Modeling of Pogo Vibration in Rockets with Staged Combustion Cycle Engine

Abstract

The modeling method of the pogo system of launch vehicles with a staged combustion cycle engine is mainly limited to the transfer matrix modeling method, which contains transcendental functions that are difficult to solve. A state-space modeling method for the pogo system of launch vehicles with a staged combustion cycle engine is proposed in this paper. First, the second-order differential dynamic equation of the gas path is constructed by approximating the exponential term in each element of the gas path with Taylor expansion and inverse Laplace transformation. Second, the liquid and gas paths are combined in the form of mass flow to establish the second-order dynamic equation of the propulsion system. Third, the state-space equation of the coupled system is obtained by combining the structural and propulsion systems. Finally, an example of a propulsion system is modeled using the transfer matrix modeling method and the proposed method to verify the correctness of the proposed method, and the stability of the model is analyzed when the parameters of the accumulator and gas path change. The major contributions are as follows: 1) the proposed method is a systematic method that is universally applicable to the pogo analysis of a launch vehicle with a staged combustion cycle engine; 2) the proposed method inherits the advantages of Rubin’s state-space method for liquid rockets.