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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.
Glenn Daehn Ph.D. Professor
Material Science and Engr.
The Ohio State University
Columbus, OH 43210 U.S.A
William Hayes Technical Principle
Aerojet Corp.
Sacramento, CA 95813-6000
U.S.A
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