Mathematical modeling method of axle thrust tilting aircraft

Abstract

The invention relates to a mathematical modeling method of an axle thrust tilting aircraft, belongs to the technical field of aircrafts, and aims to solve the problem that the mathematical modeling of the axle thrust tilting aircraft is lack of an effective and convenient method at present, and a relatively complete model can be established under the condition that computing resources are not increased too much. During modeling, block processing is carried out, the shaft thrust tilting aircraft is divided into four parts in the rotor wing direction, the wing direction, the vertical wing direction and the horizontal wing direction, an aerodynamic model is established for each part, and a dynamic model considering the wing direction, the vertical wing direction and the horizontal wing direction is established by adopting a lift line theory. For the nacelle inclination process, changes of the gravity center and the rotational inertia are considered. Compared with a traditional method, the method has the advantages that modeling of nacelle inclination is reasonably simplified, meanwhile, the force and torque forming principle and control plane analysis are added, the accuracy and rationality of the established model can be verified, and therefore a theoretical basis is provided for follow-up controller setting.

Description

Technical Field

[0001] The present invention belongs to the technical field of aircraft, and relates to a mathematical modeling method for an axial thrust tilt-rotor aircraft. Background Art

[0002] The axial thrust tilt-rotor aircraft is an important derivative type of short takeoff and vertical landing (STOVL) aircraft. As a hybrid aircraft, it combines the advantages of a rotorcraft and a fixed-wing aircraft. This type of aircraft can not only hover and take off and land vertically like a rotorcraft, but also fly forward at high speed like a fixed-wing aircraft. Each wingtip of the axial thrust tilt-rotor aircraft is equipped with a nacelle that can tilt. The nacelle can tilt within the range of 0 to 90 degrees, enabling the aircraft to flexibly switch between the rotorcraft mode, the transition mode, and the fixed-wing mode, thus having a wider flight envelope. This design brings great development potential, but also comes with multiple technical challenges.

[0003] For example, the problem of air flow disturbance between the rotor and the wing; during the transition phase, the aerodynamic parameters of the aircraft will change drastically; in addition, problems such as the aerodynamic coupling between multiple redundant control surfaces, different flight channels, and poor aerodynamic stability during high-speed flight also need to be solved. Due to the complexity of the dynamic characteristics of the axial thrust tilt-rotor aircraft, establishing a complete mathematical model is crucial for the design of the flight control system, and this is also a major difficulty in the design process. Therefore, mathematical modeling has become one of the key technical issues for axial thrust tilt-rotor aircraft.

[0004] In terms of technical background, block modeling is a technology that decomposes a complex system or a large-scale engineering problem into several smaller and relatively independent parts (referred to as "blocks" or "subsystems") for modeling and simulation. It is an effective strategy, especially when facing large-scale systems with high computational complexity, which can improve computational efficiency, maintainability, and the reusability of modules. Summary of the Invention

[0005] The purpose of the present invention is to propose a mathematical modeling method for an axial thrust tilt-rotor aircraft in view of the deficiencies of the prior art.

[0006] The purpose of the present invention is achieved through the following technical solutions: A mathematical modeling method for an axial thrust tilt-rotor aircraft, characterized in that the method includes the following steps:

[0007] Step 1: Model the changes in the center of gravity and moment of inertia during the nacelle tilting process;

[0008] Step 2: Establish an aerodynamic model of the rotor for the shaft-push tilt-rotor aircraft; the shaft-push tilt-rotor aircraft consists of two rotors tilted in opposite directions. Integrate the aerodynamic force of the blade element in the flapping plane and the moment along the propeller, take the average value of the position angle, and then multiply by the number of blades to obtain the force and moment generated by the rotor, and convert them into the force and moment in the fuselage axis system;

[0009] Step 3: Establish an aerodynamic model of the wing for the shaft-push tilt-rotor aircraft; the wing includes a slipstream area affected by the rotor wake and a free-stream area not affected by the rotor disturbance. The two parts are modeled as follows:

[0010] Calculate the force and moment in the aircraft fuselage axis system based on the position parameters of the slipstream area, and calculate the position of the aerodynamic center of the wing when the nacelle is tilted;

[0011] The free-stream area is divided into an area that is always a free-stream area and an area that changes from the slipstream area to the free-stream area due to the tilt of the nacelle; calculate the air velocity, dynamic pressure at the aerodynamic center, angle of attack of the free-stream area, and lift of the two parts of the area respectively, and then calculate the drag and moment of the free-stream area;

[0012] Step 4: Establish an aerodynamic model of the vertical tail for the shaft-push tilt-rotor aircraft; calculate the air velocity at the aerodynamic center of the vertical tail, and then calculate the dynamic pressure angle of attack and the sideslip angle of the fuselage; according to the air velocity at the aerodynamic center of the vertical tail, calculate the aerodynamic force of the vertical fin in the wind axis system, and then convert it to the aerodynamic force and moment in the body axis system;

[0013] Step 5: Establish an aerodynamic model of the horizontal tail for the shaft-push tilt-rotor aircraft; calculate the aerodynamic force of the horizontal tail and the elevator according to the treatment method of fixed-wing aircraft. The air flow at the pressure center of the horizontal tail is the sum of the body linear velocity and angular velocity; based on the air velocity, dynamic pressure, angle of attack, and sideslip angle of the fuselage located at the pressure center of the horizontal tail, calculate the lift and drag of the horizontal tail in the wind axis system, and convert the force and moment in the wind axis system into the force and moment in the body axis system.

[0014] Furthermore, the change of the center of gravity position with the nacelle tilt angle is expressed by the following formula:

[0015]

[0016] where, Δx and Δz are the changes of the center of gravity when the nacelle is tilted. R H is the height of the rotor relative to the wing, m NAC is the mass of the nacelle system, and m is the total weight of the fuselage;

[0017] The moment of inertia I changes with the nacelle tilt angle β M and its formula is:

[0018] I = I0 - KIβM

[0019] Among them, I0 is the moment of inertia of any axis in the rotor mode; KI is the coefficient of the corresponding moment of inertia.

[0020] Furthermore, calculate the velocity at the center of the rotor hub in the aircraft body axis system, as well as the tangential velocity and vertical velocity of the rotor profile. According to the blade element theory, calculate the lift and drag of the blade element, and convert them into component forces in the flapping wing plane. The projection of the blade element aerodynamics on the rotor structure axis system constitutes the unit force and moment of the rotor; Integrate the blade element aerodynamic force and the moment along the propeller, take the average value of the position angle, and then multiply by the number of blades to obtain the force and moment generated by the rotor.

[0021] Furthermore, the area of the slipstream region is estimated by the following formula:

[0022]

[0023] where S wss represents the estimated area of the slipstream region, is the maximum area of the slipstream region, and μ max is the advance ratio when the wing of the helicopter is not affected by the rotor wake in the helicopter mode;

[0024] In the rotor mode, the position of the left-wing aerodynamic center relative to the aircraft body center of gravity is P wsl0 = [x wsl y wsl z wsl T . When the nacelle is tilted, the position of the aerodynamic center of the wing is:

[0025]

[0026] where δx and δz are the changes in the center of gravity when the nacelle is tilted, and x wsl0 , y wsl0 , z wsl0 is the position of the left-wing aerodynamic center relative to the aircraft body center of gravity before the nacelle is tilted.

[0027] Furthermore, the force and moment in the aircraft body axis system are:

[0028]

[0029] where F xws1 , F ywsl , F zwsl are the force components in the aircraft body axis system, and M xwsl , M ywsl , M zwsl are the moment components in the aircraft body axis system, and α wsl ​The angle of attack for the left-wing slipstream region, D wsl represents the drag of the slipstream region, L wsl represents the lift of the slipstream region.

[0030] Furthermore, the aerodynamics of the free-stream region of the airframe axis system are:

[0031]

[0032] where F xwfl , F ywfl , F zwfl respectively represent the dynamic components of the free-stream region along the x-axis, y-axis, and z-axis; D wfl represents the drag of the free-stream region, L wfl represents the lift of the free-stream region; α wfl is the angle of attack of the left-wing free stream;

[0033] The moment of the free-stream region of the airframe axis system is:

[0034]

[0035] where M xwfl , M ywfl , M zwfl respectively represent the moment components of the free-stream region along the x-axis, y-axis, and z-axis; x wfl , y wfl , z wfl represent the position parameters of the free-stream region; M wfl represents the moment of the free-stream region.

[0036] Furthermore, the aerodynamic force of the vertical fin in the wind axis system is:

[0037]

[0038] D VT = q VT A VT C D,VT

[0039] where A VT is the stress area at the aerodynamic center of the vertical tail, C L,VT is the lift coefficient at the aerodynamic center of the vertical tail, δ is the control amount, α0 is the initial angle of attack, C l,V is the lift coefficient in the vertical direction, δ rud is the rudder control amount, C D,VT is the drag coefficient at the aerodynamic center of the vertical tail.

[0040] Furthermore, the forces and moments of the horizontal tail in the body axis system are:

[0041]

[0042] Among them, F HT is the force in the body axis system, and M HT is the moment in the body axis system.

[0043] Advantages of the present invention: When modeling the present invention, block processing is carried out. The shaft-push tilt-rotor aircraft is divided into four parts: the rotor, the wing, the vertical wing, and the horizontal wing direction. An aerodynamic model is established for each part, and the lift-line theory is adopted to establish a dynamic model considering the wing, the vertical wing, and the horizontal wing. For the nacelle tilt process, the changes in the center of gravity and moment of inertia are considered. Compared with the traditional method, this method reasonably simplifies the modeling of the nacelle tilt, and at the same time adds the analysis of the force and moment formation principle and the control plane, which can verify the accuracy and rationality of the established model, thus providing a theoretical basis for the subsequent tuning of the controller. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] The drawings are used to provide further explanation of the present invention and constitute a part of the specification. They are used together with the embodiments of the present invention to explain the present invention and do not constitute a limitation to the present invention.

[0045] Figure 1 It is a schematic diagram of the overall structure of the shaft-push tilt-rotor aircraft of the present invention.

[0046] Figure 2 It is a schematic diagram of the framework of the non-linear model of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0047] The present invention will be further described below with reference to the drawings.

[0048] As Figure 1 shown, the shaft-push tilt-rotor aircraft in the embodiment of the present invention includes a fuselage 1, on which a wing system, a tiltable propulsion device, and an axial propulsion device are installed. The wing system includes a main wing 2 and a tail wing. A flap 4 is installed inside the main wing, and an aileron 3 is installed outside the main wing. The main wing can rotate around the vertical axis of the aircraft, and can realize rapid wing folding, which is convenient for storing and transporting goods. The H-shaped tail wing of the aircraft is located at the tail of the fuselage and is composed of a horizontal tail wing and a vertical tail wing. The horizontal tail wing includes a horizontal stabilizer 8 and an elevator 9. The elevator is connected to the horizontal stabilizer 8, and the elevator 9 can rotate around the axis of the horizontal stabilizer 8. The vertical tail wing includes a vertical stabilizer 10 and a rudder 11. The rudder 11 can rotate around the vertical stabilizer 10; the elevator and rudder of the aircraft are rotationally connected to the fuselage, and a servo installed at the tail of the low-wing fuselage is used as an actuator to deflect at a certain angle. The elevator provides longitudinal stability for the aircraft, and the rudder provides yaw stability for the aircraft.

[0049] A modeling method for an axial thrust tilt-rotor aircraft provided by the present invention. The present invention uses Simulink to model the mathematical model of the aircraft, and at the same time, it can access the PX4 module for hardware-in-the-loop simulation, modify the code of PX4, experiment with different control schemes, and verify in Simulink after compilation. The official of PX4 provides a large number of instruction documents, which is convenient for further development. Therefore, the present invention can effectively support the design and verification of the control scheme of such axial thrust tilt-rotor unmanned aircraft and the development of low-level flight control algorithms for modifying the Pixhawk flight controller of the PX4 open-source autopilot. The specific method includes the following steps:

[0050] Step 1: Model the changes in the center of gravity and moment of inertia during the nacelle tilting process. When the nacelle tilts, the center of gravity of the axial thrust tilt-rotor aircraft changes in its longitudinal plane, which also causes changes in the moment of inertia. The center of gravity position and moment of inertia are functions of the nacelle angle. When the nacelle tilting angle β M = 0, the center of gravity position is the initial position. The change in the center of gravity position with the nacelle tilting angle is expressed by the following formula:

[0051]

[0052]

[0053] where, Δx, Δz are the changes in the center of gravity when the nacelle tilts. R H is the height of the rotor relative to the wing, m NAC is the mass of the nacelle system, and m is the total weight of the fuselage.

[0054] The moment of inertia I changes with the nacelle tilting angle β M and its formula is:

[0055] I = I0 - KIβ M

[0056] where, I0 is the moment of inertia of any axis in the rotor mode. KI is the coefficient of the corresponding moment of inertia.

[0057] Step 2: Establish the aerodynamic model of the rotor. Compared with the autogyro, due to the aerodynamic interference between the rotor and the wing, the mathematical model of the axial thrust tilt-rotor aircraft is much more complex. The downwash of the rotor converges at the wing and spreads along the wing to the fuselage, forming the "fountain flow effect", thereby increasing the induced velocity of the rotor. On the other hand, the blocking effect from the wing to the rotor is similar to the ground effect and reduces the induced velocity. When the axial thrust tilt-rotor aircraft flies at low speed, the fountain flow effect and the blocking effect produce an equivalent induced velocity, which means that the aerodynamic interference of the wing on the rotor can be ignored. Therefore, the axial thrust tilt-rotor aircraft can be considered equal to the aerodynamic model of an isolated rotor.

[0058] The shaft-push tilt-rotor aircraft consists of two rotors on the left and right. They tilt in opposite directions. One on the right tilts counterclockwise and one on the left tilts clockwise. Since the same modeling method is used for the two rotors, only some symbols are different. Here, the right rotor is taken as an example to establish its aerodynamic model. According to the flight dynamics theory of the rotorcraft, the external forces acting on the blade in the flapping plane include aerodynamic force, centrifugal force, gravity, inertia force, etc. The resultant moment of the above forces about the flapping hinge is 0, that is, ∑M = 0. Therefore, the rotor flapping motion equation is:

[0059]

[0060] where β is the side slip angle; I b is the blade mass moment of inertia; Ω is the blade angular velocity; M T is the blade flapping aerodynamic moment; Ms is the mass moment of the blade about the oscillating hinge;

[0061] The velocity at the center of the rotor hub in the fuselage axis system converted to the rotor hub wind axis system is:

[0062]

[0063] where, is the conversion coefficient, u h , v h , w h are the linear velocities of the x-axis, y-axis and z-axis of the aircraft at the center of the rotor hub;

[0064] The tangential velocity and vertical velocity of the rotor profile are respectively:

[0065]

[0066] where U T is the tangential velocity of the rotor profile, U P is the vertical velocity of the rotor profile, R is the hub center height, r is the blade radius, μ is the damping ratio, is the roll angle, λ0 is the initial propeller aerodynamic efficiency, v1 is the induced velocity;

[0067] According to the blade element theory, the lift and drag of the blade element are:

[0068]

[0069] where dY represents the lift of the blade element, dX represents the drag of the blade element, C x represents the blade airfoil drag coefficient, C y is the blade airfoil lift coefficient, ρ is the air density, W is the absolute velocity of the air, b is the chord length;

[0070] The components of the force converted to the flapping plane are:

[0071] dT = dYcosβ * -dXsinβ *

[0072] dQ = dXcosβ * -dYsinβ *

[0073] Wherein, β * is the inflow angle, and T and Q are the component forces in the flapping wing plane;

[0074] The projection of the blade element aerodynamics on the rotor structure shaft system constitutes the unit forces and moments dT_s, dH_s, dS_s, dM_k of the rotor. Integrating the above-mentioned blade element aerodynamic forces and the moments along the propeller, taking the average value of the position angle, and then multiplying by the number of blades, the forces and moments generated by the rotor can be obtained: thrust T s , reverse force H s , lateral force S s , moment M k . When calculating the basic forces of the rotor, its induced velocity cannot be calculated by a formula. The present invention adopts an iterative method. Given the initial value of the induced velocity in the rotor vertical velocity, the thrust of the rotor is obtained from the above formula, and a new induced velocity is calculated according to the momentum theory:

[0075]

[0076] Wherein, r is the blade radius, and R is the hub center height;

[0077] The equivalent induced velocity v 1d is:

[0078]

[0079] Wherein, λ1 is the inflow ratio, and C T is the rotor thrust coefficient. If v1 and are close enough, the iteration will exit, otherwise v1 and will be updated and it will calculate the induced velocity of the rotor and its forces and moments. Converting the forces and moments of the rotor to the fuselage shaft system, the forces and moments in this system are obtained:

[0080]

[0081] Wherein, F xR , F yR , F zR respectively represent the force components of the rotor on the x-axis, y-axis, and z-axis, and M xR , M yR , M zR are the moment components on the x-axis, y-axis, and z-axis, and xh , y h , z h are the parameters of the rotor hub center;

[0082] According to the same principle, the forces and moments of other rotors in the fuselage axis system are calculated.

[0083] Step 3: Establish the aerodynamic model of the wing. The tiltrotor aircraft has a left wing and a right wing. Taking the left wing as an example, its forces and moments are calculated. The wing is divided into two parts: the first part is the slipstream area affected by the rotor wake, and the other part is the free stream area not affected by the rotor disturbance.

[0084] It is difficult to accurately calculate the area of the slipstream area. The following formula can be used to approximately estimate this area:

[0085]

[0086] where S wss represents the estimated area of the slipstream area, is the maximum area of the slipstream area, and μ max is the advance ratio when the wing is not affected by the rotor wake in helicopter mode.

[0087] The area of the free flow area S wfs is the result of subtracting the slipstream area from the wing area.

[0088] Forces and moments in the slipstream area:

[0089] In the slipstream area, the air velocity of the wing is the sum of the induced velocity of the rotor at the wing and the velocity of the incoming flow in front.

[0090]

[0091] where M wsl is the moment in the slipstream area, u is the linear velocity of the aircraft along the x-axis, v is the linear velocity of the aircraft along the y-axis, w is the linear velocity of the aircraft along the z-axis, x wsl , y wsl , z wsl are the position parameters of the slipstream area, p is the angular velocity of the aircraft along the x-axis, q is the angular velocity of the aircraft along the y-axis, and r is the angular velocity of the aircraft along the z-axis;

[0092] In rotor mode, the position of the aerodynamic center of the left wing relative to the center of gravity of the fuselage is P wsl0 = [x wsl y wsl z wsl T . When the nacelle is tilted, the position of the aerodynamic center of the wing is:

[0093] ​

[0094] Among them, δx and δz are the changes in the center of gravity when the nacelle is tilted, and x wsl0 , y wsl0 , z wsl0 are the positions of the aerodynamic center of the left wing relative to the center of gravity of the fuselage before the nacelle is tilted.

[0095] The forces and moments in the aircraft fuselage axis system are:

[0096]

[0097] Among them, F xwsl , F ywsl , F zwsl are the force components in the aircraft fuselage axis system, M xwsl , M ywsl , M zwsl are the moment components in the aircraft fuselage axis system, α wsl is the angle of attack in the left wing slipstream area, D wsl represents the drag in the slipstream area, and L wsl represents the lift in the slipstream area;

[0098] Forces and moments in the free flow area:

[0099] In the rotor mode, its area is the smallest. Then, when the nacelle is tilted, part of the slipstream area becomes the free flow area. Therefore, the free flow area can be divided into two parts: the first part is the area that is always the free flow area, and the second part is the area that turns from the slipstream area due to the nacelle tilt. In the free flow area, the air velocity of the wing is only related to the incident flow in the front. First, calculate the air flow velocity [u wsl1 v wsl1 w wsl1 T , and calculate the dynamic pressure q wsl1 of the aerodynamic center in the first part of the free flow area and the dynamic pressure q wsl2 of the aerodynamic center in the second part of the free flow area, and the angle of attack α wsl1 in the first part of the free flow area and the angle of attack α wsl2 in the second part of the free flow area respectively. Then, calculate the lift L wsl1 due to the angle of attack in the first part of the free flow area and the lift L wsl2 due to the angle of attack in the second part of the free flow area, the drag D wsl1 in the first part of the free flow area and the drag D wsl2 in the second part of the free flow area, and the moment M wsl1 in the first part of the free flow area and the moment M wsl2 The distribution of the left wing in the free flow area is that the aerodynamics of the free flow area of the fuselage axis system is:

[0100] ​

[0101] Among them, F xwfl , F ywfl , F zwfl respectively represent the dynamic components of the free stream region of the x-axis, y-axis, and z-axis; D wfl represents the drag of the free stream region, and L wfl represents the lift of the free stream region; α wfl is the angle of attack of the left-wing free stream;

[0102] The moment of the free stream region of the fuselage axis system is:

[0103]

[0104] Among them, M xwfl , M ywfl , M zwfl respectively represent the moment components of the free stream region of the x-axis, y-axis, and z-axis; x wfl , y wfl , z wfl represent the position parameters of the free stream region; M wfl represents the moment of the free stream region;

[0105] Take the sum of the forces and moments of the left wing in the slipstream region and the free stream region, which is the force and moment received by the left wing. According to the same principle, calculate the forces and moments of the right wing. The total forces and moments on the left and right wings are the sum of the forces and moments of all wings.

[0106] Step 4: Establish the aerodynamic model of the vertical tail. Calculate the aerodynamic forces and moments of the vertical tail in the wind axis system, and then transform them into the body axis system. There are two vertical tails on the tilt-rotor aircraft, so it is necessary to develop models for the left and right tails.

[0107] Taking the left vertical tail as an example, calculate the air velocity [u VT v VT w VT T at the aerodynamic center (x VT , y VT , z VT ) of the vertical tail, and then calculate the dynamic pressure q VT , the angle of attack α VT and the sideslip angle β VT of the fuselage. According to the air velocity at the aerodynamic center of the vertical tail. Thus, the aerodynamic force of the vertical fin in the wind axis system is:

[0108]

[0109] D VT = q VT A VT C D,VT

[0110] Among them, A VT is the stress area at the aerodynamic center of the vertical tail, C L,VT is the lift coefficient at the aerodynamic center of the vertical tail, δ is the control amount, α0 is the initial angle of attack, C l,V is the lift coefficient in the vertical direction, δ rud is the rudder control amount, C D,VT is the drag coefficient at the aerodynamic center of the vertical tail;

[0111] The aerodynamic forces and moments converted to the body axis system are:

[0112]

[0113] Among them, F xVT , F yVT , F zVT respectively represent the aerodynamic force components of the x-axis, y-axis, and z-axis at the aerodynamic center of the vertical tail, M VT represents the moment at the aerodynamic center of the vertical tail, D VT is the drag at the aerodynamic center of the vertical tail, L VT is the lift at the aerodynamic center of the vertical tail;

[0114] Similarly, the forces and moments of the right vertical tail are calculated. The sum of the forces and moments of the left and right tails is the total force and moment of the vertical tail in the fuselage axis system.

[0115] Step 5: Establish the aerodynamic model of the horizontal tail. The influence of the rotor wake on the horizontal tail is small, so the rotor wake is ignored. Calculate the aerodynamic forces of the horizontal tail and elevator according to the treatment method of fixed wings. The air flow at the pressure center of the horizontal tail (x HT , y HT , z HT ) is the sum of the fuselage linear velocity and angular velocity. First, calculate the air velocity [u HT v HT w HT at the pressure center of the horizontal tail. T , and then calculate the dynamic pressure q HT , angle of attack α HT and fuselage sideslip angle β HT according to the air velocity at the pressure center of the horizontal tail. Then the lift L HT and drag D HT of the horizontal tail in the local wind axis system. The forces and moments in the wind axis system are converted to the forces and moments in the body axis system:

[0116]

[0117] Among them, F HT is the force in the body axis system, M HT is the moment in the body axis system.

[0118] As Figure 2 shown, based on the nacelle tilt angle, elevator, rudder, and throttle parameters, aerodynamic models of the rotor, wing, horizontal tail, and vertical tail are established respectively. Substituting the forces and moments calculated for each component into the 6DOF kinematic nonlinear model, the speed, attitude, and altitude position of the tiltrotor aircraft can be obtained.

[0119] Build a rotor dynamics model according to the method of the present invention. In RotorArm, wing parameters such as wing area, nacelle height, wing span, and geometric chord length can be modified according to the specific aircraft type, and the rotation direction of the rotor can also be modified, and the forces and moments of each rotor can be calculated.

[0120] In the process of modeling the wing dynamics, considering the influence of different weather and climates on the air coefficient, different experimental environments can be selected in combination with the calculation of air data, which is convenient for further research on the stability of the aircraft under various weather conditions.

[0121] Through simulation research, the lift coefficient and drag coefficient in the vertical direction are affected by the elevator, aileron, and rudder. In the horizontal tail part, not only the rudder will affect the lift coefficient and drag coefficient in the horizontal direction, but also the change of the aileron on the wing will change these coefficients. The present invention can finally establish a lift coefficient curve and a drag coefficient curve through CFD software to establish a simple and effective model.

[0122] The above embodiments are used to explain the present invention, rather than limiting the present invention. Any modifications and changes made to the present invention within the spirit and scope of the claims of the present invention fall within the protection scope of the present invention.

Claims

1. A mathematical modeling method for a thrust-tilt aircraft, characterized in that: The method comprises the following steps: Step 1: Model the changes in the center of gravity and moment of inertia during the nacelle tilting process; Step 2: Establish an aerodynamic model of the rotor for the axial-thrust tilt-rotor aircraft; the axial-thrust tilt-rotor aircraft consists of two left and right rotors tilted in opposite directions. Integrate the aerodynamic force of the blade unit in the flapping plane and the torque along the propeller, take the average value of the position angle, and then multiply it by the number of blades to obtain the force and torque generated by the rotor, and convert it to the force and torque under the fuselage shaft system; Step 3: Establish an aerodynamic model of the wing for the thrust tilt-rotor aircraft; the wing consists of two parts: the slipstream area affected by the rotor wake disturbance and the freestream area not affected by the rotor disturbance, which are modeled as follows: Calculate the forces and moments in the aircraft fuselage axis system based on the slipstream position parameters, and calculate the aerodynamic center position of the wing when the nacelle is tilted; The free flow area is divided into an area that is always a free flow area and an area that changes from a slipstream area to a free flow area when the nacelle is tilted; the air velocity, aerodynamic center dynamic pressure, free flow area angle of attack and lift are calculated for the two areas respectively, and then the free flow area drag and torque are calculated; Step 4: Establish an aerodynamic model of the vertical tail for the thrust tilt-rotor aircraft; calculate the air velocity at the aerodynamic center of the vertical tail, and then calculate the dynamic pressure angle of attack and the fuselage sideslip angle; calculate the aerodynamic force of the vertical fin in the wind axis system according to the air velocity at the aerodynamic center of the vertical tail, and then convert the aerodynamic force and torque of the fuselage axis system; Step 5: Establish an aerodynamic model of the horizontal tail for the thrust tilt-rotor aircraft; calculate the aerodynamic forces of the horizontal tail and elevator according to the fixed-wing processing method. The airflow at the pressure center of the horizontal tail is the sum of the linear velocity and angular velocity of the fuselage; based on the air flow velocity, dynamic pressure, angle of attack and sideslip angle of the fuselage at the pressure center of the horizontal tail, calculate the lift and drag of the horizontal tail in the wind axis system, and convert the forces and moments in the wind axis system into forces and moments in the body axis system.

2. The mathematical modeling method of a thrust-tilt aircraft according to claim 1, characterized in that: The change of the center of gravity position with the nacelle tilt angle is expressed as follows: Where Δx and Δz are the changes in the center of gravity when the cabin tilts. H is the height of the rotor relative to the wing, m NAC is the mass of the nacelle system, m is the total weight of the fuselage; The moment of inertia I changes with the nacelle tilt angle β M Change, the formula is: I=I0-KIβ M Where I0 is the moment of inertia of any axis in rotor mode; KI is the coefficient of the corresponding moment of inertia.

3. The mathematical modeling method of a thrust-tilt aircraft according to claim 1, characterized in that: The velocity at the center of the rotor hub in the body axis system and the tangential and vertical velocities of the rotor profile are calculated, and the lift and drag of the blade unit are calculated based on the blade unit theory and converted into the component force on the flapping plane. The projection of the blade unit aerodynamics on the rotor structure axis system constitutes the unit force and moment of the rotor; the blade unit aerodynamic force and the moment along the propeller are integrated, the position angle is averaged, and then multiplied by the number of blades to obtain the force and moment generated by the rotor.

4. The mathematical modeling method of a thrust-tilt aircraft according to claim 1, characterized in that: The area of ​​the slipstream zone is estimated by the following formula: Among them, S wss represents the estimated area of ​​the slipstream zone, is the maximum area of ​​the slipstream zone, μ max is the advance ratio when the wing is not affected by the rotor wake in helicopter mode; In rotor mode, the position of the left wing aerodynamic center relative to the fuselage center of gravity is P wsl0 =[x wsl y wsl z wsl ] T When the nacelle is tilted, the aerodynamic center of the wing is located at: Among them, δx and δz are the changes of the center of gravity when the cabin tilts, x wsl0 ,y wsl0 、z wsl0 It is the position of the aerodynamic center of the left wing relative to the center of gravity of the fuselage before the nacelle is tilted.

5. The mathematical modeling method of a thrust-tilt aircraft according to claim 1, characterized in that: The forces and moments in the aircraft fuselage axis system are: Among them, F xwsl 、F ywsl 、F zwsl Force components in the aircraft fuselage axis system, M xwsl 、M ywsl 、M zwsl is the moment component in the aircraft fuselage axis system, α wsl is the angle of attack of the left wing slipstream, D wsl is the resistance in the slipstream zone, L wsl represents the lift in the slipstream region.

6. The mathematical modeling method of a thrust-tilt aircraft according to claim 1, characterized in that: The aerodynamics of the free flow area of ​​the fuselage axis is: Among them, F xwfl 、F ywfl 、F zwfl Denote the dynamic components of the free flow area of ​​the x-axis, y-axis, and z-axis respectively; D wfl represents the resistance of the free flow area, L wfl represents the lift in the free flow area; α wfl is the angle of attack of the left wing free stream; The moment of the free flow area of ​​the fuselage axis is: Among them, M xwfi 、M ywfl 、M zwfl Represents the moment components of the free flow zone along the x-axis, y-axis, and z-axis respectively; wfl ,y wfl 、z wfl represents the free flow area position parameter; M wfl represents the moment in the free flow region.

7. The mathematical modeling method of a thrust-tilt aircraft according to claim 1, characterized in that: The aerodynamic force of the vertical fins in the wind axis system is: D VT =q VT A VT C D,VT Among them, A VT is the stress area at the aerodynamic center of the vertical tail, C L,VT is the lift coefficient at the aerodynamic center of the vertical tail, δ is the control amount, α0 is the initial angle of attack, C l,V is the lift coefficient in the vertical direction, δ rud is the rudder control quantity, C D,vT is the drag coefficient at the aerodynamic center of the vertical tail.

8. The mathematical modeling method of a thrust-tilt aircraft according to claim 1, characterized in that: The forces and moments of the horizontal tail in the body axis system are: Among them, F HT is the force in the body axis system, M HT is the moment in the body axis system.

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