A film type double-cavity air spring key parameter identification and modeling method, a storage medium and a computer program product

Abstract

The application discloses a kind of film type double-cavity air spring key parameter identification and modeling method and storage medium, computer program product, comprising: based on the first law of thermodynamics derivation film type double-cavity air spring modeling method, builds test bench, based on rack test identification effective area and gas volume change with height model parameters, according to design working condition carries out film type double-cavity air spring rack test, gathers displacement, initial temperature, force data, according to rack test data and modeling method on host computer air spring support force is calculated, and with the support force obtained by rack test is made indicator diagram and is compared, verify the accuracy of model built.The advantages of the present application are that the change rule of key parameters with height is efficiently and accurately identified, and a mathematical model with clear physical meaning, high precision and convenient for engineering application is constructed, which has high scientific research and engineering application value.

Description

Technical Field

[0001] This invention relates to the field of passenger vehicle chassis suspension modeling and control, and particularly to a method for identifying and modeling key parameters of a diaphragm dual-chamber air spring, as well as a storage medium and computer program product. Background Technology

[0002] Air springs, as a suspension elastic element, are widely used in automotive active suspensions, rail vehicles, precision instrument platforms, and high-end industrial equipment due to their excellent nonlinear stiffness characteristics, adjustable natural frequency, and good vibration isolation performance. Among them, diaphragm dual-chamber air springs, by introducing a secondary chamber and a corresponding connecting valve body, achieve richer stiffness curve adjustability and better large-stroke adaptability on top of the basic elastic characteristics of the primary chamber, providing greater potential for improving the dynamic performance of the system.

[0003] Accurate mechanical models are fundamental for the design, performance prediction, and active / semi-active suspension control of air spring systems. The core of an air spring's mechanical model relies on its internal state and geometric parameters, especially its initial volume and effective area. These parameters are not fixed but change significantly and non-linearly with piston displacement, i.e., the operating height. Therefore, accurately identifying these key parameters that vary with height and constructing a high-fidelity mechanical model based on them is a crucial prerequisite for achieving precise design and performance optimization.

[0004] Currently, most existing patents estimate stiffness based on known actual structural dimensions of the product, or model a single-chamber air spring. If the test object is a double-chamber air spring with unknown internal structural dimensions, the above methods will fail.

[0005] The present invention aims to overcome the above-mentioned defects and proposes a modeling method for diaphragm dual-cavity air springs that integrates key parameter identification, physical model construction, and modeling accuracy verification. Summary of the Invention

[0006] The technical problem to be solved by this invention is to provide a method for identifying and modeling key parameters of a diaphragm dual-cavity air spring, as well as a storage medium and computer program product. Based on the first law of thermodynamics, the thermodynamic formula of the dual-cavity air spring is derived, and the changes in its thermodynamic parameters are tested based on the constructed test bench. A parameter identification method is proposed for the formula calculation of the support force. Finally, the accuracy of the modeling is verified through comparative analysis. The air spring dynamics modeling does not rely on obtaining internal structural parameters, and the model can be directly used in the field of suspension control.

[0007] To address the above technical problems, this invention provides a method for identifying and modeling key parameters of a diaphragm-type dual-cavity air spring, including key parameter identification, a modeling method based on dynamics and thermodynamics, and a verification method. The specific steps are as follows:

[0008] Step S1: Derive the modeling method for a diaphragm double-cavity air spring based on the first law of thermodynamics; According to the constant-mass operation of a diaphragm dual-chamber air spring, the volume of the auxiliary air chamber remains constant. It is connected to the air spring via a throttle orifice, and the opening and closing of the orifice is controlled by a solenoid valve to change the stiffness. When the solenoid valve is open, the two air chambers are connected, effectively increasing the effective volume of the air spring. At this point, the stiffness becomes smaller, improving comfort. Conversely, when the solenoid valve is closed, the suspension stiffness on that side is increased. Under certain conditions, this improves handling stability by controlling roll and nose-dive during rapid acceleration, deceleration, and sharp turns, preventing severe body roll and enhancing safety.

[0009] First, define the parameters and their positive direction: absolute pressure. ; The direction of gas mass flow is the positive direction of the flow into the auxiliary gas chamber; Temperature Gas mass ,volume Taking the increase as positive; Current altitude, compression is positive; air spring support force Positive values ​​are taken for upwards. The ideal gas state constant is applied to air. Specific heat capacity ; Heat exchange coefficient; subscript These represent the additional air chamber, the air spring bladder, the initial state, and the external atmospheric environment, respectively; it is assumed that the gas law and its total differential, and the first law of thermodynamics, hold true, and each variable is represented by heat absorbed from the outside. Work done on the gas by the external environment and internal energy Increased to positive.

[0010] According to the ideal gas law of the system: (1); Because the membrane rubber airbag has a rolling characteristic, work is done on the gas by the external environment; according to the first law of thermodynamics, the heat absorbed by the gas is: (2); in: (3); First, the secondary chamber was analyzed; its volume remained unchanged. The heat absorbed ; Assumption The increase in the internal energy of the system is determined by the enthalpy of the gas flowing into it, that is: (4); Differentiating both sides of equation (4) with respect to time, we get: (5); Combined with the specific heat capacity of gas at constant pressure and specific heat capacity at constant volume Relationship, there is (6); The gas flow rate into the secondary chamber is: (7); According to the first law of thermodynamics: (8); Further analysis of the main air chamber of the air spring airbag, combined with equations (2) and (3), yields: (9); Differentiating both sides of equation (9) with respect to time, we get: (10); Combining equations (1), (6), and (10), we get: (11); Because the auxiliary air chamber and the air bladder are connected by a throttling orifice, under severe operating conditions, the air flowing through the throttling orifice will be compressed, exhibiting macroscopic damping and nonlinear characteristics. Considering the small area of ​​the throttling orifice, the airflow cannot exchange heat with the outside; therefore, in aerodynamics, this phenomenon is generally assumed to be one-dimensional isentropic flow. Theoretically, the gas mass flow rate in this phenomenon is related to the pressure before and after the connecting pipe. For air, when... hour: (12); in, The area of ​​the throttling orifice Correction factor, Main chamber gas density; determine the relationship between gas pressure, density, and temperature. Substituting into equation (12), we get: (13); At this point, the gas state equations for the two chambers have been established: Equation (1), two thermodynamic equations: Equation (8) and Equation (10), and one gas mass flow rate equation: Equation (13), corresponding to 5 unknowns. Theoretically, it can be solved; Based on the effective area of ​​the diaphragm double-cavity air spring According to the definition, the supporting force of an air spring is: (14); According to the definition of stiffness, equation (14) applies to displacement. Differentiating, we get: (15); From the above derivation, we can deduce that the effective area... The changes in height, the volume of the main and auxiliary air chambers, and the volume of the main air chamber with height are obtained through measurement or parameter identification methods, and these parameters are different for different types of products.

[0011] This modeling method considers the gas exchange of a dual-cavity air spring and does not rely on obtaining the internal structural parameters of the air spring. It solves for the changes in spring support force and stiffness based solely on the changes in thermodynamic parameters.

[0012] Step S2: Set up the test bench; The test bench includes: a hydraulic actuator, an air spring under test, gas pipelines, force sensors and displacement sensors, a vertical control rod, a pressure gauge, a thermometer, a host computer, a control cabinet, and a regulated air source. The host computer sends control signals to the control cabinet, which drives the hydraulic actuator to move up and down, thereby controlling the lifting and lowering of the test bench. The vertical control rod is used to adjust the initial height position. The regulated air source is connected to the pressure gauge and the air spring under test through gas pipelines. The force sensor and displacement sensor collect electrical signals and feed them back to the control cabinet, which then sends them to the host computer to record the actual physical quantities in real time.

[0013] After the test bench is set up, a static test is first performed. At the initial height position, the host computer sends a control signal to the control cabinet every 5mm. The control cabinet drives the hydraulic actuator to move up and down, thereby controlling the lifting and lowering of the test bench. After the air pressure stabilizes, the relative air pressure, spring compression and force sensor data are recorded. The static test data is used to identify key parameters.

[0014] Step S3: Identification of key parameters of diaphragm double-cavity air spring, based on bench testing to identify model parameters of effective area and gas volume as a function of height; A mechanical analysis was performed on the lower surface of the air spring piston auxiliary chamber. The force on the lower surface from the air spring consists of two parts: one part is the gas pressure generated by the piston area and the internal relative air pressure, which is upward; the other part is the pulling force of the airbag composite material on the piston. When the piston is outside the airbag, the pulling force of the airbag composite material on the piston is downward; when the piston moves to below the highest position of the airbag, the pulling force of the airbag composite material on the piston is upward. Therefore, the supporting force of the air spring is expressed as: (16); Among them, air on the piston surface The pressure generated for: (17); The pulling force of the airbag composite material on the piston This is the projection of the tension force generated when the airbag is stretched axially onto the vertical direction, i.e.: (18); in, This refers to the area enclosed by the outer constraint ring of the air spring. The angle formed by the contact between the airbag axis and the piston surface; based on the free thin film theory, it is assumed that within the working stroke range, the axial deformation of the airbag... Small, and the angle formed by the contact point between the airbag and the piston is approximately: (19); Then equation (16) is: (20); in, , , and It is a constant; The parameters that need to be identified are derived as follows: and ; By obtaining the change in effective area with height, the change in volume with compression can be calculated according to equation (21): (twenty one).

[0015] The above proposes a method for estimating the change of the effective area of ​​an air spring with height, transforming it into a function of height, and substituting it into equation (14) to calculate the spring support force.

[0016] Step S4: Conduct a test on the membrane double-cavity air spring bench according to the design conditions, and collect data on displacement, initial temperature, and force. The dynamic test of the test bench was performed by excitation at frequencies of 0.1Hz, 0.2Hz, 0.5Hz, 1Hz, 2Hz, 5Hz, 8Hz and 10Hz and amplitudes of 5mm, 10mm, 15mm, 20mm and 25mm, respectively, and the test was performed according to the opening and closing conditions of the solenoid valve, that is, the valve was tested as a double chamber when the valve was open and as a single chamber when the valve was closed. Step S5: Calculate the air spring support force on the host computer based on the bench test data and modeling method, and compare it with the support force obtained from the bench test using a dynamometer diagram to verify the accuracy of the model.

[0017] This invention provides a method for identifying and modeling key parameters of a diaphragm-type dual-chamber air spring. Based on bench testing, it identifies the changes in gas volume and effective area of ​​the main and auxiliary gas chambers with compression, and uses this method for accurate dynamic modeling of the dual-chamber air spring. This method has high scientific research and engineering application value.

[0018] In addition, the present invention provides a storage medium, which is a computer-readable storage medium, on which a computer program is stored, which, when executed by a processor, implements the steps of the key parameter identification and modeling method described above.

[0019] In addition, the present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the key parameter identification and modeling method described above.

[0020] The one or more technical solutions proposed in this invention have at least the following beneficial effects: efficiently and accurately identifying the variation law of key parameters with altitude, and using this to construct a mathematical model with clear physical meaning, high precision and easy engineering application, which has high scientific research and engineering application value. Attached Figure Description

[0021] The accompanying drawings, which form part of this application, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings: Figure 1 This describes the constant mass operation process of the dual-cavity air spring in a specific embodiment of the present invention. Figure 2 This is a force analysis of the piston surface in a specific embodiment of the present invention; Figure 3 This is a schematic diagram of the test bench structure for a dual-cavity air spring according to a specific embodiment of the present invention; Figure 4 This is a schematic diagram of linear fitting of the effective area and height in a specific embodiment of the present invention; Figure 5 This is a schematic diagram of linear fitting of volume and height multiplied by effective area in a specific embodiment of the present invention; Figure 6a This is a theoretical calculation diagram of a single cavity under the working conditions of an amplitude of 25mm and a frequency of 1Hz in a specific embodiment of the present invention; Figure 6b This is a theoretical calculation diagram of a dual-cavity system under the specific embodiment of the present invention with an amplitude of 25mm and a frequency of 1Hz. Figure 7a This is a theoretical calculation diagram of a single cavity under the operating conditions of an amplitude of 25mm and a frequency of 2Hz in a specific embodiment of the present invention; Figure 7b This is a theoretical calculation diagram of a dual-cavity system under the specific embodiment of the present invention with an amplitude of 25mm and a frequency of 2Hz. Figure 8a This is a theoretical calculation diagram of a single cavity under the operating conditions of an amplitude of 25mm and a frequency of 5Hz in a specific embodiment of the present invention; Figure 8b This is a theoretical calculation diagram of a dual-cavity circuit under the specific embodiment of the present invention with an amplitude of 25mm and a frequency of 5Hz. Figure 9a This is a theoretical calculation diagram of a single cavity under the working conditions of an amplitude of 25mm and a frequency of 10Hz in a specific embodiment of the present invention; Figure 9b This is a theoretical calculation diagram of a dual-cavity system under the specific embodiment of the present invention with an amplitude of 25mm and a frequency of 10Hz. Figure 10 This is a schematic diagram of the workflow of a specific embodiment of the present invention; Explanation of the labels in the diagram 1—Hydraulic actuator; 2—Air spring to be tested; 3—Gas pipeline; 4—Force sensor; 5—Vertical control lever. Detailed Implementation

[0022] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings. The executing entity of a specific embodiment of the present invention is a computing service device with data processing, network communication, and program execution functions, such as an electronic device that implements the above functions.

[0023] like Figure 10 As shown, this invention provides a method for identifying and modeling key parameters of a diaphragm-type dual-cavity air spring, including key parameter identification, a modeling method based on dynamics and thermodynamics, and a verification method. The specific steps are as follows: Step S1: Derive the modeling method for a diaphragm double-cavity air spring based on the first law of thermodynamics; Figure 1 The diagram illustrates the structure and operation of a dual-chamber air spring. The additional air chamber maintains a constant volume and is connected to the air spring via a throttle orifice. A solenoid valve controls the opening and closing of the orifice to alter the stiffness. When the solenoid valve is open, the two air chambers are connected, effectively increasing the air spring's volume and reducing stiffness for improved comfort. Conversely, when the solenoid valve is closed, the suspension stiffness on that side is increased. Under specific conditions, this improves handling stability by controlling roll and nose-dive during rapid acceleration, deceleration, and sharp turns, preventing severe vehicle tilt and enhancing safety.

[0024] like Figure 1 As shown, first define the parameters and their positive direction: absolute pressure ; The direction of gas mass flow is the positive direction of the flow into the auxiliary gas chamber; Temperature Gas mass ,volume Taking the increase as positive; Current altitude, compression is positive; air spring support force Positive values ​​are taken for upwards. The ideal gas state constant is applied to air. Specific heat capacity ; Heat exchange coefficient; subscript These represent the additional air chamber, the air spring bladder, the initial state, and the external atmospheric environment, respectively; it is assumed that the gas law and its total differential, and the first law of thermodynamics, hold true, and each variable is represented by heat absorbed from the outside. Work done on the gas by the external environment and internal energy Increased to positive.

[0025] According to the ideal gas law of the system: (1); Because the membrane rubber airbag has a rolling characteristic, work is done on the gas by the external environment; according to the first law of thermodynamics, the heat absorbed by the gas is: (2); in: (3); First, the secondary chamber was analyzed; its volume remained unchanged. The heat absorbed ; Assumption The increase in the internal energy of the system is determined by the enthalpy of the gas flowing into it, that is: (4); Differentiating both sides of equation (4) with respect to time, we get: (5); Combined with the specific heat capacity of gas at constant pressure and specific heat capacity at constant volume Relationship, there is (6); The gas flow rate into the secondary chamber is: (7); According to the first law of thermodynamics: (8); Further analysis of the main air chamber of the air spring airbag, combined with equations (2) and (3), yields: (9); Differentiating both sides of equation (9) with respect to time, we get: (10); Combining equations (1), (6), and (10), we get: (11); Because the auxiliary air chamber and the air bladder are connected by a throttling orifice, under severe operating conditions, the air flowing through the throttling orifice will be compressed, exhibiting macroscopic damping and nonlinear characteristics. Considering the small area of ​​the throttling orifice, the airflow cannot exchange heat with the outside; therefore, in aerodynamics, this phenomenon is generally assumed to be one-dimensional isentropic flow. Theoretically, the gas mass flow rate in this phenomenon is related to the pressure before and after the connecting pipe. For air, when... hour: (12); in, The area of ​​the throttling orifice Correction factor, Main chamber gas density; determine the relationship between gas pressure, density, and temperature. Substituting into equation (12), we get: (13); At this point, the gas state equations for the two chambers have been established: Equation (1), two thermodynamic equations: Equation (8) and Equation (10), and one gas mass flow rate equation: Equation (13), corresponding to 5 unknowns. Theoretically, it can be solved; Based on the effective area of ​​the diaphragm double-cavity air spring According to the definition, the supporting force of an air spring is: (14); According to the definition of stiffness, equation (14) applies to displacement. Differentiating, we get: (15); From the above derivation, we can deduce that the effective area... The changes in height, the volume of the main and auxiliary air chambers, and the volume of the main air chamber with height are obtained through measurement or parameter identification methods, and these parameters are different for different types of products.

[0026] Step S2, as follows Figure 3 As shown, the test bench was set up; The test bench includes: a hydraulic actuator 1, an air spring under test 2, a gas pipeline 3, a force sensor 4 and a displacement sensor, a vertical control rod 5, a pressure gauge, a thermometer, a host computer, a control cabinet, and a regulated air source. The host computer sends control signals to the control cabinet, which drives the hydraulic actuator 1 to move up and down, thereby controlling the lifting and lowering of the test bench. The vertical control rod 5 is used to adjust the initial height position. The regulated air source is connected to the pressure gauge and the air spring under test 2 through the gas pipeline 3. The force sensor 4 and the displacement sensor collect electrical signals and feed them back to the control cabinet, which then sends them to the host computer to record the actual physical quantities in real time.

[0027] After the test bench is set up, a static test is performed first. At the initial height, the test bench is raised and lowered every 5mm using the host computer. After the air pressure stabilizes, the relative air pressure, spring compression, and force sensor data are recorded. The key parameters are identified using the static test data.

[0028] Step S3: Identification of key parameters of diaphragm double-cavity air spring, based on bench testing to identify model parameters of effective area and gas volume as a function of height; A mechanical analysis was performed on the lower surface of the air spring piston's auxiliary air chamber. The force exerted on the lower surface by the air spring consists of two parts: one part is the gas pressure generated by the piston area and the internal relative air pressure, directed upwards; the other part is the pulling force of the airbag composite material on the piston. When the piston is outside the airbag, the pulling force of the airbag composite material on the piston is downwards; when the piston moves below the highest position of the airbag, the pulling force of the airbag composite material on the piston is upwards, such as... Figure 2 As shown; Therefore, the supporting force of the air spring is expressed as: (16); Among them, air on the piston surface The pressure generated for: (17); The pulling force of the airbag composite material on the piston This is the projection of the tension force generated when the airbag is stretched axially onto the vertical direction, i.e.: (18); in, This refers to the area enclosed by the outer constraint ring of the air spring. The angle formed by the contact between the airbag axis and the piston surface; based on the free thin film theory, it is assumed that within the working stroke range, the axial deformation of the airbag... Small, and the angle formed by the contact point between the airbag and the piston is approximately: (19); Then equation (16) is: (20); in, , , and It is a constant; The parameters that need to be identified are derived as follows: and ; By obtaining the change in effective area with height, the change in volume with compression can be calculated according to equation (21): (twenty one).

[0029] Step S4: Conduct a test on the membrane double-cavity air spring bench according to the design conditions, and collect data on displacement, initial temperature, and force. Dynamic verification tests were conducted on the test bench, with excitation at frequencies of 0.1Hz, 0.2Hz, 0.5Hz, 1Hz, 2Hz, 5Hz, 8Hz and 10Hz and amplitudes of 5mm, 10mm, 15mm, 20mm and 25mm, respectively. The tests were conducted according to the operating conditions of the solenoid valve opening and closing, i.e., the valve is double-chambered when open and single-chambered when closed.

[0030] A univariate linear regression was performed on the effective area and the air spring compression, such as... Figure 4 As shown; The effective area obtained after fitting changes with height as shown below:

[0031] The intercept represents the piston area; a difference of less than 3% from the measured radius is acceptable for verification. It is 0.9872.

[0032] Based on equation (21), a univariate linear regression was performed on the changes in effective volume and height, as follows: Figure 5 As shown: Inspection It is 0.9998.

[0033] The identified parameters are substituted into the solution of dynamic forces, and the relationship between the force and displacement of the dual-cavity air spring under different frequencies and amplitudes is finally obtained.

[0034] Step S5: Calculate the air spring support force on the host computer based on the bench test data and modeling method, and compare it with the support force obtained from the bench test using a dynamometer diagram to verify the accuracy of the model.

[0035] The theoretically solved values ​​and the bench test values ​​were plotted and compared, as shown in Figures 6-9: The maximum relative error between the theoretical calculation results and the bench test results is no more than 3.5%, which proves that the thermodynamic model of the dual-cavity air spring is accurate.

[0036] The key parameter identification and modeling method of the diaphragm double-cavity air spring of this invention efficiently and accurately identifies the variation law of key parameters with height, and uses it to construct a mathematical model with clear physical meaning, high precision and easy engineering application, which has high scientific research and engineering application value.

[0037] The present invention also provides a computer-readable storage medium having computer-readable program instructions stored thereon, the computer-readable program instructions being used to execute the key parameter identification and modeling method for the diaphragm dual-cavity air spring in the above embodiments.

[0038] The computer-readable storage medium provided in this application is, for example, a USB flash drive, but is not limited to electrical, magnetic, optical, electromagnetic, infrared, or semiconductor systems, devices, or any combination thereof. More specific examples of computer-readable storage media include, but are not limited to: electrical connections having one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM), optical fibers, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof. In this embodiment, the computer-readable storage medium is any tangible medium that contains or stores a program that is used by or in conjunction with an instruction execution system, system, or device. The program code contained on the computer-readable storage medium is transmitted using any suitable medium, including but not limited to: wires, optical fibers, radio frequency (RF), etc., or any suitable combination thereof.

[0039] The present invention also provides a computer program product, including a computer program that, when executed by a processor, implements the steps of the key parameter identification and modeling method for the diaphragm dual-cavity air spring as described above.

[0040] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for identifying and modeling key parameters of a diaphragm-type dual-cavity air spring, characterized in that: This includes the identification of key parameters for diaphragm-type dual-cavity air springs, modeling methods based on dynamics and thermodynamics, and verification methods. Step S1: Derive the modeling method for a diaphragm double-cavity air spring based on the first law of thermodynamics; Parameters and their positive direction definitions: Absolute pressure ; The direction of gas mass flow is defined as the direction of inflow into the auxiliary gas chamber; temperature Gas mass ,volume Taking the increase as positive; Current altitude, compression is positive; air spring support force Positive values ​​are taken for upward; the ideal gas state constant is used for air. Specific heat capacity ; Heat exchange coefficient; subscript These represent the additional air chamber, the air spring bladder, the initial state, and the external atmospheric environment, respectively; it is assumed that the gas law and its total differential, and the first law of thermodynamics, hold true, and each variable is represented by heat absorbed from the outside. Work done on the gas by the external environment and internal energy Increase to positive; The equations of state for the gases in the two chambers are: (1); According to the first law of thermodynamics, the heat absorbed by the gas is: （2）； in: （3）； The volume of the secondary chamber remains unchanged, that is... The heat absorbed ; Assumption The increase in the internal energy of the system is determined by the enthalpy of the gas flowing into it, that is: （4）； Differentiating both sides of equation (4) with respect to time, we get: （5）； Combined with the specific heat capacity of gas at constant pressure and specific heat capacity at constant volume The relationships are: （6）； The gas flow rate into the secondary chamber is: （7）； According to the first law of thermodynamics, the thermodynamic equation is: （8）； Further analysis of the main air chamber of the air spring airbag, combined with equations (2) and (3), yields: （9）； Differentiating both sides of equation (9) with respect to time, we get: （10）； Combining equations (1), (6), and (10), we get: （11）； For air, when hour: （12）； in, The area of ​​the throttling orifice Correction factor, Main chamber gas density; determine the relationship between gas pressure, density, and temperature. Substituting into equation (12), we obtain the gas mass flow rate equation: （13）； Based on the effective area of ​​the diaphragm double-cavity air spring According to the definition, the supporting force of an air spring is: （14）； According to the definition of stiffness, equation (14) applies to displacement. Differentiating, we get: （15）； From the above derivation, we can deduce the effective area of ​​the diaphragm double-cavity air spring. The changes in height, the volume of the main and auxiliary air chambers, and the volume of the main air chamber with height are obtained through measurement or parameter identification methods, and these parameters are different for different types of products; Step S2: Set up the test bench; The test bench includes: a hydraulic actuator, an air spring under test, gas pipelines, force sensors and displacement sensors, a vertical control rod, a pressure gauge, a thermometer, a host computer, a control cabinet, and a regulated air source. The host computer sends control signals to the control cabinet, which drives the hydraulic actuator to move up and down, thereby controlling the lifting and lowering of the test bench. The vertical control rod is used to adjust the initial height position. The regulated air source is connected to the pressure gauge and the air spring under test through gas pipelines. The force sensor and displacement sensor collect electrical signals and feed them back to the control cabinet, which then sends them to the host computer to record the actual physical quantities in real time. After the test bench is set up, a static test is first performed. At the initial height position, the host computer sends a control signal to the control cabinet every 5mm. The control cabinet drives the hydraulic actuator to move up and down, thereby controlling the lifting and lowering of the test bench. After the air pressure stabilizes, the relative air pressure, spring compression and force sensor data are recorded. The key parameters are identified using the static test data. Step S3: Identify model parameters for effective area and gas volume variation with height based on bench testing; The force exerted on the lower surface of the air spring piston's auxiliary air chamber by the air spring consists of two parts: one part is the gas pressure generated by the piston area and the internal relative air pressure, which is directed upwards; the other part is the pulling force of the airbag composite material on the piston; when the piston is outside the airbag, the pulling force of the airbag composite material on the piston is downwards; when the piston moves to below the highest position of the airbag, the pulling force of the airbag composite material on the piston is upwards. The supporting force of an air spring is expressed as: (16); Among them, air on the piston surface The pressure generated for: （17）； The pulling force of the airbag composite material on the piston This is the projection of the tension force generated when the airbag is stretched axially onto the vertical direction, i.e.: （18）； in, This refers to the area enclosed by the outer constraint ring of the air spring. The angle formed by the contact between the airbag axis and the piston surface; Based on the free membrane theory, it is assumed that within the working stroke range, the airbag undergoes axial deformation. Small, and the angle formed by the contact point between the airbag and the piston is: （19）； The supporting force of the air spring in equation (16) can be expressed as: （20）； in, , , and It is a constant; The parameters that need to be identified are derived as follows: and ; By obtaining the change in effective area with height, the change in volume with compression can be calculated according to equation (21): （21）； Step S4: Conduct a test on the membrane double-cavity air spring bench according to the design conditions, and collect data on displacement, initial temperature, and force. The dynamic test of the test bench was performed by excitation at frequencies of 0.1Hz, 0.2Hz, 0.5Hz, 1Hz, 2Hz, 5Hz, 8Hz and 10Hz and amplitudes of 5mm, 10mm, 15mm, 20mm and 25mm, respectively, and the test was performed according to the opening and closing conditions of the solenoid valve, that is, the valve was tested as a double chamber when the valve was open and as a single chamber when the valve was closed. Step S5: Calculate the air spring support force on the host computer based on the bench test data and modeling method, and compare it with the support force obtained from the bench test using a dynamometer diagram to verify the accuracy of the model.

2. A storage medium, characterized in that: The storage medium is a computer-readable storage medium, and a computer program is stored on the storage medium. When the computer program is executed by a processor, it implements the steps of the key parameter identification and modeling method for the diaphragm dual-cavity air spring as described in claim 1.

3. A computer program product, characterized in that: It includes a computer program that, when executed by a processor, implements the steps of the method for identifying and modeling key parameters of a diaphragm dual-cavity air spring as described in claim 1.

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