Modeling the stability of a throttle hydraulic drive of rocket and space systems under random load and stochastic parameters

Abstract

The use of a throttle hydraulic drive in rocket and space technology is promising due to its simplicity, reliability in operation, and low metal consumption. It has been determined that vibrations occur in the hydraulic system of rocket and space equipment under external influence. They cause unstable movement of working units, and, as a result, additional vibrations occur on the actuator. Determin- ing the stability of the throttle hydraulic drive is relevant. This will ensure that the rocket and technical system maintains specified equilibrium states or types of motion. The article solves an important scientific and technical problem of increasing the accuracy of identifying the state of a hydraulic drive with throttle control under the action of a stochastic load in rocket and technical systems. A mathematical model of the operation of a hydraulic drive with throttle control is developed based on its calculation scheme. A gen- eralized method for mathematical modeling of the probability of system stability for the mathematical expectation under a random load and in the presence of one random parameter, namely, the modulus of elasticity of the working fluid, is developed.Linearization of viscous friction forces was performed, and the schedule of the standard deviation of the random modulus of elasticity of the working fluid in the Taylor series was used. A solution to the mathematical model in the form of differential equations using a technique based on statistical linearization and expansion in the Taylor series was proposed. In this case, the stability condition of the hydraulic system is determined by the mathematical expectation in the form of the Hurwitz criterion. The stability condition of the hydraulic drive with throttle control is determined based on the probability of system stability, the value of the random external load is specified in the form of mathematical expectation and variance.