Abstract:
Electrostatic generator electrodes mounted on the outer surface of a fiber-composite rotor. The conducting strips are mounted with a slight tilt in angle such that the electrodes will experience no tension or compression effects as the rotor spins up or slows down. The compression would come about from effects associated with the Poisson Ratio. This change can eliminate any metal fatigue or loss of bonding that might have arisen if the electrodes were to be aligned with the axis.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application claims the benefit of U.S. Provisional Patent Application No. 62/207,353 titled “Electrostatic Generator/Motor Rotor Electrode System Suitable for Installation on the Outer Surface of an EMB Rotor,” filed Aug. 19, 2015, incorporated herein by reference. 
     
    
     STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT 
       [0002]    The United States Government has rights in this invention pursuant to Contract No. DE-AC52-07NA27344 between the U.S. Department of Energy and Lawrence Livermore National Security, LLC, for the operation a Lawrence Livermore National Laboratory. 
     
    
     BACKGROUND OF THE INVENTION 
       [0003]    Field of the Invention 
         [0004]    The present invention relates to devices generally referred to as the electrostatic generator/motor, and more specifically, it relates to rotor electrode configurations for such devices. 
         [0005]    Description of Related Art 
         [0006]    In the design of an Electro-Mechanical Battery (EMB) using an electrostatic generator/motor and a fiber composite rotor, on the inner surface of which are mounted magnetic bearing elements, it would be highly advantageous to be able to locate the E-S generator rotor elements on the outside of the rotor. However, in order to insure the reliability and durability of these electrodes for decades-long operation of the EMB, it is essential to take into account the effects accompanying the high centrifugal forces to which the rotor is exposed. In a typical high-performance rotor, the centrifugal radial acceleration force is of order 200,000 g. As a result of that force, the outer radius of the rotor will expand of order 2 to 3 centimeters, and, as predicted by the value of the Poisson Ratio for the composite, it will contract in axial length by a comparable amount. An electrode configuration that solves the problems arising from this circumstance through the effect of its geometric design is desirable. 
       SUMMARY OF THE INVENTION 
       [0007]    An embodiment of the invention pertains to the geometric design of foil-based E-S generator electrodes mounted on the outer surface of a fiber-composite rotor. These electrodes, if they are aligned with the axis, would be subject to geometric distortion (e.g., axial compression) that could lead to failure from metal fatigue or failure of their adhesive bonding. The compression would come about from effects associated with the Poisson Ratio. This constant, of order 0.2 for a fiber composite, describes the axial compression that must accompany the circumferential expansion coming from centrifugal forces. It is shown herein that if the foil conducting strips are mounted with a slight tilt in angle, the electrodes will experience no axial contraction or expansion effects as the rotor spins up or slows down. This change can eliminate any buckling or loss of bonding that might have arisen if the electrodes were to be aligned with the axis. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0008]      FIG. 1A  illustrates a line  10  that is 25 degrees from the vertical axis  12 . 
           [0009]      FIG. 1B  shows a fiber composite rotor  14  that is centered on a rotational axis  16 . 
           [0010]      FIG. 2  shows a fiber composite rotor identical to that of  FIG. 1B  but with an additional thin cover  20  layer placed over the electrodes. 
           [0011]      FIG. 3  shows a fiber composite rotor similar to that of  FIG. 1B  and illustrates a single electrode  30  formed from a planar stack of thin metal wires, connected electrically to each other at both ends of the stack. 
           [0012]      FIG. 4A  shows a front view of a foil electrode  40  and includes two thin longitudinally oriented pieces of wire  42 ,  44  which are included in the folds to make more rounded edges. 
           [0013]      FIG. 4B  shows an end view of the foil electrode  40  and the two thin longitudinally oriented pieces of wire  42 ,  44 . 
           [0014]      FIG. 5  shows a sectional view of one side of the rotor  50  which shows one electrode strip  52 . 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0015]    An embodiment of the present invention provides an electrode design that addresses the problems associated with the Poisson Ratio expansions and contractions that will occur at the outer surface of the rotor. The most serious problem that can arise comes from the axial contraction in length. Its effect would be to create a cyclic (once every charge/discharge cycle) axially directed compression of the foil, possibly leading to failure of the adhesive bond, or to rupture of the foil from metal fatigue, or to crinkling buckling) and straightening of its surface. Answers to this issue are described below. 
         [0016]    The value of Poisson&#39;s ratio determines the ratio of the axial contraction of the rotor relative to its expansion in circumferential length. It follows that there must exist, on the surface of the rotor, helical lines for which there is neither expansion nor contraction in length. This helical angle can be calculated. If the foil strips are oriented with respect to the rotor axis by this angle, they will experience no axial contractions or expansions as the EMB rotor cycles its rotation speed while being charged or discharged. There will, however, remain tensional stresses that may exceed the elastic limit of the foil. One solution to this problem is to impose a thin layer of elastomeric material between the foil and the rotor body, bonding it with adhesive layers between the rotor body, the elastomer, and the foil. The elastomer then would relieve the stress alluded to above. Based on this disclosure, those skilled in the art will realize other means for reducing this stress. Further, based on this disclosure, those skilled in the art will realize that electrode configurations other than foils can be utilized. 
         [0017]    A means to approach the problem is described below. It consists of using a detailed stress/strain analysis of the problem to find the tipping angle that eliminates the electrode&#39;s axial strain while at the same time subjecting the strips to acceptable tension levels, as relieved again by the use of an elastomeric backing layer. Note that the helical angle and the tipping angle are one and the same (see equation 1). When the electrodes are set at this angle they will experience no axial strain, but will be subjected to both transverse, axial and shear stress. The use of an elastomeric backing will keep these stresses to an acceptable level. 
         [0018]    The analysis yields a value for the tipping angle given as follows: 
         [0000]    
       
         
           
             
               
                 
                   φ 
                   = 
                   
                     
                       ( 
                       
                         1 
                         2 
                       
                       ) 
                     
                      
                     
                       
                         Cos 
                         
                           - 
                           1 
                         
                       
                        
                       
                         ( 
                         
                           
                             1 
                             - 
                             γ 
                           
                           
                             1 
                             + 
                             γ 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   [ 
                   1 
                   ] 
                 
               
             
           
         
       
     
         [0000]    where γ is the Poisson Ratio of the composite. Taking the value 0.22 for the Poisson ratio (S-glass/epoxy composite), the tipping angle is 25°.  FIG. 1A  illustrates a line  10  that is 25 degrees from the vertical axis  12 .  FIG. 1B  shows a fiber composite rotor  14  that is centered on a rotational axis  16 . Foil electrodes  18  are adhered to the outside surface of the rotor and are placed at an angel of 25 degrees with respect to rotational axis  16 . 
         [0019]    Thus far, this disclosure relates to means for eliminating either tension or compression forces on E-S generator/motor rotor electrodes (e.g., foil-based electrodes) located on the outer surface of a FW rotor. In one embodiment, these electrodes are held (with an adhesive) onto the non-conducting surface (e.g., glass or basalt) of a fiber composite rotor. If needed, a thin cover layer of the same fiber composite is placed over the electrodes.  FIG. 2  shows a fiber composite rotor identical to that of  FIG. 1B  but with an additional thin cover  20  layer placed over the electrodes. By using the means described above it is possible to eliminate, or to at least reduce, crinkling or metal fatigue of the electrode material over the projected decades-long lifetime of the EMB. 
         [0020]    Another way to resolve the problem just described would be to form the electrode from a planar stack of thin metal wires, connected electrically to each other at one or both ends of the stack. In this case the wires of the planar wire array would not be subjected to any significant transverse strain, but would simply separate laterally by an insignificant amount.  FIG. 3  shows a fiber composite rotor similar to that of  FIG. 1B . The figure illustrates a single electrode  30  formed from a planar stack of thin metal wires, connected electrically to each other at both ends of the stack. For comparison, the figure shows the foil type electrode described above; however, it is desirable that all of the electrodes in this embodiment are planar stacks of thin metal wires. 
         [0021]    As discussed, an aspect of the rotor electrode configuration being considered here addresses the problem of restraining the electrodes from being torn from the surface of the rotor by the centrifugal force field. In one embodiment, the electrodes may be fabricated of aluminum foil strips. One embodiment of such strips, illustrated in  FIGS. 4A and 4B , provides rounded edges made by folding a small width of the foil back on itself with the folded edge section being at the back.  FIG. 4A  shows a front view of a foil electrode  40  and includes two thin longitudinally oriented pieces of wire  42 ,  44  which are included in the folds to make more rounded edges. The wires are depicted as dashed lines because they are located behind the foil electrode  40 .  FIG. 4B  shows an end view of the foil electrode  40  and the two thin longitudinally oriented pieces of wire  42 ,  44 . Arrows  46  and  48  point to the curved part of the foil edges. This curvature increases the voltage required to create an arc between the rotor and stator electrodes. Parallel foil strips would then be laid down on the surface of the rotor, which would have been smoothed by machining. The strips would be held in place by an adhesive. If needed, the next step would be to filament wind the strips to the rotor with a thin layer (e.g., of order 0.25 mm. in thickness) of the same fiber composite that was used in filament winding the rotor. The thin foil will exert only a very small centrifugal force on this outer winding layer, thus should not compromise the rotor maximum operating speed. 
         [0022]    The rotor electrodes as described above can be incorporated into a “balanced circuit” system (See FIG. 15 in U.S. Pat. No. 7,834,513, incorporated herein by reference). In using this circuit, the rotor electrodes operate in a “virtual ground” situation. That is, the stator is divided into an upper (“plus” charged) section and a lower (“minus” charged) section. See  FIG. 5 , described below. The E-S generator capacitor is thus divided into an upper and lower half, with the rotor electrodes, which run the full length of the rotor, completing the circuit. These electrodes could be made, as discussed for example, of vertical strips of metal foil bonded to the outer surface of the rotor cell structure. The positioning and angle of the stator electrode system can be made to match the periodicity and angle of the rotor electrodes, by incorporating an azimuthal gap between them with the same periodicity. To optimize the max/min capacity ratio, the gaps between the rotor conductor strips might be made wider than the width of the strips themselves. 
         [0023]    More specifically,  FIG. 5  shows a sectional view of one side of the rotor  50  which shows one electrode strip  52 . In this embodiment, the rotor is electrically non-conductive. The figure also shows an upper series of stator electrode blades  54  and a lower series of stator electrode blades  56 . The upper series of blades  54  are in electrical contact with conductive strip  58 , which is attached to stator electrode section  60 . The lower series of blades  64  are in electrical contact with conductive strip  62 , which is attached to stator electrode section  65 . The gap between the rotor electrodes and the stator electrodes is exaggerated in the figure. Notice the gap  66  between stator section  60  and stator section  64 . If the upper and lower stator sections are formed of electrically conductive material, the conductive blades can be in direct contact with stator sections  60 ,  64  and conductive strips  58  and  62  can be omitted, For clarity, a balanced circuit similar to the one shown in FIG. 15 of U.S. Pat. No. 7,834,513 is provided. A source  80  of positive voltage is connected to inductor  82  and resistor  84  and to conductive strip  58 . A source  86  of negative voltage is connected to inductor  88  and resistor  90  and to conductive strip  62 . Note that it is beneficial if the conducting strip  53  is a plating rather than a foil. Such plating can be formed by vapor deposition. In this embodiment, a connection is made from a node  85  between resister  84  and strip  58  to a node  91  between resistor  90  and strip  62 . The connection from node  85  is made to a capacitor  94  and to a load  96  to a capacitor  98  to node  91 . Based on the teachings herein, those skilled in the art will understand that other circuits are useable with the configuration of  FIG. 5 . 
         [0024]    The foregoing description of the invention has been presented for purposes of illustration and description and is not intended to be exhaustive or to limit the invention to the precise form disclosed. Many modifications and variations are possible in light of the above teaching. The embodiments disclosed were meant only to explain the principles of the invention and its practical application to thereby enable others skilled in the art to best use the invention in various embodiments and with various modifications suited to the particular use contemplated. The scope of the invention is to be defined by the following claims,