Rapid modeling method of carrier rocket rigid-missile-shake coupling model

Abstract

The invention discloses a rapid modeling method of a carrier rocket rigid-elastic-shake coupling model, which comprises the following steps of: establishing a motion equation of a carrier rocket: establishing a mass center motion equation of the carrier rocket according to a Newton's second law, establishing a motion equation around the mass center of the carrier rocket according to a moment of momentum theorem relative to the mass center, and simplifying the carrier rocket into a one-dimensional beam model; establishing an elastic vibration equation; solving force, torque and generalized force thereof; solving expressions of gravity, thrust, control force, engine swing inertia force, aerodynamic force, aerodynamic damping force, wind disturbance force, force, torque and generalized force thereof; propellant shaking is analyzed by adopting a spring-mass-damper equivalent model; propellant shaking equations in the pitching direction and the yawing direction of the carrier rocket are established, and inertia force, inertia moment and generalized force generated by propellant shaking are established; the obtained various forces, moments and generalized forces and inertia forces, inertia moments and generalized forces generated by shaking of a propellant are substituted into a motion equation of the carrier rocket to obtain a mass center motion equation, the motion equation of the rocket is around the mass center, and a six-degree-of-freedom nonlinear total dynamical model of the carrier rocket is established when the rocket tilts and tilts; elastic vibration equations in three directions of yawing and rolling are established; and solving the carrier rocket rigid-missile-shake coupling model. According to the method, rapid numerical simulation can be carried out on the carrier rocket rigid-missile-shake coupling model, the influence of a solving result on carrier rocket attitude change is analyzed, and a foundation is laid for navigation and attitude control design of the carrier rocket.

Description

Technical Field

[0001] The present invention relates to the field of aerospace technology, and more specifically, to a fast modeling method for a rigid-flexible-slosh coupling model of a launch vehicle. Background Art

[0002] The attitude control system of a launch vehicle is one of the key components to ensure that the rocket can maintain the required flight attitude and stability during flight. This system must be able to cope with various complex external environments and internal motion factors, including rigid body motion, elastic vibration, and liquid sloshing, etc.

[0003] Rigid body motion control is the basis of the attitude control system, which is mainly achieved by adjusting the thrust direction through the rocket's thrusters. The controller calculates the required engine gimbal angles based on the attitude information obtained by the sensors and the target attitude requirements provided by the guidance system, and controls the working state of the engine gimbal angles through the actuators, thereby realizing the translational and rotational motion control of the rocket. During the rocket flight, the outer shell may be affected by airflow and other external factors, resulting in elastic vibration. To maintain flight stability and structural integrity, the attitude control system needs to control this vibration. This is usually achieved by installing vibration dampers in the rocket structure or adopting active vibration control technology, and applying corresponding forces through the actuators to suppress the vibration. Liquid sloshing in the rocket propellant tank is also one of the important factors that the attitude control system needs to consider. Liquid sloshing will cause changes in the rocket's center of mass position and moment of inertia, which will in turn affect the rocket's flight attitude and stability. To solve this problem, the controller will execute corresponding forces through the actuators based on the center of mass position information collected by the sensors to actively control the liquid sloshing and maintain the rocket's flight stability.

[0004] In summary, the launch vehicle attitude control system is a complex and critical component, which directly affects the rocket's flight stability and mission execution ability. Therefore, establishing a high-fidelity rigid-flexible-slosh coupling dynamics model of the launch vehicle and performing fast simulation calculations can effectively achieve the rocket's attitude control and ensure its safe and reliable completion of various flight missions. Summary of the Invention

[0005] The purpose of the present invention is to provide a fast modeling method for a rigid-flexible-slosh coupling model of a launch vehicle, establish a rigid-flexible-slosh coupling model of the launch vehicle, analyze its dynamic characteristics, provide a description of the system motion state, and lay a foundation for navigation and attitude control design.

[0006] The technical solution to achieve the purpose of the present invention: A fast modeling method for a rigid-flexible-slosh coupling model of a launch vehicle, comprising the following steps:

[0007] Step 1: Determine a suitable coordinate system to describe the motion of the launch vehicle. In the semi-velocity coordinate system, establish the centroid motion equation of the launch vehicle; in the body coordinate system, establish the motion equation of the launch vehicle about the centroid; in the elastic coordinate system, simplify the launch vehicle into a one-dimensional beam model and establish the elastic vibration equation of the launch vehicle.

[0008] Step 2: Considering the elastic deformation, solve the various forces, moments and their generalized forces acting on the body respectively, including gravity, the forces and moments and their generalized forces generated by the engine swing, the inertial forces, moments and their generalized forces related to the swing angle during engine swing, aerodynamic forces, the resultant force of lift and aerodynamic damping force, the resultant force of lateral force and aerodynamic damping force, aerodynamic damping moment, aerodynamic stability moment and the resultant moment of damping force moment, and the generalized forces of aerodynamic forces and aerodynamic damping force in the pitch direction and yaw direction.

[0009] Step 3: Regard the propellant in the launch vehicle tank as a spring-mass-damper system for equivalent modeling, analyze the sloshing of the propellant during the motion of the launch vehicle, and establish the motion equation of the propellant sloshing through the equivalent model.

[0010] Step 4: Substitute the forces, moments and their generalized forces obtained in Step 2 into the centroid motion equation, the motion equation about the centroid and the elastic vibration equation in Step 1 respectively. The resulting motion equations of the launch vehicle constitute a six-degree-of-freedom nonlinear full-scale dynamic model of the rocket.

[0011] Step 5: Integrate the six-degree-of-freedom nonlinear full-scale dynamic model described in Step 4 and the propellant sloshing model in Step 3 to form a rigid-flexible-slosh coupling dynamic model of the launch vehicle. According to the given initial conditions, use numerical methods to solve the equations to obtain the motion states of the launch vehicle at different times.

[0012] Furthermore, the motion equations of the launch vehicle include: centroid motion equation, motion equation about the centroid and elastic vibration equation. The forces, moments and their generalized forces to be solved include: gravity, the forces, moments and their generalized forces generated by the engine swing, the inertial forces, moments and their generalized forces related to the swing angle during engine swing, aerodynamic forces, the resultant force of lift and aerodynamic damping force, the resultant force of lateral force and aerodynamic damping force, aerodynamic damping moment, aerodynamic stability moment and the resultant moment of damping force moment, and the generalized forces of aerodynamic forces and aerodynamic damping force in the pitch direction and yaw direction.

[0013] Furthermore, in Step 3, according to the spring-mass-damper equivalent model, establish the propellant sloshing equations in the pitch direction and yaw direction of the launch vehicle, and establish the inertial forces, inertial moments and generalized forces generated by the additional propellant sloshing.

[0014] Further, in Step 4, substitute the various forces, moments, and their generalized forces obtained in Steps 2 and 3 into the rocket motion equation in Step 1 to obtain the center-of-mass motion equation, the equation of motion about the center of mass, and the elastic vibration equations of the rocket in the pitch, yaw, and roll directions.

[0015] The platforms for solving and analyzing in Step 5 include but are not limited to: Matlab.

[0016] Therefore, compared with the prior art, the present invention can achieve the following beneficial effects:

[0017] 1) It can achieve rapid modeling of the rigid-flexible-slosh coupling model of the launch vehicle. The model is generalized, reusable, and extensible, greatly improving the modeling efficiency.

[0018] 2) It can provide a systematic state description and mathematical description, laying a foundation for subsequent navigation and control design. Description of the Drawings

[0019] Figure 1 is a flowchart of the method for rapid modeling of the rigid-flexible-slosh coupling model of the launch vehicle according to the present invention.

[0020] Figure 2 is a layout diagram of the rocket engine according to the present invention.

[0021] Figure 3 is the elastic rocket body in the roll, pitch, and yaw planes.

[0022] Figure 4 is a schematic diagram of the liquid slosh equivalent model and sloshing in the pitch and yaw planes.

[0023] Figure 5 is the position and velocity vector of the rocket in the launch coordinate system.

[0024] Figure 6 is the yaw angle and roll angle of the rocket relative to the launch system.

[0025] Figure 7 gives the projection of the angle of rotation of the rocket body about the center of mass in the rocket body coordinate system.

[0026] Figure 8 is the velocity inclination angle, track yaw angle, and bank angle of the velocity coordinate system relative to the launch system.

[0027] Figure 9 is the angle of attack and sideslip angle of the velocity coordinate system relative to the rocket body coordinate system.

[0028] Figure 10 is the equivalent pitch angle, yaw angle, and roll angle of the gimbaled engine.

[0029] Figure 11It is the comparison between the pitch angle of the rocket relative to the launch system and the program angle. Specific Embodiment

[0030] In order to make the objectives, technical solutions and advantages of the present application more clear and understandable, the present application will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and are not used to limit the present application.

[0031] A rapid modeling method for the rigid-flexible-slosh coupling model of a launch vehicle includes the following steps:

[0032] Step 1: Establish the motion equations of the launch vehicle, specifically:

[0033] According to Newton's second law, the component form of the centroid motion equation in the semi-velocity coordinate system can be obtained as

[0034]

[0035] where m is the total mass of the rocket, are the components of all external forces acting on the rocket body in the elastic deformation case on the h three axes of the semi-velocity coordinate system.

[0036] If the b three axes of the rocket system are taken as the principal inertia axes of the rocket body, the motion equation about the centroid can be obtained from the momentum moment theorem relative to the centroid as

[0037]

[0038] where are the moments of inertia of the rocket body about the b three axes of the rocket system. are the moments of the external forces acting on the rocket body in the elastic deformation case about the centroid of the rocket body.

[0039] When studying elastic vibrations, the rocket is usually simplified to a one-dimensional beam model, and the elastic vibration equation is obtained as

[0040]

[0041] where are the i-th order vibration circular frequency and damping ratio in the corresponding direction, are the i-th order generalized mass and generalized force respectively.

[0042] Step 2: Solve the forces, moments and their generalized forces, specifically:

[0043] The component expression of gravity in the semi-velocity coordinate system h is

[0044]

[0045] Among them, g is the acceleration due to gravity. Since it is assumed that the position of the center of mass remains unchanged before and after elastic deformation, gravity does not generate a moment on the rocket's center of mass, and the corresponding generalized force of elastic vibration is also zero.

[0046] The swing of the engine will cause the thrust to generate a lateral component as the control force. Figure 2 The components of the resultant force of the thrusts of the four swing engines on the three axes of the rocket system b are

[0047]

[0048] Among them, P 1 is the thrust of a single engine. The components of the resultant moment of the thrust on the center of mass on the three axes of the rocket system b are

[0049]

[0050] Among them, x R and x T are the distances from the engine swing point and the rocket's center of mass to the theoretical tip of the rocket. In the elastic coordinate system E, the generalized forces of the thrust in the directions of torsional, pitch bending vibration, and yaw bending vibration are respectively

[0051]

[0052] The expression of the components of the resultant force of the swing inertia forces of the four engines in the rocket system b is

[0053]

[0054] Among them, m R and l R are the mass and swing length of a single engine respectively. The expression of the components of the resultant moment of the swing inertia moment in the rocket system b is

[0055]

[0056] Among them, is the axial apparent acceleration. The generalized forces of the inertia forces and moments related to the swing angle are

[0057]

[0058] The aerodynamic drag in the direction of the O 1 X c axis of the velocity system c is

[0059]

[0060] The resultant force of the lift and aerodynamic damping force in the direction of the O 1 Y c axis is

[0061]

[0062] In the O 1 Z c axis direction, the resultant force of the lateral force and the aerodynamic damping force is

[0063]

[0064] In the O 1 X c axis direction, the aerodynamic drag moment is

[0065]

[0066] where m dx is the rolling damping moment coefficient.

[0067] In the O 1 Y c axis direction, the resultant moment of the aerodynamic stabilizing moment and the damping moment is

[0068]

[0069] where m dy is the derivative of the yaw aerodynamic damping moment coefficient.

[0070] In the O 1 Z c axis direction, the resultant moment of the aerodynamic stabilizing moment and the damping moment is

[0071]

[0072] where m dz is the derivative of the pitch aerodynamic damping moment coefficient.

[0073] The generalized forces of the aerodynamic force and the aerodynamic damping force in the pitch direction and the yaw direction are

[0074]

[0075]

[0076] Step 3: Analyze the propellant sloshing using a spring - mass - damper equivalent model, specifically as follows:

[0077] The propellant sloshing equations in the pitch direction and the yaw direction are

[0078]

[0079] The additional propellant sloshing inertial force is

[0080]

[0081] where m p is the sloshing mass of the storage tank.

[0082] The additional inertial moment generated by sloshing is

[0083]

[0084] The generalized forces corresponding to the inertial forces and moments related to sloshing are

[0085]

[0086] Step 4: Establish a six-degree-of-freedom nonlinear total dynamics model, specifically as follows:

[0087] Substitute the various forces, moments, and their generalized forces obtained above into equations (1), (2), and (3). The equation of motion of the center of mass represented in matrix form in the semi-velocity coordinate system is

[0088]

[0089] where F BX , F BY and F BZ are additional structural interference forces, and N P is the number of propellant tanks.

[0090] The equation of motion about the center of mass in the rocket system is

[0091]

[0092]

[0093] where and are additional structural interference forces. In the elastic coordinate system E, the elastic vibration equations of the rocket in the pitch, yaw, and roll directions are

[0094]

[0095] where i = 1, 2,..., n γ .

[0096]

[0097]

[0098] Step 5: Solve the rigid-flexible-slosh coupling model of the launch vehicle.

[0099] Embodiment

[0100] To verify the effectiveness of the present invention, the following simulation is performed on the above rigid-flexible-slosh coupling model of the launch vehicle. Figure 5 The position and velocity vector diagrams of the launch vehicle in the launch coordinate system are given;Figure 6 The yaw angle and roll angle of the rocket relative to the launch system are given; Figure 7 The projection of the angle of rotation of the rocket body about the center of mass in the rocket system is given; Figure 8 The velocity inclination angle, track yaw angle, and bank angle of the velocity coordinate system relative to the launch system are given; Figure 9 The angle of attack and sideslip angle of the velocity coordinate system relative to the rocket body coordinate system are given; Figure 10 The equivalent pitch angle, yaw angle, and roll angle of the swivel engine are given; Figure 11 The comparison between the pitch angle of the rocket relative to the inertial system and the programmed angle is given. It can be seen from the figure that the change of the pitch angle coincides very well with the designed programmed angle. According to the motion description of the launch vehicle given in the figure, it can be shown that the rigid-flexible-slosh coupling model of the launch vehicle established by the present invention can well lay a foundation for the subsequent navigation and attitude control design of the launch vehicle.

[0101] The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity of description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope described in this specification.

[0102] The above-described embodiments only represent several implementation manners of the present application. The description is relatively specific and detailed, but it should not be construed as a limitation on the scope of the invention patent. It should be noted that for those of ordinary skill in the art, without departing from the concept of the present application, several deformations and improvements can still be made, and these all belong to the protection scope of the present application. Therefore, the protection scope of the patent of the present application shall be subject to the appended claims.

[0103] The parts not described in the present invention belong to the well-known technologies in the art.

Claims

1. A rapid modeling method for a launch vehicle rigid-elastic-shaking coupling model, characterized in that: The following steps are involved: Step 1: Determine a suitable coordinate system to describe the motion of the launch vehicle. In the semi-velocity coordinate system, establish the motion equation of the center of mass of the launch vehicle; in the rocket body coordinate system, establish the motion equation of the launch vehicle around the center of mass; In the elastic coordinate system, the launch vehicle is simplified into a one-dimensional beam model, and the elastic vibration equation of the launch vehicle is established; Step 2: Under the consideration of elastic deformation, various forces, moments and generalized forces acting on the rocket body are solved respectively, including gravity, force, moment and generalized forces generated by engine swing, inertial force, moment and generalized forces related to the swing angle when the engine swings, aerodynamic force, resultant force of lift and aerodynamic damping force, resultant force of lateral force and aerodynamic damping force, aerodynamic damping moment, resultant moment of aerodynamic stabilizing moment and damping force moment, and generalized forces of aerodynamic force and aerodynamic damping force in pitch and yaw directions; Step 3: Treat the propellant in the launch vehicle tank as a spring-mass-damper system for equivalent modeling, analyze the sloshing of the propellant as the launch vehicle moves, and establish the motion equation of the propellant sloshing through the equivalent model; Step 4: Substitute the force, moment and generalized force obtained in step 2 into the center-of-mass motion equation, the motion equation around the center of mass and the elastic vibration equation in step 1 respectively, and the obtained launch vehicle motion equation constitutes the six-degree-of-freedom nonlinear full-scale dynamic model of the rocket; Step 5: Integrate the six-degree-of-freedom nonlinear full-volume dynamics model described in step 4 and the propellant sloshing model in step 3 to form a rigid-elastic-sloshing coupled dynamics model of the launch vehicle. According to the given initial conditions, the numerical method is used to solve the equations to obtain the motion state of the launch vehicle at different times.

2. The rapid modeling method of the launch vehicle rigid-elastic-shake coupling model according to claim 1 is characterized by: The gravity described in step 2 is established in the semi-velocity coordinate system. Since it is assumed that the center of mass position remains unchanged before and after elastic deformation, gravity does not produce a torque on the center of mass of the rocket, and the corresponding elastic vibration generalized force is also zero.

3. The rapid modeling method of the launch vehicle rigid-elastic-shake coupling model according to claim 1 is characterized in that: The forces, torques and generalized forces generated by the launching force swing described in step 2 include launching force thrust, control force and inertial force related to the swing angle, wherein the forces and torques are established in the arrow body coordinate system, and the generalized forces are established in the elastic coordinate system.

4. The rapid modeling method of the launch vehicle rigid-elastic-shake coupling model according to claim 1 is characterized in that: The aerodynamic force, the resultant force of lift and aerodynamic damping force, the resultant force of lateral force and aerodynamic damping force, the aerodynamic damping moment, the resultant moment of aerodynamic stability moment and damping moment described in step 2 are established in the velocity coordinate system, and the forces and moments are converted to the rocket body coordinate system through the coordinate transformation matrix. The generalized forces of aerodynamic force and aerodynamic damping force in the pitch direction and yaw direction are established in the elastic coordinate system.

5. The rapid modeling method of the launch vehicle rigid-elastic-shake coupling model according to claim 1 is characterized in that: According to the spring-mass-damper equivalent model, the propellant sloshing equations in the pitch and yaw directions of the launch vehicle are established, and the inertial force, inertial moment and generalized force generated by the propellant sloshing are established, wherein the inertial force and inertial moment generated by the propellant sloshing are established in the rocket body coordinate system, and the generalized force is established in the elastic coordinate system.

6. The rapid modeling method of the launch vehicle rigid-elastic-shake coupling model according to claim 1 is characterized by: The solution platform includes but is not limited to: Matlab.

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