US 3646791 A
Method and apparatus for deforming a metal workpiece, for upsetting rivets, and for blind riveting which is accomplished by passing a stress wave through the metal workpiece or rivet sufficient to render it momentarily plastic and simultaneously forming it. The apparatus is basically comprised of means for generating a stress wave and a stress wave focusing device or amplifier. In operation, a workpiece is placed in a die or shaping means. The stress wave amplifier is then arranged to direct or focus the stress wave to the metal workpiece. Next, a stress wave is generated and passed through the stress wave focusing device, imparting a momentary state of plasticity to the metal workpiece. The momentarily plastic metal workpiece is then formed or shaped as desired.
Claims available in
Description (OCR text may contain errors)
United States Patent Leftheris Mar. 7, 1972 Inventor: Basil P. Leftheris, East Northport, NY.
Assignee: Grumman Aerospace Corporation, Long Island, N.Y.
Nov. 6, 1970 Filed:
Related U.S. Application Data Continuation-impart of Ser. No. 863,045, Oct. 2, 1969.
 References Cited UNITED STATES PATENTS 2,465,144 3/1949 Wyatt ..29/243.52
3,453,463 7/1969 Wildi ..3 10/27 3,108,325 10/1963 Harvey et al.. .....72/56 3,210,509 10/1965 Alf ..219/7.5 3,417,456 12/1968 Carlson ....29/470.l 3,475,628 10/1969 McMaster et al ..3 l0/8.2
Primary ExaminerRichard .l. Herbst A!t0rneyM0rgan, Finnegan, Durham & Pine 57] ABSTRACT Method and apparatus for deforming a metal workpiece, for upsetting rivets, and for blind riveting which is accomplished by passing a stress wave through the metal workpiece or rivet sufficient to render it momentarily plastic and simultaneously forming it. The apparatus is basically comprised of means for generating a stress wave and a stress wave focusing device or amplifier. In operation, a workpiece is placed in a die or shaping means. The stress wave amplifier is then arranged to direct or focus the stress wave to the metal workpiece. Next, a stress wave is generated and passed through the stress wave focusing device, imparting a momentary state of plasticity to the metal workpiece. The momentarily plastic metal workpiece is then formed or shaped as desired.
7 Claims, Drawing Figures PAIENTEBMAR 7 I972 3, 646. 7 91 sum 1 or 3 HG. I
BASIL P. EFTHER/S A TTORNEVJ' PATENTEDHAR 71972 3,646,791
sum 2 or 3 INVENTOR. BASIL F? lE'FTMER/J' PATENTEDHAR' 7 I972 SHEEI 3 (1F 3 INVENTOR. BASIL R LEI THEE/s ATTORNEYS METHOD AND APPARATUS FOR DEFORMING A METAL WORKPIECE, FOR UPSETTING RIVETS, AND FOR BLIND RIVETING REFERENCE TO RELATED APPLICATION The present application is a continuation-in-part of my earlier filed application Ser. No. 863,045 filed Oct. 2, 1969.
BACKGROUND OF THE INVENTION wave through the workpiece renders the metal momentarily plastic and easily deformable.
2. Description of the Prior Art At the present time, the various methods of metal forming basically employ energy in the form of an externally applied force or heat. An illustration of this can be found in metal forging, where an external force or impact is applied to a metal workpiece, which may be hot or cold, in order to form it into the desired shape. Another illustration is that where metal is heated to melting and then poured as a fluid into a mold and allowed to cool.
The distinction between cold-working and hot-working of metal rests on the relationship of the processing temperature to the recrystallization temperature of the metal. The recrystallization temperature is that temperature at which there is a marked softening of the metal being worked. Coldworking of a metal is the deformation of the metal at a temperature below the recrystallization point. More power is required for cold-deformation since the metal is harder and less ductile than the metal of the hot-working process.
In the case of metal forging, a great amount of energy is required to do the work of metal deformation which requires the utilization of large and bulky machinery. This is true whether the metal is cold-worked or hot-worked although less force is required in hot-working the metal. Examples of such machinery include power presses, hydraulic presses, drop hammers, and steam hammers.
Another metalworking process employing similar techniques is riveting. The methods of driving rivets may be divided into three broad classifications; impact, compression and combination. The impact method of upsetting rivets utilizes a succession of blows and includes hand riveting and pneumatic hammering. The compression method utilizes squeeze-riveting tools which are available for either hand or power operation and in both portable and stationary models. The combination method utilizes the compression method combined with rolling or spinning. These methods produce results which are not wholly satisfactory. Rivet failures are not uncommon and occur unpredictably in operation. Tests performed on rivets upset by conventional riveting machines indicate wide inconsistencies of failure under load. This illustrates only one instance where the present metalworking methods are inadequate and require improvement.
Another method of metal forming is by use of an expanding magnetic field as illustrated by the U.S. Pat. No. 2,976,907 to Harvey et al., issued Mar. 28, 196l. The Harvey patent discloses the use of a magnetic field established by a coil to create a pressure or force on the metal workpiece thereby deforming it to the desired shape.
More recently, laboratory investigation and study has indicated that metals may be deformed when subjected to stress waves. For example, see Large Deformation Dynamic Plasticity At An Elastic-Plastic Interface" by J. F. Bell appearing in J. Mech. Phys. Solids, 1968, Vol. 16, p. 295. in this report it is shown that a state of plasticity can be established in metal by a stress wave generated by striking two hardened metal bars together.
It should also be noted that the present state of the art includes an apparatus which utilizes the electromagnetic repulsion of two magnetic fields and the shock produced therefrom to hold a metal workpiece in position while it is deformed by other means. (Harvey et al., U.S. Pat. No. 3,108,325, FIG. I, issued Oct. 29, 1963). This technique, however, does not utilize a stress wave to render the metal plastic to thus accomplish the deformation.
It has not heretofore been possible to form metallic objects by the utilization of a stress wave passing through the metal except as an object of scientific study. There are no commercial methods which utilize this concept nor are there any commercial or scientific methods which utilize electromagnetic forces to generate a stress wave sufficient to render metal momentarily plastic.
SUMMARY OF THE INVENTION It is therefore an object of the present invention to provide a metal-forming apparatus utilizing stress waves.
It is a further object of the present invention to provide a metal-forming apparatus which is much more compact in size than present state of the art machines.
It is another object of the present invention to provide a metal-forming apparatus which may be used for riveting.
It is another object of the present invention to provide a metal-forming apparatus which may be used for blind riveting.
It is another object of the present invention to provide an improved blind rivet which may be used with the blind-riveting apparatus of the present invention.
It is another object of the present invention to provide an improved method of deforming metal workpieces and rivets.
For accomplishing the present invention, a device is provided which is comprised basically of an energy source connected to a pancake coil, a disc-shaped aluminum or copper driver adjacent to the coil, an amplifier or focusing means adjacent to the aluminum driver, and a shock-absorbing mechanism positioned to the rear of the coil. A die or other shaping means is also necessary for forming the metal workpiece into the desired shape. When the device is used for riveting or spot welding, a bucking mass is necessary on one end of the rivet or metal workpieces.
The discharge from the energy source establishes a magnetic field around the coil; this magnetic field in turn induces a current in the aluminum or copper driver. The induced current sets up a magnetic field around the driver and the interaction of the two magnetic fields causes a stress wave to be generated which is then propagated through the focusing means and into the metal workpiece to render the metal workpiece momentarily plastic.
The device for blind riveting is basically the same as above with the addition of a second driver which produces an electromagnetic repulsion which acts on the blind rivet simultaneously with and in a direction opposite to the force of the first electromagnetic repulsion to thereby upset the rivet. electromagnetic DESCRIPTION OF THE DRAWINGS The invention will be described and understood more readily when considered with the attached drawings, in which:
FIG. 1 is a schematic side elevational view of a forming device and workpiece embodying the principles of the present invention;
FIG. 2 is a schematic side elevational view of a blind-riveting device and blind rivet embodying the principles of the present invention;
FIG. 3 is a cross-sectional view of a blind rivet of the present invention showing the rivet inserted through the holes of two superimposed sheets of metal; and
FIG. 4 is a cross-sectional view of an upset blind rivet of the present invention showing the rivet clinching two superimposed sheets of metal.
DESCRIPTION OF THE PREFERRED EMBODIMENT The method and apparatus of the present invention is particularly suitable for use in forging, riveting, blind-riveting, punching and spot-welding operations. In fact, a single tool, with slight variations, may be used to accomplish each one of these operations. The variations necessary may involve a change in the energy source and/or a different sized or shaped amplifier. The common ground running through each of these operations is that a stress wave is transmitted to the metal object which increases the energy density within the metal to thereby transfonn the properties of the metal and allow the particular operation to be accomplished.
According to the method of the instant invention, a metal workpiece is deformed at a temperature below its recrystallization temperature. The workpiece is subjected to a stress wave generated by the electromagnetic repulsion of two highintensity magnetic fields, which imparts a particle velocity in the direction of propagation of the wave and simultaneously increases the stress in the workpiece. The particle velocity and stress in the workpiece are increased to a predetermined level at which the metal of the workpiece becomes momentarily plastic. The axial a momentum of the workpiece, produced by the propagation of the stress wave through the workpiece, causes a compressive deformation in the direction of propagation and an expansion at right angles to this direction of propagation. This expansion is governed by Poissons ratio which is the ratio between thelateral strain and the direct tensile strain. This compression and resulting outward expansion of the metal workpiece into a die or other confining area will produce the shape desired.
In addition to the above method of deforming a metal workpiece, the same basic concept along with the same apparatus may be used for spot welding of metals. When spot welding is desired the two metal objects are positioned such that the spot desired to be welded on each object is in contact. A stress wave is generated by the electromagnetic repulsion of two high intensity magnetic fields; this stress wave is focused on one of the metal objects. The point of contact of the two metallic objects acts as an energy sink where the energy imparted to the metal by the stress wave is converted to heat energy. The heat generated at the point of contact is high enough to locally melt the two metal objects and therefore weld them together. It has been found beneficial to this welding operation to heat one of the metal workpieces, thereby allowing for greater ease of operation.
In the case of blind riveting, the above-described concept is utilized along with a unique blind rivet. The blind rivet comprises a tubular body and a stem coaxially extending therethrough. The stem is provided at one end with a former which is drawn into the tail of the tubular body when the rivet is upset, and at the other end with means for engagement with the blind riveting tool. Part of the stem has a diameter which is greater than the inside diameter of the tubular body so that when drawn into the tubular body an interference fit results between the stem and the tubular body. Thus, a stress wave having the same properties as described above is applied to the tubular body which becomes momentarily plastic. Simultaneously, a pulling pressure is exerted on the stem which draws it into the softened metal of the tubular body. The former on the end of the stem contacts the tail of the tubular body and fonns a blind head therewith while clinching the work. Because of the relative diameters of the stern and the inside of the tubular body, an interference fit is established therebetween and also between the tubular body and the rivet hole.
Basically, the apparatus of the present invention, as depicted in FIG. I, is comprised of a power supply 8, a stress wave generator 6, a stress wave focusing means or amplifier l6, and means for reflecting the stress wave transmitted through the workpiece I8.
The power supply 8 comprises an energy source 32 and switch means 30 connected in parallel to a capacitor bank 28 which is then connected by switch means 26 to the stress wave generator 6. The stress wave generator 6 comprises a pancake coil 12 and driver 14, situated in side-by-side relationship. Driver 14 may be either aluminum or hardened copper. The stress wave generated in driver 14 passes through the amplifier or focusing means 16 and tip 24 and thence to the rivet 18. The head of the rivet 18 is in full contact with the hardened surface 22 of the bucking mass or means 20 for reflecting the stress wave transmitted through the workpiece 18.
In operation, the capacitor bank 28 is charged by energy source 32 when switch 30 is closed. After the capacitor bank is charged, switch 30 is opened and switch means 26 is closed whereby a high-amperage current pulse, of short duration, flows through the pancake coil 12, the duration of the current pulse being in the order of microseconds. A high-intensity magnetic field is set up around the coil 12 and this field intersects driver 14, which acts as a one-tum secondary winding of a transformer to thereby induce a current therein. The induced current flowing through the driver 14 sets up a high-intensity magnetic field around the driver 14. The electromagnetic repulsion established by the interaction of the two highintensity magnetic fields generates a stress wave in the driver 14 which is propagated through the amplifier l6 and tip 24 and thence through the rivet 18. The combined efi'ect of the bucking mass 20 and the passage of the stress wave through the rivet 18 causes the rivet 18 to deform axially and radially while simultaneously the mass of the amplifier 16 causes a head to be formed on the rivet 18 at the common juncture with tip 24.
The device as described above has been successfully used to upset stainless steel and titanium rivets and has also been used to spot weld two metallic workpieces. The machine can be fixed in a frame with the work being fed thereto or it can be used portably and held by the user. The only structural difference required by the two uses is that in the portable machine a bolt is threaded into the center of the base of the amplifier l6 and extends through the recoil mechanism or shock absorber 10 having a nut to hold the components in tight relationship; when used in a frame, a stud extends through the shock absorber 10 and into the amplifier 16 in order to keep the components centered.
In one illustrated embodiment, wherein the metal-forming device according to the present invention was placed in a frame and used in a riveting operation, NAS (National Aeronautical Standard) stainless steel rivets were successfully upset. The capacitor bank was of a low inductance and with the coil connected and electromagnetically coupled to the driver had an operating frequency of 20 kc./s. A high electrical current was fed to the coil by the capacitor bank. The coil included 18 turns of a rectangularly shaped copper memberi. inch by 0.080 inch. The coil was potted in polyurethane compound equivalent to 60 durometer rubber having ample elasticity, the dimensions of the coil being 1% inches thick by 6 inches in diameter and having a l-inch-diameter circular hole through the center. The driver consisted of 606l-T4 aluminum, A inch thick by 6 inches diameter and having a l-inch circular hole through the center. The 606 l-T4 aluminum was used since it is of good conductivity and sufficient strength to withstand the forces produced in the operation. The amplifier or focusing device, constructed of 4340 hardened steel, had a as inch by 6 inch diameter cylindrical base section leading into a truncated cone 6 inches long and having a %-inch diameter top to which a k-inch long cylindrical section was attached. At the tip of the focusing device a rivet set was attached having a first cylindrical section one-fourth inch long and oneeighth inch diameter inserted into the focusing device and exposing a second cylindrical section one-fourth inch long and one-half inch diameter. The shock absorber consisted of a series of rubber pads attached to the coil. A centering stud of one diameter was inserted into the circular holes of the various components and into a l-inch diameter by l-inch-deep hole in the base of the focusing device. The rivets upset by this IOI026 nnsr.
device were of a /2-inch length andfir-inch, 3/ 16-inch, /s-inch diameter. The voltage required to upset these different size rivets was respectively 7 kv., 5.2 kv., and 4 kv.
In another illustrated embodiment, which is a mere variation from that described above, a metal-forming device was used by hand, rather than in a frame, for the riveting operation. The only variations from the above example consisted of a change in dimensions of the components. The coil diameter was reduced to 4 inches, as was the diameter of the driver and the base of the focusing device. All other dimensions remained the same. Also, instead of a centering stud, a threaded bolt was fitted into the base of the focusing device and secured by a nut and washer at the end of the shock absorber.
The blind riveting apparatus of FIG. 2, which is a variation of the present invention, is comprised of a power supply 34, a The wave generator 36, a stress wave focusing means or amplifier 38, a blind rivet assembly 40, and means 42 for exerting pressure on said rivet assembly 40 in conjunction with the stress wave generated by stress wave generator 36 to form a blind head on said rivet assembly and clinch the work.
Power supply 34 comprises an energy source 44 and switch means 46 connected in parallel to a capacitor blank 48 which is then connected by switch means 50 to stress wave generator 36. Stress wave generator 36 comprises a pancake coil 52 and driver 54 situated in side-by-side relationship. The driver 54 may be either aluminum or hardened copper. The stress wave generated in the driver 54 passes through the amplifier or focusing means 38 and is transmitted to the tubular body 56 of rivet assembly 40.
Blind rivet assembly 40, as most clearly shown in FIG. 3, is basically comprised of a tubular body 56 and stem 58. The tubular body 56 is provided with head 60 at one end and with centrally located annular opening 62. Head 60 may be of any conventional form and is not limited to the countersunk form depicted. The tubular body 56 is positioned in the rivet hole provided in the work which comprises two overlapping metal I plates, designated 64 and 66. Stem 58 extends through opening 62 and is provided at one end with former 68, and at the other end with serrated portion 70. The diameter of part of stem 58 is greater than the diameter of annular opening 62 such that when former 68 is drawn into the tail of body 56 an interference fit is established between stem 58 and body 56, and between body 56 and the wall of the rivet hole. As depicted, stem 58 is tapered from former 68 toward the serrated portion 70. In another embodiment, rather than being tapered, stem 58 may be straight with a stepped portion having a diameter larger than the diameter of annular opening 62. Whether stem 58 is tapered or straight, an interference fit will result when it is drawn by the blind riveting device into the tubular body 56.
Means 42 for exerting pressure on rivet assembly to set the rivet and clinch the work is basically comprised of a rod 72, means 74 on said rod for engaging stem 58, and means for establishing a pressure on rod 72 to set the rivet.
Rod 72 is slidably mounted in the riveting device and extends centrally through coil 52, driver 54, and partially through focusing means 38. the end of rod 72 is positioned near tip 76 of focusing means 38 and is provided with means 74 for engaging stem 58 extending through an opening in tip 76. Means 74 is comprised of spring 78 and gripping jaws 80 for gripping serrated portion 70 of stem 58. Spring 82 is provided to maintain rod 72 in the forward position while travel limit stop 84 limits the rearward movement of rod 72.
Means for establishing a pressure on rod 72 to set the rivet is comprised of driver 86 connected to rod 72 and situated adjacent to coil 52 on the side opposite driver 54. Driver 86 may also be either aluminum or hardened copper as driver 54. A mass 88, which may be steel, positioned behind driver 86 and also connected to rod 72 is provided to balance the rearward thrust of the blind riveter. Foam filler 89 is provided to allow rod 72, driver 86, and mass 88 to move rearwardly during the operation or an empty space may be provided.
In operation, capacitor bank 48 is charged by energy source 44 when switch 46 is closed. After the capacitor bank is charged, switch 46 is opened and switch means 50 is closed whereby a high-amperage current pulse, of short duration, flows through pancake coil 52, the duration of the current pulse being in the order of microseconds. A high-intensity magnetic field is set up around coil 52 and this field intersects driver 54, which acts as a one-tum secondary winding of a transformer, thereby inducing a current therein. The induced current flowing through driver 54 sets up a high-intensity magnetic field around driver 54. The electromagnetic repulsion established by the interaction of the two high-intensity magnetic fields generates a stress wave in drivers 54 which is propagated through amplifier 38 and into the tubular body 56 of blind rivet assembly 40. The passage of this stress wave through the tubular body 56 causes it to become momentarily plastic and easily deformable. Simultaneously with the electromagnetic repulsion between driver 54 and coil 52 a second electromagnetic repulsion takes place between driver 86 and coil 52. A current is induced in driver 86 by the high-intensity magnetic field of coil 52. This induced current sets up a highintensity magnetic field around driver 86 which is repulsed by the field around coil 52. This repulsion is transmitted through rod 72 to stem 58 and acts to draw former 68 toward tubular body 56 to squeeze the tubular body 56 between former 68 and tip 76 of amplifier 38. Since this squeezing action occurs when the tubular body 56 is in a plastic state a blind head 92 is formed at the tail of tubular body 56 and the work is clinched, as seen in FIG. 4. Also, since the diameter of stem 58 is greater than the diameter of annular opening 62 an interference fit occurs between stem 58 and the walls of opening 62 and between the tubular body 56 and the walls of the rivet hole in the work.
In designing the prototype riveter, it was necessary to design a focusing device or amplifier to concentrate the energy of the pressure pulse generated by the magnetic coil and directed to the workpiece sufficient to successfully upset the stainless steel or titanium rivets.
The analysis of this device was accomplished by using the momentum, continuity, and stress-strain relationships used in the uniaxial propagation of stress wave pulses in solid bars.
Consider an element of a focusing or amplifying device wherein:
dx =the initial thickness of the element;
dx=the final thickness of the element and equals (fix/8x A=the cross-sectional area of the element;
r=the stress in the direction of motion;
=the strain in the direction of motion; and
x=the distance from the left end of the device.
By definition, stain equals the final thickness less the initial thickness divided by the initial thickness, or
1 0 a Partially differentiating equation (1) with respect to time, we
is=i(fi )=i( 2 (it It 6x 6x r'll (7x where u=ilxlilt the particle velocity.
Since s= E 6, equation (2) can be rewritten as:
65 8a 0 A c .2 3
where E Youngs Modulus of Elasticity. A rorn Newtons First Law of Physics we have:
6 A Ap(lx- 'dx (4) where p is the density of the material.
Mass continuity equation can be written as follows:
and for A A,
p,, (1x p (1x p dx 8x p0 p BX" Substituting for dx in equation (4), we have:
a 1 1 (22) 6x (1x0) (It (Ix 8x1, dx"
r') x iz (HA5) HMS) p 6x (1! Fix 6x 6x,
Substituting from equation (5) we have:
Q 8 (As) f 92,
61/. as s HA (it ax, A em (6):
Two forms were considered for the focusing device: a. an exponential shape governed by the formula:
A A,,e o 7 and b. a conical shape governed by the formula:
0 2 AA,. (1 (s) where:
A,,=the area of the larger or left-hand end of the focusing device;
n=a constant to be determined; R,,=1'adius of the larger end of the focusing device; x,,=the length of the focusing device; and K=the tangent of the angle described by the edge of the cone and the base of the cone. From experimental results we also have the relationship:
(du/dt) m 9 where m is a constant.
Combining equations (6), (3), (7) and (9), we are able to derive the following equation for the exponentially shaped focusing device:
5 l A), V n a (10) where:
S RuK x" Q s, 31.1,. (A 301,. A l) Taking the case where:
Utilizing equation (10), we obtain a stress multiplication S/S )=4.l.
Utilizing equation (ll), we obtain a stress multiplication s/s, )=l7.
From measurements it was determined that the pressure developed at the electromagnetic coil varied between about 5,000 and 9,000 p.s.i. and therefore an average of 7,000 p.s.i. was used.
Using the cone, the theoretical stress at the rivet was determined to be l7 7,000 p.s.i. or 9,000 p.s.i. the material of the rivet had a yield strength of 90,000 p.s.i. and, therefore, the theoretical stress developed by the focusing device at the rivet was determined to be sufficient. In the tests that followed, stainless steel rivets having a 56-inch diameter and 96- inch length were successfully upset.
Using high-speed photography it was found that the particle velocity at the small end of the focusing device was approximately 640 in./sec. Knowing this velocity and using the momentum equation, the stress at the small end of the focusing device can be calculated:
s (P /s) where: p=0.3 lb./cu. in.
therefore s=l 00,000 p.s.i.
This calculated stress compares well with the theoretical stress of 1 19,000 p.s.i.
It is to be understood that the present invention in its broader aspects is not limited to the specific elements and steps shown and described above, but also includes within the scope of the accompanying claims any departures made from such elements and steps which do not sacrifice their chief adva a es What is claimed:
1. A tool for setting blind rivets having a tubular body with a head and extending through the rivet hole of the work to be riveted. A stem extending through said tubular body, the diameter of part of said stem being greater than the inside diameter of said tubular body, said stem having a former which is drawn into the tail of said tubular body, said tool comprising:
a. means for generating a stress wave;
b. a stationary focusing means through which said stress wave propagates and is directed through said blind rivet to render the rivet momentarily plastic; and
c. means for exerting a pressure on said stem counter to and simultaneous with the application of said stress wave through said blind rivet to draw said former into said tubular body, creating an interference between said stem and said tubular body and between said tubular body and the walls of said rivet hole and for forming a blind head on the tail of said tubular body and clinching the work, which pressure is of a magnitude sufficient only to form the rivet while the rivet is momentarily in the plastic state.
2. A tool for setting blind rivets as defined, in claim I 3. A tool for setting blind rivets as defined in claim 2 wherein the means for exerting a pressure on said stem comprises:
a. a second driver coupled to said coil;
b. means for establishing an electromagnetic field around said second driver to generate a pressure due to the electromagnetic repulsion between said electromagnetic field nd a aand v w c. means for applying said pressure to said stem at the end opposite said former to draw said former into said tubular body creating an interference between said stem and said tubular body and the walls of said rivet hole and for forming a blind head on the tail of said tubular body and clinching the work.
4. A tool for setting blind rivets as defined in claim 3 wherein the means for establishing the electromagnetic fields in said first and second drivers comprises electromagnetically coupling said drivers to said coil.
5. A tool for setting blind rivets as defined in claim 4 wherein the means for applying said pressure to said stem comprises:
a. a shaft connected to said second driver and centrally passing through said tool; and
b. means on said shaft for engaging the end of said stem opposite said former.
6. A tool for setting blind rivets as defined in claim 5 wherein the focusing means is a conically shaped mass coupled to the first driver and the various components of the tool are related by the formula:
V .;i fii, i where:
s=the stress delivered to the metal workpiece at the small end of the focusing means; s =the stress developed at the large end of the focusing.
means by the electromagnetic repulsion between the coil and the driver;
R =thc radius of the large end of the focusing means;
K=the tangent of the angle described by the edge of the cone and the base of the cone:
C--the speed of sound in the material;
=the time required for the particle velocity to reach a maximum;
A =the cross-sectional area of the large end of the focusing means, i.e., the base of the cone;
A=the cross-sectional area at the small end of the focusing means;
x =the length of the focusing means.
7. A tool for setting blind rivets as defined in claim 5 wherein the focusing means is an exponentially shaped mass coupled to the first driver and the various components of the .tool are related by the formula:
where: s=the stress delivered to the metal workpiece at the small end of the focusing means; s,,=the stress developed at the large end of the focusing means by the electromagnetic repulsion between the coil and the driver; C=the speed of sound in the material; t =the time required for the particle velocity to reach a maximum; A qhe cross-sectional area of the large end of the focusing means; A=the cross-sectional area at the smaller end of the focusing means; n=the number appearing in the exponent of the equation which governs the shape of the focusing means, i.e., A=A e o, where X is the length of the focusing means.
mg? v UNITED STATES PATENT OFFICE I CERTIFICATE OF CORRECTION Patent No. 791 Dated March 7, 9
Inventor(s) Basil P Leftheris It is certified that; error appears in the above-identified patent and that said Letters Patent are hereby corrected as shown below:
' Column 3, line 25, after "axial" delete a Column 5, line 57, after "38." change "the" to The Column 6, line 13, chenge "drivers" to driver 1 Column 6, line 55', change 'dk dx I to dx dx Column 8, line 48, after "riveted" delete and change "A" to a Column 8, line 66, after "defined" delete Column 10, line 5, change to t Signed and sealed this 12th day of December 1972.
EDWARD ILFLETCHERJ'R. ROBERT GOTTSCHALK Attest lng Officer Commissionerof Patents