A Lean Testing Methodology for the Inertia Parameters of Small Rocket Stages

Abstract

This thesis presents the development, analysis, and testing of a comprehensive testing methodology for determining the mass, Center of Gravity (CoG), and principal Moments of Inertia (MoI) of small rocket stages. The methodology comprises five sequential tests, encompassing both static and dynamic procedures. The two static tests introduce innovative adaptations of established techniques. The multi-point weighing (MPW) method for the measurement of mass and horizontal CoG coordinates is modified into a suspended version, broadening its applicability, while the suspension method, measuring the CoG height, evolves into the Bifilar Suspension (BS) method, enhancing robustness and safety with the inclusion of an additional rope. The dynamic tests measure the body's MoI values, with the Bifilar Pendulum (BFP) method for roll MoI and the Compound Pendulum (CP) method for pitch and yaw MoI. Efficiency and cost-effectiveness are integral to the methodology, resulting in a streamlined testing campaign requiring minimal time and resource investment.

An analytical uncertainty analysis assessment explores the propagation of uncertainties in the employed methods, highlighting the impact of several parameters on the combined uncertainty on the results. Additionally, an analytical expression for the amplitude-dependent errors in dynamic tests is derived, providing a useful tool to predict such nonlinear effects. A simulation study numerically verifies the results from the uncertainty analysis, as well as the solution equations used for the methods.

The methodology's validation is carried out through three consecutive test campaigns. The results demonstrate the capability of the static tests to consistently determine mass and CoG coordinates with limited uncertainties. The BFP method achieves satisfactory accuracy, although unexpected deviations from the numerical predictions are observed. As for the CP method, multiple factors exert a large influence on the accuracy of the final results. Among the ones analyzed in this work are: the length of the ropes, the radius of gyration of the body, and the accuracy in the frequency measurement. Moreover, in both dynamic tests the type of suspension system is found to have an effect on the accuracy of the measurements.

While not all the intended objectives have been achieved, this thesis contributes to the understanding of testing methodologies for rocket stages, and offers insights into achieving accurate and precise results with simple and cost-effective methods.