Bifurcation and Chaos Analysis of a Supersonic Slipper–Track System

Abstract

The slipper is the critical component of a supersonic rocket sled that is in contact with the track. Due to clearance and contact effects, the supersonic slipper–track system displays pronounced nonlinearities. A comprehensive analysis, including bifurcation and chaos detection, is conducted on this system to predict the nonlinear behavior of the slipper. Kinematic and dynamic models of the system are established using the generalized coordinate and Lagrange multiplier methods. This model accounts for slipper–track clearances, track irregularities, and normal contact forces. The dynamic response of the slipper is examined both in time and frequency domain. The bifurcation analysis encompasses various parameters such as slipper velocity and length, and slipper–track clearance. Chaos identification is employed for both qualitative and quantitative assessments, utilizing phase diagrams, Poincaré sections, the trajectory of the slipper's center, and the largest Lyapunov exponent (LLE). The findings revealed significant nonlinear phenomena, including self-excited vibrations, superharmonic responses, jumping phenomena, strange attractors, and combined frequencies. Notably, this study demonstrated the potential for leveraging chaotic response to mitigate the contact forces on the slipper. These insights contribute to the rationalization of control parameters and the optimization of slipper and track design.