Three-Dimensional Aerodynamic Force Modeling Method and System for Axisymmetric Missiles Controlled by Decahedral Double Rudder Surfaces

Abstract

The present invention provides a three-dimensional aerodynamic modeling method and system for a decussate dual-rudder-controlled axisymmetric missile. Based on the mathematical principles of trigonometric series expansion and the symmetry of the missile's external shape's aileron, canard, pitch, yaw, and rudder dual-rudder control axes, a three-dimensional aerodynamic mathematical model for the missile is derived. A corresponding wind tunnel test plan is then formulated based on the missile's three-dimensional aerodynamic mathematical model. The wind tunnel test plan is used to obtain input for the missile's three-dimensional aerodynamic mathematical model. The obtained input for the missile's three-dimensional aerodynamic mathematical model is then used to solve various coefficients of the missile's three-dimensional aerodynamic mathematical model, completing the aerodynamic mathematical modeling of the entire missile. The method employed by the present invention solves the aerodynamic modeling problem for a dual-control layout of aileron, canard, pitch, yaw, and rudder controlled by dual-rudder surfaces, achieving a solution for a dual-control layout of aileron, canard, pitch, yaw, and rudder controlled by dual-rudder surfaces, thus achieving a solution for a dual-control layout of aileron, canard, pitch, yaw, and rudder controlled by dual-rudder surfaces, ...

Description

Technical Field

[0001] The present invention relates to the technical field of mathematical modeling, and more specifically, to a method and system for modeling the three-dimensional aerodynamic forces of an axisymmetric missile controlled by a decussate dual-control surface. More particularly, the present invention preferably relates to a method for modeling the three-dimensional aerodynamic forces of a "+×" axisymmetric missile controlled by a double-control surface of ailerons, canards, pitches, yaws, and rudders. Background Art

[0002] For the purpose of evaluating guidance, control, and autopilot characteristics, the most desirable aerodynamic description of the configuration is that in which M, Φ, α Φ , δ P , δ Y and δ R The force and moment C that the missile bears during the entire flight range N , C A , C Z , m X , m Y and m Z is a three-dimensional expression of the above variable function. These data can become part of the full six-degree-of-freedom missile system ballistic simulation. In order to accumulate enough aerodynamic data to provide a three-dimensional representation, a large wind tunnel test plan is required. Generally speaking, experiments are not carried out until the missile shape is basically determined. The representation method should be carefully considered and used to guide the test plan. In order to provide a representation consistent with the test data (especially in the most likely flight range) and to minimize computer storage requirements, it is necessary to conduct a substantial analysis of the data and establish a corresponding format. Among them, C N : normal force coefficient of the whole elastic body; C Z : total side force coefficient; C A : Total axial force coefficient; m X : Rolling moment coefficient of the whole missile; m Y : Yaw moment coefficient of the whole missile; m Z : pitch moment coefficient of the entire missile; X CM : missile mass center, unit m; X R : Torque data m Y 、m Z Reference point, unit: m; M: Mach number; α Φ : resultant angle of attack, unit: °, the angle between the velocity vector and the OX axis; Φ: roll angle, unit: °.

[0003] Chinese invention patent publication CN108120581A discloses a high-speed wind tunnel test apparatus and method for measuring the pitch dynamic derivatives of a rotating missile. The apparatus comprises a high-speed wind tunnel; a support mechanism for supporting the missile within the high-speed wind tunnel and capable of driving the missile to rotate and force pitch vibration; a dynamic derivative balance installed within the missile to measure the missile's torque signal; a displacement element installed on the support mechanism to measure the missile's vibration angular displacement signal; and a processor that calculates the pitch dynamic derivative for each angle of attack in a sequence of angles of attack.

[0004] Regarding the above-mentioned related technologies, the inventors believe that the space for the servo of small-diameter missiles is small, the influence of airwash is strong, and the number of wind tunnel tests is large. Summary of the Invention

[0005] In view of the defects in the prior art, the purpose of the present invention is to provide a three-dimensional aerodynamic modeling method and system for a cross-shaped dual-rudder control axisymmetric missile.

[0006] A three-dimensional aerodynamic modeling method for a cross-shaped dual-rudder control axisymmetric missile provided by the present invention comprises the following steps:

[0007] Model derivation steps: Based on the mathematical principles of trigonometric series expansion and the symmetry of the missile's aileron, canard, pitch, yaw, and rudder dual control axes, a three-dimensional aerodynamic mathematical model of the missile is derived. Based on this three-dimensional aerodynamic mathematical model, a corresponding wind tunnel test plan is formulated.

[0008] Model input acquisition steps: Use the wind tunnel test plan to obtain the input of the missile's three-dimensional aerodynamic mathematical model;

[0009] Modeling completion steps: Use the obtained input of the missile's three-dimensional aerodynamic mathematical model to solve the various coefficients of the missile's three-dimensional aerodynamic mathematical model to complete the aerodynamic mathematical model modeling of the entire missile.

[0010] Preferably, in the modeling completion step, the missile three-dimensional aerodynamic mathematical model includes:

[0011] Define a 60-dimensional column vector x = [x1, x2, ..., x 60 ] T 、A 50-dimensional column vector y=[y1,y2,…y 50 ] T and a 3D column vector z = [z1,z2,z3] T ;

[0012] Among them, x1, x2 until x 60 They are the elements of the 60-dimensional column vector x; y1, y2 until y 50are the elements of the 50-dimensional column vector y; z1, z2 and z3 are the elements of the 3-dimensional column vector z; T represents the transpose of the matrix;

[0013] x1=1, x2=cos4Φ, x3=cos8Φ, x4=δ Y cosΦ+δ P sinΦ, x7=δ Y δ P sin2Φ, x 23 =δ R (δ P cosΦ-δ Y sinΦ), x 52 =cosΦ+sinΦ,x 53 =sin2Φ,x 54 =cos3Φ-sin3Φ,x 55 =cos5Φ+sin5Φ,x 56 =sin6Φ,x 57 =cos7Φ-sin7Φ,x 58 =1,x 59 =cos4Φ,x 60 =cos8Φ;

[0014] Where Φ represents the roll angle; δ Y represents the pitch rudder angle; δ P Indicates the yaw rudder angle; δ R Indicates the aileron rudder deflection angle;

[0015] y1=sin4Φ,y2=δ P cosΦ-δ Y sinΦ, y6=δ R , y7=δ R cos4Φ, y 10 =δ R (δ YcosΦ+δ P sinΦ), y 16 =δ R δ Y δ P sin2Φ, y 42 =sinΦ-cosΦ,y 43 =cos2Φ,y 44 =sin3Φ+cos3Φ,y 45 =sin5Φ-cos5Φ,y 46 =cos6Φ,y 47 =sin7Φ+cos7Φ,y 48 =1,y 49 =cosΦ+sinΦ,y 50 = sin4Φ;

[0016] z1=1, z2=sin2Φ, z3=cos4Φ.

[0017] Preferably, in the modeling completion step, for a certain M, α Φ have

[0018]

[0019]

[0020] Among them, [a ij ] and [e ij ] is the coefficient matrix; x j Represents the elements of the 60-dimensional column vector x, y j Represents the elements of the 50-dimensional column vector y; C N Represents the total elastic normal force coefficient; C Z Indicates the total side force coefficient; C A Indicates the total axial force coefficient; m X Indicates the rolling moment coefficient of the entire projectile; m Y Indicates the yaw moment coefficient of the entire missile; m Z represents the pitching moment coefficient of the entire missile; X CM represents the missile's center of mass; X R Indicates torque data m Y and m Z Reference point; M represents the Mach number; αΦ represents the resultant angle of attack; Lr represents the reference length.

[0021] Preferably, in the modeling completion step,

[0022]

[0023]

[0024]

[0025] Among them, δ1 is the pitch rudder deflection value corresponding to the first rudder surface; δ3 is the pitch rudder deflection value corresponding to the third rudder surface; δ2 is the yaw rudder deflection value corresponding to the second rudder surface; δ4 is the yaw rudder deflection value corresponding to the fourth rudder surface; δ5 is the aileron rudder deflection value corresponding to the fifth rudder surface; δ6 is the aileron rudder deflection value corresponding to the sixth rudder surface; δ7 is the aileron rudder deflection value corresponding to the seventh rudder surface; δ8 is the aileron rudder deflection value corresponding to the eighth rudder surface.

[0026] Preferably, in the modeling completion step, starting from the basic theory of aerodynamics, the Taylor and Fourier multiple mixed series expansion technology is used to derive a three-dimensional aerodynamic interpolation model of an axisymmetric tactical missile with dual control surfaces of ailerons, canards, pitches, yaws and rudders.

[0027] According to the present invention, a three-dimensional aerodynamic modeling system for a symmetrical missile with a cross-shaped dual-rudder control surface is provided, comprising the following modules:

[0028] Model derivation module: Based on the mathematical principles of trigonometric series expansion and the symmetry of the missile's aileron, canard, pitch, yaw, and rudder dual control axes, the missile's three-dimensional aerodynamic mathematical model is derived. Based on this model, a corresponding wind tunnel test plan is formulated.

[0029] Model input acquisition module: uses wind tunnel test plan to obtain the input of missile three-dimensional aerodynamic mathematical model;

[0030] Modeling completion module: Use the obtained input of the missile's three-dimensional aerodynamic mathematical model to solve the various coefficients of the missile's three-dimensional aerodynamic mathematical model and complete the aerodynamic mathematical model modeling of the entire missile.

[0031] Preferably, in the modeling completion module, the missile three-dimensional aerodynamic mathematical model includes:

[0032] Define a 60-dimensional column vector x = [x1, x2, ..., x 60 ] T 、A 50-dimensional column vector y=[y1,y2,…y 50 ] T and a 3D column vector z = [z1,z2,z3] T;

[0033] Among them, x1, x2 until x 60 They are the elements of the 60-dimensional column vector x; y1, y2 until y 50 are the elements of the 50-dimensional column vector y; z1, z2 and z3 are the elements of the 3-dimensional column vector z; T represents the transpose of the matrix;

[0034] x1=1, x2=cos4Φ, x3=cos8Φ, x4=δ Y cosΦ+δ P sinΦ, x7=δ Y δ P sin2Φ, x 23 =δ R (δ P cosΦ-δ Y sinΦ), x 52 =cosΦ+sinΦ,x 53 =sin2Φ,x 54 =cos3Φ-sin3Φ,x 55 =cos5Φ+sin5Φ,x 56 =sin6Φ,x 57 =cos7Φ-sin7Φ,x 58 =1,x 59 =cos4Φ,x 60 =cos8Φ;

[0035] Where Φ represents the roll angle; δ Y represents the pitch rudder angle; δ P Indicates the yaw rudder angle; δ R Indicates the aileron rudder deflection angle;

[0036] y1=sin4Φ,y2=δ P cosΦ-δ Y sinΦ, y6=δ R , y7=δR cos4Φ, y 10 =δ R (δ Y cosΦ+δ P sinΦ), y 42 =sinΦ-cosΦ,y 43 =cos2Φ,y 44 =sin3Φ+cos3Φ,y 45 =sin5Φ-cos5Φ,y 46 =cos6Φ,y 47 =sin7Φ+cos7Φ,y 48 =1,y 49 =cosΦ+sinΦ,y 50 = sin4Φ;

[0037] z1=1, z2=sin2Φ, z3=cos4Φ.

[0038] Preferably, in the modeling completion module, for a certain M, α Φ have

[0039]

[0040]

[0041] Among them, [a ij ] and [e ij ] is the coefficient matrix; x j Represents the elements of the 60-dimensional column vector x, y j Represents the elements of the 50-dimensional column vector y; C N Represents the total elastic normal force coefficient; C Z Indicates the total side force coefficient; C A Indicates the total axial force coefficient; m X Indicates the rolling moment coefficient of the entire projectile; m Y Indicates the yaw moment coefficient of the entire missile; m Z represents the pitching moment coefficient of the entire missile; X CM represents the missile's center of mass; X R Indicates torque data m Y and mZ Reference point; M represents the Mach number; α Φ represents the resultant angle of attack; Lr represents the reference length.

[0042] Preferably, in the modeling completion module,

[0043]

[0044]

[0045]

[0046] Among them, δ1 is the pitch rudder deflection value corresponding to the first rudder surface; δ3 is the pitch rudder deflection value corresponding to the third rudder surface; δ2 is the yaw rudder deflection value corresponding to the second rudder surface; δ4 is the yaw rudder deflection value corresponding to the fourth rudder surface; δ5 is the aileron rudder deflection value corresponding to the fifth rudder surface; δ6 is the aileron rudder deflection value corresponding to the sixth rudder surface; δ7 is the aileron rudder deflection value corresponding to the seventh rudder surface; δ8 is the aileron rudder deflection value corresponding to the eighth rudder surface.

[0047] Preferably, in the modeling completion module, starting from the basic theory of aerodynamics, the Taylor and Fourier multiple mixed series expansion technology is used to derive a three-dimensional aerodynamic interpolation model of a tactical missile with dual control surfaces of aileron, canard, pitch, yaw and rudder to control the axis.

[0048] Compared with the prior art, the present invention has the following beneficial effects:

[0049] 1. The method adopted by the present invention solves the aerodynamic modeling of the dual-control layout of aileron-canard pitch-yaw and rudder-tail dual-control surface control "+×" axisymmetric missiles, so that the dual-control layout scheme of aileron-canard pitch-yaw and rudder-tail dual-control surface control "+×" axisymmetric missiles is solved;

[0050] 2. This invention solves the problem of limited space for servo motors in small-diameter missiles while also reducing the impact of airwash. It significantly improves the accuracy of aerodynamic data interpolation and reduces the number of wind tunnel tests, providing high-precision aerodynamic data required for full-airspace numerical simulations in ballistic and control fields.

[0051] 3. The modeling method for the three-dimensional aerodynamic interpolation model of a "+×" axisymmetric missile controlled by dual aileron, canard, pitch, yaw, and rudder surfaces provided by this invention enables analysis of missile performance across the entire flight range, not just near the trim point. Six-degree-of-freedom trajectory simulation using this mathematical model can be used to calculate missile performance when attacking maneuvering targets, re-set flight trajectories based on missile parameters measured from the launch platform, verify flight performance, and troubleshoot. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Other features, objects and advantages of the present invention will become more apparent upon reading the detailed description of non-limiting embodiments with reference to the following drawings:

[0053] Figure 1 Schematic diagram of the coordinate system and rudder angle definition of the present invention (along the heading). DETAILED DESCRIPTION

[0054] The present invention will be described in detail below with reference to specific embodiments. The following examples will help those skilled in the art to further understand the present invention, but are not intended to limit the present invention in any form. It should be noted that, for those skilled in the art, several changes and improvements can be made without departing from the scope of the present invention. These all fall within the scope of protection of the present invention.

[0055] The embodiment of the present invention discloses a modeling method for a three-dimensional aerodynamic mathematical model of a "+×" axisymmetric missile controlled by dual rudder surfaces of aileron, canard, pitch, yaw, and rudder (+× represents a cross-shaped canard and a fork-shaped rudder), such as Figure 1 As shown, a corresponding wind tunnel test plan was developed for the three-dimensional aerodynamic mathematical model of a "+×" axisymmetric missile controlled by dual ailerons, canards, pitch, yaw, and rudder surfaces. The coefficients of the three-dimensional aerodynamic mathematical model for this missile were solved based on the test results, and a full aerodynamic mathematical model for the missile was established. Based on fundamental aerodynamic theory, Taylor and Fourier multiple mixed series expansion techniques were employed to derive a three-dimensional aerodynamic interpolation model for this type of missile, which meets precise requirements while reducing wind tunnel test costs and time. Taylor is translated into Taylor in Chinese; Fourier is translated into Fourier in Chinese.

[0056] like Figure 1 The figure shows the coordinate system definition and rudder deflection angle definition of the three-dimensional aerodynamic mathematical model of a "+×" axisymmetric missile controlled by two rudder surfaces: aileron, canard, pitch, yaw, and tail rudder. This includes the rotating body axis system OXYZ. Rudder surfaces 1# and 3# are pitch rudders, 2# and 4# are yaw rudders, and 5#, 6#, 7#, and 8# are aileron rudders. P is the pitch rudder deflection, δ Y is the yaw rudder deflection, δ R Aileron rudder deflection.

[0057] Definition of rudder angle: Looking toward the missile along the hinge line, if the rudder rotates counterclockwise, the rudder angle is positive, otherwise it is negative. The pitch rudder angle, yaw rudder angle, and aileron rudder angle are calculated as follows:

[0058] δ Y :Pitch rudder angle (°):

[0059]

[0060] δ P : Yaw rudder deflection angle (°):

[0061]

[0062] δ R :Aileron rudder deflection angle (°):

[0063]

[0064] Symbols and meanings in the formula: Rotating body axis system OXYZ: Origin O: theoretical tip of the head; X-axis positive direction: along the body axis pointing to the incoming flow; Y-axis positive direction: the direction of the incoming flow velocity projected on the cross section of the projectile; Z-axis positive direction: determined according to the right-hand rule; see Appendix Figure 1 . C N : normal force coefficient of the whole elastic body; C Z : total side force coefficient; C A : Total axial force coefficient; m X : Rolling moment coefficient of the whole missile; m Y : Yaw moment coefficient of the whole missile; m Z : pitch moment coefficient of the entire missile; X CM : missile mass center, unit m; X R : Torque data m Y 、m Z Reference point, unit: m; M: Mach number; α Φ : Resultant angle of attack, unit: °(°), the angle between the velocity vector and the OX axis; Φ: Roll angle, unit: °(°), see Appendix Figure 1 . Lr: Reference length, generally the missile length, m.

[0065] The method specifically comprises the following steps:

[0066] Model derivation steps: Based on the mathematical principles of trigonometric series expansion and the symmetry of the missile's aileron, canard, pitch, yaw, and rudder dual control axes, the missile's three-dimensional aerodynamic mathematical model is derived. Based on this model, a corresponding wind tunnel test plan is formulated.

[0067] Based on the mathematical principles of trigonometric series expansion and the "+×" axisymmetric nature of the missile's dual control surfaces (ailerons, canards, pitch, yaw, and rudder) for control, a three-dimensional aerodynamic mathematical model for the missile was derived. A corresponding wind tunnel test plan was developed for this "+×" axisymmetric model of the missile's three-dimensional aerodynamic mathematical model.

[0068] Model input acquisition step: Use the wind tunnel test plan to obtain the input of the missile's three-dimensional aerodynamic mathematical model. That is, use the wind tunnel test to obtain the input of the above aerodynamic mathematical model.

[0069] (1-1) Full-body force test items with suspension and cable cover:

[0070] Table 1 Full-body force test items with suspension and cable cover

[0071]

[0072] Here, α represents the angle of attack, and Ma represents the Mach number, which is the speed divided by the speed of sound.

[0073] (1-2) Axisymmetric full-bullet force measurement test items:

[0074] Table 2 Axisymmetric shape full-bullet force measurement test items Test items

[0075]

[0076] Modeling completion steps: Utilize the acquired inputs from the missile's three-dimensional aerodynamic mathematical model to solve for the various coefficients of the missile's three-dimensional aerodynamic mathematical model, completing the modeling of the entire missile. Specifically, the acquired inputs from the aerodynamic mathematical model are used to solve for the various coefficients of the missile's three-dimensional aerodynamic mathematical model, completing the modeling. Based on the test results, the coefficients of the three-dimensional aerodynamic mathematical model for the "+×" axisymmetric missile with dual control surfaces (aileron, canard, pitch, yaw, and rudder) are solved, completing the modeling.

[0077] The mathematical model of the aerodynamic force of the entire missile is as follows, that is, the three-dimensional aerodynamic mathematical model of the missile includes the following:

[0078] Define a 60-dimensional column vector x = [x1, x2, ..., x 60 ] T 、A 50-dimensional column vector y=[y1,y2,…y 50 ] T and a 3D column vector z = [z1,z2,z3] T .

[0079] Among them, x1, x2 until x 60 They are the elements of the 60-dimensional column vector x; y1, y2 until y 50 are the elements of the 50-dimensional column vector y; z1, z2 and z3 are the elements of the 3-dimensional column vector z; T represents the transpose of the matrix.

[0080] x1=1, x2=cos4Φ, x3=cos8Φ, x4=δ Y cosΦ+δ P sinΦ, x7=δ Y δ P sin2Φ, x 23 =δ R (δ P cosΦ-δ Y sinΦ), x 52 =cosΦ+sinΦ,x 53 =sin2Φ,x 54 =cos3Φ-sin3Φ,x 55 =cos5Φ+sin5Φ,x 56 =sin6Φ,x 57 =cos7Φ-sin7Φ,x 58 =1,x 59 =cos4Φ,x 60 =cos8Φ. Where Φ represents the roll angle; δ Y represents the pitch rudder angle; δ P Indicates the yaw rudder angle; δ R Indicates the aileron deflection angle.

[0081] y1=sin4Φ,y2=δ P cosΦ-δ Y sinΦ, y6=δ R , y7=δ R cos4Φ, y 42 =sinΦ-cosΦ,y 43 =cos2Φ,y 44 =sin3Φ+cos3Φ,y 45 =sin5Φ-cos5Φ,y 46 =cos6Φ,y 47=sin7Φ+cos7Φ,y 48 =1,y 49 =cosΦ+sinΦ,y 50 =sin4Φ.

[0082] z1=1, z2=sin2Φ, z3=cos4Φ.

[0083] For a certain M, α Φ (Indicates the data corresponding to a corresponding Mach number and angle of attack, which are the six data in the formula)

[0084]

[0085]

[0086] Among them, [a ij ] and [e ij ] is the coefficient matrix; x j Represents the elements of the 60-dimensional column vector x, y j represents the elements of the 50-dimensional column vector y. Lr: Reference length, typically the missile length, in meters. cos: cosine; sin: sine; T: transpose of the matrix. Symbols are explained; unless otherwise noted, all expressions are in the axis system of the rotating body.

[0087]

[0088]

[0089]

[0090] Among them, δ1 is the pitch rudder deflection value corresponding to the first rudder surface; δ3 is the pitch rudder deflection value corresponding to the third rudder surface; δ2 is the yaw rudder deflection value corresponding to the second rudder surface; δ4 is the yaw rudder deflection value corresponding to the fourth rudder surface; δ5 is the aileron rudder deflection value corresponding to the fifth rudder surface; δ6 is the aileron rudder deflection value corresponding to the sixth rudder surface; δ7 is the aileron rudder deflection value corresponding to the seventh rudder surface; δ8 is the aileron rudder deflection value corresponding to the eighth rudder surface.

[0091] Based on the basic theory of aerodynamics, a three-dimensional aerodynamic interpolation model of an axisymmetric tactical missile with dual control surfaces of aileron, canard, pitch, yaw and rudder is derived by adopting Taylor and Fourier multiple mixed series expansion techniques.

[0092] The present invention relates to a three-dimensional aerodynamic mathematical model for a "+×" axisymmetric missile controlled by dual control surfaces of ailerons, canards, pitches, yaws, and rudders. Specifically, it addresses the issue of limited space for servo gear in small-diameter missiles. This "Modeling Method for a Three-Dimensional Aerodynamic Mathematical Model for a "+×" Axisymmetric Missile Controlled by Dual Control Surfaces of Ailerons, Canards, Pitches, Yaws, and rudders" addresses the issue of limited space for servo gear in small-diameter missiles while simultaneously mitigating the effects of airwash. This significantly improves the interpolation accuracy of aerodynamic data and reduces the number of wind tunnel tests, providing the high-precision aerodynamic data required for full-airspace numerical simulations in ballistic and control fields.

[0093] The present invention provides a modeling method for a three-dimensional aerodynamic interpolation model of a "+×" axisymmetric missile controlled by dual control surfaces: ailerons, canards, pitch, yaw, and rudders. This model can analyze missile performance throughout its entire flight range, not just near the trim point. Six-degree-of-freedom trajectory simulation using this mathematical model can be used to calculate missile performance when attacking maneuvering targets, re-determine flight trajectories based on missile parameters measured from the launch platform, verify flight performance, and troubleshoot.

[0094] Wind tunnel testing according to the embodiments of the present invention can yield coefficients for the missile's three-dimensional aerodynamic mathematical model. The method of the present invention addresses the control problem of a dual-control layout for an axisymmetric missile controlled by two control surfaces: ailerons, canards, pitch, yaw, and rudder. Necessary wind tunnel testing is conducted based on the model's characteristics, and a dynamic library of three-dimensional aerodynamic interpolation for axisymmetric missiles is compiled based on the test data for use by relevant professionals. Some items can be discarded to construct new aerodynamic models to meet the needs of different design stages. The present invention is applicable to axisymmetric missiles controlled by two control surfaces: ailerons, canards, pitch, yaw, and rudder.

[0095] The embodiment of the present invention also discloses a three-dimensional aerodynamic modeling system for a symmetrical missile with a cross-shaped dual-rudder control axis. Figure 1 As shown, it includes the following modules:

[0096] Model derivation module: Based on the mathematical principles of trigonometric series expansion and the symmetry of the missile's aileron, canard, pitch, yaw, and rudder dual control axes, the missile's three-dimensional aerodynamic mathematical model is derived. Based on this model, a corresponding wind tunnel test plan is formulated.

[0097] Model input acquisition module: Use wind tunnel test plan to obtain the input of missile three-dimensional aerodynamic mathematical model.

[0098] Modeling completion module: Use the obtained input of the missile's three-dimensional aerodynamic mathematical model to solve the various coefficients of the missile's three-dimensional aerodynamic mathematical model and complete the aerodynamic mathematical model modeling of the entire missile.

[0099] The missile three-dimensional aerodynamic mathematical model includes:

[0100] Define a 60-dimensional column vector x = [x1, x2, ..., x60 ] T 、A 50-dimensional column vector y=[y1,y2,…y 50 ] T and a 3D column vector z = [z1,z2,z3] T .

[0101] Among them, x1, x2 until x 60 They are the elements of the 60-dimensional column vector x; y1, y2 until y 50 are the elements of the 50-dimensional column vector y; z1, z2 and z3 are the elements of the 3-dimensional column vector z; T represents the transpose of the matrix.

[0102] x1=1, x2=cos4Φ, x3=cos8Φ, x4=δ Y cosΦ+δ P sinΦ, x7=δ Y δ P sin2Φ, x 23 =δ R (δ P cosΦ-δ Y sinΦ), x 52 =cosΦ+sinΦ,x 53 =sin2Φ,x 54 =cos3Φ-sin3Φ,x 55 =cos5Φ+sin5Φ,x 56 =sin6Φ,x 57 =cos7Φ-sin7Φ,x 58 =1,x 59 =cos4Φ,x 60 =cos8Φ.

[0103] Where Φ represents the roll angle; δ Y represents the pitch rudder angle; δ P Indicates the yaw rudder angle; δ R Indicates the aileron deflection angle.

[0104] y1=sin4Φ,y2=δ P cosΦ-δ Y sinΦ, y6=δ R , y7=δ R cos4Φ, y 42 =sinΦ-cosΦ,y 43 =cos2Φ,y 44 =sin3Φ+cos3Φ,y 45 =sin5Φ-cos5Φ,y 46 =cos6Φ,y 47 =sin7Φ+cos7Φ,y 48 =1,y 49 =cosΦ+sinΦ,y 50 =sin4Φ.

[0105] z1=1, z2=sin2Φ, z3=cos4Φ.

[0106] For a certain M, α Φ have

[0107]

[0108]

[0109] Among them, [a ij ] and [e ij ] is the coefficient matrix; x j Represents the elements of the 60-dimensional column vector x, y j Represents the elements of the 50-dimensional column vector y; C N Represents the total elastic normal force coefficient; C Z Indicates the total side force coefficient; C A Indicates the total axial force coefficient; m X Indicates the rolling moment coefficient of the entire projectile; m Y Indicates the yaw moment coefficient of the entire missile; m Z represents the pitching moment coefficient of the entire missile; X CM represents the missile's center of mass; X R Indicates torque data m Y and mZ Reference point; M represents the Mach number; α Φ represents the resultant angle of attack; Lr represents the reference length.

[0110]

[0111]

[0112]

[0113] Among them, δ1 is the pitch rudder deflection value corresponding to the first rudder surface; δ3 is the pitch rudder deflection value corresponding to the third rudder surface; δ2 is the yaw rudder deflection value corresponding to the second rudder surface; δ4 is the yaw rudder deflection value corresponding to the fourth rudder surface; δ5 is the aileron rudder deflection value corresponding to the fifth rudder surface; δ6 is the aileron rudder deflection value corresponding to the sixth rudder surface; δ7 is the aileron rudder deflection value corresponding to the seventh rudder surface; δ8 is the aileron rudder deflection value corresponding to the eighth rudder surface.

[0114] Based on the basic theory of aerodynamics, a three-dimensional aerodynamic interpolation model of an axisymmetric tactical missile with dual control surfaces of aileron, canard, pitch, yaw and rudder is derived by adopting Taylor and Fourier multiple mixed series expansion techniques.

[0115] Those skilled in the art will appreciate that, in addition to implementing the system and its various devices, modules, and units provided by the present invention in purely computer-readable program code, it is entirely possible to implement the same functions of the system and its various devices, modules, and units provided by the present invention in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers by logically programming the method steps. Therefore, the system and its various devices, modules, and units provided by the present invention can be considered a hardware component, and the devices, modules, and units included therein for implementing various functions can also be considered as structures within the hardware component; the devices, modules, and units for implementing various functions can also be considered as both software modules implementing the method and structures within the hardware component.

[0116] The above describes specific embodiments of the present invention. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art may make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. The embodiments of this application and the features in the embodiments may be combined with each other in any manner unless there is a conflict.

Claims

1. A three-dimensional aerodynamic modeling method for a symmetrical missile with a cross-shaped dual-rudder control axis, characterized in that: The steps include: Model derivation steps: Based on the mathematical principles of trigonometric series expansion and the symmetry of the missile's aileron, canard, pitch, yaw, and rudder dual control axes, a three-dimensional aerodynamic mathematical model of the missile is derived. Based on this three-dimensional aerodynamic mathematical model, a corresponding wind tunnel test plan is formulated. Model input acquisition steps: Use the wind tunnel test plan to obtain the input of the missile's three-dimensional aerodynamic mathematical model; Modeling completion steps: using the obtained input of the missile's three-dimensional aerodynamic mathematical model to solve the various coefficients of the missile's three-dimensional aerodynamic mathematical model, and completing the aerodynamic mathematical model modeling of the entire missile; In the modeling completion step, for a certain M, α Φ have Among them, [a ij ] and [e ij ] is the coefficient matrix; x j Represents the elements of the 60-dimensional column vector x, y j Represents the elements of the 50-dimensional column vector y; C N Represents the total elastic normal force coefficient; C Z Indicates the total side force coefficient; C A Indicates the total axial force coefficient; m X Indicates the rolling moment coefficient of the entire projectile; m Y Indicates the yaw moment coefficient of the entire missile; m Z represents the pitching moment coefficient of the entire missile; X CM represents the missile's center of mass; X R Indicates torque data m Y and m Z Reference point; M represents the Mach number; α Φ represents the resultant angle of attack; Lr represents the reference length.

2. The three-dimensional aerodynamic modeling method of a cross-shaped dual-control surface controlled axisymmetric missile according to claim 1 is characterized in that: In the modeling completion step, the missile three-dimensional aerodynamic mathematical model includes: Define a 60-dimensional column vector x = [x1, x2, ..., x 60 ] T 、A 50-dimensional column vector y=[y1,y2,…y 50 ] T and a 3D column vector z = [z1,z2,z3] T ; Among them, x1, x2 until x 60 They are the elements of the 60-dimensional column vector x; y1, y2 until y 50 are the elements of the 50-dimensional column vector y; z1, z2 and z3 are the elements of the 3-dimensional column vector z; T represents the transpose of the matrix; x1=1,x2=cos4Φ,x3=cos8Φ,x4=d Y cosΦ+δ P sinΦ, x7=d Y d P sin2Φ, x 23 =d R (d P cosΦ-δ Y sinΦ), x 52 =cosΦ+sinΦ,x 53 =sin2Φ,x 54 =cos3Φ-sin3Φ,x 55 =cos5Φ+sin5Φ,x 56 =sin6Φ,x 57 =cos7Φ-sin7Φ,x 58 =1,x 59 =cos4Φ,x 60 =cos8Φ; Where Φ represents the roll angle; δ Y represents the pitch rudder angle; δ P Indicates the yaw rudder angle; δ R Indicates the aileron rudder deflection angle; y1=sin4Φ,y2=δ P cosΦ-δ Y sinΦ, y6=δ R ,y7=δ R cos4Φ, y 10 =d R (d Y cosΦ+δ P sinΦ), y 16 =d R d Y d P sin2Φ, y 42 =sinΦ-cosΦ,y 43 =cos2Φ,y 44 =sin3Φ+cos3Φ,y 45 =sin5Φ-cos5Φ,y 46 =cos6Φ,y 47 =sin7Φ+cos7Φ,y 48 =1,y 49 =cosΦ+sinΦ,y 50 =sin4Φ; z1=1, z2=sin2Φ, z3=cos4Φ.

3. The three-dimensional aerodynamic modeling method of a cross-shaped dual-rudder control axisymmetric missile according to claim 2 is characterized in that: In the modeling completion step, Among them, δ1 is the pitch rudder deflection value corresponding to the first rudder surface; δ3 is the pitch rudder deflection value corresponding to the third rudder surface; δ2 is the yaw rudder deflection value corresponding to the second rudder surface; δ4 is the yaw rudder deflection value corresponding to the fourth rudder surface; δ5 is the aileron rudder deflection value corresponding to the fifth rudder surface; δ6 is the aileron rudder deflection value corresponding to the sixth rudder surface; δ7 is the aileron rudder deflection value corresponding to the seventh rudder surface; δ8 is the aileron rudder deflection value corresponding to the eighth rudder surface.

4. The three-dimensional aerodynamic modeling method of a cross-shaped dual-control surface controlled axisymmetric missile according to claim 1 is characterized in that: In the modeling completion step, starting from the basic theory of aerodynamics, the Taylor and Fourier multiple mixed series expansion technology is used to derive a three-dimensional aerodynamic interpolation model of an axisymmetric tactical missile with dual control surfaces of ailerons, canards, pitches, yaws and rudders.

5. A three-dimensional aerodynamic modeling system for a symmetrical missile with a cross-shaped dual-rudder control axis, characterized in that: Includes the following modules: Model derivation module: Based on the mathematical principles of trigonometric series expansion and the symmetry of the missile's aileron, canard, pitch, yaw, and rudder dual control axes, the missile's three-dimensional aerodynamic mathematical model is derived. Based on this model, a corresponding wind tunnel test plan is formulated. Model input acquisition module: uses wind tunnel test plan to obtain the input of missile three-dimensional aerodynamic mathematical model; Modeling completion module: uses the obtained input of the missile's three-dimensional aerodynamic mathematical model to solve the various coefficients of the missile's three-dimensional aerodynamic mathematical model and complete the aerodynamic mathematical model modeling of the entire missile; In the modeling completion module, for a certain M, α Φ have Among them, [a ij ] and [e ij ] is the coefficient matrix; x j Represents the elements of the 60-dimensional column vector x, y j Represents the elements of the 50-dimensional column vector y; C N Represents the total elastic normal force coefficient; C Z Indicates the total side force coefficient; C A Indicates the total axial force coefficient; m X Indicates the rolling moment coefficient of the entire projectile; m Y Indicates the yaw moment coefficient of the entire missile; m Z represents the pitching moment coefficient of the entire missile; X CM represents the missile's center of mass; X R Indicates torque data m Y and m Z Reference point; M represents the Mach number; α Φ represents the resultant angle of attack; Lr represents the reference length.

6. The three-dimensional aerodynamic modeling system for a symmetrical missile with a cross-shaped dual-rudder control axis according to claim 5 is characterized in that: In the modeling completion module, the missile three-dimensional aerodynamic mathematical model includes: Define a 60-dimensional column vector x = [x1, x2, ..., x 60 ] T 、A 50-dimensional column vector y=[y1,y2,…y 50 ] T and a 3D column vector z = [z1,z2,z3] T ; Among them, x1, x2 until x 60 They are the elements of the 60-dimensional column vector x; y1, y2 until y 50 are the elements of the 50-dimensional column vector y; z1, z2 and z3 are the elements of the 3-dimensional column vector z; T represents the transpose of the matrix; x1=1,x2=cos4Φ,x3=cos8Φ,x4=d Y cosΦ+δ P sinΦ, x7=d Y d P sin2Φ, x 23 =d R (d P cosΦ-δ Y sinΦ), x 52 =cosΦ+sinΦ,x 53 =sin2Φ,x 54 =cos3Φ-sin3Φ,x 55 =cos5Φ+sin5Φ,x 56 =sin6Φ,x 57 =cos7Φ-sin7Φ,x 58 =1, x 59 =cos4Φ,x 60 =cos8Φ; Where Φ represents the roll angle; δ Y represents the pitch rudder angle; δ P Indicates the yaw rudder angle; δ R Indicates the aileron rudder deflection angle; y1=sin4Φ,y2=δ P cosΦ-δ Y sinΦ, y6=δ R ,y7=δ R cos4Φ, y 10 =d R (d Y cosΦ+δ P sinΦ), y 16 =d R d Y d P sin2Φ, y 42 =sinΦ-cosΦ,y 43 =cos2Φ,y 44 =sin3Φ+cos3Φ,y 45 =sin5Φ-cos5Φ,y 46 =cos6Φ,y 47 =sin7Φ+cos7Φ,y 48 =1,y 49 =cosΦ+sinΦ,y 50 =sin4Φ; z1=1, z2=sin2Φ, z3=cos4Φ.

7. The three-dimensional aerodynamic modeling system for a symmetrical missile with a cross-shaped dual-control surface control axis according to claim 6 is characterized in that: In the modeling completion module, Among them, δ1 is the pitch rudder deflection value corresponding to the first rudder surface; δ3 is the pitch rudder deflection value corresponding to the third rudder surface; δ2 is the yaw rudder deflection value corresponding to the second rudder surface; δ4 is the yaw rudder deflection value corresponding to the fourth rudder surface; δ5 is the aileron rudder deflection value corresponding to the fifth rudder surface; δ6 is the aileron rudder deflection value corresponding to the sixth rudder surface; δ7 is the aileron rudder deflection value corresponding to the seventh rudder surface; δ8 is the aileron rudder deflection value corresponding to the eighth rudder surface.

8. The three-dimensional aerodynamic modeling system for a symmetrical missile with a cross-shaped dual-rudder control axis according to claim 5 is characterized in that: In the modeling completion module, starting from the basic theory of aerodynamics, the Taylor and Fourier multiple mixed series expansion technology is used to derive a three-dimensional aerodynamic interpolation model of an axisymmetric tactical missile with dual control surfaces of ailerons, canards, pitches, yaws and rudders.

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