A parametric modeling method for primary and secondary separation of launch vehicles

Abstract

A parameterized modeling method for the separation of the first and second stages of a launch vehicle includes the following methods. Step 1: Modeling the first and second sub-stage rigid bodies of the launch vehicle with parameterized structures and center of mass positions; Step 2: Modeling the forces of the launch vehicle with parameterized action positions and action directions; Step 3: Constructing a constraint device model between the first and second sub-stage rigid bodies; Step 4: Based on the above-mentioned rigid body model, force model and constraint device model, a parameterized model of the first and second stage separation system of the launch vehicle is quickly constructed by building blocks and connecting lines; Step 5: Using a comparative verification method, the parameterized model of the first and second stage separation system is simulated and verified. Therefore, the present invention is a parameterized modeling method based on the Modelica causal modeling language, which can perform rapid numerical simulation on the first and second stage separation process of the launch vehicle, and evaluate the influence of parameters on the first and second stage separation response, thereby increasing the flexibility and scalability of the model, shortening the development cycle of the launch vehicle and reducing costs.

Description

Technical Field

[0001] This invention relates to the field of aerospace technology, specifically to a parametric modeling method for the separation of the first and second stages of a launch vehicle based on the Modelica unified modeling language. Background Technology

[0002] Launch vehicles are multi-stage rockets used for space transportation, designed to deliver payloads such as artificial Earth satellites, manned spacecraft, space stations, and space probes into predetermined orbits. To reduce negative mass, increase payload capacity, and accomplish specific missions, the waste components of each stage of a launch vehicle require a reliable separation system. This separation system must ensure effective separation of the components and maximize the separation gap to prevent collisions that could affect the payload's attitude and consequently the launch mission. There are numerous examples in space launch history of launch failures due to improper first and second stage separation.

[0003] In addition, the separation process of the first and second stages of a launch vehicle needs to take into account the influence of multiple parameter deviations, such as mass characteristic deviations, initial condition deviations, and dynamic characteristic deviations. Such numerous deviations may cause the second stage engine to come into contact with or collide with the first stage interior, or even fail to separate during the separation process. Therefore, it is crucial to establish a parameterized model of the first and second stage separation system of the launch vehicle.

[0004] The first and second stage separation process involves multiple disciplines, including structural dynamics, multibody dynamics, attitude control, and aerodynamics. It relates to the launch vehicle's layout and shape selection, parameter design, and other aspects, requiring multi-physics coupled simulation. It should be understood that Modelica is a language specifically designed for unified modeling and simulation across multiple disciplines, possessing unique advantages in multi-physics coupled simulation. Due to its object-oriented, equation-based, model reusable, and hierarchical structure, Modelica can effectively model the launch vehicle's first and second stage fuel separation system. Therefore, there is an urgent need for a solution that can construct a parametric model of the launch vehicle's first and second stage fuel separation system based on the Modelica unified modeling language. Summary of the Invention

[0005] The purpose of this invention is to establish a first and second stage separation model of a launch vehicle based on the parametric modeling method of the Modelica causal modeling language, to perform rapid numerical simulation of the first and second stage separation process of the launch vehicle, and to evaluate the influence of parameters on the first and second stage separation response, thereby increasing the flexibility and scalability of the model, shortening the development cycle of the launch vehicle and reducing costs.

[0006] The technical solution to achieve the purpose of this invention is: a parametric modeling method for the separation of the first and second stages of a launch vehicle, comprising the following steps:

[0007] Based on the mass, moment of inertia, length, and diameter parameters of the first and second stages, a structural parameterized model of the rigid body of the first and second stages of the launch vehicle is constructed.

[0008] Based on the parameters of ideal centroid position, centroid axial offset, centroid lateral displacement, and centroid lateral displacement circumferential angle, establish parameterized models of centroid position for the first and second sub-levels;

[0009] Based on the parameters of the distance from the engine thrust application point to the axis, the distance from the theoretical apex, and the azimuth angle, a parameterized model of the force position of the positive thrust, the reverse thrust, and the after-effect thrust is established.

[0010] A parameterized model of the force direction is established based on the parameters of engine mounting angle, nozzle exit angle, skew angle, and skew circumferential angle.

[0011] Construct a model of the constraint device between the first and second sub-level rigid bodies;

[0012] A parameterized model of the first and second stage separation system of a launch vehicle is constructed using all the models mentioned above.

[0013] Numerical simulations of the first and second stage separation process of a launch vehicle were conducted using a parameterized model of the first and second stage separation system, and the influence of model parameters on the first and second stage separation responses was evaluated.

[0014] Preferably, the forces include the reverse thrust, after-effect thrust, and swaying force acting on the first stage, and the positive thrust acting on the second stage. The established models include parameterized sub-models for the position of positive thrust, reverse thrust, after-effect thrust, swaying force, positive thrust direction, reverse thrust direction, after-effect thrust direction, and swaying force direction.

[0015] Preferably, the sloshing force position parameterization sub-model is established based on the distance from the liquid sloshing force reference point to the theoretical cusp, the distance from the axis, and the circumferential angle parameter of the positive rotation around the established reference coordinate system x-axis;

[0016] The parameterized sub-model of the swaying force direction is obtained by rotating the vector from the swaying force reference point to the position of the swaying force application point by 90° around the positive x-axis.

[0017] The origin of the reference coordinate system is located at the center point of the tail end of the first stage. The x-axis is the longitudinal axis of the rocket, pointing towards the rocket head as positive. The y-axis is in the longitudinal symmetry plane of the rocket. The z-axis, together with the x and y axes, forms a right-handed coordinate system.

[0018] Preferably, the parameterized model of the first and second stage separation system of the launch vehicle is formed by connecting the constructed structural parameterized model, the positive thrust position parameterized sub-model, the reverse thrust position parameterized sub-model, the after-effect thrust position parameterized sub-model, the sway force action position parameterized sub-model, the positive thrust direction parameterized sub-model, the reverse thrust direction parameterized sub-model, the after-effect thrust direction parameterized sub-model, and the sway force direction parameterized sub-model through connectors. The connector includes flow variables and potential variables, and the sum of the flow variables is zero while the potential variables are equal.

[0019] Preferably, a mathematical model is established based on the physical principles, force balance equations, and torque balance equations of the parametric model of the first and second stage separation system of the launch vehicle; the Modelica unified modeling language is used to construct the model and define the interface; the interface is used to transmit force, displacement, torque, and rotation angle.

[0020] Preferably, the constraint device model consists of a constraint device, a signal generator, and a connector connected to the first and second sub-level rigid bodies. The constraint device is used to constrain the relative position, velocity, and attitude of the first and second sub-level rigid bodies, and to release the constraint when it receives a signal from the signal generator.

[0021] Preferably, after building the parameterized model of the first and second stage separation system of the launch vehicle, the parameterized model of the first and second stage separation system is simulated and verified by comparison and verification.

[0022] Preferred platforms for comparative verification include, but are not limited to: Adams and Matlab.

[0023] A parametric modeling system for the first and second stage separation of a launch vehicle includes:

[0024] The model decomposition module decomposes the first and second stage separation process of the launch vehicle into a structural parameterized model, a centroid position parameterized model, a force position parameterized model, a force direction parameterized model, and a constraint device model.

[0025] The parametric analysis module determines the parameters that can parametrically characterize each model obtained by the model decomposition module.

[0026] The model building module constructs a structural parameterized model of the rigid bodies of the first and second stages of the launch vehicle based on the mass, moment of inertia, length, and diameter parameters of the first and second stages; it establishes a parameterized model of the center of mass position of the first and second stages based on the ideal center of mass position, axial offset of the center of mass, lateral displacement of the center of mass, and circumferential angle of the lateral displacement of the center of mass; it establishes a parameterized model of the force position of the positive thrust, reverse thrust, and aftereffect thrust based on the distance from the engine thrust application point to the axis, the distance from the theoretical apex, and the azimuth angle parameters; it establishes a parameterized model of the force direction based on the engine mounting angle, nozzle exit angle, skew angle, and circumferential skew angle parameters; and it constructs a model of the constraint device between the rigid bodies of the first and second stages.

[0027] The model building module constructs a parameterized model of the first and second stage separation system of a launch vehicle by combining all the models built in the model building module. This parameterized model is used to perform numerical simulations of the first and second stage separation process of the launch vehicle and to evaluate the influence of model parameters on the first and second stage separation response.

[0028] Preferably, the forces include the retro-thrust, after-effect thrust, and swaying force acting on the first stage, and the forward thrust acting on the second stage. The established models include parameterized sub-models for the forward thrust position, retro-thrust position, after-effect thrust position, swaying force position, forward thrust direction, retro-thrust direction, after-effect thrust direction, and swaying force direction. The parameterized sub-model for the swaying force position is established based on the distance from the liquid swaying force reference point to the theoretical cusp, the distance from the axis, and the circumferential angle parameter of the positive rotation around the established reference coordinate system x-axis. The parameterized sub-model for the swaying force direction is obtained by rotating the swaying force reference point to the swaying force action position vector by 90° around the positive x-axis. The origin of the reference coordinate system is located at the center point of the first stage tail end, the x-axis is the rocket's longitudinal axis, pointing positively towards the rocket's nose, the y-axis is within the rocket's longitudinal symmetry plane, and the z-axis forms a right-handed coordinate system with the x and y axes.

[0029] Therefore, compared with the prior art, the present invention can achieve the following beneficial effects:

[0030] 1) This invention uses a causal modeling language for parametric modeling. Different coordinate systems can correspond to different parts of the system or different physical phenomena, making the expression of the calculation equations more intuitive and concise. It can reduce ambiguity in coordinate system modeling and improve semantic consistency, thus simplifying the expression of the model.

[0031] 2) Based on the Modelica language, the developed parametric models are clearly hierarchical, reusable, and scalable, greatly improving modeling efficiency.

[0032] 3) It can perform rapid numerical simulation of the first and second stage separation process of launch vehicles and evaluate the impact of parameters on the first and second stage separation response, increasing the flexibility and scalability of the model, shortening the development cycle of launch vehicles and reducing costs. Attached Figure Description

[0033] The accompanying drawings, which are included to provide a further understanding of the invention and form part of this application, illustrate exemplary embodiments of the invention and are used to explain the invention. They do not constitute an undue limitation of the invention. In the drawings:

[0034] Figure 1 This is a flowchart of the parametric modeling method for the first and second stage separation of a launch vehicle based on the Modelica unified modeling language, as described in this invention.

[0035] Figure 2 This is the primary and secondary separation theoretical model of the present invention;

[0036] Figure 3 This is the theoretical model for parameterizing the first and second-order centroid positions of the present invention;

[0037] Figure 4 This is the parameterized theoretical model of the force position and direction of the present invention, wherein (a) is the parameterized theoretical model of the force position and (b) is the parameterized theoretical model of the force direction;

[0038] Figure 5 The present invention is a force parameterization model based on the Modelica language, wherein (a) is the positive thrust model, (b) is the negative thrust model, (c) is the after-effect thrust model, and (d) is the swaying force model.

[0039] Figure 6 This invention is a constraint device model based on the Modelica language;

[0040] Figure 7 This invention is a parameterized model of the first and second stage separation system of a launch vehicle built using the Modelica unified modeling language;

[0041] Figure 8 This is a schematic diagram of the aftereffect thrust curve in the model of this invention;

[0042] Figure 9 This is a comparison chart of the X-axis displacement, velocity, acceleration, angular velocity, and angular acceleration curves of a sub-stage in the model of this invention and the Adams model;

[0043] Figure 10 This is a comparison chart of the Y-axis displacement, velocity, acceleration, angular velocity, and angular acceleration curves of a sub-stage in the model of this invention and the Adams model. Detailed Implementation

[0044] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0045] A parametric modeling method for first and second stage separation of a launch vehicle based on the Modelica unified modeling language. Its theoretical model is as follows: Figure 2 As shown, it includes the following steps:

[0046] Step 1: Rigid body modeling of the first and second stages of the launch vehicle, with parameterized structure and center of mass position, specifically:

[0047] The parameterized sub-models of the first and second stage rigid body structures include the mass, moment of inertia, length, and diameter parameters of the first and second stages. These parameters serve as constant input terms for the system's dynamic equations and the gap measurement equations of the first and second stages. These equations describe the system's state changes, input-output relationships, and internal processes, and are typically included in the solver of simulation tools. Taking the dynamic equations of the center of mass and the dynamic equations around the center of mass of the second stage as examples:

[0048]

[0049] Where M2 is the mass of the second stage, I2 is the moment of inertia of the second stage, r2 and ω2 are the position and angular velocity of the center of mass of the second stage, F2 and T2 are the force and torque acting on the second stage, and ρ2 is the force vector to the center of mass.

[0050] The parameterized sub-models for the center of mass positions of the first and second-level rigid bodies include the ideal center of mass position, the axial offset of the center of mass, the transverse displacement of the center of mass, and the circumferential angle of the transverse displacement of the center of mass. The parameterized sub-models for the center of mass positions of the first and second-level rigid bodies are established based on these parameters.

[0051] Taking the second class as an example, such as Figure 3 As shown, the ideal center of mass position r of the second sub-stage is... 2_0 In the global coordinate system:

[0052] r 2_0 =(x 2_0 y 2_0 z 2_0 ) T (3)

[0053] The second-stage centroid offset vector δ2 can be expressed as:

[0054] δ2=(δ x2 δ r2 cosθ2 δ r2 sinθ2) T (4)

[0055] In the formula δ x2 For the axial offset of the second stage's center of mass (positive along the positive x-direction), δ r2 θ2 is the transverse displacement of the second-stage centroid, and θ2 is the circumferential angle of the transverse displacement of the second-stage centroid (positive when rotating around the positive x-axis with the y-axis as the starting point).

[0056] Then the actual position r2 of the second sub-stage mass center is:

[0057] r2=r 2_0 +δ2 (5)

[0058] Step 2: Parameterizing the position and direction of action of the launch vehicle forces, specifically:

[0059] Step 2.1, Parameterization of the force position sub-model:

[0060] like Figure 4 As shown in (a), the positive thrust acts on the second stage, while the retro-thrust and after-effect thrust act on the first stage. The parameter determining the position of the three forces is the same (taking the i-th positive thrust rocket as an example), which is the distance δ from the axis. i Distance x from the theoretical cusp i (Positive along the positive x-direction), azimuth θ i (Starting from the y-axis, rotation around the positive x-axis is considered positive).

[0061] Taking the i-th retro-rocket as an example, its azimuth angle θ i for:

[0062]

[0063] In the formula, θ0 is the azimuth angle of the first retro-rocket, and n is the number of retro-rockets. The position P of the force exerted by the i-th retro-rocket. i The coordinates of a point can be represented as:

[0064] r i =(x i δ i cosθ i δ i sinθ i ) T (7)

[0065] The surface of the swaying force is the cross-section where the reference point O′ is located. The parameters determining its position P are the distance x from the reference point to the theoretical cusp, the distance δ from the axis, and the circumferential angle λ of the positive rotation about the x-axis. Its position r FS It can be represented as:

[0066] r FS =(x δcosλ δsinλ) T (8)

[0067] Step 2.2, Parameterization of the force direction sub-model:

[0068] like Figure 4 As shown in (b), the parameter determining the direction of the positive thrust, reverse thrust, and aftereffect thrust is the same: the installation angle. Nozzle exit angle β i yaw angle γ i Circumferential skew angle λ i Assume that the installation angle, nozzle exit angle, and skew angle of the i-th positive thrust rocket all occur within the plane formed by the axis and the point of force application.

[0069] To determine the direction of the positive thrust, we must first ensure that there is no circumferential angle λ. i Thrust direction n Fi Then make n Fi around the nozzle exit direction n Ni Rotation angle λ i The direction of the positive thrust can then be obtained.

[0070] The normal to the plane formed by the axis and the point of force application can be obtained from O. i P i We obtain this by rotating 90° around the positive x-axis, i.e.:

[0071] n i =(0 -sinθ) i cosθ i ) T (9)

[0072] Installation corner Nozzle exit angle β i yaw angle γ i The direction is around n i A positive rotation is considered positive, as shown. There is no circumferential angle λ. i Thrust direction n Fi It can be determined by the axial direction (1 0 0). T around n i Rotation angle The rotation matrix R is obtained. Fi for:

[0073]

[0074] There is no circumferential angle λ i Thrust direction n Fi :

[0075] n Fi =R Fi (1 0 0) T (11)

[0076] Nozzle exit direction n Ni It can be determined by the axial direction (100). T around n i Rotation angle The rotation matrix R is obtained. Ni for:

[0077]

[0078] The axial direction n at the nozzle exit can be calculated. Ni :

[0079] n Ni =R Ni (1 0 0) T (13)

[0080] Next, n Fi Around n Ni Forward rotational reverse thrust deflection circumferential angle λ i The final direction of the positive thrust can be obtained, and its rotation matrix R. FN for:

[0081] R FN =I+sin(λ) i )N Ni +(1-cos(λ i ))N i 2 (14)

[0082] Final direction of positive thrust for:

[0083]

[0084] Direction of swaying force n FS It can be obtained by rotating O′P 90° around the positive x-axis, that is:

[0085] n FS =(0 -sinλ cosλ) T (16)

[0086] This leads to a force parameterization model based on the Modelica unified modeling language, such as... Figure 5 As shown.

[0087] Step 3: Constructing the constraint device model between the first and second sub-level rigid bodies. The constraint device model consists of a constraint device, a signal generator, and connectors connecting the first and second sub-level rigid bodies. The constraint device is used to constrain the relative position, velocity, and attitude of the first and second sub-level rigid bodies, and to release the constraint upon receiving a signal from the signal generator. Specifically:

[0088] Before separation, the first and second sub-stages have no relative motion or rotation, and the constraint equations are described as follows:

[0089]

[0090] In the formula, r A and r B θ represents the intersection point of the axial direction of the first and second sub-stages with the separation surface. A and θ B These are the attitude angles of the first and second sub-stages, respectively.

[0091] Find its first and second derivatives with respect to time:

[0092]

[0093] This results in a constraint device model based on the Modelica unified modeling language, such as... Figure 6 As shown.

[0094] Step 4: Based on the rigid body model, force model, and constraint device model described above, quickly build a parametric model of the first and second stage separation system of the launch vehicle using a modular approach and connecting lines, based on the Modelica unified modeling language. Figure 7 As shown, the constructed structural parameterized model, positive thrust position parameterized sub-model, reverse thrust position parameterized sub-model, after-effect thrust position parameterized sub-model, sway force position parameterized sub-model, positive thrust direction parameterized sub-model, reverse thrust direction parameterized sub-model, after-effect thrust direction parameterized sub-model, and sway force direction parameterized sub-model are connected by connectors to form a parameterized model of the first and second stage separation system of the launch vehicle. The connector includes flow variables and potential variables, and the sum of the flow variables is zero while the potential variables are equal.

[0095] A mathematical model is established based on the physical principles, force balance equations, and torque balance equations of the parameterized model of the first and second stage separation of the launch vehicle; the model is constructed using the Modelica unified modeling language, and code development and interface definition are carried out based on the standard library; wherein, the interface is used to transmit force, displacement, torque, and rotation angle.

[0096] Step 5: Perform simulation verification of the parameterized model of the primary and secondary separation system using a comparative verification method. The comparative verification platform includes, but is not limited to, Adams and Matlab.

[0097] This invention also provides a parametric modeling system for the first and second stage separation of a launch vehicle, comprising:

[0098] The model decomposition module decomposes the first and second stage separation process of the launch vehicle into a structural parameterized model, a centroid position parameterized model, a force position parameterized model, a force direction parameterized model, a sway force position parameterized model, and a constraint device model.

[0099] The parametric analysis module determines the parameters that can parametrically characterize each model obtained by the model decomposition module.

[0100] The model building module constructs a structural parameterized model of the rigid bodies of the first and second stages of the launch vehicle based on the mass, moment of inertia, length, and diameter parameters of the first and second stages; it establishes a parameterized model of the center of mass position of the first and second stages based on the ideal center of mass position, axial offset of the center of mass, lateral displacement of the center of mass, and circumferential angle of the lateral displacement of the center of mass; it establishes a parameterized model of the force position of the positive thrust, reverse thrust, and after-effect thrust based on the distance from the engine thrust application point to the axis, the distance from the theoretical cusp, and the azimuth angle; it establishes a parameterized model of the sloshing force application position based on the distance from the liquid sloshing force reference point to the theoretical cusp, the distance from the axis, and the circumferential angle of positive rotation around the x-axis of the reference coordinate system; it establishes a parameterized model of the force direction based on the engine mounting angle, nozzle exit angle, skew angle, and skew circumferential angle; and it constructs a model of the constraint device between the rigid bodies of the first and second stages.

[0101] The origin of the reference coordinate system is located at the center point of the tail end of the first stage. The x-axis is the longitudinal axis of the rocket, pointing towards the rocket head as positive. The y-axis is in the longitudinal symmetry plane of the rocket. The z-axis, together with the x and y axes, forms a right-handed coordinate system.

[0102] The model building module constructs a parameterized model of the first and second stage separation system of a launch vehicle by combining all the models built in the model building module. This parameterized model is used to perform numerical simulations of the first and second stage separation process of the launch vehicle and to evaluate the influence of model parameters on the first and second stage separation response.

[0103] For details on the methods in the system, please refer to the explanations in the specific steps of the methods described above.

[0104] Example

[0105] To verify the effectiveness of the method of the present invention, the following simulation was performed and compared with the simulation results of the ADAMS model.

[0106] Figure 9 and Figure 10 The displacement, velocity, acceleration, angular velocity, and angular acceleration time history curves of the first and second stages of the launch vehicle in the X and Y directions are presented. It can be seen from the two figures that before the separation of the first and second stages, due to the reduction in aftereffect thrust (see...),... Figure 8The axial acceleration of both the first and second stages decreases. After separation, the first stage experiences a significant reverse thrust, causing its axial acceleration to increase sharply in the opposite direction. The second stage, having lost its aftereffect thrust, experiences only a smaller positive thrust, resulting in a decrease in acceleration. The figure also shows that the Modelica and Adams models match very well, demonstrating the correctness of the parameterized model for first and second stage separation of the launch vehicle established in this invention.

[0107] The technical features of the above embodiments can be combined in any way. For the sake of brevity, 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, they should be considered to be within the scope of this specification.

[0108] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

[0109] The parts not described in this invention are well-known technologies in the field.

Claims

1. A parametric modeling method for the separation of the first and second stages of a launch vehicle, characterized in that, Includes the following steps: Based on the mass, moment of inertia, length, and diameter parameters of the first and second stages, a structural parameterized model of the rigid body of the first and second stages of the launch vehicle is constructed. Based on the parameters of ideal centroid position, centroid axial offset, centroid lateral displacement, and centroid lateral displacement circumferential angle, establish parameterized models of centroid position for the first and second sub-levels; Based on the parameters of the distance from the engine thrust application point to the axis, the distance from the theoretical apex, and the azimuth angle, a parameterized model of the force position of the positive thrust, the reverse thrust, and the after-effect thrust is established. A parameterized model of the force direction is established based on the parameters of engine mounting angle, nozzle exit angle, skew angle, and skew circumferential angle. Construct a model of the constraint device between the first and second sub-level rigid bodies; A parameterized model of the first and second stage separation system of a launch vehicle is constructed using all the models mentioned above. Numerical simulations of the first and second stage separation process of a launch vehicle were conducted using a parameterized model of the first and second stage separation system, and the influence of model parameters on the first and second stage separation responses was evaluated.

2. The method according to claim 1, characterized in that, The forces include the reverse thrust, after-effect thrust, and swaying force acting on the first stage, and the forward thrust acting on the second stage. The established models include parameterized sub-models for the forward thrust position, reverse thrust position, after-effect thrust position, swaying force position, forward thrust direction, reverse thrust direction, after-effect thrust direction, and swaying force direction.

3. The method according to claim 2, characterized in that, The parameterized sub-model of the sloshing force position is established based on the distance from the liquid sloshing force reference point to the theoretical cusp, the distance from the axis, and the circumferential angle parameter of the positive rotation around the established reference coordinate system x-axis; The parameterized sub-model of the swaying force direction is obtained by rotating the vector from the swaying force reference point to the position of the swaying force application point by 90° around the positive x-axis. The origin of the reference coordinate system is located at the center point of the tail end of the first stage. The x-axis is the longitudinal axis of the rocket, pointing towards the rocket head as positive. The y-axis is in the longitudinal symmetry plane of the rocket. The z-axis, together with the x and y axes, forms a right-handed coordinate system.

4. The method according to claim 2, characterized in that, The parameterized model of the first and second stage separation system of the launch vehicle is formed by connecting the constructed structural parameterized model, the positive thrust position parameterized sub-model, the reverse thrust position parameterized sub-model, the after-effect thrust position parameterized sub-model, the sway force action position parameterized sub-model, the positive thrust direction parameterized sub-model, the reverse thrust direction parameterized sub-model, the after-effect thrust direction parameterized sub-model, and the sway force direction parameterized sub-model through connectors. The connectors include flow variables and potential variables, and the sum of the flow variables is zero while the potential variables are equal.

5. The method according to claim 4, characterized in that, A mathematical model is established based on the physical principles, force balance equations, and torque balance equations of the parametric model of the first and second stage separation system of the launch vehicle. The Modelica unified modeling language is used to construct the model and define the interface. The interface is used to transmit force, displacement, torque, and rotation angle.

6. The method according to claim 1, characterized in that, The constraint device model consists of a constraint device, a signal generator, and a connector that connects to the first and second sub-level rigid bodies. The constraint device is used to constrain the relative position, velocity, and attitude of the first and second sub-level rigid bodies, and to release the constraint when it receives a signal from the signal generator.

7. The method according to claim 1, characterized in that, After constructing the parameterized model of the first and second stage separation system of the launch vehicle, the parameterized model of the first and second stage separation system is simulated and verified by comparison and verification.

8. The method according to claim 7, characterized in that, Platforms for comparative verification include, but are not limited to: Adams and Matlab.

9. A parameterized modeling system for the first and second stage separation of a launch vehicle, characterized in that, include: The model decomposition module decomposes the first and second stage separation process of the launch vehicle into a structural parameterized model, a centroid position parameterized model, a force position parameterized model, a force direction parameterized model, and a constraint device model. The parametric analysis module determines the parameters that can parametrically characterize each model obtained by the model decomposition module. The model building module constructs a structural parameterized model of the rigid bodies of the first and second stages of the launch vehicle based on the mass, moment of inertia, length, and diameter parameters of the first and second stages; it establishes a parameterized model of the center of mass position of the first and second stages based on the ideal center of mass position, axial offset of the center of mass, lateral displacement of the center of mass, and circumferential angle of the lateral displacement of the center of mass; it establishes a parameterized model of the force position of the positive thrust, reverse thrust, and aftereffect thrust based on the distance from the engine thrust application point to the axis, the distance from the theoretical apex, and the azimuth angle parameters; it establishes a parameterized model of the force direction based on the engine mounting angle, nozzle exit angle, skew angle, and circumferential skew angle parameters; and it constructs a model of the constraint device between the rigid bodies of the first and second stages. The model building module constructs a parameterized model of the first and second stage separation system of a launch vehicle by combining all the models built in the model building module. This parameterized model is used to perform numerical simulations of the first and second stage separation process of the launch vehicle and to evaluate the influence of model parameters on the first and second stage separation response.

10. The system according to claim 9, characterized in that: The forces involved include the retro-thrust, after-effect thrust, and swaying force acting on the first stage, and the forward thrust acting on the second stage. The established models include parameterized sub-models for the forward thrust position, retro-thrust position, after-effect thrust position, swaying force position, forward thrust direction, retro-thrust direction, after-effect thrust direction, and swaying force direction. The parameterized sub-model for the swaying force position is established based on the distance from the liquid swaying force reference point to the theoretical cusp, the distance from the axis, and the circumferential angle parameter of the positive rotation around the established reference coordinate system x-axis. The parameterized sub-model for the swaying force direction is obtained by rotating the swaying force reference point to the swaying force action position vector by 90° around the positive x-axis. The origin of the reference coordinate system is located at the center point of the first stage tail end, the x-axis is the rocket's longitudinal axis pointing towards the rocket's nose (positive), the y-axis lies within the rocket's longitudinal symmetry plane, and the z-axis forms a right-handed coordinate system with the x and y axes.

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