Rapid analysis and optimization method for stability of undercarriage stay bar lock mechanism

Abstract

The invention discloses a rapid analysis and optimization method for the stability of an undercarriage stay bar lock mechanism, and relates to the field of stability analysis of aircraft undercarriage lock mechanisms, and the method comprises the steps: generating a lock mechanism parameter group under the current iteration frequency through employing a multi-island genetic algorithm based on a set numerical range of the lock mechanism parameter group, determining a critical unlocking position and a critical unlocking force of the lock mechanism under the current number of iterations by combining a mechanical equilibrium equation set of the undercarriage folding and unfolding mechanism and utilizing a numerical continuation method; whether the difference value between the critical unlocking force under the current iteration number and the critical unlocking force under the previous iteration number is smaller than a convergence threshold value or not is judged; if yes, the lock mechanism parameter set under the current iteration frequency serves as the optimal lock mechanism parameter set; and if not, carrying out next iteration, and returning to the set numerical range based on the lock mechanism parameter group, and generating the lock mechanism parameter group under the current iteration frequency by using the multi-island genetic algorithm. According to the invention, the parameter optimization efficiency of the lock mechanism is improved.

Description

Technical Field

[0001] The present application relates to the field of stability analysis of aircraft landing gear lock mechanisms, and in particular to a method for rapid analysis and optimization of the stability of a landing gear strut lock mechanism. Background Art

[0002] Most modern aircraft utilize retractable landing gear mechanisms to reduce aerodynamic drag. The retractable mechanism's primary function is to drive the landing gear along a specified trajectory to a designated retracted or extended position. A locking mechanism securely locks the landing gear in both the retracted and extended positions. A notable feature of the locking mechanism is that, when approaching the lock, it instantly jumps from an unstable unlocked state to a stable locked state (the reverse of the unlocking process). This moment of stability change in the locking mechanism, known as a bifurcation, occurs. Studying the critical location where bifurcations occur can effectively support the design of landing gear locking mechanisms.

[0003] Traditionally, bifurcation analysis of landing gear lock mechanism stability is performed through multiple iterations of dynamic time-domain simulation. However, this approach often involves complex models, and each change in selected parameters requires resimulating the dynamic model, which consumes significant computational time. This complexity can increase exponentially, especially when considering a large number of influencing parameters. This, to a certain extent, limits the advancement of lock mechanism design. Summary of the Invention

[0004] The purpose of this application is to provide a rapid analysis and optimization method for the stability of a landing gear strut lock mechanism, so as to improve the optimization efficiency of the landing gear strut lock mechanism.

[0005] To achieve the above objectives, this application provides the following solutions:

[0006] This application provides a rapid analysis and optimization method for the stability of a landing gear strut lock mechanism, including:

[0007] Based on the set value range of the lock mechanism parameter group, a lock mechanism parameter group under the current iteration number is generated using a multi-island genetic algorithm; the lock mechanism parameter group includes spring stiffness, spring length and installation position;

[0008] Based on the locking mechanism parameter group at the current iteration number and the mechanical equilibrium equation group of the landing gear retraction and extension mechanism, the critical unlocking position and critical unlocking force of the locking mechanism at the current iteration number are determined using the numerical continuation method;

[0009] Determine whether the difference between the critical unlocking force at the current iteration number and the critical unlocking force at the previous iteration number is less than the convergence threshold;

[0010] If yes, the locking mechanism parameter set under the current number of iterations is taken as the optimal locking mechanism parameter set;

[0011] If not, the next iteration is performed and the method returns to "generating the locking mechanism parameter group under the current number of iterations using the multi-island genetic algorithm based on the set value range of the locking mechanism parameter group".

[0012] Optionally, based on the locking mechanism parameter group at the current iteration number and the mechanical equilibrium equation group of the landing gear retraction and extension mechanism, a numerical continuation method is used to determine the critical unlocking position and critical unlocking force of the locking mechanism at the current iteration number, specifically including:

[0013] Establish the mechanical equilibrium equations of the landing gear retraction and extension mechanism;

[0014] According to the locking mechanism parameter group at the current iteration number, the mechanical equilibrium equation group is extended for the first time using the numerical extension method with the retraction and extension torque as the control parameter to obtain all equilibrium solutions of the mechanical equilibrium equation group;

[0015] determining a bifurcation point based on the eigenvalues of the Jacobian matrix at the equilibrium solution;

[0016] Using the unlocking force as a control parameter, a numerical continuation method is used to perform a second continuation starting from the bifurcation point to generate a bifurcation trajectory line;

[0017] According to the bifurcation trajectory, a critical unlocking position and a critical unlocking force of the locking mechanism at the current number of iterations are determined.

[0018] Optionally, the mechanical equilibrium equations of the landing gear retraction and extension mechanism are:

[0019]

[0020] Where k is the kth link of the landing gear retraction mechanism, F k is the force on the kth connecting rod; F joint,k is the constraint force at the joint, r k is the position vector of the force point relative to the center of mass; M ext,k is the external torque.

[0021] Optionally, determining the bifurcation point based on the eigenvalues of the Jacobian matrix at the equilibrium solution specifically includes:

[0022] Determine whether the real parts of all eigenvalues of the Jacobian matrix at the equilibrium solution are less than 0;

[0023] If so, the equilibrium solution is stable;

[0024] If not, determining whether there is a real part equal to 0 among the real parts of all eigenvalues of the Jacobian matrix at the equilibrium solution;

[0025] If so, the equilibrium solution is a critical point between stability and instability, and the critical point is used as a bifurcation point.

[0026] Optionally, determining a critical unlocking position and a critical unlocking force of the lock mechanism at a current number of iterations according to the bifurcation trajectory specifically includes:

[0027] Determining the coordinates of the cusp of the bifurcation trajectory;

[0028] The cusp coordinates are used as the critical unlocking position and critical unlocking force of the locking mechanism at the current number of iterations.

[0029] According to the specific embodiments provided in this application, this application has the following technical effects:

[0030] This application provides a rapid analysis and optimization method for the stability of a landing gear strut lock mechanism. Based on the set numerical range of the lock mechanism parameter set, a multi-island genetic algorithm is used to generate the lock mechanism parameter set for the current iteration. A numerical continuation method is used to determine the critical unlocking position and critical unlocking force of the lock mechanism for the current iteration based on the lock mechanism parameter set and the mechanical equilibrium equations of the landing gear retraction and extension mechanism. A determination is made as to whether the difference between the critical unlocking force at the current iteration and the critical unlocking force at the previous iteration is less than a convergence threshold. If so, the lock mechanism parameter set for the current iteration is determined as the optimal lock mechanism parameter set. If not, the next iteration is performed and the result is returned to "Based on the set numerical range of the lock mechanism parameter set, a multi-island genetic algorithm is used to generate the lock mechanism parameter set for the current iteration." This application can rapidly and accurately analyze the stability of the landing gear lock mechanism dynamic model as system parameters vary. Combined with bifurcation theory, the dynamic performance of the lock mechanism can be quickly determined. This solves the computational inefficiency of traditional dynamics simulation and significantly improves the efficiency of lock mechanism parameter optimization. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0032] Figure 1 A schematic flow chart of a method for rapidly analyzing and optimizing the stability of a landing gear strut lock mechanism provided in one embodiment of the present application;

[0033] Figure 2 is a flow chart of the parameter optimization design method of the strut lock mechanism proposed in this application;

[0034] Figure 3 is a flow chart of the stability bifurcation analysis method proposed in this application;

[0035] Figure 4 This is a schematic diagram of force balance modeling of a landing gear retraction and extension mechanism according to an embodiment of the present application;

[0036] Figure 5 2 is a schematic diagram of the stability bifurcation analysis results of the landing gear strut lock mechanism according to an embodiment of the present application. DETAILED DESCRIPTION

[0037] The following will be combined with the drawings in the embodiments of this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0038] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the present application is further described in detail below with reference to the accompanying drawings and specific implementation methods.

[0039] This application establishes the force balance equation of the retraction and extension mechanism, combines the numerical extension method with the bifurcation theory, and performs parameter extension in two stages: first, the equilibrium solution is extended with the retraction and extension torque as the control parameter and the bifurcation point is detected; then, the bifurcation trajectory is extended with the unlocking force as the parameter, and the critical unlocking force is determined through the cusp. Further, an optimization design method based on a multi-island genetic algorithm is proposed. Through the joint iteration of the optimization module and the extension calculation module, parameters such as spring stiffness, original length and installation position are optimized to minimize the critical unlocking force while meeting the locking capability. This application solves the problem of low calculation efficiency through traditional dynamics simulation and significantly improves the efficiency of stability analysis and parameter optimization of the locking mechanism.

[0040] In an exemplary embodiment, Figure 1 and Figure 2 As shown, a rapid analysis and optimization method for the stability of a landing gear strut lock mechanism is provided, comprising the following steps:

[0041] Step 101: Based on the set value range of the lock mechanism parameter group, a lock mechanism parameter group under the current iteration number is generated using a multi-island genetic algorithm; the lock mechanism parameter group includes spring stiffness, spring length and installation position.

[0042] Step 102: Based on the locking mechanism parameter group at the current iteration number and the mechanical equilibrium equation group of the landing gear retraction and extension mechanism, a numerical continuation method is used to determine the critical unlocking position and critical unlocking force of the locking mechanism at the current iteration number.

[0043] In practical applications, the locking mechanism parameter group at the current iteration number is input into the continuation calculation module to calculate the critical unlocking force.

[0044] Step 103: Determine whether the difference between the critical unlocking force at the current iteration number and the critical unlocking force at the previous iteration number is less than a convergence threshold.

[0045] Step 104: If yes, the locking mechanism parameter set at the current iteration number is used as the optimal locking mechanism parameter set.

[0046] Step 105: If not, proceed to the next iteration and return to “generating the locking mechanism parameter group under the current number of iterations using the multi-island genetic algorithm based on the set value range of the locking mechanism parameter group”.

[0047] If the convergence condition is not met, return to step 101 to generate a new lock mechanism parameter set until the optimal lock mechanism parameter set is output.

[0048] As an optional implementation, step 102 specifically includes:

[0049] Step 1021: Establish a set of mechanical equilibrium equations for the landing gear retraction and extension mechanism.

[0050] In practical applications, a set of mechanical equilibrium equations of the landing gear retraction and extension mechanism including spring force, unlocking force and restraint force is established.

[0051] The mechanical equilibrium equations of the landing gear retraction mechanism are:

[0052]

[0053] Where k is the kth link of the landing gear retraction mechanism, F k is the force on the kth connecting rod (usually unlocking force, retraction force, spring force); F joint,k is the constraint force at the joint, r k is the position vector of the force point relative to the center of mass; M ext,k is the external torque (usually aerodynamic force).

[0054] like Figure 3 and Figure 4 As shown, in a specific embodiment:

[0055] Step S1: Establish the force balance equation of the landing gear retraction mechanism:

[0056]

[0057] in, It represents the mutual three-dimensional force between the connecting parts of the mechanism, i represents the number of the object receiving the force, j represents the number of the object applying the force, and * represents the number of the component applying the force to component i; O is the moment point; for The force arm.

[0058] Spring force F s and unlocking force F u The expression can be expressed as follows:

[0059]

[0060] Where, and are the coordinates of the upper and lower connection points of the spring; lu is the original length of the spring; k is the spring stiffness; is the spring force F s The component of the force acting on rod 2 in the y direction; is the spring force F s The component of the force acting on rod 2 in the z direction.

[0061]

[0062] Where, and The coordinates of the upper and lower connection points of the unlocking actuator; is the unlocking force F u The component of the force acting on rod 2 in the z direction; is the unlocking force F u The component of the force acting on rod 2 in the z direction.

[0063] Step 1022: Based on the locking mechanism parameter group at the current iteration number, with the retraction and extension torque as the control parameter, the mechanical equilibrium equation group is extended for the first time using the numerical extension method to obtain all equilibrium solutions of the mechanical equilibrium equation group.

[0064] In actual application, after receiving the locking mechanism parameter group under the current number of iterations, starting from the initial solution of the mechanical equilibrium equation group of the retraction and extension mechanism, the unlocking force is kept unchanged, and the retraction and extension torque is used as the control parameter. The mechanical equilibrium equation group is extended for the first time through the numerical extension method to generate the locking rod angle-retraction and extension torque curve, and all equilibrium solutions are solved, that is, step S2.

[0065] Step S2: Using the numerical extension method, starting from the initial solution of the mechanical equilibrium equations of the retracting and extending mechanism, keeping the unlocking force unchanged, and using the retracting and extending torque as the control parameter, all equilibrium solutions of the nonlinear dynamic equations are extended.

[0066] The equilibrium solution is obtained using the numerical continuation method as follows.

[0067] The mechanical equilibrium equations of the landing gear retraction mechanism can usually be expressed as the following first-order differential equations:

[0068]

[0069] Where x∈R nRepresents the n-dimensional state variable describing the system, λ∈R m Indicates all system control parameters.

[0070] Convert formula (5) into an ordinary differential equation:

[0071]

[0072] Among them, D x f(x,λ) is the Jacobian matrix of the equation f(x,λ).

[0073] If D x If f(x,λ) is reversible, then formula (6) can be rewritten as:

[0074]

[0075] Given the initial point of the system (initial solution of the mechanical equilibrium equations):

[0076] (x,λ)=(x1,λ1)(8)

[0077] By numerically integrating formula (7) and formula (8), the solution curve of the mechanical equilibrium equations can be tracked.

[0078] If D x If f(x,λ) is not invertible, then the parameter s is added, and the corresponding constraints are added:

[0079] N(x,λ,s)=0(9)

[0080] Among them, N(x,λ,s) is the constraint equation; S is the supplementary parameter; λ is the system control parameter.

[0081] Select appropriate constraints so that the n+1 order Jacobian matrix at the singular point of formula (1) and formula (9) is full rank:

[0082]

[0083] Step 1023: Determine a bifurcation point based on the eigenvalues of the Jacobian matrix at the equilibrium solution.

[0084] As an optional implementation, step 1023 specifically includes:

[0085] Step 10231: Determine whether the real parts of all eigenvalues of the Jacobian matrix at the equilibrium solution are less than 0.

[0086] Step 10232: If yes, the equilibrium solution is stable.

[0087] Step 10233: If not, determine whether there is a real part equal to 0 among the real parts of all eigenvalues of the Jacobian matrix at the equilibrium solution.

[0088] Step 10234: If so, the equilibrium solution is a critical point between stability and instability, and the critical point is used as a bifurcation point.

[0089] Step S3: Determine the stability of the equilibrium solution by the eigenvalues of the Jacobian matrix of the equation system and find the bifurcation point. The stability determination method of the equilibrium solution is as follows:

[0090] Define x0 as the equilibrium solution of the mechanical equilibrium equations, satisfying formula (1). In addition, matrix A is the Jacobian matrix at x0 If and only if all eigenvalues λ1,λ2,…,λ n If Reλ < 0, then the equilibrium solution x0 is stable. When Reλ > 0, the equilibrium solution is unstable. However, for Reλ = 0, the equilibrium solution is the critical point between stability and instability, also known as the real bifurcation point.

[0091] Step 1024: Using the unlocking force as a control parameter, a second extension is performed starting from the bifurcation point using a numerical extension method to generate a bifurcation trajectory line.

[0092] In practical applications, the bifurcation point of the lock rod angle-retraction torque curve is detected, and the bifurcation trajectory is extended using the unlocking force as the control parameter.

[0093] Using the numerical extension method, a second extension is performed starting from the bifurcation point, using the locking / unlocking force as the control parameter, to obtain a curve (bifurcation trajectory) that shows the bifurcation point versus locking / unlocking force. The cusp of this curve corresponds to the critical unlocking position and critical unlocking force of the landing gear.

[0094] Step 1025: Determine the critical unlocking position and critical unlocking force of the locking mechanism at the current number of iterations based on the bifurcation trajectory.

[0095] In practical applications, using the unlocking force as the control parameter, a second numerical extension is performed starting from the bifurcation point to generate a bifurcation trajectory. The critical unlocking force is determined by detecting the cusp of the bifurcation trajectory (step S4). The unlocking force corresponding to the cusp of the bifurcation trajectory is the theoretical value of the critical unlocking force of the landing gear lock mechanism.

[0096] Step S4: Using the numerical extension method, a second extension is performed starting from the bifurcation point with the locking / unlocking force as the control parameter to obtain a curve of the bifurcation point and the locking / unlocking force. Figure 5 As shown in the figure, the apex of this curve corresponds to the critical unlocking position and critical unlocking force of the landing gear, where M act It is the force of contraction and expansion.

[0097] As an optional implementation, step 1025 specifically includes:

[0098] The coordinates of the cusp point of the bifurcation trajectory are determined.

[0099] The cusp coordinates are used as the critical unlocking position and critical unlocking force of the locking mechanism at the current number of iterations.

[0100] In practical applications, the cusp coordinates of the bifurcation trajectory are extracted and the critical unlocking force is returned to the optimization module.

[0101] In this embodiment, the optimization goal is to calculate the unlocking force F u The lowest optimal spring stiffness, optimal spring original length and optimal installation position. The main framework of the optimization includes the optimization module and the extension calculation module. Each optimization iteration first generates a set of random optimization variable parameters based on the rules of the multi-island genetic algorithm and passes them to the extension calculation module. Based on the extension method, the target variable critical unlocking force F can be obtained. u Angle θ with the lock rod ov It is then passed back to the optimization module to detect whether the two iterations have converged, and enter the next iterative calculation until the convergence requirements are met.

[0102] Furthermore, the process of the optimization module includes initializing the population based on the multi-island genetic algorithm, generating a parameter group of variables, calculating individual fitness, selecting the next generation of individuals according to constraints, crossover, mutation, and migration. If the previous and next iterations do not meet the convergence conditions, it will return to generate the parameter group again until the requirements are met.

[0103] Furthermore, the process of the extension calculation module includes receiving the parameter group transmitted by the optimization module, and starting to extend the mechanical equilibrium equations of the landing gear retraction mechanism based on the numerical extension method, with the retraction torque as the control parameter; extending the retraction torque and the locking rod angle (i.e., the critical unlocking position) θ ov Curve, detect the bifurcation point of the curve; starting from the bifurcation point, with the unlocking force F u is the second extension parameter, and the trajectory curve of the bifurcation point is extended; the cusp of the bifurcation point trajectory curve is detected, and the F of the cusp is u ,θ ov Input to the optimization module.

[0104] Compared to existing methods for analyzing and optimizing the stability bifurcation of landing gear strut lock mechanisms, this application provides a bifurcation analysis method for quickly and efficiently obtaining the effect of parameters on the unlocking and unlocking performance of the lock mechanism, as well as a lock parameter optimization method for quickly and efficiently improving the unlocking and unlocking performance of the lock mechanism. This method can quickly and accurately analyze how the stability of the landing gear lock mechanism's dynamic model changes with system parameters, and, combined with bifurcation theory, can quickly determine the dynamic performance of the lock mechanism.

[0105] The technical features of the above embodiments can be combined arbitrarily. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0106] This document uses specific examples to illustrate the principles and implementation methods of this application. The description of the above examples is only intended to help understand the method and core concept of this application. At the same time, for those skilled in the art, based on the concept of this application, there may be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting this application.

Claims

1. A rapid analysis and optimization method for the stability of a landing gear strut lock mechanism, characterized in that: include: Based on the set value range of the lock mechanism parameter group, the lock mechanism parameter group under the current iteration number is generated by using the multi-island genetic algorithm; The lock mechanism parameter group includes spring stiffness, spring length and installation position; Based on the locking mechanism parameter group at the current iteration number and the mechanical equilibrium equation group of the landing gear retraction and extension mechanism, the critical unlocking position and critical unlocking force of the locking mechanism at the current iteration number are determined using the numerical continuation method; Determine whether the difference between the critical unlocking force at the current iteration number and the critical unlocking force at the previous iteration number is less than the convergence threshold; If yes, the locking mechanism parameter set under the current number of iterations is taken as the optimal locking mechanism parameter set; If not, proceed to the next iteration and return to "based on the set value range of the lock mechanism parameter group, use the multi-island genetic algorithm to generate the lock mechanism parameter group under the current iteration number".

2. The method for rapid analysis and optimization of landing gear strut lock mechanism stability according to claim 1, characterized in that: Based on the lock mechanism parameter group at the current iteration number and the mechanical equilibrium equation group of the landing gear retraction and extension mechanism, the critical unlocking position and critical unlocking force of the lock mechanism at the current iteration number are determined using the numerical continuation method. Specifically, the following steps are performed: Establish the mechanical equilibrium equations of the landing gear retraction and extension mechanism; According to the locking mechanism parameter group at the current iteration number, the mechanical equilibrium equation group is extended for the first time using the numerical extension method with the retraction and extension torque as the control parameter to obtain all equilibrium solutions of the mechanical equilibrium equation group; determining a bifurcation point based on the eigenvalues of the Jacobian matrix at the equilibrium solution; Using the unlocking force as a control parameter, a numerical continuation method is used to perform a second continuation starting from the bifurcation point to generate a bifurcation trajectory line; According to the bifurcation trajectory, a critical unlocking position and a critical unlocking force of the locking mechanism at the current number of iterations are determined.

3. The method for rapid analysis and optimization of landing gear strut lock mechanism stability according to claim 2, characterized in that: The mechanical equilibrium equations of the landing gear retraction mechanism are: Where k is the kth link of the landing gear retraction mechanism, F k is the force on the kth connecting rod; F joint,k is the constraint force at the joint, r k is the position vector of the force point relative to the center of mass; M ext,k is the external torque.

4. The method for rapid analysis and optimization of landing gear strut lock mechanism stability according to claim 2, characterized in that: Determining a bifurcation point based on the eigenvalues of the Jacobian matrix at the equilibrium solution includes: Determine whether the real parts of all eigenvalues of the Jacobian matrix at the equilibrium solution are less than 0; If so, the equilibrium solution is stable; If not, determining whether there is a real part equal to 0 among the real parts of all eigenvalues of the Jacobian matrix at the equilibrium solution; If so, the equilibrium solution is a critical point between stability and instability, and the critical point is used as a bifurcation point.

5. The method for rapid analysis and optimization of landing gear strut lock mechanism stability according to claim 1, characterized in that: Determining the critical unlocking position and critical unlocking force of the lock mechanism at the current number of iterations based on the bifurcation trajectory specifically includes: Determining the coordinates of the cusp of the bifurcation trajectory; The cusp coordinates are used as the critical unlocking position and critical unlocking force of the locking mechanism at the current number of iterations.

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