WO2010017410A2

WO2010017410A2 - Rotor-stator assemblies with catenoid shaped surfaces for motor and generator applications

Info

Publication number: WO2010017410A2
Application number: PCT/US2009/053035
Authority: WO
Inventors: Chong Kyu Kim
Original assignee: Infinite Wind Energy LLC
Priority date: 2008-08-06
Filing date: 2009-08-06
Publication date: 2010-02-11
Also published as: KR20110049841A; WO2010017410A3; KR101247779B1

Abstract

A rotor-stator assembly for use in an electric motor or generator having hyperbolic cosine curve shaped surfaces.

Description

ROTOR-STATOR ASSEMBLIES WITH CATENOID SHAPED SURFACES FOR MOTOR AND GENERATOR APPLICATIONS

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of priority from the following U.S. patent applications: U.S. Patent Application No. 12/222,272, entitled "Hyper- Surface Wind Generator," filed on August 6, 2008; U.S. Patent Application No. 12/191,917, entitled "Motors Having a Hyperbolic Cosine Curve Shape," filed on August 14, 2008; and U.S. Patent Application No. 61/099,513, entitled "Catenoid Balanced Generator Embedded in Induction Motor," filed on September 23, 2008.

BACKGROUND

A variety of electrical generators and motors are known. Electrical generators convert mechanical energy into electrical energy using electromagnetic induction. Generators can be driven by a number of power sources, including wind.

The two principal types of motors available currently are alternating current (AC) motors and direct current (DC) motors. AC motors are commonly referred to as induction motors. Induction motors are widely used and are generally the preferred choice for industrial motors due to their simple, rugged construction, lack of brushes, low cost to manufacture, and the ability to control the speed of the motor. Unlike other motors, induction motors have a rotor that is not connected to an external source of voltage. The stator of an induction motor consists of wound poles that carry the supply current that induces a rotating magnetic field in the conductor, which in turn cause the rotor to turn. Because the rotor is free to turn, it follows the rotating magnetic field in the stator.

To establish a rotating magnetic field in the stator of an induction motor, the number of electromagnetic pole pairs must be the same as (or a multiple of, i.e. 2, 4, 6, etc.) the number of phases in the applied voltage. The poles must be displaced from each other by an angle equal to the phase angle between the individual phases of the applied voltage. However, for these currents to be induced, the speed of the physical rotor and the speed of the rotating magnetic field in the stator must be different, or else the magnetic field will not be moving relative to the rotor and no current will be induced.

DC motors operate by placing a current-carrying conductor (an armature) in a magnetic field perpendicular to the lines of flux. The conductor then moves in a direction perpendicular to the magnetic lines of flux. A DC motor rotates as a result of two magnetic fields interacting with each other. Voltage is transmitted through the armature coils by sliding contacts or brushes that are connected to a DC voltage source. The brushes are found on the end of the coil wires and make a temporary electrical connection with the DC voltage source.

SUMMARY

The present invention relates to motors and generators, in particular to those having a rotor and stator comprising a hyperbolic cosine curve shaped surface. Such rotor-stator assemblies provide better balance, higher torque, and greater efficiency.

In one embodiment, the present invention comprises an improved motor having a hyperbolic cosine curve shaped stator and a matching hyperbolic cosine curve shaped rotor electromagnetically coupled to the stator, which provides higher torque and better motor balance than prior motors. The motor can be an induction motor, a direct current motor, or a universal motor. Preferably, the motor is an induction motor and comprises slots in the hyperbolic cosine curve shape of the stator for accommodating a primary winding to generate a rotary magnetic field when electricity is applied to the primary winding. Such an induction motor can further comprise slots in the hyperbolic cosine curve shape of the rotor for a secondary winding to generate a torque by an electromagnetic induction between the secondary winding and the primary winding when electricity is applied to the primary winding.

In an induction motor according to the present invention, the rotor and the stator preferably have the same hyperbolic cosine curve shape, and this shape is preferably a catenoid. In one embodiment, the rotor of the induction motor can comprise two or more hyperbolic cosine curve shaped rotor portions, or alternatively can comprise a first half- hyperbolic cosine curve shaped rotor portion and a second half- hyperbolic cosine curve shaped rotor portion. The stator of the present induction motor can likewise comprise two or more hyperbolic cosine curve shaped stator portions, or alternatively can comprise an upper half-hyperbolic cosine shaped stator portion and a lower half -hyperbolic cosine shaped stator portion.

In one embodiment, the present induction motor has a stator that comprises a stator cage having 3 or more stator elements. The stator elements are each laminated, and each layer of lamination comprises a hyperbolic cosine curve shape. Such a stator can further comprise wire coils looped around each of the stator elements to create electromagnets. In this embodiment, the stator elements are preferably electrically 120 degrees apart from each other.

In a further embodiment, the present motor is a direct current motor. The stator of such a direct current motor preferably comprises two or more electromagnetic field poles, and the electromagnetic field poles preferably comprise coils of insulated copper wire wound on conductive cores in a hyperbolic cosine curve shape. This direct current motor can also include an armature rotor having a hyperbolic cosine curve shape.

Preferably, the rotor and the stator of a DC motor according to the present invention have the same hyperbolic cosine curve shape, which can be a catenoid. Such a direct current motor can be manufactured from a first half-hyperbolic cosine curve shaped rotor portion and a second half- hyperbolic cosine curve shaped rotor portion, or alternatively from two or more hyperbolic cosine curve shaped rotor portions. The stator can likewise comprise an upper half-hyperbolic cosine curve shaped stator portion and a lower half-hyperbolic cosine curve shaped stator portion, or alternatively can comprise two or more hyperbolic cosine curve shaped stator portions.

Another aspect of the present invention comprises methods of constructing an induction or DC motor. In one embodiment, this method can comprise the steps of: providing a catenoid shaped stator having a first end and a second end; providing a first half-catenoid shaped rotor portion to be inserted in the first end of the stator; providing a second half-catenoid shaped rotor portion to be inserted in the second end of the stator; aligning the first half-catenoid shaped rotor portion and the second half-catenoid shaped rotor portion to balance the motor; and connecting the first half-catenoid shaped rotor portion and the second half-catenoid shaped rotor portion.

In another embodiment of a method for constructing an induction motor, the method includes the steps of: providing a catenoid shaped rotor; providing an upper half-catenoid shaped stator portion to cover the upper portion of the rotor; providing a lower half-catenoid shaped stator portion to cover the lower portion of the rotor; aligning the upper stator portion and the lower stator portion to balance the motor; and connecting the upper stator portion to the lower stator portion enclosing the rotor.

A method of constructing a direct current motor according to the present invention can comprise the following steps: providing a catenoid shaped stator having a first end and a second end; providing a first half-catenoid shaped rotor portion to be inserted in the first end of the stator; providing a second half-catenoid shaped rotor portion to be inserted in the second end of the stator; aligning the first half-catenoid shaped rotor portion and the second half-catenoid shaped rotor portion to balance the motor; and connecting the first half-catenoid shaped rotor portion and the second half-catenoid shaped rotor portion.

In a further embodiment, a direct current motor according to the present invention can be manufactured by a method having the following steps: providing a catenoid shaped rotor; providing a upper half-catenoid shaped stator portion to cover the upper portion of the rotor; providing a lower half-catenoid shaped stator portion to cover the lower portion of the rotor; aligning the upper stator portion and the lower stator portion to balance the motor; and connecting the upper stator portion to the lower stator portion enclosing the rotor.

A further embodiment is directed to a stackable wind generator in which a plurality of rotors are stacked in parallel. Such generators are capable of generating a large amount of electrical energy, provide high efficiency, and suppress vibration in undesired direction. In particular, the present stackable hyper-surface wind generator includes a plurality of stator plates, a plurality of rotor plates and a plurality of blades capable of driving the plurality of rotor plates, wherein rotation of the plurality of rotor plates relative to the plurality of stator plates induces electricity in a plurality of coils disposed on each stator plate, and wherein at least one of the stator plates and the rotor plates are arranged co-axially with a shaft such that respective radii of the at least one of the stator plates and rotor plates are varied along the axial direction.

In another aspect, an electric generator capable of generating electric power using kinetic energy of wind includes a first plurality of rotor plates, a second plurality of rotor plates, and a first plurality of blades capable of driving the first plurality of rotor plates, a second plurality of blades being formed to enable counter-rotation with respect to the first plurality of blades, wherein rotation of the first plurality of rotor plates relative to the second plurality of rotor plates induces electricity in a plurality of coils disposed on the second plurality of rotor plates, and wherein at least one of the first and second plurality of rotor plates are arranged co-axially with the shaft such that respective radii of the at least one of the first and second plurality of rotor plates are varied along the axial direction.

DRAWINGS

Figure 1 is a perspective view of a catenoid.

Figure 2 is a perspective view of an inverse-catenoid.

Figure 3 is a diagram of a bar magnet illustrating magnet fields around the bar magnet.

Figure 4 is a graph of a torus and a hyperbolic cosine function of a catenary curve.

Figure 5 is a perspective view of a hyperbolic cosine curve shaped stator according to one embodiment of the present invention. Figure 6 is a perspective view of a hyperbolic cosine curve shaped rotor according to another embodiment of the present invention.

Figure 7 is an exploded view of a catenoid rotor according to one embodiment of the present invention.

Figure 8 is a perspective view of a complete catenoid induction motor according to a further embodiment of the present invention.

Figure 9A is a plan cross- sectional view of a prior art direct current motor.

Figure 9B is a perspective cross-sectional view of the prior art direct current motor of Figure 12A.

Figure 1OA is a plan cross-sectional view of a hyperbolic cosine curve shaped direct current motor according to another embodiment of the present invention.

Figure 1OB is a perspective cross-sectional view of the hyperbolic cosine curve shaped direct current motor of Figure 13 A.

Figure 11 is a perspective view of a vertical-axis wind turbine (VAWT) generator according to an exemplary embodiment of the present invention.

Figure 12 is a perspective view of a stackable rotors and stators within the VAWT generator according to the exemplary embodiment of Figure 10.

Figure 13 is a perspective view of a single stator including a plurality of coils within the VAWT generator according to the exemplary embodiment of Figure 10.

Figure 14 is a cross-sectional view of a stackable rotors and stators within the VAWT generator according to the exemplary embodiment of Figure 10.

Figure 15 is a side view of the stackable stators within the VAWT generator according to the exemplary embodiment of Figure 10.

Figure 16 is a perspective view of a counter-rotating vertical-axis wind turbine (VAWT) generator according to another exemplary embodiment of the present invention.

Figure 17 is a perspective view of a stackable rotors and stators within the counter- rotating VAWT generator according to the exemplary embodiment of Figure 16.

Figure 18 is a perspective view of a single stator including a plurality of coils within the counter-rotating VAWT generator according to the exemplary embodiment of Figure 16.

Figure 19 is a cross-sectional view of a stackable rotors and stators within the counter-rotating VAWT generator according to the exemplary embodiment of Figure 16. Figure 2OA is a perspective view of the counter-rotatable inner pipe within the VAWT generator according to the exemplary embodiment of Figure 16.

Figure 2OB is a perspective view of the counter-rotatable outer pipe within the VAWT generator according to the exemplary embodiment of Figure 16.

Figure 2OC is a perspective view of the counter-rotating pipes within the VAWT generator according to the exemplary embodiment of Figure 16.

Figures 21A-12C are perspective views showing the method of making the counter-rotating VAWT generator according to the exemplary embodiment of Figure 16.

Figure 22 is a side view of the stackable rotor segments within the counter-rotating VAWT generator according to the exemplary embodiment of Figure 16.

Figures 23 A-C are front view, perspective view, and side view of a horizontal-axis wind turbine (HAWT) generator according to another exemplary embodiment of the present invention.

Figure 24 is a perspective view of a stackable rotors within the HAWT generator according to the exemplary embodiment of Figures 23 A-C.

Figure 25 is a perspective view of a stackable rotors and stators within the HAWT generator according to the exemplary embodiment of Figures 23 A-C.

Figure 26 is a side view of a stackable rotors and stators within the HAWT generator according to the exemplary embodiment of Figures 23 A-C.

Figure 27 is a side elevation view of an embodiment of a combined catenoid motor and generator.

Figure 28 is an illustration of a fan comprising a catenoid generator superimposed over a graph.

Figure 29 is a perspective view of an embodiment of an induction motor and generator combination.

Figure 30 is a perspective view of another embodiment of an induction motor and generator combination.

Figure 31 is a perspective view of yet another embodiment of an induction motor and generator combination. DETAILED DESCRIPTION

In describing the features of this invention, the following terms and variations thereof are used, and such terms have the meanings given below, unless a different meaning is clearly intended by the context in which such term is used.

"Cage" refers to the short-circuiting end rings of a squirrel cage rotor that complete the "squirrel cage" which rotates when a moving magnetic field induces current in the shorted conductors.

"Catenary" refers to a curve with the Cartesian equation of y = a cosh(jc/α), such as is formed by a flexible cable of uniform density hanging from two points under its own weight. For example, cables of suspension bridges and cables attached to telephone poles form this shape.

"Catenoid" refers to a three-dimensional shape made by rotating a catenary curve around an x-axis in a Cartesian coordinate plane.

"Catenoid form" refers to a three-dimensional shape made by rotating either a hyperbolic cosine curve or an inverse hyperbolic cosine curve around an x-axis in a Cartesian coordinate plane. Catenoids and inverse catenoids are catenoid forms. A "substantially catenoid form" or similar referent refers to a shape which differs from a catenoid form by less than 10%, such that the surface of a rotor or stator comprising a substantially catenoid form can be closer or further from an axis of rotation of the rotor or stator by up to 10%. In the present disclosure, references to catenoid forms are generally understood to comprise substantially catenoid forms unless otherwise indicated or required.

"Commutation" refers to the process by which a DC voltage output is taken from an armature that has an alternating current voltage induced in it.

"Hyperbolic cosine curve shape" refers to a three-dimensional shape made by rotating a hyperbolic cosine curve around an x-axis in a Cartesian coordinate plane.

"Rotor" refers to the rotating component of a motor, generator or alternator, typically constructed of a laminated, cylindrical iron core with slots for receiving conductors, such as, for example, cast-aluminum conductors or copper conductors.

"Stator" refers to a fixed part of a motor, generator or alternator that does not rotate, typically consisting of copper windings within steel laminations. "Torus" refers to a surface of revolution generated by revolving a circle in three dimensional space about an axis coplanar with the circle, which does not touch the circle. For example, a donut or an inner tube are each examples of a torus.

"Winding" refers to a coil or coils, typically made of copper wire, wrapped around a core, usually of steel. In an alternating current induction motor, a primary winding is the stator, typically consisting of wire coils inserted into slots within steel laminations. A secondary winding of an alternating current induction motor is typically the rotor.

"Universal motor" refers to a motor that can use either an alternating current power supply or a direct current power supply.

The term "comprise" and variations of the term, such as "comprising" and "comprises," are not intended to exclude other additives, components, integers or steps. The terms "a," "an," and "the" and similar referents used herein are to be construed to cover both the singular and the plural unless their usage in context indicates otherwise.

Catenoid Forms

The present motors, generators, and combinations thereof comprise stators and rotors which have an outer surface or surfaces that comprise a hyperbolic cosine curve shape or an inverse hyperbolic cosine curve shape. Through the use of such rotors and stators, the present motors and generators are more balanced, and in addition can be more efficient since they pass through more of the electromagnetic field generated by the rotation of the motor or generator.

A catenoid, shown in Figure 1, is a surface of revolution that can be expressed in the following form (Equation 1):

x(u,v) = a-cos(u)-cosh(v/a) y(u,v) = a-cosh(v/a)-sin(u) z(u,v) = v An inverse catenoid, shown in Figure 2, is a surface of revolution that can be expressed in the following form (Equation 2):

x(u,v) = sech(u)-cos(v) y(u,v) = sech(u)-sin(v) z(u,v) = u-tanh(u)

The advantage of using catenoid forms in the present motors, for example, can be seen with reference to Figure 1. Torque in the catenoid 700 increases as the radius 704 of the catenoid 700 increases as a function of cosh(x), and motors with rotors comprising catenoid surfaces thus generate increased torque by matching the radius 704 of a catenoid instead of taking a cylinder shape, as in prior motors. The use of catenoid forms in generator applications likewise generates more energy than present generators due to the increase in torque.

In addition to providing increased force and energy, catenoid forms, such as the catenoid 700, will provide better balance than a cylinder. A center of mass 702 can be derived for the catenoid 700 and is approximately half the distance from the end points 705, while an inertial mass for the catenoid 700 can be calculated as the sum of a circular disk at the end points 705 of the catenoid 700. Therefore, a catenoid shaped rotor has a center of mass 702 at a midpoint but an inertial mass located on the hyperbolic radius 704, whereas a cylinder has its center of mass and its inertial mass at the midpoint.

The advantage of rotors and stators comprising catenoid forms can be elucidated with reference to Figures 3 and 4. Figure 3 illustrates the magnet fields 406 surrounding a bar magnet 400, which include a first magnetic field point 402, the strongest and straightest point on the bar magnet 400, and a second magnetic field point 404 representing a curved portion of the magnetic fields 406 surrounding the bar magnet 400. The second magnetic field point 404 will have as many magnetic fields 406 as the first magnetic field point 402, because the first magnetic field point 402 and the second magnetic field point 404 are both curved magnetic fields.

Prior induction motors and generators use the straightest area of magnetic fields, the first magnetic field point 402, to produce torque or energy. By contrast, the present rotors and stators produce energy or induce force at curved points relative to a second magnetic field point 404. Due to the inherent curve of the magnetic fields 406, the straightest point on the field is in fact a curve.

Figure 4 is a graph of a torus 602 and a hyperbolic cosine function of a catenary curve 604 and 606. As can be seen, the arc of the hyperbolic cosine function 604 fits into a portion of the torus circle 602. A square 608 is graphed at the point (0.5, 0.5), (0.5, 0.5) on the Cartesian plane to better illustrated the plotted curve functions. An arc portion of the torus circle 602 can be set to match the hyperbolic cosine 604 or inverse hyperbolic cosine function, with the range of the arc point located at 0 to 0.5 of the x-axis. This mathematical function shows that the catenoid 604 can be embedded directly into the torus at the lower range. The arc of the circle that is formed in the torus circle 602 is a hyperbolic cosine function, and more particularly a catenary 604. The torus 602 and the catenoid 604 are two different shapes, but share a common arc point of the circle at Cartesian coordinates 0 to 0.5 on the x axis of the graph. As can be seen, the maximum Cartesian coordinate y value of the catenary curve is 1.2, which is a 20% radial increase from the end of the square 608.

The surfaces of the present rotors and stators that comprise catenoid forms preferably conform to (match) a catenoid or inverse catenoid shape precisely. However it is to be understood that differences in the diameters of the present rotors, stators, or portions thereof can result in deviations from the shape of a catenoid or inverse catenoid of up to 10%, such that the surface of a rotor or stator can be closer or further from an axis of rotation of the rotor or stator by up to 10%, in which case the distance between an axis of rotation of the rotor- stator assembly and the surface of the rotor or stator is greater than or less than a mathematically derived catenoid form by 10%. Such differences may result from manufacturing tolerances or from other design parameters in particular embodiments. Preferably, rotor and stator surfaces deviate by less then 5% from a mathematically derived catenoid form, more preferably by less then 2%, and even more preferably by less than 1%.

Rotor- Stator Assemblies

The stators and rotors of the present rotor- stator assemblies comprise a surface or surfaces having a hyperbolic cosine curve shape or an inverse hyperbolic cosine curve shape. In one embodiment, only the rotor of a rotor-stator assembly comprises a surface having a catenoid form, which provides greater balance to the assembly during rotation of the rotor. In order to achieve the maximum efficiency and torque from the assembly, however, preferably both the rotor and stator comprise surfaces having a catenoid form.

In a preferred embodiment, the surface of a rotor or stator having a catenoid form is a continuous surface. The catenoid surface 901 of the rotor 900 of Figure 6, for example, and the rotor-stator assembly of Figures 1OA and 1OB exemplify such continuous surfaces. Alternatively, rotors and/or stators can be formed from discontinuous segments or portions whose outer surfaces contact the boundaries of a catenoid form, and thus comprise and conform to the catenoid form. In aggregate, the outer surfaces in such a rotor thus comprise a catenoid form, but in a discontinuous fashion. Figures 12 and 17 exemplify rotors (150 and 1050, respectively) made from segments whose outer surfaces comprise an inverse catenoid (190C and 1090C, respectively), i.e. such outer surfaces conform to the surface of a catenoid form.

A variety of types of rotors and stators can be used in the present rotor-stator assemblies. In induction motors and generators, the rotor can be for example a squirrel-cage rotor. Such rotors generally comprise bars of either solid copper or aluminum that span the length of the rotor, and are connected through a ring at each end, forming a cage-like shape. The core of a squirrel-cage rotor is typically built of a stack of iron laminations. The conductors in this type of rotor, however, need to be skewed slightly along the length of the rotor to reduce noise and smooth out torque fluctuations that occur due to interactions with the pole pieces of the stator.

Slip ring rotors can also be used in the present assemblies. A slip ring rotor makes an electrical connection through a rotating assembly, and generally requires the use of slip rings, also called rotary electrical interfaces, rotating electrical connectors, collectors, swivels or electrical rotary joints, which consist of a conductive circle or band mounted on a shaft and insulated from it. Electricity is transferred from the rotor to the slip ring using fixed contacts or brushes that are in contact with the slip ring.

Other rotor-stator assemblies can also comprise surfaces having a catenoid form, as described herein. For example, DC motors can also comprise such rotors and stators, as shown in Figures 1OA and 1OB. Motors

Figure 5 illustrates a stator 800 comprising a hyperbolic cosine curve shaped surface for use in a motor of the present invention. In a preferred embodiment, the surface is a catenoid. The catenoid shaped stator 800 comprises stator elements 802, 804, 806 that are laminated and form a catenoid shaped cage 808 with catenoid shaped curves created by the stator elements 802, 804, 806. In one embodiment, a wire coil can be looped around each stator element 802, 804, 806 to create electromagnets that are electrically 120 degrees apart, for a three phase motor.

Figure 6 shows a hyperbolic cosine shaped rotor 900 according to one embodiment of the present invention. While hyperbolic cosine shaped rotors and stators are preferably solid, manufacturing or cost considerations may dictate that they not be entirely solid or that they be manufactured in pieces that are then joined. For example, in a preferred embodiment, two or more catenoid rotor portions 902 and 904 can be manufactured separately and joined together around the motor shaft 910 to form a complete catenoid shaped rotor 900 inside the catenoid shaped stator 800. In one embodiment, the steel rings 906 and 908 can comprise male to female connections for joining the two halves together. In another embodiment, copper end rings 914 and 916 can comprise holes where threaded rods can be placed to lock the two half catenoid rotor portions 902 and 904 together.

As discussed above, the catenoid shaped rotor 900 and the catenoid shaped stator 800 provide more torque and better balance than a traditional cylinder shaped rotor 102. Additionally, the outer radial portion 914 of the catenoid shaped rotor 900 provides more balance to the motor. Thick copper wire 916 can be placed on the surface of a laminated steel disk 918 that is curved along a hyperbolic cosine function to provide the induction between the rotating magnetic field of the catenoid shaped stator 800 and the catenoid shaped rotor 900. In one embodiment, a laminated steel disk 914 supports the thick copper wire 916 and is shorted at the end points so it will not interfere with the electromagnetic fields induced into the catenoid shaped rotor 900 by the catenoid shaped stator 800. Thicker steel rings 906 and 908 can be used to mate the two half catenoid rotor portions 902 and 904. Figure 7 illustrates a fully assembled catenoid rotor according to one embodiment of the present invention. A motor shaft 952 is placed through the center of the catenoid rotor 950 and locked into place using collars 954 and 956. Figure 8 shows a complete catenoid induction motor 960 according to one embodiment of the present invention. The motor 960 comprises the catenoid rotor 962 that is electromagnetically connected to the stator 964. The catenoid rotor 962 is physically connected to a load 966 to perform work.

Referring now to Figures 9A and 9B, there is shown a cross sectional view of a prior art direct current motor 1200. As can be seen, a typical prior art direct current motor 1200, or direct current generator depending upon the configuration of the motor, comprises a cylindrical shaped stator portion 1202 that is electromagnetically connected to a cylindrical shaped rotor portion 1204. The DC motor comprises stationary magnetic field poles and an armature that turns on bearings in the space between the field poles. The armature of a DC motor typically comprises windings connected to commutator segments.

The disadvantages of the prior art direct current motor 1200 comes from the shape of the rotor 1204 and stator 1202. The prior art direct current motor 1300 either produces movement or generates electricity by cutting electromagnetic flux lines of force. However, the cylindrical shape of the prior art direct current motor only interacts with a small portion of the electromagnetic flux lines of force, thereby reducing the efficiency.

Referring now to Figures 1OA and 1OB, there is shown a cross-sectional view of a hyperbolic cosine curve shaped direct current motor 1300 according to another embodiment of the present invention. The stator 1302 comprises two or more electromagnetic field poles. The two or more electromagnetic field poles can comprise coils of insulated copper wire wound on conductive cores in a hyperbolic cosine curve shape. The direct current motor 1300 also has an armature rotor 1304 having a hyperbolic cosine curve shape. In a preferred embodiment, the rotor 1304 and the stator 1302 have the same hyperbolic cosine curve shape, such that the surface of the rotor 1304 that faces the stator 1302 is the inverse of the surface of the stator 1302 that faces the rotor 1304. In a particularly preferred embodiment, the hyperbolic cosine curve shape is a catenoid.

To construct the direct current motor 1300, two portions of the rotor 1304 can be constructed separately so that the rotor 1304 comprises a first half -hyperbolic cosine shaped rotor portion and a second half- hyperbolic cosine curve shaped rotor portion. Another method to construct the direct current motor 1300 is to have the rotor comprise two or more hyperbolic cosine curve shaped rotor portions that are assembled inside the stator 1302 portion of the direct current motor 1300. Alternatively, the stator 1302 can be constructed in portions such that the stator 1302 comprises an upper half -hyperbolic cosine curve shaped stator portion and a lower half-hyperbolic cosine curve shaped stator portion that can be placed around a rotor 1304, which can be constructed in separate pieces as previously described or as a single complete unit. In a preferred embodiment, the stator 1302 comprises two or more catenoid shaped stator portions that can be constructed and assembled around the rotor 1304. Although AC and DC motors have been described herein separately, one of skill in the art will appreciate that a universal motor (having both an induction motor and a direct current motor) can comprise hyperbolic cosine curve shaped rotors and stators as described herein.

Generators

When an inductive element, i.e., a wire or a coil, is placed within a magnetic field and when the inductive element rotates within the magnetic field, current is induced within the inductive element. The magnitude of the induced current depends on the strength of the magnetic field, the length of the inductive element, and the speed with which the inductive element moves within the magnetic field. The strength of the magnetic field can be enhanced by using magnets with higher magnetization. However, there are limitations on the strength of the magnets due to intrinsic material properties. Accordingly, in accordance with aspects of the present invention, efficiency of a generator is enhanced by changing the structure and design of the generator. In an exemplary embodiment of the present invention, a plurality of rotors and a plurality of stators are stacked to enhance efficiency, thereby increasing the magnitude of the induced current.

Figure 11 is a perspective view of a vertical-axis wind turbine (VAWT) generator according to an exemplary embodiment of the present invention. Figure 12 is a perspective view of a stackable rotors and stators within the VAWT generator according to the exemplary embodiment of Figure 11, Figure 13 is a perspective view of a single stator including a plurality of coils within the VAWT generator according to the exemplary embodiment of Figure 11, and Figure 14 is a cross-sectional view of a stackable rotors and stators within the VAWT generator according to the exemplary embodiment of Figure 11. Key advantages of the VAWT arrangement are that the blades 130 do not have to be pointed into the wind to generate electricity. This is an advantage on sites where the wind direction is highly variable. In other words, VAWTs can utilize winds from varying directions. Vertical-axis turbine generators 100 can be installed on the ground. Alternatively, because the speed of wind is generally faster at a higher altitude, vertical-axis turbine generators 100 can be mounted on towers or building rooftops.

As shown in Figures 11-14, an exemplary embodiment of a VAWT generator 100 according to the present invention includes a frame 110, a shaft 120 that is rotatably connected to the frame 110, a plurality of blades 130 that are connected to the shaft 120 through a base 140, a plurality of rotors 150 including a plurality of permanent magnets 150M, which are connected to the rotatable shaft 120, and a plurality of stators 180 including a plurality of coils 180C . The plurality of stators 180 and plurality of rotors 150 within the VAWTs are vertically arranged. The rotating blades 130 within the VAWT generator 100 convert the kinetic energy of wind into rotational momentum of a shaft 120 independent of the direction of the wind. When the plurality of rotors 150 rotate, the plurality of coils 180C and the wires 180W within the plurality of stators 180 experiences change in the magnetic field generated by the plurality of permanent magnets 150M within the plurality of rotors 150. Accordingly, electricity is generated in the plurality of coils 180C and wires 180W within the plurality of stators 180.

As shown in Figures 12 and 14, a plurality of rotors 150 includes a plurality of rotor plates 150P and a plurality of alternating magnets 150M. The plurality of rotor plates 150P are fixed with one another by rods 160. Each rotor 150 is interposed between each stator 180 and is stacked to enhance the efficiency of the generator 100, thereby increasing the overall magnitude of the induced current.

As shown in Figure 13, there are three sets of wires 180W on each stator 180 that electrically connect the plurality of coils 180C to one another within a single stator plate 180P. Of course, more or fewer sets of wires can be used. Although not completely shown, each coil 180C has input and output wires. The input and output wires of each coil that form the three pairs of wires 180W that electrically connect the plurality of coils 180C to one another are shown in Figure 13. However, the input and output wires of each coil that are connected to pass through the holes 170H within the hub 170 are not shown. Stabilizing screws 170S can be used to cast the wires together with the hub 170. The holes 170H within the hub 170 are used to pass the wires through to the next stack of stator 180. The hub 170 may be made of metal, including aluminum, or other suitable material.

In an exemplary embodiment of the present invention, the wind generator 100 is reliable and stable because vibration in undesired directions due to turbulence can be suppressed. Angular momentum of an object rotating around a reference point is a measure of the extent to which the object will continue to rotate around that point unless an external torque is applied. Mathematically, the angular momentum with respect to a point on the axis around which an object rotates is related to the mass of the object, and the distance of the mass to the axis. According to the theory of conversation of angular momentum, a system's angular momentum remains constant unless an external torque acts on it. In other words, torque is the rate at which angular momentum is transferred into or out of the system.

Accordingly, in a closed system, wherein no external torque is applied to the objects within the system, the time derivative of angular momentum, i.e., the torque, is zero. An example of the conservation of angular momentum can be easily seen in an ice skater as he brings his arms and legs closer to the axis of rotation. Because angular momentum is the product of the velocity of the object and the distance of the object to the axis of rotation, the angular velocity of the skater necessarily increases by bringing his body closer to the axis of rotation, thereby decreasing the body's overall moment of inertia.

The plurality of blades 130 of the wind generator 100 are designed to convert linear motions of wind into rotational motions of the plurality of rotors 150. In an ideal condition, the plurality of rotors 150 would only have spin angular momentum wherein the plurality of rotor 150 rotates around the shaft 120. However, because the blades 130 are not ideal and also because the direction of wind is not homogeneous in space, the plurality of rotors 150 not only have spin angular momentum when external torque is applied to the blades 130, but also have non-zero orbital angular momentum. Orbital angular momentum is an orbital motion of the shaft 120 itself, which would cause vibration of the wind generator 100 and further generate friction between the plurality of rotors 150 and the plurality of stators 180. Accordingly, having a non-zero orbital angular momentum would decrease the spin angular momentum thereby degrading the efficiency of the wind generator 100. In the exemplary embodiment of the present invention, the geometric dimensions of the stacked rotors 150 and stators 180 are designed to suppress the orbital angular momentum thereby enhancing the reliability and stability of the wind generator. In a preferred embodiment, the stacked rotors comprise outer surfaces which follow the contours of either a catenoid or inverse catenoid configuration in order to have a larger radial center of mass while maintaining the surface area of the entire generator 100.

Figure 15 is a view of the stackable stators within the VAWT generator according to the exemplary embodiment of Figure 10. In Figure 15, the rotors are not shown to simplify the structure. As shown in Figure 15, the plurality of coils 180C within each layer of stator 180 are structured to form a sphere 190S. In addition, as shown in Figure 12, the plurality of rotor plates 150P are structured to form an inverse catenoid surface 190C. These geometric dimensions of the plurality of rotors 150 and stators 180 suppress the orbital angular momentum of the plurality of rotors 150 and stators 180 thereby enhancing the reliability and stability of the wind generator.

In another exemplary embodiment, the length of the plurality of coils 180C can be varied along the axial direction. More particularly, the length of the plurality of coils 180C can be increased and subsequently decreased along the axial direction.

In another exemplary embodiment, the plurality of coils 180C within each layer of stator 180 and the plurality of rotor plates 150P can be arranged in the axial direction such that respective radii are varied along the axial direction. More particularly, the plurality of coils 180C within each layer of stator 180 can be arranged in the axial direction such that respective radii are linearly increased and subsequently decreased along the axial direction and at the same time, the plurality of rotor plates 150P can be arranged in the axial direction such that respective radii are linearly increased and subsequently decreased along the axial direction. In another exemplary embodiment, the plurality of coils 180C within each layer of stator 180 can be arranged in the axial direction such that respective radii are linearly decreased and subsequently increased along the axial direction and at the same time, the plurality of rotor plates 150P can be arranged in the axial direction such that respective radii are linearly decreased and subsequently increased along the axial direction. In another exemplary embodiment, the plurality of coils 180C within each layer of stator 180 can be structured to form a catenoid surface, and at the same time the plurality of rotor plates 150P can be structured to form a catenoid surface. In another exemplary embodiment, the plurality of coils 180C within each layer of stator 180 can be structured to form an inverse catenoid surface and at the same time, the plurality of rotor plates 150P can be structured to form an inverse catenoid surface. In another exemplary embodiment, the plurality of coils 180C within each layer of stator 180 can be structured to form an inverse catenoid surface and at the same time, the plurality of rotor plates 150P can be structured to form a sphere. In yet another exemplary embodiment, the plurality of coils 180C within each layer of stator 180 can be structured to form a sphere and at the same time, the plurality of rotor plates 150P can be structured to form a sphere.

Figure 16 is a perspective view of a counter-rotating vertical-axis wind turbine (VAWT) generator according to another exemplary embodiment of the present invention, Figure 17 is a perspective view of a stackable rotors and stators within the counter-rotating VAWT generator according to the exemplary embodiment of Figure 16, Figure 18 is a perspective view of a single stator including a plurality of magnets within the counter- rotating VAWT generator according to the exemplary embodiment of Figure 16, and Figure 19 is a cross-sectional view of a stackable rotors and stators within the counter-rotating VAWT generator according to the exemplary embodiment of Figure 16.

In this exemplary embodiment of the present invention, a counter rotation scheme is implemented to enhance the efficiency. In related art generators, kinetic energy is transformed into rotational energy by rotating the rotors. In this embodiment, rather that having the stators fixed, the stators are connected to an additional independent set of blades that are oriented in the opposite direction with respect to the orientation of the set of blades that are connected to the rotors (which will be referred to as the "first plurality of rotors"). Accordingly, the stators will be referred to as the "second plurality of rotors." In other words, there are first plurality of rotors 1050 and second plurality of rotors 1080 that rotate independently of each other wherein the blades 1030B of the second plurality of rotors 1080 are oriented such that the first plurality of rotors 1050 and the second plurality of rotors 1080 counter-rotate.

An exemplary embodiment of the counter-rotating VAWT generator 1000 according to the present invention includes a frame 1010, a shaft 1020 that is rotatably connected to the frame 1010, a first plurality of blades 1030A that are connected to the shaft 1020 through a first base 1040A, a second plurality of blades 1030B that are connected to the shaft 1020 through a second base 1040B, a first plurality of rotors 1050 that are connected to the inner pipe 1020A of the shaft 1020, and a second plurality of rotors 1080 that are connected to the outer pipe 1020B of the shaft 1020. As shown in Figures 7-10, the first plurality of rotors 1050 and the second plurality of rotors 1080 within the counter-rotating VAWTs are vertically arranged.

The first plurality of rotating blades 1030A within the counter-rotating VAWT generator 1000 convert the kinetic energy of the wind into rotational momentum of the inner pipe 1020A. At the same time, the second plurality of rotating blades 1030B converts the same kinetic energy of the wind into a rotational momentum of the outer pipe 1020B, which rotates in the opposite direction of the inner pipe 1020A. Because the first plurality of rotors 1050 rotate in the opposite direction of the second plurality of rotors 1080, the plurality of coils 1080C and the wires 1080W within the second plurality of rotors 1080 experiences twice as fast of a change in the magnetic filed generated by the plurality of permanent magnets 1050M within the first plurality of rotors 1050. Accordingly, electricity is generated in the plurality of coils 1080C and wires 1080W within the second plurality of rotors 1080 more efficiently.

As shown in Figures 8 and 10, a first plurality of rotors 1050 includes a first plurality of rotor plates 1050P and a plurality of alternating magnets 1050M. The first plurality of rotor plates 1050P are fixed with one another by rods 1060. As shown in Figure 18, there are three sets of wires 1080W on each second plurality of rotors 1080 that electrically connect the plurality of coils 1080C to one another within a single rotor plate 1080P. Of course, more or fewer sets of wires can be used. Although not completely shown, each coil 1080C has input and output wires. The input and output wires of each coil that form the three pairs of wires 1080W that electrically connect the plurality of coils 1080C to one another are shown in Figure 13. However, the input and output wires of each coil that are connected to pass through the holes 1070H within the hub 1070 are not shown. Stabilizing screws 1070S can be used to cast the wires together with the hub 1070. The holes 1070H within the hub 1070 are used to pass the wires through to the next stack of rotors 1050 and 1080. The hub 1070 may be made of a metal including aluminum or other suitable material Figure 2OA is a perspective view of the counter-rotatable inner pipe within the VAWT generator according to the exemplary embodiment of Figure 16, Figure 2OB is a perspective view of the counter-rotatable outer pipe within the VAWT generator according to the exemplary embodiment of Figure 16, and Figure 2OC is a perspective view of the counter- rotating pipes within the VAWT generator according to the exemplary embodiment of Figure 16.

As shown in Figure 2OA, a pair of inner bearings 1021 A, a pair of bearing caps 1022B, and the inner pipe holder 1023 are formed to allow the inner pipe 1020A to freely rotate against the inner bearing 1021A. As shown in Figure 2OB, the shaft 1020 comprises an inner pipe 1020A and an outer pipe 1020B that are spaced apart and do not touch each other. The outer bearing 102 IB and the outer bearing cap 1022B are components attached on the top are bottom of the outer pipe 1020B. The inner circumference of outer bearing 102 IB holds the inner pipe 1020A. This allows the outer pipe 1020B to rotate freely along the axis parallel to the inner pipe 1020A. Figure 2OC shows a complete assembly of the counter- rotating pipes 1020A and 1020B, which comprises two sets of bearings that hold each pipe so that each can rotate freely in opposite directions.

Figures 21A-12C are perspective views showing the method of making the counter-rotating VAWT generator according to the exemplary embodiment of the present invention. As shown in Figure 21 A, the first layer of a first plurality of rotor plates 1050P is inserted into the shaft 1020 and rods 1060 and a first layer of the plurality of alternating magnets 1050M are formed thereon. Subsequently, as shown in Figure 21B, the first layer of a second plurality of rotor plates 1080P is inserted into the shaft 1020 and a first layer of the plurality of coils 1080C are formed thereon. In addition, a hub 1070 and a counter-rotatable outer pipe (not shown) are formed to fix the second plurality of rotor plates 1080P. Then, as shown in Figure 21C, the second layer of a first plurality of rotor plates 1050P is inserted into the shaft 1020 and rods 1060 and a second layer of the plurality of alternating magnets 1050M are formed thereon. One of ordinary skill in the art would recognize that this sequence can be repeated until a desired number of layers are formed.

Similar to the VAWT generator according to the first exemplary embodiment, the first and second plurality of blades 1030Aand 1030B of the wind generator 1000 are designed to convert linear motions of wind into rotational motions of the first and second plurality of rotors 1050 and 1080. Because the first and second plurality of blades 1030A and 1030B are generally not ideal and also because the direction of wind is generally not homogeneous in space, the first and second plurality of rotors 1050 and 1080 not only have spin angular momentum when external torque is applied to the first and second plurality of blades 1030A and 1030B, but also have non-zero orbital angular momentum, which would cause vibration of the wind generator 1000 and further generate friction between the first and second plurality of rotors 1050 and 1080. Accordingly, having a non-zero orbital angular momentum would decrease the spin angular momentum, thereby degrading the efficiency of the wind generator 1000.

In the exemplary embodiments of the present invention, the geometric dimensions of the first and second plurality of rotors 1050 and 1080 are designed to suppress the orbital angular momentum thereby enhancing the reliability and stability of the wind generator. Figure 22 is a side view of the stackable rotors within the counter-rotating VAWT generator according to the exemplary embodiment of Figure 16. In Figure 22, the first plurality of rotors 1050 are not shown to simplify the structure. As shown in Figure 22, the plurality of coils 1080C within the second plurality of rotors 1080 are structured to form a sphere 1090S. On the other hand, as shown in Figure 17, the first plurality of rotor plates 1050p are structured to form an inverse catenoid surface 1090C. A catenoid and inverse catenoid surfaces are pseudo-spheres that have the same surface area as a sphere. Accordingly, an advantage of having either a catenoid or inverse catenoid configuration is to have a larger radial center of mass, while maintaining the surface area of the entire generator 100.

On another exemplary embodiment, the length of the plurality of coils 1080C can be varied along the axial direction. More particularly, the length of the plurality of coils 1080C can be increased and subsequently decreased along the axial direction.

In another exemplary embodiment, the first plurality of rotor plates 1050P and the plurality of coils 1080C can be arranged in the axial direction such that respective radii are varied. In another exemplary embodiment, the first plurality of rotor plates 1050P can be arranged in the axial direction such that respective radii are linearly increased and subsequently decreased along the axial direction and at the same time, the plurality of coils 1080C can be arranged in the axial direction such that respective radii are linearly decreased and subsequently increased along the axial direction. In another exemplary embodiment, the first plurality of rotor plates 1050P can be structured to form a catenoid surface and at the same time, the plurality of coils 1080C can be structured to form a catenoid surface. In another exemplary embodiment, the first plurality of rotor plates 1050P can be structured to form an inverse catenoid surface and at the same time, the plurality of coils 1080C can be structured to form an inverse catenoid surface. In another exemplary embodiment, the first plurality of rotor plates 1050P can be structured to form a sphere and at the same time, the plurality of coils 1080C can be structured to form an inverse catenoid surface. In yet another exemplary embodiment, the first plurality of rotor plates 1050P can be structured to form a sphere and at the same time, the plurality of coils 1080C can be structured to form a sphere.

An exemplary embodiment wherein the plurality of stators and the plurality of rotors form catenoid surfaces, thereby forming a catenoid within a catenoid, will be shown in a horizontal-axis wind turbine (HAWT) generator configuration. Figures 23 A-C are front view, perspective view, and side view of a horizontal-axis wind turbine (HAWT) generator according to another exemplary embodiment of the present invention, Figure 24 is a perspective view of a stackable rotors within the HAWT generator according to an exemplary embodiment of Figures 23A-C, Figure 25 is a perspective view of a stackable rotors and stators within the HAWT generator according to the exemplary embodiment of Figures 23A- C, and Figure 26 is a side view of a stackable rotors and stators within the HAWT generator according to the exemplary embodiment of Figures 23 A-C.

An exemplary embodiment of the HAWT generator 2000 according to the present invention includes a frame 2010, a plurality of blades 2020 that are connected to the shaft 2060, which is rotationally connected to the frame 2010, a tail 2030, a cover 2040, a plurality of rods 2050, a plurality of stators 2100 including a plurality of stator plates 2100P and a plurality of coils 2100C, and a plurality of rotors 2200 including a plurality of rotor plates 2200P and a plurality of permanent magnets 2200M.

As shown in Figures 23A- 18, the rotating blades 2020 within the HAWT generator 2000 convert the kinetic energy of the wind into rotational momentum of a shaft 2060. The blades 2020 use engineered airfoils that capture the energy of the wind. However, unlike VAWT generators, the cover 2040 must face the wind for the conversion of kinetic energy of wind into rotational momentum of the shaft 2060. The tail 2030 allows the wind generator 2000 to track the direction of the wind as the wind shifts direction, thereby enabling the cover 2040 and the blades 2020 to turn accordingly to face the wind.

When the plurality of rotors 2200 rotate, the plurality of coils 2100C within the plurality of stators 2100 experience change in the magnetic field generated by the plurality of permanent magnets 2200M within the plurality of rotors 2200. Accordingly, electricity is generated in the plurality of coils 2100C within the plurality of stator 2100.

The plurality of blades 2020 of the wind generator 2000 are designed to convert linear motions of wind into rotational motions of the plurality of rotors 2200. In an ideal condition, the plurality of rotors 2200 would only have spin angular momentum wherein the plurality of rotors 2200 rotates around the shaft 2060. However, because the blades 2020 are not ideal and also because the direction of wind is not homogeneous in space, the plurality of rotors2200 not only have spin angular momentum when external torque is applied to the blades 2020, but also have non-zero orbital angular momentum, which contributes to decreasing the spin angular momentum thereby degrading the efficiency of the wind generator 2000.

In the exemplary embodiment of the present invention, the geometric dimensions of the plurality of rotors 2200 and the plurality of stators 2100 are designed to suppress the orbital angular momentum thereby enhancing the reliability and stability of the wind generator. As shown in Figure 23C, the plurality of stators 2100 and the plurality of rotors 2200 can form catenoid surfaces, thereby forming a catenoid within a catenoid. In addition, as shown in Figure 26, the plurality of stator plates 2100P can be structured to form a catenoid surface while the plurality of rotor plates 2200P are structured to form a cylinder.

In another exemplary embodiment, the plurality of stator plates 2100P can be structured to form an inverse catenoid surface while the plurality of rotor plates 2200P are structured to form a cylinder. In another exemplary embodiment, the plurality of stator plates 2100P can be structured to form an inverse catenoid surface while the plurality of rotor plates 2200P are structured to form a sphere. In yet another exemplary embodiment, both the plurality of stator plates 2100P and the plurality of rotor plates 2200P can be structured to form either an inverse catenoid surface or a sphere. Motor- Generator Combinations

Induction motors have many different applications, all of which involve a load on a shaft for delivering energy. In one embodiment of the present invention, a single or multilayer catenoid generator is included on a shaft together with an induction motor, and in this way three-phase electricity can be generated as a motor is operating at a continuous normal load. Adding a load disk with a radius dictated by hyperbolic function, in particular a hyperbolic cosine function, results in offsetting the load on the shaft. This allows induction motors to operate and generate electricity at the same time.

Figure 27 is an illustration of a catenoid motor which also includes a catenoid generator. In this embodiment of a combined motor and generator device 500, the device 500 includes a coil winding 501, a squirrel cage 502, a base mounter 503 for the motor case, and a stator mount 506. The surface 507 of the squirrel cage rotor 502 of the motor portion 510 of the device 500 comprises a catenoid form 515, and the rotor 505 of the generator portion 511 of the present device 500 likewise comprises a rotating magnet disk whose outer surface conforms to the same catenoid form 515 which forms the surface 507 of the rotor 502 (i.e., an extension of the theoretical catenoid form would contact an outer surface of the rotor 505).

By locating a first generator portion 512 on one axial side of the motor 510 and a second generator portion 513 on a second side of the motor 510, and by conforming the outer peripheries of each of the rotors of the generator portions 512 and 513 to the same catenoid form 515, the AC motor and generator are balanced and can thus coexist in the same device 500. In addition, as electromagnetic strength weakens by the distance squared, the outer layer of a catenoid induction motor has nearly zero fields due to the inverse square nature of magnetic fields, which allows a permanent magnetic disk to be added to the outer layer and be statically balanced. This embodiment of the present invention is preferably used in applications that run continuously for a prolonged period of time, such as fans and compressors.

Currently, motor applications such as fans include a load (fan turbine) on a shaft. This is statically balanced due to the light weight of the turbine relative to the AC motor and its rigid mounting. As a whole, the overall balance to the fan motor is ignored. Depending upon the size of a fan and airflow requirement, the horsepower of current motors is matched up to produce the desired result. Using a hyperbolic cosine function, however, it is possible to balance a fan turbine relative to an induction motor. To do this, the graph of hyperbolic function sech(x) is scaled so that shaft length represents the boundary of the motor and (x) limits. Although the present generator concept can comprise catenoid shapes, this application adapts an existing induction motor into a generator-motor by embedding a catenoid generator that is statically balanced through the use of the hyperbolic function.

An example of this is shown in Figure 28, which shows a fan 520 superimposed over a graph. A single layer generator 526 comprises a rotor-stator assembly having one or more outer surfaces that conform to a catenoid form 527 extended toward the end of the shaft. An example of a counterbalancing load is a three-blade turbine 521, commonly used as commercial exhaust fans with a direct or belt connection. Fan blades are usually an aluminum or composite plastic. This load is a factor that will be referred to as (u). Each blade's center of mass can be found by balancing a wing at a time. The center of mass location is where most of the motor kinetic energy is going to turn the fan for a propeller airflow result. All three blades must be statically balanced. The rotor 503 is part of an induction motor with a shaft 502. The rotating magnetic disk of the generator 526 mounts at plates 524 and 525. To be hyperbolically balanced, the radius of the disk is lsech(x), where the x value can be picked from the graph.

By adjusting the radius of the propeller, its center of mass can meet the boundary of the catenoid form 527. A rotor-stator assembly of the generator portion 526 counter weights the opposite side of the shaft to balance the entire system. By balancing hyperbolically, the whole system is balanced from the turbine to the end of the shaft. Instead of having to use a counter weight disk, a generator having surfaces conforming to a catenoid form balances the overall system.

Figure 29 another embodiment of a combined induction motor and generator. The motor 530 is covered by metal a container with caps and screws that hold the shaft 545 together, as with standard induction motors. A half catenoid generator 544 with a single stator 536 is mounted to the motor 532. Mounting portion 532 locks into a mating portion 531 which is at the base of the generator 544. An alternating magnetic disk 540 is placed using a rotor 537. The motor shaft 545 connects directly to the rotor 537 and a key way is used to lock disk 539. The base and the disk 540 are spaced at 0.25 inch apart via slight shaft enlargement. The alternating magnetic disk does not touch the motor cap 531. This allows the base 532 to have thread rod 535 to hold stator 536. Once the stator and the first layer of the disk are in place, the outer disk 541 can be attached using a screw from 538 to 539. The radius of disks 540 and 541 can be obtained from the graph of Figure 28.

Figure 30 is a perspective view of another embodiment of a combined motor and catenoid generator. 551 is the propeller cap which can be widened to minimize the air flow at the center area because motor cylinder 552 and the catenoid generator 553 tend to block the air flow. This small change with cap size will insure that the flow of air is maximized.

Figure 31 illustrates is a modified industrial blow fan 560. Instead of embedding the catenoid generator 561 coaxially with an induction motor, the generator 561 is mounted to balance the blades of a fan 562, as in the embodiment of Figure 28, but in this case the motor 563 is placed in mechanical communication with a shaft 564, such as through a belt 565. In this scenario, only the fan and generator are balanced out.

Although the present invention has been discussed in considerable detail with reference to certain preferred embodiments, other embodiments are possible. The drawings and the associated descriptions are thus provided to illustrate embodiments of the invention and not to limit the scope of the invention. The steps disclosed for the present methods are not intended to be limiting nor are they intended to indicate that each step is necessarily essential to the method, but instead are exemplary steps only. Therefore, the scope of the appended claims should not be limited to the description of preferred embodiments contained in this disclosure. All references cited herein are incorporated by reference in their entirety.

Claims

What is claimed is:

1. A rotor-stator assembly for use in an electric motor or generator, comprising: a) a stator comprising one or more surfaces having a catenoid form; and b) a rotor comprising one or more surfaces having a catenoid form, wherein the rotor is electromagnetically coupled to and rotatable relative to the stator.

2. The rotor-stator assembly of claim 1, wherein the rotor comprises a plurality of rotor segments, and wherein each rotor segment comprises an outer surface conforming to the catenoid form.

3. The rotor-stator assembly of claim 1, wherein the distance between an axis of rotation of the rotor and the surface of the rotor is greater than or less than the catenoid form by 5%.

4. The rotor-stator assembly of claim 1, wherein the catenoid form is an inverse- catenoid.

5. The rotor-stator assembly of claim 1, wherein the catenoid form is a catenoid.

6. The rotor-stator assembly of claim 5, comprising a plurality of stator plates and a plurality of rotor plates, wherein the stator plates and the rotor plates are arranged co-axially with a shaft such that respective radii of the stator plates and rotor plates are varied along the axial direction so as to form a catenoid form.

7. An induction motor comprising the rotor-stator assembly of claim 1.

8. The induction motor of claim 7, further comprising slots in the stator for accommodating a primary winding to generate a rotary magnetic field when electricity is applied to the primary winding.

9. The induction motor of claim 7, further comprising slots in the rotor for a secondary winding to generate a torque by an electromagnetic induction between the secondary winding and the primary winding of the stator when electricity is applied to the primary winding.

10. The induction motor of claim 7, wherein the rotor comprises two or more rotor portions.

11. The induction motor of claim 7, wherein the stator comprises two or more stator portions.

12. The induction motor of claim 7, where the stator further comprises: a) a stator cage comprising 3 or more stator elements; and b) wire coils looped around each of the stator elements to create electromagnets.

13. The induction motor of claim 7, further comprising: a shaft having a proximal end, a distal end, and a longitudinal extent, wherein the rotor-stator assembly is disposed on the shaft along its longitudinal extent; a first generator portion comprising at least one rotor disposed on the shaft proximally with respect to the rotor-stator assembly; and a second generator portion comprising at least one rotor disposed on the shaft distally with respect to the rotor-stator assembly, wherein the rotors of the first generator portion and the second generator portion comprise outer surfaces which conform to the catenoid form of the rotor-stator assembly.

14. An induction motor and generator, comprising the rotor-stator assembly of claim 1, comprising a shaft having a longitudinal extent; a motor mechanically connected to the shaft for rotating the shaft; a propeller attached at a first point along the longitudinal extent of the shaft; and a rotor-stator assembly disposed around the shaft, the rotor being electromagnetic ally coupled to and rotatable relative to the stator, wherein the rotor-stator assembly is attached at a second point along the longitudinal extent of the shaft, wherein the propeller, shaft, and rotor-stator assembly are statically balanced, and wherein the rotor-stator assembly generates electricity when the motor rotates the shaft.

15. An electric generator comprising the rotor-stator assembly of claim 1, further comprising a plurality of turbine blades attached to a shaft, the shaft being mechanically connected to the rotor.

16. A direct current motor comprising the rotor-stator assembly of claim 1.

17. The direct current motor of claim 16, wherein the stator further comprises two or more electromagnetic field poles, and wherein the two or more electromagnetic field poles comprise coils of wire wound on conductive cores in a catenoid form.

18. The direct current motor of claim 16, wherein the rotor is an armature rotor.

19. The direct current motor of claim 16, wherein the rotor comprises two or more rotor portions.

20. The direct current motor of claim 16, wherein the stator comprises two or more stator portions.