Electric-Field Induction Motor with Discrete Circuit Elements and Improved Rotor Dynamics

Alex S. Miller; Jeffrey H. Lang

cs.ROOct 27, 2026

Electric-Field Induction Motor with Discrete Circuit Elements and Improved Rotor Dynamics

Authors: Alex S. Miller, Jeffrey H. Lang

Organizations: Dept. of Aeronautics and Astronautics Massachusetts Institute of Technology Cambridge, USA · Dept. of Electrical Eng. and Computer Sci. Massachusetts Institute of Technology Cambridge, USA

Abstract

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. Electric-field induction motors consist of a set of stator electrodes which induce opposite charges onto a movable rotor surface. In earlier work, rotor surfaces for electric-field induction motors have been made of single continuum materials, which are limited in possible resistivity, permittivity and circuitry characteristics. To enhance design freedom, we develop a rotor for electric-field-based machines which may be constructed out of discrete circuit components between a finite number of conductive vanes. 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 frequency using the skin depth effect. We propose, analyze, design and demonstrate a macro-scale electric-field induction motor which uses circuitry on the rotor surface to emulate the deep bar'' design, providing improved torque over a wide range of speeds.

Figures & tables

Fig. 1 : Diagram showing the electromechanical operation of an electric-field induction motor. The stator electrodes are driven with a traveling sinusoidal excitation which induces charge on the rotor surface. Charge relaxation on the rotor surface results in shear force between the rotor and stator, causing the rotor to move.

Fig. 2 : Diagram showing simplified topologies of electro-quasistatic induction motors including (a) the traditional electro-quasistatic induction motor with a continuous rotor conductor material. (b) electro-quasistatic induction motor with discrete rotor resistors such as developed in this work. (c) electro-quasistatic induction motors with circuits on the rotor to shape the speed-torque characteristics, such as developed in this work. (d) electro-quasistatic induction motors with circuits made from two or more layers of continuous material on the rotor with circuits that change the speed-torque characteristics.

Panel of Figure 3 — Fig. 3 : Circuit between rotor vane electrodes on electro-quasistatic induction motor with discrete rotor resistors, $R_{\mathrm{0}}$ , and parasitic vane capacitance, $C_{\mathrm{vane}}$ .

Fig. 4 : Rotor design for electro-quasistatic induction motor using discrete resistors. (a) Front of rotor circuit board, showing discrete resistors. (b) Back of rotor circuit board, showing electrode vanes.

Panel of Figure 5 — Fig. 5 : Circuit between rotor vane electrodes to achieve a frequency-dependent rotor time constant, $\tau_{\mathrm{R}}$ , as a function of slip frequency. This design emulates a “deep bar” rotor common in magnetic-field machines, with the goal of achieving both high starting torque and high efficiency at nominal operating speed.

Fig. 6 : Circuit board design for electric-field induction motor rotor exhibiting improved rotor dynamics. (a) Front of circuit board, showing discrete resistor and capacitor networks. (b) Back of circuit board, showing rotor electrode vanes.

Parameter	Value	Description
$V_{\mathrm{excitation}}$	$420\text{\,}\mathrm{V}$	Excitation amplitude per phase
$R_{\mathrm{o}}$	$28\text{\,}\mathrm{mm}$	Motor outer active radius
$R_{\mathrm{i}}$	$9\text{\,}\mathrm{mm}$	Motor inner active radius
$R_{\mathrm{R,o,mech}}$	$33\text{\,}\mathrm{mm}$	Rotor mechanical outer radius
$R_{\mathrm{R,i,mech}}$	$8\text{\,}\mathrm{mm}$	Rotor mechanical inner radius
$\Delta_{\mathrm{ri}}$	$1.6\text{\,}\mathrm{mm}$	Thickness of rotor insulator

TABLE I : Parameters for motor model. Values for

G

R_{0}

R_{1}

C_{1}

, and

C_{\mathrm{vane}}

vary, and are described elsewhere.

Rotor #	$R_{0}$	$R_{1}$	$C_{1}$	$C_{\mathrm{vane}}$
1	$300\text{\,}\mathrm{M\SIUnitSymbolOhm}$	N/A	N/A	$0.68\text{\,}\mathrm{pF}$
2	$940\text{\,}\mathrm{M\SIUnitSymbolOhm}$	N/A	N/A	$0.68\text{\,}\mathrm{pF}$
3	$940\text{\,}\mathrm{M\SIUnitSymbolOhm}$	$470\text{\,}\mathrm{M\SIUnitSymbolOhm}$	$1\text{\,}\mathrm{pF}$	$0.68\text{\,}\mathrm{pF}$
4	$940\text{\,}\mathrm{M\SIUnitSymbolOhm}$	$470\text{\,}\mathrm{M\SIUnitSymbolOhm}$	$2\text{\,}\mathrm{pF}$	$0.68\text{\,}\mathrm{pF}$
5	$940\text{\,}\mathrm{M\SIUnitSymbolOhm}$	$470\text{\,}\mathrm{M\SIUnitSymbolOhm}$	$0.3\text{\,}\mathrm{pF}$	$0.68\text{\,}\mathrm{pF}$

TABLE II : Rotor parameters

Fig. 7 : Rotor admittance as a function of frequency for the rotors tested in this paper with parameters in Table II .

Panel of Figure 10 — Fig. 8 : Test stand design for electro-quasistatic induction motor with discrete components. (a) Top view showing rotor, stator, and contrast patch for optical speed sensor. (b) Slanted view showing hybrid V-jewel and aerostatic bearing with $<$ $0.5\text{\,}\mathrm{\SIUnitSymbolMicro N}\text{\,}\mathrm{m}$ of static friction. (c) Side view showing adjustable z-axis stage which changes gap thickness, achieving $<$ $200\text{\,}\mathrm{\SIUnitSymbolMicro m}$ gap and accommodating interchangeable test rotors.

Fig. 9 : High voltage amplifier setup for electrostatic motors, with 6 channels of $900\text{\,}\mathrm{V}$ pp linear amplifiers.

Fig. 10 : Load characterization of induction motor using power-off spindown tests.

Fig. 11 : Speed measurements taken for a variety of relative air gap distances between the rotor and the stator, with corresponding torque values using Eq. 16 , for a rotor with

0.94\text{\,}\mathrm{G\SIUnitSymbolOhm}

resistors at a fixed excitation of

300\text{\,}\mathrm{Hz}

. The absolute gap values may be calculated using the motor model in Eq. 3 and Eq. 16 , as represented on the plot.

Fig. 12 : Torque as a function of slip frequency,

\omega_{\mathrm{s}}

, for a rotor with discrete

0.94\text{\,}\mathrm{G\SIUnitSymbolOhm}

rotor resistors. Experimental data are given and compared to a model which includes parasitic capacitance between rotor vanes. The limit without parasitic capacitance, where

C_{\mathrm{par}}\to 0

, represents the continuous rotor conductor case.

Panel of Figure 15 — Fig. 13 : Steady-state torque plotted as a function of slip frequency, plotted with the model from Section II , III and IV , for a (a) wide (b) narrow frequency range, with a shared legend. Circuits on the rotor enable a balance of high starting torque and high efficiency with a minor decrease to peak torque, adding an additional parameter for electrostatic motor designers.

Fig. 14 : Rotor surface resistance comparison from Nagle [ 29 ] in the solid lines, with “deep bar” options added, shown with the dashed lines.

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Macro-Scale Electrostatic Origami Motor

Alex S. Miller, Leo McElroy, Jeffrey H. Lang

Dept. of Aeronautics and Astronautics Massachusetts Institute of Technology Cambridge, USA · Independent Researcher Cambridge, USA · Dept. of Electrical Eng. and Computer Sci. Massachusetts Institute of Technology Cambridge, USA

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Origami structures have been an active area of research due to their high volume-to-mass ratio, packability, and shape adaptability. Previously-developed actuated foldable structures have either embedded linear actuators into the structure, or have attached non-folding rotary motors to the exterior structure. Further, in prior work, actuators directly embedded in the structure of folding media all contributed to linear or folding motion, not to continuous rotary motion. On the macro-scale there has not yet been a folding continuous rotary actuator. This paper details the development and testing of the first macro-scale origami rotary motor that can be folded flat, and then unfurled to operate. Using corona discharge for torque production, the prototype motor achieved an expansion ratio of over 3.8:1, reached a top speed of 1720 rpm when driven at -30 kV, and exhibited a maximum motor torque over 0.25 mNm with an active component torque density of 0.11 Nm/kg.

Abstract

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