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Aero-Elasticity Analysis of Spinning Projectile

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This work was pursued in order to develop in-house capability in the area of aero-elasticity of rockets and missiles. The aerodynamic lift of rocket body, esp. on nose and tail, contribute to the rocket bending deformation, causing forward shift of the rocket XCp. The analysis focuses on estimation of divergence velocity, i.e. when XCp coincides with CG and thus, on overall stability of rocket during flight. The current work was of interest to a customer from the defense sector, who is engaged with development of higher impulse, higher speed and longer range artillery rocket.

Zeus Numerix developed an aero-elasticity analysis tool based on the mode summation method. Finite element model using standard beam elements was employed. The following fundamental was solved as an Eigen value problem: [Φ]T([K]-(qdS)[CNα])[φ]=0. The tool estimated the dynamic divergence pressure (pressure at which the structural restoring moments are exceeded by the aerodynamic moments) and zeta factor (ratio of flexible lift force to rigid lift force).

Illustration
Bending of Rocket at High Angle of Attack

Customer supplied input data such as length wise distribution of EI, mass and aerodynamic coefficient. A very good agreement of results i.e. Q divergence, zeta factor and shift of CG was achieved. The safety factor for body divergence was more than 10, hence the projectile was deemed free from aero-elastic divergence. The work has been extended to account for thrust imbalances, rotation and full transient analysis.

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