Abstract:
An energy-storing flywheel assembly is provided with a flywheel having a vertically-oriented axis of rotation, a shaft connected to the flywheel, and a cageless ball thrust bearing rotatably supporting a lower end of the shaft. The flywheel may be formed from a stack of flywheel discs and is preferably relatively large-radiused and massive. The ball thrust bearing includes a stator having a set of three free-floating bearing balls contained within a cylindrical stator recess; a rotor rotatably mounted over the stator which likewise contains a set of three free-floating bearing balls within a cylindrical stator recess, and a single, middle bearing ball centrally disposed between and in mutual engagement with the three bearing balls of the stator and the three bearing balls of the rotor. In operation, the relatively massive flywheel is rotated at a peripheral speed that approaches but does not exceed the speed of sound to avoid fluid drag and the danger of explosive shattering.

Description:
RELATED APPLICATIONS 
     This application claims priority of provisional patent application Ser. No. 61/791,559 filed Mar. 15, 2013. 
    
    
     FIELD 
     This invention generally relates to devices for storing mechanical energy, and is particularly concerned with an energy storing flywheel and cageless ball bearing assembly. 
     BACKGROUND 
     Interest in flywheels as energy storage devices has increased recently as a result of the movement toward “green” energy produced from windmills, as such flywheels could be used in a windmill-based electrical power station to provide power output during periods when ambient winds are low. Such flywheels may also be used in solar-based electrical power stations to provide power output after sunset. 
     Flywheel energy storage has a number of advantages that make it an attractive design option. Compared with other ways to store electricity, flywheel energy storage systems have long lifetimes, lasting decades with little or no maintenance. Full-cycle lifetimes quoted for flywheels range from between 10 5  and 10 7  start-stop cycles of use. Such systems also have a potentially high energy density (100-130 W·h/kg, or 360-500 kJ/kg), in addition to large maximum power output. The energy efficiency (ratio of energy out per energy in) of flywheels can be as high as 90%. Typical capacities range from 3 kWh to 133 kWh. Rapid charging or discharging of a flywheel system can occur in less than 15 minutes. 
     Because the energy storage capacity of a flywheel increases with the square of its rotational speed, most energy-storing flywheel systems are designed to operate at very high rotational speeds (e.g. 10,000-60,000 rpms or more). But while such high speed rotation advantageously increases the energy storage capacity of the system, it also results in a number of disadvantages. High speed flywheels must be precision-constructed of high tensile strength material to maintain balance and structural integrity during operation. To cope with the frictional losses associated with such high speeds, precision bearings are necessary. In some systems, conventional ball or roller bearings are used wherein the ball or roller bearings are caged within concentric races. To reduce friction to acceptable levels and to insure longevity, the cages, races and balls or rollers of such mechanical bearings must be machined to exacting tolerances. To further reduce friction, some flywheel energy storage systems use pressurized air or repulsive magnet bearings. However, such levitating-type bearings substantially increase the costs associated with such systems and impose practical limitations on the weight of the flywheel. Because of the potential dangers associated with an explosive shattering of the flywheel caused by the large centrifugal forces generated at such high speeds, it is necessary to contain them within a thick-walled housing or a recess in the ground. For flywheels rotated at speeds high enough to exceed the sound barrier around their periphery, it is desirable to at least partially evacuate the interior of the housing to eliminate the resulting turbulent air drag losses, and the wear around the outer edge of the flywheel due to air friction. All of these requirements increase the overall cost of the system. 
     SUMMARY 
     In view of the aforementioned shortcomings associated with high-speed flywheel designs, there is a need for a flywheel design that maintains all or most of the energy-storing advantages of prior art flywheel systems but which is simpler in construction, easier and less expensive to manufacture, and safer to operate. To these ends, the energy-storing flywheel assembly of the invention comprises a flywheel having a vertically-oriented axis of rotation; a shaft assembly connected to the flywheel and having an axis of rotation that is collinear with the axis of rotation of the flywheel, and a cageless ball thrust bearing rotatably supporting a lower end of the shaft assembly. The cageless thrust bearing includes a stator having a cylindrical recess, and a set of three free-floating bearing balls contained within the stator recess; a rotor rotatably mounted over the stator, the rotor having a cylindrical recess that is coaxial with the stator cylindrical recess and which likewise contains a set of three free-floating bearing balls, and a single, middle bearing ball centrally disposed between and in mutual engagement with the three bearing balls of the stator and the three bearing balls of the rotor. 
     The three bearing balls contained in the stator and the three bearing balls contained in the rotor preferably have a same diameter. The diameter of the middle bearing ball may be no less than the ⅔ of the diameter and no greater than twice the diameter as that of the three bearing balls contained in the stator and the three bearing balls contained in the rotor. The single, middle bearing ball preferably contacts the three bearing balls of the stator and the three bearing balls of the rotor at about a 45° angle from a plane that intersects a center of the middle bearing ball. 
     The cageless ball thrust bearing eliminates both the cages and races associated with conventional ball bearings, greatly simplifying the over-all structure of the flywheel assembly without any significant compromise in friction reduction or bearing longevity. Moreover, the high load capacity of such a cageless ball thrust bearing allows the energy storage to be accomplished via the use of a relatively massive and large-radiused flywheel rotating at substantially slower speeds relative to prior art flywheels having similar energy storage capacities. Such a higher mass, slower speed flywheel in turn allows the use of cheaper, lower-tensile strength materials for the flywheel and reduces the possibility of explosive shattering of the flywheel due to centripetal forces. 
     The flywheel is preferably continuously solid at every point along its radius, and the amount of mass per unit of circumferential length remains constant or increases in a radially outward direction. The flywheel may be formed from a plurality of stacked, disc-shaped flywheel sections for ease of construction and assembly. Each flywheel section is preferably formed from pelletized metal such as steel or lead imbedded in a matrix of plastic material, and includes a continuous metal rim around its outer periphery to increase the flywheel&#39;s tensile strength and decrease the risk of centrifugal shattering during operation. Plastic washers are preferably disposed between adjacent stacked flywheel sections in order to level and uniformly engage the stacked flywheel sections over their horizontal surfaces. The washers also serve as disc brake-like energy absorbers in the event of a catastrophic failure of the flywheel assembly wherein either the vertical shaft assembly or one of the flywheel sections of the assembly seizes. In such a case, the washers would allow for a gradual slowing down of the rotating flywheel sections by heating up and melting. 
     The invention further encompasses a cageless ball thrust bearing that comprises a stator having a cylindrical recess, and a set of three free-floating bearing balls contained within the stator recess; a rotor rotatably mounted over the stator, the rotor having a cylindrical recess that is coaxial with the stator cylindrical recess and which likewise contains a set of three free-floating bearing balls, and a single, middle bearing ball centrally disposed between and in mutual engagement with the three bearing balls of the stator and the three bearing balls of the rotor, wherein the middle bearing ball has a same or nearly same diameter as that of the three bearing balls contained in the stator and the three bearing balls contained in the rotor. 
     The diameter of the bearing balls is preferably sufficiently smaller than the diameter of the cylindrical stator and rotor recesses that contain them such that the three bearing balls contained in both the stator and rotor cylindrical recesses do not contact one another when uniformly spaced 120° around their respective recesses. The radius of the stator and rotor recesses may be at least 108% of the diameter of the bearing balls contained in each. The single, middle bearing ball preferably contacts the three bearing balls of the stator and the three bearing balls of the rotor at between about a 45° and 60° angle from a plane that intersects a center of the middle ball bearing, and more preferably at a 45° angle so that the load on the bottom and side walls of the stator and rotor recesses is equalized. 
     In a method of operation of the flywheel and bearing assembly, the flywheel is rotated at a speed such that an outer periphery of the flywheel approaches but does not exceed the speed of sound to avoid supersonic turbulence and drag that would otherwise occur. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1A  is a side cross-sectional view of the energy-storing flywheel and bearing assembly of the invention; 
         FIG. 1B  is an enlargement of the area circled in phantom in  FIG. 1A , illustrating the particulate metal/plastic matrix constitution of the flywheel sections; 
         FIG. 2  is a top plan view of the energy-storing flywheel and bearing assembly illustrated in  FIG. 1  along the line  2 - 2 ; 
         FIG. 3  is a bottom cross-sectional view of the energy-storing flywheel and bearing assembly along the line  3 - 3 ; 
         FIG. 4  is an enlarged cross sectional side view of the ball thrust bearing of the invention; 
         FIGS. 5A and 5B  are plan cross sectional views of the thrust bearing illustrated in  FIG. 4  along the lines  5 A- 5 A and  5 B- 5 B, and 
         FIGS. 6A-6I  illustrate the orbital and rotational movement of the bearing balls within the stator of the bearing throughout 18 rotations of the shaft assembly. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
     With reference now to  FIGS. 1A ,  2 , and  3  the flywheel and bearing assembly  1  comprises a support frame  3  having a base plate  5 . Centrally disposed on the upper surface of the base plate  5  is a protruding annular wall  6 . The upper, inner surface of the annular wall  6  includes a bearing  7  which is preferably a bronze annular sleeve-type bearing. Bolt holes  8   a ,  8   b  best seen in  FIG. 2  are symmetrically spaced on either side of the annular wall  6  to the base plate  5  to be securely mounted on the floor of a building. While only two such bolt holes  8   a ,  8   b  are shown in the Figures, the actual number in a practical embodiment would be much higher (for example sixteen or so) in order to effectively resist the shear and torque forces that will occur between the base plate  5  and the floor of the enclosing building (not shown) during the operation of the assembly  1 . A pair of vertically-standing side members  9   a ,  9   b  are connected at their bottom ends to opposite ends of the base plate  5 , and are further connected at their top ends to a top member  10  that is best seen in  FIG. 3 . The top member  10  has a central, circular opening  11 . The base plate  5 , side members  9   a ,  9   b  and top member  10  are all preferably formed from structural steel or other relatively strong alloy. Connection between the base plate  5 , side members  9   a ,  9   b  and top member  10  may be by weld joints, bolts, or any strong, conventional attachment technique. With reference to  FIGS. 1A and 2 , the top member  10  includes a bearing plate  13  having a centrally positioned ball bearing  15 , and four bores  17  for receiving mounting bolts  18 . The bores  17  are oversized relative to the threaded shafts of the bolts  18  to allow the position of the bearing plate  13  to be adjusted relative to the top member for a purpose that will become evident hereinafter. 
     With reference again to  FIG. 1A , the flywheel and bearing assembly  1  further comprises a shaft assembly  20  having a vertically-oriented axis of rotation. Shaft assembly  20  is rotatably mounted within the support frame  3 , and includes a spindle  22 , a disc-shaped support table  24 , and an enlarged base portion  26 . A pulley  28  is fixedly mounted on the shaft assembly  20  to transmit torque to the shaft assembly  20  from a drive belt (not shown) that mechanically links the pulley  28  to a driven shaft. In the above-ground embodiment of the invention illustrated in  FIG. 1 , the pulley  28  is fixedly mounted around the base portion  26 . However, in a below-ground embodiment of the invention, the pulley  28  would be fixedly mounted at the upper end of the spindle  22  above the walls of the recess containing the flywheel and bearing assembly  1  so that the pulley  28  could be easily engaged to an above-ground drive belt. The spindle  22 , disc-shaped support table  24 , and enlarged base portion  26  are all concentrically aligned with co-linear axes of rotation so that the shaft assembly  20  can rotate at slow speeds (relative to prior art flywheels) of up to about 5000 rpms without undue vibration. While the diameter of the support table may be of any size and still fall within the purview of the invention, a preferred diameter ranges from about 3 to 20 ft. The bottom end of the spindle  22  is fixedly connected to the support table  24  and the base portion  26 , but is also removably mounted to these components via a joint  29  formed in part from a cylindrical recess that extends through the disc-shaped support table  24  as shown. Joint  29  may for example include screw threads on the outer surface of the bottom end of the spindle  22  that are mutually-engageable to complementary screw threads circumscribing the inner surface of the recess of the joint  29 . Alternatively, joint  29  may include set screws that interlock the cylindrical bottom end of the spindle  22  within the cylindrical recess of the joint  29 . The removability of the spindle  22  from the support table  24  greatly facilitates the installation of the flywheel  35 , as will become evident hereinafter. The upper end of the spindle  22  extends through the circular opening  11  of the top member  10  and is rotatably connected to the bearing plate  13  via ball bearing  15 . The base portion  26  of the shaft assembly  20  is rotatably journaled within the protruding annular wall  6  of the base plate  5  of the frame  3  via bronze bearing  7  and a cageless ball thrust bearing  30 . 
     With reference again to  FIGS. 1A and 2 , the flywheel  35  of the assembly  1  preferably comprises a plurality of disc-shaped flywheel sections  37   a ,  37   b  and  37   c  stacked over one another as shown. The division of the flywheel  35  into flywheel portions  37  renders the flywheel  35  easier to manufacture, transport, and install over the disc-shaped table  24  of the shaft assembly  20  since it is easier to handle several lighter-weight flywheel sections  37  than the entire flywheel  35  at once. Each flywheel section  37  includes a peripheral rim  39  formed from steel or other strong alloy to ensure that the section  37  will not fly apart during operation due to centripetal forces. Each flywheel section  37  further includes a central annular bushing  41  formed from bronze or the like that closely and slidably fits around the outside surface of the spindle  22  to prevent wobbling that could otherwise occur between the sections  37  and the spindle  22  during rotational operation. With reference now to  FIG. 1B , the flywheel sections  37  are principally formed from metal particles or granules  43  encased in a matrix of plastic material  45 . In one example of the invention the metal particles  43  are formed from lead, and the plastic material is a high-density polyethylene (HDPE) plastic. Re-cycled plastic milk bottles are a preferred source of such plastic material. If the plastic material constituted 20% by volume of each flywheel section  37  and particulate lead constituted the remaining 80% of the volume, the density of each flywheel section  37  would be about 578 lbs./ft. 3 . Of course, particulate scrap steel could also be used in which case the density of the flywheel sections would be about 403 lbs./ft. 3  While the lower density would lower the over-all energy storage capacity of the resulting flywheel  35 , the very low cost of scrap steel vs. lead may more than offset this disadvantage. Exemplary dimensions of the flywheel sections  37  may be 7 feet in diameter, and four inches in thickness. Such dimensioning renders the flywheel sections  37  relatively easy to manufacture and transport, as such a section  37  when made from a 20%-80% by volume mixture of HDP and particulate scrap steel would weigh about 5,167 lbs. or 2.58 tons. 
     As best seen in  FIG. 1A , disc-shaped washers  47  are disposed between the support table  24  and the bottom-most flywheel section  37   c  and also between the remaining flywheel sections  37   b  and  37   a . Preferably, these washers are made of the same plastic material (e.g. HDPE) used to form the plastic matrix  45  of the flywheel sections  37   a - 37   c . The function of these washers is two-fold. First, the washers  47  plastically deform in response to the compressive loads applied to them by the weight of the flywheel sections  37   a - 37   c . This plastic deformation fills in any gaps in the surface-to-surface contact between the flywheel sections  37   a - 37   c  and increases the frictional interface between them. This increased frictional interface in turn mechanically unitizes the flywheel sections  37   a - 37   c  so that the torque applied by the support table  24  is effectively transmitted to all of the flywheel sections at once. Second, in the event of a catastrophic failure caused by, for example, the seizure of the shaft assembly  20  within the frame  3 , the washers  47  would act as “disc brakes” between the support table  24  and adjacent flywheel sections  37   a - 37   c  and would gradually slow the rotating flywheel sections down by heating up and melting. 
     With reference now to  FIGS. 4 ,  5 A and  5 B, the ball thrust bearing  30  of the invention comprises a stator  50  formed from a stator cup  51  closely fitted into a cylindrical recess  52  in the base plate  5 . Such close fitting may be accomplished by chilling the cup  51  sufficiently below the expected ambient temperature of the assembly  1  to induce enough thermal contraction to allow it to be inserted into the recess  52 . Recess  52  includes a lubricant outlet  54  that extends through the circular floor of the stator cup  51 . Outlet  54  is connected to a lubricant source  56 . Three cageless, free-floating bearing balls  58   a ,  58   b  and  58   c  are contained within the cup  51 . Bearing balls  58   a ,  58   b  and  58   c  are preferably precision-made from steel or stainless steel and may have case-hardened and/or chrome-plated exteriors to reduce wear and increase longevity. The material forming the annular wall and circular floor of the stator  50  that contains the bearing balls  58   a ,  58   b  and  58   c  should have the same hardness as the surface of the bearing balls. It would be possible of course to dispense with the stator cup  51  and to use the annular and circular surfaces of the cylindrical recess  52  for this purpose. However, the provision of a separate stator cup  51  that can be precision-machined out of an alloy having the same hardness as the bearing balls  58   a ,  58   b  and  58   c  is greatly advantageous over the use of the recess  52  to contain the bearing balls, since it is far easier to machine a relatively small shell  51  to the tolerances needed in the bearing  30  than the recess  52  in the large and base plate  5 . In short, such a design allows the cylindrical recess  52  to be fabricated with looser tolerances than the bearing  30  and further allows the surrounding portion of the stator  50  and the base plate  5  to be formed from a wide range of common and inexpensive steel alloys instead of an alloy having a very specific hardness. 
     In absolute terms, the diameter of the bearing balls may range considerably, but are from one-half inch to one foot diameter in the preferred embodiment. In relative terms, the diameter of the bearing balls  58   a ,  58   b  and  58   c  are the same, and large enough so that the bearing balls closely approach one another when uniformly spaced 120° around the stator recess  52 , but small enough such that they do not contact one another when uniformly spaced 120° around the stator recess  52 . To avoid such contact (and the resultant undesirable friction) the radius of the stator cup  51  is a little less than 108% of the diameter of the bearing balls  58   a ,  58   b  and  58   c  contained therein. 
     The ball thrust bearing  30  further includes a rotor  60  formed in the bottom end of the enlarged cylindrical base portion  26  of the shaft assembly  20 . Like the previously-described stator  50 , rotor  60  includes a cylindrical cup  61  disposed in a closely-fitting cylindrical recess  62  that contains three upper bearing balls  64   a ,  64   b  and  64   c . These upper bearing balls  64   a ,  64   b  and  64   c  are preferably the same diameter, type, and surface harness as the lower bearing balls  58   a ,  58   b  and  58   c . The material forming the walls of the cylindrical cup  61  of the rotor  60  should have the same hardness as the surface of the bearing balls  64   a ,  64   b  and  64   c . An annular retaining wall  66  circumscribes the inner edge of the rotor recess  62  and helps to retain the bearing balls  64   a ,  64   b  and  64   c  during assembly of the bearing  30 . A single, middle bearing ball  70  contacts the three bearing balls  58   a ,  58   b  and  58   c  of the stator and the three bearing balls  64   a ,  64   b  and  64   c . Again, middle bearing ball  70  is preferably the same diameter, type, and surface hardness as the lower and upper bearing balls  58   a ,  58   b  and  58   c  and  64   a ,  64   b  and  64   c  although it is within the scope of the invention for the middle bearing ball  70  to have a diameter that is between ⅔rds to twice the diameter of the lower and upper bearing balls. While the angle of contact between the middle bearing ball  70  and the bearing balls of the stator  50  and rotor  60  can range between about a 45° and 60° angle from a plane that intersects a center of the middle bearing ball, an angle of about 45° is preferred as such angular contact causes each of the bearing balls of the stator  50  and rotor  60  to apply a same pressure to the annular interior walls of the circular bottom or top walls of their respective bearing cups  51  and  61 . Such uniformity of pressure promotes even wear on the bearing cup walls, thereby increasing longevity of the bearing  30 . 
     The thrust bearing  30  operates in a manner similar to a driven double planetary gear. The bearing balls  58   a ,  58   b  and  58   c  and  64   a ,  64   b  and  64   c  rotate around the bearing cups  51 ,  61  at one-seventh to one-ninth the rotational speed of the shaft assembly  20 , thereby minimizing wear between the bearing balls and the stator and rotor cups  51 ,  61 . Hence if the flywheel turns at 50 rpms, the lower and upper sets of bearing balls  58   a ,  58   b  and  58   c  and  64   a ,  64   b  and  64   c  will rotate around the walls of their respective cups  51 ,  61  at a maximum of about 10 rpms. The three upper and three lower bearing balls will self-space themselves 120° apart within a few rotations of the shaft assembly  20 , thus obviating the need of precision-made ball cages which not only reduces the expense of the ball thrust bearing  30 , but also reduces the friction, allowing the flywheel and bearing assembly  1  to store energy for longer periods of time. Each of the lower and upper bearing balls  58   a ,  58   b  and  58   c  and  64   a ,  64   b  and  64   c  exerts only ⅙ the total load applied to the bearing  30  to the walls of its respective cups  51 ,  61 . Since each bearing ball contacts its respective stator and rotor cups  51 ,  61  at two points (i.e. one point on the annular side wall and one point on the circular wall of its respective cup) the total load applied to the bearing  30  is distributed over twelve points within the stator and rotor cups  51 ,  61  of the bearing  30 . When the middle bearing ball  70  contacts the lower and upper bearing balls  58   a ,  58   b  and  58   c  and  64   a ,  64   b  and  64   c  at the preferred 45° angle, the load is distributed equally among the twelve points of contact. One other advantage associated with the design of the ball thrust bearing  30  is that it is to some degree self-adjusting if the applied thrust is a few degrees off center from its axis of rotation since the middle bearing ball  70  will continue to distribute the thrust load uniformly or very near uniformly despite minor misalignment. By contrast, a normal thrust bearing requires all balls in a circular cage to be equally loaded for best operation and life; otherwise one of the bearing balls is pinched in one area and unloaded on the other side. Hence conventional thrust bearings under high loads are much less able to accommodate off-center load misalignments. 
     The bearing balls  58   a ,  58   b  and  58   c  and  64   a ,  64   b  and  64   c  and  70  are all preferably formed from high tensile strength steel, such as ASTM A514. Such a material has a Young&#39;s Modulus of over 29,000,000 psi and a yield strength on the order of 690 Mpa or over 100,000 psi. Such material properties allows the thrust bearing  30  to bear very high compressive loads as each of the bearing balls  58   a ,  58   b  and  58   c  and  64   a ,  64   b  and  64   c  and  70  elastically deforms at its points of contact with adjacent bearing balls and the walls of the stator cup  51  and rotor cup  61  during operation, and constantly springs back into its original shape as these points of contact move around its spherical outer surface. Stainless steel may also be advantageously used and has the added benefit of corrosion resistance. 
     The combination of the vertical orientation of the shaft assembly  20  and the cageless ball thrust bearing  30  results in several mechanical synergies. First, such a combination requires only a single, high-load bearing  30  in order to operate. By contrast, energy-storing flywheels having horizontal axes require two high-load bearings, thereby increasing the expense of the flywheel assembly. Second, the wear on the single high-load bearing  30  is highly uniform, whereas the wear on the pair of high-load bearings used in horizontal shaft flywheel assemblies is concentrated around the lower half of the bearings. Finally, the high load applied to the thrust bearing  30  by the flywheel  35  advantageously serves to separate the lower and upper bearing balls  58   a ,  58   b  and  58   c  and  64   a ,  64   b  and  64   c  120° apart around the stator and rotor, thereby obviating the need for cages for separating the bearing balls. 
       FIGS. 6A-6I  illustrate other advantages associated with the ball thrust bearing  30  of the invention. These figures are based on empirical tests conducted by the applicant, and illustrate both the orbital and rotational movement of the bearing balls within the recess  52  of the stator  50  of the bearing  30  throughout eighteen rotations of the shaft assembly  20 . Throughout these eighteen rotations, the three bearing balls  58   a ,  58   b  and  58   c  orbit the annular wall of the recess  52  twice, which is expected. What is not expected is the finding the bearing balls  58   a ,  58   b  and  58   c  do not rotate in any discernible pattern while orbiting the recess  52 . More specifically, the bearing balls  58   a ,  58   b  and  58   c  do not rotate around a single axis as they orbit. While  FIGS. 6A-6I  illustrate only two orbits the three bearing balls  58   a ,  58   b  and  58   c , the applicant has confirmed the lack of any discernible pattern in ball rotation over many more orbits than the ones illustrated. This same last of discernible rotational pattern may be reasonably inferred to apply to the upper set of bearing balls  64   a ,  64   b  and  64   c . There are two substantial advantages associated with the non-patterned bearing ball rotation. First, the results of the applicant&#39;s tests indicate that wear over the surfaces of the bearing balls  58   a ,  58   b  and  58   c  and  64   a ,  64   b  and  64   c  will be uniform instead of concentrated at specific points on the bearing balls. Secondly, these test results indicate that lubricant from the outlet  54  will be spread evenly over the surfaces of all the bearing balls  58   a ,  58   b  and  58   c  and  64   a ,  64   b  and  64   c  and the middle ball  70 . 
     As an example of the amount of kinetic energy that the flywheel and bearing assembly  1  is capable of storing, let us assume that the flywheel  35  of the assembly  1  illustrated in  FIGS. 1A-3  consisted of three flywheel sections  37   a - 37   c  that were 7 feet in diameter and one foot in thickness (even though a more preferred thickness is four inches). Let us assume further that the flywheel sections are made from an 80%-20% mixture of pelletized steel and HDPE. Since the volume of a cylinder is V=πR 2 h, the volume of such a flywheel would be (3.1416) (12.25 ft. 2 ) (3 ft.)=115.45 ft. 3  Since the density of the flywheel would be 403 lbs./ft. 3 , the total mass of the flywheel  35  would be 46,528 lbs. To avoid breaking the sound barrier, let us further assume that the flywheel was initially rotated at a speed of 3000 rpms (or 50 rotations per second). At such a rotational speed, the outer edge of the rims  39  of the flywheel sections  37   a - 37   c  would be moving at a linear speed of 1100 ft. per second, which is just under the sea level supersonic limit of 1126 ft. per second. The energy of a rotating disc may be computed according the following formula:
 
 E   k =¼ω 2   MR   2  
 
In the above formula, E equals energy, ω=radians per second, M=mass of the flywheel, and R=the radius of the flywheel. Accordingly, if ω=314 radians per second, M=46,528 lbs., and R 2 =12.25 ft. 2 , the total energy in foot pounds is (0.25)×(98,596)×(46,528)×(12.25)=14,049,141,230 ft.lbs. Since 1 kilowatt hour (kWh)=2,655,223.74 foot pounds (ft lb), the flywheel and bearing assembly  1  of this example would be storing 5,291 kilowatt hours of energy. According to some authorities, the average power consumption of a residential power customer in the US is 940 kilowatt hours (kWh) per month. Accordingly the energy stored in the aforementioned example of a flywheel and bearing assembly  1  of the invention could supply such a residential power customer with electricity for about five and a half months (assuming no frictional losses).
 
     The invention has been described in detail with particular reference to certain preferred embodiments thereof, but it will be understood that variations and modifications can be effected within the spirit and scope of the invention. For example, a below-ground embodiment of the flywheel and bearing assembly can be made which largely obviates the need for a support frame  3 . In such an alternative embodiment of the invention, the top member  10  and bearing plate  13  would be detachably mounted via bolts or the like in bridge-like fashion over the center of the recess containing the assembly  1 . The flywheel  28  would be mounted on the top end of the spindle  22  above the bearing plate  13  to afford easy access to a drive belt.