5.1 Introduction

In order to accelerate the development of the MT-EM process, two demonstration trials involving actual, full size automotive body panels were undertaken. Attempting full-scale applications at such an early stage in the process technology development was viewed as a means to test practical design methods and to provide preview and feedback to process development on real application problems. The inherent simplification of a system when scaled to convenient laboratory size can inadvertently mask real application problems. A prime example is in the estimation of the process energy requirements. Arbitrarily constructed laboratory test system can generally be designed small enough that the equipment capacity becomes a non-issue and serious weakness in the estimation method can be glossed over. Similar arguments can be proffered for the design of the driver coils and electrical bus work. Ideas that seem to work fine at a few kilo joules and kilo amperes can literally come apart

at much higher energy and current levels. In particular, direct experience was desired concerning the design of full-scale work coils operated at near limit energy levels and their integration into the match tooling.

Two major deviations from standard automotive stamping practice were accepted for these early, full-scale trials. First, there was no attempt to install the MT-EM process into a press machine. The pre-forms were stamped out and transferred to tools containing the work coils were the EM phase was performed as a second operation. Second, the tools used for the EM phase were not made of a malleable grade of cast iron, standard for production tools. Except for the imbedded coils, the trial tools were made from a special iron filled plastic material recently developed for prototype stamping tools. The deviations from what might be considered standard stamping practice conditions are not deemed to affect the applicability of the trial experiences to the development of actual MT-EM automotive application.

The full-scale trial part problems were chosen by a group of engineers from the major American automobile manufacturers and consisted of a hood feature line and a door inner panel lock face. The two parts and the sections of those parts chosen for MT-EM application were considered to span the geometry variations most troublesome to produce in aluminum by the conventional matched tool method. The hood feature trial was the least ambitious of the two and undertaken first.
 

5.2 General design considerations

Before the detailed numerical analysis methods, reviewed in chapter 4, can be effectively applied, a preliminary system design must be generated. Simple applications utilizing relatively inexpensive tooling may not require a high degree of process optimization at the design stage in any case. To arrive at a good initial design point and to predict at least a lower bound on the energy requirements of an application, a good pencil and paper design method is needed. Ideally the method is simple enough that a pocket digital calculator is sufficient to conduct a few preliminary design iterations. Further, the method must be accurate enough to render the results dependable, if only as upper or lower bounds. Approximate design methods for the quasi-static, conventional matched tool forming portion of the MT-EM process have been available for many years. These methods will not be discussed here but can be found in many texts books on metal forming such as those by W. F. Hosford and E. M. Mielnik [43, 54].

Only a brief experience with the design space of EM portion of MT-EM applications is required to recognize that there actually are no time invariant factors in the process except mass. The simple, inductively coupled RLC circuit presented in Chapter 3 becomes quite complicated when the inductance capacitance and resistance are all taken as time dependent variables. Additionally, the deformation mechanics of the work piece during the EM phase are complicated by the fact that temperature effects are present and the inertial terms of the force balance equations are significant, even dominant. However, assuming constant circuit parameters does allow coarse predictions of the system response using simplified geometry and energy balance relations. The simplifying assumption that underlies the method must be kept in mind. Adding insupportable layers of sophistication in an attempt to improve the accuracy should be avoided. The computer simulation methods in chapter 4 should be employed when the detail and accuracy of the preliminary design methods are insufficient.

Two questions that must be addressed early in any new application design are: "Is the general level of plastic deformation require to finish the feature from the pre-form shape available through EM pulse forming?" and "How much energy will be required from the capacitor bank?" The first question is best answer by previous experience with the alloy of the part in question. As a very general rule of thumb, the total useful strain available to the MT-EM process is about 50% greater than the quasi-static limit strain for the alloys commonly used for stamped parts. The distribution of the strain will be dictated to an appreciable extent by the geometry of the coil and the eddy current density (see chapter three). More will be said on this subject later. The second question is, of course, related to the first in that plastic work is part of the energy required from the bank. However it is usually the smallest fraction. Both of the questions will point to a new preform design iteration when the answers lie beyond the capabilities of EM forming. The assessment of the EM energy required will quickly becomes the prime issue of the early stage of a MT-EM process design. To address this question, the simple geometry and energy method outlined below was developed. The method was generally based on others applied to axisymmetric parts presented in the literature [17, 34, 10, 3, and 13]. However, nowhere in the literature was found a method directly applicable to the MT-EM conditions or presented as a clear step by step procedure.

To apply the method, presented below, of estimating EM energy requirements, some preliminary information is required. One should have in hand the following

1) Part feature pre-form and final shape.

2) An estimate of the strain level in the pre-form.

3) The material data of the part sheet

4) The geometry and material properties of a preliminary coil design.

5) The geometry and material properties of the coil-bank connection.

6) The electrical properties of the surrounding tool material.

7) The effective resistance and inductance of the capacitor bank up to the coil lead connection bus

For frequencies below 500 kHz, the radiation energy can be ignored [67]. A simplifying assumption used for this analysis is that the majority of the work done and energy expended occurs within the first current cycle. This assumption is common in the literature reviewed and is also supported by the high-speed array camera images of the coupon expansion tests reported in Chapter 3. Accepting the truncation approximation, the energy terms can be expanded as follows for first current cycle of the discharge:

where  = effective bank capacitance

= effective bank current

= effective system inductance

= effective system resistance

V₀ = capacitor charge voltage

V_T = capacitor voltage after time 

= period of 
 

Once the system is assembled the effective system parameters can be calculated directly from measured current-time data. In order to estimate  before building the system the parameters of 5.1b can only be approximated. The accuracy and completeness of the parameter estimations along with the time invariant assumption, limit the predicted bank energy such that, even with care, significant error can be expected. However, this level of accuracy can be sufficient in the initial process design stage. The real value of such a rough model lie more in assessing relative merits of competing designs than accurate predictions.

The estimation of  and  proceeds by expanding the parameters into their major constituent parts for separate evaluation. The effective system parameters are constructed as:

where the subscripts B, C and l stand for bank, coil and leads. The coil induction will include the effect of the coupling with the work piece and therefore indirectly also includes the work piece resistance effect. Work piece resistance generates and additional energy loss term due to eddy currents, which increases the effective resistance of the system as seen by the bank. This proximity resistance is represented by the p subscript term. It is important to keep the parameters for the bank-coil connecting leads separate from the coil since the leads are not affected by the presence of the work piece and can be a major source of hidden inefficiency if not properly designed. It will be assumed the parameters of the capacitor bank including the bus are known from shunted tests. What remains is to estimate the coil and lead parameters by methods consistent with the required accuracy of the bank energy prediction. The sequence of the following calculation steps is not critical as long as the prerequisite values are available.

Step 1: Estimate the coil and lead inductance:

Given the initial design geometry and material of the coil and leads, the formulas found in Grover [36] or other older electrical engineering handbooks can be applied. Curved coils (not doubled back) can be flattened and the inductance of more complicated branching geometry can be assembled as series or parallel combinations of simple geometry elements. Unless specified otherwise, the inductance calculated by these formulas are for isolated coils and transmission lines. The effect of the work piece and any surrounding conductive, nonmagnetic, material will be to lower the inductance of the coil as seen by the bank. Close proximity of ferromagnetic material will have a smaller effect but tend to increase the inductance of the coil. In either case, the effect is fairly small after a few centimeters and is therefore any change in coil inductance is chiefly due to the presents of the worksheet. Unless the leads are surrounded closely by a metal duct or conduit, their open inductance value can be used. Texts and handbooks such as Grover provide methods for calculating the mutual inductance of the surrounding metal bodies and net effect on the coil or bus inductance. However, these calculations can become quite tedious and much better results can be obtained from commercial electromagnetic analysis programs with similar levels of effort.

Two other options are available for finding component inductance values. First, the flat plan of the coil work face can be translated from the design to a thin sheet of metal with electrical properties similar to the proposed coil. The inductance of this flat coil mock-up can be measured while covered by a plastic or paper layer and metal sheet simulating the work piece. The inductance measurement instrument used must be able to measure in the micro henry range and supply an excitation signal of approximately the same frequency as expected from the completed system. If the coil is easily to prototype, more accurate results can be obtained if not constrained by the accuracy of the induction meter. Figure 5.1 shows a lab set-up to measure the covered inductance of a work coil. In using this method , it must be kept in mind that both the resistivity of the cover sheet and the stand off distance (coil-work gap) affect the resultant effective inductance. Therefore, the cover sheet and gap should be as close to the actual system values as possible.

A simpler method is to use existing data from several coil faces of differing geometry and size that are candidates for the general type of EM and have been mocked-up and measured as described above. As long as the cover sheet and surrounding material resistivity are close to the those of the proposed design then the ratios of covered to open inductance should also be similar. The data from inductance test for a mock-up similar in plan to the door trial coil, is assembled in Table 5.1(not generated by the set-up shown in Fig. 5.1). Data from other mock-ups are provided in Appendix B. Examination of data so generated for the general class of the trial parts, show that the ratio of covered to open inductance, for intermediate frequencies around 10k Hz, is approximately 0.25 for open inductance of 2.0 micro henry or less. The ratio drops to about 0.12 for open inductance of about 8.0 micro henry. Using the open coil inductance and the bank capacitance and the frequency relation , the best ratio can be quickly found. Using equation 5.2, the estimated system inductance,, can now be assembled and the system undamped frequency, required for the next, step can be calculated.
 
 

 
 

Figure 5.1: Lab set-up for measuring inductance of prototype work coils cover by part sheet. The components are labeled:

P- part, Cl-coil, SG- signal generator, DCS-digital oscilloscope, IB-inductance bridge.

Step 2: Estimate the coil , lead and proximity resistance.

With the system undamped frequency, approximating the actual damped frequency,, the coil and leads skin depth of the current can be estimated with equation 5.5 that is the same as 3.17 but in terms of resistivity .

The resistance of the coil is calculated by the standard conductor resistance equation

where is the conductor length and  is the effective conductor cross sectional area given by the product of cross section perimeter and the skin depth. Note that equation 5.6 gives good estimates for conductor cross section aspect ratios < 2. At higher aspect ratios 5.6 will under estimate the conductor resistance since the current will not be evenly distributed around the conductor perimeter. In wide thin conductors, the current will concentrate at the farthest edges of the conductor so as to minimize the number of magnetic flux lines encircling the current [67]. Just as for the inductance estimations, the resistance of the more complicated branched coils such as a 3-Bar or multi- element leads, the effective component resistance is formulated as series of parallel combinations of sub elements. The general form for combining resistive (or inductive) elements can be found in any elementary text on electric circuits and is provided here for completeness (replace R with L for combining inductors).

Proximity resistance is the increase in effective system resistance seen by the bank, due to the energy supplied to resistance heating of the work piece. The power loss per unit area of surface with conductance,, and incident magnetic field,, is given by Stoll [65] as  which can be written in terms of flux density, , and eddy current area  and related to part of the effective resistance by the coil current .

Where  is the conductance of the work piece is the coil current generating the eddy current through  in area. If the work piece is within a few millimeters of the coil face, can be approximated by the area of the coil elements facing the work piece. Except for branched coils like a 3-Bar, the coil current is the same as the bank current. This system resistance term will generally be small in comparison with the others and can therefore often be neglected, at least initially. If this term is included its assessment will be more direct when the require flux and current are determined.

Step 3: Estimation of the system effective current 

The estimation of  is the key to this method since it is the common factor in the inductive and resistive energy groups. Estimation of requires quantities calculated in four sub steps to be acquired first.

Step 3a: Estimation of the plastic work required

Given the initial pre-form geometry and the final desired part shape, the energy needed for plastic deformation can be estimated using:

Where proportional loading and uniform condition, such as plane strain is assumed. The full details of choosing a constitutive equation, determining the limits of integration etc. are available in any good text on metal forming. In many cases, a plane strain condition can be assumed. The final strain can be approximated by using a simple change in line length, ignoring redundant work. A constitutive equation which is simple, fairly accurate, includes prestrain and whose constants, n and K ,, are available for many alloys of interest is given by:

If the plane strain condition is assumed, the strain energy can be written as:

Equation 5.9 will produce acceptable results if the required strain is rather small, less than static failure strain. However, EM forming will often be used to produce plastic deformations beyond the static failure strain where equation 5.9 and 5.10 are not defined. Applying equation 5.9 in such cases will likely seriously over estimate the plastic work. One reason for the over estimation is that the energy levels required to obtain the high plastic strains will likely induce local current heating with a corresponding reduction in flow stress as discussed in Chapter 3. A solution to this problem might be to use a constitutive equation, such as the Johnson-Cook relation, , which accounts for thermal effects and larger strains [46]. The attended complexity involved with using such relations would however violate the simplicity tenant set down for this pencil and paper analysis. The development of constitutive relations for plastic flow in the EM regime is, in fact, still an active research area. For these reasons the purpose of this rough model may best be served by using an elementary, ideal plastic relation for assessing plastic work. Assuming ideal plastic behavior equation 5.7 becomes

Determining a proper value for constant flow stress is an obvious source of additional error. In the absence of material data, the average of the yield and ultimate strengths might be used to take rough account of the thermal softening.

Step 3b: Determination of the kinetic energy desired for work piece.

Free form coupon test data (see Chapter 3) indicates that for ductile aluminum alloy, a velocity of about 200. m/sec. will be sufficient to ensure the benefits of inertial suppression of local necking. The kinetic energy is approximated by considering the deforming sheet area as a free body, ignoring the restraining forces of the tensile stress in the sheet along the boundaries of the deformation area. This approximation assumes the energy in the work piece, at any time during deformation, is the superposition of kinetic and strain energies. The boundary is defined as the contour line representing some arbitrarily small iso-strain. This contour line will usually be close to the perimeter of the coil. The kinetic energy term is then given, using the coil face area, , the sheet density, D, and thickness t_s, by the familiar relation:

During deformation, after the acceleration period, the kinetic energy is transferred into plastic work. If the acceleration is large, the period is short and the strain produced during it will be small. The magnetic energy absorption of the work piece can then be considered as a serial transfer process of magnetic field energy to kinetic energy that is dissipated by plastic work and other non-conservative terms (which are ignored). This implies a constant mechanical energy term such that; . Accepting this analysis provides a means to determine minimum work piece velocity .

From experience it is seen that velocity should not be less than 100m/sec to maintain a minimum level of neck stabilization.

Step 3c: Calculation of the acceleration distance from the magnetic pressure.

The total energy of the work piece at any time during deformation, , must be supplied by the magnetic field generated by the coil. Initially the magnetic field or flux is confined, by the opposing field of the eddy currents, to the stand off volume between the work sheet and the coil. This compression of the magnetic flux generates a pressure, analogous to a fluid pressure but acting only on the sheet and the coil. The magnetic pressure is define as:

where  and  is the flux density on the coil and opposite side of the sheet. can be determined if the penetration of the magnetic field into the sheet is known. The differential equation, which describes the diffusion of a magnetic field into a conductor has the same form as heat diffusion (the Laplace equation). The form of the solution is therefore also the same. The instantaneous value of magnetic field in the sheet at depth y as a function of the surface value, skin depth (), frequency is, from a derivation by Stoll [65] as ;. This equation indicates that the magnetic flux density, B, () in the sheet has a logarithmic decay and lags the coil side surface by  radians. If the skin depth is equal a fourth of the sheet thickness the flux magnitude will be less than 2% of the coil side . However, this condition will seldom be met when forming thin gage sheets with large coils. Fortunately because the flux density appears as a square term in 5.11a, fairly high flux leakage can be accepted. A 25% flux leakage through the sheet will reduce  by only about 6%. If it is desired to take leakage into account a estimated leakage ratio, can be included such that  so that the magnetic pressure becomes:

where 

Experimental evidence and numerical simulations in free forming of rings indicates that the usual EM event scenario consists of a rise to peak velocity followed by a deceleration period [77, 78]. Both experimental and computational EM ring expansion results by W. H. Gourdin [78] are shown in Figure 5.2 .

During deceleration, the remaining kinetic energy is dissipated into plastic work, gas compression and heat. If the work piece strikes a die face, there will be additional losses due to impact. In this first approximation of required bank energy, gas compression, deformation heating and die impact are considered negligible. Assuming uniform acceleration over the first  current cycle,, fixes the require magnetic pressure in terms of velocity v, sheet thickness ts, sheet density, D and damped frequency at:

The magnetic pressure acting on the sheet during the deformation represents the energy that the coil is feeding into the sheet which is required to be equal to the kinetic and strain energy terms. The form of this relation is

where  is the volume swept out by the sheet while  is acting. However, the coil must first fill the standoff gap volume, with flux to generate  initially. The energy density of a magnetic field is given by , but  so that magnetic energy in the initial gap is:

Therefore, the portion of the coil flux energy, used to generate the velocity and strain of the work piece is the sum of the initial gap energy plus the "flow work" of the sheet displacement

By combining equation 5.15 , 5.16 and 5.17 to eliminate the common terms gives a relationship between coil energy and system parameters.

Note that equation 5.16 estimates only the fraction of the total coil energy that is generating the pressure on the sheet. The remainder is contained in the rest of the magnetic field surrounding the coil. Total energy of an inductor can be found if the product of magnetic field and differential volume is integrated over the volume that the field occupies,  . The field volume integral can be broken into the sum of the work gap volume and the remainder.

The coil field fraction Kc, is the ratio of the field energy supplied to the work piece to the total energy of the coil during the first cycle that can be written as:

5.18 simple states that if the work piece completely surround the coil, all the coil energy can be used. However, for most sheet forming, not more than half the field can be applied in which case the coil field energy will be twice that

given by equation 5.16 so that the total required coil energy is estimated by

(5.21)

Step 4: Assembly of the estimate the energy required from capacitor bank .

With and the effective discharge current,B, can be calculated using the inductor energy relation.

B is the effective or rms value for the first current cycle and is the same for all elements in the circuit so that the estimated bank energy is given by:

To assess the eddy current resistance losses a value for , is required. However, it will be more accurate to isolate the eddy current resistive energy term and to limit it to the acceleration period so that; . Redefining it using equations 5.7, 5.13b and 5.14 produces equations 5.23b and 5.24.

If careful assessments are made of the component values of 5.23, the predicted energy required should be a lower bound due to the truncation of the current to a single cycle. This estimate should be dependable enough to help in initial design decisions, especially if used as a comparative measure for evaluating alternative coil and lead designs. Users should keep clearly in mind the simplifying approximations of this analysis:

PartPar	, H	, H	, *	, *					, m2	, m3
Hood	1.00E-7	5.9E-8	6.20E-4	1.57E-4	0 .5	0.36	4	0.05	1.12E-2	1.12E-5
Door a*	1.93E-7	2.59E-7	1.06E-3	4.2E-4	0.5	0.36	2	0.25	4.06E-2	4.06E-5
Door b1	1.04E-7	2.28E-7	4.43E-4	4.2E-4	0.5	0.36	4	0.21	1.74E-2	1.74E-5
Door b2	1.50E-7	1.22E-7	9.0E-4	2.0E-4	0.5	0.36	4	0.21	1.74E-2	1.74E-5

* pre-form and coil geometry : a= stretch form 2 turn, b1= draw-in 3-bar, b2= draw-in 2 turn

The definitions of the values in Table 5.2 can be found in the preceeding text and are summerized below.
 

= work coil inductance , Henrys

= work coil lead inductance, Henrys

= work coil resistance, Ohms

= work coil lead resistance, Ohms

= work coil effect ratio

= magnetic field leakage factor

  = ratio of cycle period to acceleration period

= effective work piece strain required

= work coil face area, sq. meters

= work coil- sheet gap volume, cubic meters

Part	value type	, rad/sec	rad/sec	joules	amps
Hood	calc.	58600.	5150.	16800.	187000
	actual	59800.	5070.	27000.*	313700
	% error	-2.0	1.6	- 37.	-40
door I	calc.	41800.	3150.	68400.	275000.
	actual	43000	4190.	43200.+	188700.
	% error	-2.8	-25.	58.	45.7
door IIa	calc.	47060.	3327.	33000.	225000.
	actual	NA	NA	48000.+	NA
	% error	NA	NA	31.+	NA
door IIb	calc.	50500.	4090.	22600.	187000.
	actual	46200.	7896.	24000.+	199000.
	% error	9.	-48.	-6	-6.

To add some clarification to the data in Table 5.3, it should be noted that the hood shown indications of significant impact velocity in much of the forming area which would require energy not accounted for in the analysis. At a discharge level of 18kJ, the hood feature was substantially formed with much less impact indicated. The error between the prediction and the 18kJ test is -7% for energy and -6% for rms current.

The door I preform geometry inner panel did not under go the 0.25 true plane strain that was calculated by line length change between the preform and desired geometry. The analysis assumes only stretching occurs during deformation. Even minor amounts of draw-in from surrounding material will reduce the strain levels in the EM forming area. Draw-in was evident in the door inner trials, which reduced the measured strain to an average of approximately 0.16. The predicted bank energy required for this level of uniform plane strain is 41 kJ, which reduces the predicted error to -5% for energy and 12% for rms current.

Door IIa and IIb used different coil designs with the same preform geometry. Coil B1 was a 3-bar while IIb was a 2 turn with the same face area of IIa. Three bar coils have lower efficiency, which is clear from the results listed in table 5.3. Moreover, the method is considerably farther off in predicting the required energy in this case than for the hood. One consideration is that in the case of the hood, the metal requiring the most strain was covered more completely by the high pressure area generated by the coil that is not true for the door 3-bar coil. However, this condition is more nearly met by the IIa coil design and might therefore account for the better prediction. The method may have produced better results if closed attention was given to assessing the value of the coil ratio K, which describes the fraction of the total coil field energy that is transferred to the work piece.

In addition to providing an estimate of bank energy and its general distribution in the system, this method provides a means of assessing the internal impulse forces in coil and the coil reaction against its support structure once the system current is estimated. For example, if the coil bar cross section are round or some what square, the force generated between coil elements can be roughly estimated by using the relation for the force per unit length, l, generated between parallel current filaments I1 and I2, d length units apart given by:

Of course, if the coil bars are rectangular and close together, 5.25 will give a very poor estimate of the force between them. More accurate relationships for various cross section geometry can be found in older texts. and handbooks of electric power engineering such as Grover [36] .

The energy estimation method presented here is intended only as a tool to aid in the early stages of a MT-EM process design. Like any other tool it has limitations which can be accepted and possibly improved if clearly understood. In addition the results available with such a tool are dependent, to some extent on the skill of the user. The real value, of such approximations lie in the their use in comparing competing design ideas, as has been stated previously. Additionally, estimation methods often aid in the generation of new ideas from which solutions follow.
 

5.3 Full scale MT-EM trials

Initial coupon tests indicated a synergistic effect increasing limit plastic strain levels was possible in combining quasi-static and high velocity forming methods for aluminum alloy stamping. Experimentation with coil geometry and materials produced results that further supported the expectation of success at full auto body panel size parts. The sponsors of this research believed that the technology thus far demonstrated was sufficiently advanced to attempt solution to real scale aluminum stamping problems. The cost differential between laboratory and auto scale technology demonstrations is at least an order of magnitude . However, the review panel of industrial sponsors believed that only successful, production scale demonstrations would gain the attention of the decision makers of their industry. "Bread pans and simulation graphs donít excite many production people." From a research stand point full size demonstrations afforded a chance at uncovering hidden scale driven problems with the method as mentioned in the introduction to this chapter.
 

5.3.1 Automobile hood feature line extension trial

Figure 5.3 shows one of the automobile hoods used in the trail. These 6111-T4 hoods were in production at the time of the trial. The original design intention was that the valley creases would run from each side of the windscreen, down the hood and around the nose to each side of the grill insert. During the prototype phase of production tool development, the valley crease could not be run to the grill area without producing wrinkles in the hood nose. The problem was correctly identified as bucking caused by unsupported compression of the material as the tool attempts to shorten the line length at the bottom of the crease traversing the hood nose. The object of this trial was to design and build an EM tool, which could extend the crease valley feature line(s) around the nose of the hood as originally intended. The extended feature valley crease could not exhibit buckling or restrict marks were the extended feature blended with the first form area.

The amount of plastic strain, required to complete the hood crease was only a few percent. The fact that the sheet could not be supported by tool surfaces during compression was the problem to be solved with EM pulse forming. Various options for constraining the high-pressure area of the magnetic field over the narrow path of the valley crease were considered. High magnetic pressure outboard of the crease area would likely leave a impact mark in the sheet similar to a restrike mark in matched tools. The solution arrived at was the 3-bar coil concept. The 3-bar coil concept was subsequently also used in the coupon tests described in Chapter 3. The coils for the hood and coupon tests are similar electrically in that the center bar carries the total current and the each of the two outer bars return half the total current. The 3-bar coil configuration is not as energy efficient as a single turn coil consisting of the outer bars of the coil only. However the 3-bar design is well suited to forming very high aspect ratio features which are not very deep. A simple straight, flat, trial coil, 4.75 cm x 30.00 cm was built of rectangular yellow brass bar stock and tested to validate the fundamental concept. The coil was pulsed against a flat sheet 6111-T4, (8.0 cm x 35.0 cm x 0.08 cm) at 12. kJ, backup by a 2.5 cm thick sheet of neoprene (60 durometer) about twice as wide as the test sheet. The result was a bead the same width as the center bar (1.0 cm), formed in the sheet the same length as the center bar, approximately 0.5 cm high and having a nearly parabolic cross section. The sheet outboard of the bead had a slight dihedral away from the bead but no wrinkles. A question remained as to how well a 3-bar would form a feature similar to the hood crease around a radius like the nose curvature of the hood. Since the 3-bar design was inexpensive and easily made from bar stock, a second trial coil fixture was built and tested. The second three bar coil, 4.75 cm wide by 92.0 cm long was constructed with a 15 cm radius through a 120 degree bend at the mid-point Figure 5.4 shows the first trial coil with a test bead sheet and the second, mounted in a two half, plywood fixture, also with a test sheet. The top half of the second coil fixture carried a plastic die insert to form the test sheets against. Either stretch or compression beads could produce by interchanging the coil and the die insert from the male half to the female.
 
 

The results of the 3-bar trial coil tests provided an empirical basis for the design of the hood crease feature coil along with a expectation of its efficiency. Geometrically, the hood coil was quite similar to the curved trial coil with a few notable exceptions. First, the hood coil was not plainly curved. Second, it was not level across the bars in cross section. The coil face needed to carry the same contours as the hood valley crease area to be reformed within approximately 1.0 mm to maintain good magnetic field coupling. Last, the hood coil needed to be structurally self sufficient capable of resisting the internal forces generated during operation with minimal reliance on containment by tool material in which it was embedded. This last condition was supported by the trial coil tests which indicated loss of efficiency when surrounded too closely by a contiguous, conducting, support form material such as steel or aluminum. Conversely, epoxies and other polymers in heavy section have neither adequate stiffness nor toughness to contain the internal coil impulse forces attendant with the estimated pulse energy levels.

Figure 5.5 is an approximate schematic of the geometry of the hood coil. Contact between the outer bars through the steel clamps was allowed since the outer bars are at very nearly the same potential. Since the steel clamps were thin and parallel to the magnetic field they developed very little eddy current and therefore did not reduce the coil force on the hood. Using the simple energy analysis presented in section 5.2, the peak coil current were estimated and applied to determining peak internal forces of the coil. It is these forces which size the clamping plates or tie rods used to maintain structural integrity of the coil.

As reported earlier, a principal structural design rule for MT-EM coils is sufficient strength to handle discharge forces independent of the surrounding tool material. The peak current was predicted to be 264000. amperes by the method presented in the previous section. Internal forces of the coil, tending to spread the coil bars apart, at peak current were estimated at 210 kN. Steel clamps were designed so that the span strength of the coil bars matched the load capacity of the clamps. The arrangement and size of the clamps shown in Figure 5.5 resulted from the analysis of coil current and forces with an additional safety margin provided by the tooling material.

Figures 5.6b shows an enlarged view of the left hand side of the symmetric hood nose area as it is currently produced. The valley crease running down from the top right of the picture disappears into a shallow blend area between the top of the grill and head lamp areas. Figure 56a is the right hand side of the hood after the EM pulse form operation. The valley crease feature appears in Fig. 5.6a as the original design intent, crisply continuing around the hood nose to the bottom of the grill area. The results of the EM restrike were not prefect, since a small wave, not visible in 5.6a, remained in the outboard area of the feature at the mid point of the nose curvature. However, no restrike marks were produced and the transition between matched tool and the EM formed zones of the feature is smooth. Nearly all of the intended geometry change of the feature was accomplished in this first EM tooling design and test iteration.

Shown in Figure 5.7a and 5.7b is the finished EM tool with the imbedded coil used for the EM restrike of the hood feature. These tools, manufactured by International Tooling Technology Ltd. in Detroit Michigan, are made from a new, iron filled castable product that is a room temperature curred, epoxy like material. This material is currently being used in place of low melt temperature zinc alloys such as Kirksite for prototype and short run production. Cost of producing MT-EM tools for auto body parts using the new iron filled epoxy is significantly lower than other constructions including the soft zinc metals [79]. Additional advantages of the material are that eddy currents are arrested due to the small particle size of the iron filler while the mass, is about 70% that of iron. Mass is a desirable property in MT-EM tools as it supplements the tool material stiffness in providing local resistance to deflection at high work piece impact velocities. Greater detail of the construction process for these castable MT-EM tools will be given in the section describing the door inner panel trial.

Generally, the tooling worked well, performing fairly close to expectation despite the fact that the results, as reported above, were not entirely satisfactory. The low amplitude waviness on the outboard side in the hood nose area was, in part due to a excessive air pressure between the sheet and the die. Forming into shallow closed pockets like the hood rework geometry, requires either very good venting or evacuation to a level of about 10 Torr. At sheet velocities above 100 m/s, entrapped air can easily be compressed to pressures great enough to generate reverse bubbles in the sheet. For the hood tool, evacuation was conducted through a manifold hole in the die body below the feature restrike area. A series of small holes drilled along the bottom of the feature groove connected the restrike pocket area to the manifold hole. Placing a bead of vacuum grease around its perimeter where no deformation would occur sealed the restrike area. When the tool was closed and bolted together, the grease acted as a temporary gasket. This method proved to be inadequate and unreliable even with a 5. hp pump. The result was vacuum levels between 60 and 150 Torr for most tests. Production tooling will obviously require more attention to maintaining proper vacuum levels.

Confounded with the vacuum problem was the effect of a non-optimized magnetic pressure distribution. The 3-Bar coil configuration was designed without the aid of a numerical model so only a very crude idea of the pressure distribution could be established. Because the hood restrike area actually required a shortening of the cross sectional line length of the groove, the sheet experienced compressive stresses and strains. If the pressure is not properly distributed during the EM pulse, local bucking is possible especially if aided by uneven, counter gas pressures.
 

5.3.2 Automobile door inner panel trial

Of the hundreds of stampings that are required to make an automobile, one of the most difficult has been the inner door panel. Inner door panels are generally deep stampings with many different bosses. Pockets and recesses needed to accommodate the window, latch-lock, and hinge mechanisms. Figure

1.2a shows the door inner panel and was used to graphically introduce the problematic nature of conventional aluminum sheet forming. The door geometry and existing tools were very far from what would be required for a successful aluminum stamping (see fig. 1.2b). A decision was therefore made to concentrate on a particular section of the part considered to be the most difficult. If the most difficult area could be generated by the MT-EM process, generating the entire part by several local EM applications would be considered a linear extension of the demonstration. Initially only the lower hinge face corner was considered for the demonstration. The reasons were that this corner is very commonly the trouble spot on steel inner door production and the limited area of the corner would keep the project costs to a minimum. Later it was decided to rework the entire hinge face area. Figure 5.8 shows a steel door inner with the target areas for EM forming indicated.

Preliminary investigations and a small scale experiment where conducted with a plastic die model of the desired corner geometry supply by Mr. E. Herman of General Motors. The corner geometry defined by the plastic die was full size, it was the fact that the test was no conducted with the actual door inner tooling and full preform that made it a "small scale" test. A branched, 2-turn coil was designed and constructed in order to conduct a limited number of tests with the plastic die block to determine if a demonstration using the actual tooling might be successful. Figure 5.9 shows the die block and the coil used for the small scale tests. The surface of the plastic die represented the limit geometry for the corner that could be successfully formed in 6111-T4, , as determined by E. Herman. Note that the coil shown in Fig. 5.9 is a variation of the 3-Bar concept used in the hood trials. The design idea behind the coil geometry was to produce a high pressure area along the bisector line of the corner and somewhat lower pressures in remaining plan area of the corner flat. The side area pressures required where determined to be higher than what would be generated by the side legs of a simple delta shaped 3-Bar coil without over driving the center.

Figure 5.10 shows a fully formed corner section made with the test system of Fig. 5.9. The part was formed with a 24 kJ discharge, using a 6111-T4 sheet with no prestain and die evacuation. The largest strains occured near the apex of the corner and were approximately 18% majo, 11% minor, engineering biaxial tension.

 

Figure 5.10: Lower hinge face corner, trial door inner panel, 6111-T4,

24 kJ discharge using tooling in Fig. 5.9, peak strain, at apex, [.18, .11] engr.

Upon the reviewing the positive results of the small scale corner tests it was decided to go forward with a similar demonstration using the actual door inner panel Kirksite press tooling. Unfortunately, wrinkling in the lower hinge face corner, dubbed off area was found to be impossible to prevent in a conventional stretch-draw operation for the preform panels. In discussions with the sponsors, principally L. Du Bois and E. Herman of General Motors, a decision was made to avoid wrinkling by eliminating any draw-in and producing the preform panels in a pure stretch form operation.

In making this decision it was accepted that the entire hinge face geometry need to be dubbed of and replaced with EM forming. A concept schematic of the MT-EM hinge face forming system is provided by Fig. 5.11a&b

Engineers from the sponsors conducted analysis of various alternative preform panel shapes by finite element methods. The result of the analysis indicated that the both the hinge face and lock face of the panel would need to be reduced from 90 to 45 degrees and the sheet locked from draw-in to produce a pre-form panel of finish depth. In reality a significant portion of the panel face geometry required softening as well before the tools could be bottomed-out and the full depth generated. Further analysis by engineers from the aluminum supplier indicated that limited draw-in could be allowed if the hinge face was replaced by a large radius. A large radius geometry would resulted in lower pre-strain levels and shorter throw distance required of the EM process. However, the radius geometry allowing draw-in made EM forming more difficult by reducing the volume in the tool for embedding a work coil and increasing the local geometric stiffness of the part. Due to cost savings in producing the form tools using the cast iron filled epoxy system, it was decided to produce both pre-form shapes to gain direct experience with the two major trade-offs in pre-form design. Schematic cross sections of the two hinge face pre-form shapes are shown in Figure 5.12 a & b. Estimates of the energy required for a EM second operation to finish the panel hinge face needed preliminary coil designs as well as the calculation of the plastic work for each pre-form shape.

Plastic work was estimated by simple change in line length, assuming plane uniform strain and ideal plastic behavior. The strain energy estimate for finishing geometry I was 2.26 kJ and 1.04 kJ for geometry II. Coil concepts for these geometries as well as the hood feature were developed based on heuristics and elementary calculations which were subsequently organized into the energy estimation method presented in section 5.2.
 
 

Development of the energy method was, in part, driven by these full-scale demonstrations. Until the full scale test parts were attempted, the capacity of the bank installed in the laboratory was sufficient. Coupon sizes can usually be chosen so that more than enough energy for any experiment can be supplied. System energy requirements are dependent on the interaction of all the components with the coil design as a dominant factor.

Experience with the hood feature, the shorter throw required and the limited space, led to the use of a 3-bar configuration for the first coil built for geometry II (IIa in table 5.3). Geometry I required uniform engineering strain of 0.28 by line length for completion and had less volume restriction which indicated that a multi-turn, race track, coil would be a good candidate configuration. Coil bar strength and keeping inductance down to prevent flux leakage at lower ringing frequencies, pointed to a two turn, race track design. The coil bar cross section for both geometries were decided by estimated internal loading and restraint design as discussed for the hood coil. The cross section for both cases, as well as the hood coil, was a 1.0 x 3.0 cm with the 1.0 cm width used at the coil face. Since a fairly large bar section was chosen, lower conductivity could be tolerated and yellow brass was selected as the coil material. Added advantages of the brass material were ease of machining and silver brazing. The brazing quality was of importance, as the coil legs were to be fabricated from bar stock, bent and hand ground to fit the pre-form stamping and silver brazed into a near final shape assembly. After brazing, the coils were cross drilled through at the mid- plane. The through holes where fitted with insulated alloy steel tie rods which also passed through insulation blocks which kept the coil bar spaced apart while the rod kept the whole assembly from expanding. Tie rods were used in place of the clamp plates in the hood coil due to lack of tool volume to accommodate the clamps. The tie rods proved to be an easier design to implement despite the greater part count. Once the coil tie rods and blocks were in place and tight, a coil assembly was "spotted-in" to refit it to the inner surface of the pre-form so as to maintain a even 1.0 mm stand-off distance between the coil face and the panel. The stand-off volume was the minimum required to electrically insulate the coil from the sheet. Inadequate insulation will allow an arc to jump to the sheet and then to an adjacent coil bar, shorting the coil. The occurrence of a coil face arc is to be avoided as the extreme temperature generated in the arc will completely destroy the insulation along the path. In the case of polymer materials, the carbon soot generated invades every crack and crevice in the surrounding material. This very fine soot will promote subsequent arcing and must be completely removed before an effective repair can be accomplished. In order to reduce the electric potential stress of the coil insulating/potting material, all coil bar corners should carry at least a 0.5 mm radius.

Another, somewhat counter intuitive, design rule that was discovered for potting the work coils is to avoid using reinforcing cloth. While carbon fiber is an obvious mistake, both Kevlar and glass fiber cloth will promote coil face arcing. The reasoning is that the shock waves generated during discharge cause microscopic de-lamination between the matrix and fiber which can link up and open a path having significantly lower resistance to arcing than the matrix material. Coil face arcing was an initial problem with both 2-turn coils and neither 3-bar. This result formed some of the basis for the design rule since there are lower intensity E fields generated between the center and outer legs of a 3-bar per ampere than a 2-turn coil In addition, neither had reinforcing cloth over the face area. A delaminated area, caused by a face arc on the geometry I, 2-turn coil is shown in Figure 5.13 after being cleaned and repaired with a layer of epoxy resin.
 
 

The face arcing of the IIb door coil was cured by removing the reinforced epoxy facing and routing the potting between the coil legs down past the face level by 4-5 mm. The coil bar edge radii were increased to 1. 0 mm before the face was re-coated with a urethane plastic which was softer but much tougher than the previously used epoxy. The routed depth was not filled with new coating so that any cracks formed at the high field corner areas could not propagate to the adjacent coil leg. Pictured in Figure 5.14 are both the pre-form geometry I, 2-turn coil and geometry IIa 3-bar coil after final fitting, previous to potting in the tool cassette. The significant width difference between the coils is apparent as are the tie rods. In their nested positions on sections of the pre-form panels, the restraint clearance problem is also apparent . Figure 5.15 shows a close-up of the geometry I coil from a different perspective.
 
 

Figure 5.15: 2-turn coil for door geometry I and panel

section with coil face development layout

For the hood feature extension trial discussed in the previous section, the work coil was potted directly in the lower form tool during the at the same time the tool was poured. Although this design worked for the trial, it became apparent that any problems that might have occurred with the coil would have been difficult to remedy with the coil being an integral part of the form tool. During the initial tool design stage of the door inner panel trial, the fact that there were two different pre-form geometries along with repair concerns, led to the cassette concept for coil mounting suggested by L. Dubois of G.M. and D. Cedar of I.T.T.. Instead of the direct potting of the work coil into the form tool a cassette sub-volume of the tool which encased the coil and coil leads, was delineated. The volume of the cassette was chosen in a way which would allow the easy removal form the main tool body while maintaining repeatable registration and adequate support during discharges. A non-conducting material, was desired for the cassette matrix to reduce the coil insulation problem inherent with the high iron volume fraction material used for the form tool body. Two casting urethanes were used. The geometry I, 2-turn and geometry IIa 3-bar coil cassettes were cast using a high strength and hardness urethane that was marketed for use in short run prototype stamping tools. This material had the same intended application as the iron filled material used for the form tools. Performance of the unfilled urethane tooling material was less than satisfactory. The material proved to be too brittle to with stand the shock waves generated during discharge. Small cracks began to appear in the coil cassettes after several discharges, in areas which were experiencing tensile loads from coil expansion forces. Besides becoming a structural concern, those cracks which appeared between coil legs presented a reduced resistance to arcing, especially at the higher energy levels which required higher capacitor voltage. Arcing did occur in the geometry I coil which led to the use of a tougher, lower hardness urethane for the matrix of the second geometry II coil (IIb). This tough room temperature cure, casting urethane was developed especially for potting of highly loaded, large electric motor coils. Performance of the tough urethane appeared to be better than the tool grade urethane with no appearance of cracks. Although face arcing did occur at higher energy levels, the cause could be attributed more to the presents of reinforcing cloth over the coil face and sharp coil bar corners, as previously discussed. A detailed specification sheet of the coil cassette potting material is provided in Appendix B. Figure 5.16a and b are photographs of two of the three coil cassettes fabricated. Figure 5.16c and d show coil IIb after removal of the kevlar reinforced facing , routing and re-coating required to prevent surface arcing. The coil leads which are visible emerging from the top of the lead chimney on the right of figure 5.16a, connect to the bank bus though custom screw lug blocks.

a) Geometry I, coil cassette b) Geometry II, coil b cassette
 
 

c) Coil IIb with facing removed d) Close-up of routing of coil IIb
 

Figure 5.16: Door inner panel coil cassettes for EM finish forming

of hinge face.

All cassettes have nearly identical body shape since they were cast into the same main tool body. Only the coil face geometries of the cassettes differ to accommodate the particular pre-form shape. Not only was tooling costs reduced a great deal; repairs could be made to a work coil while the main tool was being used with another cassette. A large saving in the elapse time required to perform the door trials resulted from the decision to use a coil cassette. Based on the trial experience, the cassette design approach is the best choice for production application of the MT-EM process. If cast iron or steel is required for the form tools of a fully integrated MT-EM process, the coil cassette is nearly a required approach. From a design standpoint however, the cassette concept includes in addition to a pocket to pot the coil into. a means of easy removal and replacement. Preferably, coil replacement could happen without removing the entire tool from the press.

The tool construction to be described, with the exeption of the geometry I and IIa coils, was conducted by the same company that manufactured the hood tools, International Tooling Technology Ltd. of Detroit. Figure 5.17a. shows the mold box for casting the form tool section which will hold the coil cassette and lock the pre-form panel in position in the die half during the EM forming operation. Set in position on a pre-form panel, which is held by vacuum in the original Kirksite female die half, is a wooden core pattern that is fixed in the mold box to generate the cassette cavity when the mold box is filled with the iron-epoxy material. Figure 5.17b shows the competed form tool section with the geometry I cassette installed and the geometry II coil a cassette on the floor. Note that the EM tool section includes the binder surface and draw bead which were needed to prevent draw-in of the pre-form panel during the EM pulse.
 
 

The tool built to produce the pre-form panels was fabricated in a similar manner except the entire punch was cast onto the Kirksite female with the hinge face end of the punch as a separate section. The two different pre-form panel geometries were made by changing out the hinge face section. The sectioning of the forming punch saved time and material only during the tool fabrication. Die try-out effort required to generate good pre-form panels was about the same as if two entirely different tools were used. However, the total effort required to obtain good pre-form panels was small compared to a normal conventional matched tool process since all the difficult geometry had been removed, by design, and given to the EM forming phase.

The hinge end of the pre-form panels are shown in Figure 5. 18 a and b which should be referenced to Figure 5.12 a and b. Comparison of 5.18a with 5.18b brings to focus the significant difference in the amount of EM forming required to obtain the final hinge face geometry. Note also that geometry I, at an average of about 12%, carries twice the pre-strain as geometry II in the EM forming area. Geometry II was not originally considered possible by some stamping experts. Good geometry II panels were produced but required very careful consideration and control of the press speed, blank holder pressure, draw bead sizing, tool alignment and lubrication. In this respect geometry II does represent a limit shape in matched tool forming for the material and general part type.
 
 

Figure 5.19a shows the Kirksite die assembled with a pre-form panel and the top coil tool bolted in position during a EM forming trial. The plumbing on the side of the die and the hose connected to it is part of the vacuum system used to reduce the atmospheric pressure between the pre-form sheet and the die face. Forming a sheet into a closed corner at deformation velocities of 200 m/sec with full atmosphere of air will generate resisting pressures high enough to push the sheet back toward the coil usually causing reverse bubbles in the forming area. Certain geometries can simply be vented. However, actively evacuating the form volume of the die produces more consistent results. The vacuum level required is not great; ten Torr is generally sufficient. In a production system the required die venting can be altered to provide an appropriately sealed exhaust manifold which would be connected to a vacuum pump and surge tank through an electrically operated gate valve. The operation of the valve would be properly sequenced by the same controller that triggers the bank discharge. The control logic is simple enough that a mechanical linkage solution is quite feasible but likely much more expensive than a small digital processor. In the EM door trial tooling the lack of a complete blank holder and bead with a sealing means for the die- sheet volume, required an ad-hoc sealing method. After a few trials using vast quantities of grease, a clean and recyclable method was found which employed a visco-plastic silicone compound used in extrusion polishing methods. A thick bead of the silicon material was laid down on the die surface in a closed path surrounding the EM forming area. The material spread to fill all the voids between the sheet and the die by the weight and clamp force of the coil tool section. Since the material has no yield strength, the seal lasted only a few minutes, which was generally long enough. After opening the tool and removing the test panel, the silicone putty that did not adhere to the tool surfaces could easily and cleanly be removed in nearly a continuous strip. The material could then be consolidated (balled up) and reused with very little loss. Figure 5.19b shows the open door panel die with a bead of silicone putty in place just previous to setting in a test panel.
 
 

Presented in Figure 5.20 are the final trial panels from all pre-form geometries and coil combinations. Also included as 5.20a is a steel door panel made in the Kirksite die before the aluminum panel trials began. The best over all performance was realized with the draw-in pre-form, geometry II with the 2- turn coil b. Trial results with pre-form geometry I were quite similar to geometry II coil b results although requiring higher energy levels. Geometry I was the only door trials that experienced splitting during EM forming. Geometry II with coil a, the original 3-bar produced the poorest result in that the hinge face was least fully formed. The full bank could not be applied to the 3-bar coil, due to consistent problems with the lead connection failures. Unfortunately, the current probe failed during the IIa-coil trials so that no reliable current records exist to confirm the suspicion that very high peak currents were causing the lead connection failures. Unusually low forming efficiency in comparison to the geometry I trials was traced to the high lead inductance of the 3-bar coil system (see table 5.2). The overall low equivalent inductance of the 3-bar system caused the high currents while magnetic flux in the work piece gap was still inadequate since a disproportionate amount of bank energy resided in the field surrounding the leads, unavailable for deformation work. The IIa coil lead was un-potted and cut back to stubs close to the back of the coil. A coaxial lead assembly having only 10% of the original lead inductance was designed and installed which resulted in a significant improvement in forming efficiency but not enough to finish form the hinge face to the same level as the geometry I trials (see Fig. 5.15d). Moreover, the reduced system inductance increased the discharge current and made the connector problem worse.

Coil design IIb was initiated after the trials displayed the inadequacy of the 3-bar design for the door application. The compact 2-turn design concept was selected. The precision that coil-IIb required essentially eliminated the simple hand fabrication method used on for coil-I and IIa. In addition this redesign could serve as an informal test of industry level design and manufacturing method for the EM work coils. Following this plan, the a geometry II panel was laser scanned in a coordinate measurement system to acquire the numeric data that would be available after the design and FEM modeling of a formal pre-form development. I.T.T. Ltd., the lead vendor of the door panel tooling, was supplied with a mechanical design that was based on the EM forming and affiliated structural requirements. The tool designers at I.T.T. merged the required face plan of the work coil (coil-IIb) with the pre-form geometry to produce a 3-D numerical model of the entire coil. The coil geometry was translated into control code for a traveling wire electro-discharge machine (EDM) and a four axis machining center. The wire EDM was used to cut the coil plan first. The coil and drop were kept together and stabilized before being mounted in the machining center where the coil face contour, including insulation allowances and back surfaces were machined. After passing the form inspection. The machined coil and drop assembly was precision cross drilled for the tie rod restraints before the drop was finally removed. After deburring and the require coil bar edge radii were machine, the lead bars were silver brazed in place and the restraining tie rods installed. The entire assembly was finally coated with high dielectric varnish before being potted in the cassette. No hand fitting was require on this coil assembly. Views of the potted IIb coil cassette are shown in Figure 5.16 and the open coil assembly in Figure 5.21. Note that the lead bars are close together and secured with closely spaced insulated tie rod assemblies.
 
 

Coil II-b demonstrated significantly higher forming efficiency than the 3-bar configuration and produced the best finished panel. However, due to lack of experience with the new dispersion strengthened cooper material used in the coil, a poorly brazed lead failed and the coil produced only a few panels. Strain readings of selected door panels from geometry I and geometry IIa trials were taken to assess the extent and distribution of plastic deformation generated by the EM forming phase as well as the total for the hybrid process.

In the case of Geometry I, the strains are presented in two ways. First, in Figure 5.22 the dynamic strains imparted in electromagnetic forming are shown. These were obtained by gridding the sample after press forming, before the 40.8 kJ bank discharge was applied. Strains were measured with circle grids. In all cases the minor strains are very near zero and there are no tears anywhere on this panel (i.e., one may expect to be obtain even higher strains than this). Total strains can be estimated by adding to these values those obtained in press forming. By the Alcan report, this is fairly uniform at about 11% over this area. Thus total strains over 20% are common in this region.

In order to assess total thickness strains, a section was cut from a finished panel (#10) which had been formed with a 43 kJ discharge. Strains were measured at locations defined by Figure 5.22 at a belt height of 36.8 cm above the bottom of the door.

Figure 5.24 shows the measured thickness strain values. Total strains are all near 20% lower much lower than predicted by the simple change of line length analysis or the 2-D numerical simulation conducted by G.M. engineers. Stretch and draw-in from areas on the punch face obviously aided in forming the final shape by reducing the strain level developed in developed in the electromagnetic forming phase.

The only geometry II panel that was circle gridded after mechanical forming and formed was prematurely given away after a sponsor's meeting. As a result only total thickness strains of the panels will be present here. Total thickness strains were assessed with the same method used on geometry I panels: slices were cut from the panels and a micrometer was used to measure thickness and strain was calculated. The locations of strain measurements are shown in Figure 5.25 below. The measurement stations are 6.4 mm apart and two sections 25.4 cm and 33.7 cm above the bottom of the door was measured. Total thickness strains are shown in Figure 5.26. The strains developed in electromagnetic forming are rather small. However, a significant change in geometry was accomplished. This suggests that draw-in may have aided the forming of geometry II as well as I.

The strain values obtained in this study are somewhat smaller than expected. The strains developed from Geometry I are very uniform, as is desired. And in the case of Geometry II we have not broken any panels with the first-generation coil and the strain analysis suggests that it is still rather far from failure. This all suggests that this geometry should form very well with the two-turn coil that was in fact the result. The general result of the full scale trials is that two-stage MT-EM hybrid process seems robust and allows much design flexibility that has not yet been exploited.

Robustness does not mean that there are not difficult design issues in implementation of the process. One such issue involves the reliable transfer of the very large transient currents from the bank bus collector to the work coil. This connection must be designed with care since low inductance is required to improve forming efficiency. Low Inductance means that the conducting elements must be close together which combines with high currents to generate very high internal loading. For these reasons coaxial designs have a distinct advantage over parallel bus bar constructions. However coaxial designs are more restrictive in terms of the actual connections. Failures of the bus to work coil connector assembly were experienced during the door panel trials. These failures all occurred at the highest energy levels Figure 29 shows a coaxial connector (a) and a parallel bar connector (b) both of which failed at approximately 45kJ
 
 

The Door Inner panel trials results show one aspect of design flexibility of the hybrid forming process that has been little discussed to this point. That is: the MT-EM process provides a means of tailoring the strain distribution in a panel in addition to improving formability. In conventional match-tool forming the strain distribution is largely determined by the interplay between geometry, friction and physical characteristics of the sheet. If the punch nose radii are sharp, the material on the punch face is locked and under utilized while high strain areas are generated in the side walls. Parts with geometry

like door inner with many bosses and beads on the punch face can completely lockout large areas of the sheet from sharing the deformation strain. This door inner has this situation exactly. The MT-EM process allowed the punch nose radius at a high side wall strain area, the hinge face, to be increased by a factor of ten allowing draw-in at much low and better distributed strains. The EM pulse was then used to generate the final geometry. Strain distribution within the EM pulse area can also be manipulated by the geometry and electrical characteristics of the coil. Different coil generated strain distributions can be seen in a comparison between the thickness strain generated in Geometry II by the 3-bar coil, as shown in Fig. 5.26, and that generated by coil b, the two turn coil, shown in Fig. 5.27. As discussed in Chapter 3 the highest strains coincide in the work piece with the areas experiencing the highest current density that occurs where the magnetic field density is greatest. For the 3-bar the greatest B field is at the center bar were as for the 2-turn coil b the center has a minimum field density. Therefore between the freedom in pre-form geometry and the coil design, the MT-EM process engineer has a much larger domain in which to seek a solution to difficult aluminum panel forming problems.
 

5.4 Future work

Obvious to anyone who has read though this document is the fact that a great deal of work remains to be done before the MT-EM hybrid process can be applied to the production of large aluminum sheet parts. What has been demonstrated is the fundamental utility of the process. Some of the important areas of future work are summarized below. The list should not be considered exhaustive as investigating these topics, will certainly uncover additional problems.

• Better constitutive relations and failure criterion for materials of interest under the conditions of the MT-EM.

• Refinement and benchmarking of the computer simulation code for the robust modeling of the EM forming.

• Establishment of a robust set of design rules to optimize the levels of quasi-static and dynamic forming for any given application.

• Design requirements for an integrated software system to effectively simulate the entire MT-EM process for cost effective and efficient application of the MT-EM to a broad range of industrial applications.