Optimal Design of a Rotating Bar for Kinetic Energy Storage

Abstract

A thin homogeneous rotating bar of variable width is considered for the purpose of storing kinetic energy. The objective of the design is to find the shape of the bar for which, in the presence of constraints on the geometry and strength of the bar, the Specific Kinetic Energy (SKE) is maximal. An upper bound for the SKE of a finite length bar is derived and a discrete formulation is presented by which an approximate optimal profile for arbitrary design parameters and rotational speeds can be obtained numerically. Applying a parametric study, in which optimal designs for a sequence of rotational speeds were observed, a general configuration of the exact optimal profile was concluded. The parametric study reveals the existence of three speed intervals, each characterized by a common type of optimal design. The optimal SKE corresponding to the ultimate rotational speed reaches a value very close to the theoretical upper bound, namely, that of a thin ring. The model gives insight into the nature of optimal designs and serves as a simple and rapid computational tool for finding the optimal profile for arbitrary bar parameters and rotational speeds.