METAL 2008 13.-15.5.2008 Hradec nad Moravicí

APPLICATION OF PULSED ELECTROMAGNETIC ENERGY

FOR SHAPE CALIBRATION OF COMPOUND CURVED THIN

PLATES

Vincent J. Vohnout Ph.D. Associate Professor

Technological Studies

Bemidji State Univ.

Bemidji, MN 56601 U.S.A.

vvohnout@bemindjistate.edu

Glenn Daehn Ph.D. Professor

Material Science and Engr.

The Ohio State University

Columbus, OH 43210 U.S.A

daehn.1@osu.edu

William Hayes Technical Principle

Aerojet Corp.

Sacramento, CA 95813-6000

U.S.A

William.Hayes@Aerojet.com

Abstract The use of electromagnetic (EM) energy pulses to form thin metal plate and sheet has

been a fairly well known, if not a widely practiced process for about 50 years. The EM pulses,

generated by the discharge of a set of electric capacitors has been most often applied to

axisymmetric clinching, swaging and bulging type forming operations. Development work by

the authors and others, in the last decade has led to application of the technique to high

velocity forming of large, open shell components and to integration into general metal

stamping operations. It was found that the large pressures generated by the EM pulses were

also sufficient to generate material strains without gross material movement. This fact was

then used to demonstrate the ability of a properly designed process to eliminate spring back in

a mechanically formed part and thus calibrate the shape to the desired standard. This paper

will discuss the general process with examples. In particular, the application of the process to

the calibration of a saddle shaped sector of a rocket nozzle will be discussed in detail. This

example illustrates the full advantages of this method in terms of selective strain distribution

and interactive tuning.

Section 1. Introduction

Figure 1 is a schematic of the original types of coils and components that electromagnetic

pulse forming was applied. Coils are attached to electric capacitor bank of 1 to100+ kilo-joule

capacity. The details of effective generation of the pressure distributions by the Lorenz forces

resulting from the impressed-induced capacitor discharge

currents has been well documented and available to the

interested reader elsewhere [Wilson 1964, Bruno1968,

Batygin 1999]. The extensions of the basic non-

axisymmetric version of the technique, suggested by

Figure 1c, to larger open shell stampings has been the

subject of work by two of the authors [Vohnout 1998,

Daehn 1999]. One common attribute of the older

axisymmetric and newer open shell applications is that the

electromagnetic (EM) pulse energy is used to accelerate

the sheet metal adjacent the coil elements to fairly high

velocities (50 to 200 m/sec.). A good deal of the metal

forming efficacy of the process derives from the rapid

conversion of the kinetic energy into plastic strain of the

local sheet elements, especially during impact with the

form die surface. Useable plastic strains, significantly

beyond those indicated by quasi-static forming limit

diagrams, are documented for these EM forming methods

Figure 1. Conventional types

of EM forming coils:

a) axisymmetric compression

b) axisymmetric expansion

c) flat pancake

METAL 2008 13.-15.5.2008 Hradec nad Moravicí

[Balanethiram 1994, Vohnout 1999]. During the development of the hybrid (MT-EM) process

that combined EM forming with conventional matched tool stamping, the authors realized that

a variation of the process could be effectively applied to the correction/elimination of spring

back. Moreover, it was found that the acceleration of the local sheet elements to high velocity

was not an essential requirement in this process variation to correct spring back in the

otherwise conventionally formed part.

Section 2 Experiments

Figure 2 shows the results of a preliminary experiment into the application of EM pulse

energy to the correction of spring back in a simple U shaped aluminum sheet metal part. This

early experiment did not use a coil especially designed for the elimination of the springback.

Rather, the coil and fixture was from a previous experiment in the extended plasticity by high

velocity EM pulse forming. The part shape of Figure 2 is actually the pre-form of the final

deep vee indicated by the die shape. However, this shape, with two 25 mm corner radii, could

not have been better chosen to accentuate the springback or elastic recovery, in a pure bend

formed part. Modification of the 900 vee die for the EM springback control required only the

installation of the “block” identified in Figure 2b. A flat coil was already embedded in the

face of the punch as required by the original deep vee, high velocity forming experiments. The

action of the test fixture to produce a springback part was simply to place a flat work sheet

between the die and punch in the open fixture then hydraulically close the fixture until the

work sheet was held very tightly against the block of Figure 2b. While the test part was thus

under the load of the

punch, the capacitor bank

attached to the coil was

discharged. Figure 2a

shows three parts after

the described process.

All three parts where

clamped in the test

fixture under the same

load condition; several

kN force applied to the

punch. As expected, with

only the mechanical

action of the fixture, the part sprung open excessively after being released from the fixture.

Application of an EM pulse discharge of modest energy levels significantly improved the part

shape conformation with the punch shape as illustrated in Figure 2b. EM discharges

significantly higher than 6kJ resulted in over-bending the part (included angle < 900 ). Since

the part was constrained from motion both globally and locally by the clamping force of the

fixture, the change in strain condition which improved the part shape was strictly due to the

effect of the impressed and induced currents generated by the EM discharge. Changes in the

strain distribution due to the EM pulse were too small to be reliably measured by circle grid or

standard micrometer readings. Also, from the location of the coil bars indicated in Figure 2b,

the EM pulses only altered the strain distribution on the flat central section of the part not in

the 25mm corner radii where the majority of the mechanically produced strain is located. The

principal result of this simple experiment was the realization that EM pulse energy could be

applied to the correction of springback in stampings without the need to alter the form tool

shape from the ideal part for “over bending” or “coining” purposes. Since the form tool can

maintain its ideal shape, the application of EM pulse energy can be viewed as a true shape

no pulse

4kJ

6kJ

Pure bend forming

(a) (b)

Figure 2. a)Spring back parts with EM pulse treatment and

b) Test fixture

Punch w/ coil

Die

Part

+ -

Block

METAL 2008 13.-15.5.2008 Hradec nad Moravicí

calibration method that can be actively adjusted to accommodate changes in part material or

mechanical processing with a simple increase in EM pulse energy by increasing the system

capacitor charge. In addition, the EM calibration of the part can take place within the primary

mechanical forming process, in many cases. This technique was successfully extended, by the

authors and associates, to other materials and simple U shaped geometries commonly seen

among automotive parts. In addition, the technique was applied to a complex, multi-layer

diffusion bonded copper alloy part for which mechanical calibration was not an option. An

overview of the results of these efforts has been recently presented. [Iriondo 2006]. The

application to the simple automotive U channel parts was a direct extension of the simple

experiment reported above and will not be further discussed here. The remainder of this paper

will focus on the details of the shape calibration of the more complex copper alloy part.

Section 2.2 Application to complex parts

Figure 3 contains both a photograph of a quarter sector of a rocket motor nozzle (a) and

the computer generated 3D of the original male (punch) form tool half (b). The part is

approximately 1.0 meter long with widths of 0.41, 0.21 and .12 meters at the exhaust, intake

and throat sections respectively. Seven panels are required to form a nozzle.

Panel thickness was approximately 10 mm and comprised of a number of diffusion bonded

layers that provided for internal slots in the axial direction of the panel for the cooling of the

nozzle by the liquid rocket fuel. Figure 4 is

a schematic approximation of the internal

geometry of a nozzle panel. The panel

material was predominately copper alloy

with a stainless steel layer at the hot gas

face. Although the panel has a fairly

complex axial profile, the radial cross

section geometry was of primary

importance. Ideally the panel should have a true circular arc cross section at any axial station

with the minimum cross sectional internal radius of 57 mm indicating the mid-plane of the

throat section. After the initial hot pressing, nozzle panels have essentially the shape shown

by Figure 3a. However, the panel cross sectional radii were found sprung open (too large) at

any station along the center line axis of the panel. Shape calibration by a secondary

mechanical hot press operation, using the same form tools, produced unacceptable results.

Possibly a new form tool with different (smaller) cross sectional radii might have been

developed as a solution but many trials would undoubtedly have been required. Many

experiments are generally required for empirical development of springback compensated

form tools for standard sheet/plate material. Fewer could not be expected with the complex

internal geometry of the nozzle panel. In addition the fabrication of the flat pre-form panels

(a) (b)

Figure 3. Nozzle sector (a) and nozzle form tool (b)

Figure 4. Schematic of panel internal geometry

SS

Al

METAL 2008 13.-15.5.2008 Hradec nad Moravicí

was a time intensive and expensive process which made any extended trial and error

development process very unattractive. From familiarity with results of the early experiments

described in section 2.1, William Hayes, the principle development engineer on this new

rocket nozzle for Aerojet Corp. presented the calibration of nozzle panel to the two other

authors of this paper as a challenging problem for EM pulse forming methodology.

Section 2.3 Development of the EM pulse system for the nozzle panel calibration

A first step to applying an EM shape calibration system to the rocket nozzle panel was to

decide on some EM pressure distribution that would best effect the elimination of the

springback of the panel. It was especially important to correct the throat mid-plane radius to

the ideal design dimension as nearly as possible. It is well known that if a flat coil face is very

close to a high conducting surface, the magnetic flux will be largely contained in the space

between the current carrier and the conducting surface. Such a closely coupled inductive

system will generate the repulsive magnetic pressure on the workpiece directly under the coil

bars. For such a system the working pressure distribution is the same as the coil face shadow

on the workpiece. The induction of the coil-workpiece can be approximated by a current trace

above a conductive half space which is given by

L = µ0(h

w)D (1)

where w is the width of the coil bar and h is the separation between the bar and the workpiece

and D is the total length of the coil bars.

Since it is the time rate of change of current and its peak level that determine the capacity of

the coil to perform deformation work, it is essential that at least a reliable lower bound

estimate of the discharge current be known. The specific EM pressures/forces needed to

correct the springback of the panel were left to the experimental phase due to the many

confounding factors. However, from previous work it was known that the system would need

to provide peak currents at the 100kA level with some spare capacity. The system current

response can be estimated by modeling it as a simple RLC circuit described by

d2I(t)

dt 2+ 2ξω

dI(t)

dt+ω 2I(t) = 0 (2)

Solving for I(t) gives

)sin(1

)(2

0

teL

CV

tI ts ωξ

ξω−

−= ; where

ss LCR

2

1=ξ and

CLs1=ω (3)

The system inductance Ls and resistance Rs in (3) are the effective composite values of the

capacitor bank and the coil/workpiece. C is taken simply as the rated capacitance of the bank,

other capacitance terms being

negligible.

The electromagnetic pressure

distribution of the coil was arrived at

from basic material mechanics and

experience from a previous sub-scale

trial. A “4-turn” coil path layout was

settled on as a compromise to lower

system inductance from a “5-turn”

with more a uniform pressure Figure 5. Rocket Nozzle Panel with reforming

coil face laid out with 6 mm copper tape

METAL 2008 13.-15.5.2008 Hradec nad Moravicí

distribution but a significantly larger estimated inductance from equation (1). The 4-turn

layout was then mocked-up with 6mm wide copper foil tape applied to the a sample nozzle

panel as seen in Figure 5. The inductance of the mock-up was measured with a digital

inductance bridge and compared to a simple wire over a conducting plane length-of line

model calculation. Based on the mock-up information, results from equations (1) to(3) and the

100 KA peak current requirement, the bank energy estimated was less than half of the a

available 48 kJ. With confidence that the mock-up layout would lead to an effective if not

optimal coil, the detail design effort commenced.

Section 2.4 Detail coil design and construction

Time and cost considerations dictated a fabricated brazed coil design in lieu of a single

monolithic machined structure. Another primary design decision was to use the ideal panel

outside surface shape as the template for the coil face contours rather than the outside of a hot

formed panel whose contours were distorted by elastic recovery. The rational was that the EM

coupling between the coil and workpiece would increase during the calibration process as the

panel was brought into conformity with the form tool. The coil system mechanical design

was generated using a high performance, solid modeling CAD package. This effort was

further aided by the CAD solid model files of the nozzle panel and form tool supplied by the

Aerojet Corp. For design and fabrication simplicity, the coil path was divided into sections

which could be cut from a flat plate of an industrial grade copper alloy. All coil bars are 9.7

mm thick and nominally 76mm in depth from the panel outer surface. Bar thickness was

chosen to spread the EM discharge pressure across approximately two of the internal panel

slots depicted in Figure 4 in an effort to minimize local distortion of the outer skin of the

panel. Each major coil bar face contour was taken from the longitudinal section plane of the

panel which contained the layout path and the nozzle axis. The 4-turn coil layout of Figure 5

became 8 flat plate bars radially distributed across the panel on 7.35 deg. intervals. Figure 6

shows the solid CAD models of a typical longitudinal coil bar and the coil assembly on the

nozzle panel.

Only the first 3-4mm of the coil bar adjacent to the panel carries current. The remaining

bar depth is required for strength and reaction mass. The keyhole cutouts seen in the coil bars

in Figure 6 provide potting lock-in and additional surface area for distribution of the discharge

reaction into the coil potting. Slotting of the back of the coil bars eliminate possible stray

currents and provide minor enhancements to coil efficiency. Each bar is cut down to

approximately 25 mm at each end to aid the brazing process by restricting heat flow from the

joint. In order to accurately braze the coil bars together, the bars had to be oriented and

securely fixed in their proper location. A fixture tool for this purpose was cast from high

(a) (b)

Figure 6 . CAD models of a typical longitudinal coil bar (a) and the coil assembly

against the nozzle panel (b)

METAL 2008 13.-15.5.2008 Hradec nad Moravicí

temperature molding plaster using a female epoxy panel mold mounted in a plywood

surround. The coil bars were held in place on the fixture by clamp nuts on threaded studs cast

in place between coil bar positions. The coil joints were oxy-acetylene torch brazed using a

Ag-Cu-Zn-Sn (BAg-7) filler metal. The partially brazed coil mounted on the plaster brazing

fixture and completed coil brazement mounted on the potting fixture are shown in Figure 7.

Proper mounting and potting of the coil was essential to the performance of the coil in the

nozzle panel shape calibration process. The potting material and housing was required to

restrain the coil both from the primary discharge reaction from the induced current in the

panel and from the internal coil forces generated between coil bars. In addition the potted coil

needed to precisely nest the coil for accurate and repeatable EM pressure distribution. More

importantly, the potting material needed to provide a high level of electrical isolation between

adjacent coil bars and between the coil face and the workpiece. The capacitor bank used for

these trials has a maximum charge voltage of 10kV and energy storage limit of 48kJ. A inter-

coil or coil-workpiece arc, at even a fairly low bank energy setting, would severely damage or

destroy the coil. A urethane potting material

(Conathane TU971) was chosen for its high strength

and toughness for crack resistance and for its

dielectric strength. Figure 8 is a picture of the coil

potted in the welded steel support housing

immediately after removal from the potting mold-

fixture (caulking not entirely removed).

The operation of the coil system was simple Once

the potted coil assembly was leveled and connected

to the bus of the capacitor bank, a panel was placed

on the self aligning coil face with an intervening plastic (Mylar) isolation sheet. The male

form tool was then lowered onto and aligned with the back of the panel. The first trials used

no other restraint besides the mass of the form tool. Results from the first trials indicated that

the form tool mass did not provide sufficient restraint. Consequently, a system of 4, threaded

tie rods were added (see Figure 9).

(a) (b)

Figure 7. Partially assembled coil on the brazing fixture (a) and the complete coil

brazement mounted on the potting fixture (b)

Figure 8. Coil potted in housing

(a) (b)

Figure 9. Nozzle panel EM calibration system; (a) open, showing panel

nested on coil and (b) with form tool clamped in place by tie rods.

METAL 2008 13.-15.5.2008 Hradec nad Moravicí

A torque wrench was used to apply a repeatable preload to the calibration process. The best

results were obtained with the system preloaded to 50-70 ft-lbs on the front (R.H. fig. 9b) rods

and 20-30 ft-lbs on the rear rods.

Section 3. Results and conclusions

One of the inherent advantages of applying this method to spring back correction is that

EM coupling is not degraded by workpiece movement as is the general case for EM pulse

forming. The specific advantage is that a sequential series of EM pulses can be applied. It was

found that the best calibration results were obtained applying a modest preload to the coil-

form tool assembly with the tie rods and using a series of 6 EM pulses of 12-15 kJ each.

These pulses had peak currents is the 150-200 kA range. Figure 10 summarizes the results of

the Nozzle panel calibration trials. Comparing the “Deviation from Nominal” plots for EM

sized edges and the Hot sized edges shows a major improvement at the panel throat area,

which are the most critical area of the panel geometry. The right hand side of Figure 10

shows significant panel deviation from the nominal outside of the throat region. This effect

was thought to be principally due to a distortion of the coil geometry attributed to excessive

shrinkage of the potting material during curing. The shrinkage reduced the EM coupling of the

coil-work piece in this region leading to the poor calibration in this region. It was related that

the subsequent assembly process for the nozzle could compensate for larger form deviation at

the positive panel end but could not at the throat section. Consequently, this full scale rocket

nozzle panel calibration by EM pulse methods was considered a success despite the poor

fidelity shown at the positive stations in Figure 10. Moreover, since the poorly calibrated

panel areas can be strongly correlated to coil fabrication errors, a fairly straight forward

improvement to the process is known. Moreover, the results of these EM calibration trials

were considered sufficient to establish the technique as an integral part of this unique rocket

nozzle fabrication methodology.

0.10

0.15

0.20

0.25

0.36

-38.1 -25.4 -12.7 0 12.7 25.4 38.1

Axial Station - Distance from Throat Plane, (cm)

Deviation From Nominal (mm)

EM Sized edges

EM Sized ctrline

Hot Sized edges

Hot Sized ctrline

Projected Contour Deviation Range

w/ EMF Coil Iteration

Known area of EMF coil

contour deviation

0.10

0.15

0.20

0.25

0.36

-38.1 -25.4 -12.7 0 12.7 25.4 38.1

Axial Station - Distance from Throat Plane, (cm)

Deviation From Nominal (mm)

EM Sized edges

EM Sized ctrline

Hot Sized edges

Hot Sized ctrline

EM Sized edges

EM Sized ctrline

Hot Sized edges

Hot Sized ctrline

Projected Contour Deviation Range

w/ EMF Coil Iteration

Known area of EMF coil

contour deviation

Figure 10. Nozzle panel deviation from nominal at centerline and at panel

edges for both conventional hot sizing and EM calibration

METAL 2008 13.-15.5.2008 Hradec nad Moravicí

Section 4 References

BALANETHIRAM, V. S, DAEHN G. S., 1994, Scripta Metall. et Mater., 30, 515.

BRUNO, E. J. ed, 1968, High Velocity Forming Of Metals, (rev. ed., ASTME, Dearborn MI,)

BATYGIN, YURI V., DAEHN, GLENN S., 1999, The Pulse Magnetic Fields for Progressive

Technologies, Kharkov, Karkiv Oblast Ukraine Columbus, Ohio U.S.A.

DAEHN, G.S., VOHNOUT, V.J., DUBOIS, L. 1999, Improved formability with

electromagnetic forming: Fundamentals and a practical example, , Proc. TMS Annual

Meeting; Sheet Forming, San Diego, Ca, Feb.

IRIONDO, E., GONZALEZ, B. GUTIERREZ, M., VONHOUT, V., DAEHN, G., HAYES,

B., 2006, Electromagnetic springback reshaping, Proc. 2nd International Conference on High

Speed Forming, Dortmund, Germany

VOHNOUT, VINCENT J., 1998 A Hybrid Quasi-static-Dynamic Process for Forming Large

Sheet Metal Parts From Aluminum Alloys, (Ph.D. Dissertation), The Ohio State University,

Columbus, Ohio, Sept.

VOHNOUT, V. J., DAEHN, G. S., SHIVPURI, R., 1999, A hybrid quasi-static-dynamic

process for increased limiting strains in the forming of large sheet metal aluminum parts,

Proc. 6th Internation. Conference on Plasticity Technology, Nuremburg, Germany, Sept. 9-23