A Deformed Geometry Synthesis Technique for Determining Stacking and Cryogenically Induced Preloads for the Space Launch System
The Space Launch System (SLS) stacking and Core Stage (CS) fueling induce significant preloads that contribute to the liftoff pad separation “twang”. To accurately capture this, an approach is required that can replicate the physics of all SLS physical stacking steps, CS cryogenic shrinkage, associated geometric nonlinearities, and the transient behavior and decay of the preloads with changing boundary conditions as the vehicle separates from the pad. The Deformed Geometry Synthesis (DGS) approach presented here satisfies the above requirements. DGS determines induced preloads by modeling components in their deformed geometry states and then enforcing compatibility by closing the resulting “deadbands”. DGS seamlessly integrates into the multibody modal synthesis framework and does not require the use of artificial external loads to enforce preloads or post-processing steps to remove their influence. Since DGS iterates to solve for the deformed state inclusive of geometric nonlinearities, running linearized parametrics to exercise different potential orientations of ball jointed struts that connect the CS to Boosters for cryo-shrinkage analyses is entirely avoided. Relative to the transient behavior and decay of stacking and cryo-induced preloads with SLS liftoff pad separation, this is an area of considerable interest to the SLS program. To capture this in the most accurate way possible, DGS algorithms are designed to work with Henkel-Mar nonlinear pad separation algorithms which operate on the separating longitudinal and lateral degrees of freedom (DoFs) between the vehicle and the pad. As the separating DoFs release, in whatever manner as dictated by the interface geometries, interface loads and interface flexibilities as well as the external loading on the vehicle, the subject preloads generate a complex twang/decay time-trace as dictated by the physics of the problem. This paper presents DGS numerical verification against the closed-form solution for Timoshenko’s 3 ball-jointed strut preload problem. This problem is then extended by the authors to the geometric nonlinear case where DGS is compared to the Newton-Raphson solution of the nonlinear equations. Next, DGS is utilized to solve the SLS stacking and cryogenic shrinkage coupled loads analyses. Finally, Henkel-Mar pad separation simulations are executed that isolate the impact of the induced preloads’ twang and decay characteristics.