Thursday, June 27, 2013

Experimental Analysis of Spinning Wheels with 6 Degrees of Freedom Shows Their Behavioral Similarity to Electrical Inductors

(I have been invited to present these findings at the annual ASME conference in San Diego in November of this year.)

The behavior of a single spinning wheel in gimbals is a well-documented subject; however, the interaction between multiple spinning wheels is less fully explored. Some researchers have hypothesized that spinning wheels could be mathematically modeled after electrical inductors, suggesting that the interaction between multiple spinning wheels might mirror that of multiple inductors in proximity with each other. The goal of the current set of experiments was to examine the interaction between two gimbaled spinning wheels with six degrees of freedom embedded in one scaffolding and observe their behavioral similarity to electrical inductors.

    Two aluminum spinning wheels (1 in. thick and 1 ft. diameter) were secured in two sets of gimbals each. These subassemblies were supported in a light-weight, stand-alone aluminum scaffolding that allowed rolling, rotation and translation. The spinning wheels rotated at 5000 rpm. The first set of gimbals was driven by high-torque motors and the second set of gimbals was driven by a motor with a high-torque gear box and a programmable servo drive. Multiple sets of experiments were run to apply torques of various profiles, from straight to sinusoidal at different maximum currents and speeds. Video and electrical data were recorded for analysis.

    The spinning wheels showed behaviors such as large inertia amplification about the main shaft and subassembly shafts, coupling with each other so that the behavior of one spinning wheel is dependent on the behavior of the other and the ability to steer the scaffolding. Mathematically, these behaviors are similar to those of electrical inductors, and such an analogy between inductors and offset, gimbaled spinning wheels finds support in Generalized Machine Theory.

Generalized Machine Theory opines that only a “few ultimate types of elements…form the building blocks of the great variety of engineering structure” (Kron, Tensors for Circuits, Second Edition, 1969, Page xxiii) and classes inductors among those building blocks: however, at present there exist no mechanical devices that are analogues of the electrical inductor. Spinning wheels in the offset, gimbaled suspension of the prototype tested are great candidates for such devices. The experimental results indicate that it might be possible to build new machines that use powered spinning wheels at their heart, with designs analogous to electrical machines, capacitor-inductor oscillators, transformers, and so on.

Experiment 10.10