Development and optimization of a multibumper design model for spacecraft protective structures

Abstract The development and optimization of a design model for multibumper spacecraft protective structures to defeat orbital space debris is presented. The Marshall Space Flight Center (MSFC) Materials and Processes (M&P) Laboratory Hypervelocity Impact Database is first filtered to experiments comprising metallic configurations without multilayered insulation present and for projectile velocities exceeding 2.5 km/sec. This filtering results in 337 single, double, and triple bumper hypervelocity impact experiments. Regression variables of interest include projectile diameter, density, velocity, and impact angle, bumper standoff distances, bumper densities and thicknesses, wall density and thickness, and number of bumpers. The dependent regression variable is the total number of plate penetrations, beginning with the wall and continuing through the witness plates. A unique intrinsically linear regression form, which accounts for the number of bumpers employed and invokes a posynomial (polynomial with positive coefficients, positive valued independent variables, and real valued exponents) form, is chosen based on a comparison of various regression forms using correlation coefficient and F-statistic as measures of effectiveness. The least squares regression is performed followed by an ANOVA, tests of the correlation and F value, and graphical examination of residuals. Regression results indicate that statistically significant least squares is possible using the chosen form on the MSFC M&P database with small residual effects. Generic nonlinear regression forms are also investigated. The resulting regression model is next used in the formulation of a nonlinear optimization program. This program is devised to minimize the protective structures areal density subject to a limitation on total standoff distance between the first bumper and the wall. The decision variables of interest are the optimal values of the areal densities of the bumpers and wall, as well as the optimal individual standoff distances. The problem is solved using the dual transformation of geometric programming. The optimal independent variables and minimum system areal density are solved for analytically in terms of the systemic parameters. A sensitivity analysis to these parameters is then performed. Additionally, the optimal number of bumpers is evaluated in this sensitivity study. The most significant results from a hypervelocity impact standpoint are that additional hypervelocity impact tests and analyses should be performed to support understanding of multiple bumper, large particle diameter, large separation, large particle mass density, various particle impact angles, and spallation phenomenologies. Additionally, more emphasis should be placed on understanding the transition regions between particle shatter, melt, and vaporization, while less emphasis should be placed on small velocity differences within these regions. Major protective structures design results indicate that for Space Station Freedom impact scenarios of interest, and within the limitations of the regressed hypervelocity impact database, at most four metallic bumpers are optimal. In particular, a transition region from optimal number of bumpers of 2 to 3 (and 3 to 4) has been identified for particle diameters in the 0.25–0.5 cm (and 1 to 1.25 cm) range. An interesting transition region from 3 to 4 optimal number of bumpers has been discovered for standoff distances between 10 and 15 cm. Furthermore, the optimal protective structures design sensitivity to impact angle is very low. Finally, the results of this investigation indicate that this combination of regression form and resulting optimization approach is useful in identifying protective structures design trends for spacecraft subject to hypervelocity impact environments.