Parameter calculation method and system for landing gear buffer system nonlinear dynamic analysis model

Abstract

This invention discloses a method and system for calculating parameters of a nonlinear dynamic analysis model of a landing gear buffer system. The method includes: Step 1, obtaining the structural and physical parameters of the aircraft landing gear buffer and tires; using the chord-moment maximization method, dividing the buffer cylinder compression stroke, buffer cylinder compression speed, and tire vertical compression into multiple discrete segments; Step 2, constructing a nonlinear piecewise linear equivalent simplified model of the aircraft landing gear buffer system based on the structural and physical parameters of the aircraft landing gear buffer and tires, as well as the segmented intervals; Step 3, calculating the equivalent stiffness and equivalent damping coefficient of the aircraft landing gear buffer system based on the nonlinear piecewise linear equivalent simplified model of the aircraft landing gear buffer system. This invention can meet the dual requirements of computational accuracy and efficiency for airport bridge dynamic analysis during the entire process of aircraft taking off and landing on runway bridges, including low-speed taxiing on taxiway bridges and takeoff and landing.

Description

Technical Field

[0001] This invention belongs to the field of bridge engineering and is used for the dynamic performance analysis of aircraft-loaded bridges (including taxiway bridges and runway bridges) during the entire process of aircraft takeoff and landing. It relates to a method and system for calculating parameters of a nonlinear dynamic analysis model of a landing gear buffer system. Background Technology

[0002] In recent years, my country's civil aviation transportation industry has experienced rapid development, with passenger and cargo throughput and aircraft takeoffs and landings continuously increasing. Multi-runway operation has become a fundamental condition for ensuring air transport capacity. While airports face enormous construction demands, they also encounter the following severe challenges: On the one hand, limited by existing infrastructure and construction land, new runways or taxiways need to consider their intersections with existing or planned road / rail networks, rivers, and pipelines; on the other hand, due to the limitations of mountainous and coastal terrain, traditional methods such as high embankments and land reclamation involve large-scale engineering and environmental damage. In airport construction, taxiway bridges and runway bridges are important structural forms that adapt to complex terrain and embody the concept of green development. They can effectively reduce the amount of earthwork excavation and backfilling during airport construction and avoid road network or river diversions. Taxiway bridges and runway bridges have broad application prospects in mountainous and near-shore areas.

[0003] Aircraft-loaded bridges are characterized by small spans, high height-to-span and width-to-span ratios, and exhibit significant plate-shell effects in their stress behavior. The internal stress distribution is uneven, and the stress mechanisms are complex. Therefore, in-depth and systematic analysis of the dynamic performance of airport bridges under aircraft dynamic loads is crucial for ensuring the safe operation of these bridges. Aircraft loads acting on these bridges are characterized by large values, small distribution ranges, and complex dynamic characteristics. As the hub for load transfer between the aircraft and the runway bridge, the landing gear buffer system is not only the core device for absorbing impact energy and achieving vibration reduction, but also a key component ensuring the flight safety of passenger aircraft and the reliable service performance of the runway bridge. Throughout the aircraft landing process, the landing gear hydropneumatic buffers and tire stiffness and damping exhibit significant nonlinear time-varying characteristics and spatially uneven distribution. During the landing impact, the buffer stiffness exhibits a nonlinear hardening trend with the compression stroke, while the surge in compression rate causes a rapid increase in damping. During the taxiing and braking phase, the buffer's compression stroke and stiffness remain relatively stable, while the damping is adjusted in real time by the variable oil orifice to continuously reduce vibration of the aircraft. At the moment of takeoff, the buffer's rebound damping is significantly greater than the compression damping, effectively suppressing any possible aircraft bouncing.

[0004] Given the complexity of aircraft dynamic characteristics, early studies often employed simplified methods such as moving concentrated forces, harmonic loads, and two-mass linear spring-damped models to simulate aircraft dynamic loads and conduct vibration response analysis of airport pavements / bridges, in order to reduce the difficulty of analysis. While these methods provided some convenience for the study of forced vibrations of structures, they failed to consider the influence of key factors such as the nonlinear mechanical characteristics of aircraft landing gear on the dynamic response of bridges, thus making it difficult to accurately characterize the dynamic behavior of the entire interaction between aircraft and bridges. With the development of numerical simulation technology, refined three-dimensional modeling techniques for aircraft based on multibody dynamics have become increasingly mature. While this method can comprehensively reflect the vibration information of the aircraft body and has important reference value for aircraft design and the study of airport bridge dynamic characteristics, its complex modeling and high computational cost make it difficult to promote its application in bridge engineering.

[0005] As the above analysis shows, many scholars have achieved significant results in aircraft load model research. However, existing aircraft load models, due to oversimplification or complex modeling and large computational load, struggle to meet the dual requirements of computational accuracy and efficiency in bridge structural dynamics analysis. Therefore, there is an urgent need to study the nonlinear characteristics of aircraft landing gear buffers and establish a numerical calculation and analysis model applicable to the entire aircraft landing process, considering the nonlinear dynamic characteristics of the aircraft landing gear buffer system. Thus, based on the working principle of aircraft landing gear buffers and their structure and physical parameters, this paper proposes a rapid calculation method to satisfy the parameters of simplified dynamic analysis models for different aircraft types. Determining the nonlinear equivalent stiffness and damping parameters of the aircraft landing gear buffer system is particularly important. These parameters reflect the nonlinear dynamic behavior of the aircraft landing gear, providing the foundation for establishing a nonlinear multi-degree-of-freedom mass-spring-damping system model for aircraft loads. This model can then be applied to the dynamic analysis of aircraft-loaded bridges to ensure the safe design and operation of airport bridges and promote the sustainable and healthy development of aircraft-loaded bridges. Summary of the Invention

[0006] The purpose of this invention is to provide a method and system for calculating parameters of a nonlinear dynamic analysis model of a landing gear buffer system, so as to solve the problem that the nonlinear dynamic characteristics of the landing gear buffer system are not considered in the existing aircraft load model, thereby meeting the dual requirements of calculation accuracy and efficiency for airport bridge dynamic analysis.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0008] In a first aspect, the present invention provides a method for calculating parameters of a nonlinear dynamic analysis model of a landing gear buffer system, specifically including the following steps: Step 1: Obtain the structural and physical parameters of the aircraft landing gear buffers and tires, including: the initial pressure of the gas in the low-pressure chamber of the buffer. Initial pressure of gas in the high-pressure chamber of the buffer Buffer effective air pressure area Initial volume of the low-pressure chamber Initial volume of the high-pressure chamber Oil density , buffer effective pressure oil area Oil hole constriction coefficient Total area of ​​oil holes ; Buffer mass Tire quality Buffer cylinder compression stroke and compression speed Tire vertical deformation Tire inflation pressure Tire material damping ratio Maximum compression stroke of the shock absorber cylinder and maximum compression speed Maximum vertical compression of the tire The chord spacing maximization method is used to divide the shock absorber cylinder compression stroke, shock absorber cylinder compression speed, and tire vertical compression into multiple discrete points, thus obtaining multiple segmented intervals; specifically: Discrete points of the compression stroke of the buffer cylinder:

[0009] Discrete points of the compression velocity of the buffer cylinder:

[0010] Tire vertical compression segment discrete points:

[0011] Step two: Based on the structural and physical parameters of the aircraft landing gear buffer and tires obtained in step one, as well as the segmented intervals, construct a nonlinear piecewise linear equivalent simplified model of the aircraft landing gear buffer system, including the following stiffness and damping calculation formulas: (1) The calculation expression for the piecewise polygonal equivalent air spring stiffness considering the nonlinear dynamic characteristics of the aircraft landing gear buffer system is as follows if it is a single-cavity oil-gas buffer:

[0012] In the formula, For the first Each buffer cylinder compression stroke segmented interval The equivalent air spring stiffness inside. These are the start and end points of the j-th compression stroke interval of the buffer cylinder, respectively; It is an index for a variable process; This represents the initial pressure of the gas in the low-pressure chamber. This represents the initial volume of the low-pressure chamber. This refers to the effective pressure area of ​​the buffer. For a dual-chamber oil-gas type buffer, the following formula applies:

[0013] In the formula: ,in This is the volume of gas in the low-pressure chamber when the gas pressures in the low-pressure chamber and the high-pressure chamber are equal.

[0014] (2) The calculation expression for the piecewise polygonal equivalent damping coefficient of the buffer considering the nonlinear dynamic characteristics of the aircraft landing gear buffer system is shown in the following formula:

[0015] In the formula, For the first The equivalent damping coefficient of each buffer cylinder within the segmented compression speed range; and These are the end and start velocities of the velocity segment intervals, respectively. The structure constant of oil damping, .

[0016] (3) The calculation expression for the tire piecewise linear equivalent tire stiffness considering the nonlinear dynamic characteristics of the aircraft landing gear buffer system is shown in the following formula:

[0017] In the formula, For the first Equivalent tire stiffness within the tire compression deformation range; , The tires were in the 1st month respectively. Vertical deformation at the beginning and end of each compression deformation zone; Inflation pressure for the tires; , , and These are the parameters to be fitted.

[0018] (4) The calculation expression for the tire piecewise linear equivalent damping coefficient considering the nonlinear dynamic characteristics of the aircraft landing gear buffer system is shown in the following formula:

[0019] In the formula, For the first Tire compression deformation zone The equivalent damping coefficient within, The tires are respectively j The beginning and end points of each compression deformation zone; The damping ratio of the tire material; For tire quality; Inflate the tires to the specified pressure.

[0020] Step 3: Based on the nonlinear segmented piecewise linear equivalent simplified model of the aircraft landing gear buffer system constructed in Step 2, calculate the equivalent stiffness and equivalent damping coefficient of the aircraft landing gear buffer system to obtain the equivalent air spring stiffness of each segment of the buffer cylinder compression stroke range, the equivalent damping coefficient of each segment of the buffer cylinder compression speed range, and the equivalent tire stiffness and equivalent damping coefficient of each tire compression deformation range.

[0021] Furthermore, the initial gas pressure in the low-pressure chamber of the buffer... Initial pressure of gas in the high-pressure chamber of the buffer (Dual-chamber oil-pneumatic shock absorber), tire inflation pressure All measurements were obtained using pressure sensors; the effective pressure area of ​​the buffer... , buffer effective pressure oil area Initial volume of the low-pressure chamber Initial volume of the high-pressure chamber All were calculated using laser ranging; the compression stroke of the buffer cylinder was obtained. and compression speed Vertical deformation of the tire The tire material damping ratio is measured under static or dynamic load using a displacement sensor or laser rangefinder. Take 0.2; the polyvariant process index It is 1.2; Secondly, this invention provides a method for calculating parameters of a nonlinear dynamic analysis model of a landing gear buffer system. This method differs from step two of the method in that it constructs the model based on the latest theoretical calculation formulas for the air spring force, hydraulic damping force, tire vertical force, and tire damping force of various types of aircraft buffers. Specifically, based on the structural and physical parameters and segmented intervals of the aircraft landing gear buffer and tires obtained in step one, the model is constructed using the latest theoretical calculation formulas for the air spring force, hydraulic damping force, tire vertical force, and tire damping force of various types of aircraft buffers. The method employs the chord spacing maximization method and the energy equivalence principle to construct a simplified nonlinear piecewise polygonal equivalent model of the aircraft landing gear buffer system.

[0022] Thirdly, the present invention provides a general-purpose calculation device for the parameters of a nonlinear dynamic analysis model of an aircraft landing gear buffer system, comprising a parameter acquisition module, a calculation model construction module, and a parameter calculation module; wherein: The parameter acquisition module is used to perform the following functions: acquire the structural and physical parameters of the aircraft landing gear buffers and tires, including: the initial pressure of the gas in the low-pressure chamber of the buffer. Initial pressure of gas in the high-pressure chamber of the buffer Buffer effective air pressure area Initial volume of the low-pressure chamber Initial volume of the high-pressure chamber Oil density , buffer effective pressure oil area Oil hole constriction coefficient Total area of ​​oil holes ; Buffer mass Tire quality Buffer cylinder compression stroke and compression speed Tire vertical deformation Tire inflation pressure Tire material damping ratio Maximum compression stroke of the shock absorber cylinder and maximum compression speed Maximum vertical compression of the tire The chord spacing maximization method is used to divide the shock absorber cylinder compression stroke, shock absorber cylinder compression speed, and tire vertical compression into multiple discrete points, thus obtaining multiple segmented intervals; specifically: Discrete points of the compression stroke of the buffer cylinder:

[0023] Discrete points of the compression velocity of the buffer cylinder:

[0024] Tire vertical compression segment discrete points:

[0025] The computational model construction module is used to implement the following functions: Based on the structural and physical parameters and segmented intervals of the aircraft landing gear buffer and tires obtained by the parameter acquisition module, it constructs a nonlinear piecewise linear equivalent simplified model of the aircraft landing gear buffer system, including the following stiffness and damping calculation formulas: (1) The calculation expression for the piecewise polygonal equivalent air spring stiffness considering the nonlinear dynamic characteristics of the aircraft landing gear buffer system is as follows if it is a single-cavity oil-gas buffer:

[0026] In the formula, For the first Each buffer cylinder compression stroke segmented interval The equivalent air spring stiffness inside. These are the start and end points of the j-th compression stroke interval of the buffer cylinder, respectively; It is an index for a variable process; This represents the initial pressure of the gas in the low-pressure chamber. This represents the initial volume of the low-pressure chamber. This refers to the effective pressure area of ​​the buffer. For a dual-chamber oil-gas type buffer, the following formula applies:

[0027] In the formula: ,in This is the volume of gas in the low-pressure chamber when the gas pressures in the low-pressure chamber and the high-pressure chamber are equal.

[0028] (2) The calculation expression for the piecewise polygonal equivalent damping coefficient of the buffer considering the nonlinear dynamic characteristics of the aircraft landing gear buffer system is shown in the following formula:

[0029] In the formula, For the first The equivalent damping coefficient of each buffer cylinder within the segmented compression speed range; and These are the end and start velocities of the velocity segment intervals, respectively. The structure constant of oil damping, .

[0030] (3) The calculation expression for the tire piecewise linear equivalent tire stiffness considering the nonlinear dynamic characteristics of the aircraft landing gear buffer system is shown in the following formula:

[0031] In the formula, For the first Equivalent tire stiffness within the tire compression deformation range; , The tires were in the 1st month respectively. Vertical deformation at the beginning and end of each compression deformation zone; Inflation pressure for the tires; , , and These are the parameters to be fitted.

[0032] (4) The calculation expression for the tire piecewise linear equivalent damping coefficient considering the nonlinear dynamic characteristics of the aircraft landing gear buffer system is shown in the following formula:

[0033] In the formula, For the first Tire compression deformation zone The equivalent damping coefficient within, The tires are respectively j The beginning and end points of each compression deformation zone; The damping ratio of the tire material; For tire quality; Inflate the tires to the specified pressure.

[0034] The parameter calculation module is used to perform the following functions: based on the nonlinear piecewise linear equivalent simplified model of the aircraft landing gear buffer system constructed by the calculation model construction module, the equivalent stiffness and equivalent damping coefficient of the aircraft landing gear buffer system are calculated, and the equivalent air spring stiffness, equivalent damping coefficient of each segment of the buffer cylinder compression stroke range, and equivalent tire stiffness and equivalent damping coefficient of each segment of the tire compression deformation range are obtained.

[0035] Fourthly, the present invention provides an electronic device, the electronic device comprising: Memory, used to store executable instructions; A processor, when executing executable instructions or computer programs stored in the memory, implements the method of the present invention described above.

[0036] Fifthly, the present invention provides a computer-readable storage medium storing executable instructions or a computer program, characterized in that the executable instructions, when executed by a processor, implement the method of the present invention described above.

[0037] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention nonlinearly segments and transforms the stiffness and damping of aircraft landing gear into piecewise linear models. Based on the chord-moment maximization method and the energy equivalence principle, it establishes a multi-segment piecewise linear model that considers the nonlinear dynamic characteristics of the landing gear buffer system throughout the entire takeoff and landing process, relating it to the landing gear structure and physical parameters. This solves the problem of distortion in the dynamic characteristics of a single linear model of the aircraft landing gear buffer system during takeoff and landing, providing a scientific and efficient general calculation method for the unknown stiffness and parameters of existing nonlinear aircraft landing gear models. This method can reliably and accurately calculate the unknown stiffness and damping parameters of nonlinear buffers and wheels in the load models of various aircraft models. Through rigorous theoretical derivation, this method can reliably and accurately calculate the unknown nonlinear stiffness and damping parameters of the buffer system in the aircraft load model required for the dynamic analysis of airport bridge structures, without requiring complex nonlinear numerical iteration solutions. Compared with existing refined numerical simulation methods for aircraft load models, this significantly improves the calculation efficiency of unknown parameters for airport bridge dynamic analysis throughout the entire takeoff and landing process.

[0038] In summary, the nonlinear unknown parameters of the aircraft landing gear buffer system constructed in this invention provide a reliable parameter input basis for the construction of existing simplified analysis models of aircraft dynamics. It can meet the dual requirements of computational accuracy and efficiency for airport bridge dynamic analysis during the entire process of aircraft taking off and landing on runway bridges at low speeds on taxiway bridges. Attached Figure Description

[0039] Figure 1 This is a simplified diagram of a single-chamber and dual-chamber hydropneumatic buffer model of an aircraft landing gear. (The diagram shows...) a —Low-pressure air chamber; b —Oil cavity; c —Oil return hole; d —Oil inlet; e —Oil return chamber; f —Cylinder block; g —plunger; h -piston; i —High-pressure air chamber.

[0040] Figure 2 This is a schematic diagram of the compression stroke of a single-chamber oil-gas buffer model and a wheel model. (See diagram:) S —Buffer compression stroke; —Buffer compression speed; —Tire vertical compression.

[0041] The technical solution of the present invention will be further explained and described below with reference to the accompanying drawings and specific embodiments. Detailed Implementation

[0042] Combination Figure 1 and Figure 2 The method for calculating parameters of the nonlinear dynamic analysis model of the landing gear buffer system provided in this invention is as follows: Step 1: Obtain the structural and physical parameters of the aircraft landing gear buffers and tires, including: the initial pressure of the gas in the low-pressure chamber of the buffer. Initial pressure of gas in the high-pressure chamber of the buffer (Dual-chamber oil-gas buffer), effective pressure area of ​​the buffer Initial volume of the low-pressure chamber Initial volume of the high-pressure chamber (Dual-chamber oil-gas buffer), oil density , buffer effective pressure oil area Oil hole constriction coefficient Total area of ​​oil holes ; Buffer mass Tire quality Buffer cylinder compression stroke and compression speed Tire vertical deformation Tire inflation pressure Tire material resistance ratio The maximum compression stroke of the buffer cylinder. and maximum compression speed Maximum vertical compression of the tire The compression stroke of the buffer cylinder, the compression speed of the buffer cylinder, and the vertical compression of the tire are divided into multiple discrete points to obtain multiple segmented intervals. Specifically, the discrete points of the compression stroke of the buffer cylinder: (1) Discrete points of the compression velocity of the buffer cylinder: (2) Tire vertical compression segment discrete points: (3) The methods for measuring or obtaining each parameter are as follows: (1) Initial pressure of gas in the low-pressure chamber of the buffer Initial pressure of gas in the high-pressure chamber of the buffer (Dual-chamber oil-gas type shock absorber): The initial pressure of the air chamber is measured by a pressure sensor through a pre-reserved pressure measuring port on the air chamber of the aircraft landing gear shock absorber. If the air chamber of the shock absorber is not equipped with a pressure measuring port, a hole can be opened in the shell of the air chamber of the aircraft landing gear shock absorber to install a pressure sensor and then measure the initial pressure of the air chamber.

[0043] (2) Effective air pressure area of ​​the buffer Calculations can be made by examining the structure and physical parameters of the buffer or by using measuring instruments (such as laser rangefinders), both of which are common methods in this field.

[0044] (3) Initial volume of the low-pressure chamber Initial volume of the high-pressure chamber (Dual-cavity oil-gas buffer): Calculations based on the buffer's structural parameters or by measuring instruments (such as laser rangefinders) are common methods in this field.

[0045] (4) Oil density The density is measured using a hydrometer under standard conditions and according to standard measurement methods. The hydrometer can be installed in the oil pipe or oil circuit system connected to the oil reservoir of the oil buffer to measure the oil density, thereby avoiding interference with the normal operation of the buffer.

[0046] (5) Effective oil pressure area of ​​the buffer The calculation is obtained by combining the construction parameters of the buffer, or by measuring and calculating using measuring instruments (such as laser rangefinders), both of which are common methods in this field.

[0047] (6) Oil hole constriction coefficient : Obtained through measurements and calculations conducted via fluid dynamics experiments.

[0048] (7) Total area of ​​oil holes The method is to calculate the weighted average based on the area and number of the main oil hole and the return oil hole, or to calculate the weighted average based on the measurement of the geometric parameters of the oil hole using measuring instruments (such as microscope rangefinders). Both of these are common methods in this field.

[0049] (8) Buffer mass and tire quality This can be obtained by measurement using a precision electronic scale, which is a common method in this field.

[0050] (9) Tire inflation pressure Measuring tire inflation pressure using pressure sensors on the valve stems of aircraft tires is a common practice in this field.

[0051] (10) Vertical deformation of the tire The deformation of a tire is measured under static or dynamic loads using a displacement sensor or laser rangefinder.

[0052] (11) Polymorphism index The value is obtained by referring to a table or by experimental measurement based on the thermodynamic state of the gas in the buffer. For the rapid compression process of the air spring in this invention, the conventional value in the art is between 1.0 and 1.4, and it is taken as 1.2 in this invention.

[0053] (12) Tire material damping ratio The value is obtained by consulting relevant rubber tire material manuals or by conducting tire damping ratio tests, both of which are common methods in the field. The value is generally taken as 0.1 to 0.3, and is taken as 0.2 in this invention.

[0054] (13) Maximum compression stroke of the shock absorber cylinder Maximum compression speed and the maximum vertical compression of the wheels The method is to determine the target aircraft's structural design parameters, landing weight, and dynamic simulation or measured historical data for special operating conditions (such as hard landing, high-speed taxiing, etc.), which is a conventional approach in this field.

[0055] Step 2: Based on the structural and physical parameters of the aircraft landing gear buffer and wheels obtained in Step 1, derive and establish a nonlinear piecewise linear equivalent simplified model of the aircraft landing gear buffer system: 1. Construction of Nonlinear Stiffness Model for Aircraft Landing Gear Buffer (1) Axial force of aircraft landing gear buffer It is caused by air spring force Oil damping force Buffer structure limiting force and internal friction Composition. During the normal operation phase of the buffer, the structural limiting force... Meanwhile, due to the internal friction of the buffer Generally small, the structural limiting force of the buffer can usually be ignored. and internal friction Therefore, the axial force of the aircraft landing gear buffer It can be represented as: (4) (2) Regarding the axial force of the buffer in equation (4) The composition, considering the working principle of landing gear buffers (single-chamber and double-chamber), includes the air spring force. The following formula can be used for calculation: Single-chamber oil-gas buffer (5) Dual-chamber oil-gas buffer (6) In the formula: This refers to the compression stroke of the buffer cylinder. This refers to the critical compression stroke of the buffer cylinder, which is the compression stroke of the buffer cylinder when the gas pressure in the low-pressure chamber is equal to that in the high-pressure chamber. ; This represents the initial pressure of the gas in the low-pressure chamber. This represents the initial pressure of the gas in the high-pressure chamber; It is the volume of gas in the low-pressure chamber when the gas pressure in the low-pressure chamber is equal to that in the high-pressure chamber; This represents the initial volume of the low-pressure chamber. This represents the initial volume of the high-pressure chamber. This refers to the effective pressure area of ​​the buffer. As a polytropic index, during the adiabatic process =1.4, during isothermal processes =1.0; Atmospheric pressure.

[0056] (3) As can be seen from equations (5) to (6), the air spring stiffness of the buffer has extremely strong nonlinearity, which is difficult to be directly applied to the analysis and research of aircraft dynamics. In order to avoid distortion of the buffer stiffness in different working stages by using a single linearized buffer stiffness, the air spring force-compression stroke in the entire compression stroke is divided into multiple curves, as shown in equation (1), and it is ensured that the air spring force of each curve has a good linear correlation with its compression stroke.

[0057] (4) Introduce the "farthest point criterion" (i.e., the chord distance maximization method) to measure the distance from the origin on the air spring force-compression stroke curve. With the maximum compression stroke point The point with the largest perpendicular distance between the two lines is defined as the first segment point. Its coordinates on the air spring force-compression stroke curve are: At this time, vertical distance The calculation formula is as follows, and the calculation is performed. The value of .

[0058] (7) (5) Using the chord distance maximization method, the distance from the origin on the air spring force-compression stroke curve is calculated. With the first segment point The point with the largest perpendicular distance between the two lines is defined as the second segment point. At this time, the maximum chord spacing is The method of maximizing the chord distance is used to measure the distance from the first segment point on the force-compression stroke curve of the air spring. With the maximum compression stroke point The point with the largest perpendicular distance between the two lines is defined as the third segment point. At this time, the maximum chord spacing is And calculate separately. Yu The value of .

[0059] (6) Continue to use the chord pitch maximization method to adjust the distance from the origin on the air spring force-compression stroke curve. With the second segment point The point with the largest perpendicular distance between the two lines is defined as the fourth segment point. At this time, the maximum chord spacing is The method of maximizing chord distance is used to measure the distance from the third segment point on the air spring force-compression stroke curve. With the maximum compression stroke point The point with the largest perpendicular distance between the two lines is defined as the fifth segment point. At this time, the maximum chord spacing is This cycle repeats until... It will be less than a certain limit, such as 0.1; and will , , … Sort by ascending order, assuming Then take .

[0060] (7) According to the principle of energy equivalence, in any... Each buffer travel segment interval Inside, among which linearized spring stiffness Both nonlinear air springs and nonlinear air springs have the same elastic potential energy within the same buffer compression stroke.

[0061] (8) Taking a single-chamber oil-gas buffer as an example, the air spring force described in formula (5) The elastic potential energy stored within this segmented interval is: (8) Integrating equation (8), we get: (9) (9) In the interval Piecewise linearized stiffness Since is a constant, its corresponding elastic potential energy is: (10) (10) According to the principle of energy equivalence, we have Combining equations (9) and (10), we get: (11) (11) The linearized stiffness of each segmented interval can be solved by equation (11). And we get the following formula: (12) Similarly, by analogy with equations (5) to (12), the linearized stiffness of each segment interval of the dual-cavity oil-gas buffer can also be calculated. As shown in equation (13), the detailed derivation process will not be repeated here.

[0062] (13) In the formula: .

[0063] 2. Construction of Nonlinear Damping Model for Aircraft Landing Gear Buffer (12) Regarding the oil damping force in equation (4) Assuming the oil is an incompressible fluid, the oil damping force can be calculated using the following formula: (14) In the formula: The density of the oil; This refers to the effective pressure oil area of ​​the buffer. Let be the area of ​​the oil hole. Here, it is assumed that the area of ​​the oil hole is a constant value during both forward and reverse strokes. The oil hole constriction coefficient; Let be the compression speed of the buffer cylinder, assuming downward compression of the buffer cylinder is positive.

[0064] (13) Let the oil damping structural constant be... Then equation (14) can be transformed into: (15) (14) As can be seen from equation (15), the damping force of the buffer oil also has strong nonlinearity, which is difficult to be directly applied to the analysis and research of aircraft dynamics. In order to avoid distortion in different working stages by using a single damping coefficient of the buffer oil, the oil damping force-compression speed in the entire compression stroke is divided into multiple curves, as shown in equation (2), and it is ensured that the oil damping force of each curve has a good linear correlation with its compression speed.

[0065] (15) Introduce the "farthest point criterion" (i.e., the chord distance maximization method) to measure the distance from the origin on the oil damping force-compression speed curve. With the point of maximum compression speed The point with the largest perpendicular distance between the two lines is defined as the first segment point. Its coordinates on the oil damping force-compression speed curve are At this time, vertical distance The calculation formula is as follows, and the calculation is performed. The value of .

[0066] (16) (16) Using the chord moment maximization method, the oil damping force-compression speed curve is located at a distance from the origin. With the first segment point The point with the largest perpendicular distance between the two lines is defined as the second segment point. At this time, the maximum chord spacing is The method of maximizing chord distance is used to measure the distance from the first segment point on the oil damping force-compression speed curve. With the maximum compression stroke point The point with the largest perpendicular distance between the two lines is defined as the third segment point. At this time, the maximum chord spacing is And calculate separately. Yu The value of .

[0067] (17) Repeat this process until... Less than a certain limit (where (e.g., up to 0.1); and will , , … Sort by ascending order, assuming Then take .

[0068] (18) The nonlinear equation of the oil damping force is linearized piecewise, that is, in any... Each buffer travel segment interval Inside, among which The integral area of ​​the real nonlinear damping force is equal to the integral area of ​​the linear equivalent damping force.

[0069] (19) The damping force of the buffer oil described in equation (15) in the segmented interval The integral area within is: (17) Integrating equation (17), we get: (18) (20) Assume that in the interval The equivalent linear damping coefficient of the internal oil fluid is Then the equivalent damping force of the oil in this interval is (in The integral area of ​​) is: (19) (21) According to Combining equations (18) and (19), we get: (20) (22) The linearized stiffness of each segmented interval can be solved by equation (20). And we get the following formula: (twenty one) 3. Construction of Nonlinear Stiffness Model for Aircraft Tires (23) Establish the relationship between aircraft tire stiffness and damping and their internal structural parameters using a method similar to the one described above. Assume the tire mass is... inflation pressure Vertical deformation The vertical force of the tires. It can be calculated using equation (22): (twenty two) In the formula, , , and The parameters to be fitted are determined by combining the structural design parameters of the target aircraft and the dynamic simulation or measured historical data of special operating conditions (such as hard landing, high-speed taxiing, etc.).

[0070] (24) From equation (22), it can be seen that when When the value is constant, the vertical stiffness of the aircraft tire still exhibits strong nonlinearity, making it difficult to directly apply to aircraft dynamics analysis. In order to avoid distortion in different working stages by using a single linearized tire stiffness, the vertical force-compression deformation within the entire tire compression deformation is divided into multiple curves, as shown in equation (3). It is also ensured that the vertical force of the tire in each curve corresponds to its compression deformation. It exhibits a good linear correlation.

[0071] (25) Introduce the "farthest point criterion" (i.e., the chord distance maximization method) to measure the distance from the origin on the tire vertical force-compression deformation curve. With the maximum compression stroke point The point with the largest perpendicular distance between the two lines is defined as the first segment point. Its coordinates on the vertical force-compression deformation curve are: At this time, vertical distance The calculation formula is as follows, and the calculation is performed. The value of .

[0072] (twenty three) (26) Using the chord maximization method, the distance from the origin on the tire vertical force-compression deformation curve is calculated. With the first segment point The point with the largest perpendicular distance between the two lines is defined as the second segment point. At this time, the maximum chord spacing is The method of maximizing chord distance is used to measure the distance from the first segment point on the tire vertical force-compression deformation curve. Point of maximum compressive deformation The point with the largest perpendicular distance between the two lines is defined as the third segment point. At this time, the maximum chord spacing is And calculate separately. Yu The value of .

[0073] (27) This process is repeated until... (in The value must be less than a certain limit, such as 0.1; and... , , … Sort by ascending order, assuming Then take .

[0074] (28) Based on the principle of energy equivalence, the complex nonlinear equation of the vertical force of the tire is linearized piecewise, that is, in any... Tire compression stroke segmentation range Inside, among which linearized tire stiffness Nonlinear tire stiffness has the same energy over the same compression stroke.

[0075] (29) Vertical force of tire In this segmented interval The nonlinear elastic potential energy within is: (twenty four) Integrating equation (24), the nonlinear elastic potential energy is obtained as follows: (25) (30) In the interval Internal piecewise linearized stiffness Since is a constant, its corresponding elastic potential energy is: (26) (31) According to the principle of energy equivalence, we have Combining equations (25) and (26), we get: (27) (32) The linearized stiffness of the tire in each segment can be solved by equation (27). And we get the following formula: (28) 4. Construction of Nonlinear Damping Model for Aircraft Tires (33) Existing research has shown that tire inflation pressure, compression, and compression deformation rate have relatively little impact on the nonlinear characteristics of damping. Therefore, in conjunction with structural dynamics, segmented damping of aircraft tires... It can be represented as: (29) In the formula, The damping ratio of the rubber material in aircraft tires is typically taken as 0.1 to 0.3. For tire quality.

[0076] (34) will Substituting the value and equation (28) into equation (29), we can obtain the segmented equivalent damping of the aircraft tire: (30) Step 3, Application of Aircraft-Runway Bridge Interaction Dynamics Analysis: Based on the calculation formulas derived in Step 2, a relevant analysis program is developed. The landing gear buffer system structure and physical parameters of specific aircraft models (such as A380, A320, B737, C919, etc.) are substituted into the program. The program automatically calculates and generates stiffness matrix arrays and damping matrix arrays corresponding to different displacement and velocity ranges. During the dynamic analysis of the aircraft-runway bridge coupled system, a mass-pieced spring-pieced damping system is constructed based on the above parameters (including buffer mass, buffer equivalent stiffness and equivalent damping coefficient, tire mass, tire equivalent stiffness and equivalent damping coefficient). Within each integration step of the simulation calculation, the software extracts the relative displacement and velocity of the current landing gear buffer system in real time, automatically finding and calling the piecewise linearized stiffness of the buffer and tire within the corresponding segmented interval. , and damping coefficient , It participates in solving matrix assembly and calculation.

[0077] Because the method of this invention avoids the distortion of numerical simulation results caused by using a single linear stiffness and damping when the buffer and wheels are deeply compressed, and avoids the iterative divergence caused by traditional nonlinear differentiation, it can accurately and efficiently calculate the stress, deformation and other dynamic responses of airport runway bridges during the entire process of takeoff (high-speed taxiing) and landing (instantaneous impact and taxiing braking) of various types of aircraft, and can also accurately capture the dynamic response characteristics of aircraft buffers and wheels.

[0078] In summary, this invention nonlinearly segments and transforms the stiffness and damping of aircraft landing gear into piecewise linear equations. It then employs the chord-moment maximization method and the energy equivalence principle to further transform these nonlinearly segmented and piecewise linear equations, constructing a simplified nonlinear piecewise linear equivalent model of the aircraft landing gear buffer system. The equivalent air spring stiffness, equivalent damping coefficient, and equivalent tire stiffness and equivalent damping coefficient for each segment of the buffer cylinder's compression stroke range, as well as for each segment of the tire's compression deformation range, are solved. This proposed solution overcomes the following difficulties: ① The complexity of the nonlinear characteristics of the aircraft landing gear buffer system: The nonlinear stiffness characteristics of the landing gear air springs and wheels are affected by factors such as compression. If a single linearization parameter is used, it will mask the phenomenon of a sharp increase in stiffness in the deep compression section. The landing gear hydraulic damping coefficient and the wheel damping coefficient are affected by compression and compression speed. Using a single linearization for them will also cause distortion of the dynamic behavior of the aircraft landing gear buffer system. That is, the equivalent method of single linearization of stiffness and damping is difficult to meet the calculation accuracy requirements of the aircraft throughout the takeoff and landing process. To accurately simplify the stiffness and damping parameters into a continuous piecewise linear model, it is necessary to overcome the problem of complex nonlinear constitutive relations of the aircraft landing gear buffer system. That is, based on the load-displacement or load-velocity relationship curves of air spring force, hydraulic damping force, tire vertical force and its damping force, and considering the working principle of single-cavity and dual-cavity hydraulic buffers, the piecewise linear interval of stiffness and damping is reasonably divided by the chord spacing maximization method.

[0079] ② Application of Energy Equivalence and Piecewise Linearization: The energy storage and dissipation process of an aircraft landing gear buffer system involves the dynamic coupling process of gas expansion and compression. This requires accurate modeling and integration of the energy changes of the aircraft landing gear buffer system under different buffer configurations (single-cavity, dual-cavity) and operating conditions. Furthermore, to achieve high-precision piecewise linearization of stiffness and damping, the energy equivalence principle needs to be used to unify the energy changes of the nonlinear system with the equivalent energy storage and dissipation of piecewise intervals. Achieving this requires overcoming complex integration, point selection strategies using the chord moment maximization method, and the continuity design of piecewise linearization of stiffness and damping parameters.

[0080] The nonlinear piecewise linear stiffness and damping parameters determined by the method of this invention can avoid complex finite element nonlinear iterations while ensuring accuracy, and can meet the requirements for rapid analytical calculation of stiffness and damping in simplified dynamic models of different aircraft models. Furthermore, it can be used for the dynamic study of aircraft-loaded bridges, and its application in the dynamic analysis of aircraft-loaded bridges is as follows: ① Establish a mass-segmented spring-segmented damping model: Construct a simplified aircraft load model using the derived expressions for the stiffness and damping parameters of each segment of the buffer and wheel. Characterize the nonlinear dynamic characteristics of the aircraft during takeoff and landing by the dynamic behavior of the mass-segmented spring-segmented damping system.

[0081] ② Construct an aircraft-bridge coupled system: Combine the finite element model of a long-span taxiway or runway bridge with the simplified aircraft load model described above to form an interactive dynamic coupled system. The bridge model should include all structural elements, loads, and support boundary conditions to accurately reflect the static and dynamic characteristics of the airport bridge.

[0082] ③ Aircraft-Bridge Interaction System Dynamics Simulation: Transient dynamics numerical simulation of the aircraft-bridge interaction system is conducted. The calculation program extracts the relative displacement and velocity of the current aircraft's buffer system in real time, automatically calls the stiffness and damping parameters of the corresponding segmented intervals, and precisely controls the actual nonlinear dynamic action of the aircraft landing gear buffer system on the airport bridge during the entire takeoff and landing process of various aircraft types. It can quickly and accurately calculate the stress, deformation, and other dynamic responses of the airport bridge during the entire takeoff (high-speed taxiing) and landing (instantaneous impact, taxiing braking) process, thereby comprehensively evaluating the dynamic performance of the airport bridge.

Claims

1. A method and system for calculating parameters of a nonlinear dynamic analysis model of a landing gear buffer system, characterized in that, Includes the following steps: Step 1: Obtain the structural and physical parameters of the aircraft landing gear buffers and tires, including: the initial pressure of the gas in the low-pressure chamber of the buffer. Initial pressure of gas in the high-pressure chamber of the buffer Buffer effective air pressure area Initial volume of the low-pressure chamber Initial volume of the high-pressure chamber Oil density , buffer effective pressure oil area Oil hole constriction coefficient Total area of ​​oil holes ; Buffer mass Tire quality Buffer cylinder compression stroke and compression speed Tire vertical deformation Tire inflation pressure Tire material damping ratio Maximum compression stroke of the shock absorber cylinder and maximum compression speed Maximum vertical compression of the tire The chord spacing maximization method is used to divide the shock absorber cylinder compression stroke, shock absorber cylinder compression speed, and tire vertical compression into multiple discrete points, thus obtaining multiple segmented intervals; specifically: Discrete points of the compression stroke of the buffer cylinder: Discrete points of the compression velocity of the buffer cylinder: Tire vertical compression segment discrete points: ； Step two: Based on the structural and physical parameters of the aircraft landing gear buffer and tires obtained in step one, as well as the segmented intervals, construct a nonlinear piecewise linear equivalent simplified model of the aircraft landing gear buffer system, including the following stiffness and damping calculation formulas: (1) The calculation expression for the piecewise polygonal equivalent air spring stiffness considering the nonlinear dynamic characteristics of the aircraft landing gear buffer system is as follows if it is a single-cavity oil-gas buffer: In the formula, For the first Each buffer cylinder compression stroke segmented interval The equivalent air spring stiffness inside. These are the start and end points of the j-th compression stroke interval of the buffer cylinder, respectively; It is an index for a variable process; This represents the initial pressure of the gas in the low-pressure chamber. This represents the initial volume of the low-pressure chamber. This refers to the effective pressure area of ​​the buffer. For a dual-chamber oil-gas type buffer, the following formula applies: In the formula: ,in This represents the volume of gas in the low-pressure chamber when the gas pressures in the low-pressure chamber and the high-pressure chamber are equal. (2) The calculation expression for the piecewise polygonal equivalent damping coefficient of the buffer considering the nonlinear dynamic characteristics of the aircraft landing gear buffer system is shown in the following formula: In the formula, For the first The equivalent damping coefficient of each buffer cylinder within the segmented compression speed range; and These are the end and starting velocities of the velocity segment intervals, respectively. The structure constant of oil damping, ; (3) The calculation expression for the segmented polygonal equivalent tire stiffness considering the nonlinear dynamic characteristics of the aircraft landing gear buffer system is shown in the following formula: In the formula, For the first Equivalent tire stiffness within the tire compression deformation range; , The tires were in the 1st month respectively. Vertical deformation at the beginning and end of each compression deformation zone; Inflation pressure for the tires; , , and The parameters to be fitted; (4) The calculation expression for the tire piecewise linear equivalent damping coefficient considering the nonlinear dynamic characteristics of the aircraft landing gear buffer system is shown in the following formula: In the formula, For the first Tire compression deformation zone The equivalent damping coefficient within, The tires are respectively j The beginning and end points of each compression deformation zone; The damping ratio of the tire material; For tire quality; Inflation pressure for the tires; Step 3: Based on the nonlinear segmented piecewise linear equivalent simplified model of the aircraft landing gear buffer system constructed in Step 2, calculate the equivalent stiffness and equivalent damping coefficient of the aircraft landing gear buffer system to obtain the equivalent air spring stiffness of each segment of the buffer cylinder compression stroke range, the equivalent damping coefficient of each segment of the buffer cylinder compression speed range, and the equivalent tire stiffness and equivalent damping coefficient of each tire compression deformation range.

2. The method and system for calculating parameters of the nonlinear dynamic analysis model of the landing gear buffer system as described in claim 1, characterized in that, The initial pressure of the gas in the low-pressure chamber of the buffer Initial pressure of gas in the high-pressure chamber of the buffer Tire inflation pressure All measurements were obtained using pressure sensors; the effective pressure area of ​​the buffer... , buffer effective pressure oil area Initial volume of the low-pressure chamber Initial volume of the high-pressure chamber All were calculated using laser ranging; the compression stroke of the buffer cylinder was obtained. and compression speed Vertical deformation of the tire Measurements are obtained using displacement sensors or laser rangefinders under static or dynamic loads.

3. The method and system for calculating parameters of the nonlinear dynamic analysis model of the landing gear buffer system as described in claim 1, characterized in that, The polyvariable process index Let it be 1.

2.

4. The method and system for calculating parameters of the nonlinear dynamic analysis model of the landing gear buffer system as described in claim 1, characterized in that, The damping ratio of the tire material Take 0.

2.

5. The method for calculating parameters of the nonlinear dynamic analysis model of the landing gear buffer system as described in claim 1, characterized in that, Step two involves the following replacement: Based on the structure and physical parameters of the aircraft landing gear buffer and tires obtained in Step one, as well as the segmented intervals, and according to the latest theoretical calculation formulas for the air spring force, hydraulic damping force, tire vertical force, and tire damping force of various types of aircraft buffers, a nonlinear segmented piecewise linear equivalent simplified model of the aircraft landing gear buffer system is constructed using the chord pitch maximization method and the energy equivalence principle.

6. A parameter calculation system for a nonlinear dynamic analysis model of a landing gear buffer system, characterized in that, The module comprises a parameter acquisition module, a computational model construction module, and a parameter calculation module; among which: The parameter acquisition module is used to perform the following functions: acquire the structural and physical parameters of the aircraft landing gear buffers and tires, including: the initial pressure of the gas in the low-pressure chamber of the buffer. Initial pressure of gas in the high-pressure chamber of the buffer Buffer effective air pressure area Initial volume of the low-pressure chamber Initial volume of the high-pressure chamber Oil density , buffer effective pressure oil area Oil hole constriction coefficient Total area of ​​oil holes ; Buffer mass Tire quality Buffer cylinder compression stroke and compression speed Tire vertical deformation Tire inflation pressure Tire material damping ratio Maximum compression stroke of the shock absorber cylinder and maximum compression speed Maximum vertical compression of the tire The chord spacing maximization method is used to divide the shock absorber cylinder compression stroke, shock absorber cylinder compression speed, and tire vertical compression into multiple discrete points, thus obtaining multiple segmented intervals; specifically: Discrete points of the compression stroke of the buffer cylinder: Discrete points of the compression velocity of the buffer cylinder: Tire vertical compression segment discrete points: ； The computational model construction module is used to implement the following functions: Based on the structural and physical parameters and segmented intervals of the aircraft landing gear buffer and tires obtained by the parameter acquisition module, it constructs a nonlinear piecewise linear equivalent simplified model of the aircraft landing gear buffer system, including the following stiffness and damping calculation formulas: (1) The calculation expression for the piecewise polygonal equivalent air spring stiffness considering the nonlinear dynamic characteristics of the aircraft landing gear buffer system is as follows if it is a single-cavity oil-gas buffer: In the formula, For the first Each buffer cylinder compression stroke segmented interval The equivalent air spring stiffness inside. These are the start and end points of the j-th compression stroke interval of the buffer cylinder, respectively; It is an index for a variable process; This represents the initial pressure of the gas in the low-pressure chamber. This represents the initial volume of the low-pressure chamber. This refers to the effective pressure area of ​​the buffer. For a dual-chamber oil-gas type buffer, the following formula applies: In the formula: ,in This represents the volume of gas in the low-pressure chamber when the gas pressures in the low-pressure chamber and the high-pressure chamber are equal. (2) The calculation expression for the piecewise polygonal equivalent damping coefficient of the buffer considering the nonlinear dynamic characteristics of the aircraft landing gear buffer system is shown in the following formula: In the formula, For the first The equivalent damping coefficient of each buffer cylinder within the segmented compression speed range; and These are the end and starting velocities of the velocity segment intervals, respectively. The structure constant of oil damping, ; (3) The calculation expression for the segmented polygonal equivalent tire stiffness considering the nonlinear dynamic characteristics of the aircraft landing gear buffer system is shown in the following formula: In the formula, For the first Equivalent tire stiffness within the tire compression deformation range; , The tires were in the 1st month respectively. Vertical deformation at the beginning and end of each compression deformation zone; Inflation pressure for the tires; , , and The parameters to be fitted; (4) The calculation expression for the tire piecewise linear equivalent damping coefficient considering the nonlinear dynamic characteristics of the aircraft landing gear buffer system is shown in the following formula: In the formula, For the first Tire compression deformation zone The equivalent damping coefficient within, The tires are respectively j The beginning and end points of each compression deformation zone; The damping ratio of the tire material; For tire quality; Inflation pressure for the tires; The parameter calculation module is used to perform the following functions: based on the nonlinear piecewise linear equivalent simplified model of the aircraft landing gear buffer system constructed by the calculation model construction module, the equivalent stiffness and equivalent damping coefficient of the aircraft landing gear buffer system are calculated, and the equivalent air spring stiffness, equivalent damping coefficient of each segment of the buffer cylinder compression stroke range, and equivalent tire stiffness and equivalent damping coefficient of each segment of the tire compression deformation range are obtained.

7. An electronic device, characterized in that, The electronic device includes: Memory, used to store executable instructions; A processor, when executing executable instructions or computer programs stored in the memory, implements the method according to any one of claims 1 to 5.

8. A computer-readable storage medium storing executable instructions or a computer program, characterized in that, When the executable instructions are executed by the processor, they implement the method described in any one of claims 1 to 5.

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