The use of advanced dielectric liquids and manufacturing techniques for enhanced surface area per unit volume, along with other multiplicative gains, is enabling macro-scale electrostatic machines with competitive torque densities. This emergence prompts the need for circuit modeling-that guides machine design and drive controls-rooted in the canon of well-established electromagnetic machinery practices. In this study, prior dielectric and manufacturing innovations are combined with a newly developed unified electrostatic machine d−q-axis framework to form a machine that demonstrates industrial utility. Design, equivalent circuits, and performance are validated by an experimental prototype intended for low-speed direct-drive servo actuators. A prototype electrostatic machine was constructed entirely of aluminum and printed circuit boards, and possesses active material torque densities ࣙ1.4 Nm/kg and ࣙ2.65 Nm/L without the need for forced air or liquid cooling. Additional features include near zero loss at stall and low torque ripple. Index Terms-Capacitance, d-q equivalent circuits, electric machines, electrostatic machines, medium voltage. NOMENCLATURE Symbols Meaning j, a Ý(−1), constant complex vector e j 2π /3 . v, i Transient voltage (V) and current (A). V, I Steady state voltage (V) and current (A). d s , d r Duty ratio of stator and rotor traces. N Number of rotor plates. C, G Capacitance (F), conductance (S). r Resistance (Ω) or radius (m).
P, λPole number, angular period (rad). r i , r o , gActive inner radius, outer radius, gap (m). ε 0 , ε x Vacuum and material permittivities (F/m). γ Torque angle (rad).
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.