Patent Publication Number: US-2021184599-A1

Title: Electrostatic Motor

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation of U.S. patent application Ser. No. 16/277,584, titled “Electrostatic Motor,” filed Feb. 15, 2019, and claims priority to U.S. Provisional Patent Application No. 62/631,263, titled “Electrostatically polarized, radial implementation motor,” filed Feb. 15, 2018, the entire contents of each of which are hereby incorporated by reference herein, for all purposes. 
    
    
     BACKGROUND 
     Technical Field 
     The present invention relates to electrostatic motors and, more particularly, to electrostatic motors having cylindrical rotors separated from cylindrical stators by dielectric fluids and optionally electrets disposed on surfaces of the cylindrical rotors or stators. 
     Related Art 
     Various configurations of electrostatic motors have been used since the mid-1700s. However, these motors performed very poorly and largely fell out of favor as much more powerful electromagnetic motors became available. Most electric motors in use today rely on electromagnetic effects to produce torque, whereas electrostatic motors use electrostatic forces. Early efforts at electrostatic motor design are reviewed in by Oleg Jefimenko, “Electrostatic Motors, Their History, Types, and Principles of Operation,” ISBN 978-1935023470, Integrity Research Institute, 2011. Notably, Jefimenko and his student Walker explored use of electrets for constructing electrostatic motors, building on the work of Russian physicist A. N. Gubkin, whose work suggested the possibility of an electret-based motor. The electret motors built by Jefimenko and Walker performed well compared to their early predecessors, but very poorly in comparison to conventional electromagnetic electric motors. Their designs were suitable as proofs-of-concept, but suffered from fundamental defects, which made the designs untenable for further commercial development. 
     Other elements of electret-based electrostatic motors were introduced by Japanese researchers Tada and Genda. However, the electret configurations of these motors were poorly designed. They pursued configurations similar to the Gubkin configuration explored by Jefimenko and Walker. Tada and Genda&#39;s motors were limited by the breakdown strength of air. 
     Other potentially relevant prior art includes U.S. Pat. No. 3,696,258, U.S. Pat. Publ. No. 2006/0006759, U.S. Pat. Nos. 3,433,981 and 8,264,121. 
     Beginning in the 1980s, several academic groups built MEMS-scale electrostatic motors that did not use electrets. None of these designs can be scaled up to be competitive with conventional electromagnetic motors, as they depend on physical effects suited only to micro-scale construction, inasmuch as they would operate very inefficiently if scaled to dimensions comparable to commercial electric motors. 
     Recently, Professor Daniel Ludois of the University of Wisconsin founded C-Motive Corporation to commercialize electrostatic motors. The company&#39;s electrostatic motor includes interleaved metal pegs or plates, which circulate in a dielectric fluid. See, for example, U.S. Pat. No. 9,479,085, U.S. Pat. Publ. No. 2016/0344306 and U.S. Pat. Publ. No. 2016/0099663. 
     Prior art electrostatic motors, even prior art electrostatic motors that include electrets or dielectric fluids, suffer from various problems, such as high weight, low maximum rotation rate, very large volumes of dielectric fluid and power supplies requiring very high voltages. 
     SUMMARY OF EMBODIMENTS 
     An embodiment of the present invention provides an electrostatic motor. The electrostatic motor includes a rotor, a stator and a dielectric. The rotor is rotatable about a rotation axis. The rotor defines a first cylindrical surface. The first cylindrical surface has a longitudinal axis, which is coincident with the rotation axis. The rotor has a first plurality of charge members disposed circumferentially on the first cylindrical surface. The first plurality of charge members is disposed circumferentially on the first cylindrical surface. As discussed herein, each charge member of the first plurality of charge members may include an electret, an electrode or both an electret and an electrode. 
     The stator defines a second cylindrical surface. The second cylindrical surface counterfaces the first cylindrical surface. The second cylindrical surface is spaced apart from the first cylindrical surface. The second cylindrical surface is parallel to the first cylindrical surface, and the second cylindrical surface registers with the first cylindrical surface. The stator has a second plurality of charge members disposed circumferentially on the second cylindrical surface. The second plurality of charge members is disposed circumferentially on the second cylindrical surface. As with the first plurality of charge members, each charge member of the second plurality of charge members may include an electret, an electrode or both an electret and an electrode. 
     One surface of the first and second cylindrical surfaces is an outside cylindrical surface, and the other surface of the first and second cylindrical surfaces is an inside cylindrical surface. That is, the stator may define an inside cylindrical surface that defines a volume, and the rotor may include a cylinder that fits within the volume defined by the stator&#39;s inside cylindrical surface. Conversely, the rotor may define an inside cylindrical surface that defines a volume, and the stator may include a cylinder that fits within the volume defined by the rotor&#39;s inside cylindrical surface. In either case, the first and second surfaces define a cylindrical shell therebetween. 
     The cylindrical shell has a finite, non-zero thickness, i.e., the space between the rotor&#39;s cylindrical surface and the stator&#39;s cylindrical surface. The rotor&#39;s cylindrical surface does not touch the stator&#39;s cylindrical surface. The dielectric fills the cylindrical shell. The dielectric takes the shape of a cylindrical shell. 
     In any embodiment, the dielectric may include a dielectric fluid. 
     In any embodiment, the dielectric fluid may be pressurized to greater than about 101 kPa absolute pressure. 
     In any embodiment, the electrostatic motor may include means for pressurizing the dielectric fluid to greater than about 101 kPa absolute pressure. 
     In any embodiment, the electrostatic motor may include a filter in fluid communication with the cylindrical shell and a pump configured to circulate the dielectric fluid from the cylindrical shell, through the filter and then back to the cylindrical shell. 
     In any embodiment, at least one surface of the first and second cylindrical surfaces may define a plurality of features that extend proud of the at least one surface. In any embodiment, the each feature of the plurality of features may include a chevron shape. 
     In any embodiment, the dielectric may include a partial vacuum. 
     In any embodiment, one plurality of charge members of the first and second pluralities of charge members may include a plurality of electrets arranged such that adjacent electrets are of opposite charge, and the other plurality of charge members of the first and second pluralities of charge members may include a first plurality of electrodes. 
     In any embodiment, charges on adjacent electrets of the plurality of electrets may be sufficient to exceed breakdown voltage of air over a distance equal to spacing between the adjacent electrets. 
     In any embodiment, the one plurality of charge members further comprises a second plurality of electrodes. 
     In any embodiment, the electrostatic motor may also include a plurality of charging electrodes, one charging electrode of the plurality of charging electrodes for each respective electret of the plurality of electrets. Each charging electrode may be disposed below, i.e., away from the cylindrical surface, and in intimate contact with, the respective electret. 
     In any embodiment, the one plurality of charge members of the first and second pluralities of charge members may include a first plurality of electrodes, and the other plurality of charge members of the first and second pluralities of charge members may include a second plurality of electrodes. 
     In any embodiment, the electrostatic motor may also include an electronic circuit configured to energize and commutate one plurality of charge members of the first and second pluralities of charge members. 
     In any embodiment, the rotor may define a plurality of first cylindrical surfaces. Each first cylindrical surface may have a respective longitudinal axis coincident with the rotation axis. Each first cylindrical surface may have a first plurality of charge members disposed circumferentially thereon. The stator may define a plurality of second cylindrical surfaces. Each second cylindrical surface may counterface, and be spaced apart from, a corresponding one of the first cylindrical surfaces. Each second cylindrical surface may have a second plurality of charge members disposed circumferentially thereon. 
     In any embodiment, the electrostatic motor may include a hydrostatic bearing. The hydrostatic bearing may be configured to support the rotor within the stator. The hydrostatic bearing may define a plurality of fluid ports. Each fluid port extends from an outer surface of the stator to an inner surface of the stator. At least some of the fluid ports extend through the second plurality of charge members. One end of each fluid port may be in fluid communication with the cylindrical shell. 
     Another embodiment of the present invention provides a rotor for an electrostatic motor. The rotor includes a cylinder. The cylinder is rotatable about a rotation axis. The cylinder defines a first cylindrical surface. The first cylindrical surface has a longitudinal axis that is coincident with the rotation axis. The rotor has a plurality of electrets disposed circumferentially on the first cylindrical surface. 
     The rotor also has a plurality of charging electrodes, one charging electrode of the plurality of charging electrodes for each respective electret of the plurality of electrets. Each charging electrode being disposed below, i.e., away from the cylindrical surface, and in intimate contact with, its respective electret. The plurality of charging electrodes is electrically accessible via at least one electrically conductive port through a surface of the rotor. The port may be at the same level as the cylindrical surface, or the port may be located in a depression in the cylindrical surface. The port may be located on a boss. The port may be located elsewhere on the rotor. 
     Yet another embodiment of the present invention provides a method of manufacturing a rotor for an electrostatic motor. The method includes forming a plurality of electrets, such that the plurality of electrets is disposed circumferentially on a cylindrical surface of the rotor. The method also includes preventing formation of an air path between adjacent electrets of the plurality of electrets. 
     In any embodiment, preventing formation of the air path may include applying a dielectric fluid to the cylindrical surface. 
     In any embodiment, preventing formation of the air path may include forming a partial vacuum around the cylindrical surface. 
     An embodiment of the present invention provides a fixture for contact charging a cylindrical electret workpiece having a longitudinal axis. The fixture includes a first plurality of spaced-apart electrodes. The first plurality of spaced-apart electrodes is arranged along an imaginary cylindrical surface having a longitudinal axis coincident with the longitudinal axis of the workpiece. All electrodes of the first plurality of spaced-apart electrodes are electrically connected together to form a first circuit. The fixture also includes a second plurality of spaced-apart electrodes arranged along the imaginary cylindrical surface. All electrodes of the second plurality of spaced-apart electrodes are electrically connected together to form a second circuit. The second circuit is electrically isolated from the first circuit. Each electrode of the second plurality of spaced-apart electrodes is disposed between two adjacent electrodes of the first plurality of spaced-apart electrodes. 
     In any embodiment, the fixture may also include an electrically insulated cylinder disposed around, and in intimate contact with, either an outer surface or an inner surface of the first and second pluralities of spaced-apart electrodes. A longitudinal axis of the electrically insulated cylinder is coincident with the longitudinal axis of the workpiece. 
     In any embodiment, the fixture may include means for changing diameter of the electrically insulated cylinder, thereby changing diameter of the imaginary cylindrical surface. 
     In any embodiment, the fixture may include a screw configured to change the diameter of the electrically insulated cylinder, thereby changing the diameter of the imaginary cylindrical surface. 
     Yet another embodiment of the present invention provides a fixture for contact charging a cylindrical electret workpiece having a longitudinal axis. The fixture includes an electrode assembly that includes a first elongated electrode, a second elongated electrode and an electrically insulated material between the first and the second electrode. The first electrode is electrically isolated from the second electrode. A longitudinal axis of the first electrode is parallel to a longitudinal axis of the second electrode and parallel to the longitudinal axis of the workpiece. The electrode assembly is translatable, between a first position and a second position, along an axis perpendicular to the longitudinal axis of the workpiece. The electrode assembly is configured such that, in the first position, the first and second electrodes are in intimate physical contact with a cylindrical surface of the workpiece. The electrode assembly is configured such that, in the second position, the first and second electrodes are spaced apart from the surface of the workpiece. 
     In any embodiment, the electrode assembly may be configured such that the cylindrical surface of the workpiece is an outside cylindrical surface of the workpiece. 
     In any embodiment, the electrode assembly may be configured such that the cylindrical surface of the workpiece is an inside cylindrical surface of the workpiece. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The invention will be more fully understood by referring to the following Detailed Description of Specific Embodiments in conjunction with the Drawings, of which: 
         FIG. 1  is an isometric diagram, and  FIG. 2  is a perspective cut-away diagram, of an assembled electrostatic motor, according to an embodiment of the present invention. 
         FIG. 3  is an exploded isometric view of the electrostatic motor of  FIGS. 1-2 . 
         FIG. 4  is an exploded isometric view of a rotor assembly of the electrostatic motor of  FIGS. 1-2 . 
         FIG. 5  is an end view, and  FIG. 6  is a cross-sectional view of the electrostatic motor of  FIGS. 1-3 . 
         FIG. 7  is an enlarged view of a portion of  FIG. 6 . 
         FIG. 8  is a side view, and  FIG. 9  is a cross-sectional view of the electrostatic motor of  FIGS. 1-3 . 
         FIG. 10  is a cross-sectional view of the electrostatic motor of  FIGS. 1-3 , similar to  FIG. 9 , but with additional detail, and  FIG. 11  is an enlarged view of a portion of  FIG. 10 , showing forces generated within the motor. 
         FIG. 12  is an enlarged view of a portion of  FIG. 9  showing motor components, and 
         FIG. 13  is the enlarged view of the portion of  FIG. 9  showing forces and resulting rotation of the rotor. 
         FIG. 14  is an enlarged view of a portion of  FIG. 9  showing regions of conductive material within the rotor that form embedded charging electrodes, according to an embodiment of the present invention. 
         FIG. 15  is an isometric view,  FIG. 16  is a side view,  FIG. 17  is a cross-sectional view and  FIG. 18  is an enlarged view of a portion of the rotor with an optional coating of an electrically conductive material, according to an embodiment of the present invention. 
         FIG. 19  is an isometric diagram illustrating a contact charging fixture, according to an embodiment of the present invention. 
         FIG. 20  is an isometric diagram of the contact charging fixture of  FIG. 19 , with an outer cylinder removed for clarity. 
         FIG. 21  is a side view of the contact charging fixture of  FIG. 19 . 
         FIG. 22  is a cross-sectional view through the contact charging fixture of  FIG. 21 , and 
         FIG. 23  is an enlarged view of a portion of  FIG. 22 . 
         FIG. 24  is an isometric diagram of a mask with an aperture, through which ions may be guided to corona-charge a defined region in an electret cylinder or other curved surface, according to an embodiment of the present invention. 
         FIG. 25  is an isometric schematic diagram of an apparatus, including the mask of  FIG. 24 , of a corona charging system, according to an embodiment of the present invention. 
         FIGS. 26, 27 and 28  are respective exploded, cut-away exploded and cut-away assembled perspective view diagrams of an electrostatic motor that includes multiple concentric cylindrical rotors and stators, according to an alternate embodiment of the present invention. 
         FIG. 29  is an isometric diagram illustrating a contact charging fixture, spaced apart from a dielectric cylinder, according to another embodiment of the present invention. 
         FIG. 30  is an isometric diagram illustrating the contact charging fixture of  FIG. 29  in contact with the dielectric cylinder, according to the embodiment of the present invention. 
         FIG. 31  is an isometric diagram of a hydrostatic or aerostatic bearing between a rotor and a stator of an electrostatic motor, according to an embodiment of the present invention. 
         FIG. 32  is a cross-sectional view of a portion of the rotor and stator shown in  FIG. 31 , showing one fluid port of the hydrostatic or aerostatic bearing, according to an embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF SPECIFIC EMBODIMENTS 
     Definitions 
     As used herein, including in the claims, unless otherwise indicated in context, the following terms shall have the following meanings. 
     A cylinder (or circular cylinder) is a curvilinear surface, not necessarily a solid. A cylinder is the locus of points traced by a finite-length line segment rotated about an axis, where the line segment is co-planar with the axis, but the line segment is not perpendicular to the axis. The line segment may be straight, curved or formed of a plurality of straight and/or curved sub-segments. If the line segment is parallel to the axis, the cylinder is a conventional right cylinder. If, however, the line segment is not parallel to the axis, the cylinder may be tapered, i.e., shaped like a cone or a portion of a cone. 
     A circular hollow cylinder (or cylindrical shell) is a three-dimensional region bounded by two circular cylinders having the same axis, two parallel sides and two parallel (not necessarily equal diameter) annular bases perpendicular to the cylinders&#39; common axis. 
     Commutation is a process of switching electric current and/or voltage in motor phases to generate motion. Brushed motors have physical brushes to achieve this process twice or more per rotation, while brushless direct current (BLDC) electric motors do not. Due to the nature of their design, BLDC motors can have any number of pole pairs for commutation. Similarly, electrostatic motors can have any number of electrodes for commutation. 
     An electrode is an electrical conductor through which electric current and/or charge enters or leaves an object, substance or region. 
     An electret is a material that retains a permanent or semi-permanent electric charge after exposure to a strong electric field. 
     A dielectric (or dielectric material) is an electrical insulator that can be polarized by an applied electric field. 
     An electrical conductor is a material having an electrical resistivity less than about 10 −6  Ω-m. 
     An electrical insulator is a material having an electrical resistivity greater than about 10 −6  Ω-m. 
     A partial vacuum is a region with a gaseous pressure less than about 40 Pa. A partial vacuum is a dielectric. 
     A fluid is any liquid, gas, supercritical fluid or multiphase mixture of liquid, gas and/or supercritical fluid that has a suitably high dielectric breakdown strength, permittivity and/or low viscosity. 
     Cylindrical Electrostatic Motor 
     Embodiments of the present invention provide electrostatic motors that improve upon the efficiency, weight and cost of conventional electromagnetic electric motors and electric motor-driven systems. These embodiments operate more efficiently over a wider range of speeds than conventional electric motors and known electrostatic motors, weigh less and cost less. By operating more efficiently than conventional motors, machines powered by these embodiments are less costly to operate, because they consume less power. The improved efficiency of these embodiments, in combination with their low weight, enable vehicles to travel further and/or bear a larger payload, since a lower volume and mass of batteries, or other energy storage devices, is required. The lower cost and weight of these embodiments is due to the replacement of expensive and heavy materials used in conventional electromagnetic motors, such as magnets, copper wire and electrical steels, with inexpensive, lightweight electret materials and/or thin, conductive electrodes. 
     These motors can be used to power a wide range of machines that now rely on electromagnetic electric motors. The list of potential applications includes, but is not limited to: vehicles (including primary drivetrain and auxiliary motors for motor vehicles, drones, etc.), aircraft, watercraft (including boats and underwater vehicles), electric tools, robots, manufacturing/material handling equipment, construction equipment, HVAC (heating, ventilation, and air conditioning) equipment, toys and medical devices. The motors are also capable of operating as generators, so they have applications in electricity generation, energy scavenging and hybrid motor/generators. 
       FIG. 1  is an isometric diagram, and  FIG. 2  is a perspective cut-away diagram, of an assembled electrostatic motor  100 , according to an embodiment of the present invention.  FIG. 1  shows a case  102 , front end cap  104  of the case  102 , shaft  106  and axis  108 .  FIG. 2  shows a cylindrical rotor  202  with a plurality of alternatingly charged electrets, represented by electrets  204  and  206 , disposed on an outside surface of the rotor  202 . The rotor  202  rotates about the axis  108 . A plurality of electrodes, represented by electrodes  208 ,  210 ,  212  and  214 , is disposed on an inside cylindrical surface of a dielectric substrate  215  to form a stator  216 . Ones of the electrets  204 - 206  of the rotor  202  register with, counterface, are coaxial with, and spaced apart from, the electrodes  208 - 214  of the stator  216  to define a cylindrical shell between the electrets  204 - 206  and the electrodes  208 - 214 , although the number of electrets  204 - 206  need not equal the number of electrodes  208 - 214 . In some embodiments, the cylindrical shell may be on the order of 100s of μm thick. In other embodiments, the cylindrical shell may be thicker or thinner than 100s of μm thick. A dielectric fluid (not shown in  FIG. 2 ), or a partial vacuum, fills the cylindrical shell. 
     Force generated by any electric motor is defined by the well-known Lorentz force equation (1): 
         F=qv×B+qE   (1)
 
     In magnetic motors, the value of the term qv depends on an electric current in a coil of wire, and the value of the term B depends on the strength of a magnetic field from a permanent magnet or an electromagnet. In an electrostatic motor, the value of the term qE depends on the strengths of a static charge (q) and an electric field (E). 
       FIG. 3  is an exploded isometric view of the electrostatic motor  100 .  FIG. 3  shows the case  102 , front end cap  104  and shaft  106 , front and rear bearings  300  and  302 , respectively, rear end cap  304 , the dielectric substrate  215  on which are formed or disposed drive electrodes  306  (corresponding to electrodes  210 - 224  in  FIG. 2 ), such as in slots  308 , and a rotor assembly  310 . Collectively, the dielectric substrate  215  and the electrodes  306  form the stator  216 . 
       FIG. 4  is an exploded isometric view of the rotor assembly  310 , including the shaft  106 , an electret cylinder  400 , which includes alternatingly polarized electrets  402  (or alternatively electrically conductive bands, or alternatively both electrets and electrically conductive bands), and front and rear end caps  404  and  406 , respectively. 
       FIG. 5  is an end view, and  FIG. 6  is a cross-sectional view, of the electrostatic motor  100 .  FIG. 7  is an enlarged view of a portion of  FIG. 6 , as indicated by an arrow  600 . Much of the motor  100  can be empty, as indicated at  602 , thereby reducing its weight, compared to conventional electromagnetic motors. A cylindrical shell  700  is defined between the electrets  402  and the drive electrodes  306 . 
       FIG. 8  is a side view, and  FIG. 9  is a cross-sectional view, of the electrostatic motor  100 . A portion  900  of  FIG. 9  is shown enlarged in  FIGS. 12 and 13 .  FIG. 10  is a cross-sectional view of the electrostatic motor  100 , similar to  FIG. 9 , but with additional detail.  FIG. 10  illustrates a rotor  1000  and a stator  1002  with a dielectric fluid  1004  therebetween.  FIG. 11  is an enlarged view of a portion  1006  of  FIG. 10 , showing forces, exemplified by repulsion and attraction forces  1100  and  1102 , respectively, generated within the motor  100 . Dimensions of the electrets and electrodes are exaggerated for clarity. 
       FIG. 12  is an enlarged view of a portion of  FIG. 9  showing motor components, and  FIG. 13  is the enlarged view of the portion of  FIG. 9  showing forces and resulting rotation of the rotor assembly  310 . In  FIG. 13 , attractive and repelling forces between drive electrodes and electrets (or rotor electrodes) are indicated at  1300  and a direction of net rotation of the motor  100 , caused by torque resulting from the forces  1300 , is indicated by an arrow  1302 . 
     Rotor with Electrodes Embedded in Bulk Electret Material to Facilitate Charging 
     In some embodiments, the rotor includes electrically conductive material embedded in the bulk electret material to form embedded charging electrodes. These electrodes facilitate contact charging, without need for external charging fixtures, thus simplifying the process for manufacturing an electret rotor. Furthermore, the rotor surface can be submerged in dielectric fluid during charging, which prevents air breakdown near the rotor surface or accumulation of charged particles on the rotor, providing further advantages.  FIG. 14  is an enlarged view of a portion  900  of  FIG. 9 , which shows a cross-section through the motor, showing regions of conductive material within the rotor that form embedded charging electrodes  1400 . Optionally, additional regions of electrically conductive material (not shown) may be disposed on the outer surface of the rotor, radially registered with, but radially spaced apart from, the embedded charging electrodes  1400 . Embodiments with both outer and embedded charging electrodes provide choices for charging the electrets. Charging the electrets can be performed by applying a voltage across circumferentially adjacent charging electrodes on the outside of a rotor, across circumferentially adjacent charging electrodes on the inside of a rotor and across radially adjacent charging electrodes, i.e., one charging electrode on the outside of the rotor and one charging electrode on the inside of the rotor. Charging the electrets according to these choices yields different charge patterns and charge densities. 
     To embed electrodes within a bulk electret material, a layer of conductive material may be deposited on the surface of a cylinder of electret material using known methods, such as sputtering or chemical vapor deposition (CVD). The conductive material is patterned, such as through shadow masking, to form discrete electrodes. Next, a layer of electret material is deposited on top of the electrodes deposited in the previous step, burying most of the conductive material. The electret material may be deposited by over-molding, chemical vapor deposition or any other suitable method. The final layer of electret material is prevented from covering a small region of each embedded electrode, such as by masking or other suitable method, such that portions of the embedded electrodes remain physically accessible for connection to a voltage source. 
     The electret material is then polarized by connecting adjacent, embedded electrodes to positive and negative poles of a voltage source, respectively, which thereby creates an electric field within the electret material between the adjacent embedded electrodes, causing that portion of material to become polarized. 
     In some embodiments, charging electrodes  1400  of every other electret are electrically connected together within the rotor, forming two circuits, one circuit for electrets that are to be positively charged, and the other circuit for electrets that are to be negatively charged. Nevertheless, each electret is considered to have a respective charging electrode  1400 . 
     In the embodiment shown in  FIGS. 1-13 , electrets are disposed on the surface of the rotor assembly  310 , and electrodes  306  ( 208 - 214 ) are disposed on the inside surface of the stator  216 . However, in some other embodiments, the electrets are disposed on the inside surface of the stator  216 , instead of or in addition to the electrodes  306  ( 208 - 214 ), and other electrodes are disposed on the surface of the rotor assembly  310 . In these embodiments, electrical signals are sent to the rotor assembly  310 , rather than the stator  216 , such as via brushes or slip rings, to commutate the motor  100 . 
     In the embodiment shown in  FIGS. 1-13 , the rotor assembly  310  is disposed within the stator  216 , and the rotor assembly  310  is a cylinder with an outside surface that counterfaces an inside cylindrical surface of the stator  216 . The rotor assembly  310  spins within the stator  216 . However, in some other embodiments, the rotor assembly  310  spins outside the stator  216 . In these other embodiments, the stator is configured as a cylinder with electrodes and/or electrets on its outside surface, and the rotor defines an inside cylindrical surface that counterfaces the stator. 
     In general, electrostatic motors generate torque by electrostatic attraction or repulsion between charged surfaces. Motors, according to embodiments of the present invention, include a cylindrical rotor  202  ( FIG. 2 ) with an outer surface made of a plurality of polarized electret materials and/or conductive electrodes, represented by electrets  204 - 206 . The motors also include a case  102  with a cylindrical arrangement of conductive electrodes, represented by electrodes  208 - 214  that surround the rotor  202 . The electrodes  208 - 214  collectively form a stator  216 . A thin cylindrical shell of dielectric fluid (not shown in  FIG. 2 ), but shown at  1004  in  FIGS. 10 and 11 , is situated between the outer surface of the rotor  202  and the stator  216 . In some embodiments, as little as a few milliliters of dielectric fluid fill the space between the outer surface of the rotor  202  and the stator  216 . 
     Some embodiments use electret rotors. In these embodiments, electrets  204 - 206  ( 402 ) and drive electrodes  208 - 214  ( 306 ) are arranged such that by applying positive and negative voltages to the drive electrodes  306 , electrically charged regions  402  on the rotor  102  are electrostatically attracted to, or repelled from, nearby electrodes  306 , causing a net torque to be applied to the rotor, causing it to rotate, as schematically illustrated in  FIG. 11 . The electrodes  208 - 214  ( 306 ) are manufactured onto a substrate material, such as alumina, with a high dielectric constant to prevent discharges (arcing) between the electrodes. By varying the polarities of voltages on the drive electrodes  208 - 214  ( 306 ) over time, a sustained clockwise or counterclockwise torque is applied to the rotor  1002 , causing continuous rotation of the shaft. The magnitude of the torque depends on the intensities of the electric fields that the electrodes  208 - 214  ( 306 ) apply to the rotor  1002 , charge on the electrets  204 - 206  ( 402 ), number of counterfacing electrode/electret pairs (although there need not necessarily be equal numbers of electrets on the rotor as electrodes on the stator) and radius at which the electrets are disposed from the center of the shaft. Optionally, each electrode  208 - 214  ( 306 ) is surrounded by an electrically, floating-potential conductive guard ring or field plate, exemplified by ring  1106 , to shape the electric field of the electrode  306 , as is known in the art. 
     The angle subtended by each electrode (equivalently, the circumferential width of each electrode) can be made very small, on the order of 1 Thus, the stator may have a very large number of drive electrodes. The number of drive electrodes can thus greatly exceed the number of polarized regions of electret material, thus a very large number of phases may be independently activated to reduce torque ripple and improve motor efficiency. 
     An external power supply (not shown) applies voltages to the drive electrodes, and a switching circuit (not shown) modulates the voltages, i.e., commutates the motor, depending on the real-time angular position of the rotor, such that a net torque is consistently applied in a desired orientation. The power supply and switching circuit energize the electrodes to commutate the motor in a manner analogous to a conventional brushless direct current motor. The angular position of the rotor may be sensed using an electrostatic method described herein, or by conventional angular position sensors, such as optical encoders, Hall effect sensors or the like. The switching circuit may include semiconductor devices, such as field-effect transistors, bipolar transistors, commutator brushes and other related components capable of switching high voltages, as is well known in the art. 
     In an alternate embodiment, the electrets are either replaced or supplemented with conductive electrodes (“rotor electrodes”), and the rotor electrodes are charged by an external voltage source. 
     Dielectric Fluid Between Rotor and Stator 
     In general, large electric fields are not stable, because air becomes conductive, i.e., ionizes (breaks down), in an electric field exceeding approximately 3 MV/m. The dielectric fluid  1004  ( FIG. 10 ) in some motor embodiments enables very high electric fields to be applied to the rotor from the electrodes without breakdown, enabling much higher torque than would be possible with an air gap between the electrodes and the electrets/rotor electrodes. A low viscosity dielectric fluid is preferred, such as an alkane hydrocarbon fluid or fluorocarbon fluid, since low viscosity enables high shaft rotation speeds with low fluid frictional losses. However, a high viscosity dielectric fluid may be suitable where relatively low shaft speed is acceptable, such as in a robot arm. 
     Suitable dielectric fluids may include alkanes, perfluorocarbons, purified water, silicone oil, mineral oil and other chemicals known in the art. Suitable nanoparticles may be added to the dielectric fluid to increase electrical breakdown strength. 
     In an alternate embodiment, the dielectric fluid is a high partial vacuum established within the motor case, such as by a vacuum pump. A vacuum-compatible rotary seal, such as a ferrofluidic seal or end-face mechanical seal, as known in the art, enables the rotating motor shaft to penetrate the case without loss of vacuum. A high partial vacuum can replace the dielectric fluid because it has a very high electric field breakdown strength. In some embodiments, the partial vacuum has a pressure below about 1 mTorr (0.13 Pa). Specific vacuum requirements depend on electrode (or electret) spacing and drive voltage and may be calculated by reference to Paschen&#39;s law. Such a partial vacuum provides an efficiency advantage because fluid friction energy losses that would result from dielectric fluid are eliminated. 
     In a related embodiment, a dielectric fluid is installed in the cylindrical shell between the rotor and case, but air in the remainder of the empty space within the case is replaced by a partial vacuum or an inert gas, such as nitrogen. Replacement of the air is advantageous for maintaining purity of the dielectric fluid, which may otherwise become contaminated by atmospheric gases within the air. 
     Multiple Concentric Cylindrical Arrangement 
     In another alternate embodiment, multiple concentric cylindrical arrangements, exemplified by cylinders  2700  and  2702 , of polarized electret material are attached to one or more discs, such as disc  2704 , that are attached to the shaft  106 , as shown in  FIGS. 26-28 . One or more other discs, exemplified by disc  2706 , are attached to the case and support electrodes that are disposed in multiple concentric cylindrical arrangements, exemplified by cylinders  2708 ,  2710  and  2712 . The electrodes extend from these discs  2708 - 2712  to apply electric fields to the multiple electret cylinders  2700 - 2702 . It should be noted that electrodes and electrets may be disposed on one or both surfaces of each cylinder  2708 - 2712  and  2700 - 2702 , for example as shown at  2714  and  2716 . This configuration provides more torque than with a single electret cylinder and is suited to applications where a large diameter is available for a motor, but length of the motor is limited. The disadvantage of this approach is that the weight of the motor is increased. 
       FIG. 15  is an isometric view,  FIG. 16  is a side view, and  FIG. 17  is a cross-sectional view of the electret cylinder  400  of the rotor assembly  310 .  FIG. 18  is an enlarged view of a portion  1700  of the electret cylinder  400 . As shown in  FIG. 18 , in another embodiment, the electret rotor is coated in a thin layer of electrically conductive material  1800 , which concentrates electret charge near the surface of the rotor and also concentrates the electric field emanating from electrode pairs at the surface of the rotor. By concentrating both the electric field from the electrodes and the charge from the electrets close to the rotor surface, a higher torque can be applied to the rotor than if the conductive coating is absent. 
     Furthermore, the electrically conductive material  1800  prevents direct physical contact between the dielectric fluid  1004  and the electrets  402 . Such contact can cause an accumulation of charge that damages the electrets  402 . In some embodiments, the layer of electrically conductive material  1800  is segmented by electrically insulative material, exemplified by electrical insulators  1802 . Optionally, the electrically conductive material  1800 , or ones of the segments of electrically conductive material, is connected to a voltage supply to recharge depleted electrets. 
     Dielectric Fluid Filtration 
     Performance of the dielectric fluid may degrade over time by infiltration of particles, bubbles and/or dissolved atmospheric gases. To exclude these contaminants, a rotary seal may be installed at the end(s) of the case, where the shaft protrudes. Suitable rotary seals include ferrofluidic seals and end-face mechanical seals. 
     Another method for avoiding performance loss due to particle, bubbles and/or dissolved gases is to enable the dielectric fluid to be replenished from a reservoir of purified dielectric fluid. The dielectric fluid reservoir may be pressurized with an atmosphere of inert gas, such as nitrogen, and routed to the interior of the motor. When it becomes necessary to replace the fluid, a mechanical or electronically actuated valve may be opened to drain the contaminated dielectric fluid, and to allow the fluid stored in the reservoir to displace the contaminated fluid. The reservoir is preferably a detachable cartridge, which can be replaced as necessary to maintain optimal dielectric fluid quality. 
     In another embodiment, a large pressure is externally applied to the dielectric fluid. When pressurized, the dielectric fluid can support a larger electric field without breakdown than when no pressure is applied. This beneficial effect increases approximately linearly with increased pressure above atmospheric pressure. The pressure may be generated mechanically, such as with a compressed spring that applies force to a piston situated in fluid communication with the dielectric fluid, or with a pressurized, inert gas, such as nitrogen, that applies pressure to a surface of the dielectric fluid. An additional benefit of this configuration is that the pressurized fluid acts as a hydrostatic bearing, which helps stabilize and lower friction on the rotor, and maintain a very small gap between the rotor and the stator. One advantage of the small gap between the rotor and the stator is that the motor can produce a large torque, relative to other configurations that would require a larger gap. Another advantage of the small gap is that the motor can be operated with lower voltages than would be required if the gap were larger. In a related embodiment, the surface of the rotor is patterned with three-dimensional features, such as chevron shapes exemplified by chevron  1500  in  FIG. 15 , that locally increase the pressure of the dielectric fluid when the rotor is in motion, as indicated by an arrow  1502 , boosting the fluid&#39;s breakdown strength. 
     Accumulation of charged particles on the surfaces of electrets may cancel the electret charges and degrade performance of the motor. Some embodiments include a charging and cleaning mode, in which a sufficiently large voltage is applied between each adjacent pair of electrodes. The large voltage creates a strong electric field gradient, which displaces entrapped particles from the surfaces of the electrets while also polarizing the electrets to a desired level of charge. 
     Some embodiments include components to continuously, periodically or occasionally clean the contaminated dielectric fluid of particles, bubbles and/or dissolved gases. In some such embodiments, impellers extending from the rotor cause the dielectric fluid to be pumped through a filter, such as a porous membrane or an electrostatic or magnetic filter. An advantage of an electrostatic filter is that the motor&#39;s electric power supply may be sufficient to power the electrostatic filter. In both of the above embodiments, the impellers, which form an internal pump, may be replaced by a conventional, secondary pump, such as a peristaltic pump, scroll pump or other suitable fluid pump. 
     Real-Time Angular Measurement of Rotor/Shaft 
     Some embodiments detect real-time angular position of the rotor assembly  310 , without a need for additional sensors, such as optical encoders, magnetic sensors, resolvers or the like. It is useful to detect the rotor position, for accurate rotor positioning and speed control, and doing so without additional sensors simplifies the motor and reduces its cost, size and weights. In these embodiments, to measure the shaft  106  angle, the rotor is extended such that a small portion of each charged electret band, or rotor electrode, extends past the ends of the drive electrodes. A secondary arrangement of two or more sensing electrodes is attached to the interior of the case, near the extended portion of the rotor, and is electrically isolated from the electrodes that are used to apply torque to the rotor. As the rotor spins, the motion of the electrets causes electrical charges to be induced on the sensing electrodes. The physics of electrostatic induction causes the magnitudes of these charges to vary in relation to the angle of the shaft, and the charges can be measured using standard voltage measurement circuits, as are known in the art. The angular position of the shaft can be inferred by the magnitude of these measured voltages. 
     Geometry of Cylindrical Electrostatic Motor 
     Embodiments of the present invention include a particular geometric arrangement of electrets  402 , or rotor electrodes, and drive electrodes  306  that is distinct from previous motors. In particular, disposing the electrets  402  and/or electrodes on a cylindrical surface, rather than on a surface of a disk or on pegs, provides advantages. For example, all the electrets  402  and/or electrodes are disposed a radial distance (for example, the radius of the rotor&#39;s electret cylinder  400 ) from the shaft  106 . Therefore, electrostatic forces  1300  acting on these electrets  402  and/or electrodes act through a moment arm equal to the radius to apply torque to the shaft  106 . In disc-based electrostatic motors, charges acting on portions of the disc close to the shaft apply far less torque than charges acting on portions of the disc close to the circumference of the disc. Furthermore, electret rotor embodiments combine two elements that have not previously been combined in a rotary motor: (1) electrets  402  and (2) dielectric fluid  1004 . 
     Both surfaces in contact with the dielectric fluid  1004 , i.e., the surface of the rotor  1000  and the surface of the stator  1002 , are smooth, relative to conventional electric motors, thus these smooth surfaces create much less fluid drag than conventional motors, leading to improved efficiency of the electrostatic motor. The volume of dielectric fluid  1004  used to fill the gap  700  between the rotor and stator is very small, relative to other motors (such as the motor described in U.S. Pat. Publ. No. 2016/0344306) that use dielectric fluid, owing to the small distance between the rotor  1000  and the stator  1002 . Thus, the fluid weight is also small, the cost of the fluid is low compared to motors that require a larger volume of fluid, and the fluid is easier to dispose of. 
     The embodiments described herein were arrived at with the aid of advanced computer modeling tools, such as finite element analysis, which were not available to earlier generations of electrostatic motor designers, and required multiple design iterations and experimentation with geometry and material properties. Furthermore, the electret rotor embodiments were inspired in part by our knowledge and experience with state-of-the-art electret materials and manufacturing methods, which were not known to earlier designers, such as Jefimenko and Walker, and also our analysis of state-of-the-art, high-breakdown dielectric fluids. 
     Several textbooks have “taught away” from pursuing electrostatic motors at scales larger than the micro-scale, arguing that the breakdown strength of air presents a fundamental limitation, discouraging inquiry into the subject. 
     Methods and Apparatus for Charging Defined Regions on a Cylindrical Electret 
     Another aspect of the present invention involves apparatus and methods for contact charging defined regions on a cylindrical electret. Conventional contact charging is a well-known method for polarizing flat electrets. However, conventional contact charging methods are inadequate for charging defined regions on a cylindrical electret.  FIG. 19  illustrates a contact charging fixture  1900  that may be used to polarize a cylinder of electret material  400  with multiple, positively charged regions and multiple negatively charged regions. The cylinder of electret material  400  is inserted into a bore  1902  of the contact charging fixture  1900 , by advancing the cylinder  400  in a direction shown by an arrow  1904 . The contact charging fixture  1900  includes an arrangement of electrically conductive electrodes, exemplified by electrodes  1906 ,  1908  and  1910 , attached to a non-conducting cylinder  1912 . The non-conducting cylinder  1912  maintains physical separation between positively charged and negatively charged portions of the conductive electrodes  1906 - 1910 , thus preventing electrical shorting between them. 
       FIG. 20  is a view of the contact charging fixture  1900 , with the non-conductive cylinder  1912  removed for clarity. The number of charging electrodes, here exemplified by charging electrode  2000 , is equal to the number of regions on the electret cylinder  400  that will become polarized during contact charging. A first electrically conductive ring  2002  at one end of the charging fixture is an electrically common point for one group of charging electrodes. A second electrically conductive ring  2004  at the opposite end of the charging fixture is an electrically common point for a second group of charging electrodes, to be charged with opposite polarity to those charged with electrodes common to the first conductive ring  2002 . To charge the electret cylinder, one pole from an electrical power supply (not shown) is connected to the first ring  2002 , and the opposite pole is connected to the second ring  2004 . Electric fields are thus created within the electret cylinder between positive and negative charging electrodes  2000 , causing electret material within the electric fields to be polarized. 
     It is advantageous to apply pressure from electrodes to electrets during contact charging. The contact charging fixture  1900  may apply pressure to the electret cylinder, for example by selectively constricting the fixture around the electret cylinder or by expanding the fixture before insertion of the electret cylinder and then, after insertion of the electret cylinder, elastically contracting around the electret cylinder. The charging fixture&#39;s diameter may be made compliant by removing portions of material  2006  from one or both end rings  2002  and  2004 . In  FIG. 20 , the end rings  2002  and  2004  are shown to be completely severed to define gaps  2006  and  2008  in the end rings. Compliance may be also be increased without severing the rings, such as by selectively removing material, as is commonly done to create flexural springs using well-known methods. To constrict the charging fixture about an electret cylinder, the end ring diameters may, for example, be reduced by wrapping a tensionable strap around either end ring or both end rings or around the structure shown in  FIG. 20  or around the non-conductive cylinder  1912 , or by bridging a gaps  2006  and  2008  with respective screws (not shown), such that rotation of the screws draws opposing faces of the gaps together. 
       FIG. 21  is a side view of the contact charging fixture  1900  with an electret cylinder  400  (not visible) inserted therein.  FIG. 22  is a cross-sectional view through both the contact charging fixture  1900  and the electret cylinder  400 .  FIG. 23  is an enlarged view of a portion  2200  of  FIG. 22 . A charging electrode  2000  is shown in a charging configuration, with an inner, curved surface interface  2300  of the charging electrode  2000  in intimate contact with a region that will become an electret  402  (once polarized) on the electret cylinder  400 . The curved surface  2300  may be coated with a conductive liquid, such as mercury, or another conductive material, such as gallium or a eutectic alloy, preferably with a lower melting point than the charging electrode to promote transfer of charges to the electret by liquid charging. Liquid-contact charging is a method known to those with ordinary skill in the art for charging of flat electrodes. 
     Although the contact charging  FIG. 1900  has been described for use in creating electrets on the outside surface of a cylindrical surface, the contact charging  FIG. 1900  can, with suitable modifications, be used to create electrets on the inside surface of a cylindrical surface. In this case, the non-conductive surface  1912  may be placed on the inside of the electrodes  1906 - 1910 , rather than on the outside, and electrodes  1906 - 1910  may be placed inside the cylinder to be processed. After the fixture  1900  is inserted into the cylinder, the fixture  1900  may be expanded to apply pressure on the inside of the cylinder. Alternatively, the fixture  1900  may be constricted before being inserted into the cylinder, and then allowed to expand once inside the cylinder to apply the pressure to the inside of the cylinder. 
     The contact charging fixture  1900  described with reference to  FIGS. 19-23  is configured to form all the electrets  402  on the cylindrical surface at once. However, in an alternative embodiment, some of the electrodes  1906 - 1910  are omitted, so as to form a subset of the electrets  402  in a single step. The pressure from the contact charging fixture  1900  may be released, the fixture  1900  may be rotated, relative to the cylinder, and then another set of electrets may be formed. 
     In some circumstances, such as when the electrets  402  are particularly small, it may be advantageous to form the electrets  402  in pairs or other small groups, relative to the total number of electrets  402 , rather than all at once. Another contact charging fixture, an embodiment of which is shown in  FIGS. 29 and 30 , enables forming groups of electrets on a cylindrical surface, without forming all of the ultimate electrets at once. This embodiment facilitates repeating the process of forming groups of electrets on successive locations on the cylindrical surface, including rotating the cylinder between forming each group of the electrets. 
       FIG. 29  is an isometric diagram illustrating a contact charging fixture  2900  disposed above a dielectric cylinder  2902  in preparation for forming a pair of electrets, and  FIG. 30  is an isometric diagram illustrating the contact charging fixture  2900  in intimate physical contact with the dielectric cylinder  2902  workpiece. The contact charging fixture  2900  includes two electrodes  2904  and  2906 , respectively, and an electrically insulative member  2908  separating the two electrodes  2904  and  2906 . The two electrodes  2904  and  2906  and the electrically insulative member  2908  between the two electrodes  2904  and  2906  collectively form an electrode assembly  2910 . End surfaces  2912  and  2914  of the electrodes  2904  and  2906  that contact the dielectric cylinder  2902  should form cylindrical sectors. The dielectric cylindrical workpiece  2902  has a longitudinal axis  2916 . Each electrode  2904  and  2906  has a respective longitudinal axis  2918  and  2920 . The longitudinal axes  2918 ,  2920  of the two electrodes  2904  and  2906  and the longitudinal axis  2916  of the workpiece  2902  are all parallel to each other. 
     The electrode assembly  2910  is translatable between two positions, represented by  FIGS. 29 and 30 , respectively. The electrode assembly  2910  is translatable along an axis  2922  that is perpendicular to the longitudinal axis  2916  of the workpiece  2902 . In use, the two electrodes  2904  and  2906  are electrically coupled to an electrical power supply  3000  ( FIG. 30 ), and the electrode assembly  2910 , specifically the electrodes  2904  and  2906 , is brought into intimate physical contact with the surface of the dielectric cylinder  2902 , as shown in  FIG. 30 , creating an electric field  3002  within the dielectric cylinder  2902  and thereby forming two electrets on a surface of the workpiece  2902 . Pressure should be applied by the contact charging fixture  2900 , specifically the electrodes  2904  and  2906 , on the surface of the dielectric cylinder  2902 . 
     Once the electrets are formed, the electrical power supply  3000  may be disconnected and the electrode assembly  2910  is withdrawn from the surface of the dielectric cylinder  2902 , as shown in  FIG. 29 . Then, the dielectric cylinder  2902 , or the contact charging fixture  2900 , is rotated, for example as indicated by an arrow  3004 , a distance to index the contact charging fixture  2900 , relative to the dielectric cylinder  2902 , to a position of the next set of electrets. The forming process is repeated for each subsequent set of electrets. 
     Although the electrode assembly  2910  is shown with two electrodes  2904  and  2906 , the electrode assembly  2910  may include any number of electrodes. Thus, although described as forming two electrets at a time, the contact charging fixture  2900  may form any number of electrets at a time. As with the contact charging fixture  1900  ( FIG. 19 ), with suitable modifications, the contact charging fixture  2900  may be configured to form electrets on an inside surface of a cylinder. 
     Another embodiment of the present invention is a method for corona-charging defined regions in an electret cylinder. Corona charging of flat electrets is known. However, as noted, charging curved electrets poses problems for conventional charging methods.  FIG. 24  is an isometric diagram of a mask  2400  with an aperture  2402 , through which ions may be guided to corona-charge a region defined by the aperture  2402  in an electret cylinder or other curved surface.  FIG. 25  is an isometric/schematic diagram of the mask  2400 , without the electret cylinder, but with other components of a corona charging system, according to an embodiment of the present invention. These components include an electrode  2500 , a conductive mesh  2502 , and an array of one or more sharp, electrically conductive needles  2504  (a “needle array”). 
     The wall of an electret cylinder (not shown for clarity) is positioned between the electrode  2500  and the aperture  2402 . A first voltage source  2506  is connected to the needle array  2504 , causing air to ionize near the needle points. The potential between the electrode  2500 , which has opposite polarity to the needles  2504 , accelerates ions through the aperture  2402  and onto the electret cylinder. The mask  2400  prevents ions from reaching areas of the electret cylinder, other than a region exposed through the aperture  2402 . The mesh grid  2502  is connected to a second voltage source  2508  with the same polarity as the first voltage source  2506  used to charge the needles  2504 , but of a lower amplitude. The mesh grid  2502  promotes uniform distribution of charge on the electret cylinder. 
     The charged region on the electret is given a positive or negative charge, depending on the polarity of voltage sources  2506  and  2508 , respectively. Reversing the polarity of both voltage sources  2506  and  2508 , or exchanging the relative positions of (a) the needle array  2504  and mesh grid  2502  and (b) the electrode  2500 , causes an electret region to be charged to the opposite polarity. Alternating regions of positive and negative charge may be created on the electret cylinder by: (1) charging a region of the electret cylinder with a first charge, then (2) rotating the electret cylinder, relative to the mask, so the aperture  2402  reveals an uncharged region of the electret cylinder, then (3) corona charging the uncharged region with a charge opposite the first charge and repeating the process for the remaining desired regions. The needle array  2504 , the mesh grid  2502 , the mask  2400  and the electrode  2500  are maintained in a fixture orientation, relative to one another. 
     In an alternative embodiment for corona charging, multiple regions on the electret cylinder may be simultaneously charged. In this embodiment, the mask  2400  contains multiple apertures  2402 , and the electrode  2500  forms a complete cylinder, or at least has portions disposed under each aperture  2402 . A separate needle array  2504  is positioned above each aperture  2402 . All the needle arrays  2504  are made electrically common to the needle array voltage source  2506 . The mesh grid  2502  forms a complete cylinder, enclosing the mask  2400 , or at least has portions disposed between each needle array  2504  and its corresponding aperture  2402 . Activating the voltage sources causes a pattern of polarized regions to be created on the electret cylinder. An equal number of polarized regions of the opposite polarity may be created by: (1) charging a plurality of regions of the electret cylinder, then (2) disconnecting the voltage sources, (3) rotating the electret cylinder, relative to the mask, such that the apertures  2402  align with un-polarized regions of electret material, and then (4) reconnecting the voltage sources  2506  and  2508 , but with reversed polarity. 
     In another embodiment, two sets of voltage sources, needle arrays, mesh grids and electrodes are used, with each set configured to charge the electret cylinder with an opposite charge. In this embodiment, the mask defines an aperture for each region of the electret cylinder that is to be charged. This embodiment does not require rotating the electret cylinder. Both polarities of regions on the electret cylinder may be charged simultaneously, or each polarity may be charged in turn. 
     Contact charging, liquid contact charging and corona charging are described in Kao, Kwan Chi, “Dielectric Phenomena in Solids,” ISBN 9780123965625, Academic press, 2504. 
     Imbedded Electrets 
     Rather than form the electrets in the cylinder of electret material  400 , the electrets may be formed as separate strips or other suitable shapes and attached to the cylinder. The electrets may be attached to the surface of the cylinder, such as by a suitable adhesive. Alternatively, the electrets may be press fit or interference fit into suitable grooves in the surface of the cylinder. Optionally, the electrets may have a cross-sectional shape, such as a trapezoid, that locks into a similar cross-sectional shape defined by the groove, when the electret is pressed into the groove. 
     Hydrostatic or Aerostatic Bearing 
       FIG. 31  is an isometric diagram of a hydrostatic or aerostatic (depending on whether the dielectric fluid  1004  is a liquid or a gas) bearing  3100  between a rotor  1000  and a stator  1002  of an electrostatic motor. For simplicity of explanation, the term hydrostatic, as used herein, including in the claims, means hydrostatic or aerostatic. The hydrostatic bearing  3100  defines a plurality of ports, represented by ports  3102 ,  3104  and  3106 , extending through respective electrodes  402 .  FIG. 32  is a cross-sectional view of a portion of the rotor  1000  and stator  1002  showing one fluid port  3102  of the hydrostatic bearing  3100  extending through one of the electrodes  306 . Dielectric fluid flows, as indicated by an arrow  3200 , as a result of rotation  3202  of the rotor  1000  into the cylindrical shell defined between the rotor  1000  and the stator  1002 . The dielectric fluid flow supports the rotor  1000  within the stator  1002 . 
     While the invention is described through the above-described exemplary embodiments, modifications to, and variations of, the illustrated embodiments may be made without departing from the inventive concepts disclosed herein. For example, although specific parameter values, such as dimensions and materials, may be recited in relation to disclosed embodiments, within the scope of the invention, the values of all parameters may vary over wide ranges to suit different applications. Unless otherwise indicated in context, or would be understood by one of ordinary skill in the art, terms such as “about” mean within ±25%. 
     As used herein, including in the claims, the term “and/or,” used in connection with a list of items, means one or more of the items in the list, i.e., at least one of the items in the list, but not necessarily all the items in the list. As used herein, including in the claims, the term “or,” used in connection with a list of items, means one or more of the items in the list, i.e., at least one of the items in the list, but not necessarily all the items in the list. “Or” does not mean “exclusive or.” 
     Disclosed aspects, or portions thereof, may be combined in ways not listed above and/or not explicitly claimed. In addition, embodiments disclosed herein may be suitably practiced, absent any element that is not specifically disclosed herein. Accordingly, the invention should not be viewed as being limited to the disclosed embodiments.