A method of dynamic modeling for flight motion simulation of a variable geometry aircraft with any number of rotating components

Abstract

This invention relates to the field of multibody system dynamics, specifically a dynamic modeling method for simulating the flight motion of a morphing aircraft with an arbitrary number of rotating components. The method first abstracts the morphing aircraft as a tree-like multibody system containing virtual rigid bodies and virtual hinges. Rigid bodies and hinges are uniformly numbered using a depth-first traversal search, with the relative rotation angles between rigid bodies used as generalized coordinates. Then, a path matrix is ​​used to describe the system topology, and the center-of-mass velocity, center-of-mass acceleration, angular velocity, and angular acceleration of each rigid body are derived using the generalized coordinates. Next, based on the above kinematic parameters, the deflection velocity, deflection angular velocity, generalized active force, and generalized inertial force are calculated and substituted into the Kane equations to establish the multibody system dynamic equations. Finally, the dynamic equations are solved, and the motion state is updated according to a set time step, repeating the process until the simulation of the set duration is completed. This invention has strong versatility and good scalability, and is applicable to the flight motion simulation of morphing aircraft with an arbitrary number of rotating components.

Description

Technical Field

[0001] This invention relates to the field of multibody system dynamics, specifically to a dynamic modeling method for simulating the flight motion of a variant aircraft with an arbitrary number of rotating components. Background Technology

[0002] Traditional high aspect ratio fixed-wing aircraft require good airport support conditions for takeoff and landing, and also have relatively strict requirements for weather conditions, which affects the application effect of the aircraft. In order to improve the rapid deployment capability of fixed-wing aircraft and expand their application scenarios, folding variant drones have emerged.

[0003] The moving parts of foldable variant drones are typically connected by rotary hinges. A foldable variant aircraft designed by the China Academy of Aerospace Aerodynamics has up to 13 moving parts, each connected by a rotary hinge; a double-folding tube-launched drone designed by Northwestern Polytechnical University has up to 7 moving parts, each connected by a rotary hinge.

[0004] Foldable variant UAVs have significant configuration variations due to different mission requirements, but existing dynamic modeling methods for variant UAVs are often specific to certain configurations and have poor scalability. For example, in Chinese patent application CN117852322A, entitled "A Dynamic Modeling Method and Device for Variant Aircraft Based on the Principle of Virtual Power", the dynamic modeling of a given variant aircraft is based on the virtual power method. The generalized coordinates defined are only for specific configurations and motion conditions. If the number or relative position of rotating parts changes, all dynamic equations need to be re-derived, resulting in poor scalability and versatility. Summary of the Invention

[0005] To address the aforementioned issues, this invention proposes a dynamic modeling method for simulating the flight motion of a variator aircraft with an arbitrary number of rotating components. By introducing virtual rigid bodies and virtual hinges, the multi-rigid-body system is abstracted into a tree system. A depth-first traversal search is used to uniformly number the rigid bodies and hinges, and the system topology is described based on a path matrix. A general dynamic model is established by combining the Kane equations, thereby solving the problem that existing variator aircraft dynamic modeling methods are only applicable to specific configurations and require re-deriving all dynamic equations when the number or relative position of rotating components changes.

[0006] The technical solution of the present invention specifically includes the following steps:

[0007] Step 1: Abstract the variator aircraft with an arbitrary number of rotating parts into a form composed of... A rotating hinge and A multi-rigid-body system consisting of several rigid bodies is defined with the origin of the ground inertial coordinate system as a virtual rigid body, designated as rigid body 0. One rigid body is randomly selected from the system as rigid body 1. The virtual hinge between rigid bodies 0 and 1 is defined as hinge 1, and its position is set at the centroid of rigid body 1. Starting from rigid body 1, a depth-first search is used to sequentially number the real rigid bodies and real hinges in the system, resulting in the final numbering of the real rigid bodies in the multi-rigid-body system. The actual hinge number is ;

[0008] The relative rotation angles of rigid body 1 with respect to rigid body 0, the relative rotation angles of rigid body 2 with respect to rigid body 1, and so on, are deduced. The rigid body is relative to The relative rotation angle of the rigid body is used as the generalized coordinate of the system;

[0009] Step 2: Use the generalized coordinates defined in Step 1 to represent the center-of-mass velocity, center-of-mass acceleration, angular velocity, and angular acceleration of each rigid body in the system;

[0010] Step 3: Based on the obtained center-of-mass velocity, center-of-mass acceleration, angular velocity and angular acceleration of each rigid body, calculate the deflection velocity, deflection angular velocity, generalized active force and generalized inertial force of each rigid body, substitute them into the Kane equation, and obtain the dynamic equation of the multibody system.

[0011] Step 4: Solve the dynamic equations of the multibody system obtained in Step 3, obtain the generalized rate derivative, update the generalized rate according to the set time step, and update the position and attitude of the center of mass of each rigid body according to the expressions of the center of mass velocity and angular velocity of each rigid body obtained in Step 2 according to the set time step.

[0012] Step 5: Repeat steps 2 to 4 at set time intervals; accumulate the current simulation time after each execution of steps 2 to 4; stop the loop and end the simulation when the accumulated simulation time reaches the set total simulation time.

[0013] Furthermore, in step 1, the rule for using depth-first traversal search to sequentially number the real rigid bodies and real hinges in the system is as follows:

[0014] Starting with rigid body 1, find all its circumscribed rigid bodies, and randomly select one of them as rigid body 2. Then, number the hinge between rigid body 1 and rigid body 2 as hinge 2. Next, find all the circumscribed rigid bodies of rigid body 2, and randomly select one of them as rigid body 3. Then, number the hinge between rigid body 2 and rigid body 3 as hinge 3.

[0015] Until a certain numbered rigid body, let's assume it is... Rigid body number 1, rigid body and The hinge between the rigid bodies is numbered as follows: Hinge number 1; assuming The rigid body has no external rigid bodies and returns to... The inner rigid body of the rigid body, i.e. Rigid body number 6, found Let the next external rigid body be numbered as . Rigid body number 1, rigid body and The hinge between the rigid bodies is numbered as follows: No. 1 hinge;

[0016] And so on until all A rigid body and Each hinge is numbered.

[0017] Furthermore, the inner rigid body and the outer rigid body are specifically defined as: [the rigid body is defined using...] This indicates that the hinge will be used It means that if exist arrive On the way, it is called for The inner rigid body, denoted as ,if exist arrive On the way, it is called for The outer rigid body, denoted as ;and Directly connected inner rigid bodies are called The inner rigid body, and The directly connected outer rigid body is called The external rigid body.

[0018] Furthermore, step 2 includes the following sub-steps:

[0019] Step 21: Consider virtual rigid bodies and virtual hinges, and treat the multi-rigid-body system as being composed of... rigid body and A rotating hinge The tree system consists of a path matrix. The structure of a multi-rigid-body system is described; let the row number of the matrix be the hinge index, the column number be the rigid body index, and the element in the j-th row and i-th column of the path matrix be... Defined as:

[0020]

[0021] Step 22: Use the generalized coordinates defined in Step 1 to represent the angular velocity and angular acceleration of each rigid body in the system;

[0022] In a group of n+1 rigid bodies and n rotational hinges In the tree system, let The internal and external rigid bodies of the hinge connection are and , will with The unit vector parallel to the axis of rotation of the hinge is defined as... Hinge pivot base vector For a system containing n rotational hinges The tree system yields an n-order pivot-based vector array.

[0023]

[0024] Relative to its inner rigid body relative angular velocity It can be represented as:

[0025]

[0026] In the formula, the superscript T indicates the transpose operation. The derivative of the generalized coordinates in step 1;

[0027] Relative to its inner rigid body Relative angular acceleration It can be represented as:

[0028]

[0029] In the formula, the superscript T indicates the transpose operation. The second derivative of the generalized coordinates in step 1;

[0030] In a tree system, any rigid body Absolute angular velocity in an inertial frame equal angular velocity of a rigid body And from arrive The relative angular velocities of all adjacent rigid bodies along the path are expressed as follows using the path matrix T:

[0031]

[0032]

[0033] In the formula, for The matrix arranged (where for (inscribed rigid body); This is the path matrix, where the superscript T indicates the transpose operation;

[0034] Substituting the expressions for relative angular velocity and relative angular acceleration into the above equation, we get:

[0035]

[0036]

[0037] definition ,definition Furthermore, the angular velocities and angular accelerations of each rigid body are obtained as follows:

[0038]

[0039]

[0040] Step 23: Use the generalized coordinates defined in Step 1 to represent the center-of-mass velocity and acceleration of each rigid body in the system;

[0041] To describe the position of the center of mass of each rigid body in the system and the relative position of the hinges within the rigid body system, body hinge vectors and path vectors are introduced. Let the rigid body... It is a rigid body The inner rigid body, in the rigid body It has an internal hinge. and external hinge ; Defined by rigid bodies Center of mass Pointer to Associated arbitrary external hinge vector The body hinge vector is defined by the rigid body. Internal hinge , pointing towards the outer rigid body The vector of the external hinge is called the path vector. The path vector and the body hinge vector satisfy the following relationship: For pass Pointing to any rigid body Their path vectors are all ,Right now:

[0042]

[0043] for In special circumstances, only The hinge is on the path, and has:

[0044]

[0045] Only when The time path vector is meaningful for hour, ;

[0046] Let the center of mass of rigid body 0 be... That is, the origin of the inertial coordinate system, let it be... Pointing to hinge #1 (i.e., the center of mass of rigid body No. 1) The vector of ) is Then the center of mass of any rigid body in the system Compared to position vector Represented as The sum of the path vectors on the path:

[0047]

[0048] in, It is any rigid body on the path To rigid body The path vector, due to It describes a rigid body The relative positions of the two hinges are such that the derivative is determined only by... angular velocity Therefore, for Differentiation yields:

[0049]

[0050] In the formula, The derivative of the path vector. The rigid body obtained in step 22 The angular velocity; and then the velocity of the center of mass of each rigid body. and rigid body center of mass acceleration The expression:

[0051]

[0052]

[0053] In the formula, and Hinge No. 1 Relative to the origin of the inertial coordinate system The vector derivative and second derivative of , if rigid body 1 is stationary relative to the inertial frame, then and Zero;

[0054] Substituting the expressions for the angular velocity and angular acceleration of each rigid body obtained in step 22 into the above equation, we obtain the expressions for the center-of-mass velocity and center-of-mass acceleration of each rigid body in terms of generalized rate:

[0055]

[0056]

[0057] In the formula, Represents the identity matrix. It is an n-order block vector array. It is an n-order vector array. This is to represent the acceleration term generated by the inner rigid body entrainment.

[0058] Furthermore, step 3 includes the following sub-steps:

[0059] Step 31: Calculate the r-th deflection velocity and r-th deflection angular velocity of the multi-rigid-body system using the following formula:

[0060]

[0061]

[0062] In the formula, This represents the r-th partial velocity of the i-th rigid body. This represents the r-th deflection angular velocity of the i-th rigid body. Representation matrix The element in row i and column r, Representation matrix The element in row i and column r;

[0063] Step 32: Calculate the r-th generalized active force and the r-th generalized inertial force of the multi-rigid-body system using the following formula:

[0064]

[0065]

[0066] In the formula, Let r represent the r-th generalized active force of the i-th rigid body. This represents the r-th partial generalized inertial force of the i-th rigid body. and This represents the principal vector of the principal force acting on the i-th rigid body and the principal moment of the active force about the center of mass. and Let represent the principal vector of the inertial force acting on the i-th rigid body and the principal moment of the inertial force about the center of mass; where, Including aerodynamic forces and gravity, This includes aerodynamic torque; aerodynamic forces and aerodynamic torques are obtained by unsteady solutions using CFD methods.

[0067] The principal forces acting on each rigid body and the principal moments about the center of mass Inertial force principal vector and the principal moments about the center of mass The arranged matrices are denoted as follows: , , , This will further integrate the r-th generalized active force of the entire system. and generalized inertial force Represented as:

[0068]

[0069]

[0070] The principal vector of inertial force and principal moments about the center of mass We can express this using the formulas for the acceleration of the center of mass and the angular acceleration of a rigid body:

[0071]

[0072]

[0073] In the formula, A matrix representing the mass composition of rigid bodies at each level. This represents a matrix consisting of the moments of inertia of rigid bodies of various orders about their centers of mass. Defined as: The above-mentioned principal inertial force vector and principal moments about the center of mass Substituting the expression into the generalized inertial force In the expression, we get

[0074]

[0075]

[0076] Step 33: Generalized active force and generalized inertial force Substituting the expression into the Kane equation:

[0077]

[0078] Rearranging these equations into a system of linear equations, we obtain the dynamic equations of the multibody system as follows:

[0079]

[0080] In the formula, the coefficient matrix Defined as: ,vector Defined as: , Defined as: .

[0081] Furthermore, step 4 includes the following sub-steps:

[0082] Step 41: Solve the dynamic equations of the multibody system obtained in Step 3 to obtain the generalized rate derivative:

[0083]

[0084] Step 42: At the current time step Within this range, the generalized rate derivative is integrated to obtain the updated generalized rate of the system, denoted by the superscript "". "Indicates the updated result:

[0085]

[0086] In the formula, The generalized rate represents the rate at the start of the current time step. This is the starting time of the current time step. This is the current time step;

[0087] Step 43: Substitute the updated generalized velocity of the system obtained in Step 42 into the angular velocity expression of each rigid body obtained in Step 22 and the centroid velocity expression of each rigid body obtained in Step 23 to obtain the updated angular velocity and centroid velocity of each rigid body.

[0088] Step 44: Within the current time step ∆t, integrate the updated velocity and angular velocity of each rigid body to obtain the updated position. and posture :

[0089]

[0090] .

[0091] Beneficial effects:

[0092] This invention proposes a dynamic modeling method for simulating the flight motion of a variator aircraft with an arbitrary number of rotating components. By introducing virtual rigid bodies and virtual hinges, the multi-rigid-body system is abstracted into a tree system. A depth-first search is used to uniformly number the rigid bodies and hinges, and the system topology is described based on a path matrix. A general dynamic model is established using Kane's equations, thus solving the problem that existing variator aircraft dynamic modeling methods are only applicable to specific configurations and require re-deriving all dynamic equations when the number or relative positions of rotating components change. Compared to existing technologies, this invention has the following advantages:

[0093] 1. High versatility: The dynamic model established by this invention is applicable to variant aircraft with any number of rotating parts. Regardless of how many rigid bodies and rotational hinges the system contains, a unified modeling framework can be used for processing, without the need to derive dynamic equations separately for each configuration.

[0094] 2. Good scalability: When the configuration of the aircraft changes, such as adding or removing rotating parts or changing the connection method of parts, only the path matrix and related geometric parameters need to be updated. The overall form of the dynamic equations remains unchanged, and there is no need to rebuild the equation system, which can greatly reduce the modeling workload.

[0095] Furthermore, by introducing depth-first traversal search and path matrix, this invention expresses the complex kinematic and dynamic relationships of multi-rigid-body systems in a unified matrix form, which facilitates programmed implementation and numerical solution, thereby improving simulation efficiency. Attached Figure Description

[0096] Figure 1 This is a flowchart illustrating the implementation of an embodiment of the present invention;

[0097] Figure 2 This is a schematic diagram of the deployment process of the rotating variant UAV in an embodiment of the present invention;

[0098] Figure 3 This is a schematic diagram showing the numbering of the rigid body and hinges of the rotating variant UAV in an embodiment of the present invention;

[0099] Figure 4 This is a schematic diagram of the tree structure of a multi-rigid-body system in an embodiment of the present invention;

[0100] Figure 5 This is a schematic diagram illustrating the relationship between the body hinge vector and the path vector in an embodiment of the present invention;

[0101] Figure 6 This is a graph showing the change of wing deployment angle over time in an embodiment of the present invention;

[0102] Figure 7 This is a graph showing the change of normal force of each component over time during the unfolding process in an embodiment of the present invention. Detailed Implementation

[0103] To make the technical problems solved, the technical solutions, and the beneficial effects of this invention clearer and to enable those skilled in the art to better understand the invention, the invention will be further described in detail and in full below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the invention.

[0104] This embodiment uses Figure 2 Taking the rotating variant UAV as an example, the dynamic modeling method for flight motion simulation of a variant aircraft with an arbitrary number of rotating parts proposed in this invention is used to perform dynamic modeling of its flight motion simulation.

[0105] like Figure 1 As shown in this embodiment, a dynamic modeling method for simulating the flight motion of a variant aircraft with an arbitrary number of rotating components includes the following steps:

[0106] Step 1: Abstract the variator aircraft with an arbitrary number of rotating parts into a form composed of... A rotating hinge and A multi-rigid-body system consisting of several rigid bodies is defined with the origin of the ground inertial coordinate system as a virtual rigid body, designated as rigid body 0. One rigid body is randomly selected from the system as rigid body 1. The virtual hinge between rigid bodies 0 and 1 is defined as hinge 1, and its position is set at the centroid of rigid body 1. Starting from rigid body 1, a depth-first search is used to sequentially number the real rigid bodies and real hinges in the system, resulting in the final numbering of the real rigid bodies in the multi-rigid-body system. The actual hinge number is ;

[0107] The relative rotation angles of rigid body 1 with respect to rigid body 0, the relative rotation angles of rigid body 2 with respect to rigid body 1, and so on, are deduced. The rigid body is relative to The relative rotation angle of the rigid body is used as the generalized coordinate of the system;

[0108] In this embodiment, the rule for using depth-first search to sequentially number the real rigid bodies and real hinges in the system is as follows:

[0109] Starting with rigid body 1, find all its circumscribed rigid bodies, and randomly select one of them as rigid body 2. Then, number the hinge between rigid body 1 and rigid body 2 as hinge 2. Next, find all the circumscribed rigid bodies of rigid body 2, and randomly select one of them as rigid body 3. Then, number the hinge between rigid body 2 and rigid body 3 as hinge 3.

[0110] Until a certain numbered rigid body, let's assume it is... Rigid body number 1, rigid body and The hinge between the rigid bodies is numbered as follows: Hinge number 1; assuming The rigid body has no external rigid bodies and returns to... The inner rigid body of the rigid body, i.e. Rigid body number 6, found Let the next external rigid body be numbered as . Rigid body number 1, rigid body and The hinge between the rigid bodies is numbered as follows: No. 1 hinge;

[0111] And so on until all A rigid body and Each hinge is numbered.

[0112] The inner rigid body and the outer rigid body are specifically defined as: [The rigid body is defined using...] This indicates that the hinge will be used It means that if exist arrive On the way, it is called for The inner rigid body, denoted as ,if exist arrive On the way, it is called for The outer rigid body, denoted as ;and Directly connected inner rigid bodies are called The inner rigid body, and The directly connected outer rigid body is called The external rigid body.

[0113] In this embodiment, as Figure 3 As shown, the rotating variant UAV consists of two real rigid bodies: the fuselage and the rotatable wing, and a real hinge between them. Virtual rigid body 0 is located at the origin of the inertial coordinate system. After a depth-first search, the fuselage is designated as rigid body 1, and the wing as rigid body 2. Virtual hinge 1 connects rigid body 0 to the fuselage, and hinge 2 connects the fuselage to the wing. The relative rotation angle of rigid body 1 (the fuselage) relative to virtual rigid body 0 is... The relative rotation angle of rigid body wing No. 2 relative to rigid body fuselage No. 1 As the generalized coordinates of the system:

[0114]

[0115] Step 2: Represent the center-of-mass velocity, center-of-mass acceleration, angular velocity, and angular acceleration of each rigid body in the system using the generalized coordinates defined in Step 1; specifically including the following sub-steps:

[0116] Step 21: Consider virtual rigid bodies and virtual hinges, and treat the multi-rigid-body system as being composed of... rigid body and A rotating hinge The tree system consists of a path matrix. The structure of a multi-rigid-body system is described; let the row number of the matrix be the hinge index, the column number be the rigid body index, and the element in the j-th row and i-th column of the path matrix be... Defined as:

[0117]

[0118] In this embodiment, the multi-rigid-body system is considered as a tree system consisting of 3 rigid bodies and 2 rotational hinges, with a system path matrix. as follows:

[0119] ;

[0120] Step 22: Use the generalized coordinates defined in Step 1 to represent the angular velocity and angular acceleration of each rigid body in the system;

[0121] In a group of n+1 rigid bodies and n rotational hinges In a tree system, such as Figure 4 As shown, let The internal and external rigid bodies of the hinge connection are and , will with The unit vector parallel to the axis of rotation of the hinge is defined as... Hinge pivot base vector For a system containing n rotational hinges The tree system yields an n-order pivot-based vector array.

[0122]

[0123] Relative to its inner rigid body relative angular velocity It can be represented as:

[0124]

[0125] In the formula, the superscript T indicates the transpose operation. The derivative of the generalized coordinates in step 1;

[0126] Relative to its inner rigid body Relative angular acceleration It can be represented as:

[0127]

[0128] In the formula, the superscript T indicates the transpose operation. The second derivative of the generalized coordinates in step 1;

[0129] In a tree system, any rigid body Absolute angular velocity in an inertial frame equal angular velocity of a rigid body And from arrive The relative angular velocities of all adjacent rigid bodies along the path are expressed as follows using the path matrix T:

[0130]

[0131]

[0132] In the formula, for The matrix arranged (where for (inscribed rigid body); This is the path matrix, where the superscript T indicates the transpose operation;

[0133] Substituting the expressions for relative angular velocity and relative angular acceleration into the above equation, we get:

[0134]

[0135]

[0136] definition ,definition Furthermore, the angular velocities and angular accelerations of each rigid body are obtained as follows:

[0137]

[0138] ;

[0139] In this embodiment, for a tree system comprising 3 rigid bodies and 2 rotational hinges, the second-order pivot-based vector array is obtained as follows:

[0140]

[0141] exist At that time, the initial rotation axis basis vector is:

[0142]

[0143]

[0144] The final angular velocities and angular accelerations of each rigid body in the tree system are:

[0145]

[0146]

[0147] in , Substituting the pivot basis vector and the path matrix, we get:

[0148]

[0149] ;

[0150] Step 23: Use the generalized coordinates defined in Step 1 to represent the center-of-mass velocity and acceleration of each rigid body in the system;

[0151] To describe the position of the center of mass of each rigid body in the system and the relative positions of the hinges within the rigid body system, body hinge vectors and path vectors are introduced, such as... Figure 5 As shown, assume a rigid body It is a rigid body The inner rigid body, in the rigid body It has an internal hinge. and external hinge ; Defined by rigid bodies Center of mass Pointer to Associated arbitrary external hinge vector The body hinge vector is defined by the rigid body. Internal hinge , pointing towards the outer rigid body The vector of the external hinge is called the path vector. The relationship between the path vector and the body hinge vector is as follows:

[0152]

[0153] This formula explains that, for pass Pointing to any rigid body Its path vectors are ;for In special circumstances, only The hinge is on the path, therefore:

[0154]

[0155] By definition, only when The time path vector is meaningful for hour, ;

[0156] Let the center of mass of rigid body 0 be... That is, the origin of the inertial coordinate system, let it be... Pointing to hinge #1 (i.e., the center of mass of rigid body No. 1) The vector of ) is Then the center of mass of any rigid body in the system Compared to position vector Represented as The sum of the path vectors on the path:

[0157]

[0158] in, It is any rigid body on the path To rigid body The path vector, due to It describes a rigid body The relative positions of the two hinges are such that the derivative is determined only by... angular velocity Therefore, for Differentiation yields:

[0159]

[0160] In the formula, The derivative of the path vector. The rigid body obtained in step 22 The angular velocity; and then the velocity of the center of mass of each rigid body. and rigid body center of mass acceleration The expression:

[0161]

[0162]

[0163] In the formula, and Hinge No. 1 Relative to the origin of the inertial coordinate system The vector derivative and second derivative of , if rigid body 1 is stationary relative to the inertial frame, then and Zero;

[0164] Substituting the expressions for the angular velocity and angular acceleration of each rigid body obtained in step 22 into the above equation, we obtain the expressions for the center-of-mass velocity and center-of-mass acceleration of each rigid body in terms of generalized rate:

[0165]

[0166]

[0167] In the formula, Represents the identity matrix. It is an n-order block vector array. It is an n-order vector array. This is to represent the acceleration term generated by the inner rigid body entrainment.

[0168] In this embodiment, the path vector describes the relative positional relationship between the hinges of the system. for:

[0169]

[0170] Expressions for the velocity and acceleration of the center of mass of each rigid body, expressed in terms of generalized rate:

[0171]

[0172]

[0173] in, , , Substituting the results from the above, we get:

[0174]

[0175] .

[0176] Step 3: Based on the obtained center-of-mass velocity, center-of-mass acceleration, angular velocity, and angular acceleration of each rigid body, calculate the deflection velocity, deflection angular velocity, generalized active force, and generalized inertial force of each rigid body. Substitute these values ​​into the Kane equations to obtain the dynamic equations of the multibody system. This includes the following sub-steps:

[0177] Step 31: Calculate the r-th deflection velocity and r-th deflection angular velocity of the multi-rigid-body system using the following formula:

[0178]

[0179]

[0180] In the formula, This represents the r-th partial velocity of the i-th rigid body. This represents the r-th deflection angular velocity of the i-th rigid body. Representation matrix The element in row i and column r, Representation matrix The element in row i and column r;

[0181] Step 32: Calculate the r-th generalized active force and the r-th generalized inertial force of the multi-rigid-body system using the following formula:

[0182]

[0183]

[0184] In the formula, Let r represent the r-th generalized active force of the i-th rigid body. This represents the r-th partial generalized inertial force of the i-th rigid body. and This represents the principal vector of the principal force acting on the i-th rigid body and the principal moment of the active force about the center of mass. and Represents the principal vector of the inertial force acting on the i-th rigid body and the principal moment of the inertial force about the center of mass;

[0185] The principal forces acting on each rigid body and the principal moments about the center of mass Inertial force principal vector and the principal moments about the center of mass The matrices arranged are denoted as follows: , , , This will further integrate the r-th generalized active force of the entire system. and generalized inertial force Represented as:

[0186]

[0187]

[0188] The principal vector of inertial force and principal moments about the center of mass We can express this using the formulas for the acceleration of the center of mass and the angular acceleration of a rigid body:

[0189]

[0190]

[0191] In the formula, A matrix representing the mass composition of rigid bodies at each level. This represents a matrix consisting of the moments of inertia of rigid bodies of various orders about their centers of mass. Defined as: The above-mentioned principal inertial force vector and principal moments about the center of mass Substituting the expression into the generalized inertial force In the expression, we get

[0192]

[0193] ;

[0194] In this embodiment, the generalized active force of the system is:

[0195]

[0196] In the formula, The primary driving force of the system, including aerodynamic forces. and gravity , , which is the principal moment of the main force acting on the system about the center of mass, including the aerodynamic moment; the aerodynamic force and aerodynamic moment are obtained by unsteady solution using the CFD method.

[0197] In this embodiment, the generalized inertial force of the system is:

[0198]

[0199] The details are as follows:

[0200]

[0201] In the formula, the mass and moment of inertia properties of each component of the system are as follows:

[0202]

[0203]

[0204]

[0205]

[0206] Step 33: Generalized active force and generalized inertial force Substituting the expression into the Kane equation:

[0207]

[0208] Rearranging these equations into a system of linear equations, we obtain the dynamic equations of the multibody system as follows:

[0209]

[0210] In the formula, the coefficient matrix Defined as: ,vector Defined as: , Defined as: .

[0211] Step 4: Solve the dynamic equations of the multibody system obtained in Step 3 to obtain the generalized rate derivatives. Update the generalized rates according to the set time steps. Based on the expressions for the center-of-mass velocities and angular velocities of each rigid body obtained in Step 2, update the position and attitude of the center-of-mass of each rigid body according to the set time steps. This includes the following sub-steps:

[0212] Step 41: Solve the dynamic equations of the multibody system obtained in Step 3 to obtain the generalized rate derivative:

[0213]

[0214] Step 42: At the current time step Within this range, the generalized rate derivative is integrated to obtain the updated generalized rate of the system, denoted by the superscript "". "Indicates the updated result:

[0215]

[0216] In the formula, The generalized rate represents the rate at the start of the current time step. This is the starting time of the current time step. This is the current time step; in this embodiment, it is set as follows: ;

[0217] Step 43: Substitute the updated generalized velocity of the system obtained in Step 42 into the angular velocity expression of each rigid body obtained in Step 22 and the centroid velocity expression of each rigid body obtained in Step 23 to obtain the updated angular velocity and centroid velocity of each rigid body.

[0218] Step 44: Within the current time step ∆t, integrate the updated velocity and angular velocity of each rigid body to obtain the updated position. and posture :

[0219]

[0220]

[0221] Step 5: with Steps 2 to 4 are executed cyclically at intervals; the current simulation time is accumulated after each execution of steps 2 to 4; when the accumulated simulation time reaches the set total simulation time, the loop stops and the simulation ends. In this embodiment, the total simulation time is set to 1.5s.

[0222] The results of kinematic simulation of the rotating variant unmanned vehicle using the method of this invention are as follows: Figure 6 , Figure 7 As shown.

[0223] Depend on Figure 6 As can be seen, during the wing deployment process obtained using the method of this invention, the final deployment angle of the left wing reaches 90°, and the final deployment angle of the right wing reaches 64°, with the deployment process lasting approximately 1.2 seconds. In the 0.2-0.6 second stage, the wing deployment speed is relatively slow, and the change in deployment angle is gradual; in the 0.6-1.4 second stage, the deployment speed significantly accelerates, and the left and right wings exhibit asymmetrical deployment characteristics. Simulation results show that the method of this invention can accurately capture the kinematic characteristics of a multi-rotating component system.

[0224] Within a simulation duration of 1.5 seconds, the simulation results using the method of this invention converged and stabilized, the wing deployment angle changed smoothly, the normal force changed continuously, and there were no numerical oscillations or divergences, verifying the numerical stability of the dynamic modeling method based on the Kane equation of this invention.

[0225] Depend on Figure 7 It can be seen that the normal forces acting on each component during deployment exhibit complex coupled variation characteristics. The peak normal force on the fuselage, left wing, and right wing is approximately 750 N, and the lowest value is approximately -1500 N. During the 0.2 s to 0.8 s phase, the normal forces on all three components are positive and show similar trends; during the 0.8 s to 1.2 s phase, the normal forces rapidly decrease to negative values, with the left wing reaching its lowest value before the right wing; after 1.2 s, the normal forces gradually recover. This result indicates that the method of this invention can effectively capture the dynamic coupling characteristics of multi-rigid-body systems.

[0226] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.

Claims

1. A dynamic modeling method for simulating the flight motion of a variant aircraft with an arbitrary number of rotating components, characterized in that: Includes the following steps: Step 1: Abstract the variator aircraft with an arbitrary number of rotating parts into a form composed of... A rotating hinge and A multi-rigid-body system consisting of several rigid bodies is defined with the origin of the ground inertial coordinate system as a virtual rigid body, designated as rigid body 0. One rigid body is randomly selected from the system as rigid body 1. The virtual hinge between rigid bodies 0 and 1 is defined as hinge 1, and its position is set at the centroid of rigid body 1. Starting from rigid body 1, a depth-first search is used to sequentially number the real rigid bodies and real hinges in the system, resulting in the final numbering of the real rigid bodies in the multi-rigid-body system. The actual hinge number is ; The relative rotation angles of rigid body 1 with respect to rigid body 0, the relative rotation angles of rigid body 2 with respect to rigid body 1, and so on, are deduced. The rigid body is relative to The relative rotation angle of the rigid body is used as the generalized coordinate of the system; Step 2: Use the generalized coordinates defined in Step 1 to represent the center-of-mass velocity, center-of-mass acceleration, angular velocity, and angular acceleration of each rigid body in the system; Step 3: Based on the obtained center-of-mass velocity, center-of-mass acceleration, angular velocity and angular acceleration of each rigid body, calculate the deflection velocity, deflection angular velocity, generalized active force and generalized inertial force of each rigid body, substitute them into the Kane equation, and obtain the dynamic equation of the multibody system. Step 4: Solve the dynamic equations of the multibody system obtained in Step 3, obtain the generalized rate derivative, update the generalized rate according to the set time step, and update the position and attitude of the center of mass of each rigid body according to the expressions of the center of mass velocity and angular velocity of each rigid body obtained in Step 2 according to the set time step. Step 5: Repeat steps 2 to 4 at set time intervals; accumulate the current simulation time after each execution of steps 2 to 4; stop the loop and end the simulation when the accumulated simulation time reaches the set total simulation time.

2. The dynamic modeling method for simulating the flight motion of a variant aircraft with an arbitrary number of rotating components according to claim 1, characterized in that: Step 1 employs a depth-first search, and the specific rules for numbering the real rigid bodies and real hinges in the system are as follows: Starting with rigid body 1, find all its circumscribed rigid bodies, and randomly select one of them as rigid body 2. Then, number the hinge between rigid body 1 and rigid body 2 as hinge 2. Next, find all the circumscribed rigid bodies of rigid body 2, and randomly select one of them as rigid body 3. Then, number the hinge between rigid body 2 and rigid body 3 as hinge 3. Until a certain numbered rigid body, let's assume it is... Rigid body number 1, rigid body and The hinge between the rigid bodies is numbered as follows: Hinge number 1; assuming The rigid body has no external rigid bodies and returns to... The inner rigid body of the rigid body, i.e. Rigid body number 6, found Let the next external rigid body be numbered as . Rigid body number 1, rigid body and The hinge between the rigid bodies is numbered as follows: No. 1 hinge; And so on until all A rigid body and Each hinge is numbered.

3. The dynamic modeling method for simulating the flight motion of a variant aircraft with an arbitrary number of rotating components according to claim 2, characterized in that: The inner rigid body and the outer rigid body are specifically defined as: [The rigid body is defined using...] This indicates that the hinge will be used It means that if exist arrive On the way, it is called for The inner rigid body, denoted as ,if exist arrive On the way, it is called for The outer rigid body, denoted as ;and Directly connected inner rigid bodies are called The inner rigid body, and The directly connected outer rigid body is called The external rigid body.

4. The dynamic modeling method for simulating the flight motion of a variant aircraft with an arbitrary number of rotating components according to claim 1, characterized in that: Step 2 includes the following sub-steps: Step 21: Consider virtual rigid bodies and virtual hinges, and treat the multi-rigid-body system as being composed of... rigid body and A rotating hinge The tree system consists of a path matrix. The structure of a multi-rigid-body system is described; let the row number of the matrix be the hinge index, the column number be the rigid body index, and the element in the j-th row and i-th column of the path matrix be... Defined as: Step 22: Use the generalized coordinates defined in Step 1 to represent the angular velocity and angular acceleration of each rigid body in the system; In a group of n+1 rigid bodies and n rotational hinges In the tree system, let The internal and external rigid bodies of the hinge connection are and , will with The unit vector parallel to the axis of rotation of the hinge is defined as... Hinge pivot base vector For a system containing n rotational hinges The tree system yields an n-order pivot-based vector array. Relative to its inner rigid body relative angular velocity It can be represented as: In the formula, the superscript T indicates the transpose operation. The derivative of the generalized coordinates in step 1; Relative to its inner rigid body Relative angular acceleration It can be represented as: In the formula, the superscript T indicates the transpose operation. The second derivative of the generalized coordinates in step 1; In a tree system, any rigid body Absolute angular velocity in an inertial frame equal angular velocity of a rigid body And from arrive The relative angular velocities of all adjacent rigid bodies along the path are expressed as follows using the path matrix T: In the formula, for The matrix arranged (where for (inscribed rigid body); This is the path matrix, where the superscript T indicates the transpose operation; Substituting the expressions for relative angular velocity and relative angular acceleration into the above equation, we get: definition ,definition Furthermore, the angular velocities and angular accelerations of each rigid body are obtained as follows: Step 23: Use the generalized coordinates defined in Step 1 to represent the center-of-mass velocity and acceleration of each rigid body in the system; To describe the position of the center of mass of each rigid body in the system and the relative position of the hinges within the rigid body system, body hinge vectors and path vectors are introduced. Let the rigid body... It is a rigid body The inner rigid body, in the rigid body It has an internal hinge. and external hinge ; Defined by rigid bodies Center of mass Pointer to Associated arbitrary external hinge vector The body hinge vector is defined by the rigid body. Internal hinge , pointing towards the outer rigid body The vector of the external hinge is called the path vector. The path vector and the body hinge vector satisfy the following relationship: For pass Pointing to any rigid body Their path vectors are all ,Right now: for In special circumstances, only The hinge is on the path, and has: Only when The time path vector is meaningful for hour, ; Let the center of mass of rigid body 0 be... That is, the origin of the inertial coordinate system, let it be... Pointing to hinge #1 (i.e., the center of mass of rigid body No. 1) The vector of ) is Then the center of mass of any rigid body in the system Compared to position vector Represented as The sum of the path vectors on the path: in, It is any rigid body on the path To rigid body The path vector, due to It describes a rigid body The relative positions of the two hinges are such that the derivative is determined only by... angular velocity Therefore, for Differentiation yields: In the formula, The derivative of the path vector. The rigid body obtained in step 22 The angular velocity; and then the velocity of the center of mass of each rigid body. and rigid body center of mass acceleration The expression: In the formula, and Hinge No. 1 Relative to the origin of the inertial coordinate system The vector derivative and second derivative of , if rigid body 1 is stationary relative to the inertial frame, then and Zero; Substituting the expressions for the angular velocity and angular acceleration of each rigid body obtained in step 22 into the above equation, we obtain the expressions for the center-of-mass velocity and center-of-mass acceleration of each rigid body in terms of generalized rate: In the formula, Represents the identity matrix. It is an n-order block vector array. It is an n-order vector array. This is to represent the acceleration term generated by the inner rigid body entrainment.

5. The dynamic modeling method for simulating the flight motion of a variant aircraft with an arbitrary number of rotating components according to claim 1, characterized in that: Step 3 includes the following sub-steps: Step 31: Calculate the r-th deflection velocity and r-th deflection angular velocity of the multi-rigid-body system using the following formula: In the formula, This represents the r-th partial velocity of the i-th rigid body. This represents the r-th deflection angular velocity of the i-th rigid body. Representation matrix The element in row i and column r, Representation matrix The element in row i and column r; Step 32: Calculate the r-th generalized active force and the r-th generalized inertial force of the multi-rigid-body system using the following formula: In the formula, Let r represent the r-th generalized active force of the i-th rigid body. This represents the r-th partial generalized inertial force of the i-th rigid body. and This represents the principal vector of the principal force acting on the i-th rigid body and the principal moment of the active force about the center of mass. and Let represent the principal vector of the inertial force acting on the i-th rigid body and the principal moment of the inertial force about the center of mass; where, Including aerodynamic forces and gravity, This includes aerodynamic torque; aerodynamic forces and aerodynamic torques are obtained by unsteady solutions using CFD methods. The principal forces acting on each rigid body and the principal moments about the center of mass Inertial force principal vector and the principal moments about the center of mass The arranged matrices are denoted as follows: , , , This will further integrate the r-th generalized active force of the entire system. and generalized inertial force Represented as: The principal vector of inertial force and principal moments about the center of mass We can express this using the formulas for the acceleration of the center of mass and the angular acceleration of a rigid body: In the formula, A matrix representing the mass composition of rigid bodies at each level. This represents a matrix consisting of the moments of inertia of rigid bodies of various orders about their centers of mass. Defined as: The above-mentioned principal inertial force vector and principal moments about the center of mass Substituting the expression into the generalized inertial force In the expression, we get Step 33: Generalized active force and generalized inertial force Substituting the expression into the Kane equation: Rearranging these equations into a system of linear equations, we obtain the dynamic equations of the multibody system as follows: In the formula, the coefficient matrix Defined as: ,vector Defined as: , Defined as: .

6. The dynamic modeling method for simulating the flight motion of a variant aircraft with an arbitrary number of rotating components according to claim 1, characterized in that: Step 4 includes the following sub-steps: Step 41: Solve the dynamic equations of the multibody system obtained in Step 3 to obtain the generalized rate derivative: Step 42: At the current time step Within this range, the generalized rate derivative is integrated to obtain the updated generalized rate of the system, denoted by the superscript "". "Indicates the updated result: In the formula, The generalized rate represents the rate at the start of the current time step. This is the starting time of the current time step. This is the current time step; Step 43: Substitute the updated generalized velocity of the system obtained in Step 42 into the angular velocity expression of each rigid body obtained in Step 22 and the centroid velocity expression of each rigid body obtained in Step 23 to obtain the updated angular velocity and centroid velocity of each rigid body. Step 44: Within the current time step ∆t, integrate the updated velocity and angular velocity of each rigid body to obtain the updated position. and posture : 。

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