Features of mathematical modeling of nonlinear Pogo oscillations of launch vehicles

The paper presents nonlinear non-stationary mathematical models of oscillations of the two-staged expendable R-36 and R-36M rockets developed in the USSR, which as dynamic systems were unstable with respect to Pogo during the operation of the first-stage engine. The model nonlinear functions, leading to the limitation of the Pogo amplitudes of oscillations, reflect the physical processes of cavitation in pumps and dissipation of oscillation energy in the rocket structure. The results of mathematical modeling of the Pogo oscillations of the R-36 and R-36M rockets show that the Pogo instability can occur both in case of coincide the rocket structure natural vibration frequency and the liquid propellant oscillations frequency in the engine propulsion system, and in case of those frequencies are noticeably distant from each other. In the first case, the limitation of the amplitudes of Pogo oscillations occurs due to a decrease in the resonant interaction of the liquid propellants in the feedlines of propulsion system and the rocket structure with an increase in the amplitude of Pogo oscillations. The nonlinear dependence of the pump cavitation elasticity on the engine regime parameters determines this limitation of the amplitudes of Pogo oscillations. The limitation of the amplitudes of Pogo oscillations in the second case occurs due to an increase in the dissipation of launch vehicle structure vibrational energy.