Quantitative analysis method for dynamic stability of spinning flyer based on eccentricity of center of mass

Abstract

The invention relates to the technical field of aerodynamics, in particular to a mass center eccentricity-based spinning flyer dynamic stability quantitative analysis method. The method comprises the following steps: constructing a six-degree-of-freedom dynamic model containing a mass center eccentricity additional inertial effect; determining a test working condition, performing simulation under the test working condition, and obtaining aerodynamic torque data of the asymmetric flow field; obtaining an interpolation table for the test condition based on the asymmetric flow field aerodynamic torque data; carrying out coupling simulation based on the six-degree-of-freedom kinetic model and the interpolation table of the test working conditions, and outputting state parameters of the spinning flyer; and quantitative indexes are extracted based on the state parameters of the spinning flyer. According to the method, dynamic simulation can be realized through interpolation coupling, the stability rule of the spinning flyer is quantified according to mechanisms, and quantitative analysis is effectively and accurately performed on the dynamic stability of the spinning flyer.

Description

Technical Field

[0001] This application relates to the field of aerodynamics, and in particular to a method for quantitative analysis of the dynamic stability of spinning objects based on center-of-mass eccentricity. Background Technology

[0002] Flight stability is a core indicator determining the mission accuracy of an aircraft. During actual manufacturing and assembly, center-of-gravity eccentricity is inevitable, disrupting the axisymmetry of the aircraft and introducing additional inertial forces and moments, causing translational-rotational coupling and ultimately affecting flight characteristics. Existing aircraft stability analysis methods have the following shortcomings: Oversimplification of dynamic models: Traditional six-degree-of-freedom models often ignore the additional inertial effect of center-of-mass eccentricity, and cannot accurately capture the asymmetric aerodynamic load and motion coupling caused by eccentricity, resulting in large errors in stability analysis; The impact of flow field mechanisms on stability cannot be quantified, and the verification methods are limited. Most analyses rely on pure simulation or pure theoretical derivation, without combining experimental data to determine the authenticity of aerodynamic forces, resulting in insufficient engineering applicability of the conclusions. Summary of the Invention

[0003] To address the aforementioned issues, this application provides a quantitative analysis method for the dynamic stability of spinning objects based on centroid eccentricity, which can accurately capture the coupling relationship between centroid eccentricity, asymmetric flow field, and dynamic instability.

[0004] According to one aspect of the embodiments of this application, a method for quantitative analysis of the dynamic stability of a spinning object based on centroid eccentricity is proposed, the method comprising: Construct a six-degree-of-freedom dynamic model with added inertial effects due to center-of-mass eccentricity; The test conditions with axial eccentricity, lateral eccentricity and longitudinal eccentricity as test variables are determined, and simulation is carried out under the test conditions to obtain asymmetric flow field aerodynamic torque data. An interpolation table for the test conditions is obtained based on the asymmetric flow field aerodynamic moment data. Coupled simulation is performed based on the six-degree-of-freedom dynamic model and the interpolation table of the test conditions to output the state parameters of the spinning flying object; Quantitative indices are extracted based on the state parameters of the spinning object to perform quantitative analysis of the dynamic stability of the spinning object.

[0005] In the above scheme, the construction of a six-degree-of-freedom dynamic model with added inertial effects due to centroid eccentricity includes: Based on the Newton-Euler equations, with the theoretical center of mass of the spinning flying object as the origin of the body coordinate system, the inertial coordinate system and the body coordinate system are defined. Determine the differential equations of motion containing the centroid eccentricity, wherein the differential equations of motion include positional equations, translational equations, and rotational equations; The six-degree-of-freedom dynamic model is determined based on the positional relationship equation, the translational motion equation, and the rotational motion equation. The six-degree-of-freedom dynamic model is a linearly coupled system.

[0006] In the above scheme, the positional relationship equation is determined through the following steps: Determine the eccentricity vector of the actual center of mass of the spinning object in the body coordinate system; Determine the rotation matrix between the inertial coordinate system and the volume coordinate system; Determine the position of the origin of the volume coordinate system in the inertial coordinate system; The positional relationship equation is determined based on the position of the origin of the body coordinate system in the inertial coordinate system, the rotation matrix, and the eccentric vector of the actual center of mass of the spinning object in the body coordinate system.

[0007] In the above scheme, the equation of translational motion is determined through the following steps: Determine the mass and angular velocity of the spinning object; Determine the velocity of the origin of the volume coordinate system within the volume coordinate system; Determine the net external force acting on the spinning object; The equation of translational motion is determined based on the mass of the spinning object, the angular velocity, the velocity of the origin of the body coordinate system in the body coordinate system, and the net external force.

[0008] In the above scheme, the rotational motion equation is determined through the following steps: Determine the inertial tensor of the spinning object about the origin of the body coordinate system; Determine the resultant external moment of the resultant external force about the origin of the body coordinate system; The rotational motion equation is determined based on the translational motion equation, the inertia tensor, and the net external torque.

[0009] In the above scheme, determining the six-degree-of-freedom dynamic model based on the positional relationship equation, the translational motion equation, and the rotational motion equation includes: The positional relationship equation, the translational motion equation, and the rotational motion equation are spatialized to obtain the six-degree-of-freedom dynamic model.

[0010] In the above scheme, the test conditions include multiple test sub-conditions, and the acquisition of asymmetric flow field aerodynamic torque data includes: For each of the aforementioned test sub-conditions, the drag coefficient, lateral force coefficient, normal force coefficient, roll moment coefficient, pitch moment coefficient, and yaw moment coefficient obtained under the test sub-condition are acquired. The drag coefficient, the lateral force coefficient, the normal force coefficient, the roll moment coefficient, the pitch moment coefficient, and the yaw moment coefficient are used as the aerodynamic moment data of the asymmetric flow field.

[0011] In the above scheme, obtaining the interpolation table for the test condition based on the asymmetric flow field aerodynamic moment data includes: The asymmetric flow field aerodynamic moment data are organized into the interpolation table according to the mapping relationship between the axial eccentricity, lateral eccentricity, and longitudinal eccentricity and the time series under the test conditions.

[0012] In the above scheme, the coupled simulation based on the six-degree-of-freedom dynamic model and the interpolation table of the test conditions, outputting the state parameters of the spinning aircraft, includes: Determine the flight speed, characteristic area, and characteristic length of the spinning object; The actual torque of the spinning object is determined based on the flight speed, the characteristic area, and the characteristic length. Based on the actual torque, the six-degree-of-freedom dynamic model is solved using the fourth-order Runge-Kutta method to obtain the position, velocity, angular velocity, and attitude angle of the spinning object; The position, velocity, angular velocity, and attitude angle of the spinning object are its state parameters.

[0013] In the above scheme, the extraction of quantitative indicators based on the state parameters of the spinning aircraft includes: Based on the state parameters of the spinning object, the trajectory index, attitude index, and flow field coupling index of the spinning object are extracted. The trajectory index is used to characterize the maximum deviation of the actual center of mass of the spinning object in the three-axis directions; The attitude parameters are used to characterize the root mean square angular velocity, nutation amplitude, and decay rate of the spinning aircraft. The coupling index is used to characterize the vortex shedding frequency and the Magnus force coefficient.

[0014] The beneficial effects of this application are as follows: This application constructs a six-degree-of-freedom dynamic model with added inertial effects due to centroid eccentricity to solve the error caused by centroid eccentricity. Then, it determines the test conditions with axial eccentricity, lateral eccentricity, and longitudinal eccentricity as test variables, and performs simulation under the test conditions to obtain asymmetric flow field aerodynamic torque data. Since traditional methods use the "symmetry assumption", they cannot accurately capture the asymmetric aerodynamic load and motion coupling caused by eccentricity. However, the asymmetric flow field aerodynamic torque data of this application can solve this problem, thereby improving the accuracy of the analysis.

[0015] Coupled simulation is performed using a six-degree-of-freedom dynamic model and an interpolation table of the experimental conditions to output the state parameters of the spinning object. Based on these state parameters, quantitative indices are extracted to quantitatively analyze the dynamic stability of the spinning object. In this way, dynamic simulation can be achieved through interpolation coupling, and the stability characteristics of the spinning object can be quantified by mechanism, enabling effective and accurate quantitative analysis of its dynamic stability. Attached Figure Description

[0016] Figure 1 A flowchart illustrating the method for quantitative analysis of dynamic stability of spinning objects based on centroid eccentricity provided in this application embodiment; Figure 2 A flowchart illustrating the overall logic of the method for quantitative analysis of dynamic stability of spinning objects based on centroid eccentricity, as provided in this application embodiment. Figure 3 This is a schematic diagram illustrating the definition of the inertial coordinate system and the volume coordinate system provided in the embodiments of this application. Detailed Implementation

[0017] To enable those skilled in the art to better understand the solutions of this application, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0018] It should be noted that while some processes described in the specification, claims, and accompanying drawings include multiple steps appearing in a specific order, it should be clearly understood that these steps may not be performed in the order they appear herein, or may be performed in parallel. The step numbers are merely used to distinguish different steps and do not themselves represent any execution order. Furthermore, descriptions such as "first," "second," or "objective" in this document are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. "Multiple" in this document refers to at least two.

[0019] It is worth noting that, in the specific embodiments of this application, data related to dynamic model parameters and the state parameters of spinning objects are involved. When the above embodiments of this application are applied to specific products or technologies, permission or consent from the target object is required, and the collection, use, and processing of related data must comply with relevant laws, regulations, and standards. For example, when an embodiment of this application needs to obtain data related to dynamic model parameters and the state parameters of spinning objects, separate permission or consent from the target object can be obtained through pop-up windows or redirection to a confirmation page. After obtaining the separate permission or consent from the target object, the necessary dynamic model parameters and the state parameters of spinning objects required for the normal operation of the embodiments of this application can then be obtained.

[0020] The following provides a detailed description of the specific implementation methods of the embodiments of this application: Please see Figure 1 , Figure 1 This is a flowchart illustrating the method for quantitative analysis of the dynamic stability of a spinning object based on centroid eccentricity, as provided in the embodiments of this application. Figure 1 The illustrated method for quantitative analysis of the dynamic stability of spinning objects based on center-of-mass eccentricity includes: Step 110: Construct a six-degree-of-freedom dynamic model with added inertial effects due to center-of-mass eccentricity; Step 120: Determine the test conditions with axial eccentricity, lateral eccentricity and longitudinal eccentricity as test variables, and perform simulation under the test conditions to obtain asymmetric flow field aerodynamic torque data. Step 130: Obtain an interpolation table for the test conditions based on the asymmetric flow field aerodynamic torque data; Step 140: Perform coupled simulation based on the six-degree-of-freedom dynamic model and the interpolation table of the test conditions, and output the state parameters of the spinning flight object; Step 150: Extract quantitative indicators based on the state parameters of the spinning object, and perform quantitative analysis on the dynamic stability of the spinning object according to the quantitative indicators.

[0021] First, it should be noted that there are various types of spinning flying objects, such as military projectiles, rockets, and satellites, as well as sports objects like basketballs and footballs. This application uses a projectile as an example of a spinning flying object, combining steps 110-150 and... Figure 2 The following is a detailed explanation: In step 110, a six-degree-of-freedom dynamic model with the added inertial effect of the center of mass eccentricity is constructed. Specifically, this can be achieved by defining the inertial coordinate system and the body coordinate system based on the Newton-Euler equations, with the theoretical center of mass of the spinning flying object as the origin of the body coordinate system. Determine the differential equations of motion containing the centroid eccentricity, wherein the differential equations of motion include positional equations, translational equations, and rotational equations; The six-degree-of-freedom dynamic model is determined based on the positional relationship equation, the translational motion equation, and the rotational motion equation. The six-degree-of-freedom dynamic model is a linearly coupled system.

[0022] More specifically, based on the Newton-Euler equations, an inertial coordinate system is defined with the theoretical center of mass of the projectile (i.e., the theoretical center of mass of the spinning object) as the origin of the body coordinate system. with volume coordinate system ,like Figure 3 As shown, Figure 3 This is a schematic diagram illustrating the definitions of the inertial coordinate system and the volume coordinate system. Figure 3 In the diagram, O is the reference point (geometric center), and C is the actual center of mass, which is also the actual center of mass of the rotating flying object. This is the offset of the actual centroid relative to the reference point. For the actual center of mass C in the inertial coordinate system Location, With reference point O in the inertial coordinate system Position, A is from the volume coordinate system to inertial coordinate system The rotation matrix can be represented by the following equation: ; From this, we can derive the differential equation of motion involving the centroid and eccentricity: Positional relationship equation: The actual center-of-mass position vector of the projectile (spinning projectile) satisfies: ; in, The origin of the body coordinate system is at The position of A in the system is Tie The rotation matrix of the system, The actual center of mass of the spinning object is in The eccentric vector (constant value) in the system.

[0023] The equations of translational motion, considering the additional inertial forces (centrifugal force, tangential inertial force) caused by eccentricity, satisfy: ; Where m is the mass of the projectile (the mass of a spinning projectile). The origin of the body coordinate system is at The velocity in the system, The angular velocity of the projectile (spinning object). The total external force, also known as the resultant external force (including aerodynamic force and gravity).

[0024] Equation of rotational motion: Considering the additional inertial torque caused by eccentricity, it satisfies: ; ; in, Let the inertial tensor of the projectile (spinning projectile) about the origin of the body coordinate system be given. The resultant external torque.

[0025] State spatialization: Rearrange the above equations into a linearly coupled system. ; in, ; ; The meanings of the symbols used in this application are shown in the table above: It is the identity matrix. F is the cross product matrix, and F is the load vector, which facilitates numerical solution.

[0026] In step 120, the test conditions with axial eccentricity, lateral eccentricity, and longitudinal eccentricity as test variables are determined, and simulation is performed under the test conditions to obtain asymmetric flow field aerodynamic torque data. Specifically, multi-condition CFD simulation is used to obtain asymmetric flow field aerodynamic torque data. Working condition design: Orthogonal experimental design is adopted, with axial eccentricity as the main factor. Lateral eccentricity Longitudinal eccentricity For each variable, there are 3 levels (e.g. , =±3mm, =±3mm), an orthogonal array is selected, with a total of 9 working conditions, covering the eccentricity parameter space; CFD simulation settings: Geometric model: Based on the actual size of the projectile, eccentricity is achieved by moving the internal mass block to maintain the shape and mesh topology consistency; Physical model: The SST k-ω turbulence model is adopted to capture asymmetric flow field separation and vortex shedding, and the incoming flow velocity is changed to the typical flight speed of the projectile (e.g., 300m / s). Monitoring and output: Monitor drag coefficient CD, lateral force coefficient CY, normal force coefficient CN, roll moment coefficient Cl, pitch moment coefficient Cm, yaw moment coefficient Cn, and output the time series of aerodynamic moment coefficients and flow field visualization results (pressure cloud map, vorticity map) for each working condition. In step 130, the data obtained from the monitoring above is preprocessed, and the coefficients output by CFD (i.e., under each experimental sub-condition) are organized into an interpolation table according to "eccentricity-time" for subsequent dynamic model coupling.

[0027] In step 140, a coupled simulation is performed based on the six-degree-of-freedom dynamic model and the interpolation table of the test conditions to output the state parameters of the spinning aircraft. Here, based on the CFD interpolation table obtained above, the linear ND interpolation method is used to obtain the aerodynamic coefficients and moment coefficients in real time according to the eccentricity and projectile attitude of the current dynamic simulation, and convert them into actual moments. ; in, air density, Where S is the flight speed, S is the characteristic area of ​​the projectile (spinning projectile), and L is the characteristic length of the projectile (spinning projectile). Numerical solution: The above six-degree-of-freedom linear coupled system is solved using the fourth-order Runge-Kutta method, and the position, velocity, angular velocity and attitude angle of the projectile (spinning projectile) are output. The simulation time covers the transient and quasi-steady-state stages of the flow field.

[0028] In step 150, quantitative indicators are extracted based on the state parameters of the spinning object to perform quantitative analysis on the dynamic stability of the spinning object according to the quantitative indicators.

[0029] Here, stability index extraction involves extracting quantitative indicators from the simulation results. Trajectory index: The maximum deviation of the actual center of mass of a spinning object in the x / y / z (three axes) directions; Attitude parameters: root mean square angular velocity, nutation amplitude and decay rate; Flow field coupling index: vortex shedding frequency (FFT analysis) curve), Magnus force coefficient ( and (correlation), where This is the lateral force coefficient. It is an eccentric vector.

[0030] In some embodiments, after obtaining the quantitative indicators, experimental verification can also be performed. The stability law of the mechanistic quantification and optional experimental verification are as follows: Mechanistic analysis: Combining quantitative indicators with flow field visualization results (i.e., asymmetric flow field aerodynamic torque data), the following core principles are quantified: Transient phase: Asymmetric distortion dominates, with additional inertial force following. Growth, trajectory deviation growth rate and Proportional; Quasi-steady-state stage: vortex shedding-nutation coupling dominates, with a "critical eccentricity for instability". ",when At that time, the root mean square velocity of the angular velocity increases exponentially; Rotational condition: The Magnus effect enhances asymmetric distortion, making Reduced by approximately 10%; Optional wind tunnel test verification: A three-component balance is used to conduct wind tunnel tests on each test sub-condition to verify the accuracy of the CFD aerodynamic coefficients (error controlled within 5%), and to correct the dynamic simulation parameters to improve the credibility of the conclusions.

[0031] The following is an example illustration: Parameter settings Basic parameters of the projectile: mass m = 5kg, characteristic length L = 0.5m, characteristic area S = 0.01m², inertia tensor = diag([0.1, 0.5, 0.5]) kg . m2; Eccentricity level: = 0 / 4 / - 4mm, = 0 / 3 / - 3mm, ρz = 0 / 3 / - 3mm, design 9 working conditions according to L9(3) orthogonal array; CFD simulation parameters: 2 million grids, SST k-ω turbulence model, incoming flow velocity 300 m / s, simulation time 0.1 s, output step size 1 × 10-4 s; Dynamic simulation parameters: fourth-order Runge-Kutta method, time step 1 × 10⁻⁵ s, initial state, , , .

[0032] Implementation process A six-degree-of-freedom dynamic model was constructed, and based on the linearly coupled system, a solver was developed using a numerical computing platform to achieve the fourth-order Runge-Kutta method solution. Complete CFD simulations for 9 operating conditions and output aerodynamic torque coefficient data, including operating condition 5 ( = 5mm, =3mm, = 0) The curve shows that there are periodic fluctuations in the quasi-steady-state stage (vortex shedding frequency 120Hz). Coupled with CFD data and dynamic model, simulation results show that the maximum lateral trajectory deviation in condition 5 is 0.12m, which is 6 times that of the eccentric-free condition (0.02m), and the angular velocity... The root mean square value is 0.8 rad / s, which is 4 times that of the eccentric condition (0.2 rad / s); Mechanism analysis: The critical eccentricity for instability of the projectile was determined. = 3.2mm, when When the diameter is >3.2 mm, the coupling between vortex shedding and nutation causes the root mean square velocity of the angular velocity to increase exponentially. (Optional) Wind tunnel test: Conduct the test under the condition of ρc = 0 / 3 / 5mm and measure the results. The error between the CFD simulation values ​​and the actual values ​​was 4%, verifying the accuracy of the method.

[0033] In summary, compared with the prior art, this application has the following beneficial effects: Significantly improved model accuracy: By introducing additional inertial forces and moments caused by the eccentricity of the center of mass into the fully coupled six-degree-of-freedom dynamic model, the limitations of the traditional "symmetric projectile assumption" are effectively overcome. This allows for a more accurate characterization of the asymmetric aerodynamic loads and motion coupling caused by the eccentricity, thereby improving the accuracy and reliability of flight stability analysis.

[0034] Deep quantification of fluid-structure interaction mechanism: It realizes the staged and quantitative analysis of key fluid-structure interaction mechanisms such as "asymmetric distortion-vortex shedding-Magnus effect" and projectile dynamics behavior, and can reveal the intrinsic law of stability evolution with eccentricity, such as the existence of critical eccentricity and the dominant stage of different physical effects, providing a new quantitative analysis paradigm for flight stability research.

[0035] Strong engineering guidance and high optimization efficiency: This method can output a clear centroid eccentricity control threshold, which can be directly used to guide the structural design, processing and loading process of projectiles; at the same time, the multi-condition orthogonal experimental design strategy adopted can efficiently cover a wide parameter space with fewer simulations, which helps to significantly reduce the optimization cost and cycle in the engineering design stage.

[0036] Strong engineering guidance and high optimization efficiency: This method can output a clear centroid eccentricity control threshold, which can be directly used to guide the structural design, processing and loading process of projectiles; at the same time, the multi-condition orthogonal experimental design strategy adopted can efficiently cover a wide parameter space with fewer simulations, which helps to significantly reduce the optimization cost and cycle in the engineering design stage.

[0037] Therefore, this application obtains aerodynamic torque coefficients by constructing a computational fluid dynamics (CFD) model (i.e., a six-degree-of-freedom dynamic model) of the spinning aircraft; it calculates the dynamic stability parameters of the spinning aircraft by coupling the nonlinear dynamic equations (differential equations of motion) with the CFD model; it designs orthogonal experiments to quantify the sensitivity of stability indices under different eccentricities and different test sub-conditions; and (optionally) verifies the simulation results through wind tunnel tests. This application effectively solves the problems of traditional methods ignoring the centroid eccentricity caused by manufacturing errors, the disconnect between dynamic modeling and aerodynamic simulation, and the limited verification methods. It can significantly improve the accuracy and reliability of stability analysis of spinning aircraft, and provide data support for the design optimization and quality control of spinning aircraft.

[0038] Furthermore, the terms “comprising” and “including”, and any variations thereof, are intended to cover non-exclusive inclusion, such that a process, method, system, product, or apparatus that includes a series of steps or units is not necessarily limited to those steps or units that are explicitly listed, but may include other steps or units that are not explicitly listed or that are inherent to such process, method, product, or apparatus.

[0039] It should be understood that in this application, "at least one (item)" means one or more, and "more than" means two or more. "And / or" is used to describe the relationship between related objects, indicating that three relationships can exist. For example, "A and / or B" can represent three cases: only A exists, only B exists, and both A and B exist simultaneously, where A and B can be singular or plural. The character " / " generally indicates that the preceding and following related objects are in an "or" relationship. "At least one (item) of the following" or similar expressions refer to any combination of these items, including any combination of single or plural items. For example, at least one (item) of a, b, or c can represent: a, b, c, "a and b", "a and c", "b and c", or "a and b and c", where a, b, and c can be single or multiple.

[0040] It should be understood that in the description of the embodiments of this application, "multiple" means two or more, "greater than", "less than", "exceeding" etc. are understood to exclude the number itself, and "above", "below", "within" etc. are understood to include the number itself.

[0041] In the several embodiments provided in this application, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces, or indirect coupling or communication connection between apparatuses or units, and may be electrical, mechanical, or other forms.

[0042] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of the embodiments of this application, depending on actual needs.

[0043] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0044] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0045] It should also be understood that the various implementation methods provided in this application can be combined arbitrarily to achieve different technical effects.

[0046] In the embodiments of this application, the terms "module" or "unit" refer to a computer program or part of a computer program that has a predetermined function and works with other related parts to achieve a predetermined goal, and can be implemented wholly or partially using software, hardware (such as processing circuitry or memory), or a combination thereof. Similarly, a processor (or multiple processors or memory) can be used to implement one or more modules or units. Furthermore, each module or unit can be part of an overall module or unit that includes the functionality of that module or unit.

[0047] The above is a detailed description of the embodiments of this application. However, this application is not limited to the above embodiments. Those skilled in the art can make various equivalent modifications or substitutions without departing from the spirit of this application. All such equivalent modifications or substitutions are included within the scope defined by the claims of this application.

Claims

1. A method for quantitative analysis of the dynamic stability of a spinning object based on center-of-mass eccentricity, characterized in that, The method includes: Construct a six-degree-of-freedom dynamic model with added inertial effects due to center-of-mass eccentricity; The test conditions with axial eccentricity, lateral eccentricity and longitudinal eccentricity as test variables are determined, and simulation is carried out under the test conditions to obtain asymmetric flow field aerodynamic torque data. An interpolation table for the test conditions is obtained based on the asymmetric flow field aerodynamic moment data. Coupled simulation is performed based on the six-degree-of-freedom dynamic model and the interpolation table of the test conditions to output the state parameters of the spinning flying object; Quantitative indices are extracted based on the state parameters of the spinning object to perform quantitative analysis of the dynamic stability of the spinning object.

2. The method for quantitative analysis of the dynamic stability of spinning objects based on center-of-mass eccentricity according to claim 1, characterized in that, The construction of the six-degree-of-freedom dynamic model with added inertial effects due to centroid eccentricity includes: Based on the Newton-Euler equations, with the theoretical center of mass of the spinning flying object as the origin of the body coordinate system, the inertial coordinate system and the body coordinate system are defined. Determine the differential equations of motion containing the centroid eccentricity, wherein the differential equations of motion include positional equations, translational equations, and rotational equations; The six-degree-of-freedom dynamic model is determined based on the positional relationship equation, the translational motion equation, and the rotational motion equation. The six-degree-of-freedom dynamic model is a linearly coupled system.

3. The method for quantitative analysis of dynamic stability of spinning objects based on center-of-mass eccentricity according to claim 2, characterized in that, The positional relationship equation is determined through the following steps: Determine the eccentricity vector of the actual center of mass of the spinning object in the body coordinate system; Determine the rotation matrix between the inertial coordinate system and the volume coordinate system; Determine the position of the origin of the volume coordinate system in the inertial coordinate system; The positional relationship equation is determined based on the position of the origin of the body coordinate system in the inertial coordinate system, the rotation matrix, and the eccentric vector of the actual center of mass of the spinning object in the body coordinate system.

4. The method for quantitative analysis of the dynamic stability of spinning objects based on centroid eccentricity as described in claim 3, characterized in that, The equation of translational motion is determined through the following steps: Determine the mass and angular velocity of the spinning object; Determine the velocity of the origin of the volume coordinate system within the volume coordinate system; Determine the net external force acting on the spinning object; The translational motion equation is determined based on the mass of the spinning object, the angular velocity, the velocity of the origin of the body coordinate system in the body coordinate system, and the net external force.

5. The method for quantitative analysis of the dynamic stability of spinning objects based on centroid eccentricity according to claim 4, characterized in that, The equation of rotational motion is determined through the following steps: Determine the inertial tensor of the spinning object about the origin of the body coordinate system; Determine the resultant external moment of the resultant external force about the origin of the body coordinate system; The rotational motion equation is determined based on the translational motion equation, the inertia tensor, and the net external torque.

6. The method for quantitative analysis of dynamic stability of spinning objects based on center-of-mass eccentricity according to claim 5, characterized in that, The determination of the six-degree-of-freedom dynamic model based on the positional relationship equation, the translational motion equation, and the rotational motion equation includes: The positional relationship equation, the translational motion equation, and the rotational motion equation are spatialized to obtain the six-degree-of-freedom dynamic model.

7. The method for quantitative analysis of dynamic stability of spinning objects based on center-of-mass eccentricity according to claim 1, characterized in that, The test conditions include multiple test sub-conditions, and the acquisition of asymmetric flow field aerodynamic torque data includes: For each of the aforementioned test sub-conditions, the drag coefficient, lateral force coefficient, normal force coefficient, roll moment coefficient, pitch moment coefficient, and yaw moment coefficient obtained under the test sub-condition are acquired. The drag coefficient, the lateral force coefficient, the normal force coefficient, the roll moment coefficient, the pitch moment coefficient, and the yaw moment coefficient are used as the aerodynamic moment data of the asymmetric flow field.

8. The method for quantitative analysis of the dynamic stability of spinning objects based on center-of-mass eccentricity according to claim 1, characterized in that, The process of obtaining the interpolation table for the test conditions based on the asymmetric flow field aerodynamic moment data includes: The asymmetric flow field aerodynamic moment data are organized into the interpolation table according to the mapping relationship between the axial eccentricity, lateral eccentricity, and longitudinal eccentricity and the time series under the test conditions.

9. The method for quantitative analysis of dynamic stability of spinning objects based on center-of-mass eccentricity according to claim 8, characterized in that, The coupled simulation based on the six-degree-of-freedom dynamic model and the interpolation table of the test conditions outputs the state parameters of the spinning aircraft, including: Determine the flight speed, characteristic area, and characteristic length of the spinning object; The actual torque of the spinning object is determined based on the flight speed, the characteristic area, and the characteristic length. Based on the actual torque, the six-degree-of-freedom dynamic model is solved using the fourth-order Runge-Kutta method to obtain the position, velocity, angular velocity, and attitude angle of the spinning object; The position, velocity, angular velocity, and attitude angle of the spinning object are its state parameters.

10. The method for quantitative analysis of the dynamic stability of a spinning object based on centroid eccentricity according to claim 1, characterized in that, The extraction of quantitative indicators based on the state parameters of the spinning object includes: Based on the state parameters of the spinning object, the trajectory index, attitude index, and flow field coupling index of the spinning object are extracted. The trajectory index is used to characterize the maximum deviation of the actual center of mass of the spinning object in the three-axis directions; The attitude parameters are used to characterize the root mean square angular velocity, nutation amplitude, and decay rate of the spinning aircraft. The coupling index is used to characterize the vortex shedding frequency and the Magnus force coefficient.

Images