Multibody Dynamic Modeling And Simulation Of Liquid-Propellant Launch Vehicles

Liquid-propellant launch vehicle is a typical time-varying system and also acomplicated dynamic coupling system, whose dynamic problems are extremelysignificant for the design and developing process. This paper has researched on themodeling and simulation of liquid-propellant launch vehicles based on the method ofmultibody dynamics. Three are mainly three parts within this paper:Firstly, multibody dynamic modeling methods were presented for all aspects of thedynamics of liquid-propellant launch vehicles. Based on the finite segment approach, aflexible multibody system was established for the empty launch vehicle withoutpropellant. D’Alembert-Lagrange principle for variable mass particles was presentedand a multibody dynamic modeling element for the flexible propellant tank withvariable mass was described with the method of Lagrange multiplier. A equivalentmechanical model was presented for the small-amplitude sloshing of variable-massliquid tanks and the dynamic model for a mass-varying particle was generated withinthe multibody dynamics framework. Time-varying control loop was realized in themultibody system by way of state space equations with non-constant coefficientmatrices. With the constraint force equation approach, dynamic separation process wasmodeled for the multibody launch vehicles. By applying the harmonic wavesuperposition method, stochastic pressure on the launch vehicle within transonic flightwas generated based on the power spectrum density. And other time-varying forces suchas gravity and aerodynamic force were modeled considering the geometry and rotationof the earth. The governing equation for the launch vehicle system is a group ofdifferential algebraic equations, which can be solved numerically by BDF methodstogether with Newton-Raphson iteration. Several validation examples were given forthe modeling methods given in the paper. Comparison between multibody simulationresults and reference or theoretical results showed that the multibody modelingapproach presented in the paper works well.Secondly, a large strap-on liquid-propellant launch vehicle was modeled as amultibody system with the modeling methods given in the previous part and accuratemultibody dynamic simulation was conducted for the atmospherical flight and booster separation of the launch vehicle. Multibody dynamic simulations realized the couplinganalysis of attitude, trajectory, sloshing, mass variation and structural vibration. Basedon multibody simulation, the dynamic behaviors such as attitude motion, propellantsloshing, flight trajectory and separation process were predicted and also structuralvibration and dynamic inner forces were analyzed. Rotational angles of nozzles,structural dynamic gaps for some critical positions and envelops for the whole vehicleand the whole flight were examined in detail. Numerical results showed that randompressure within transonic flight causes attitude, nozzle angles and dynamic inner forcesto vibrate strongly only during the transonic process, but has no significant influence ontrajectory, while its effect on propellant sloshing will continue for a period of time afterthe transonic stage.Finally, the stability analysis for the “structure-control-Pogo” coupling loop of theliquid-propellant launch vehicle was realized by the approach of multibody dynamics.Effects of the coupling between the control loop and Pogo loop were investigated.Respective stabilities for control loop, Pogo loop and “structure-control-Pogo” couplingloop were analyzed and compared, illustrating that control loop could affect the Pogostability, and the spatial coupling modes of large strap-on launch vehicles couldstrengthen the coupling between control loop and Pogo loop. Thus stability analysis forthe “structure-control-Pogo” coupling loop is necessary especially for large launchvehicles.