Dynamic simulation modeling method for multi-wheel multi-strut aircraft
Through iterative calculation and force balance constraint equations, the vertical force and rotation center coordinates of the tires of multi-wheel multi-pillar aircraft are determined, which solves the problems of low accuracy and computational complexity in the existing technology, and achieves more efficient dynamic simulation evaluation.
Patent Information
- Application Number
- CN202411906269.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-23
- Publication Date
- 2025-03-28
AI Technical Summary
In the prior art, when constructing dynamic simulation modeling of multi-wheel multi-pillar aircraft, the error and computational complexity of the rotation center position lead to low accuracy and low computational efficiency.
By estimating the coordinates of the instantaneous rotation center of the aircraft, the change of the grounding point of the buffer support tire is estimated, and iteratively calculated based on the force balance constraint equation and the moment balance constraint equation to determine the vertical force of each buffer support tire and the instantaneous rotation center coordinate of the aircraft.
Improves calculation accuracy and aircraft turn dynamics simulation evaluation efficiency, reduces errors and simplifies the calculation process.
Smart Images
Figure CN119720388A_ABST
Abstract
Description
Technical Field
[0001] The present application belongs to the technical field of aircraft design, and in particular relates to a dynamic simulation modeling method for a multi-wheel and multi-prop aircraft. Background Art
[0002] The landing gear of existing large aircraft uses a multi-wheel and multi-strut structure arranged in series in front and behind the fuselage, thus forming a multi-point (greater than three points) hyperstatic support. When designing an aircraft or performing turning control, designers need to build a full-aircraft tire turning model to evaluate the aircraft's turning characteristics.
[0003] In the prior art, some dynamic simulation modeling methods take into account that the multiple wheels and multiple pillars on each side of the fuselage are relatively concentrated, so the multiple wheels and multiple pillars on one side are simplified into a fulcrum - a virtual main pillar, thereby forming a classic front three-point layout. For the load relationship between multiple main pillars that is different from the three-point layout, through exploratory research, a suitable load unevenness coefficient between each main pillar is given, and the total load is averaged and multiplied by the unevenness coefficient to obtain the ground load of a single pillar. However, the rotation center of the turning mechanics model is the intersection of the front wheel vertical line and the main wheel vertical line. When the rotation center is not at the intersection of the above vertical lines, errors will occur.
[0004] In addition, there are some dynamic simulation modeling methods, using foreign dynamic simulation software such as MSC's ADAMS or Siemens' LMS. The above method builds a complete full-machine model, which contains sub-models of each pillar and each wheel. Each sub-model is assigned corresponding mechanical parameters, and a time-based numerical algorithm (i.e. force = mass * acceleration) is used to solve the dynamic model. When the time increment is small enough, it has good accuracy. This method is too complicated to model the whole machine, and the calculation process is opaque due to encryption technology, so some parameters cannot be determined. Summary of the invention
[0005] In order to solve the above problems, the present application provides a dynamic simulation modeling method for a multi-wheel and multi-strut aircraft, wherein the landing gear system of the aircraft has 7 buffer struts, each buffer strut is connected to two wheel tires, wherein the front landing gear has one buffer strut, and the main landing gear includes three pairs of front and rear buffer struts, and the method includes:
[0006] Step S1, estimating the center coordinates of the instantaneous rotation of the aircraft;
[0007] Step S2, estimating the tire contact point position change values of the seven buffer pillars;
[0008] Step S3, based on the pre-constructed force balance constraint equations in three directions and the moment balance constraint equations in three directions of the circular motion of the aircraft around the center coordinate, the vertical force of the tire of each buffer strut in the vertical direction, the engine thrust and the instantaneous rotation center coordinate of the aircraft are iteratively calculated.
[0009] Preferably, in step S3, the force balance constraint equation constructed includes the force balance equation in the centrifugal direction of circular motion, the force balance equation in the tangential direction of circular motion and the force balance equation in the vertical direction, and the moment balance constraint equation constructed includes the heading moment balance, pitch moment balance and roll moment balance around the center of gravity when the aircraft turns.
[0010] Preferably, in the force balance constraint equation and the moment balance constraint equation, the lateral friction force F of the tire is ce,i The vertical force F in the vertical direction of the tire 竖直,i Constrained by the following model:
[0011] F ce,i =μ*F 竖直,i ;
[0012] Where μ is the lateral friction coefficient, which is calculated based on the pre-built lateral friction coefficient, the tire’s own characteristic parameters, and the vertical force F 竖直,i The function relationship between the aircraft speed, ground wetness parameters, ground material parameters, yaw angle and braking force input parameters is calculated and obtained.
[0013] Preferably, the yaw angle and braking force input parameters are constrained by the following models f1, f2, f3 and f4:
[0014] Tire yaw angle = f1 (center coordinate of instantaneous rotation of the aircraft, change in position of tire contact points of seven buffer struts);
[0015] Tire side slip force = f2 (tire yaw angle, wheel braking force);
[0016] The tire yaw angle corresponding to the maximum tire side slip friction coefficient = f3 (wheel braking force);
[0017] Aircraft yaw angle = f4 (the resultant force and moment provided by all tires).
[0018] Preferably, step S3 further includes:
[0019] Step S31, calculating six variables under different environmental parameters according to the force balance constraint equation and the moment balance constraint equation, the six variables including the resultant vertical force of the front landing gear tire, the resultant vertical force of the three front and rear main landing gear tires on the left side, the resultant vertical force of the three front and rear main landing gear tires on the right side, the engine thrust and the instantaneous rotation center coordinates of the aircraft, and the environmental parameters including the aircraft weight, the front wheel steering angle, the height of the center of gravity of the aircraft, the front and rear position of the center of gravity of the aircraft, the speed of the aircraft, the pavement material and dryness and humidity of the runway, and the wheel braking force;
[0020] Step S32: Determine the vertical support force of all tires of the aircraft according to the vertical force of the tires and the deformation coordination condition.
[0021] Preferably, in step S3, the final solution method is determined by trial calculation of the Newton iteration method and obtaining the optimal solution after trial calculation of all ergodic solutions within a specific range.
[0022] The present application solves mutually related coupled analysis variables based on an iterative algorithm or an exhaustive algorithm, thereby improving calculation accuracy and improving the efficiency of aircraft turning dynamics simulation evaluation. BRIEF DESCRIPTION OF THE DRAWINGS
[0023] Figure 1 It is a flow chart of a preferred embodiment of the present application's method for dynamics simulation modeling of a multi-wheel and multi-prop aircraft.
[0024] Figure 2 This application Figure 1 A schematic diagram of the tire layout of the landing gear system of the illustrated embodiment.
[0025] Figure 3 Schematic diagram of tire layout of another embodiment.
[0026] Figure 4 This application Figure 1 Schematic diagram of the aircraft tire speed and sideslip force caused by tire yaw in the illustrated embodiment.
[0027] Figure 5 This is the flow chart of Newton iteration method to calculate the optimal solution. DETAILED DESCRIPTION
[0028] In order to make the purpose, technical scheme and advantages of the implementation of this application clearer, the technical scheme in the implementation of this application will be described in more detail in combination with the drawings in the implementation of this application. In the drawings, the same or similar reference numerals throughout represent the same or similar elements or elements with the same or similar functions. The described implementation is a part of the implementation of this application, not all of the implementations. The implementation described below with reference to the drawings is exemplary and is intended to be used to explain this application, and cannot be understood as a limitation on this application. Based on the implementation in this application, all other implementations obtained by ordinary technicians in this field without making creative work are within the scope of protection of this application. The implementation of this application is described in detail below in combination with the drawings.
[0029] This application provides a dynamic simulation modeling method for a multi-wheel and multi-prop aircraft, such as Figure 1 As shown, it mainly includes:
[0030] Step S1, estimating the center coordinates of the instantaneous rotation of the aircraft;
[0031] Step S2, estimating the tire contact point position change values of the seven buffer pillars;
[0032] Step S3, based on the pre-constructed force balance constraint equations in three directions and the moment balance constraint equations in three directions of the circular motion of the aircraft around the center coordinate, the vertical force of the tire of each buffer strut in the vertical direction, the engine thrust and the instantaneous rotation center coordinate of the aircraft are iteratively calculated.
[0033] The modeling object of this application is a multi-wheel multi-strut heavy aircraft. The aircraft landing gear system simulated in the modeling has 7 buffer struts and 14 wheel tires, such as Figure 2 and Figure 4 As shown, alternative embodiments may also have more buffer pillars, such as Figure 3 As shown in the figure. Each buffer strut corresponds to two wheel tires, and these two wheel tires are analyzed as one landing gear tire. In addition, the modeling is optimized according to the characteristics of the aircraft mechanism, that is, the dynamic behavior is coupled by several landing gear struts without follow-up turning ability and several landing gear struts with controllable turning.
[0034] In step S3 of the present application, the mathematical model is simplified to the uniform circular motion of the center of gravity of the aircraft around the instantaneous rotation center, and the simplified model is used as a reference standard for evaluation and analysis. The mathematical model uses six equations to solve six variables: the equations are the force balance in the three directions of x, y, and z and the moment balance in the three directions of the aircraft dynamics process; the variables are the x-axis coordinates and y-axis coordinates of the instantaneous rotation center of the aircraft, the engine thrust, and the three tire vertical support force intermediate variables. Among them, the three tire vertical support force intermediate variables are finally associated with the vertical support force of each tire of the multi-wheel multi-pillar landing gear aircraft through the deformation coordination conditions of the aircraft structural strength analysis.
[0035] In the process of model solving, firstly, in step S1, the approximate instantaneous rotation center coordinates of the aircraft are estimated through engineering experience, and then the dynamic model is solved in step S3 to solve the x-axis coordinates and y-axis coordinates of the instantaneous rotation center of the aircraft, the engine thrust, and the three tire vertical support force intermediate variables, so as to obtain the dynamic simulation evaluation results of the aircraft. Among them, in step S2, by giving the seven tire contact point position change values, the seven contact point position vertical forces can be further calculated, and then the landing gear buffer strut force-tire contact point position change value curve derivative is obtained, which is convenient for the subsequent parameter calculation of the dynamic equation. In addition, when performing iterative calculations, when the difference between two consecutive tire vertical forces is less than the set value, it is considered that the six nonlinear equations are calculated and converged.
[0036] In some optional embodiments, in step S3, the force balance constraint equation constructed includes the force balance equation in the centrifugal direction of circular motion, the force balance equation in the tangential direction of circular motion, and the force balance equation in the vertical direction, and the moment balance constraint equation constructed includes the heading moment balance, pitch moment balance, and roll moment balance around the center of gravity when the aircraft turns.
[0037] In this embodiment, based on kinematics (the motion state of all moving bodies under the velocity vector), geometry (the initial input parameters of the aircraft), and dynamics (uniform circular motion), this embodiment only defines the centripetal acceleration, and does not define other linear accelerations and angular accelerations, and obtains the force balance equation in the centrifugal direction of the circular motion:
[0038] Right now:
[0039] Among them, F ce,i is the lateral friction of the ith tire, F gun,i is the rolling friction of the ith tire, T is the engine thrust, γ i is the projection angle of the lateral friction force of the i-th tire in the direction of the centrifugal force, is the projection angle of the rolling friction of the ith tire in the direction of the centrifugal force, δ is the projection angle of the engine thrust in the direction of the centrifugal force, m is the mass of the aircraft, v is the turning speed of the aircraft, and r is the turning radius.
[0040] The force balance equation in the tangential direction of circular motion is:
[0041] Right now:
[0042] Among them, γ' i is the projection angle of the lateral friction force of the i-th tire in the tangential force direction, is the projection angle of the rolling friction of the ith tire in the direction of the tangential force, and δ' is the projection angle of the engine thrust in the direction of the tangential force.
[0043] The heading moment balance about the center of gravity when the aircraft turns (no angular acceleration):
[0044] Right now:
[0045] Among them, dγ i , are the force arms of the lateral friction moment gravity center and the force arms of the rolling friction moment gravity center of the i-th tire respectively; M 轮i is the self-aligning torque contribution brought by the tire sideslip angle of the i-th tire; Mt is the additional torque brought by the aircraft engine.
[0046] Vertical force balance:
[0047] Right now:
[0048] Among them, G is the total weight of the aircraft.
[0049] Moment balance of pitch:
[0050] ∑M 俯仰绕重心 =0, that is, M 前起支持力力矩 +M 主起支持力力矩 +M 所有轮胎摩擦力力矩 =0.
[0051] Rolling moment balance:
[0052] ∑M 滚转绕机身轴线 =0, that is, M 左主起支持力力矩 +M 右主起支持力力矩 +M 所有轮胎摩擦力力矩 =0.
[0053] In some optional embodiments, in the force balance constraint equation and the moment balance constraint equation, the lateral friction force F of the tire is ce,i(also known as tire side slip force) and the vertical force F of the tire in the vertical direction 竖直,i Constrained by the following model:
[0054] F ce,i =μ*F 竖直,i ;
[0055] Where μ is the lateral friction coefficient, which is calculated based on the pre-built lateral friction coefficient, the tire’s own characteristic parameters, and the vertical force F 竖直,i The function relationship between the aircraft speed, ground wetness parameters, ground material parameters, yaw angle and braking force input parameters is calculated and obtained.
[0056] In some optional embodiments, the yaw angle and braking force input parameters are constrained by the following models f1, f2, f3 and f4:
[0057] Tire yaw angle = f1 (center coordinate of instantaneous rotation of the aircraft, change in position of tire contact points of seven buffer struts);
[0058] Tire side slip force = f2 (tire yaw angle, wheel braking force);
[0059] The tire yaw angle corresponding to the maximum tire side slip friction coefficient = f3 (wheel braking force);
[0060] Aircraft yaw angle = f4 (the resultant force and moment provided by all tires).
[0061] In some optional embodiments, as the tire yaw angle increases, after the tire maximum sideslip force friction coefficient monotonically increases to a maximum value (this stage is a nonlinear monotonic increase), the model considers the tire yaw angle corresponding to the tire maximum sideslip force friction coefficient until the tire yaws 90°. In the second stage, the tire sideslip force linearly decays to the drag tire sideslip force when the tire yaws 90°.
[0062] In this embodiment, the modeling is optimized for the characteristics of the turning condition of the aircraft, that is, the large yaw angle of the tire is simulated, and the side slip force generated by the yaw will be coupled with the wheel braking force. The above models f1-f4 can be obtained through experiments or simulations. Therefore, this application takes into account the situation that the lateral force friction coefficient decreases after the tire lateral force reaches the limit under the large yaw angle of the tire, the yaw of the tire is coupled with the brake, and the large yaw angle causes the tire to drag (that is, the tire does not rotate), so that the calculation results are more in line with reality.
[0063] In some optional implementations, step S3 further includes:
[0064] Step S31, calculating six variables under different environmental parameters according to the force balance constraint equation and the moment balance constraint equation, the six variables including the resultant vertical force of the front landing gear tire, the resultant vertical force of the three front and rear main landing gear tires on the left side, the resultant vertical force of the three front and rear main landing gear tires on the right side, the engine thrust and the instantaneous rotation center coordinates of the aircraft, and the environmental parameters including the aircraft weight, the front wheel steering angle, the height of the center of gravity of the aircraft, the front and rear position of the center of gravity of the aircraft, the speed of the aircraft, the pavement material and dryness and humidity of the runway, and the wheel braking force;
[0065] Step S32: Determine the vertical support force of all tires of the aircraft according to the vertical force of the tires and the deformation coordination condition.
[0066] In this embodiment, the deformation coordination condition of the aircraft is taken into account, and the iteration parameter is increased as follows:
[0067] The vertical displacement of the front landing gear strut connection point on the fuselage, the vertical displacement of the first main landing gear strut connection point on the fuselage, the vertical displacement of the second main landing gear strut connection point on the fuselage, the vertical displacement of the third main landing gear strut connection point on the fuselage, the vertical displacement of the fourth main landing gear strut connection point on the fuselage, the vertical displacement of the fifth main landing gear strut connection point on the fuselage, and the vertical displacement of the sixth main landing gear strut connection point on the fuselage. In the analysis of each rocker arm main landing gear, the angle between the rocker arm and the fuselage is derived from the corresponding tire rolling friction and its tire vertical force, thereby deriving the vertical displacement of the fuselage position point to meet the deformation coordination condition, that is, step S32, as Figure 5 shown.
[0068] In some optional implementations, in step S3, the final solution method is determined by trial calculation of the Newton iteration method and obtaining the optimal solution after trial calculation of all ergodic solutions within a specific range.
[0069] In this embodiment, the optimal solution is obtained after solving all traversal solutions within a specific range, and the initial sampling point of the final approximate root of the Newton iteration method is determined. This embodiment uses computer trial calculation to determine the robustness of the iterative process of nonlinear equations. The essence is the Newton iteration method. The explanation of the trial calculation is: the method to ensure that the approximate root of the Newton iteration method is located in the mathematically solvable region R is trial calculation, and the traversal method is used to search for the approximate root sampling point. Finally, based on engineering experience, the rationality of the approximate root sampling point is manually checked. Because the turning model is complex, if the initial sampling point selection range of the calculation method is incorrect, the numerical calculation will diverge.
[0070] The calculation process of this application does not involve time parameters, the calculation result is a constant, and the required variable does not change or fluctuate with the passage of time. In step S3, since the simplified model motion trajectory is specified as a circle with equal curvature radius, the centripetal acceleration and tangential acceleration are input constants and do not change with time (the direction of acceleration does not change in the local coordinate system of the aircraft). Since the centripetal acceleration and tangential acceleration are input constants, the formula on the right side of the equal sign of the force balance equation based on acceleration will not change with time (force balance equation: the resultant force on the aircraft = aircraft mass * aircraft acceleration).
[0071] This application uses the coordinate value of the instantaneous center of rotation position point of the aircraft turning as a mathematical model for iterative solution variables, and focuses on studying the influence of tire sideslip of multi-wheel and multi-pillar landing gear aircraft on turning performance, which is different from the analysis method of three-point landing gear aircraft; based on iterative algorithms or exhaustive algorithms, the mutually related coupled analysis variables are solved, and the variable value results of the algorithm satisfy all pre-constructed constraint equations, thereby improving the calculation accuracy; in the dynamics simulation method, the simplified model eliminates the time variable, thereby improving the efficiency of aircraft turning dynamics simulation evaluation.
[0072] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application shall be based on the protection scope of the claims.
Claims
1. A dynamic simulation modeling method for a multi-wheel and multi-prop aircraft, characterized in that: The landing gear system of the aircraft has 7 buffer struts, each buffer strut is connected to two wheel tires, wherein the front landing gear has one buffer strut, and the main landing gear includes three pairs of front and rear buffer struts, and the method includes: Step S1, estimating the center coordinates of the instantaneous rotation of the aircraft; Step S2, estimating the tire contact point position change values of the seven buffer pillars; Step S3, based on the pre-constructed force balance constraint equations in three directions and the moment balance constraint equations in three directions of the circular motion of the aircraft around the center coordinate, the vertical force of the tire of each buffer strut in the vertical direction, the engine thrust and the instantaneous rotation center coordinate of the aircraft are iteratively calculated.
2. The dynamics simulation modeling method for a multi-wheel and multi-prop aircraft according to claim 1, characterized in that: In step S3, the force balance constraint equations constructed include the force balance equation in the centrifugal direction of circular motion, the force balance equation in the tangential direction of circular motion, and the force balance equation in the vertical direction. The moment balance constraint equations constructed include the heading moment balance, pitch moment balance, and roll moment balance around the center of gravity when the aircraft turns.
3. The dynamics simulation modeling method for a multi-wheel and multi-prop aircraft as claimed in claim 2, characterized in that: In the force balance constraint equation and the moment balance constraint equation, the lateral friction force F of the tire is ce,i The vertical force F in the vertical direction of the tire 竖直,i Constrained by the following model: F ce,i =μ*F 竖直,i ; Where μ is the lateral friction coefficient, which is calculated based on the pre-built lateral friction coefficient, the tire’s own characteristic parameters, and the vertical force F 竖直,i The function relationship between the aircraft speed, ground wetness parameters, ground material parameters, yaw angle and braking force input parameters is calculated and obtained.
4. The dynamic simulation modeling method for a multi-wheel and multi-prop aircraft as claimed in claim 3, characterized in that: The yaw angle and braking force input parameters are constrained by the following models f1, f2, f3 and f4: Tire yaw angle = f1 (center coordinate of instantaneous rotation of the aircraft, change in position of tire contact points of seven buffer struts); Tire side slip force = f2 (tire yaw angle, wheel braking force); The tire yaw angle corresponding to the tire maximum sideslip friction coefficient = f3 (wheel braking force); Aircraft yaw angle = f4 (the resultant force and moment provided by all tires).
5. The dynamic simulation modeling method for a multi-wheel and multi-prop aircraft according to claim 1, characterized in that: Step S3 further includes: Step S31, calculating six variables under different environmental parameters according to the force balance constraint equation and the moment balance constraint equation, the six variables including the resultant vertical force of the front landing gear tire, the resultant vertical force of the three front and rear main landing gear tires on the left side, the resultant vertical force of the three front and rear main landing gear tires on the right side, the engine thrust and the instantaneous rotation center coordinates of the aircraft, and the environmental parameters including the aircraft weight, the front wheel steering angle, the height of the center of gravity of the aircraft, the front and rear position of the center of gravity of the aircraft, the speed of the aircraft, the pavement material and dryness and humidity of the runway, and the wheel braking force; Step S32: Determine the vertical support force of all tires of the aircraft according to the vertical force of the tires and the deformation coordination condition.
6. The dynamic simulation modeling method for a multi-wheel and multi-prop aircraft according to claim 1, characterized in that: In step S3, the final solution method is determined by trial calculation of the Newton iteration method and the optimal solution after trial calculation of all ergodic solutions within a specific range.