Although the nonterrestrial applications for gyroscopes demand an optimized, lightweight, 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, despite the fact that higher speeds might provide significantly improved mass and volume efficiency (ref. 1). Also, designs are often based on one material, chosen a priori, and on the performance of a finite-element stress analysis to determine the minimum margin under operating conditions (ref. 2). Clearly, this approach is over conservative and does not make use of the efficiency that could be provided through design and material selection. For example, a 22- to 60-percent savings of package volume or a 15- to 48-percent savings of mass could be realized, depending on the required momentum, with lower momentum rotors having higher savings.
To investigate these benefits, the Naval Research Laboratory solicited researchers from the NASA Glenn Research Center and the Ohio Aerospace Institute (OAI) to perform an analytical stress analysis, applicable to both composite (anisotropic) and metallic (isotropic) gyroscope momentum wheels. The stress analysis was combined with an anisotropic failure criterion to enable the failure (rupture) prediction of the momentum wheel due to angular velocity and gimbal maneuver loading. A factor of safety was incorporated, and a sizing (optimization) procedure was developed and implemented in a computer code.
Comparison of the equally weighted performance index as a function of inner-to-outer-radius ratio, X (= a/b) for the Gr/Ep PMC, SiC/Ti MMC, AerMet 100, and stainless steel
for t = 1 in. and H = 1700 ft-lbf-sec.
The preceding plot compares the optimum momentum wheel designs for four materials considered--graphite/epoxy (Gr/Ep) polymer matrix composite (PMC), SiC/Ti metal matrix composite (MMC), AerMet 100, and stainless steel--for an equally weighted performance index (which accounts for both mass and volume efficiency) versus inner-to-outer-radius ratio X in the case of an H = 1700 ft-lbf-sec momentum wheel with an out-of-plane thickness t of 1 in. A factor of safety of 2 was employed, and the momentum wheels were sized to ultimate strength. This figure shows that the stainless steel design is inferior over the entire range of X values. At lower X values (below 0.4), the remaining three materials are comparable in terms of performance index. As the value of X increased, the PMC’s performance index increased much more rapidly than those of the other materials and reached a maximum value that is approximately 75-percent higher than that of the MMC and AerMet 100. This is due to the PMC’s extremely low density. The PMC reached its optimum design at X = 0.81, whereas the other three materials reached their optimum designs at X = 0.74.
From the following log-log plot below of H per unit package volume (H/PkV) versus H per unit mass (H/m) for the previous four materials and four angular momentums (95, 325, 700, and 1700 ft-lb-sec) with an out-of-plane thickness of 1 in., it is clear that the PMC provides the best design (as measured by this performance index) given equal weight to both mass and volume: that is, using a -1 line of slope. Also plotted on this figure is a -2.7 line of slope that intersects an extreme point of both the PMC and AerMet 100 curves. This indicates that in order for the AerMet 100 material design to be competitive with the PMC material design, the package volume must be 2.7 times more important than mass to the design of the gyroscope momentum wheel. Using such a performance index enables designers to quantify the required tradeoff space. More details can be found in reference 3.
Comparison of angular momentum per unit mass as a function of angular momentum
per unit package volume for Gr/Ep PMC, SiC/Ti MMC, AerMet 100, and stainless
steel for t = 1 in. and various values of H.
Last updated: December 14, 2007
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