Rocket fairing spinoff evaluation method

Abstract

The present application belongs to the field of aerospace separation technology, and particularly relates to a rocket fairing rotating separation evaluation method. It aims to solve the problem of long cycle and high cost caused by the dependence of traditional fairing rotating separation scheme on high-fidelity simulation and physical test. By simplifying the half fairing as an analysis object of rigid body planar motion, the mass center kinematics and dynamics equations of the half fairing rotating around a fixed point are established. Then, the Runge-Kutta method is used to solve the mathematical model by cyclic iteration to obtain the motion trajectory parameters in the separation process. Finally, the separation motion trajectory is visualized based on the trajectory parameters, and the collision risk is evaluated by analyzing the relative position relationship between the trajectory and the rocket body. Based on the physical simplified model and numerical calculation method, the rapid and safe evaluation of the fairing separation process is realized, which greatly shortens the design verification cycle, and significantly reduces the evaluation cost due to the pure numerical calculation.

Description

Technical Field

[0001] This invention belongs to the field of aerospace separation technology, specifically relating to a method for evaluating the rotational separation of a rocket fairing. Background Technology

[0002] While a rocket is flying within the atmosphere, the fairing protects payloads such as satellites from aerodynamic and thermal loads. Once the rocket reaches a certain altitude, the air becomes thinner, and aerodynamic effects become negligible. At this point, the fairing must be promptly separated from the rocket body and jettisoned to reduce the rocket's unproductive load and optimize its flight trajectory. Fairings typically consist of two or more lobes, with rotational separation being a mainstream method. This method works by using pyrotechnics or mechanisms to drive each lobe to rotate around a hinge axis, utilizing centrifugal force to detach it from the rocket. The entire dynamic process resembles a lotus flower opening.

[0003] Currently, the safety assessment of fairing rotation separation schemes mainly relies on high-fidelity multibody dynamics simulations, large-scale ground simulation tests, or wind tunnel tests. Dynamics simulations require building complex full-rocket models in specialized software and setting numerous contact, load, and boundary conditions for simulation calculations. This results in complex high-fidelity dynamics simulation models, high computational resource consumption, and lengthy single simulation times, making rapid iteration and parameter optimization difficult in the early design stages. Meanwhile, ground tests and wind tunnel tests require manufacturing physical prototypes or scaled-down models to reproduce the separation process or aerodynamic environment in specific facilities to observe its trajectory and dynamic characteristics. This makes ground tests and wind tunnel tests extremely costly and time-consuming, failing to meet the rapid development pace required for modern spacecraft. Therefore, the existing safety assessment methods for fairing rotation separation schemes suffer from long cycles and high costs, limiting their application in the initial screening and conceptual design stages of fairing separation schemes, thus hindering improvements in design efficiency and cost reduction.

[0004] In view of this, the present invention is hereby proposed. Summary of the Invention

[0005] One objective of this invention is to solve the problems of long cycles and high costs caused by the reliance on high-fidelity simulation and physical experiments in traditional fairing rotation separation methods.

[0006] To achieve the above objectives, the present invention provides a method for evaluating the rotational separation of a rocket fairing, comprising:

[0007] The semi-fair is simplified into an analytical object undergoing rigid planar motion, and its kinematic and dynamic equations of center of mass rotation about a fixed point of rotation are established.

[0008] Based on the aforementioned kinematic and dynamic equations of the center of mass, the Runge-Kutta method is used to solve the motion trajectory parameters of the semi-fairing before it leaves contact with the rocket through iterative methods; wherein, the motion trajectory parameters include the coordinates of the center of mass and the rotation angle at different times;

[0009] Based on the motion trajectory parameters, the separation trajectory of the semi-fairing is visualized and generated. By analyzing the relative positional relationship between the motion trajectory and the rocket body, the risk of collision in the separation scheme is assessed.

[0010] Furthermore, the step of establishing the kinematic and dynamic equations of the center of mass is based on the following assumptions: the influence of friction is ignored; the direct influence of gravitational acceleration is ignored; and the forces acting on the semi-fairing are only inertial forces and the active forces generated by the separation device.

[0011] Furthermore, the step of simplifying the semi-fairing into an analytical object undergoing rigid planar motion and establishing its kinematic and dynamic equations of mass rotation around a fixed rotation point includes: establishing a planar coordinate system, where the origin (O) is the center of the separation surface between the fairing and the rocket body, the Y-axis coincides with the rocket's axis of symmetry and points towards the rocket's nose, and the X-axis points towards the rotational separation direction of the semi-fairing; establishing the relationship between the center of mass coordinates and the rotation angle based on the motion trajectory parameters and trigonometric functions; performing kinematic analysis on the relationship between the center of mass coordinates and the rotation angle to obtain the linear velocity equations of the semi-fairing's center of mass in the X and Y axis directions; performing acceleration analysis on the linear velocity equations to obtain the linear acceleration equations in the X and Y axis directions; and establishing the angular acceleration equations of the semi-fairing rotating around the rotation point R based on the rigid body rotation law.

[0012] Furthermore, the step of establishing the relationship between the centroid coordinates and the rotation angle based on the motion trajectory parameters and trigonometric functions includes: defining the distance from the centroid of the semi-fairing to the rotation point R as L, and the fixed angle between the line connecting the centroid and point R and the separation surface circle as L. The rotation angle is Before the fairing separates from the rocket, the centroid coordinates (Xcg, Ycg) of the semi-fairing satisfy the following relationship:

[0013] Where r is the radius of the separation circle between the fairing and the rocket body; where, , , It is a fixed constant, angle. It is a function that changes with time t, that is .

[0014] Further, the step of performing kinematic analysis on the relationship between the center of mass coordinates and the rotation angle to obtain the linear velocity equations of the semi-fairing center of mass in the X and Y axis directions includes: based on the geometric relationship between the semi-fairing center of mass coordinates (Xcg, Ycg) and the rotation angle θ, obtaining the linear velocity equations of the semi-fairing center of mass in the X and Y axis directions by taking the first derivative of the center of mass coordinate equation with respect to time t.

[0015] ;in, It is the linear velocity of the center of mass of the semi-fair in the X-axis direction; It is the linear velocity of the center of mass of the semi-fair in the Y-axis direction; It is angular velocity.

[0016] Further, the step of performing acceleration relationship analysis on the linear velocity equation to obtain the linear acceleration equation in the X and Y axis directions includes: taking the first derivative of the linear velocity equation with respect to time t to obtain the linear acceleration equation of the semi-fairing's center of mass in the X and Y axis directions:

[0017] ;in, It is the linear acceleration of the center of mass of the semi-fairing in the X-axis direction. It is the linear acceleration of the center of mass of the semi-fairing in the Y-axis direction. It is angular acceleration.

[0018] Furthermore, the step of establishing the angular acceleration equation for the rotation of the semi-fairing about the rotation point R based on the rigid body fixed-axis rotation law includes: the expression for the angular acceleration equation is:

[0019] ;in, Let R be the moment of inertia of the semi-fairing about the point of rotation. For rocket axial overload, For the quality of a semi-fairing, It is the acceleration due to gravity. The driving torque generated by the separation device.

[0020] Furthermore, the step of solving the motion trajectory parameters of the semi-fairing before separation from the rocket using the Runge-Kutta method through iterative processes based on the kinematic and dynamic equations of the center of mass includes: defining the motion state of the semi-fairing at time t as a state vector Y(t), which consists of rotation angle, angular velocity, and center of mass coordinates; constructing a system of first-order differential equations of the state vector Y(t) with respect to time t based on the linear velocity equation and the angular acceleration equation; and setting the initial state for numerical solution: when time t=0, the rotation angle is... =0, angular velocity =0, the center of mass is at the initial position, and the linear velocity is zero; Iterative calculation: starting from t=0, iterate step by step with a preset time step Δt, using the Runge-Kutta method combined with the linear acceleration equation to update the state vector until the termination condition is met; for each time step, calculate the state vector for the next time step based on the current state vector; after each iteration, determine the rotation angle in the current state vector. Whether the preset departure angle Φ is reached or exceeded; if θ < Φ, continue iterative solution; if θ ≥ Φ, terminate iteration; record the state vector Y(t) corresponding to all time steps from t=0 to the termination time to obtain the state vector sequence, which is the motion trajectory parameter.

[0021] Furthermore, the step of visually generating the separation trajectory of the semi-fairing based on the motion trajectory parameters, and assessing the collision risk of the separation scheme by analyzing the relative positional relationship between the motion trajectory and the rocket body, includes: determining the initial conditions of inertial motion, combining them with all the motion trajectory parameters to analyze the complete motion trajectory of the semi-fairing, and drawing the contour attitude of the semi-fairing at different times in the plane coordinate system; drawing the contour attitude of a series of consecutive times and the envelope of the rocket body on the same graph to form a dynamic trajectory diagram of the separation process; determining whether there is a minimum safe gap between the contour of the semi-fairing and the envelope of the rocket body at any time; if there is a gap greater than the minimum safe gap at all times, the scheme is deemed safe; if there is contour overlap or a gap less than or equal to the minimum safe gap, a collision risk is deemed to exist.

[0022] Further, the step of determining the initial conditions for inertial motion, combining them with all the motion trajectory parameters to analyze the complete motion trajectory of the semi-fairing, and drawing the contour attitude of the semi-fairing at different times in the plane coordinate system includes: obtaining the state vector at the termination time, obtaining the angular velocity and linear velocity at the separation time, and using them as the initial conditions for the semi-fairing to perform inertial motion after separation from contact; calculating the complete motion trajectory of the semi-fairing from the start of separation to the free flight stage after separation from contact based on all the motion trajectory parameters and the initial conditions for inertial motion; the motion trajectory of the free flight stage is obtained by substituting the initial conditions into the uniform motion and uniform rotation model; and drawing the contour attitude of the semi-fairing at different times in the plane coordinate system based on the complete motion trajectory.

[0023] Based on the foregoing description, those skilled in the art will understand that this invention simplifies the semi-fairing into an analytical object undergoing rigid planar motion, establishing its kinematic and dynamic equations of rotation around a fixed point, thus laying a theoretical foundation for calculation. Secondly, the Runge-Kutta method is used to iteratively solve this mathematical model to obtain the trajectory parameters during the separation process. Finally, the separation trajectory is visualized based on these parameters, and the collision risk is assessed by analyzing its relative position to the rocket body. This invention aims to solve the problems of long cycles and high costs associated with traditional fairing rotation separation methods that rely on high-fidelity simulations and physical experiments. By using a simplified physical model and numerical calculation methods, it achieves rapid safety assessment of the fairing separation process, significantly shortening the design verification cycle. Furthermore, because it is based on pure numerical calculations, it significantly reduces assessment costs. Attached Figure Description

[0024] The accompanying drawings, as part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments and descriptions of the invention are used to explain the invention, but do not constitute an undue limitation of the invention. Obviously, the drawings described below are merely some embodiments, and those skilled in the art can obtain other drawings based on these drawings without creative effort. In the drawings:

[0025] Figure 1 This is a flowchart of the steps of the rocket fairing rotation separation evaluation method in some embodiments of the present invention;

[0026] Figure 2 This is a schematic diagram of the coordinate system in some embodiments of the present invention;

[0027] Figure 3 This is a schematic diagram of a dynamic trajectory diagram in some embodiments of the present invention. Detailed Implementation

[0028] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments will be clearly and completely described below with reference to the accompanying drawings. The following embodiments are used to illustrate the present invention, but are not intended to limit the scope of the present invention.

[0029] Those skilled in the art should understand that the embodiments described below are merely a part of the embodiments of the present invention, and not all of the embodiments of the present invention. These partial embodiments are intended to explain the technical principles of the present invention and are not intended to limit the scope of protection of the present invention. Based on the embodiments provided by the present invention, all other embodiments obtained by those skilled in the art without creative effort should still fall within the scope of protection of the present invention.

[0030] The following reference Figures 1 to 3This document will provide a detailed description of the rocket fairing rotation separation evaluation method in some embodiments of the present invention. Figure 1 This is a flowchart of the steps of the rocket fairing rotation separation evaluation method in some embodiments of the present invention; Figure 2 This is a schematic diagram of the coordinate system in some embodiments of the present invention; Figure 3 This is a schematic diagram of a dynamic trajectory diagram in some embodiments of the present invention.

[0031] In some embodiments of this invention, a method for evaluating the rotational separation of a rocket fairing is provided. This method, based on a mathematical model and a rapid simulation approach using numerical calculations, transforms the complex three-dimensional separation dynamics problem of the rocket fairing into a quickly solvable two-dimensional rigid body kinematics and dynamics problem through reasonable physical simplification. The separation trajectory is obtained using an efficient numerical algorithm. Compared to traditional fairing separation verification methods that heavily rely on dynamic simulations, ground tests, or wind tunnel tests, which are not only costly but also have lengthy preparation and testing cycles, failing to meet the demands of rapid iterative development of modern spacecraft, this invention can replace or partially replace high-fidelity physical simulations and tests at a lower cost and faster speed.

[0032] The rocket fairing rotational separation evaluation method of this invention can be applied to the conceptual design stage. By inputting different separation torques, hinge positions, and other parameters, the separation trajectory can be obtained immediately, thereby comparing the advantages and disadvantages of different schemes and performing parameter sensitivity analysis and optimization. It can also be used to quickly screen numerous candidate schemes before conducting expensive full-system dynamics simulations or ground tests, eliminating schemes with obvious collision risks to save on later verification costs. Alternatively, if a separation anomaly occurs in a flight test or simulation, the method of this invention can be used to quickly reproduce the conditions, analyze possible causes (such as insufficient separation torque, abnormal overload, etc.), and provide clues for fault investigation.

[0033] like Figure 1 As shown, the rocket fairing rotation separation evaluation method includes:

[0034] Step S110: Simplify the semi-fairing into an analysis object undergoing rigid planar motion, and establish its kinematic and dynamic equations of center of mass rotating around a fixed rotation point.

[0035] Taking the fairing half as the analysis object, it is assumed that it undergoes rigid body planar motion during the rotation and separation process. In order to balance the accuracy, simplicity and computational efficiency of the model, friction and the influence of gravitational acceleration are ignored. Only the inertial force and the main force during separation are considered to act on the half.

[0036] Specifically, the semi-fair is first simplified as a rigid body. It is assumed that the semi-fair will not undergo elastic deformation or structural deformation during the separation process, that is, the distance between any two points inside the fairing remains unchanged. Thus, the mass distribution of the entire semi-fair can be simplified to a point (center of mass) to study its translation, and its attitude change is described by rotation about the center of mass or a fixed point. This is based on the classical mechanics analysis of rigid body motion and avoids complex elasticity calculations.

[0037] Secondly, the motion trajectory of the semi-fairing is simplified to planar motion, assuming that the motion trajectory of the semi-fairing is completely confined within a two-dimensional plane. For an axisymmetric rocket and its rotational separation, its main motion can be regarded as motion within a certain plane of symmetry. By greatly simplifying the six-degree-of-freedom problem, which requires three spatial coordinates and three attitude angles, into a three-degree-of-freedom problem, which only requires two translational coordinates and one rotational coordinate, the computational load is reduced by an order of magnitude.

[0038] Then, the motion of the semi-fairing is defined as rotation about a fixed point. It is clear that the rotational motion of the semi-fairing is about a point that is fixed relative to the rocket body (which can be set as the hinge point R). This decomposes the complex motion into a simple fixed-axis rotation, so that the dynamic equation can be established by directly applying the law of rigid body rotation about a fixed axis.

[0039] Friction exists at the rotating hinges or contact points of the rocket fairing, but its magnitude is typically an order of magnitude lower than the enormous driving torque generated by the separation device. Therefore, during the brief separation process, the work done by friction (the energy consumed) has a negligible impact on the overall trajectory, and its influence can be ignored to improve computational speed. Furthermore, considering friction usually requires introducing a complex force term related to the contact normal force and opposite in direction to the motion, which complicates the torque equation and introduces a friction coefficient that is difficult to measure precisely, reducing the stability of the overall evaluation process. Ignoring friction results in a "cleaner" equation, a more stable numerical solution, and less prone to computational fluctuations due to the nonlinear characteristics of friction. Based on this, the kinematic and dynamic equations of the center of mass in this invention assume the neglect of friction, greatly simplifying the model and improving computational speed and reliability. While this may lead to a slight overestimation of the separation velocity (due to the neglect of frictional energy dissipation), such a slightly conservative estimate is generally acceptable, and even beneficial, for safety considerations in engineering design.

[0040] Assuming the direct effect of gravitational acceleration is ignored, this essentially means ignoring the direct impact of gravity on the overload caused by the enormous thrust generated by the rocket engine. Because the rocket is in high-speed flight during fairing separation, its engine generates tremendous thrust, causing a very high axial overload (n) on the rocket body. y Its value is much greater than 1, for example, n y=4g means the acceleration is four times the acceleration due to gravity. At this point, the gravitational force itself (1g) and the inertial force generated by the overload (n) are... y Compared to *g), it has become a secondary factor, and the model has already passed overload n. y The calculation includes the indirect effects of gravity, namely the acceleration state of the spacecraft, while the gravity term g alone is negligible. Therefore, the direct effect of gravitational acceleration can be ignored in the calculation. Simultaneously, removing the mg term directly from the dynamic equations makes the equations simpler and more consistent with the actual force conditions of the rocket during powered flight. This assumption makes the model more suitable for high-altitude separation during powered flight. If used to evaluate separation in the initial stage of rocket launch or the terminal stage of the trajectory (where n...),... y If the value is very small, then the error will be relatively large.

[0041] Assuming that the forces involved are only inertial forces and the active forces generated by the separation device, which ignores the direct effects of friction and gravitational acceleration, this assumption clearly identifies the factors affecting the separation trajectory as several key parameters: M R (Design variables), n y (Flight conditions), m, I R L (structural properties) is beneficial for parametric research and optimization, making the model clearly show that the separation trajectory is the result of the combined action of active control force and inertial force of the flight environment.

[0042] Based on the above assumptions, the kinematic and dynamic equations of the center of mass rotating about a fixed rotation point (R) are established.

[0043] like Figure 2 As shown, a planar coordinate system is first established, where the origin (O) is the center of the separation surface between the fairing and the rocket body, the Y-axis coincides with the rocket's axis of symmetry and points towards the rocket's head, and the X-axis points towards the direction of rotational separation of the semi-fairing.

[0044] Then, based on the motion trajectory parameters and trigonometric functions, the relationship between the centroid coordinates and the rotation angle is established, specifically:

[0045] Let L be the distance from the centroid of the semi-fair to the point of rotation (R), and let L be the fixed angle between the line connecting the centroid and point R and the separation surface circle. The rotation angle is Before the fairing separates from the rocket, the coordinates of the center of mass (Xcg, Ycg) of the half-fairing satisfy the following relationship:

[0046] ;

[0047] in, Let be the radius of the separation circle between the fairing and the rocket body; where, , , It is a fixed constant, angle. It is a function that changes with time t, that is .

[0048] The above relationship can represent the position of the center of mass coordinates, and then the velocity can be obtained by differentiating the position of the center of mass coordinates with respect to time. Specifically, kinematic analysis is performed on the relationship between the center of mass coordinates and the rotation angle to obtain the linear velocity equations of the center of mass of the semi-fairing in the X and Y axis directions.

[0049] More specifically, based on the geometric relationship between the centroid coordinates (Xcg, Ycg) of the semi-fairing and the rotation angle θ, the linear velocity equations of the centroid of the semi-fairing in the X-axis and Y-axis directions are obtained by taking the first derivative of the centroid coordinate equation with respect to time t:

[0050] ;

[0051] in, It is the linear velocity of the center of mass of the semi-fair in the X-axis direction; It is the linear velocity of the center of mass of the semi-fair in the Y-axis direction; It is angular velocity.

[0052] Acceleration is obtained by differentiating the linear velocity equation with respect to time. Specifically, by analyzing the acceleration relationship of the linear velocity equation, the linear acceleration equations in the X and Y axes are obtained.

[0053] More specifically, by taking the first derivative of the linear velocity equation with respect to time t, we obtain the linear acceleration equations of the semi-fairing's center of mass in the X and Y axes:

[0054] ;

[0055] in, It is the linear acceleration of the center of mass of the semi-fairing in the X-axis direction. It is the linear acceleration of the center of mass of the semi-fairing in the Y-axis direction. It is angular acceleration.

[0056] Establish the angular acceleration equation: Based on the law of rigid body rotation about a fixed axis, establish the angular acceleration equation for the semi-fairing rotating about the rotation point R. The law of rigid body rotation about a fixed axis is: Net external torque = Moment of inertia × Angular acceleration, i.e. .

[0057] The resultant external torque of this invention It mainly consists of two parts: the active driving torque M provided by the separation device. R The torque generated by inertial forces and the active driving torque provided by the separation device are known inputs. Due to the axial overload n of the rocket... y This is equivalent to having a mass of size n at the centroid. yThe inertial force *mg is opposite in direction to the acceleration (i.e., downward). The lever arm of this force to the point of rotation R is L*cos(θcg+θ). The direction of this torque is opposite to the driving torque M. R Conversely, it is negative. Therefore, the net external torque is:

[0058] =-(n y *mg)*[L*cos(θcg+θ)]+M R

[0059] Substituting the net external torque into the rotational law, we obtain the expression for the angular acceleration equation as follows:

[0060] ;

[0061] in, Let R be the moment of inertia of the semi-fairing about the point of rotation. For rocket axial overload, For the quality of a semi-fairing, It is the acceleration due to gravity. The driving torque generated by the separation device.

[0062] Step S120: Based on the kinematic and dynamic equations of the center of mass and the Runge-Kutta method, the motion trajectory parameters of the semi-fairing before detaching from the rocket are solved by iterative process.

[0063] The Runge-Kutta method is an iterative numerical algorithm for solving initial value problems of ordinary differential equations. Based on the known dynamic laws (differential equations) of a system and its initial state, it predicts the state of the system at any future time. By performing multiple "trial" slope calculations within a calculation step and averaging them, a high-precision numerical solution is obtained.

[0064] The motion trajectory parameters include the centroid coordinates and rotation angles at different times.

[0065] The motion state of the semi-fairing at time t is defined as the state vector Y(t), which is composed of the rotation angle θ and angular velocity. Composed of the centroid coordinates (Xcg, Ycg), the state vector Y(t) can be expressed as:

[0066] Y(t) = [θ(t), [(t), Xcg(t), Ycg(t)]^T. Where T denotes transpose.

[0067] Based on the linear velocity equation and the angular acceleration equation, a system of first-order differential equations dY / dt=f(t,Y) for the state vector Y(t) with respect to time t is constructed, where the function f is defined by the following equation:

[0068] dθ / dt= ;

[0069] d / dt=(1 / I R )[-n y mgL*cos(θcg+θ)+M R ];

[0070] dXcg / dt=L sin(θcg+θ);

[0071] dYcg / dt=L cos(θcg+θ).

[0072] Set the initial state for the numerical solution: when time t=0, rotate the angle. =0, angular velocity =0, the centroid coordinates are at the initial position, and the linear velocity is zero;

[0073] Iterative calculation: Starting from t=0, the calculation iterates step by step with a preset time step Δt, updating the state vector using the Runge-Kutta method combined with the linear acceleration equation until the termination condition is met. For each time step, the state vector for the next time step is calculated based on the current state vector. The linear acceleration equation is mainly used in conjunction with the Runge-Kutta method in the intermediate step of calculating the slope.

[0074] In some specific embodiments, the Runge-Kutta method employs a fourth-order Runge-Kutta method, and the specific steps for each iterative update of the state vector include: assuming n is the time step, and the current time is t. n The state vector is Y n The goal is to calculate t after time Δt. {n+1} The new state Y of the moment {n+1} .

[0075] t n This represents the time corresponding to the nth time step.

[0076] Y n The system state vector calculated at the nth time step, i.e., Y(t n ).

[0077] The iterative process starts from n=0 (the initial state) and gradually calculates n=1,2,3,... until the termination condition is met.

[0078] Calculate the first slope K1: based on the current time t n and the current state vector Y n The slope K1 of the first-order differential equation system at the starting point can be directly calculated using the following formula:

[0079] K1=f(t n ,Y n ).

[0080] Calculate the second slope K2: Use the first slope K1 to estimate the first intermediate state vector Y after half a step size. 中间1 And calculate the slope K2 of the first-order differential equation system in this first intermediate state, using the following formula:

[0081] Y 中间1 =Y n +(Δt / 2)*K1;

[0082] K2=f(t n +Δt / 2,Y 中间1 );

[0083] Δt represents the time step, which is the entire simulation time (e.g., from the start of fairing separation t=0 to the point of no contact t=t). end The time interval is divided into multiple time periods, where Δt represents the fixed step size of each time interval.

[0084] Calculate the third slope K3: Use the second slope K2 to estimate the second intermediate state vector Y after half a step. 中间2 And calculate the slope K3 of the first-order differential equation system in this second intermediate state, using the following formula:

[0085] Y 中间2 =Y n +(Δt / 2)*K2;

[0086] K3=f(t n +Δt / 2,Y 中间2 ).

[0087] Calculate the fourth slope K4: Use the third slope K3 to estimate the third intermediate state vector Y after a full step size. 中间3 And calculate the slope K4 of the first-order differential equation system in this third intermediate state, using the following formula:

[0088] Y 中间3 =Y n +Δt*K3;

[0089] K4=f(t n +Δt,Y 中间3 );

[0090] Weighted average and updated state: The four slopes K1, K2, K3, and K4 are weighted and averaged to obtain the comprehensive slope Y. {n+1} The calculation formula is as follows;

[0091] Y{n+1} =Y n +(Δt / 6)*(α*K1+β*K2+γ*K3+δ*K4);

[0092] Where α is the weight value of slope K1, β is the weight value of slope K2, γ is the weight value of slope K3, and δ is the weight value of slope K4. All weight values ​​are set based on operator experience or actual needs, and are not limited here.

[0093] The state vector is then updated to the next time step, and this process is repeated iteratively.

[0094] After each iteration, it is determined whether the rotation angle θ in the current state vector reaches or exceeds the preset escape angle Φ. If θ < Φ, the iteration continues; if θ ≥ Φ, the iteration terminates. The preset escape angle Φ can be set based on the operator's experience or the actual situation, and is not limited here.

[0095] Record the state vector Y(t) corresponding to all time steps from t=0 to the termination time to obtain the state vector sequence, which is the motion trajectory parameter.

[0096] Among them, the linear velocity of the motion trajectory parameter ( , ) and angular velocity The expression can be set as:

[0097] .

[0098] Step S130: Based on the motion trajectory parameters, the separation motion trajectory of the semi-fairing is visualized and generated. By analyzing the relative positional relationship between the motion trajectory and the rocket body, the risk of collision in the separation scheme is assessed.

[0099] Specifically, step S130 includes:

[0100] Step S131: Determine the initial conditions of inertial motion, combine them with all motion trajectory parameters to analyze the complete motion trajectory of the semi-fair, and draw the contour attitude of the semi-fair at different times in the plane coordinate system.

[0101] Step S131 includes: obtaining the state vector at the termination moment, and obtaining the angular velocity and linear velocity at the separation moment, which are used as the initial conditions for the semi-fairing to undergo inertial motion after separation from contact. Based on all motion trajectory parameters and the initial conditions for inertial motion, the complete motion trajectory of the semi-fairing from the start of separation to the free flight phase after separation from contact is calculated. The motion trajectory during the free flight phase is calculated by substituting the initial conditions into the uniform motion and uniform rotation models. Based on the complete motion trajectory, the contour attitude of the semi-fairing at different moments is plotted in a planar coordinate system.

[0102] like Figure 3 As shown, in step S132, the contour attitude of a series of consecutive moments and the envelope of the rocket body are plotted on the same graph to form a dynamic trajectory graph of the separation process.

[0103] Step S133: Determine whether a minimum safe clearance exists between the outline of the semi-fair and the rocket body envelope at any given time. The minimum safe clearance is set based on the actual parameters of the fairing or in combination with the operator's experience; no specific limit is imposed here.

[0104] Step S134: If there is a gap greater than the minimum safety gap at all times, the scheme is deemed safe.

[0105] Step S135: If there is contour overlap or the clearance is less than or equal to the minimum safety clearance, then a collision risk is determined.

[0106] Those skilled in the art will understand that this invention simplifies the semi-fairing into an analytical object undergoing rigid planar motion, establishing its kinematic and dynamic equations of rotation around a fixed point, thus laying a theoretical foundation for calculations. Secondly, the Runge-Kutta method is used to iteratively solve this mathematical model to obtain the trajectory parameters during the separation process. Finally, the separation trajectory is visualized based on these parameters, and the collision risk is assessed by analyzing its relative position to the rocket body. This invention aims to solve the problems of long cycles and high costs associated with traditional fairing rotation separation methods that rely on high-fidelity simulations and physical experiments. By using a simplified physical model and numerical calculation methods, it achieves rapid safety assessment of the fairing separation process, significantly shortening the design verification cycle. Furthermore, because it is based on pure numerical calculations, it significantly reduces assessment costs.

[0107] Furthermore, those skilled in the art will understand that although some embodiments herein include certain features included in other embodiments but not others, combinations of features from different embodiments are intended to be within the scope of the invention and form different embodiments. For example, in the claims, any of the claimed embodiments can be used in any combination.

[0108] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-described technical content to create equivalent embodiments without departing from the scope of the present invention. The implementation schemes in the above embodiments can be further combined or replaced. Any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A method for evaluating the rotational separation of a rocket fairing, characterized in that, include: The semi-fair is simplified into an analytical object undergoing rigid planar motion, and the kinematic and dynamic equations of its center of mass rotating about a fixed point of rotation are established. Based on the aforementioned kinematic and dynamic equations of the center of mass, the Runge-Kutta method is used to solve the motion trajectory parameters of the semi-fairing before it leaves contact with the rocket through iterative methods; wherein, the motion trajectory parameters include the coordinates of the center of mass and the rotation angle at different times; Based on the motion trajectory parameters, the separation trajectory of the semi-fairing is visualized and generated. By analyzing the relative positional relationship between the motion trajectory and the rocket body, the risk of collision in the separation scheme is assessed.

2. The method according to claim 1, characterized in that, The steps for establishing the kinematic and dynamic equations of the center of mass are based on the following assumptions: Ignore the effect of friction; Ignoring the direct effect of gravitational acceleration; The forces acting on the semi-fairing are only inertial forces and the active forces generated by the separation device.

3. The method according to claim 2, characterized in that, The steps of simplifying the semi-fairing into an analytical object undergoing rigid planar motion and establishing its kinematic and dynamic equations of motion around a fixed point of rotation include: Establish a planar coordinate system, where the origin (O) is the center of the separation surface between the fairing and the rocket body, the Y-axis coincides with the rocket's axis of symmetry and points towards the rocket's head, and the X-axis points towards the rotational separation direction of the semi-fairing; Based on the motion trajectory parameters and trigonometric functions, establish the relationship between the centroid coordinates and the rotation angle; A kinematic analysis was performed on the relationship between the center of mass coordinates and the rotation angle to obtain the linear velocity equations of the center of mass of the semi-fairing in the X and Y axis directions. An acceleration relationship analysis was performed on the linear velocity equation to obtain the linear acceleration equations in the X and Y axis directions; Based on the rigid body rotation law, the equation for the angular acceleration of the semi-fairing rotating about the rotation point R is established.

4. The method according to claim 3, characterized in that, The step of establishing the relationship between the centroid coordinates and the rotation angle based on the motion trajectory parameters and trigonometric functions includes: Define the distance from the centroid of the semi-fairing to the rotation point R as L, and the fixed angle between the line connecting the centroid and point R and the separation surface circle as . The rotation angle is Before the fairing separates from the rocket, the centroid coordinates (Xcg, Ycg) of the semi-fairing satisfy the following relationship: ； Where r is the radius of the separation circle between the fairing and the rocket body; where, , , It is a fixed constant, angle. It is a function that changes with time t, that is .

5. The method according to claim 4, characterized in that, The step of performing kinematic analysis on the relationship between the center of mass coordinates and the rotation angle to obtain the linear velocity equations of the semi-fairing center of mass in the X and Y axis directions includes: Based on the geometric relationship between the centroid coordinates (Xcg, Ycg) of the semi-fairing and the rotation angle θ, the linear velocity equations of the centroid in the X-axis and Y-axis directions are obtained by taking the first derivative of the centroid coordinate equation with respect to time t: ； in, It is the linear velocity of the center of mass of the semi-fair in the X-axis direction; It is the linear velocity of the center of mass of the semi-fair in the Y-axis direction; It is angular velocity.

6. The method according to claim 5, characterized in that, The step of performing acceleration relationship analysis on the linear velocity equation to obtain the linear acceleration equations in the X and Y axis directions includes: Taking the first derivative of the linear velocity equation with respect to time t, we obtain the linear acceleration equations of the center of mass of the semi-fairing in the X and Y axes: ； in, It is the linear acceleration of the center of mass of the semi-fairing in the X-axis direction. It is the linear acceleration of the center of mass of the semi-fairing in the Y-axis direction. It is angular acceleration.

7. The method according to claim 6, characterized in that, The step of establishing the angular acceleration equation for the semi-fairing rotating about the rotation point R based on the rigid body fixed-axis rotation law includes: The equation for angular acceleration is: ； in, Let R be the moment of inertia of the semi-fairing about the point of rotation. For rocket axial overload, For the quality of a semi-fairing, It is the acceleration due to gravity. The driving torque generated by the separation device.

8. The method according to claim 7, characterized in that, The step of solving the trajectory parameters of the semi-fairing before separation from the rocket using the Runge-Kutta method through iterative processes based on the kinematic and dynamic equations of the center of mass includes: The motion state of the semi-fairing at time t is defined as the state vector Y(t), which is composed of the rotation angle, the angular velocity, and the centroid coordinates. Based on the linear velocity equation and the angular acceleration equation, a system of first-order differential equations of the state vector Y(t) with respect to time t is constructed. Set the initial state for the numerical solution: when time t=0, rotate the angle. =0, angular velocity =0, the centroid coordinates are at the initial position, and the linear velocity is zero; Iterative calculation: Starting from t=0, iterate step by step with a preset time step Δt, using the Runge-Kutta method combined with the linear acceleration equation to update the state vector until the termination condition is met; for each time step, calculate the state vector of the next time step based on the current state vector; After each iteration, determine the rotation angle in the current state vector. Check if the preset breakaway angle Φ has been reached or exceeded; if θ < Φ, continue iterative solution; if θ ≥ Φ, terminate iteration. Record the state vector Y(t) corresponding to all time steps from t=0 to the termination time to obtain the state vector sequence, which is the motion trajectory parameter.

9. The method according to claim 8, characterized in that, The steps of visually generating the separation trajectory of the semi-fairing based on the motion trajectory parameters, and assessing the risk of collision of the separation scheme by analyzing the relative positional relationship between the motion trajectory and the rocket body, include: Determine the initial conditions for inertial motion, combine them with all the motion trajectory parameters to analyze the complete motion trajectory of the semi-fair, and draw the contour attitude of the semi-fair at different times in the plane coordinate system. The contour attitude at a series of consecutive moments is plotted with the envelope of the rocket body on the same graph to form a dynamic trajectory diagram of the separation process; Determine whether, at any given moment, there exists a minimum safe clearance between the outline of the semi-fair and the envelope of the rocket body; If the gap is greater than the minimum safety margin at all times, the solution is considered safe. If there is contour overlap or the minimum safe clearance is less than or equal to the minimum safe clearance, then a collision risk is determined.

10. The method according to claim 9, characterized in that, The steps of determining the initial conditions for inertial motion, combining them with all the motion trajectory parameters to analyze the complete motion trajectory of the semi-fair, and drawing the contour attitude of the semi-fair at different times in the plane coordinate system include: Obtain the state vector at the termination moment, and get the angular velocity and linear velocity at the separation moment, and use them as the initial conditions for the semi-fairing to perform inertial motion after separation from contact. Based on all the motion trajectory parameters and the initial conditions of the inertial motion, the complete motion trajectory of the semi-fairing from the start of separation to the free flight phase after the contact is broken is calculated; the motion trajectory of the free flight phase is obtained by substituting the initial conditions into the uniform motion and uniform rotation model. Based on the complete motion trajectory, the outline posture of the semi-fair at different times is drawn in the plane coordinate system.

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