High Velocity Sheet Metal Forming:
State of the Art
and
Prognosis for Advanced Commercialization

Prepared by:

Glenn S. Daehn
Department of Materials Science and Engineering
The Ohio State University
Columbus, OH
 

Summary

This document is intended to represent a fairly comprehensive summary of the state of the art in high velocity metal forming. This is a technology that has limited use at the present. However, it has been demonstrated that formability is increased, wrinkling is suppressed and these processes are easily carried out. All of these suggest that it may represent an important technology in addressing current issues in sheet metal forming. This report addresses in detail the basics of high velocity forming techniques based on capacitor bank discharge (electromagnetic forming and electrohydraulic forming), discusses the ways in which these methods can be used to solve current sheet metal forming issues, describes the areas in which the further research is required in order for the technology to gain wide acceptance, lists the organizations doing work in this area and describes their activities, and implicit in this report are suggestions on how investments in this technology may produce significant rewards.
 
 

I. Introduction

There is currently a strong desire to use significantly more aluminum in automotive body applications. However, there are several significant obstacles to the introduction of aluminum sheet components. High velocity forming addresses the problems that arise when one tries to form aluminum panels with the existing technology that has been optimized for sheet steel. These include: 1) The forming limits of aluminum are significantly lower than those for steel. Aluminum is particularly prone to tearing at bends. This limits the shapes that can be fabricated and slows die design, die tryout and application. 2) As the elastic modulus of aluminum is lower than that of steel, springback is more severe and it is difficult to keep dimensional tolerances. 3) Conventional die tryout with mating male and female dies is always slow and expensive. It would be desirable if at least prototypes could be produced with one-sided die sets. This would speed time-to-market.

As a result of this there is renewed interest in superplastic and high rate superplastic forming to form auto body components. These techniques have the advantages of delivering exceptional formability, potentially giving good dimensional tolerance and delivering rapid time-to-market as one-sided dies are employed. There are several potentially severe drawbacks with this technique as well. For example, the temperature and strain-rate of the blank must be carefully controlled to maintain formability. Also, the material is quite soft at temperature, so removal from a hot die may cause loss in dimensional accuracy. These temperature control issues largely limit the productivity of this technique even if economical high rate superplastic alloys can be developed. Also, it is not clear if as-formed components will have acceptable mechanical properties without additional heat treatment, and/or care to avoid cavitation. These issues cast real doubt on the economical development of this technology for mass production in the foreseeable future.

The Ohio State group has been investigating, in a generic sense, how high velocity deformation affects the ability to make useful components from sheet metal. This line of work was fairly actively pursued between about 1955 and 1970, but there has been very little research done in the past 25 years. In the ëoldí literature[1,2] it was well established that high velocity metal forming was able to form complex components with one-sided dies and that springback is minimal. In this work, two particularly commercially-attractive techniques were developed; electromagnetic forming and electrohydraulic forming. Equipment for electromagnetic forming is commercially available and it has been used to form and assemble nearly-axisymmetric parts for over 30 years now, but has seen little development over that time. Electrohydraulic forming has hardly seen any development in commerce or research over the same period, it appears.

This report largely covers what is new in the field of electromagnetic metal forming. As there are relatively few institutions working in this area (see Appendix A for a fairly complete Who's Who summary) much of the work reported is from the Ohio State group. There are excellent introductions to this field that largely cover what has been done prior to 1970 (see for example 3-9).

Key methods and features of high velocity metal forming

High velocity metal forming was studied fairly extensively between about 1955 to 1970 [1-3]. Several methods were considered including explosive forming with both high explosives and mixtures of combustible gases. Also, methods based on the discharge of capacitor banks were explored. These have intrinsic advantages in that there is no need to store explosives and discharge can be highly reproducible. We believe that such methods have the best potential for commercial use in mass-production. Two capacitor-discharge based forming methods are discussed next.

The work done in the 50ís and 60ís establishes that these techniques are quite versatile. It was demonstrated that there is very little springback (as a result of this, electromagnetic forming is commonly used to assemble concentric tubular components). Tolerances of ±0.005" are common with components about 10" in diameter. Also, these were known as rapid methods to make parts because only a single die is required and fracture was seldom seen. A wide variety of parts have been formed this way.
 
 

Electrohydraulic Forming

In this technique, an electric arc discharge is used to convert electrical energy to mechanical energy for metal deformation. A capacitor bank delivers a pulse of high current across two electrodes held at a short distance from each other and submerged in fluid (water or oil). The electric arc discharge that occurs, rapidly vaporizes the surrounding fluid and creates a shock wave. The workpiece which is kept in contact with the fluid is deformed into an evacuated die. A schematic illustration of the electrohydraulic forming process is shown in Fig. 1. The potential sheet forming capabilities of such submerged arc discharge processes have been recognized since the mid 1940ís. During the 1950ís and early 1960ís, the basic process was developed into production systems. This work took place in several countries, including the USSR. It was principally for and by the aerospace industries. By 1970, forming machines based on submerged arc discharge, were available from machine tool builders. The Cincinnati Shaper Co. in Ohio built machines ranging in size from about 35 to 150 kJ output power. A few of the larger aerospace fabricators built machines of their own design to meet specific part fabrication requirements. Two such units were the Sonaform and Electroform machines. Both of these where spun-off into separate machine tool businesses.

Electrohydraulic forming is a variation of the older, more general, explosive forming method. The only fundamental difference between these two techniques is the energy source and subsequently, the practical size of the forming event. Very large capacitor banks are needed to produce the same amount of energy as a modest mass of high explosive. This makes electrohydraulic forming capital intensive for large parts. On the other hand, the electrohydraulic method was seen as better suited to automation due to the fine control of multiple, sequential energy discharges and the relative compactness of the electrode-media containment system. As mentioned, at least three companies were producing turn-key electrohydraulic forming systems in the late 1960ís. However, by 1980 all had discontinued production. Several systems are still in use at aerospace fabrication facilities today. However, the process never became widely used. There are various opinions concerning the reasons for this. Two reasons cited are the need for media containment and the consumable nature of the discharge electrodes. Both of these characteristics made the automation of electrohydraulic forming generally more problematic than electromagnetic forming. Electohydraulic forming can generate workpiece velocities on the order of 200 m/s.

Figure 1. Schematic illustration of the ectrohydraulic forming process. 2. Electromagnetic Forming:

Electromagnetic forming is the only high velocity forming technique to gain significant acceptance in commercial metal working. The electromagnetic forming technique has been in use commercially for the last 30 years. It has been mostly used for joining and assembly of concentric parts. The minimal springback inherent in all high velocity forming processes makes for high quality joints. One of the most common applications is the compression crimp sealing and assembly of axisymmetric components such as automotive oil filter canisters. As the name implies, electromagnetic forces are used in this technique to form the material. A current pulse from a capacitor bank is passed through a coil which is placed in proximity to a workpiece. The current pulse causes a high magnetic field around the coil. This field induces an eddy current in the workpiece and an associated secondary magnetic field. The two fields are repulsive and the force of magnetic repulsion causes the deformation of the workpiece. The designed shape and electrical characteristics of the coil depends on the workpiece. Coils can be developed for most practical forming geometries including for forming flat sheets. Fig. 2 is a schematic illustration of electromagnetic forming showing a) solenoidal and b) flat forming coils.

The nature of this technique makes it very suitable for automation. Results obtained are very repeatable because the energy discharge characteristics are controlled by the essentially non-changing electrical parameters of the system and precise control of the capacitor bank charge voltage. The fundamental physical characteristic of this technique is that the deformation forces are initially only the magnetic body forces within the material generated by the eddy currents induced by the drive coils. Surface pressures occur only upon contact with the form tool. This can provide deformation capabilities that are difficult to obtain with other forming methods. Because the technique is based on relatively simple electromagnetics, it is very amenable to analytical or numerical modeling.

Figure 2. Schematic illustration of electromagnetic forming showing (a) solenoidal and (b) flat forming. 3. Forming Based on Foil Vaporization

In one other possible technique, the capacitor bank is shorted across an insulated metal film (e.g., aluminum foil) and the metal vaporization is used to provide a force between the sample and a more massive tool. This can then be used to accelerate the workpiece. There has been little published wherein this technique has been used. However, from scant data [10],. the technique does appear to be fairly efficient and flexible relative to traditional electromagnetic forming. For example Mike Fisher of Battelle reports that a 44kJ capacitor discharge from 15 kV is capable of accelerating a steel plate (1cm x 7.5 cm x 10 cm) to a velocity of 200 m/s. The resultant kinetic energy represents about 30% of the energy that was stored in the capacitor bank. Typical electromagnetic forming processes are about 10% efficient or less. Some rather informal recent experiments at Ohio State also indicate that this technique produces significantly higher efficiency than traditional electromagnetic forming. The other advantages of this technique are that forming operations of this type are not limited by the strength of a coil. Strong monolithic tools can be used on both sides of the workpiece. Also, the back-side tool and foil can easily be shaped to accommodate pre-forms of varied shape. This technique appears very promising for short-run or prototype production, but there is very little published experience with it.
 
 


II. Fundamental Attributes of High Velocity Forming

There are a number of common attributes to all high velocity forming methods that make them amenable to forming sheet metal. In the following sections the generic features of high velocity forming that relate well to sheet metal forming are discussed.

Formability

In the literature of the 1960's and 70's there are some isolated reports that high velocity forming can increase the formability of many common metals both in tensile testing and in sheet form. The most complete of these investigations was carried out by W.W. Wood and co-workers [11-13]. Their studies demonstrated modest increases (10-50%) for a variety of materials over a range of workpiece velocities. They also identified several materials for which increases in formability were not apparent. Their work was based primarily on the study of materials accelerated by explosive discharge and no solid correlations between material properties or structure and high velocity formability were noted. Also, it should be noted that these studies were carried out before the development of the forming limit diagrams by Keeler and Goodwin [14,15].

It was the fairly recent experiments of Balanethiram and Daehn [16,17] that lead the Ohio State group to enthusiastically pursue electromagnetic forming. 2024-T4 aluminum as well as annealed OFHC copper and IF iron were studied in these experiments. The setup was fairly simple as illustrated in Figure 3. The sheet metal was expanded into a right conical die using two boundary conditions. In the first, hydraulic pressure was used to expand the sheet slowly into the cavity and in the second a shock wave generated by discharging capacitor banks caused the sheet to enter the die with a velocity on the order of 200 m/s. This latter case is traditional electrohydraulic forming. Further details on these experiments are published elsewhere [16-18].

Figure 3. Schematic of system used for hydraulic and electrohydraulic forming of sheet metals into a right conical die. The results of these experiments were quite striking. In the low-velocity hydraulic expansion experiments, all of the sheet metals failed in accord with the forming limit diagram. In the high velocity forming experiments the sheet metal extended to strains in excess of 100% in a mode very close to plane strain in each case. This represents an increase in the plane strain failure strain of 3-5 times for these materials. This is especially significant as most materials in forming practical components fail in a strain state very near plane strain.

Irrespective of the possible mechanisms that are responsible for this increase in ductility (which are discussed below) its observation has much practical importance. These experiments clearly demonstrate that ordinary materials can undergo relatively easily-implemented room temperature process that increase their formability to levels several times their ordinary values. Superplasticity is normally required for such levels of ductility and this method provides this without specially-processed materials, or controlled temperatures or strain rates. In the remainder of this section the present understanding of why such high levels of ductility are observed in this process with the goal of developing rules which can be used to designing manufacturing processes that make use of this extended ductility.

Reasons and Analysis

In the sections below each of the factors that are believed to provide increased ductility are listed and the evidence for their importance is discussed. In the cone-forming experiments above, we believe that several of these factors are simultaneously important.

1. intrinsic stabilization of defects

One of the most straightforward ways to explain the observed increases in ductility is by considering the effect of inertia on a neck that is forming in a tensile sample that is being extended in one dimension. A series of papers on this effect has been written by Daehn and co-workers [16,17,19,20]. The most comprehensive and advanced of these is one by Hu and Daehn [19]. The basic idea in all of these analyses is similar and is based on the analysis of a simple uniaxial tensile test. At relatively low strains, the sample may deform in a uniform manner. In such the local velocity of any location of the sample will vary linearly with its location as shown schematically as the stable curve in Figure 4. After the Considere instability point (i.e., load maximum), a sharp velocity gradient may be developed in the sample where on one side of a growing neck the sample will move with the velocity of the moving crosshead and on the other side it will remain stationary. This velocity gradient is accommodated over the short region of the neck. This velocity gradient is also shown in Figure 4. In going from the stable state to the localized state, there must be a change in the velocity profile of the sample. The change from the stable to the localized velocity profile takes place over some time period Æt. This change in velocity over time (acceleration) produces non-uniform inertial forces in the sample.


Figure 4. Schematic description of the evolution of a simple tension test. Up to the point of maximum load deformation is stable. Once localization is severe, there may be a sharp discontinuity in the velocity-position relation. Figure 5 shows the right hand side of the sample introduced in Figure Y, and we will let the center of the sample be the origin of the position (x) coordinate system and define velocity as zero at this location. In going from the stable state to the localized velocity profile, each location of the sample must go through a velocity change. The inertial force at each location can be calculated by Newtonís law, where acceleration is estimated as the change in velocity, Æv, divided by the time period between the end of stable flow and localization.
 
 

Figure 5. Right hand side of the sample introduced in Fig. 6 with associated velocity and force profiles. The inertial force is not present in quasi-static deformation and tends to increase the stress in the perfect part of the sample. After some simple manipulations detailed elsewhere, [17] an estimate of the critical velocity required to increase sample formability can be found from estimating when the sample stress increases a given fraction at the gripped end, f1 , where a reasonable value for f1 may be between 0.01 and 0.1. Using this, Vcrit can then be expressed as:

It is interesting to note here that it is the crosshead velocity, rather than material strain rate that is important in determining if there will be increased formability due to inertial effects. This distinguishes this effect from changes in the materialís constitutive law, which would be expected to scale with strain rate. Again, the origin of the effect is that the inertial forces act to diffuse deformation throughout the sample by increasing the stress at the gripped end. Similar explanations for increased ductility in uniaxial tension have been offered by Follansbee and co-workers[21].

A more advanced approach to these ideas was provided by Hu and Daehn wherein a simple uniaxial tensile sample and radially expanding axisymmetric ring were deformed in high velocity tension and modeled with a one-dimensional finite element method approach [ 19]. Two separate geometries were studied. The first is the same uniaxial tensile sample as studied previously. With that sample, as the crosshead velocity is driven up (i.e., the velocity of the driven end of the sample) a velocity is eventually approached where the sample end velocity approaches the velocity a deformation wave can propagate through the sample. At this velocity, known as the von Karman velocity, the ductility of the sample drops off significantly and the sample necks off at the driven end. Stress-strain behavior of a series of uniaxial samples deformed at varied velocities are shown in Figure 6.

Figure 6. Engineering stress-strain curves at various extension velocities for uniaxial tension with n = 0.25 and m = 0.02. Note that increased ductility is only noted over a limited range of velocities and only modest increases are noted. The other geometry studied was an axisymmetric ring that is deformed by radial outward expansion. Physically this can be done, and has been done, both by explosive expansion [22] and electromagnetic ring expansion [20,23]. In this geometry there is no wave that propagates along the length of the sample. The deformation state at each point of the ring is nominally identical (although an imperfection is included in the model to aid simulated sample failure). As a result of this there is no analog of the von Karman velocity. Strain to failure increases monotonically with increasing sample expansion velocity. The predicted strain to failure in both uniaxial tension and ring expansion is shown in Figure 7. Also in this plot the critical velocity at which ductility increases V1 and that at which it falls off, V2, are shown. The paper provides estimates of how these parameters vary with material properties.

Figure 7. The variation of the total elongation with test velocity for both uniaxial tension and ring expansion (n = 0.25 and m = 0.02). Figure 8 shows comparisons of these predictions to experimental data [13, 20]. In general the agreement between the predictions and observations is excellent in terms both of trends and absolute magnitudes. This suggests that these models do capture the essence of the localization process in ductile materials that fail by necking (however, there are many second-order effects that may be very important in many cases which are presently ignored).

These observations can also be used to interpret and design high velocity forming operations. First, with respect to designing forming processes this shows the importance of understanding material boundary conditions. If treated properly, inertial effects can significantly increase the ductility of materials by making necking more difficult. However, if von Karman wave propagation effects are produced, the material ductility may be significantly reduced. Second, with respect to understanding the origin of the dramatically increased ductility seen in the conical sheet forming tests of Balanethriam and Daehn, inertial stabilization of necks is not a sufficient explanation. Figure 7 shows that we can often increase the uniform strain of materials by about a factor of two. However in the cone-forming experiments, up to five fold increases in ductility were noted. Further reasons for extended ductility must be sought.

One last aspect that should be noted is that formability truly is a function of forming velocity. If a ring is expanded in an unconstrained manner at high velocity it will fragment into many small pieces however the strain measured by the reduction in cross section at the center of the fragments will show that strain increases as velocity increases. At first it may appear that this 'improved ductility' is not useful as the ring has fragmented. However when a cylindrical die is used to arrest the ring before it fractures, we find that we can expand the ring to larger diameters than would be available without fracture if the ring were not arrested. Hence in may be useful to use excess energy in forming and a die to arrest the motion of a workpiece to attain the highest formability.

(a)

Figure 8. Comparisons between experimental observations and the models of uniaxial tension and ring expansion. (a) The variation of the average uniform elongation with extension velocity for tensile tests. Square symbols, dashed lines and solid lines represent the experimental data, simplified curves drawn by Wood et. al. and numerical simulations, respectively, (b) The variation of the average uniform elongation with expansion velocity for expanding ring tests. 2. sample size effects and apparent changes in anisotropy

It was also recently demonstrated that sample size or shape has a significant effect on strain to failure in ring expansion. While the section above showed that a numerical model could quite satisfactorily predict strain to failure values for slender rings 30mm in diameter with a 1mm x 1 mm cross section, very different results were obtained if taller rings were studied [24]. Similar studies were carried out with 6061-T4 aluminum and annealed OFHC copper. In either case rings 30mm in diameter with a 1mm thick wall and varied heights were studied (1mm to 16 mm tall). In each geometry, these rings were expanded at with a range of velocities over which they may stretch without failure or fracture into many segments. Figure 9 shows the maximum strain without failure as a function of ring height for a both the 6061-T4 and the OFHC Copper. It should be noted that the initial 'launch' velocity here is constrained to be a value that is sufficiently low that it does not cause failure of the sample. If the sample is constrained such that it will reach a die before tearing, even higher strains are possible before failure. Despite this factor that limits the strains that are accessible, very high exentsions are available simply by changing the geometry of the component being formed. In the case of the 6061T4 aluminum, 70% extension is available from a material that only exhibits 26% in static extension.

Figure 9. Possible circumfrential extension without failure in unconstrained expansion as a function of ring height for 6061-T4 and annealed OFHC copper in ring expansion. There are a few possible reasons for this unusual behavior. It very much seems to be related to apparent changes in the apparent anisotropy of deformation of these tubes. Figure E shows a composite forming limit diagram for 6061-T4 formed from the published FLD as well as the high velocity cone forming experiments of Balanethiram [16-18] and the tube expansion experiments. While this plot shows the major point that has been made so far; major strain increases with tube height, it also shows that the minor strain (i.e., contraction strain of the height of the tube) also increases (or becomes more negative) as tube height increases. This strong influence of strain state on accessible material extension is well known and is demonstrated by the slope of the forming limit curve in the left side of the diagram.

This change in deformation anisotropy is referred to as the r-value where r is the ratio of the width strain to thickness strain in uniaxial tension. It is well known that materials with high r-values are generally more formable than those with low r-values. It must be noted that in the current tests with tube expansion, the stress state is not strictly uniaxial any more. The magnetic field can induce an axial pressure on the tube and also the constraints imposed by volume conservation and inertia also may affect the apparent r-value in tube expansion. This issue has been addressed to an extent by Fenton [25] and the modeling of Pon and Bechtel [26], but a full understanding of how the material's intrinsic anisotropy, sample shape and deformation conditions all contribute to producing the material's final apparent anisotropy in high velocity deformation.
 
 

Figure 10. Forming limit diagram showing the published FLD as well as low rate data, unfailed strain states reached in the cone forming work of Balanethiram and tube expansion data (marked with corresponding tube heights). 3. inertial ironing

Again, the 3 to 5 fold increases in ductility seen in the cone forming experiments of Balanethiram may be also partly attributed to the fact that a sheet-like geometry was used instead of a slender, rod-like one. However this effect also seems to be too weak to explain the dramatic increases in formability that were observed. Another effect that may have importance is what may be termed 'inertial ironing'. Figure G schematically shows both traditional and inertial ironing. Traditional ironing is used to make many components where large reductions in wall thickness are needed (such as two-piece beverage cans). This technique is usually limited to reducing the wall of cylindrical components. Inertial ironing takes place when a relatively deformable material strikes a plastically hard one at a high velocity and its deceleration produces forces large enough to deform it. One can imagine a lead bullet striking a hardened steel target and developing a pancake shape to appreciate inertial ironing. When two elastic bodies strike with a velocity Vo, the maximum stress (pressure, P) at impact is:

where r is the density and c is the velocity of propagation of the waves generated upon impact. This is equal to  for longitudinal waves in a bar. The subscripts 1 and 2 represent the two materials being brought into contact.

When one or both of the bodies are plastic, the situation is somewhat more complicated as the stress calculated in the elastic case may plastically deform the one of the bodies. In this case the dynamics of the now depend upon plastic deformation rather than linear elastic behavior. However simple estimates can be developed. In most cases we are interested in the stress developed upon the deceleration of a thin deformable sheet striking a massive die. Let the sheet have an initial velocity, Vo, density r, and thickness t. It will come to rest in a time period between when it strikes the die and its center of gravity moves some distance d. If we make the reasonable assumption acceleration is uniform over this period, the average force at the workpiece, die interface can be calculated as:

This equation may appear to be in variance with that for the elastic impact as pressure goes with velocity squared the latter and linear velocity in the former. This can be reconciled by considering that the deflection during impact in the elastic case will increase linearly with impact pressure. In the simplified latter equation, one must develop a reasonable estimate for d, which should increase with impact velocity.

In a typical electromagnetic forming operation the workpiece speed is near 150 m/s, sample thickness is 2 mm and upon impact with a steel die, only a maximum of about 0.5mm of deformation is expected. Based on this we find that through-thickness stresses on the order of 135 MPa (20 ksi) are accessible. This is on the order of the flow stress of aluminum. Thus, this effect is very able to affect deformation characteristics in forming. It is postulated that this through thickness compressive stress can act something like the stress state in rolling to squeeze the material in the through-thickness direction to produce stable stretching in the plane of the sheet. Also, as will be discussed later, this through thickness stress also can be used to produce coining-like operations and may be important in the reduction of springback in high velocity forming.

Figure 11. Schematic diagram of traditional (left) and inertial ironing. In the latter case impact of the workpiece and the die produce a large through-thickness compressive stress in the deformable sheet. 3. changes in material constitutive behavior

All of the analyses described above that deal with inertial stabilization of neck growth, changes in observed anisotropy and inertial ironing are all essentially inertial effects. That is, they do not depend on the intrinsic behavior of the material (its constitutive behavior), and they do not depend on changes in intrinsic behavior with strain rate. Many ductile metals show the kind of trend illustrated below in Figure 12 where flow stress increases slowly and smoothly with strain rate up to a strain rate near 103 s-1, at which point material flow stress increases fairly rapidly with increasing strain rate. There has been significant discussion about both the observations of this [27] as well as its micromechanical interpretation [28]. In more recent literature Follansbee has argued that this effect, which appears to be strain rate sensitivity is instead due to an increase in the rate of strain hardening with increasing strain rate[29]. Recent experimental analyses [30] support this view.
 
 
 
 
 
 
 
 
 
 
 
 
 

Figure 12. Effect of strain rate on the flow stress of Armco iron [Rinders and Kunze]. Another issue that could affect the constitutive behavior of the materials being tested is their temperature. In electromagnetic experiments both electrical resistive heating as well as deformation work heat the sample. In the case of aluminum this may be particularly potent, as aluminum has essentially zero strain rate sensitivity at room temperature but this increases at moderate temperatures (this is significant in the low ductility and formability of aluminum at room temperature). Thus, it is possible that the increase in temperature in electromagnetic forming also aids its increase in ductility.

It is not presently possible to completely assess the extent to which changes in constitutive behavior may impact the formability values measured in the experiments cited above. In the case of the electrohydraulic forming of conical sections from flats, [16,17] these effects are though to be minimal, as similar results were seen in three very different materials (copper, aluminum and iron), resistive heating is eliminated and the estimated strain rates are all beneath 1000 s-1, where significant changes in constitutive behavior are thought to occur. However, in the ring expansion experiments strain rates can exceed 104 s-1 and heating due to both deformation and resistance can be significant (the maximum strain rates obtainable with this technique are limited by reaching the melting temperature of the rings. Thus, in these cases it is reasonable to expect that some changes in constitutive behavior may affect material formability.

Regardless of how changes in formability come about, whether by inertia, strain-rate sensitivity, strain hardening, or thermal effects, the observation of increased formability and ductility at high strain rates is very reproducible and robust. It has been seen in many materials under many conditions. This suggests that the effects are largely inertial, as these effects are seen in all the experiments. Furthermore, as high velocity forming techniques are generally easy to implement, they can be used to improve material formability even if the origin of the effects is not completely understood.

4. Further Observations

Following the theme of applying improved material ductility obtained in high velocity forming even if it is not fully understood in this section a number of examples are given in the following. Figures 13, 14 and 15 show examples of simple components that have been formed by the electrohydraulic forming of aluminum sheet. In the first case (Figure I), strains near 100% in nearly plane-strain were measured in this rectangular box-like component. The measured strains far exceed those predicted as being safe in a usual forming limit diagram. Figure J shows that a sharp crease at the top of a conical section can also be formed rather simply. In the example in Figure K, 6061 aluminum is formed in the full-hard (T-6) temper. All of these examples require ductility that is beyond what is typically observed at conventional strain rates. Simple one-sided dies were used without any iterative process in either the development of their shapes or boundary conditions. This technique is rather similar to superplasticity in many respects, most notably strains to failure are much higher than under typical conditions and simplified forming procedures can be used. As a result, the word hyperplasticity has been coined to describe this effect [17].
 
 


Figure 13. Rectangular bump formed in 6061-T4. This was accomplished with nearly pure stretching. Major strains of 100% near plane strain were measured in this part.
Figure 14. Close up of corner in 45o angular section of a stretched 6061-T4 diaphragm. This was accomplished with nearly pure stretching. Note that very sharp corners are possible.
 
 
 
 
Figure 15. Component formed in 6061-T6 (i.e., full hard!) condition. This demonstrates that materials with limited ductility can be formed in this way. This improves component strength to weight ratios, while allowing higher precision in formed shapes. In many situations it may be desirable to largely form a component in quasi-static deformation and then use high velocity forming in selected regions where exceptional formability or dimensional accuracy is required. In such cases it is important to know how what the formability characteristics of previously deformed materials will be. Vincent Vohnout at Ohio State has recently been examining this issue and Figure 16 comes from his work. In this materials were pre-strained in quasi-static tension in a near-plane-strain condition and then deformed again in tension using an electromagnetic impulse on a nominally flat sheet. The results show that while much of the deformation is carried out in a quasi-static manner, the combined operation results in strains that are much larger than can be obtained in a single quasi-static operation. Work is currently active in this area.

Figure 16. Results of experiments wherein a flat blank was first pre-strained using large gridded samples in a quasi-static manner using a standard testing machine and then deformed at high strain velocity using electromagnetic impulse. The work shows that even if pre-strains very near the safe limit strain are imparted, subsequent high velocity deformation results in total strains that are significantly in excess of that which can be attained from a single quasi-static operation. With respect to the later, more practical, examples of improved formability in high rate forming; these all show the potential of the technique for enabling the fabrication of geometries that are presently impossible. Previous to this a somewhat quantitative discussion of formability at high rate was presented. At the present time, it is not possible to closely link these two aspects in a quantitative way. The practical experiments are still too complicated with respect to boundary conditions and a number of effects are superimposed simultaneously (increased temperature, strain rate gradients, impact at varied velocity, etc.). As a result of these complications it may be some time before quantitative predictions of ductility at high velocity is possible. Despite this, it is important to reiterate that these techniques offer flexibility not found in traditional forming and in general formability does increase with increasing workpiece velocity.

Inhibited Wrinkling

The previous section of this review demonstrated that instability in the form of fracture is inhibited by high velocity forming. In addition to this, wrinkling or buckling instabilities are inhibited by high velocity forming. This can be demonstrated in two different types of experiments which were both recently carried out by M. Padmanabhan [31]. In the first a simple single turn coil (a piece of 6061-T6 aluminum with a hole cut in the center and a slot that creates a current path around the hole) was used to compress 2" diameter aluminum and copper rings of various height onto a 1" diameter centered mandrel. A typical series of results is shown in Figure 17. This shows that as the discharge energy increases the rings become much more circular. In particular rings folding back on themselves that takes place at low energy is absent at high discharge energies and velocities. It is thought that the deformation is more stable (i.e., the ring remains nearly circular through the process). However it is still possible that ironing-like effects after impact tend to smooth deformation, even if the rings are initially somewhat kinked. High speed photography will elucidate this in the near future.

In another series of tests, aluminum and copper disks were accelerated using a flat spiral coil at a truncated conical hardened steel form at various energies. The results presented in Figure 18 show a trend very similar to that shown with the rings. At low energy numerous wrinkles form in the sheets where line length must be reduced to conform to the shape. As energy increases they fit the form of the conical sections practically perfectly (as documented later). This is a significant observation because typically increased binder loads are required to eliminate wrinkling. This has two disadvantages. First, the bound portion of the sample must later be trimmed, wasting material and necessitating another operation. Second, as binder loads are increased this typically necessitates further stretching of the sample and this reduces the effective formability of the material. Lastly it is significant to note that for the 6061-T4 aluminum samples shown in Figure 18 strains near 100% in plane strain are seen in the conical section of the samples.

Figure 17. 6061-T6 rings compressed using a single turn coil onto a mandrel one half the original ID o f the ring. E denotes discharge energy in this work. As compression velocity increases the propensity for wrinkling or buckling decreases.


Figure 18. Example of intertial inhibition of wrinkling. In each case the T-4 aluminum sheet is simply thrown at a steel sample with a truncated conical shape. Forming is accomplished by impact at varied velocity. As launch energy (indicated) increases, launch velocity increases. Equipment shown in Figure 20 was used. While there are few, if any, models that one can use to directly analyze how sample velocity affects wrinkling in these and other practical sample configurations, some simple qualitative ideas and observations demonstrate that increasing velocity tends to inhibit wrinkling. First consider a one-dimensional situation. Imagine driving a rather long bar into a wall. If this is done in a quasi-static way a relatively long bar would buckle at the buckling load and collapse. In contrast if the end load is dynamic the bar will largely collapse along its axis. This is the basis for the Taylor impact test that is used in characterizing material behavior at high strain rate and long-rod penetrators that are commonly used to defeat high-performance armor. The main difference between the quasi static and dynamic situations is that if a buckle is to form at high velocity, the bar must move at a high rate out of plane and this motion is resisted by inertia. It is more difficult to imagine how this effect becomes important in sheet forming, but it is qualitatively postulated to be similar; in order for wrinkles to form a more complex form of motion is required than the mode that develops a smooth shape. The deviation from the smooth-shape velocity profile requires additional acceleration that is resisted by inertia.

Coining and Impact

In the subsection of this report on inertial ironing equations for estimating the pressures that exist at the workpiece-die interface were presented and it was stated that pressures on the order of or exceeding the material yield stress could be obtained. This is quite significant because normally in sheet metal forming membrane stresses are used and advantage is taken of the sheet being relatively thin. Thus, local pressures are typically less than the material yield stress by large factors. As a result of this, if fine surface details are required (such as those found on coins, for example), coining presses are typically used. In these systems, surface pressures exceeding of 50 ksi are common. In order to experimentally estimate the pressures that exist in electromagnetic forming, standard quarters (coins) were attached to the front face of the dies used for forming the truncated cones shown in Figure 18. 6061-T4 sheet aluminum was impacted with the dies with the coins in place. At typical forming energies (about 10 kJ) the impression of the face of the coin is left very clearly in nearly full detail on the aluminum sheet. Companion experiments were carried out where a static load applied by a test frame was used to press coins into 6061-T4 sheet. A pressure of about 35 ksi was required to obtain a similar image. This demonstrates experimentally that the impact pressures are indeed very high and that they may be used to practical advantage in developing useful surface characteristics.

As another example of how the high surface pressure can enable unique and possibly useful structures a sheet of common 6061-T4 was electromagnetically accelerated and impacted with a die that had the shape of a rounded corner. One of the faces of this die was polished and a sheet of 240 grit sandpaper was affixed to the central area of that face. The result of that experiment is shown in Figure 19. What is shown is that the portion of the sheet that impacted the polished die has a mirror-like finish, while the area that contacted the sandpaper has a dull, matte finish. The high impact pressures provide forming on small length scales which allow desired surface finishes to be formed.

Figure 19. Results of a demonstration wherein a sheet of 1 mm thick was electromagnetically thrown at the corner of a softened cube die with one surface polished and partly covered with emery paper. Where the die was polished, the aluminum has a mirror-like finish and where the paper was it has a matte finish. This demonstrates a possible method of decorating metal as well as the high pressures developed on impact. Light and Agile Manufacturing Systems

The fact that these high velocity forming operations are all carried out over very short length scales means that equipment design based on the consideration of static force is inappropriate. In most ways this translates to being able to use much lighter, simpler tooling. For example, consider what kind of tooling would be required to form the partly polished, partly matte finished part shown in Figure 19. In order to get the kind of surface detail seen there, coining-like pressures are required; about 30 ksi for this aluminum alloy. Considering the area of the part, this comes to a total force of about 150 tons. Normally such an operation would be carried out in a very sizable press. In this case the forming operation was performed in the system shown in Figure 20. The system simply consists of a coil that accelerates the aluminum sheet at a die, inside an evacuated steel tube. The die is not bolted into place, it is simply held down by its own weight and inertia (and possibly the force due to the vacuum acting over the tool). Because the force is transient, the pressure wave naturally disperses and no large columns are required to transmit it as is the case in traditional equipment.

Another advantage of forming systems like those described above is that there is no need for blank holders or regions of the blank that are held and later trimmed. This is very different than traditional forming in that to make shallow cups the edges are typically held with one action while another punch forms the cup. Then trimming takes place. This is required to avoid wrinkling in traditional forming. In this process a sheet can simply be draped over a tool at high velocity and with good alignment trimming may be eliminated. High rate forming may also be applied to stretch forming, more similar to traditional metal forming, as well as sheet forming as described above.

Another example of how very simple tooling may be used to perform work that would be difficult or impossible is provided in the section on Cladding and Assembly.
 
 

Figure 20. Equipment used to form samples shown in Figures 18 and 19. Despite the large pressures that existed on impact (causing coining over the whole sample) the die, which is shown held by the crane, was simply held down by its own weight and vacuum acting over about one square foot. Springback

It appears that high velocity forming significantly reduces the amount of springback encountered when forming sheet metal. Although there has not been a great deal of careful study of this, there is some compelling evidence from both recent studies of electromagnetic forming [31] and older studies of explosive forming [32,33]. A detailed review of the older work as well as new results are provided in the M.S. Thesis of M. Padmanabhan [31], and a summary of many of the main points and observations follows.

Traditional analyses of springback stress that its origin is differential elastic strains through the thickness of a sheet while it is being formed. Factors that reduce this gradient minimize springback [34]. As a result of this, one of the most common methods of reducing springback is to superimpose tension on bending such that at the conclusion of the bending operation the stresses (and hence the elastic strains) are nearly equal through the thickness of the sheet. We may also postulate that if a large through-thickness stresses are present these may also make differential elastic stresses through the thickness hard to maintain and springback may be reduced. This qualitative postulate is borne out to a degree by experiments carried out by Yamada et. al. [35]. They studied the deformation of rectangular titanium plates into a spherical section steel die both at low rates and high rates. In the static case, the plate was pressed between the dies and high velocity forming was done using impulsive hydraulic pressure. The main purpose of their study was to determine the effect of compressive stress in the thickness direction on springback. In quasi static conditions, they found that as the pressure on the specimen increased, springback decreased. In the dynamic experiments, springback was found to decrease with increasing collision speed and for collision speeds in excess of 66 m/s, springback is found to be negative, i.e. the radius of curvature of the sample is smaller than that of the die. For a collision speed of 47 m/s, the springback is very close to zero. This suggests that springback could be eliminated or made minimal by using an optimum collision speed. The explanation for reduction in springback with increasing through thickness pressure is supported by comparison of the high rate forming with the low rate forming results. Figure 21 is a plot of springback as a function of compressive stress for both the low rate and high rate experiments. Thus, it appears final contours can be controlled to some extent by tailoring through thickness pressure. Another observation complicates this somewhat. That is the shape of the sample was also measured by high speed photography and it is rather different at low and high velocity. At low velocity the sample tends to deform at the center while at high velocity it tends to deform from the outer edges in. These differences in its deformation path may also ultimately affect springback.

Figure 21: Compressive stress dependence of springback in static and high speed bending [35]. These trends of minimum springback at an intermediate energy are observed in more recent metal forming experiments. Coordinate measurements were performed on samples formed onto the truncated cone die after forming at various energies. These results are shown in Figure 22. At low energies the sample does not completely meet the die and is wrinkled, as demonstrated previously. As energy is increased the sheet completely conforms to the tool and coordinate measurement shows that over most of the area the shape of the tool and the inner surface of the sheet take the same shape within the resolution of the equipment (the resolution, in this case is largely limited by appropriately indexing the shapes of the tool and sheet in space). There is a small bubble-like anomaly at the center of the flat section of the sheet where the shapes also deviate. This likely due to small amounts of entrapped gas and imperfect vacuum. At high energies the sheet and die no longer conform well. In particular the outer ends of the circular sheets tend to flare off of the tool. This is likely due to rebound of the sheet off the tool. This is a form of springback that is unique to high velocity forming and should be considered in process design. It is possible that the application of proper impedance matching or momentum traps could effectively treat modify this behavior.

Figure 22. Comparison of coordinate measurements of the tool and samples of 1100-0 aluminum formed at 2.125kJ and 6.95kJ, left and right, respectively. In the case of the 2kJ discharge, the shape of the tool and sheet are experimentally indistinguishable over most of the tool surface. Strains in excess of 70% are seen, near plane strain, in the sheet formed at higher energy. The previous examples (and those shown in the later section on cladding and assembly) show that there is much reason to believe springback can be reduced and dimensional tolerance improved by appropriate application of high velocity forming. A further understanding of the fundamentals will allow this to become integrated in design. Presently good analytical techniques are still somewhat lacking (but should be based on traditional solid-mechanics numerical analysis. However, it is clear there are new opportunities here for precision metal forming as the character of springback in high rate forming should be different in quasi-static forming because the boundary conditions are very different.
 
 

III. Solutions Offered by High Velocity Forming

Hybrid Techniques

Many of the components that one may want to form by high velocity methods may be relatively massive (such as automotive outer body panels). Though there are no fundamental limitations to the size of the parts that can be made by electromagnetic forming, larger parts means more energy required which translates into larger capacitor banks and higher initial capital expenditure. It is possible to locally gain the advantages of high velocity forming by doing most of the forming work using traditional methods and strategically use high velocity forming where required due to formability or other reasons. This is denoted a hybrid forming process. Two methods of carrying this out are offered below.

Electrohydraulic forming may be integrated with press forming using a matched tool set with electromagnetic coils built into sharp corners and other difficult- to- form contours. The matched tools would form the parts of the workpiece which can be easily formed at low velocities using mechanical energy from the press. This semi-formed workpiece would then be subjected to high rate forming with the electromagnetic coils to complete the forming operation. This can all be accomplished with a single set of tooling. A schematic of such a process is shown in Fig. 23. This concept is largely being followed in the PNGV projects that are described in a later section of this document.
 
 


Figure 23. Schematic of a hybrid matched tool- electromagnetic forming process. The metal sheet is pre-formed by the matched tool set, followed by electromagnetic forming to complete the deformation.   Similarly , electrohydraulic forming could be combined with hydroforming, providing some possible benefits. The a quasi static, fluid pressure hydroforming process becomes more difficult and expensive as required forming pressures increase. Most systems are limited to pressures of about 25 ksi. These high pressures that exist over the entire surface of the part also require fairly massive restraint systems. By integrating hydroforming with an electrical discharge spark gap in the fluid at the end of the pressure cycle, this may enable the formation of the sharp corners and bends which normally require very high static pressures.

Painted Surfaces

It is obvious that because electromagnetic forming only typically involves contact on one side of the sample, it is an excellent method for forming components with painted or polished surfaces. In an extension to this idea it has also been demonstrated by Maxwell Labs that forming can be done through protective covers such as plastic bags to maintain extreme cleanliness in fabricated assemblies. Manufacturing engineers with a degree of creativity should be able to exploit these features in useful and profitable ways.

Thin Sheet forming

Thin sheets are often particularly difficult to form via traditional routes as very small compressive stresses in the plane of the sheet will produce wrinkling or buckling. The advantages discussed previously with respect to buckling and wrinkling aid the forming of thin sheets. Furthermore, as relatively small forces are required to form thin sheets, the demands on coil performance are not nearly as severe as they are with more structural members. The one complicating factor in the fabrication of thin components is that unless the sample is thicker than the electromagnetic skin depth (which is a function of the material conductivity and discharge frequency--see Appendix C for details) the process will have quite low efficiency.

This process has been shown to be useful. Recently, The AWS Group of Wheeling WV, which makes components for speakers, designed new Ti diaphragms for their speakers based on a new concept. However, forming the 0.002 in. thick diaphragms for their components proved to be impossible using either matched tool forming (poor formability) or spinning (wrinkling). AWS, in collaboration with The Ohio State University has developed an electromagnetic forming process using a flat spiral electromagnetic coil. The workpiece, a 0.002 in thick Ti sheet, is laid on top of an Al driver sheet which is kept in contact with the spiral coil and a current pulse is passed through the coil, causing the driver and the workpiece to be launched into a evacuated female die. The diaphragms are being commercially manufactured currently with the electromagnetic forming technique at AWS. A photograph of the manufactured part is shown in Fig. 24.
 
 

Figure 24. Speaker diaphragm brought into commercial production by AWS corporation. This is .002" thick Ti that is formed into a female die that is evacuated with the aid of an aluminum driver and electromagnetic actuation. This is the only reproducible method the company could develop to fabricate this part. Aerospace or Short-Run Production Forming

The issues in short-run production are typified in by an example part provided by Cessna. They build about a hundred numbers of several specific parts annually that might become part of the Citation executive jet skin. A typical cable cover pan is shown in Figure 25. There is a very long manufacturing plan for this part that includes cycles in which the component is hydroformed to a safe strain, annealed, further hydroformed, annealed, hydroformed again then solutionized, quenched, aged, finish sized and trimmed. Electromagnetic forming can offer a much less expensive and energy intensive manufacturing schedule. The following is presently being investigated: The flat aluminum blank is first solutionized and quenched, formed to final shape in a single electromagnetic event, artificially aged and trimmed. This saves two costly annealing processes, forming processes and much hand work. This can be accomplished using a system similar to that discussed elsewhere in this report with either a male or female tool. Due to the component's geometry forming it is only possible with the extended formability in high velocity forming. The intermediate anneals are required to provide sufficient formability when traditional methods are used.

This is but one specific example of how electromagnetic forming may be used to address short-run production situations wherein formability is limited. In many ways it is ideally suited as only one sided dies are required and there are many operations in which many discrete processing steps may be eliminated or combined into a single step.

Figure 25 A typical Cessna Citation component, a cable cover pan. About 100 of these particular components are produced each year. Cladding/Assembly

The place where electromagnetic forming has found the most application in manufacturing is in the assembly of axisymmertic components. Prototypical of this is the simple compression of a ring onto a shaft. The work of M. Padmanabhan shows that very significant crimping forces can be easily obtained (See Figure 26). This basic method of using axisymmetric compression or expansion to assemble components has seen much application and is well documented by the basic reference works in this area as well as in marketing information from companies such as Maxwell-Magneform. Possibly the most demanding application of this technique is used commercially by Boeing wherein torque tubes for the 777 and other aircraft are manufactured by simply compressing a hollow aluminum tube over a splined cylinder attached to a yoke which is manufactured in steel. This assembly has been shown to be much stronger and fatigue resistant than those produced by the previous method of riveting. The technique used here was pioneered by Grumman Aircraft and royalties for use of the method are paid by Boeing to Northrop-Grumman.

It is important to note that in these procedures, springback is eliminated. Intimate contact with pressures similar to an interference fit between the crimped material and the other surface exists. It is easy to envision either using two metals that might react or including brazing material and applying heat to develop metallurgically bonded surfaces. Such a process is not documented in the literature, but should be easy to develop.

Figure 26. Force required to press an aluminum ring (originally 5.08 cm, OD, 1.651 mm thick, 6061-T6) off of steel mandrels of varied diameter with varied discharge energy). Despite there being no metallurgical bonding in this procedure, very high forces can be required to remove the ring.

 

IV. Factors Limiting the Application of These Techniques

Coil Strength

Coil strength is a key constraint in the electromagnetic forming of sheet components. At a minimum, equal and opposing forces will exist in a coil (or actuator system) and the workpiece. And with multi-turn coils, the actual situation is more difficult, as individual windings may attract or repel one another with great force. This force between conductors may damage insulation and if arcing takes place between conductors, the coil will typically fail quickly. As there can be significant voltage differences between one part of a coil and another, damage in the insulation will result in arcing and when this takes place the coil may be quickly destroyed.

The Metals Handbook chapter by M. Plum of Maxwell Magneform summarizes well the situation and conventional wisdom with respect to coil design [4]. All of the designs discussed are essentially axisymmetric based on spiral winding of the conductor. Also, maximum working pressures are stated for a number of common coil designs (these are pressures at which the coils can withstand long-term industrial use. For general purpose compression coils, copper-beryllium field shapers are often used and the maximum working pressure will depend largely on the geometry and materials properties of the field shaper but this should be near about 15 ksi. For expansion coils that consist of copper windings over fiberglass cores working pressures should not exceed about 5ksi. Flat forming is typically done with flat spiral wound copper that is embedded in fiberglass and epoxy. The working pressure for these coils typically does not exceed 5ksi. The highest compressive stresses (50 ksi) are generally generated by what are known as wafer coils. In these coils massive copper beryllium (or dispersion strengthened copper) are joined in a semi-permanent fashion with the primary conductors and currents are induced in the large field shapers. This is the type of coil is being used for the compressive assembly of torque which was discussed previously.

Although the pressure levels discussed above may sound small, many forming operations are easily performed at these stress levels. The following discussion illustrates this. First to deform a feature in a sheet of strength sf with a radius of curvature, r, and thickness t a pressure of sf(t/r) is required. These conditions are easily achieved with thin sheets and relatively weak materials like aluminum. Furthermore the values listed above are for pressures upon launch of the sheet. Much higher pressures are typically encountered on the deceleration of the sheet upon impact with the die, as was discussed with coining and impact.

In addition to the largely traditional approaches described by Plum [4], there are a number of other approaches to forming features that require higher pressures or entail non-circular geometries. First, there has been an extensive amount of work carried out in the former Soviet Union and a number of coil designs have been designed, described and closed-form analytical tools developed for them. Much of this work is described in their 1977 Electromagnetic Forming Handbook. Significant among this work are efforts to design and produce high-reliability actuators for forming nominally flat sheets. A typical design of an actuator of this type is shown in Figure 27. The design concept is similar to that used in field shapers in general purpose coils, wherein the primary windings induce a current in the massive central copper block and it is the field from currents in that block that accelerate the sheet metal. The design of this coil makes it very robust for delivering large forces and pressures. The main forces are carried by the copper core. The primary disadvantage of field shapers is that they are less efficient than direct induction as losses take place in coupling the primary windings to the copper core. This is reduced in the present design by recessing the windings into the core. Based on the author's qualitative experience with a coil of this design at the Rockwell International Science Center as well as with simpler direct-induction pancake coils, the winding and core design is significantly less efficient (due to different coil sizes and sample shapes, a careful comparison is impossible). However, the coil has repeatedly handled the entire 16 kJ discharge of that bank without any signs of damage.

Figure 27. Schematic diagram of the Cu or Cu-Be core that is the main component of elecromagnetic forming coils formed by Karhov State University in Ukraine. Several conductor windings fill the recesses in the core. Further details on the construction of this coil are presented in Belyy Electromagnetic Forming Handbook. IAP Research of Dayton, Ohio (www.iap.com) is involved in a NIST-ATP program that involves using electromagnetic impulse to compact metallic powders. Through this exercise they have developed coils that can exert pressures up to 80 ksi and these coils are presently in regular use. While IAP has not published details on how this is being done in prior work funded by EMTEC they have disclosed that they have been using rather traditional coil designs from the high magnetic field community (see [36] for a review of this field) and often these designs are fabricated from high strength steels. Although these materials have low electrical conductivity relative to copper or aluminum because the lengths are short and the cross sections are large, effective forming systems still result even with steel coils (see Appendix B for first-order analysis methods).

Another approach has recently been proposed by the Ohio State group and is now being experimentally tested. Virtually all of the actuator geometries produced to date are based on a nominally circular current path. Another possible type of actuator design is shown in Figure 28. The main feature of such coils is that the central conductor or conductors have an outward current flow that is balanced by return flow on either side. This geometry several advantages over common designs. First, the current flow down the center gives pressure in the center of the coil. In spiral coils there is no pressure at the coil center as the flux has a minimum there. Second, the actuator geometry is easily extended to make components with high aspect ratios or unusual shapes. It would be straightforward to bend these coils to make shapes that are singly or doubly curved. Third, as the primary conductors carry current in opposite directions the force between them is attractive and they repel the workpiece. As such it is fairly easy to robustly insulate such a coil. Tests with these coils to date have shown them to be quite robust and efficient. It is important to note that with this approach, the pressure distribution from the coil as well as the forces between conducting elements can be tailored in coil design. The tools discussed below in the analytical techniques section may be useful in this. The concept mentioned here of designing coils to minimize (or make less damaging) the forces between windings has been considered extensively by the high field magnetics community (see Moon for examples) but does not appear to have been considered strongly by the electromagnetic forming community. Innovative coil designs supported by modern numerical analysis seems to be very important n moving the field of electromagnetic forming forward.
 
 




Figure 28. Example of an irregularly shaped actuator for that was designed for forming the component shown in Figure 25. In application this is machined from 0.5" 6061-T6 aluminum and embedded in epoxy. Lastly there are coil-less approaches to high velocity forming. Electrohydraulic forming is fairly well developed, but is not easily implemented for high production rates as electrode tips tend to wear at high rates. As mentioned earlier intense pressure pulses can also be generated by foil vaporization. This technique may have a significant niche in forming for low-volume production. Also, it is possible to directly run current through the workpiece and this will then repel nearby conductive surfaces (or those with an opposing current).

Numerical Modeling

As alluded to in the pervious section, with the availability of robust 3-dimensional electromagnetic design tools, one may be able to design coils, pressure distributions and (eventually) spatial and temporal velocity distributions in the sheet being deformed that are very conducive to forming a given component. The examples shown in Figures 25 and 28 show the kings of parts that would greatly benefit from the availability of tested and robust design tools. Thus, such tools would benefit both the development of the coils as well as the overall forming process. A short report of the status of this area follows.

For some time there have been efforts at developing models of electromagnetic forming. The work done in the 60ís is largely closed-form and largely follows the procedures shown in Appendix B. More advanced versions of this closed-form approach are presented in the 1977 Ukranian Electromagnetic Forming Handbook.. The main limitation of these kinds of approaches are that only time-independent scalar quantities are easily obtained (such as peak pressure, for example).

At the next level of complexity equivalent circuit approaches are used to treat the temporal part of the problem while averaging the spatial issues. This approach has been shown by several workers in the field [20,23,37]. Generally good correlation to experimental results is found for geometrically simple problems with these methods. Similarly there are a number of three-dimensional codes that can calculate electromagnetic fields, but this is done in a quasi-static manner (that is plasticity or non-uniform body acceleration are not treated). These codes are typically used for things like designing electric motors.

In two dimensions the Lawerence Livermore National Laboratory code CALE (C Language Arbitrary Lagrangian-Eulerian) can treat problems in two dimensions that have both spatial and temporal variations [38]. It includes plasticity, acceleration as well as electromagnetic complications such as magnetic field diffusion into conductors. This allows one to study largely axisymmetric problems. The recent work of Gregg Fenton [25] has shown that for a large number of essentially axisymmetric problems the CALE models provide accurate and robust simulations. The code is still presently maintained as primarily a research code. As a result it is not terribly easy to use, but it is flexible.

There are no fundamental reasons that codes cannot be developed that are three dimensional and contain plasticity, electromagnetics and inertia, etc. However, there are presently no commercial codes with all of this flexibility. The author has been told by a PAMSTAMP representative that PAMSTAMP has been modified and is used this way in Europe, but no documentation is available. Smooth Particle Hydrocodes are another class of numerical models that can treat these problems. Along these lines, a new type of SPH algorithm was developed by Doug. Everhart of ARA, Inc. in late 1995 called "Gradient SPH." This new algorithm differs from traditional SPH algorithms in that it focuses on the gradients that are approximated using the SPH method. A re-normalization procedure is used at each time step to adjust the SPH interpolation kernel and optimize the accuracy of the gradient approximation. A special treatment is used in SPHERE to accommodate electro-magnetics. The SPHERE code is very versatile. The integrated method of treating material deformation and electro-magnetics allows the treatment of extremely complicated shapes. The code allows 2-D rectangular, 2-D axisymmetric, and 3-D analyses with no restriction on material shape. Recent work with the code shows that it can faithfully simulate results that exist in the literature.

Capacitor Bank Availability and Capabilities

The last major issue that limits the application of electromagnetic forming is the status of the basic equipment. The capacitors and switching devices both have limited lives wherein their life-expectancy is dependent upon how hard they are used. The capacitors themselves usually have a rated lifetime of some number of cycles (often 105) and if the conditions are less demanding their lifetime may be longer. Increased lifetime results from reduced charging voltage or decreased amount of current reversal. Current reversal can also be minimized by good system design. There are two primary sources of capacitors in the US; Maxwell Technologies, of San Diego (http://www.Maxwell.com) and Aerovox of NewBedford, MA (http://www.Aerovox.com).

The situation may be even more serious with respect to high current switching devices. The traditional method for switching power from the charged capacitors to the coil is through a tube-like device called an ignitron. These are filled with liquid mercury and a small spark ionizes the vapor and this breakdown can carry very large currents. These devices have limited lives (up to 106 cycles, however) and being based on mercury disposal and/or refurbishing becomes an issue. Furthermore, they are only manufactured by one U.S. Company; Richardson Electronics of LaFox, IL (http://Rell.com). There are, however, other approaches to high power / high current switching that are emerging. The most promising are based on solid-state switching. These are close to the capabilities needed in electromagnetic forming, but because the market is small they are not currently available commercially. Progress in this area is covered in a bi-annual IEEE meeting on pulsed power that is covered in the IEEE Journal of Plasma Science.
 
 

V. Concluding Remarks

This report is intended to show in some detail that there is much promise in electromangetic fomming and that it may represent a cost effective solution to many of the forming problems that are commonly encountered in forming materials of moderate formability, such as aluminum. In its present state it is not developed to the level where aggressvie sheet forming may be routine. However, with a committment to engineering the required sub-technologies, it may have a significant impact in manufacturing in a few years.

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38. R. Tipton, CALE Users Manual, Lawerence Livermore National Laboratory, M.S. L-35, P.O. Box 808 Livermore, CA 94550, Jan. 1995

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    Acknowledgments and Notes
 

This 'status report' has largely been made possible through my interactions with my Ohio State research group over the past five years. It is the original work and literature research of that group that has made this report possible. That group includes: Marina Altynova, V. S. Balanethiram, Gregg Fenton, Xiaoyu Hu, Padmanabhan Mahadavan, Amit Tamhane and Vincent Vohnout. Amit Tamhane was especially helpful in prrofing and helping with references in the final version of this report. Finally I wish to express my appreciation to the Rockwell International Science Center who made my sabbatical there possible and who permitted me to work on this report. In particular Dallis Hardwick, Pat Martin and Murray Mahoney made my stay very enjoyable and rewarding.
 
 

Any questions or comments regarding this report may be addressed to:

Glenn Daehn
Department of Materials Science and Engineering
The Ohio State University
2041 College Road
Columbus, OH 43210

ph 614/292-6779
fax 614/292-1537
e-mail Daehn.1@osu.edu