect of L1 on magnetic force along Path 2: (a) Along the X-axis and (b) along the Z-axis. 4.3. Distance of Center Line between the Sheet and Left Section of Coil (L2) 4.3. Distance of Center Line between the Sheet and Left Section of Coil (L2) Based4.3. Distance on the of resultsCenter Line shown between in Figuresthe Sheet7 and and Left8, Section the magnetic of Coil (L2) force on the left side of the sheet is largerBased thanBased on that the on on theresults the results right shown shown side in of in Figures theFigures sheet, 7 7 andand with 8, athethe di magnetic ffmagneticerent value force force ofon on L1.the the left Therefore, leftside side of the itof issheet the necessary sheet is is tolarger appropriatelylarger than than that that on move theon the right the right sheetside side of toof the the off sheet,set sheet, the withwith center a differentdifferent line of value value the sheetof ofL1. L1. Therefore, from Therefore, the it left is itnecessary part is necessary of the to coil. to IfappropriatelyL1appropriately= 95 mm ,move L3 move= the20 the mm,sheet sheet and to to offset theoffset resistivity the the center center of line the ofof diethe the sheet was sheet setfrom from to the 5e-7 the left Ωleft partm., part of Figure the of coil.the9 showscoil.If L1 If= L1 the = · current95 mm,95 mm,distributionL3 = L3 20 = mm,20 mm, on and the and the sheet the resistivity resistivity with a di offf oferent thethe die value was for setset L2. to to 5e-7 The 5e-7 magneticΩ ·m.,Ω·m., Figure Figure force 9 shows on9 shows the the left currentthe side current of the distribution on the sheet with a different value for L2. The magnetic force on the left side of the sheet sheetdistribution decreased, on the while sheet the with magnetic a different force value on the for right L2. sideThe magnetic of the sheet force increased on the withleft side the of decrease the sheet in decreased, while the magnetic force on the right side of the sheet increased with the decrease in L2. L2.decreased, The optimum while the value magnetic of L2 is force0.7 mm,on the corresponding right side of tothe a nearlysheet increased consistent with current the densitydecrease on in both L2. The optimumThe optimum value value of L2of L2is is−0.7 −−0.7 mm, mm, corresponding corresponding toto a a nearly nearly co consistentnsistent current current density density on both on both sidessides of the of sheet.the sheet. sides of the sheet.

FigureFigure 9. E 9.ﬀ Effectect of of L2 L2 onon current density. density. (a) L2 (a) = L2−2 mm,= 2(b mm,) L2 = (−b1) mm, L2 =(c) L21 = mm, −0.7 mm, (c) L2 and= (d)0.7 L2 mm, − − − and (=d 0) L2mm.= 0 mm. Figure 9. Effect of L2 on current density. (a) L2 = −2 mm, (b) L2 = −1 mm, (c) L2 = −0.7 mm, and (d) L2 Figure 10a shows the distribution of magnetic force on Path 2 along the X-axis. It could not Figure= 0 mm. 10a shows the distribution of magnetic force on Path 2 along the X-axis. It could not signiﬁcantlysignificantly inhibit inhibit the the magnetic magnetic force force distribution distribution along along the the X-axis X-axis onon the the sheet sheet by appropriately by appropriately moving the sheet. If L2 is equal to −0.7 mm, a magnetic force along the Z-axis occurs at both sides of movingFigure the sheet.10a shows If L2 isthe equal distribution to 0.7 mm, of magnetic a magnetic force force on along Path the2 along Z-axis the occurs X-axis. at bothIt could sides not of the sheet. − thesignificantly sheet. inhibit the magnetic force distribution along the X-axis on the sheet by appropriately moving the sheet. If L2 is equal to −0.7 mm, a magnetic force along the Z-axis occurs at both sides of the sheet.

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Figure 10. Magnetic force on the sheet after offset of the sheet from the coil: (a) Along the X-axis and Figure 10. Magnetic force on the sheet after offset of the sheet from the coil: (a) Along the X-axis and Figure 10. Magnetic force on the sheet after(b) alongoffset theof the Z-axis. sheet from the coil: (a) Along the X-axis and (b) along the Z-axis. (b) along the Z-axis. 4.4.4.4. Width of Sheet (L3) 4.4. Width of Sheet (L3) AccordingAccording toto the the results results shown shown in Figure in Figure 10, the magnetic10, the magnetic force on the force sheet on can the be symmetricallysheet can be distributedsymmetricallyAccording on thedistributed to sheet the byresults appropriatelyon the shown sheet by movingin appropFigure theriately sheet.10, the moving However, magnetic the the sheet. force magnetic However,on forcethe sheet onthe both magnetic can sides be ofsymmetricallyforce the on sheet both is much sidesdistributed largerof the thansheeton the that is sheet much at the by larger middle approp th ofanriately the that sheet movingat the if L3 middle the= 20 sheet. mm.of the However, Therefore, sheet if theL3 the =magnetic width 20 mm. of theforceTherefore, sheet on both should the sideswidth be changed. of of the the sheet sheet Figure is should much 11 shows largerbe change the th distributionand. that Figure at the of11 magnetic middleshows theof force thedistribution onsheet the sheetif L3 of = alongmagnetic 20 mm. the X-Therefore,force and on Z-axes the the sheet withwidth along di ffoferent the the sheet X- and should widths. Z-axes be With withchange the di increased.fferent Figure sheet in 11 sheet showswidths. width, the With thedistribution magneticthe increase of force magnetic in alongsheet theforcewidth, X-axis on the the at magnetic bothsheet sheet along force sides the along significantlyX- and the Z-axesX-axis decreased. atwith both di fferentsheet If the sides sheetsheet widthsignificantly widths. is equalWith decreased. tothe 20 increase mm andIf the in 25 sheet mm, thewidth,width magnetic isthe equal magnetic force to 20 on mmforce Path and along 2 along25 mm, the the X-axisthe Z-axis magnetic at showsboth force sheet a concave on sides Path shape.significantly 2 along If the the Z-axis sheetdecreased. widthshows If is athe equalconcave sheet to 30widthshape. mm is andIf equalthe 40 sheet mm, to 20 width the mm magnetic andis equal 25 forcemm, to 30 the on mm Pathmagnetic and 2 along40 mm, force the the on Z-axis magnetic Path appears 2 along force as the aon centralZ-axis Path 2 protrusionshows along athe concave Z-axis shape. Ifshape.appears L2 = If27 asthe mm, a sheetcentral which width protrusion is equalis equal to shape. to the 30 length mmIf L2 and = of 27 the40 mm, mm, left which partthe magnetic of is the equal coil, force to the the on magnetic length Path 2of along force the left the on partPathZ-axis of 2 alongappearsthe coil, the theas Z-axis a magnetic central is distributed protrusion force on uniformly.Path shape. 2 al Ifong L2 the = 27 Z-axis mm, iswhich distributed is equal uniformly. to the length of the left part of the coil, the magnetic force on Path 2 along the Z-axis is distributed uniformly.

FigureFigure 11.11. EEffectffect of sheet widthwidth onon magneticmagnetic force:force: (a)) AlongAlong thethe X-axisX-axis andand ((bb)) alongalong thethe Z-axis.Z-axis. 5. ManufacturedFigure 11. Effect Process of sheet and width Magnetic on magnetic Analysis force: for (a Coil) Along the X-axis and (b) along the Z-axis. 5. Manufactured Process and Magnetic Analysis for Coil 5. ManufacturedFigure 12 shows Process the and flow Magnetic chart of manufacturingAnalysis for Coil process for the flat spiral uniform pressure coil. First,Figure a high-strength12 shows the flow insulating chart materialof manufacturin is selectedg process as the supportingfor the flat framespiral foruniform the coil. pressure Many insulatingcoil. FigureFirst, materials,a 12high-strength shows such the as flowinsulati nylon, chartng bakelite, materialof manufacturin and is epoxyselectedg plate, process as the can supportingfor be selected.the flat framespiral In this foruniform paper, the coil. the pressure epoxyMany coil.insulating First, amaterials, high-strength such insulatias nylon,ng materialbakelite, isand selected epoxy as plate, the supporting can be selected. frame forIn thisthe coil.paper, Many the insulating materials, such as nylon, bakelite, and epoxy plate, can be selected. In this paper, the

Materials 2019, 1211, 1963x FOR PEER REVIEW 1110 of 17 16 epoxy plate was selected due to its high strength (bending strength greater than 340 MPa) and plateinexpensive was selected price. dueAccording to its high to the strength design (bending paramete strengthrs of the greater coil in than Figure 340 MPa)2 and and the inexpensive simulation price.results According in Chapter to 4, the the design CNC parametersmachining ofwas the used coil into Figureobtain2 theand groove the simulation in epoxy results plate, inas Chapter shown in 4, Figurethe CNC 12a. machining Then, the was 3*6 used mm to2 copper obtain the wires groove were in manually epoxy plate, winded as shown according in Figure to 12 thea. Then,shape theof the 3*6 groove,mm2 copper as shown wires werein Figure manually 12b. winded The shape according of winding to the shape coil ofcontains the groove, a spiral as shown and intwo Figure straight 12b. Thesegments. shape The of winding two straight coil containssegments a spiralwere used and twoto subsequently straight segments. connect The to the two discharge straight segmentsdevice to wereform useda current to subsequently loop. Figure connect12c shows to thethe dischargeassembly deviceresult of to the form epoxy a current sheetloop. and the Figure winding 12c shows wire. Sincethe assembly the winding result wire of the was epoxy embedded sheet and in the windingepoxy board, wire. there Since existed the winding small wiregap. wasIn order embedded to avoid in the epoxyshaking board, of the there winding existed wire small during gap. the In forming order to avoidprocess, the the shaking assembled of the coil winding was encapsulated wire during withthe forming epoxy process,resin. Thus, the assembleda working coil coil was which encapsulated can be used with epoxyfor the resin. electromagnetic Thus, a working forming coil whichexperiment can be was used obtained, for the electromagnetic as shown in Figure forming 12d. experiment Figure 12e wasis an obtained, actual diagram as shown of inthe Figure assembly 12d. resultFigure of 12 thee is coil an actualand the diagram epoxy board. of the assembly result of the coil and the epoxy board.

Figure 12. ManufactureManufacture process process for for a acoil: coil: (a) ( aMake) Make a groove a groove in epoxy in epoxy plate plate with with CNC CNC machining; machining; (b) (wireb) wire winding; winding; (c) (assemble;c) assemble; and and (d) ( dencapsulate) encapsulate with with epoxy. epoxy. (e ()e The) The actual actual coil coil before before encapsulated. encapsulated. Under the condition that the sheet width is 30 mm, Figure 13 shows the distribution of magnetic Under the condition that the sheet width is 30 mm, Figure 13 shows the distribution of magnetic force along the Z-axis on the ﬂat spiral uniform pressure coil at 20 µs. It can be found that the direction force along the Z-axis on the flat spiral uniform pressure coil at 20 μs. It can be found that the of magnetic force acting on the winding along the Z-axis. Thus, the direction of the magnetic force in direction of magnetic force acting on the winding along the Z-axis. Thus, the direction of the winding is opposite to the direction of sheet deformation. In order to more clearly describe the direction magnetic force in winding is opposite to the direction of sheet deformation. In order to more clearly

Materials 2019, 12, 1963 11 of 16 Materials 2019, 11, x FOR PEER REVIEW 12 of 17 Materials 2019, 11, x FOR PEER REVIEW 12 of 17 ofdescribe the magnetic the direction force onof the magnetic winding, specialforce on regions, the winding, named special A and regions, B, were named selected, A asand shown B, were in describe the direction of the magnetic force on the winding, special regions, named A and B, were Figureselected, 13 asa. shown in Figure 13a. selected, as shown in Figure 13a.

Figure 13. Magnetic force on the coil (Unit: N). (a) Legend; (b) vector diagram. Figure 13. Magnetic force on the coil (Unit: N). (a) Legend; (b) vector diagram. In FigureFigure 14 14,, the the regions regions A A and and region region B of B the of coilthe arecoil totallyare totally subjected subjec toted electromagnetic to electromagnetic forces In Figure 14, the regions A and region B of the coil are totally subjected to electromagnetic alongforces thealong Z-axis. the Z-axis. Both region Both region A and A region and region B contain B contain ﬁve turns five wires.turns wires. The internal The internal three turnsthree wiresturns forces along the Z-axis. Both region A and region B contain five turns wires. The internal three turns arewires subjected are subjected to a large to a electromagnetic large electromagnetic force along force thealong Z-axis. the Z-axis. The external The external two turns two wires turns have wires a wires are subjected to a large electromagnetic force along the Z-axis. The external two turns wires smallhave a Z-axis small electromagneticZ-axis electromagnetic force. However, force. However, the external the external two turns two wires turns are wires subjected are subjected to a certain to a have a small Z-axis electromagnetic force. However, the external two turns wires are subjected to a magneticcertain magnetic force along force the along X-axis. the Thus,X-axis. the Thus, ﬁve the turns five wires turns of wires the region of the A region and B haveA and a tendencyB have a certain magnetic force along the X-axis. Thus, the five turns wires of the region A and B have a totendency be compressed. to be compressed. However, However, the electromagnetic the electromagnetic force along force the X-axisalong the is much X-axis smaller is much compared smaller tendency to be compressed. However, the electromagnetic force along the X-axis is much smaller tocompared the one alongto the theone Z-axis, along the and Z-axis, the coil and wire the is coil packaged wire is inpackaged a high-strength in a high-strength epoxy board epoxy which board has compared to the one along the Z-axis, and the coil wire is packaged in a high-strength epoxy board awhich large has resistance a large toresistance compression. to compression. Therefore, theTherefore, possibility the ofpossibility the coil failingof the incoil the failing X direction in the isX which has a large resistance to compression. Therefore, the possibility of the coil failing in the X relativelydirection is small. relatively small. direction is relatively small.

Figure 14. Magnetic force on special region (Unit: N). (a) Region A with 3D view; (b) region A with 2D Figure 14. Magnetic force on special region (Unit: N). (a) Region A with 3D view; (b) region A with view; (c) region B with 3D view; and (d) region B with 2D view. Figure2D view; 14. ( cMagnetic) region B force with on3D specialview; and region (d) region(Unit: N).B with (a) Region2D view. A with 3D view; (b) region A with 2D view; (c) region B with 3D view; and (d) region B with 2D view. In order to further illustrate the advantages of the flat spiral uniform pressure coil proposed in In order to further illustrate the advantages of the flat spiral uniform pressure coil proposed in this paper, the deformation process of the sheet by the conventional uniform pressure coil and the this paper,In order the to deformation further illustrate process the ofadvantages the sheet ofby thethe flat conventional spiral uniform uniform pressure pressure coil proposedcoil and the in flat uniform pressure coil was analyzed, as shown in Figure 15. It can be seen that a die structure is thisflat uniformpaper, the pressure deformation coil was process analyzed, of the as sheet shown by in the Figure conventional 15. It can uniform be seen pressurethat a die coil structure and the is required during the deformation of the sheet. The differences between the two uniform pressure coils flatrequired uniform during pressure the deformation coil was analyzed, of the assheet. shown The in differences Figure 15. Itbetween can be seenthe two that uniform a die structure pressure is are as follows: (1) The flat pressure coils require a flat spiral winding and an epoxy plate supporting requiredcoils are duringas follows: the deformation(1) The flat pressureof the sheet. coils The require differences a flat spiralbetween winding the two and uniform an epoxy pressure plate coilssupporting are as frame;follows: (2) (1) the The conventional flat pressure uniform coils pressurequirere a coil flat needs spiral to winding be winded and with an epoxya 3D shape, plate supporting frame; (2) the conventional uniform pressure coil needs to be winded with a 3D shape,

Materials 2019, 11, x FOR PEER REVIEW 13 of 17

and an epoxy plate supporting frame must be inserted in the winding wire. Moreover, it needs to manufacture a high conductivity external channel. It also needs to fill the region between metal outer channel and the 3D winding wire with insulating material to avoid contact. Therefore, the planar pressure coil proposed in this paper has a simple manufacturing process and a low manufacturing cost. The deformation process of the sheet corresponding to the conventional uniform pressure coil is shown in Figure 15a,b. If the sheet has no deformation, the distance between the upper part of the coil and the outer channel is set to be h1, while the lower part of the coil and the sheet is set to h2. After the coil discharge, the upper part of the coil and the outer channel, as well as the lower part of the coil and the sheet will all generate a magnetic field concentration. As a result, the upper and lower parts of the coil are subjected to the magnetic force of F1 and F2, and the direction of the magnetic field force is away from the sheet and the outer channel, respectively. Thus, if h1≈h2, F1≈F2. However, the distance between the lower portion of the coil and the sheet (h3) is greatly increased if the sheet deforms. As a result, the strength of the magnetic field between the lower portion of the coil and the sheet material is greatly reduced, so the electromagnetic force (F4) obtained at the lower portion of the coil is greatly reduced. Since the distance between the upper part of the coil and the outer channel does not change, the upper part of the coil is still subjected to a large electromagnetic force F3. Thus, F3 > F4 after sheet deformation. Under this state of magnetic force, the upper portion of the coil will push the insulating material and cause the lower portion of the coil to bulge, which will cause the coil to fail, as shown in Figure 1d. Moreover, the conventional pressure coil has difficulty handling the failure of the coil. The deformation process of the flat spiral pressure coil proposed in this paper is shown in Figure 15c,d. In the initial stage of sheet deformation, the coil wire is subjected to an electromagnetic Materialsforce (F5)2019 away, 12, 1963 from the direction of sheet deformation. If the sheet deforms, the distance between12 of 16 the sheet and the coil increases, and the electromagnetic force (F6) becomes smaller. Moreover, the frame;direction (2) of the the conventional magnetic field uniform force pressureis still away coil needsfrom the to bedirection winded of with the asheet 3D shape, deformation. and an epoxyWhile platethe coil supporting is made, the frame coil mustwires be are inserted embedded in the in windingthe grooves wire. made Moreover, of the high-strength it needs to manufacture epoxy board. a highThe epoxy conductivity board has external a large channel. thickness It alsoand can needs full toy ﬁllwithstand the region the betweenreaction force metal along outer the channel Z-axis. and the 3DTherefore, winding the wire flat with spiral insulating pressure material coil propos to avoided in contact.this paper Therefore, can produce the planara uniform pressure magnetic coil proposedforce distribution in this paper on the has sheet, a simple reduce manufacturing the manufacturing process difficulty, and a low reduce manufacturing manufacturing cost. cost, and enhance the service life for the coil.

Figure 15. Deformation process under uniform magnetic pressure. (a) Initial condition in a conventional Figure 15. Deformation process under uniform magnetic pressure. (a) Initial condition in a uniform pressure coil; (b) a deformed sheet in a conventional uniform pressure coil; (c) initial condition conventional uniform pressure coil; (b) a deformed sheet in a conventional uniform pressure coil; (c) in a flat spiral uniform pressure coil; and (d) a deformed sheet in a flat spiral uniform pressure coil. initial condition in a flat spiral uniform pressure coil; and (d) a deformed sheet in a flat spiral Theuniform deformation pressure coil. process of the sheet corresponding to the conventional uniform pressure coil is shown in Figure 15a,b. If the sheet has no deformation, the distance between the upper part of the coil 6. Sheet Deformation after Coil Discharge and the outer channel is set to be h1, while the lower part of the coil and the sheet is set to h2. After the coil discharge, the upper part of the coil and the outer channel, as well as the lower part of the coil and the sheet will all generate a magnetic field concentration. As a result, the upper and lower parts of the coil are subjected to the magnetic force of F1 and F2, and the direction of the magnetic field force is away from the sheet and the outer channel, respectively. Thus, if h1 h2, F1 F2. However, the distance ≈ ≈ between the lower portion of the coil and the sheet (h3) is greatly increased if the sheet deforms. As a result, the strength of the magnetic field between the lower portion of the coil and the sheet material is greatly reduced, so the electromagnetic force (F4) obtained at the lower portion of the coil is greatly reduced. Since the distance between the upper part of the coil and the outer channel does not change, the upper part of the coil is still subjected to a large electromagnetic force F3. Thus, F3 > F4 after sheet deformation. Under this state of magnetic force, the upper portion of the coil will push the insulating material and cause the lower portion of the coil to bulge, which will cause the coil to fail, as shown in Figure1d. Moreover, the conventional pressure coil has di fficulty handling the failure of the coil. The deformation process of the flat spiral pressure coil proposed in this paper is shown in Figure 15c,d. In the initial stage of sheet deformation, the coil wire is subjected to an electromagnetic force (F5) away from the direction of sheet deformation. If the sheet deforms, the distance between the sheet and the coil increases, and the electromagnetic force (F6) becomes smaller. Moreover, the direction of the magnetic field force is still away from the direction of the sheet deformation. While the coil is made, the coil wires are embedded in the grooves made of the high-strength epoxy board. The epoxy board has a large thickness and can fully withstand the reaction force along the Z-axis. Therefore, the flat spiral pressure coil proposed in this paper can produce a uniform magnetic force distribution on the sheet, reduce the manufacturing difficulty, reduce manufacturing cost, and enhance the service life for the coil. Materials 2019, 12, 1963 13 of 16

Materials 2019, 11, x FOR PEER REVIEW 14 of 17 6. Sheet Deformation after Coil Discharge Figure 16 shows the experimental device and the deformed sheet at different discharge Figure 16 shows the experimental device and the deformed sheet at different discharge voltages. voltages. The EMF equipment was manufactured by Central South University. The main parameters The EMF equipment was manufactured by Central South University. The main parameters are: are: The maximum discharge-energy (200 kJ), rated voltage (25 kV), and capacitance (640 μF). A The maximum discharge-energy (200 kJ), rated voltage (25 kV), and capacitance (640 µF). A Rogowski Rogowski coil was used to measure the pulse current data passing through the working coil. An coil was used to measure the pulse current data passing through the working coil. An oscilloscope was oscilloscope was used to record the current data. Finally, this current data were imported into used to record the current data. Finally, this current data were imported into numerical simulation numerical simulation software to calculate the magnetic force and dynamic forming process. Figure software to calculate the magnetic force and dynamic forming process. Figure 16b shows a forming die 16b shows a forming die made by Q235 steel, and the sheet is deformed after the coil is discharged. made by Q235 steel, and the sheet is deformed after the coil is discharged. Figure 16c shows a forming Figure 16c shows a forming die processed by an epoxy plate, and it can be seen that the sheet is not die processed by an epoxy plate, and it can be seen that the sheet is not deformed after the discharge of deformed after the discharge of the coil. This is because the lager and uniform induced the current the coil. This is because the lager and uniform induced the current generated on the sheet using the generated on the sheet using the steel die. Figure 16d shows the final deformation results of the steel die. Figure 16d shows the final deformation results of the sheets at different sheet widths. sheets at different sheet widths.

Figure 16. Experimental device and the deformed sheet. (a) 200 kJ EMF equipment; (b) steel die; Figure 16. Experimental device and the deformed sheet. (a) 200 kJ EMF equipment; (b) steel die; (c) (c) epoxy plate die; and (d) a deformed sheet with a different sheet width. epoxy plate die; and (d) a deformed sheet with a different sheet width. Electromagnetic forming involves the coupling of electromagnetic fields, structural fields, and temperatureElectromagnetic fields. If forming the coil discharges,involves the a coupling large current of electromagnetic will be generated fields, on thestructural sheet, whichfields, mayand temperature fields. If the coil discharges, a large current will be generated on the sheet, which may cause thermal softening. In the field of electrically assisted forming, Egea et al. [19] used electrically cause thermal softening. In the field of electrically assisted forming, Egea et al. [19] used electrically assisted (EA) wire drawing to enhance the formability, ductility, and elongation of the wire specimen. assisted (EA) wire drawing to enhance the formability, ductility, and elongation of the wire It is observed that electropulsing induces an ultrafast annealing process, which decreases the hardness specimen. It is observed that electropulsing induces an ultrafast annealing process, which decreases in the center and surface of specimens. Valoppi et al. [20] used double-sided incremental forming the hardness in the center and surface of specimens. Valoppi et al. [20] used double-sided with electrically-assisted forming to manufacture a difficult-to-form Ti6Al4V sheet. They found the incremental forming with electrically-assisted forming to manufacture a difficult-to-form Ti6Al4V formability and the geometric accuracy were increased, and the forming force was reduced. In addition, sheet. They found the formability and the geometric accuracy were increased, and the forming force the joule effect prevented the surface defect from cracking. was reduced. In addition, the joule effect prevented the surface defect from cracking. However, the effects of temperature on electromagnetic forming are often ignored. This is because However, the effects of temperature on electromagnetic forming are often ignored. This is there is no significant temperature rise on the part, although the induced current was generated on the because there is no significant temperature rise on the part, although the induced current was part after discharge. For example, Cui et al. [21] showed the tube had a temperature rise of about 5 ◦C generated on the part after discharge. For example, Cui et al. [21] showed the tube had a temperature after discharge based on a numerical simulation. In order to further explain why the temperature rise rise of about 5 °C after discharge based on a numerical simulation. In order to further explain why on the sheet during the electromagnetic forming process is small, a thermocouple sensor was used to the temperature rise on the sheet during the electromagnetic forming process is small, a thermocouple sensor was used to measure temperature on the sheet. The error for the thermocouple

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Materials 2019, 11, x FOR PEER REVIEW 15 of 17 Materials 2019, 11, x FOR PEER REVIEW 15 of 17 measure temperature on the sheet. The error for the thermocouple sensor was 0.1 C. The experiment sensor was ± 0.1 °C. The experiment found that the temperature on the± sheet◦ before and after foundsensor thatwas the ± 0.1 temperature °C. The experiment on the sheet found before that and afterthe temperature discharge was on almost the sheet unchanged, before and as shown after discharge was almost unchanged, as shown in Figure 17. indischarge Figure 17 was. almost unchanged, as shown in Figure 17.

Figure 17. Temperature changes (a) before discharge and (b) after discharge. Figure 17. TemperatureTemperature changes ( a) before discharge and (b) after discharge.discharge.

Using the planarplanar spiralspiral uniform-pressureuniform-pressure coil andand byby selectingselecting thethe optimumoptimum technologicaltechnological Using the planar spiral uniform-pressure coil and by selecting the optimum technological parameters,parameters, Figure 18 shows the deformation result resultss of sheet material under different diﬀerent sheet widths. parameters, Figure 18 shows the deformation results of sheet material under different sheet widths. TheThe maximummaximum displacementdisplacement at the sheetsheet centercenter graduallygradually increased with the decrease in sheetsheet The maximum displacement at the sheet center gradually increased with the decrease in sheet width.width. Moreover, the didifferenceﬀerence inin displacementdisplacement betweenbetween the center of the sheet and the edgeedge ofof thethe width. Moreover, the difference in displacement between the center of the sheet and the edge of the sheet decreased.decreased. sheet decreased.

Figure 18.18. Deformed shape shape with with different different sheet sheet widths: widths: (a) L3 (a=) 25L3 mm,= 25 (mm,b) L3 (=b)30 L3 mm, = 30 and mm, (c) L3and= (40c) mm.L3 = Figure 18. Deformed shape with different sheet widths: (a) L3 = 25 mm, (b) L3 = 30 mm, and (c) L3 = 40 mm. Figure40 mm. 19 shows the profiles on Path 3 and displacement at special points (A and B) obtained from the experiment and simulation with different sheet widths. The profiles between the experiment and Figure 19 shows the profiles on Path 3 and displacement at special points (A and B) obtained simulationFigure showed 19 shows a slight the profiles deviation on andPath small 3 and error displacement at Points A at and special B. The points maximum (A and errors B) obtained between from the experiment and simulation with different sheet widths. The profiles between the experimentfrom the experiment and simulation and at simulation A and B points with were diff allerent less thansheet 5.5%. widths. Therefore, The theprofiles simulation between method the experiment and simulation showed a slight deviation and small error at Points A and B. The hasexperiment a high accuracy and simulation to predict showed electromagnetic a slight sheetdeviation forming and using small a flaterror spiral at Points uniform-pressure A and B. The coil. maximum errors between experiment and simulation at A and B points were all less than 5.5%. maximum errors between experiment and simulation at A and B points were all less than 5.5%. Therefore, the simulation method has a high accuracy to predict electromagnetic sheet forming Therefore, the simulation method has a high accuracy to predict electromagnetic sheet forming using a flat spiral uniform-pressure coil. using a flat spiral uniform-pressure coil.

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Figure 19. Simulation method verification: (a) A and B points and (b) sheet profiles. Figure 19. Simulation method verification: (a) A and B points and (b) sheet profiles. 7. Conclusions 7. Conclusion In this study, a new uniform-pressure coil with a planar structure was designed. The influencing factorsIn onthis magnetic study, forcea new distribution uniform-pressure were analyzed coil with by a FEM. planar Some structure conclusions was weredesigned. obtained, The asinfluencing follows: factors on magnetic force distribution were analyzed by FEM. Some conclusions were obtained, as follows: (1) (1).A dieA die with with resistivity resistivity 5e-7 5e-7Ω mΩ·m and and a spacinga spacing of of 95mm 95mm between between the the left left and and right rightparts parts ofof thethe · 2 coilcoil were were used, used, and aand current a current density density larger thanlarger 1.31e9 than A1.31e9/m with A/m the2 with same the flowing same direction flowing wasdirection generated was on generated the sheet. on By the slightly sheet. moving By slightly the sheet,moving the the magnetic sheet, the forces magnetic were distributedforces were symmetricallydistributed alongsymmetrically the direction along of the the direction sheet deformation. of the sheet deformation. (2) (2).The The optimum optimum sheet sheet width width was was equal equal to the to length the length of the of left the part left of part the of coil, the corresponding coil, corresponding to the mostto uniformthe most magnetic uniform magnetic force along force the along Z-axis the distribution Z-axis distribution on the sheet. on the sheet. (3) (3).Compared Compared with with the the structure structure and and magnetic magnetic force force on aon traditional a traditional uniform uniform pressure pressure coil, coil, the flatthe uniformflat uniform pressure pressure coil proposed coil proposed in this paper in this can paper produce can a uniformproduce magnetica uniform force magnetic distribution force on thedistribution sheet, reduce on the the sheet, manufacturing reduce the di manufactfficulty, reduceuring difficulty, manufacturing reduce cost, manufacturing and enhance cost, the serviceand lifeenhance for the the coil. service life for the coil. (4) (4).By comparingBy comparing the experimentalthe experimental results, results, it was it foundwas found that the that simulation the simulation results results have a have higher a analysishigher precision. analysis Theprecision. maximum The errorsmaximum between erro experimentrs between andexperiment simulation and at simulation A and B points at A wereand all B less points than were 5.5%. all less than 5.5%.

AuthorAuthor Contributions:Contributions: TheThe researchresearch waswas conceivedconceived byby X.C.X.C. andand L.J.;L.J.; D.Q.D.Q. andand Z.D.Z.D. plannedplanned andand performedperformed allall thethe experiments;experiments; A.X.A.X. collectedcollected allall data;data; TheoreticalTheoretical andand experimentalexperimental analysisanalysis werewere performedperformed byby X.C.,X.C., D.Q.,D.Q., andand Z.D.;Z.D.,; The The manuscript manuscript was was reviewed reviewed by X.C.,by X.C., H.Y., H.Y. and, A.X.,and TheA.X., manuscript The manuscript was written was written by X.C.; by with X.C.; support with fromsupport all co-authors.from all co-authors. Funding: Funding: This work waswas supportedsupported byby thethe NationalNational NaturalNatural ScienceScience FoundationFoundation ofof ChinaChina (Grant(Grant Nos.Nos. 5177556351775563 and 51405173), Innovation Driven Program of Central South University (Grant number: 2019CX006), State Key Laboratoryand 51405173), of Materials Innovation Processing Driven andProgram Die & of Mould Central Technology, South University Huazhong (Grant University number: of Science 2019CX006), and Technology State Key (No.Laboratory P2017-013) of Materials and the Processi Projectng of and State Die Key & LaboratoryMould Technology, of High PerformanceHuazhong University Complex Manufacturing,of Science and CentralTechnology South (No. University P2017-013) (ZZYJKT2017-03), and the Project Guangzhou of State Science Key Laboratory and Technology of High Plan Performance Project (201707010472) Complex andManufacturing, The project wasCentral supported South University by Open Research (ZZYJKT2017- Fund of03), State Guangzhou Key Laboratory Science of and High Technology Performance Plan Complex Project Manufacturing,(201707010472) Centraland The South project University was supported (No. Kfkt2018-02). by Open Research Fund of State Key Laboratory of High ConﬂictsPerformance of Interest: ComplexThe Manufacturing, authors declare Cent noral conﬂict South of University interest. (No. Kfkt2018-02).

Conflicts of Interest: The authors declare no conflict of interest. References

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