US3737694A

US3737694A - Fanned circular filament rotor

Info

Publication number: US3737694A
Application number: US00264930A
Authority: US
Inventors: D Rabenhorst
Original assignee: Johns Hopkins University
Current assignee: Johns Hopkins University
Priority date: 1972-06-21
Filing date: 1972-06-21
Publication date: 1973-06-05
Anticipated expiration: 1990-06-05

Abstract

The invention is in inertial energy storage device wherein a central hub holds a multiplicity of anisotropic filaments, the filaments extending from the hub in fixed relation thereto and in parallel planes perpendicular to an axis of rotation taken through the hub. The majority of the filaments in each of the parallel planes are disposed in fixed, arcuately fanned positions, the radius of curvature of the filaments being dependent on the location of said filaments within the hub. A particular feature of the present invention is that each parallel plane of filaments is disposed at angles to adjacent planes of filaments to reduce aerodynamic drag and increase the dynamic stability of the structure.

Description

1 June5,1973

United States Patent 1 Rabenhorst 3,512,022 5/1970 Gilbert 10/74 [54] FANNED CIRCULAR FILAMENT ROTOR [75] Inventor:

Primary Examiner-J. D. Miller J Rabenhorst Silver Sprmg Assistant Examiner-Mark O. Budd [73] Assignee: The Johns Hopkins University, Bal- AttorneyJohn S. Lacey and Robert E. Archibald [57] ABSTRACT The invention is in inertial energy storage device wherein a central hub holds a multiplicity of anisotropic filaments, the filaments extending from the timore, Md.

[22] Filed:

June 21, 1972 hub in fixed relation thereto and in parallel planes per- [52] US. Cl. ........................310/74, 15/179, 15/181 pendicular to an axis of rotation taken through the hub. The majority of the filaments in each of the 74/572, 310/51 ...H02k 7/00, Fl6h 33/02 Field of Search.........................

parallel planes are disposed in fixed, arcuately fanned 310/51, 74, 261; positions, the radius of curvature of the filaments 74/572 5 i 15/ 179 being dependent on the location of said filaments within the hub. A particular feature of the present ins1 Int.Cl...........

[56] References Cited vention is that each parallel plane of filaments is disposed at angles to adjacent planes of filaments to reduce aerodynamic drag and increase the dynamic /181 stability of the structure. ...15 179 15/179 18 Claims, 11 Drawing Figures N n m E m m T m m A m m P mum S m m m S ARC D E 636 T 266 .1 999 N HHH U 22 PATENTED JUN 5 73 sum 7 0r 7 FANNED CIRCULAR FILAMENT ROTOR STATEMENT OF GOVERNMENT INTEREST The invention herein described was made in the course of or under a contract or subcontract thereunder, with the Department of the Navy.

CROSS-REFERENCE TO RELATED APPLICATIONS The present invention generally relates to the subject matter described in co-pending U. S. Patent application, Ser. No. 60,047, filed July 31, 1970, now abandoned entitled Filament Rotor Structures, and particularly relates to the subject matter of Serial No. 167,643, filed July 30, 1971, now U.S. Pat. No.

3,698,262, issued Oct. 17, 1972 entitled Fixed Ele-' ment Rotor Structures, both patent applications by David W. Rabenhorst.

BACKGROUND OF THE INVENTION 1. Field of Invention The invention relates to energy storage devices, such as flywheels, and particularly to performanceoptimized high-speed rotary structures. Application of the invention ranges from use as the sole power source of a quiet, pollution free urban vehicle to use as a home power supply unit.

2. Description of the Prior Art The flywheel has been used for centuries as an efficient energy storage device; Since the flywheel is an inertial device governed by the laws of kinetic energy, maximum performance is obtained at maximum speed, the performance being generally quadrupled with a two-fold increase in speed. The speed of a rotating body, however, cannot be increased beyond its bursting limit. In the prior art, three general flywheel configurations are predominant, namely, the flat disc type characterized by smooth parallel surfaces between the hub and the periphery; the rim type having a massive peripheral portion secured to the hub by spokes or a solid wheel portion; and the more recently developed optimized disc.

Materials used to fabricate high-energy flywheels must have large specific strengths (strength/density) to enable the structure to be rotated at a high velocity. High strength steel has ordinarily been chosen as flywheel material. However, the strength/density ratio of an isotropic steel structure is substantially less than that obtainable with modern anisotropic filamentary materials. High strength filaments typically exhibit substantially greater" strength-to-density characteristics over the best isotropic materials, such as steel or titanium. Only a small portion of this strength advantage can be used in the prior art flywheels due to the inherent isotropic stresses in these structures. In the rim type flywheel, stresses normal to the wound filaments exist at all locations other than the outer edge. Additionally, the problem of attachment of the rim to the hub, requiring additional weight, has been a principal factor inhibiting further development of this flywheel structure.

The present inertial energy storage device offers substantial improvement in usable energy density due not only to the advantageous utilization of the high uniaxial strength of filamentary materials, but also to the efficient packaging density provided by the invention. The structure of the invention permits substantial utilization of the uniaxial strength of each filament while packaging a-multiplicity of filaments within a compact volume.

The significance of the present energy storage device is best understood by its application to the urban vehicle. Although flywheels have been used in short-range vehicles, such as in the Swiss Oerlikon bus and in the British Gyreacta transmission,'th0se devices produced only about three watt-hours per pound. Thus, energy density of the devices was even lower than that of available lead-acid batteries at the same discharge rate. However, certain characteristics of flywheels caused their use in preference to storage batteries, despite the problems then encountered in the use of flywheel structures. Firstly, the flywheel can be charged and discharged virtually an infinite number of times without degrading performance. Secondly, it can be charged at any reasonable rate. Thirdly, it can be discharged at any rate within the design limitations of ancillary equipment without degrading performance. These capabilities are largely responsible for the proposed use of flywheels in pollution-free urban vehicles. In most previous proposals, the rapid discharge capability of the flywheel has been primarily used to lend increased acceleration power to the vehicle in order to minimize the overall size of the main propulsion power plant. The

present energy storage device provides a power plant of sufficient energy density to also enable its economic and practical use as the primary energy source in an urban vehicle.

SUMMARY OF THE INVENTION The present invention provides an improved high performance energy storage device wherein a central hub holds a multiplicity of anisotropic filaments, the filaments extending from the hub in fixed relation thereto and in parallel planes perpendicular to an "axis of rotation taken through the hub. The anisotropic filaments are held within the device in fixed, predetermined positions, the filaments being supported and held in position by arcuate internal support surfaces and by matrix material within the hub. All but one of the filaments in each of the several planes is fanned within the device to an arcuate position, the radius of curvature of each filament being dependent on the location of the filament within the hub. A particularly important feature of the preferred embodiment of the invention is that the parallel planes of filaments are disposed at relative angles of to each other to reduce aerodynamic drag and increase the dynamic stability of the structure. Another important feature of the invention is that the anisotropic filaments extend through the hub and carry their respective tension loads essentially along their longitudinal axes during rotation of the device.

The present invention may be fabricated with extended bearing surfaces, or torque extensions which project from the hub on either side of each filament and lie in the plane of the filament. In extreme high torque situations, the portions of each filament which extend radially from the hub bear against the arcuate bearing surfaces of the torque extensions to provide support to the filaments without increasing the stress on the filaments.

The invention further provides in another embodiment thereof an end mass which is affixed to the ends of each filament to provide additional mass to the structure.

Accordingly, the principal object of the invention is to provide a high power-density energy storage device which also has a high energy density capability.

It is another object of the invention to provide an improved rotary energy storage device which is comprised of anisotropic filaments or rods held in fixed positions within a central hub, the filaments being fanned out to a predetermined curvature, and adjacent parallel planes of the arcuate filaments being disposed at angles to each other.

A further object of the invention is to provide a rotary energy storage device which can be readily and efficiently made from a large number of small discrete rod-like elements in order to minimize the likelihood of simultaneous failure of all such elements and thus maximize the safety of the device.

It is also an important object of the invention to provide bearing surfaces for each filament comprising a rotary energy storage device for relieving high torque loading on the filaments.

A still further object of the invention is to provide a rotary energy storage device wherein end masses are affixed to the ends of the anisotropic filamentary rods comprising the device to improve the energy storage capabilities thereof.

Additional objects, advantages and uses of the invention will become apparent from the following detailed description of the preferred embodiments thereof.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a plan view of a hub lamina comprising the element mounting means of the invention;

FIG. 2 is a section of the hub lamina of FIG. 1 taken along line 2-2 thereof;

FIG. 3 is an elevation of the hub lamina of FIG. 1;

FIG. 4 is a plan view of the lamina with the elements held therein;

FIG. 5 is a schematic illustrating the relationships for determining the position of each anisotropic element within the hub lamina;

' FIG. 6 is a perspective of the structure formed by alternately disposing lamina of FIG. 4 at right angles within a flywheel structure;

FIG. 7 is a plan view of a hub lamina having torque extensions disposed between the anisotropic elements;

FIG. 8 is an enlarged perspective of one of the torque extensions;

FIG. 9 is a schematic illustrating the structural principles of the torque extensions;

FIG. 10 is a perspective of an end mass which is attachable to the outer end portion of each element; and,

FIG. 11 is an enlarged view of a plurality of elements forming a portion of the present flywheel structure and having end masses attached to the elements.

DESCRIPTION OF THE PREFERRED EMBODIMENTS The performance, i.e., the stored kinetic energy of a rotary energy storage device, is directly proportional to the usable specific strength of the material used in the fabrication of the device. Isotropic materials, such as solid steel, have most often been used in the construction of kinetic energy structures, or flywheels. However, the best isotropic material exhibits only a small fraction of the strength-to-density of anisotropic materials, such as boron filaments, graphite fibers, or certain glass fibers. Flywheels configured to utilize a significant portion of the anisotropic strength of uniaxial filamentary or whisker material have been shown to be capable of increased performance relative to flywheels composed of isotropic materials. The present invention essentially comprises an improvement of the fixed-fanned brush" flywheel configuration disclosed and claimed in a co-pending application, Ser. No. 167,643, entitled Fixed Element Rotor Structures, by the same inventor. The improved structure disclosed herein exhibits increased dynamic stability and reduced aerodynamic drag over the prior structure. Further, the essentially laminar hub used to hold the anisotropic filamentary elements of the invention provides substantial improvement in fabrication costs and effort.

Although hub mounting means other than that to be particularly described hereinafter may be used to practice the invention, the particular hub construction which has proven to be of great utility for efficiency of manufacture is shown in detail in FIGS. 1, 2 and 3. In these views a hub lamina 2 is seen to comprise a circular base 4 having raised arcuately contoured walls 6 disposed on the upper surface thereof at equal distances from a diametrically disposed longitudinal axis of symmetry 8 extending through the geometrical center of said lamina 2. A diametrically disposed transverse axis of symmetry 10 intersects the longitudinal axis 8 at the geometrical center of the lamina 2 and at a right angle thereto. Between the arcuately contoured walls 6 and rising from the upper surface of the base 4 are arcuate projections 12 which define grooves 14 into which anisotropic filamentary elements 16 are fitted, the ele ments 16 being held within the grooves 14 in fixed, predetermined positions by the curved walls of said projections 12. For simplicity, only four of the elements 16 are shown in phantom in FIG. 1. In actual practice, each of the grooves 14 has one of the elements 16 disposed therein, as shown in FIG. 4. The walls 6 further join an outer circular wall 18, which wall 18 extends around the perimeter of the circular base 4. FIG. 3 shows a plurality of slots 19 in the wall 18 through which the elements 16 extend, the slots forming a tooth-like pattern in said wall. The lamina 2 is further formed with an annular lip 19 which extends about the perimeter of the upper surface of said lamina. An annular shoulder 21 is formed in the lamina 2 and extends about the perimeter of the lower surface thereof. The annular lip 19 and shoulder 21 mate with corresponding structure on adjacent laminae 2 when the laminae are brought into contact, i.e., the annular lip 19 of a first lamina 2 mates with the annular shoulder 21 of the adjacent lamina 2 immediately beneath the firstmentioned lamina. Adhesive means (not shown) disposed on the respective annular lips 19 and shoulders 21 aids in bonding the laminae 2 into a unitary structure, as will be further described hereinafter.

FIG. 4 illustrates the complete structure of the hub lamina 2 with all of the elements 16 in place. This structure may be more fully understood by reference to the axes of

symmetry

8 and 10. The pattern formed by the elements 16 lying in the grooves 14 shown to the right of the longitudinal axis 8 is duplicated in mirror image to the left of said axis 8. Similarly, the pattern formed by the elements 16 lying in the grooves 14 above the transverse axis of symmetry 10 is duplicated in mirror image below the axis 10. Those portions of the elements 10 which extend externally of the grooves 14 in the lamina 2 are aligned along extended radii of the circle formed by the circular base 4. The elements 16 must be positioned within the hub lamina 2 with the proper curvature in order for the portions of the elements 16 extending externally of said lamina 2 to be aligned as described. The element 16a lying along the longitudinal axis of symmetry 8 is the only element in the lamina 2 which is positioned to permit maximum utilization of the strength-to-density of the anisotropic filamentary material of which the element is comprised. However, proper choice of the radii of curvature of the remaining elements 16, as well as the rela tionship between the diameter of the element and its modulus of elasticity, allows utilization of a significant portion of the strength-to-density of said elements.

The position of each of the elements 16 within the lamina 2 may be determined from the relationships illustrated in FIG. 5. In FIG. 5 a single element 16 is schematically shown in its predetermined location within the lamina 2, the displacement of the element 16 from the longitudinal axis of symmetry 8 being taken as the normal from the longitudinal axis of said element 16 to the axis 8 along the transverse axis of symmetry 10. Those portions of the element 16 extending beyond the circle 20, which circle is defined by the perimeter of the circular lamina 2, lies along an extended radius r of the circle 20 drawn to the point of intersection of the longitudinal axis of the element and said circle. The tangent to the circle 20 through the aforementioned point of intersection defines the radius of curvature R of that portion of the element 16 lying within the lamina 2. In particular, the radius of curvature R is that portion of the tangent lying between the aforementioned point of intersection of the circle 20 and the intersection of the tangent with the extended transverse axis of symmetry 10. The angle 0 between the radius of curvature R and the extended transverse axis of symmetry 10 is identical to the angle defined by the longitudinal axis of symmetry 8 and the extended radius r with which the element 16 aligns beyond the circle 20. Thus, each of the grooves 14 shown in FIGS. 1 and 2 has its curvature determined according to the desired curvature for the element 16 being held therein.

The relationships between the above-described values define both the position of the elements 16 within the hub lamina 2 and the curved path of the grooves 14. Given a displacement D of a particular element 16 from the longitudinal axis of symmetry 8 and the radius r of the hub lamina 2, the radius of curvature R for the element 16 may be determined from the relationship:

The two outermost elements 16 shown in FIG. 4, each one of which elements 16 is held between respective arcuately contoured walls 6 and the projections 12 immediately adjacent thereto, have outer portions which extend from the lamina 2 at angles of 45 with the longitudinal axis of symmetry 8. A value of 0 of 45 may be taken to be a practical maximum in order to limit the stress loss of the outermost elements 16 to an acceptable value. The elements 16 diverge from the longitudinal axis of symmetry 8 in progressively greater degrees of curvature, i.e., the innermost elements 16 having a greater radius of curvature than the outermost elements 16, the elements 16 adjacent to the straight element 16a having the largest radii of curvature and the outermost elements 16 having the smallest radii of curvature. Midportions of the elements 16 may be fixed within the grooves 14 and supported therein by a matrix material 20. The thickness of each lamina 2 is essentially dependent upon the diameter 'of the elements 16, the lamina 2 being typically 1.5 times the diameter of the elements if both hub lamina 2 and element 16 are comprised of the same material. Higher density and higher strength/density elements 16 would require thicker hub laminae for the same choice of hub material. Thus, if the elements were 10 mil diameter steel wire filaments, the lamina 2 would be pressed or chemically milled from 0.015 inch circular steel plates.

As shown in FIG. 6, a fanned element flywheel 30 is fabricated by stacking a plurality of the elementbearing hub laminae 2 each lamina 2 being preferably turned at a angle to adjacent laminae 2. The longitudinal axis of symmetry 8 of a given lamina 2 has the same orientation within the flywheel 30 as the transverse axes of symmetry 10 of the adjacent laminae 2. The laminae 2 are bonded together to form an essentially cylindrical hub which is sandwiched between hub plates 32 having shaft elements 34 formed integrally therewith, the shaft elements 32 extending axially from the plates 32 and along the axis of rotation of the flywheel 30.

The flywheel 30 may also be formed in an alternate fashion which would be less efficient volumetrically and aerodynamically. In particular, the outermost elements 16 of FIG. 4 may define an angle 6 smaller than 45. For example, if 0 equalled 30, the outermost elements 16 would be bent less and would thus take greater advantage of their uniaxial strengths. However,

stacking of the laminae 2 would not produce the structure shown in FIG. 6. A lamina 2 having elements 16 disposed therein with 0 equal to 30 might then be stacked either at right angles to other such laminae 2 or even at lesser angles thereto in a spiralling fashion. However, the flywheel 30 shown in FIG. 6 is clearly the most efficient embodiment of the inventive concept described above.

A major advantage of the present structure is the favorable failure mode of the flywheel 30 relative to conventional isotropic flywheels composed of materials such as steel. An isotropic steel flywheel normally ruptures into two to four large fragments if design parameters are exceeded or if structural flaws develop, thereby resulting in the disastrous release of several high kinetic energy fragments. This type of catastophic failure is avoided with the present structure. For example, the failure of one of the anisotropic elements 16 gives an advance warning of impending rotor failure. Even when one or all of the elements 16 fail, the failing elements are essentially reduced to dust or to small strawlike fragments. Since only a small percentage of the kinetic energy of the flywheel is transmitted to a containing structure, the kinetic energy in'the elements 16 appears to be dissipated by microfracture of the elements 16 and of any matrix materialused either to bond the elements 16 into the flywheel 30 or to bond anisotropic filamentary materials together to form the rod-like elements 16. Since the elements 16 can internally absorb a large portion of the failure energy, the traditional containment problem associated with high energy flywheels is substantially relieved.

The nature of the anisotropic elements 16 may now be further defined as to materials suitable for use and as to the potential structural form of the elements. While anisotropic filamentary material of virtually any composition is potentially usable, certain materials naturally exhibit greater uniaxial tensile strength/density ratios than others. Boron filaments, graphite fibers, glass fibers, and even high strength steel wire are examples of suitable filamentary materials. Single filaments, such as steel music wire, which have a sufficiently large diameter to be singly disposed in each of the grooves 14 of FIG. 1 are available. However, the elements 16 would normally be formed from a plurality of anisotropic filaments bonded together by a suitable matrix material to form each of the rod-like elements 16. The filaments are aligned in straight, parallel relation in each of the elements 16. Examples include boron filaments in an epoxy or magnesium matrix, graphite fibers in epoxy, and E-glass or S-glass in an epoxy or polyester matrix. High purity quartz, fused silica, various organic fibers and a variety of whisker-based materials represent other anisotropic filamentary materials from which the elements 16 may be fabricated.

Referring briefly again to FIGS. 4 and 6, it can be seen that stacking of the element-bearing hub laminae 2 with their longitudinal axes of symmetry 8 extending in the same direction within the structure would produce the fixed-fanned brush rotor configuration described and claimed in co-pending patent application, Ser. No. 167,643, by the same inventor. While the rotor configuration of this co-pending patent application may be conveniently fabricated by use of the hub laminae 2, several dynamic advantages result from the alternately normal relation of the laminae 2 within the flywheel 30. Since the elements 16 are essentially disposed equally in all directions over the total rotor faces, the flywheel 30 has reduced aerodynamic drag and increased dynamic stability due to the close resemblance of the overall configuration to a turbulent disc. The present flywheel 30 does not require a hub of sufficient strength to carry the tension loading on the elements 16 since the tension load on each element 16 is carried by the element itself, the local stress vector acting on each element 16 being effectively directed along its longitudinal axis.

FIGS. 7 and 8 illustrate a hub lamina 40 which is identical to the hub lamina 2 except for the provision of extended bearing surfaces 42 formed on torque extensions 44. The torque extensions 44 are knob-like projections which extend from a peripheral wall 46 between each of the elements 16. The surfaces 42 on opposite sides of each torque extension 44 face the element 16 lying therebetween. Each surface 42 preferably has a curvature defined by the radius of curvature of the outermost element 16, Le, the element 16 having the smallest radius of curvature. The surfaces 42 on either side of each element 16 are so formed, thereby allowing acceleration or deceleration of the flywheel in either direction. These bearing surfaces 42 do not contact the elements 16 during ordinary operation since the elements 16 extend radially from the hub lamina 40 externally thereof. However, extreme high torque conditions can displace the elements 16 against the surfaces 42, said surfaces 42 then providing support for the elements to prevent excessive bending loads on the radially-extended portions thereof at the points where they extend beyond the hub. The surfaces 42 may of course be formed other than as specifically described above, differing curvatures of the surfaces being potentially suitable for various applications.

FIG. 9 schematically illustrates the relationship between the positions of an element 16 during both high torque and normal conditions. The angle a is the angle between the transverse axis of symmetry 10 of the lamina 40 and the tangent taken from the origin of the radius of curvature R of a particular element 16 to the point where the element 16 intersects the perimeter of the lamina 40. The angle B is the angle between the transverse axis of symmetry 10 and the tangent taken from the origin of the radius of curvature R of the element 16 to the point where the element 16 extends beyond the torque extension 44. The difference between B and a may be termed the set back angle of the torque extension 44 and may be chosen according to the power density required for an application. Generally, a set back angle (B a) of 3 allows a power density within the capability of the element material and sufficiently large for known applications. The element 16 is seen in its normal position in unbroken lines, that portion of the element 16 extending externally of the lamina 40 lying along an extended radius r of the lamina 40. High torque conditions cause the element 16 to be displaced toward and against one of the surfaces 42, as shown in broken lines, depending on the direction of rotation of the lamina 40. Thus, even when maximum design torque is applied to the flywheel, the stress in the individual element 16 remains unaffected since neither the tension load nor the radius of curvature of the element has been altered beyond the radius of curvature of the most sharply curved element 16.

A further embodiment of the invention is shown in FIGS. 10 and 11. FIG. 10 particularly illustrates a wedge-like end mass 50 which is reduced at its inner end portion 52 and flares slightly to an enlarged outer end portion 54. To maximize the volume of the mass 50, the upper and lower plane surfaces are flat and parallel to each other. The faces of the mass 50 around the edges thereof are rectangular. A longitudinal channel 56 extends centrally through the end mass 50 from the inner end portion 52 to the outer end portion 54. It is not necessary for each channel 56 to extend the full length of the masses 50 in order to assure that said channels provide sufficient contact area to be bonded to the end portions of an anisotropic element comprising a flywheel configured according to the present invention. FIG. 11 illustrates the attachment of a plurality of the end masses 50 to a plurality of anisotropic elements 58 comprising a flywheel 60. As in previous embodiments of the invention, the elements 58 may be single anisotropic filaments or composite rods comprised of a multiplicity of parallel anisotropic filamentary members. Each-element 58 extends into the channel 56 and is bonded therein by a suitable adhesive. The end masses 50 simply add mass to the flywheel 60 at an advantageous location within said flywheel, thereby allowing increased energy storage per unit volume, but at a sacrifice in energy storage per unit weight. With the end masses 50 attached to the elements 58, the flywheel 60 may be operated at a lower angular velocity. The end mass 50 may assume shapes other than that shown in FIG. 10. The shape shown is simply one volumetrically desirable form for said mass.

It is believed obvious that modifications of the concepts described herein may be practiced without departing from the scope of the invention. In particular,

hub means for holding portions of the filament-like members, the hub means comprising disc-like laminae, each of said lamina having arcuate surfaces for holding the members in fixed, arcuate positions, the laminae being bonded together with their geometrical centers aligned along the axis of rotation of the device to produce a unitary hub structure.

2. The energy storage device of claim 1 wherein portions of the filament-like members are held within the hub means, the member disposed in a plane through the longitudinal axis of each lamina and perpendicular to the transverse axis thereof being straight and the members on either side of said plane having portions thereof within the lamina fixed into predetermined arcuate configurations.

3. The energy storage device of claim 1 and further comprising torque extensions on each laminae, the extensions being disposed on either side of each of the members and in the plane occupied by the member, the extensions having bearing surfaces against which the member may be supported on displacement of portions of said member from their original positions.

4. The energy storage device of claim 1 and further comprising end masses attached to the filament-like members at their outer end portions.

5. The energy storage device of claim 1 wherein the radius of curvature of the fixed arcuate portion of each of the members in a particular lamina is dependent upon the distance of said member from a plane taken through the longitudinal axis of the lamina and perpendicular to the transverse axis thereof, the radius of curvature of each said member being determined according to the relationship:

where:

R radius of curvature of a given member;

r radius of the hub means; and

D distance from the given member to the said plane.

6. The energy storage device of claim 5 wherein adjacent laminae are disposed at angles of 90 to each other. 1

7. The energy storage device of claim 6 wherein portions of the members extend externally of the hub means and are aligned along radii emanating from the 'axis of rotation of the device.

8. The energy storage device of claim 1 wherein each lamina is essentially circular and further comprises arcuate internal walls which define a plurality of arcuately shaped gooves, one each of the filament-like members lying within each of said grooves and being biased to an arcuate configuration by said walls.

9. The energy storage device of claim 8 and further comprising an annular lip around the perimeter of the upper surface of each lamina and an annular shoulder around the perimeter of the lower surface of each lamina, the lips and shoulders of adjacent laminae mating on justaposition of said laminae with the geometrical centers of the laminae aligned along the axis of rotation of the device.

10. The energy storage device of claim 8 wherein the longitudinal axes of the laminae are disposed at angles to each other.

11. The energy storage device of claim 8 and further comprising matrix means for maintaining the members in fixed positions within the hub means.

12. The energy storage device of claim 1 wherein the laminae hold the members in planes perpendicular to the axis of rotation of the device.

13. The energy storage device of claim 12 wherein the members are disposed around the full periphery of the hub means.

14. An energy storage device having an axis of rotation extending transversely therethrough, comprising a plurality of filament-like members, the longitudinal axes of major portions of said members extending radially from the axis of rotation of the device; and,

hub means for holding the members in planes perpendicular to the axis of rotation of the device.

the hub means being comprised of discrete disc like laminae, each said lamina having arcuate internal means for holding the filament-like members in fixed, predetermined positions, portions of the members within each lamina being arcuate, the longitudinal axes of the laminae being disposed at angles to each other. 15. An energy storage device having an axis of rotation extending transversely therethrough, comprising a plurality of anisotropic, filament-like members having maximum strength-to-density along their longitudinal axes the longitudinal axes of major portions of said members extending radially from the axis of rotation of the device; and, hub means for holding the members in planes perpendicular to the axis of rotation of the device,

the hub means being comprised of discrete disc-like laminae, each said lamina having arcuate walls internally thereof, the walls being curved toward each other and toward the axis of rotation of the device, the walls further holding the filament-like members in fixed, predetermined positions, portions of the members within each lamina being arcuate, the longitudinal axes of the laminae being disposed at angles to each other.

16. The energy storage device of claim 15 wherein adjacent laminae are disposed at angles of to each other.

17. An energy storage device having an axis of rotation extending transversely therethrough, comprising a plurality of filament-like members,

hub means for holding portions of the filament-like members at the centers thereof, and

end masses attached to the filament-like members at their outer end portions.

18. An energy storage device having an axis of rotation extending transversely therethrough, comprising a plurality of filament-like members,

hub means for holding portions of the filament-like members, and

torque extensions on said hub means, the extensions being disposed on either side of each of the members and in the plane occupied by the member, the extensions having bearing surfaces against which the member may be supported on displacement of portions of said member from their original positions.

Claims

1. An energy storage device having an axis of rotation extending transversely therethrough, comprising a plurality of filament-like members, hub means for holding portions of the filament-like members, the hub means comprising disc-like laminae, each of said lamina having arcuate surfaces for holding the members in fixed, arcuate positions, the laminae being bonded together with their geometrical centers aligned along the axis of rotation of the device to produce a unitary hub structure.

5. The energy storage device of claim 1 wherein the radius of curvature of the fixed arcuate portion of each of the members in a particular lamina is dependent upon the distance of said member from a plane taken through the longitudinal axis of the lamina and perpendicular to the transverse axis thereof, the radius of curvature of each said member being determined according to the relationship: R ( 1/2 r2/D - D ) where: R radius of curvature of a given member; r radius of the hub means; and D distance from the given member to the said plane.

6. The energy storage device of claim 5 wherein adjacent laminae are disposed at angles of 90* to each other.

7. The energy storage device of claim 6 wherein portions of the members extend externally of the hub means and are aligned along radii emanating from the axis of rotation of the device.

14. An energy storage device having an axis of rotation extending transversely therethrough, comprising a plurality of filament-like members, the longitudinal axes of major portions of said members extending radially from the axis of rotation of the device; and, hub means for holding the members in planes perpendicular to the axis of rotation of the device. the hub means being comprised of discrete disc-like laminae, each said lamina having arcuate internal means for holding the filament-like members in fixed, predetermined positions, portions of the members within each lamina being arcuate, the longitudinal axes of the laminae being disposed at angles to each other.

15. An energy storage device having an axis of rotation extending transversely therethrough, comprising a plurality of anisotropic, filament-like members having maximum strength-to-density along their longitudinal axes the longitudinal axes of major portions of said members extending radially from the axis of rotation of the device; and, hub means for holding the members in planes perpendicular to the axis of rotation of the device, the hub means being comprised of discrete disc-like laminae, each said lamina having arcuate walls internally thereof, the walls being curved toward each other and toward the axis of rotation of the device, the walls further holding the filament-like members in fixed, predetermined positions, portions of the members within each lamina being arcuate, the longitudinal axes of the laminae being disposed at angles to each other.

16. The energy storage device of claim 15 wherein adjacent laminae are disposed at angles of 90* to each other.

17. An energy storage device having an axis of rotation extending transversely therethrough, comprising a plurality of filament-like members, hub means for holding portions of the filament-like members at the centers thereof, and end masses attached to the filament-like members at their outer end portions.

18. An energy storage device having an axis of rotation extending transversely therethrough, comprising a plurality of filament-like members, hub means for holding portions of the filament-like members, and torque extensions on said hub means, the extensions being disposed on either side of each of the members and in the plane occupied by the member, the extensions having bearing surfaces against which the member may be supported on displacement of portions of said member from their original positions.