Design and Optimization of Composite Gyroscope Momentum Wheel Rings

Abstract Stress analysis and preliminary design/optimization procedures are presented for gyroscope momentum wheel rings composed of metallic, metal matrix composite, and polymer matrix composite materials. The design of these components involves simultaneously minimizing both true part volume and mass, while maximizing angular momentum. The stress analysis results are combined with an anisotropic failure criterion to formulate a new sizing procedure that provides considerable insight into the design of gyroscope momentum wheel ring components. Results compare the performance of two optimized metallic designs, an optimized SiC/Ti composite design, and an optimized graphite/epoxy composite design. The graphite/epoxy design appears to be far superior to the competitors considered unless a much greater premium is placed on volume efficiency compared to mass efficiency. I. Introduction Gyroscopes use the conservation of angular momentum in order to measure or control orientation. Often referred to as control momentum gyroscopes (CMGs), these systems are used in aircraft, satellites, spacecraft, and ships (refs. 1 and 2) (see fig. 1) when they are cost and mass effective. A key component of a gyroscope is the momentum wheel, also sometimes referred to as the CMG flywheel. It is this spinning component that stores the angular momentum that can be used by the system for control or sensing purposes and thus, along with its hub, drives the design of the gyroscope system. While the non-terrestrial applications for gyroscopes demand an optimized light-weight and low-volume design, the momentum wheel design has not typically been optimized. For example, heritage designs have predominantly used a standard operating rotational speed of 6000 rpm on which legacy bearing designs have been based, despite the fact that higher speeds will provide significantly improved mass and volume efficiency (ref. 1). Designs are also often based on one material chosen a priori and a finite element stress analysis to determine the minimum margin under operating conditions (refs. 1 and 3). Clearly, this approach tends to be overly conservative, and a good deal of efficiency that could be captured through design and material selection is being left on the table. Further, with the development of efficient and reliable gyroscopes, additional system weight saving are possible by utilizing the gyroscope for energy storage as well as control (refs. 4 and 5). This paper presents an analytical stress analysis, applicable to both composite (anisotropic) and metallic (isotropic) gyroscope momentum wheel rings. The stress analysis is combined with an anisotropic failure criterion to enable the failure (rupture) prediction of the momentum wheel ring due to angular velocity and gimbal maneuver loading. A factor of safety is incorporated, and a sizing (optimization) procedure is presented, which was implemented in a computer code. While the method considers only a single rotating ring (rather than multiple momentum wheel rings, the hub, and the shaft), it is highly efficient and thus well suited for preliminary design and sizing studies in which hundreds or thousands of potential designs may be considered. Full system design, requiring a detailed finite element