Electrostatic induction machine having improved rotor dynamics

Abstract

Described herein are rotors for electrostatic induction machines and have improved dynamics, and machines using the same. According to one aspect, a rotor includes a substrate; a plurality of conductive segments formed on a first surface of the substrate; and circuitry electrically connecting sets of the plurality of conductive segments. The circuitry can include resistive elements each connecting two or more of the conductive segments. Additional circuitry, such as additional resistive and capacitive elements, can be used to emulate a magnetic "deep bar" rotor. According to another aspect, a rotor includes: a substrate; a first conductive layer disposed on a surface of the substrate; and a second conductive layer disposed on the first conductive layer, wherein the second conductive layer has a lower conductivity and permittivity compared to first conductive layer.

Description

Docket No.: MIT-714AWO / 26340ELECTROSTATIC INDUCTION MACHINE HAVING IMPROVED ROTOR DYNAMICSCROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit under 35 U.S.C. §119 of U.S. Provisional Patent Application No. 63 / 745,038 filed on January- 14, 2025, which is incorporated herein by reference in its entirety'.BACKGROUND

[0002] Electric field-based actuators and machines lead the design space at the nanoscale and in biological systems, while having the potential to be used in favorable macroscale applications which prioritize minimal mass, performance in a vacuum, or performance in high temperatures.

[0003] Electrostatic induction machines, such as motors and generators, include a set of stator electrodes which induce opposite charges onto a movable rotor surface.Previously, rotor surfaces for electrostatic induction motors were made of single continuum materials, which are limited in possible resistivity, permittivity, and circuitrycharacteristics.

[0004] Magnetic field induction motors, which are common in machinery, often utilize “deep bar’?rotors, consisting of conducting bars which decrease the rotor time constant with increasing slip frequency using the skin depth effect.SUMMARY

[0005] Electrostatic motors have been developed since the 1700s. The first known rotary- electrostatic motors consisted of a glass spoke rotor on pin bearings mounted between two Leyden jars with opposite charge. Charges from these Leyden jars were deposited onto the glass spokes, which then repelled from their respective Leyden jars, and attracted to the other side, where the charges were received in the opposite Leyden jar. This was a substantial advance over previous oscillatory but not necessarily rotary- devices.Docket No.: MIT-714AWO / 26340

[0006] Building on this advance, a ’‘corona motor” was built which deposited charges similarly, but on a continuous glass surface instead of on discrete glass rods, majorly increasing the torque.

[0007] The next type of electrostatic motor, developed in 1889, was a variable capacitance motor, which relied on capacitor plates being forced inwards due to the electric field between them. Unlike corona motors, variable capacitance motors require alternating current (AC) drive electronics; variable capacitance motors are synchronous machines in the sense that the rotor will rotate at the same speed as the electric field. After these synchronous variable capacitance motors, in 1892 asynchronous electrostatic induction machines were developed. These used charges induced onto a poorly conducting surface to rotate, analogous to the magnetic field induction machines currently used today.

[0008] In 1969, more elegant designs for induction electrostatic machines were developed, utilizing more resourceful manufacturing techniques, and increasing the number of electrodes in the motor. These designs demonstrated an induction motor using an array of glass plates with a resistive coating surrounded by electrodes.

[0009] With the emergence of micro electro-mechanical manufacturing techniques, many new electrostatic actuation systems emerged. Some of the early micromotors were variable capacitance machines built using “wobble” bearings, which facilitated tightly- controlled gaps with 2D manufacturing techniques. Induction micromotors were first proposed by Bart and Lang, who presented an integrated linear model, contrasted the induction micromotors with variable capacitance micromotor proposals, and provided suggestions for manufacturing. Huanga made additional fabrication advances including developing spiral groove aerodynamic thrust bearings. Bart’s induction motor was elaborated on by Nagle et al. (S.F. Nagle, C. Livermore, L.G. Frechette, R. Ghodssi, and J.H. Lang, “An electric induction micromotor,” Journal of Microelectromechanical Systems, 14(5): 1127-1143, October 2005). who added analysis of the material interfaces, and presented a model of various torque-speed curves for potential dimensions and material properties. Nagle et al. then proceeded to manufacture and operate a tethered (non-rotating) induction micromotor, and conducted torque measurements, confirming the model presented. Nagle et al. presented a detailed set of fabrication procedures, and notedDocket No.: MIT-714AWO / 26340the key constraints that drove the design as being the feature size of the air gap, insulator thicknesses and electrode spacing.

[0010] Subsequently. Livermore at MIT fabricated a similarly sized MEMS electrostatic induction motor, which operated at 3.5 pN m torque, and speeds of over 55,000 rpm, and was supported by a pressurized aerostatic air bearing. Smaller devices enabled by the MEMS scale generally require faster driving electronics. Neugebauer used careful switching techniques to prototype a six-phase five-level inverter, capable of up to 2 MHz at 300 V in coordination with the micromotor projects at MIT. In an effort to construct a microfabricated gas-powered generator, Steyn fabricated a 6-phase MEMS induction machine with an attached power harvesting circuit and successfully achieved net power generation at speeds above 200 krpm.

[0011] Additional modeling advances were made by Melcher in 1981, who presented an analysis of a linear electrostatic motor as well as studies of charge in various physical media. Choi and Dunn elaborated upon Melcher's analysis and applied it to a physical motor, constructing rotors made out of Bakelite and Plexiglas. Their motor had a gap of 0.635 mm, but with an exceptionally large 30 cm diameter rotor in a radial field configuration with rigid bearings. Despite this relatively large gap, the large motor led to a respectable aspect ratio. This prior analysis w as translated by Krein into a lumped parameter model, which was further developed by Nagle et al. into a model similar to the T-model used in magnetic induction machine power system design. Nagle et al. made further modeling advancements, taking into account the dissipative material properties in the rotor in more detail.

[0012] Other significant advances in induction motors were in bearings and controls. Moser and Higuchi implemented a similar air bearing to the micromotors but on a macro scale, achieving a 100 pm air gap. They noted that in tests with both air bearings and pin bearings with glass rotors they had runout < 1 pm, due to a stable self-centering effect. They further suggested a scheme for sensorless control, but striving for absolute position reference, then successfully implemented a field-oriented position control scheme.

[0013] Dadkhah with Higuchi implemented a simple macro scale air bearing and did further testing, presenting torque-speed curves. While single-gap designs are useful forDocket No.: MIT-714AWO / 26340positioning and tuning gap sizes, designs with stacked electrostatic interfaces have the potential to offer more torque per total system volume. Thus, Hosobata with Higuchi developed a layered design of flexible film layers separated by spacer beads and lubricated by a dielectric liquid. They added external circuit elements such that the motor may be operated in resonance, simplifying drive electronics.

[0014] Similar to the air bearing architectures previously used, Xu used the same techniques but with a diamagnetic levitation scheme, which reduced air friction and allowed the system to operate in a vacuum. Their implementation was shown to lead to a large gap of 500 um, but the technique holds potential for niche applications.

[0015] In induction machines, a critical parameter for determining the torque and speed characteristics is the time constant of the rotor. The rotor time constant is set by the rotor resistance multiplied by the system capacitance. The system capacitance is composed of the air gap capacitance as well as the capacitance due to the gaps between the stator electrodes and a conductive surface of the rotor (which may comprise a plurality of vanes or other conductive segments spatially arranged on a surface of the rotor, according to some embodiments).

[0016] In electrostatic induction machines previously developed, the time constant was set by finding appropriate material properties of a homogeneous material. Glass was a common choice for a bulk material (also referred to as a '‘continuous material” or “continuum material”) with the electromechanics carefully measured. Some prior machines used coated glass in a conductive material such as Indium-Tin-Oxide (ITO) to decrease the surface resistivity from around 1014Q for untreated glass to around 106Q with ITO. In addition, other materials have also been used such as moderately doped polysilicon film. Plexiglas and Bakelite. While deposition techniques can allow for consistent resistivity7across the device, it is challenging to find a suitable material for any arbitrary resistivity or permittivity7.

[0017] To provide more resistivity options, described herein are rotor designs based on discrete circuit components (e.g., resistive elements) which can match a material of arbitrary resistivity. In some examples, a rotor may be constructed out of discrete circuit components (or “discrete components” for short) connected between a finite number ofDocket No.: MIT-714AWO / 26340conductive vanes (or other conductive segments) corresponding to rotor electrodes. The conductive vanes may be formed on a surface of the rotor, and the discrete components can be formed on the same surface or a different surface of the rotor. In the latter case, the discrete components (e.g., resistive elements) can be connected to the conductive vanes that are intended to convey the rotor properties (e.g., using vias).

[0018] Also described are rotor designs including additional circuitry' (e.g., a network of resistive and capacitive elements) on a rotor surface to emulate the "‘deep bar" design previously used with magnetic field induction motor. Such designs can provide improved torque over a wide range of speeds including improved starting torque without sacrificing motor efficiency.

[0019] Forming a plurality of conductive segments (e.g., vanes) on the surface of a rotor allows the use of discrete components to create precise rotor resistivities, thereby enabling repeatability' beyond what a fabrication plant can offer. Beyond that, additional circuitry (capacitive and additional resistive elements) can be used, for example, to create “deep rotor bars.” The conductive segments allow the discrete components to take command of the rotor behavior.

[0020] Disclosed rotor designs can be incorporated into electric field (or “electrostatic”) induction machines that further include a stator having electrodes configured to induce charges onto a rotor surface (e g., on the surface comprising conductive vanes). Control electronics can be provided to deliver voltage waveforms to the electrodes. In some examples, an electrostatic induction machine can include one or more sensors, such as an optical sensor to measure the speed (e.g.. rotation speed) of the rotor.

[0021] The general concepts, structures, and techniques disclosed herein can be applied to design and construct electrostatic induction machines having improved rotor dynamics, including but not limited to rotary motors, rotary generators, linear motors, and linear generators.

[0022] According to one aspect of the present disclosure, a rotor for an electrostatic induction machine includes: a substrate; a plurality of conductive segments formed on aDocket No.: MIT-714AWO / 26340first surface of the substrate; and circuitry electrically connecting sets of the plurality of conductive segments.

[0023] The circuitry can be disposed on a second surface of the substrate opposite from the first surface. The rotor can further include a plurality of vias to connect the first surface of the substrate to the second surface of the substrate. The circuitry can be disposed at least partially on the first surface of the substrate. The rotor can have a disc shape and the conductive segments can be conductive vanes arranged radially on a circular planar surface thereof. The circuitry can connect adjacent pairs of the conductive vanes. The circuitry can be arranged around an outer perimeter or inner perimeter of the circular planar surface. The rotor can have a drum shape with the conductive segments arranged on a curved inner or outer wall thereof.

[0024] The circuitry can include a plurality of resistive elements each connecting two or more of the conductive segments. The circuitry can include a plurality of resistive elements with two or more resistive elements in series connecting two or more of the conductive segments. The circuitry can include a plurality of networks each having one or more resistive elements and one or more capacitive elements, each of the networks connecting two or more of the conductive segments. The substrate can be or include a printed circuit board (PCB).

[0025] According to another aspect of the present disclosure, a rotor for an electrostatic induction machine includes: a substrate; a first conductive layer disposed on a surface of the substrate; and a second conductive layer disposed on the first conductive layer, wherein the second conductive layer has a lower conductivity and permittivity’ compared to first conductive layer.

[0026] A rotor such as described above can be used within a motor or a generator.

[0027] According to another aspect of the present disclosure, an electric field induction machine can include a rotor such as described above and further include a stator having a plurality of electrodes separated from the conductive segments of the rotor by an air gap. The machine can further include a controller configured to generate one or more voltage waveforms applied to excite the stator electrodes.Docket No.: MIT-714AWO / 26340

[0028] According to another aspect of the present disclosure, an electric field induction machine can include a plurality of rotors such as described above along with a plurality of stators, each having a electrodes separated from the conductive segments of a corresponding one of the plurality of rotors by an air gap. The plurality of rotors can be connected by a shaft. At least two of the rotors can be formed on opposite sides of a common substrate.

[0029] It should be appreciated that individual elements of different embodiments described herein may be combined to form other embodiments not specifically set forth above. Various elements, which are described in the context of a single embodiment, may also be provided separately or in any suitable sub-combination. It should also be appreciated that other embodiments not specifically described herein are also within the scope of the following claims.BRIEF DESCRIPTION OF THE DRAWINGS

[0030] The manner of making and using the disclosed subject matter may be appreciated by reference to the detailed description in connection with the drawings, in which like reference numerals identity7like elements. Disclosed features may be more fully understood from the following description of the drawings in which various aspects of the concepts and embodiments described herein are described. The drawings are not necessarily to scale, or inclusive of all elements of a system, emphasis instead generally being placed upon illustrating the concepts,

[0031] Fig. 1 is a schematic side view of an electrostatic induction machine showing its electromechanical operation.

[0032] Fig. 2 is a block diagram showing an example of a system including an electrostatic induction machine in which disclosed rotor designs can be provided.

[0033] Fig. 3A is a front view of a stator that can be used within an electrostatic induction machine.

[0034] Fig. 3B shows an enlarged section of Fig. 3 A.Docket No.: MIT-714AWO / 26340

[0035] Fig. 4A is a back view of a rotor showing electrode vanes formed on a surface thereof.

[0036] Fig. 4B shows an enlarged section of Fig. 4A.

[0037] Fig. 4C is a front view of the rotor of Fig. 4A, showing discrete components formed on a surface opposite from the electrode vanes.

[0038] Fig. 4D shows an enlarged section of Fig. 4C.

[0039] Fig. 4E is a schematic diagram showing a printed circuit board (PCB) layout that can be used to implement the rotor of Figs. 4A and 4C.

[0040] Fig. 5 is a circuit diagram show7an example of a circuit that may be used to connect two rotor electrodes to emulate a “deep bar’" design found in magnetic field induction motors.

[0041] Fig. 6 is a circuit diagram show another example of a circuit that may be used to connect two rotor electrodes to emulate a “deep bar"’ design found in magnetic field induction motors.

[0042] Fig. 7A is a back view of rotor emulating a “deep bar” design, showing electrode vanes formed on a surface thereof.

[0043] Fig. 7B shows an enlarged section of Fig. 7A.

[0044] Fig. 7C is a front view of the rotor of Fig. 7 A, showing discrete components formed on a surface opposite from the electrode vanes.

[0045] Fig. 7D shows an enlarged section of Fig. 7C.

[0046] Fig. 7E is a schematic diagram showing a PCB layout that can be used to implement the rotor of Figs. 7A and 7C.

[0047] Figs. 8 and 9 are graphical diagrams showing rotor speed versus torque for various different rotor designs.Docket No.: MIT-714AWO / 26340

[0048] Figs. 10A-E are schematic side views of electrostatic induction machines using various different rotor designs and circuit topologies.

[0049] Fig. 11 is a cross-sectional view of an electrostatic induction machine having a plurality of stators and rotors in a stacked arrangement.

[0050] Fig. 12A a front view of a double-sided rotor for an asynchronous electrostatic induction machine featuring discrete components on the front inside of a vane structure.

[0051] Fig. 12B shows an enlarged section of Fig. 12A.

[0052] Fig. 12C is a back view of the double-sided rotor of Fig. 12A, showing corresponding electrode vanes on the back.DETAILED DESCRIPTION

[0053] Fig. 1 illustrates electromechanical operation of an electrostatic induction machine 100, show n here as an electric induction motor. The machine 100 can be a rotary' machine or a linear machine. Disclosed structures and techniques can be employed with both disc-shaped rotary machines having electrodes disposed on planar surfaces of the stator and rotor, and “drunf’-shaped rotary machines having electrodes disposed around the curved inner / outer walls of the stator and rotor (e.g., the curved inner walls of a drumshaped stator and the curved outer walls of a drum-shaped rotor that fits inside the stator, or vice-versa). In the case of a disc-shaped machine, the view of Fig. 1 may correspond to a close-up view of the sides of a circular stator and rotor, which appear approximately linear. In the case of a drum-shaped machine, the view of Fig. 1 may correspond to a close-up top view of the curved walls of the stator and rotor, which also appear approximately linear. The general concepts, structures, and techniques disclosed herein are not limited to motors and can also be applied to generators.

[0054] Illustrative machine 100 includes a stator 102 and a rotor 104 separated by an air gap 105. Stator 102 includes a plurality of electrodes 106a, 106b, etc. (106 generally) formed on an insulative substrate 108. Rotor 104 includes a conductive layer 110 affixed to an insulative substrate 112. Stator 102 and rotor 104 can be arranged such that a surface of the rotor conductive layer 110 faces and is separated by stator electrodes 106 by the airDocket No.: MIT-714AWO / 26340gap 105. In some embodiments of the present disclosure, stator 102 and / or rotor 104 may be constructed using a printed circuit board (PCB).

[0055] Conventionally, the rotor conductive layer 110 was provided as a bulk material, such as glass coated in a conductive material such as Indium-Tin-Oxide (ITO), moderately doped poly silicon film, Plexiglas, or Bakelite. According to embodiments of the present disclosure, rotor conductive layer 110 can be formed from a plurality' of conductive vanes connected by discrete circuit components to achieve arbitrary resistivity / permittivity that may not be possibly or practically achieved using bulk material. According to other embodiments, rotor conductive layer 110 can be provided as a bulk material, but rotor 104 can include additional layers of material to emulate a magnetic ’'deep bar’' design.

[0056] In operation, a voltage waveform can be applied to stator electrodes 106 to induce opposite electric fields in each adjacent pair of electrodes. The voltage waveform can be generated by external electronics, such as electronics wi thin a motor controller (or “driver’"), not shown in Fig. 1. In some examples, the voltage waveform can be a stepped square wave. The external electronics can excite the stator electrodes 106 to produce a potential wave which travels around the stator 102 with a speed exceeding that of the rotor 104. The corresponding distribution of charges on the stator electrodes 106 induces charges (sometimes referred to as image charges) on the surface of the rotor conductive layer 110 across the airgap 105. As illustrated in Fig. 1, the conduction process is driven by a tangential electric field, so the rotor charges lag behind the stator waves to produce that field. The tangential electric field acts on the rotor charges to impart a tangential surface stress on the rotor, which in turn results in a motoring torque. In the case of a generator, the rotor speed exceeds that of the traveling stator waves, and so the process is reversed.

[0057] Various techniques and circuits for controlling an electrostatic induction machine known in the art may be used in conjunction with disclosed embodiments, including but not limited to those presented in Nagle et al. and books on magnetic induction machines.

[0058] Fig. 2 shows an example of a system 200 including an electrostatic induction machine in which disclosed rotor designs can be utilized. System 200 includes anDocket No.: MIT-714AWO / 26340electrostatic induction machine comprising a stator 202 and a rotor 204 provided within housing 206. In some examples, stator 202 may be implemented using a PCB (“stator board'’). Stator 202 and rotor 204 of Fig. 2 can be the same as or similar to stator 102 and rotor 104, respectively, of Fig. 1. A shaft 205 can be connected to a center of the rotor 204 for mechanical connection with a gear or other machine component. In some examples, housing 206 can be molded plastic formed to house the stator board. In some examples, housing 206 can be omitted.

[0059] System 200 can include a controller 208 (or “driver”) that can be connected (or “tethered”) to the electrostatic induction machine via one or more signal paths. As shown, controller 208 can generate a voltage waveform 210 that is applied to electrodes of the stator 202. In some examples, voltage waveform 210 can be a sine wave. In some examples, voltage waveform 210 can include multiple waveforms of different phases (e.g., six phases of sine wave separated by 60°). Each voltage waveform 210 can be connected to stator 202 over a separate wire or other type of conductive path. Controller 208 can receive power 212 from an external power source (e.g., a battery or other voltage source, or a cunent source). Controller 208 can include analog and digital circuitry configured to perform the functions described herein and / or various techniques for controlling an electrostatic induction machine known in the art. Controller can be constructed using a PCB, for example. In some examples, controller 208 can include an 800 V 3-phase linear amplifier-based inverter.

[0060] System 200 can include one or more sensors used to control or monitor operation of the electrostatic induction machine. For example, controller 208 can include voltage sensing circuitry’ (e.g., resistor dividers of the controller output 210) and / or current sensing circuitry'. As another example, a speed sensor 214 can be included within the machine housing 206 to sense the speed of rotor 204. In some cases, speed sensor 214 may be integrated onto the stator PCB. In some cases, rotor 204 can include one or more visual markings (e.g., light colored markings printed on the rotor PCB) and speed sensor 214 can be an optical sensor configured to detect those markings and thus determine the rotor speed. Speed sensor 214 can provide an analog or digital output signal 216 conveying rotor speed information (e.g., in terms of revolutions per minute, RPM, radians per second, etc.). As shown, the speed sensor output signal 216 can be received by controller 208. InDocket No.: MIT-714AWO / 26340some examples, controller 208 can adjust the voltage waveform 210 (e.g., to adjust the frequency, magnitude, or shape thereof). In some cases, controller 208 can change the stator excitation amplitude and frequency in response to its internal voltage and current readings. The technique of using only the current and voltage waveforms without the additional optical speed sensor is called “sensorless” control. In some embodiments, and as discussed in detail below, the rotor can be configured to emulate a magnetic “deep bar,” in which case speed control may not be necessary' (active speed control is an accepted alternative to a “deep bar” design, but may be relatively expensive and challenging for certain applications such as high speed machines).

[0061] Controller 208 can optionally include a two-way data bus 218. Data bus 218 can be used, for example, to send commands to controller 208 from an external system or device and / or can be used to output sensor information obtained within system 200 (e.g., rotor speed information).

[0062] Fig. 3A shows an example of a stator 300 that can be used within an electrostatic induction machine. Fig. 3B shows an enlarged section 320 from Fig. 3A.

[0063] Illustrative stator 300 includes a plurality of conductive vanes 302a, 302b, etc. (302 generally) corresponding to stator electrodes. In the example shown, each set of six (6) neighboring electrodes are used to implement a sine wave of voltage, with each electrode in the set configured to receive a voltage that is shifted by 60 degrees from its neighbors. The sine wave is repeated twenty-two (22) times around the stator, for a one-hundred and thirty -two (132) electrodes in total. The repetition number, m — 22, corresponds to the stator periodicity7, using the notation of Nagle et al. Other number of phases and stator periodicities (and thus total electrodes) can be used. Conductive vanes 302 can be formed of a metal (e.g., Silver, Gold, etc.) deposited on the stator board or made using a wafer process (e.g., Silicon). In general, the stator vanes can be formed of any material that is significantly more conductive than the rotor material onto which it induces charge.

[0064] At the outer perimeter of the stator board, groups of six (6) connectors 306a, 306b, etc. (306 generally) are provided for connecting to six (6) phases of sine wave forDocket No.: MIT-714AWO / 26340driving the motor. Of note, multiple groups of connectors 306 are provided for mechanical reasons and any of the groups can be used interchangeably.

[0065] So as to require only one amplifier to excite all electrodes in a given phase, all the electrodes for that phase can be connected together. This can be done by connecting the electrodes to one of six concentric conductive rings on the back side of the stator (not shown). Vias 304a, 304b, etc. can be provided to connect each vane on the front side of the stator to the appropriate conductive ring on the back side. The conductive rings can be arranged at different radii, hence a staggered pattern of vias can be used, such as shown in Fig. 3B.

[0066] In some embodiments, electrodes can be provided on both sides of a stator 300, which can be useful in a machine having a stack of rotors such as shown in Fig. 11 and discussed below.

[0067] Figs. 4A-E shows an example of a rotor 400 that can be used within an electrostatic induction machine. Fig. 4A is a back view of the rotor 400, Fig. 4B shows an enlarged section 420 from Fig. 4A, Fig. 4C shows a front view of the rotor 400, Fig. 4D shows an enlarged section 440 from Fig. 4C, and Fig. 4E shows a PCB layout 460 that can be used for the rotor 400.

[0068] Referring to Figs. 4A and 4B, illustrative rotor 400 can include a plurality of conductive vanes 402a, 402b, etc. (402 generally) formed on a first surface 403a of an insulative substrate 404. Conductive vanes 402 correspond to rotor electrodes. In some examples, rotor 400 may be constructed using a PCB that serves as the insulative substrate 404. Conductive vanes 402 can be formed of a metal (e.g., Silver, Gold, etc.) deposited on the first substrate surface 403a or made using a wafer process (e.g., Silicon).

[0069] As shown, substrate 404 can have a planar circular shape with a central opening 406. Conductive vanes 402 can be arranged radially on the first substrate surface 703a, wdth each vane extending substantially from the central opening 406 towards the outer circumference of substrate 404. This layout is sometimes referred to as a “pinwheel.” While Fig. 4A and other embodiments are described herein as having conductive “vanes,” more generally a rotor can be formed from a plurality of conductive segments spatiallyDocket No.: MIT-714AWO / 26340arranged on a surface of the rotor and connected by discrete circuit elements such as resistors.

[0070] The rotor electrodes (i.e., vanes) should generally be spaced out differently than those of the stator, such that they intentionally do not match up. For instance, the stator can include one-hundred and thirty -two (132) electrodes whereas the rotor can include one-hundred and thirty-one (131) electrodes. The number of stator electrodes and rotor electrodes can be selected to avoid a preferential alignment in which all stator electrodes line up with all rotor electrodes at the same time. To facilitate this, a prime number of rotor (or stator) electrodes can be used as in this example. In some examples, the rotor can have a much higher number of electrodes than stator electrodes.

[0071] The rotor central opening 406 can be sized to receive a shaft for mechanical connection with a gear or other machine component. While rotor 400 may be designed for use in a rotary' machine (e.g., a disc- or drum-shaped machine), the general concepts, structures, and techniques described herein can be applied to other ty pes of electrostatic induction machines such as linear motors or generators.

[0072] As shown, adjacent conductive vanes 402 can be physically isolated from each other on the surface of the substrate 404. That is, the vanes 402 may correspond to discrete regions of conductive material. However, the vanes 402 can be electrically connected together using discrete circuit components provided on an opposite surface of the substrate 404, as discussed in detail below. To provide electrical connectivity between the vanes 402 on one side of the substrate and the discrete circuit components on the other, a plurality of vias 408a. 408b, 408c, 408d, etc. (408 generally) can be formed through the planar thickness of the substrate 404 to link the two sides. In the example shown, two (2) vias 408 can be located along each of the conductive vanes 402 towards the outer ends. For reference, vias 408a and 408b are labeled for conductive vane 402a, and vias 408c and 408d are labeled for conductive vane 402b.

[0073] Figs. 4C and 4D show a plurality of discrete circuit elements 410a, 410b, etc. (410 generally) formed on a second, opposite surface 403b of the insulative substrate 404. Discrete circuit elements 410 can be provided as resistors, for example. The resistors canDocket No.: MIT-714AWO / 26340be denoted Ro. The type, size, and / or value of the resistors can be selected to control the overall rotor resistivity. In one example, 470 MO resistors may be used.

[0074] Each discrete circuit element 410 can be connected across a pair of adjacent conductive vanes 402 (Fig. 4B) and every adjacent pair of vanes 402 can connected by a different one of the plurality of discrete circuit elements 410. For example, discrete circuit element 410a (e.g., a resistor) can be connected at one end to via 408b of vane 402a (Fig. 4B) and at the other end to via 408c of vane 402b (Fig. 4B). This arrangement can be further seen in the PCB layout 460 of Fig. 4E.

[0075] Referring to PCB layout 460 of Fig. 4E, two adjacent conductive vanes 462a and 462b each have (i.e., are in contact with) a respective pair 464a, b and 464c, d of vias. The two vanes 462a, b are connected via a resistor 466 that is connected to via 464b at one end and to via 464c at the other end. Likewise for all other adjacent conductive vanes on the rotor. Of note, while the conductive vanes 462a, 462b and the resistor 466 are all illustrated in Fig. 4E, these elements can be located on opposite sides of the rotor board as previously discussed.

[0076] Arbitrary' resistivity / permittivity of the rotor electrode surface, and thus rotor time constant, can be achieved for example through selection of the material used to form the conductive vanes 402 as well as the type, size, and / or value of the discrete circuit elements 410. The rotor resistivity / permittivity is also affected by the geometry (e.g., length, width, spacing) of the conductive vanes.

[0077] While the example of Figs. 4A-D show each adjacent pair of rotor vanes connected by a single discrete element (e.g., a single resistor), other circuitry can be used to interconnect the vanes. For example, two or more resistive elements can be connected in series or parallel across a pair of vanes. As another example, one or more resistive elements in combination with one or more capacitive elements may be used. Such alternatives may be useful for increasing the rotor time constant in cases where high enough value resistors are not easily available. More generally, tw o or more rotor electrodes can be interconnected using a set of discrete circuit elements arranged in parallel, series, or another network topology. The conductive vanes connected by the discrete circuit elements may be adjacent or non- adjacent. Moreover, a single discreteDocket No.: MIT-714AWO / 26340circuit element or a set of discrete circuit elements can be used to connect two or more conductive vanes.

[0078] The discrete circuit elements, while electrically connected to the vanes, may be physically disposed on the rotor in an appropriate location, for example, on the opposite side of the rotor and connected by vias as in Figs. 4A-4D, or on same side as the conductive vanes. The later approach can be used to form dual- or multi-stage electrostatic induction machines. In some examples, discrete components can be integrated into the rotor substrate more directly; for instance, dense electrode structures may be added to increase capacitance.

[0079] Another variant of using discrete components is manufacturing a system with a set of discrete vanes, then coating a continuous resistive material on top. This essentially turns a continuous material into a large number of discrete materials electrically. By vary ing the spacing between the vanes, a large variety of resistance values may be obtained, even using the same continuous material option.

[0080] As an alternative to using discrete circuit elements, a circuit for interconnecting a set of rotor electrodes can be manufactured in layers of bulk material, such as by having layers of selectable resistivity adjusted with ion implantation with electrodes in between.

[0081] The rotor electrodes / vanes should generally be spaced out differently than those of the stator, such that they intentionally do not match up. For instance, one-hundred and thirty -two (132) stator electrodes can be used, and one-hundred and thirty -one (131) rotor vanes can be used. A rotor with a much higher number of rotor vanes than stator electrodes would also be appropriate, likely better if there were sufficient room for the resistive elements. In the prototype, rotor and stator structures are constructed using printed circuit boards. The discrete circuit elements on the rotor can be commercial resistors; the resistors in an early prototype were 470 Mil

[0082] As shown in Fig. 4C, one or more visual markings can be printed or otherwise formed onto second substrate surface 403b (e.g., on the front side of the rotor). A single visual marking 412 is shown at the “3 o’clock’" position of the rotor. Other numbers and placements of visual markings can be used. The visual markings can be used by an opticalDocket No.: MIT-714AWO / 26340speed sensor to detect rotational speed of the rotor during operation. Likewise, visual markings could be provided on a linear rotor for detecting linear velocity.

[0083] Turning to Figs. 5 and 6, a critical challenge in constructing motors for high speed, low torque applications is in overcoming the startup torque caused by static friction. Some existing macro-scale electrostatic motors must be “flicked” to start. The “deep bar” rotor is one approach to increase the starting torque of induction machines. Various embodiments extend the work done on magnetic induction “deep bar” rotors to electrostatic “deep bar” rotors (i.e. , rotors for electrostatic induction machines that emulate the torque effects produced by magnetic induction “deep bar” rotors).

[0084] In a conventional (non-“deep bar”) magnetic induction machine, magnetic fields are induced into a ferrous material which dissipate with a frequency -independent time-constant. That is, the time constant of the magnetic field in the rotor is the same at high operating frequencies as it is at low operating frequencies. To increase starting torque, magnetic field induction machines often employ a technique called “deep bar” rotors, where the rotor is made out of conductive bars of thickness that varies with distance from the stator.

[0085] In a good conductor,where 5 is the skin depth that the wave travels in the medium, is the frequency of the wave (set by the relative speed between the excitation wave on the stator and the rotor speed), p, is the magnetic permeability, and o is the conductivity of the material.

[0086] Since the electromagnetic waves go deeper into the conductive material at lower frequencies, this principle can be used to construct frequency-dependent behavior. In a magnetic induction motor, the thickness of the conductive bars can be varied to increase starting torque.

[0087] While the construction of “deep bar” rotors is a commonly accepted technique in magnetic field induction machines, the inventors are not aware of it ever being used in electrostatic induction machines. In an electrostatic induction machine, the time constant isDocket No.: MIT-714AWO / 26340set by the resistivity of the rotor, and the sum of system capacitances (such as between the different electrode elements). To make an electrostatic “deep bar” rotor, the time constant of the rotor must vary as a function of frequency, with longer time constants desired at lower frequencies, and shorter time constants desired at higher frequencies.

[0088] The frequency of interest is uiretatjVe, where^relative ^excitation m^mechanical ■ (2)

[0089] Thus, (^relative (sometimes referred to as slip speed) will be highest when the mechanical speed is lowest (low mechanical frequency corresponds to high relative frequency). It is appreciated herein that one relatively inexpensive way to achieve this is by manufacturing additional circuitry (e.g., a network of discrete circuit elements) on the rotor to interconnect sets of electrodes. This circuit can be designed to have favorable frequency-dependent characteristics. Using a speed sensor incorporated with the electrostatic induction machine (e.g., speed sensor 214 of Fig. 2), the starting torque of the electrostatic “deep bar” rotor can be compared directly to a conventional design. This circuit may either be manufactured using sets of discrete components, or manufactured in layers of bulk material, such as by having layers of selectable resistivity adjusted with ion implantation with electrodes in between.

[0090] Fig. 5 shows an example of a circuit 500 that may be used in a “deep bar” rotor design. In more detail, circuit 500 can be used to connect two or more rotor electrodes (e.g., conductive vanes 402 of Fig. 4B) and can be formed on a surface of the rotor insulative substrate (e.g., on the opposite surface from the conductive vanes, or the same surface). In some examples, a rotor can include a copy of circuit 500 for each conductive vane, connecting that vane to an adjacent vane.

[0091] Illustrative circuit 500 includes a first terminal 502a that can be connected to a first rotor electrode, a second terminal 502b that can be connected to a second rotor electrode, first resistor 504 (7?0), a second resistor 506 R ), and a capacitor 508 ( ). First resistor 504 (7?0) is connected across the terminals 502a. Second resistor 506 and capacitor 508 are connected in series, and also across the terminals 502a,b.Docket No.: MIT-714AWO / 26340

[0092] In contrast to the non-"deep bar” implementation of Figs. 4A-E which includes a single resistive element (Ro) between adjacent vanes, circuit 500 includes an additional resistor 508 (R^ along with a capacitor 508 (C- . The additional resistive and capacitive elements create a frequency dependence which provides improved starting torque.

[0093] Thus, an electrostatic version of a “deep bar” rotor circuit can be achieved by adding capacitive and resistive circuit elements. Employing such a “deep bar” architecture in an electrostatic induction machine provides for smooth transitions between two bounding rotor resistivity values. Moreover, it can eliminate the need for active speed control (e.g., using an optical sensor).

[0094] Turning to Fig. 6, the electrostatic “deep bar” may also be constructed in multiple stages of discrete components. For example, as shown, a circuit 600 can further include a third resistor 510 (7?2) and a second capacitor 512 (C2) connected in series and across the terminals 502a.b. This approach can be extended to an arbitrary number of resistors and capacitors (e.g., N resistors and N-l capacitors).

[0095] As an alternative to using discrete circuit elements to emulate “deep bar” torque effects, multiple layers of continuum materials may be used, such as described below in the context of Figs. 10B and 10C.

[0096] Figs. 7A-E shows another example of a rotor 700 that can be used within an electrostatic induction machine. Compared to rotor 400 of Fig. 4, rotor 700 includes additional circuitry connecting the conductive vanes to emulate “deep bar” torque effects. Fig. 7A is a back view of the rotor 700, Fig. 7B shows an enlarged section 720 from Fig.7A, Fig. 7C shows a front view of the rotor 700, Fig. 7D shows an enlarged section 740 from Fig. 7C, and Fig. 7E shows a PCB layout 760 that can be used for the rotor 700.

[0097] Referring to Figs. 7A and 7B, illustrative rotor 700 can include a plurality of conductive vanes 702a, 702b, etc. (702 generally) formed on a first surface 703a of an insulative substrate 704. Conductive vanes 702 correspond to rotor electrodes. In some examples, rotor 700 may be constructed using a PCB that serves as the insulative substrate 704. Conductive vanes 702 can be formed of a metal (e.g., Silver, Gold, etc.) deposited on the first substrate surface 703a or made using a wafer process (e.g., Silicon).Docket No.: MIT-714AWO / 26340

[0098] As shown, substrate 704 can have a planar circular shape with a central opening 706. Conductive vanes 702 can be arranged radially on the first substrate surface 703a, with each vane extending substantially from the central opening 706 towards the outer circumference of substrate 704. Other spatial arrangements of conductive segments can be used.

[0099] The rotor electrodes (i.e., vanes) should generally be spaced out differently than those of the stator, such that they intentionally do not match up. For instance, the stator can include one-hundred and thirty -two (132) electrodes whereas the rotor can include one-hundred and thirty-one (131) electrodes. In some examples, the rotor can have a much higher number of electrodes than stator electrodes.

[0100] The rotor central opening 706 can be sized to receive a shaft for mechanical connection with a gear or other machine component. While rotor 700 may be designed for use in a rotary' machine, the general concepts, structures, and techniques described herein can be applied to other types of electrostatic induction machines such as linear motors or generators.

[0101] As shown, adjacent conductive vanes 702 can be physically isolated from each other on the surface of the substrate 704. That is, the vanes 702 may correspond to discrete regions of conductive material. However, the vanes 702 can be electrically connected together using circuitry provided on an opposite surface of the substrate 704, as discussed in detail below. To provide electrical connectivity between the vanes 702 on one side of the substrate and the circuitry on the other, a plurality' of vias can be formed through the planar thickness of the substrate 704 to link the two sides. In the example shown, each conductive vane 702 contacts three separate vias. For example, conductive vane 702a contacts a first via 708a located along its length and contacts two additional vias 708b, 708c by way of conductive traces 709 extending outwards from vane 702a tow ards the outer circumference of the substrate 704. Likewise for each of the other conductive vanes in the pinwheel layout.

[0102] Figs. 7C and 7D show circuitry formed on a second, opposite surface 703b of the insulative substrate 704 to interconnect sets of the conductive vanes 702. In this example, adjacent vanes are connected using three resistors and one capacitor. By way ofDocket No.: MIT-714AWO / 26340illustration, conductive vanes 702a and 702b of Fig. 7B can be connected by resistors 710a-c and capacitor 712 of Fig. 7D. Relating Fig. 7D to Fig. 5, resistors 710a and 710b can collectively correspond to resistor 504 (Ro), resistor 710c can correspond to resistor 506 (R-t), and capacitor 712 can correspond to capacitor 508 (C-t). The pair of resistors 710a, 710b can be connected in series to effectively provide a single resistive element with increase resistance. This may be done due to the low values of available resistors from a manufacturer, or due to other considerations. As can also be seen in Fig. 7D, resistors 710a and 710b can respectively contact vias 708a and 708b of conductive vane 702a (Fig. 7B). While not visible in Fig. 7D, capacitor 712 can contact the third via 708c of conductive vane 702a (Fig. 7B). This arrangement can be further seen in the PCB layout 760 of Fig.7E.

[0103] Referring to PCB layout 760 of Fig. 7E, adjacent conductive vanes 762a and 762b each have (i.e., are in contact with) three vias 764a-c and 764d-f, respectively. The two vanes 762a, b are connected via three resistors 766a-c and a capacitor 768. The resistors 766a and 766b can be connected in series. One end of resistor 766a can be connected to via 764a, one end of resistor 766c can be connected to via 764e, and one end of capacitor 768 can be connected to via 765c. Likewise for all other adjacent conductive vanes on the rotor. Of note, while the conductive vanes 762a, 762b and circuit elements 766a, 766b, 766c, 768 are all illustrated in Fig. 7E, these elements can be located on opposite sides of the rotor board as previously discussed.

[0104] Arbitrary resistivity / permittivity' of the rotor electrode surface, and thus rotor time constant, can be achieved for example by adjusting the geometry (e.g., length, width, spacing) of the conductive vanes, selecting the material used to form the conductive vanes 702, and / or by selecting the type, size, and / or value of the circuit elements 710a, 710b, 712.

[0105] As shown in Fig. 7C, one or more visual markings can be printed or otherwise formed onto second substrate surface 703b (e.g., on the front side of the rotor). A single visual marking 714 is shown at the “3 o’clock” position of the rotor. Other numbers and placements of visual markings can be used. The visual markings can be used by an opticalDocket No.: MIT-714AWO / 26340speed sensor to detect rotational speed of the rotor during operation. Likewise, visual markings could be provided on a linear rotor for detecting linear velocity.

[0106] Various rotor design alternatives discussed above in the context of Figs. 4A-D may be applied to the rotor 700 of Fig. 7.

[0107] Turning to Figs. 8 and 9, to illustrate the effect of “deep bar’" emulation of an electrostatic induction motor, the analysis previously described was applied to the motor in Nagle et al.

[0108] Fig. 8 shows a plot 800 with a horizontal axis corresponding to rotor mechanical speed and a vertical axis corresponding to rotor torque. Curves 802a-e correspond to a rotor design using individual resistors ( / ?0) to interconnect sets of rotor electrodes for different resistor values. Curve 804 corresponds to a “deep bar” rotor design using two resistors and a capacitor (7?0, Rt, ) to interconnect sets of rotor electrodes.

[0109] Of note, in a deep bar rotor, the controller does not need to necessarily adjust the stator excitation frequency. For a constant frequency, the motor is at zero mechanical speed, then the relative frequency is maximized, and the deep bar circuit is used to achieve higher starting torque. If the motor is near the slip speed, then the deep bar circuit is not used. The plots of Figs. 8 and 9 are for a fixed stator excitation frequency; for different frequencies the various curves would translate left or right in the plot.

[0110] Fig. 9 shows a similar plot 900 for a macro-scale version. In plot 900, curves 902a-f correspond to a non-“deep bar” rotor design for different values of Ro, whereas curves 904a, b correspond to a “deep bar” rotor design for different values of Ro, Rr, Cr.

[0111] Figs. 10A-E schematically illustrate various different rotor designs and circuit topologies that may be used within an electrostatic induction machine, according to embodiment of the present disclosure. In each of these figures, a stator is shown as having a substrate 1002 and a plurality of electrodes 1004 formed on a surface thereof.

[0112] Fig. 10A shows a conventional rotor design. Here, a rotor 1000 comprises a substrate 1006 with a layer of bulk conductive material 1008 (e.g., glass) formed on a surface thereof.Docket No.: MIT-714AWO / 26340

[0113] Fig. 10B shows another rotor design. Here, a rotor 1020 comprises an additional layer of bulk conductive material 1010 sandwiched between conductive material 1008 and substrate 1006. Material 1008 closer to the air gap can be selected to have lower conductivity’ and permittivity relative to material 1010. In this way, rotor 1020 can mimic the magnetic diffusion of ‘'deep bar” rotors using multiple layers of bulk material.

[0114] Fig. 10C shows another modification of the conventional rotor design. Here, a rotor 1040 comprises two additional layers of bulk conductive material 1010, 1012.Material 1008 closest to the air gap can be selected to have lowest conductivity and permittivity and material 1012 furthers from the air gap can be selected to have highest conductivity and permittivity. In this way, rotor 1040 can mimic the magnetic diffusion of ‘"deep bar” rotors using multiple layers of bulk material.

[0115] Fig. 10D shows a rotor design using discrete circuit elements. Here, a rotor 1060 includes a plurality’ of electrodes 1014 (e.g., conductive vanes in a pinwheel layout) formed on one side of substrate 1006 and a plurality of discrete circuit elements 101 formed on the opposite side of substrate 1006. As shown, adjacent pairs of rotor electrodes 1014 can be connected by a discrete circuit element (e.g., a resistor, or multiple series-connected resistors).

[0116] Fig. 10E shows a rotor design using circuitry configured to emulate a “deep bar” design found in magnetic field induction motors. Here, adjacent pairs of rotor electrodes 1014 are connected by circuitry such as two resistors and a capacitor (e.g., using the circuit topology of Fig. 5) or by additional stages of discrete elements (e.g., using the circuit topology of Fig. 6).

[0117] Various combinations of the rotor designs and circuit topologies shown in Figs. 10A-E may be used.

[0118] Tumingto Fig. 11, in designing an electrostatic motor system, itmay be desirable to stack rotors and stators to have several active layers. In this case, a rotor board (e.g., PCB) can have conductive vanes on both sides connected by vias, and the discrete circuit components may be provided on one or both sides of the board. Each side of theDocket No.: MIT-714AWO / 26340board can act as a separate rotor, separated from a corresponding stator by an air gap. The rotor boards can thus be referred to as double-sided rotors. Likewise, a stator board can have electrodes on both sides and referred to as a double-sided stator.

[0119] An illustrative machine 1100 includes a plurality of stator boards 1102a, 1102b, 1102c, 1102d, etc. (1102 generally) and a plurality of rotor boards 1104a, 1104b, 1104c, 1104d, etc. (1104 generally). The stator boards 1102 and rotor boards can have planar geometries, with the planes perpendicular to the page of Fig. 11. The rotor boards 1102 can be connected to a central shaft 1106 such that they all rotate together. The stator boards 1104 can be fixed to internal surfaces of the machine 1100, as shown. Each rotor board 1102 can have conductive vanes on both sides and air gap-separated by a corresponding side of a stator board 1104. In the example shown, the outer stator boards 1102a and 1102e can have electrodes on a single side (i. e.. single-sided stators), whereas inner stator boards 1102c-d can have electrodes on both sides (i.e., double-sided stators). While five (5) stator boards and four (4) rotor boards are shown in Fig. 11, other numbers of boards can be used.

[0120] Figs. 12A-C show an example of a double-sided rotor 1200 that can be used within the machine 1100 ofFig. 11. A stator similar to that shown in Figs. 3A and 3B can be provided as a single- or double-sided rotor and used within the machine 1100 of Fig. 11.

[0121] Figs. 12A is a front view of the double-sided rotor 1200, Fig. 12B shows an enlarged section 1220 from Fig. 12A, and Fig. 12C show s a back view' of the double-sided rotor 1200.

[0122] Illustrative rotor 1200 includes a first plurality of conductive vanes 1202a, 1202b, etc. (1202 generally) formed on a front side 1203a of the rotor 1200, and a second plurality of conductive vanes 1204a, 1204b, etc. (1204 generally) formed on a back side 1203b of the rotor 1200. Each of the front-side vanes 1202a, 1202b, etc. can be connected to a corresponding one of the back-side vanes 1204a, 1204b, etc. using a respective via 1206a, 1206b, etc. (1206 generally).Docket No.: MIT-714AWO / 26340

[0123] Discrete circuit components 1208 can be manufactured on the front side 1203a, arranged around an inner perimeter of the rotor 1200 as shown. The discrete circuit components 1208 can directly connect adjacent pairs of front-side vanes 1202 and indirectly connect adjacent pairs of back-side vanes 1204 by way of the vias 1206. In other examples, discrete circuit components can be provided on both sides of a double-sided rotor. In this case, vias 1206 may be omitted. The discrete circuit components 1208 can include individual resistors, multiple series-connected resistors, netw orks of resistors and capacitors, etc. Any of the circuitry disclosed herein may be used on a double-sided rotor such as that of Figs. 12A-C.

[0124] Various embodiments of the concepts, systems, devices, structures and techniques sought to be protected are described. It should, however, be appreciated that alternative embodiments can be devised without departing from the scope of the concepts, systems, devices, structures and techniques described herein. It is noted that various connections and positional relationships (e.g., over, below, adjacent, etc.) are set forth betw een elements in the following description and in the drawings. These connections and / or positional relationships, unless specified otherwise, can be direct or indirect, and the described concepts, systems, devices, structures and techniques are not intended to be limiting in this respect. Accordingly, a coupling of entities can refer to either a direct or an indirect coupling, and a positional relationship between entities can be a direct or indirect positional relationship.

[0125] As an example of an indirect positional relationship, references in the present description to forming layer "A" over layer "B" include situations in which one or more intermediate layers (e g., layer "C") is between layer "A" and layer "B" as long as the relevant characteristics and functionalities of layer "A" and layer "B" are not substantially changed by the intermediate layer(s).The following definitions and abbreviations are to be used for the interpretation of the claims and the specification. As used herein, the terms "comprises," "comprising,’" "includes," "including," "has," "having," "contains" or "containing." or any other variation thereof, are intended to cover anon-exclusive inclusion. For example, a composition, a mixture, process, method, article, or apparatus that comprises a list of elements is not necessarily limited to only those elements but canDocket No.: MIT-714AWO / 26340include other elements not expressly listed or inherent to such composition, mixture, process, method, article, or apparatus.

[0126] It is to be understood that the disclosed subject matter is not limited in its application to the details of construction and to the arrangements of the components set forth in the following description or illustrated in the drawings. The disclosed subject matter is capable of other embodiments and of being practiced and carried out in various ways. Also, it is to be understood that the phraseology and terminology employed herein are for the purpose of description and should not be regarded as limiting. As such, those skilled in the art will appreciate that the conception, upon which this disclosure is based, may readily be utilized as a basis for the designing of other structures, methods, and systems for carrying out the several purposes of the disclosed subject matter. Therefore, the claims should be regarded as including such equivalent constructions insofar as they do not depart from the spirit and scope of the disclosed subject matter.

[0127] As used herein, the terms “processor’" and “controller” are used to describe electronic circuitry that performs a function, an operation, or a sequence of operations. The function, operation, or sequence of operations can be hard coded into the electronic circuit or soft coded by way of instructions held in a memory device. The function, operation, or sequence of operations can be performed using digital values or using analog signals. In some embodiments, the processor or controller can be embodied in an application specific integrated circuit (ASIC), which can be an analog ASIC or a digital ASIC, in a microprocessor with associated program memory. in a digital signal processor (DSP), and / or in a discrete electronic circuit, which can be analog or digital. A processor or controller can include internal processors or modules that perform portions of the function, operation, or sequence of operations. Similarly, a module can include internal processors or internal modules that perform portions of the function, operation, or sequence of operations of the module. A single processor or other unit may fulfill the functions of several means recited in the claims.

[0128] While electronic circuits shown in figures herein may be shown in the form of analog blocks or digital blocks, it will be understood that the analog blocks can be replaced by digital blocks that perform the same or similar functions and the digital blocksDocket No.: MIT-714AWO / 26340can be replaced by analog blocks that perform the same or similar functions. Analog-to-digital or digital-to-analog conversions may not be explicitly shown in the figures but should be understood.

[0129] Various embodiments of the concepts systems and techniques are described herein with reference to the related drawings. Alternative embodiments can be devised without departing from the scope of the described concepts. It is noted that various connections and positional relationships (e.g., over, below, adjacent, etc.) are set forth between elements in the claims, detailed description, and drawings. These connections and / or positional relationships, unless specified otherwise, can be direct or indirect, and the claimed inventions are not intended to be limiting in this respect. Accordingly, a coupling / connection of entities can refer to either a direct or an indirect coupling / connection, and a positional relationship between entities can be a direct or indirect positional relationship. As an example of an indirect positional relationship, references in the present description to element or structure A coupled / connected to element or structure B include situations in which one or more intermediate elements or structures (e.g., element C) is provided between elements A and B regardless of whether the characteristics and functionalities of elements A and / or B are substantially changed by the intermediate element(s).

[0130] Furthermore, it should be appreciated that relative, directional or reference terms (e.g. such as ‘‘above,’’ “below,” “left,” “right,” “top,” “bottom,” “vertical,” “horizontal,” “front,” “back,” “rearw ard." “forward,” etc.) and derivatives thereof are used only to promote clarity7in the description of the figures. Such terms are not intended as, and should not be construed as, limiting. Such terms may simply be used to facilitate discussion of the drawings and may be used, where applicable, to promote clarity of description when dealing with relative relationships, particularly with respect to the illustrated embodiments. Such terms are not, however, intended to imply absolute relationships, positions, and / or orientations. For example, with respect to an object or structure, an “upper” or “top” surface can become a “lower” or “bottom” surface simply by turning the object over. Nevertheless, it is still the same surface and the object remains the same.Docket No.: MIT-714AWO / 26340

[0131] The terms '‘disposed over,” '‘overlying,” ‘"atop,” ‘'on top,” “positioned on” or “positioned atop” mean that a first element, such as a first structure, is present on a second element, such as a second structure, where intervening elements or structures (such as an interface structure) may or may not be present between the first element and the second element. The term “direct contact” means that a first element, such as a first structure, and a second element, such as a second structure, are connected without any intermediary elements or structures between the interface of the two elements. The term “connection"’ can include an indirect connection and a direct connection.

[0132] The terms “approximately” and “about” may be used to mean within ±20% of a target value in some embodiments, within ±10% of a target value in some embodiments, within ±5% of a target value in some embodiments, and yet within ±2% of a target value in some embodiments. The terms “approximately” and “about” may include the target value. The term “substantially equal” may be used to refer to values that are within ±20% of one another in some embodiments, within ±10% of one another in some embodiments, within ±5% of one another in some embodiments, and yet within ±2% of one another in some embodiments.

[0133] The term “substantially” may be used to refer to values that are within ±20% of a comparative measure in some embodiments, within ±10% in some embodiments, within ±5% in some embodiments, and yet within ±2% in some embodiments. For example, a first direction that is “substantially” perpendicular to a second direction may refer to a first direction that is within ±20% of making a 90° angle with the second direction in some embodiments, within ±10% of making a 90° angle with the second direction in some embodiments, within ±5% of making a 90° angle with the second direction in some embodiments, and yet within ±2% of making a 90° angle with the second direction in some embodiments.

[0134] In the foregoing detailed description, various features are grouped together in one or more individual embodiments for the purpose of streamlining the disclosure. This method of disclosure is not to be interpreted as reflecting an intention that each claim requires more features than are expressly recited therein. Rather, inventive aspects may lie in less than all features of each disclosed embodiment.Docket No.: MIT-714AWO / 26340

[0135] As used in the claims or elsewhere herein, the term “comprising” does not exclude other elements or steps, and the indefinite article “a” or “an” does not exclude a plurality.

[0136] Additionally, the term "exemplary" is used herein to mean "serving as an example, instance, or illustration. Any embodiment or design described herein as "exemplary" is not necessarily to be construed as preferred or advantageous over other embodiments or designs. The terms "one or more" and "one or more" are understood to include any integer number greater than or equal to one, i.e. one, two, three, four, etc. The terms "a plurality" are understood to include any integer number greater than or equal to two, i.e. two, three, four, five, etc. The term "connection" can include an indirect "connection" and a direct "connection".

[0137] References in the disclosure to “one embodiment,” “an embodiment,” “some embodiments,” or variants of such phrases indicate that the embodiment(s) described can include a particular feature, structure, or characteristic, but every embodiment can include the particular feature, structure, or characteristic. Moreover, such phrases are not necessarily referring to the same embodiment(s). Further, when a particular feature, structure, or characteristic is described in connection knowledge of one skilled in the art to affect such feature, structure, or characteristic in connection with other embodiments whether or not explicitly described.

[0138] Use of ordinal terms such as “first,” “second,” “third,” etc., in the claims to modify a claim element does not by itself connote any priority, precedence, or order of one claim element over another or the temporal order in which acts of a method are performed, but are used merely as labels to distinguish one claim element having a certain name from another element having a same name (but for use of the ordinal term) to distinguish the claim elements.

[0139] The disclosed subject matter is not limited in its application to the details of construction and to the arrangements of the components set forth in the detailed description or illustrated in the drawings. The disclosed subject matter is capable of other embodiments and of being practiced and carried out in various ways. As such, those skilled in the art will appreciate that the conception, upon which this disclosure is based,Docket No.: MIT-714AWO / 26340may readily be utilized as a basis for the designing of other structures, methods, and systems for carr i ng out the several purposes of the disclosed subject matter. Therefore, the claims should be regarded as including such equivalent constructions insofar as they do not depart from the spirit and scope of the disclosed subject matter.

[0140] Although the disclosed subject matter has been described and illustrated in the foregoing exemplary' embodiments, it is understood that the present disclosure has been made only by way of example, and that numerous changes in the details of implementation of the disclosed subject matter may be made without departing from the spirit and scope of the disclosed subject matter.

[0141] Other variations to the disclosed embodiments can be understood and effected by those skilled in the art in practicing the claimed invention, from a study of the drawings, the disclosure, and the appended claims.

[0142] The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to obtain an advantage.

[0143] Any reference signs in the claims should not be construed as limiting the scope.

[0144] All publications and references cited herein are expressly incorporated herein by reference in their entirety'.

Claims

Docket No.: MIT-714AWO / 26340CLAIMS1. A rotor for an electrostatic induction machine, the rotor comprising:a substrate;a plurality of conductive segments formed on a first surface of the substrate; and circuitry electrically connecting sets of two or more the plurality of conductive segments.

2. The rotor of claim 1 wherein the circuitry is disposed on a second surface of the substrate opposite from the first surface.

3. The rotor of claim 2 comprising a plurality of vias to connect the first surface of the substrate to the second surface of the substrate.

4. The rotor of claim 1 wherein the circuitry is disposed at least partially on the first surface of the substrate.

5. The rotor of claim 1 having a disc shape, wherein the conductive segments are conductive vanes arranged radially on a circular planar surface thereof.

6. The rotor of claim 5 wherein the circuitry connects adjacent pairs of the conductive vanes.

7. The rotor of claim 5, wherein the circuitry is arranged around an outer perimeter or inner perimeter of the circular planar surface.

8. The rotor of claim 1 having a drum shape w ith the conductive segments arranged on a curved inner or outer wall thereof.Docket No.: MIT-714AWO / 263409. The rotor of claim 1 wherein the circuitry includes a plurality of resistive elements each connecting two or more of the conductive segments.

10. The rotor of claim 1 wherein the circuitry includes a plurality of resistive elements with two or more resistive elements in series connecting two or more of the conductive segments.

11. The rotor of claim 1 wherein the circuitry includes a plurality of networks each having one or more resistive elements and one or more capacitive elements, each of the networks connecting two or more of the conductive segments.

12. The rotor of claim 1 wherein the substrate comprises a printed circuit board (PCB).

13. A motor comprising the rotor of claim 1.

14. A generator comprising the rotor of claim 1.

15. An electric field induction machine comprising:the rotor as in claim 1 ; anda stator having a plurality of electrodes separated from the conductive segments of the rotor by an air gap.

16. The electric field induction machine of claim 15 further comprising:a controller configured to generate one or more voltage waveforms applied to excite the stator electrodes.

17. An electric field induction machine comprising:a plurality of rotors as in claim 1 ; andDocket No.: MIT-714AWO / 26340a plurality of stators, each having electrodes separated from the conductive segments of a corresponding one of the plurality of rotors by an air gap.

18. The electric field induction machine of claim 17 wherein the rotors are connected by a shaft.

19. The electric field induction machine of claim 17 wherein at least two of the rotors are formed on opposite sides of a common substrate.

20. A rotor for an electrostatic induction machine, the rotor comprising:a substrate;a first conductive layer disposed on a surface of the substrate; anda second conductive layer disposed on the first conductive layer, wherein the second conductive layer has a lower conductivity and permittivity compared to first conductive layer.

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