Design method for dynamic stiffness of membrane type air spring

Abstract

The invention relates to the field of vehicle air suspension systems, in particular to a design method for dynamic stiffness of a membrane type air spring, which comprises the following steps of: analyzing the air spring, accurately searching a mathematical relationship among design parameters, vibration frequency and dynamic stiffness of the air spring, and constructing a dynamic stiffness calculation model of the membrane type air spring; and according to the vehicle performance target requirement, in combination with a'dynamics-air spring dynamic stiffness calculation model 'joint simulation model, reasonable parameters such as a dynamic stiffness target value are determined, then various design parameters are reversely calculated by utilizing a membrane type air spring dynamic stiffness calculation model, and a plurality of air spring schemes meeting the requirement are formed. Finally, a scheme meeting envelope checking is selected in combination with the air spring motion envelope requirement, the selected scheme is substituted into the joint simulation model for calculation, the scheme with the optimal whole vehicle performance serves as the final dynamic stiffness design scheme, the design period is short, the calculation precision is high, the process is simple and convenient, and the production efficiency of the air spring can be greatly improved.

Description

Technical Field

[0001] This invention relates to the field of vehicle air suspension systems, and more specifically to a design method for the dynamic stiffness of a diaphragm air spring. Background Technology

[0002] As a core elastic element of a vehicle suspension system, air springs operate based on the compressibility of gas and the deformation characteristics of the airbag structure, providing dynamic support to the suspension system during vehicle operation. Leveraging their nonlinear stiffness characteristics, they can adapt to changes in vehicle driving conditions (such as load fluctuations and road surface excitations), optimizing the dynamic response of the suspension system by adjusting their stiffness and height in real time. This significantly improves vehicle handling stability, ride comfort, and off-road performance, making them a key technological component in modern vehicle engineering. These air springs are typically manufactured by automotive component manufacturers and then integrated into vehicles by OEMs. The OEMs then verify whether the dynamic stiffness of these air springs meets the requirements (i.e., whether it is within the target dynamic stiffness range). Dynamic stiffness is a core performance parameter of air springs, directly determining the vibration response characteristics of the vehicle under dynamic loads. In complex driving conditions, vehicles experience dynamic loads such as high-frequency road surface excitations, acceleration and deceleration inertial forces, and steering lateral forces. The dynamic stiffness characteristics of the air springs directly affect the vehicle's response efficiency and quality to these loads. A scientifically sound dynamic stiffness design can effectively suppress resonance peaks and reduce vibration transmission rate, ensuring the ride comfort and safety of vehicles under various operating conditions. Therefore, precisely designing the dynamic stiffness of air springs is a key step in optimizing suspension system performance and meeting the stringent requirements of modern vehicles for comfort and handling.

[0003] In other words, for OEMs, the core requirement is whether air spring manufacturers can produce products that meet the vehicle's dynamic vibration response requirements according to a given target dynamic stiffness value. Currently, the specific process of traditional dynamic stiffness design methods is as follows:

[0004] 1. Based on the established vehicle performance targets related to air springs, and using the suspension off-frequency theory formula and empirical value range, determine the target value of dynamic stiffness;

[0005] 2. Determine the air spring scheme, obtain the static stiffness of the air spring through theoretical calculation and finite element simulation, and derive the dynamic stiffness design value by combining the dynamic-to-static ratio to meet the dynamic stiffness target set in the first step.

[0006] 3. Make a sample, conduct a dynamic stiffness test, and compare the test value with the target value. If the target value is met, the dynamic stiffness design of the air spring is completed. If the target value is not met, continue to repeat steps 1-3 until the dynamic stiffness of the air spring meets the target.

[0007] 4. Install the air spring prototype on the vehicle and evaluate its overall handling stability, ride comfort, and other performance aspects. If the vehicle performance targets related to the air spring are not met, continue to optimize the dynamic stiffness target value and repeat steps 2-4 until the target is achieved. At this point, the air spring dynamic stiffness design is complete.

[0008] The determination of the dynamic-to-static ratio requires three stages:

[0009] (1) Sample preparation and data acquisition: To meet the needs of multiple projects, we will carry out structural design of multiple schemes, manufacture self-developed samples and purchase benchmark products to form a test set, and conduct dynamic and static stiffness tests according to standards to ensure data standardization.

[0010] (2) Data analysis and empirical value derivation: Statistical analysis of test data is conducted to determine the distribution range of dynamic-static ratio, and probability theory and mathematical statistics methods are used to extract empirical values ​​of dynamic-static ratio that can be used in engineering.

[0011] (3) Dynamic stiffness design and iterative optimization: Based on the static stiffness model, the structural parameters are initially determined. If there are similar samples in the database, the measured dynamic-static ratio is directly used. If there are no matching samples, the previous empirical values ​​are called and multiplied by the static stiffness calculation value to obtain the dynamic stiffness estimate. By comparing with the design target, the structural parameters are repeatedly adjusted and the design-test-calculation process is repeated until the sample is made and the dynamic stiffness is verified by actual measurement to meet the standard, thus completing the full process iteration.

[0012] However, this traditional method has significant drawbacks, including:

[0013] 1. The target value of dynamic stiffness determined based on the theoretical formula and empirical range of suspension off-frequency cannot be directly equated to the overall vehicle performance standards related to air springs. Air springs designed based on this, after identification of experimental parameters, need to be verified through vehicle handling, steering, and ride comfort performance simulation or real vehicle testing. This carries the risk of redesign, is time-consuming, labor-intensive, and costly.

[0014] 2. Existing methods for identifying dynamic stiffness parameters require testing the sample to obtain the dynamic stiffness curve, and then identifying parameters such as effective cross-sectional area, effective cross-sectional area change rate, and internal pressure change rate based on the general expression of dynamic stiffness, which can then be used for vehicle performance simulation. However, this process depends on sample testing and has significant limitations.

[0015] 3. Obtaining the dynamic-to-static ratio requires a significant investment of resources in sample manufacturing and testing, and the obtained empirical values ​​are limited by the sample and testing conditions, making it difficult to guarantee accuracy;

[0016] 4. The design process requires multiple iterations of design, prototype manufacturing, and performance testing, resulting in long development cycles, high costs, and low efficiency, making it difficult to meet the requirements of modern OEMs for short product development cycles and controllable costs.

[0017] In summary, there is a significant contradiction between the actual production process of a single air spring and the entire vehicle:

[0018] Air spring manufacturers typically focus on ensuring the static stiffness of their products meets the target value for dynamic stiffness provided by vehicle manufacturers (e.g., using the technical solution disclosed in patent document CN117454695A), but cannot ensure that the dynamic stiffness of the products after assembly into the vehicle meets expectations. In order to ensure that the dynamic stiffness of the assembled air springs meets the target value, vehicle manufacturers generally adopt the traditional design method based on static stiffness and dynamic-to-static ratio (i.e., indirectly deriving the dynamic stiffness by obtaining the static stiffness of the air spring and determining the dynamic-to-static ratio).

[0019] While theoretically OEMs could directly obtain static stiffness parameters from manufacturers and thus determine the dynamic stiffness ratio to complete the dynamic stiffness design, the current method of obtaining this ratio heavily relies on systematic testing and data analysis. This requires preparing multiple self-developed prototypes and industry benchmark products, constructing a test suite, conducting dynamic and static stiffness tests according to standards, and then extracting empirical values ​​for the dynamic-static ratio from the test data using mathematical statistics. Due to limitations in sample size and testing conditions, the accuracy of these empirical values ​​is difficult to guarantee, leading to insufficient reliability of the dynamic stiffness target values ​​derived by OEMs based on these values. Furthermore, the actual dynamic stiffness of products manufactured by manufacturers based on these target values ​​after assembly cannot be guaranteed to meet expectations.

[0020] Therefore, how to solve the problems of the above-mentioned traditional methods and achieve efficient and precise design of the dynamic stiffness of air springs in the whole vehicle has always been a huge problem that needs to be solved by those skilled in the art. Summary of the Invention

[0021] The purpose of this invention is to address the shortcomings of existing technologies by providing a design method for the dynamic stiffness of diaphragm air springs. This method first analyzes the air spring to accurately explore the intrinsic relationship between its various design parameters, vibration frequency, and dynamic stiffness, constructing a dynamic stiffness calculation model for the diaphragm air spring. Then, based on the overall vehicle performance requirements, and combined with a joint simulation model of "dynamics-air spring dynamic stiffness calculation model," reasonable target values ​​for dynamic stiffness and other parameters are determined. Next, the diaphragm air spring dynamic stiffness calculation model is used again to calculate the various design parameters in reverse, forming multiple air spring schemes that meet the requirements. Then, considering the air spring motion envelope requirements, the scheme that meets the envelope check is selected. Finally, the selected scheme is input into the joint simulation model of "dynamics-air spring dynamic stiffness calculation model" for calculation, and the scheme that optimizes the overall vehicle performance is selected as the final dynamic stiffness design scheme, thus completing the dynamic stiffness design of the air spring. Compared to traditional methods for designing dynamic stiffness, this invention significantly shortens the design cycle, has advantages such as high calculation accuracy and a simple process, and can greatly improve the production efficiency of air springs.

[0022] The objective of this invention is achieved through the following scheme: a design method for the dynamic stiffness of a diaphragm air spring, comprising the following steps:

[0023] 1) Based on the mechanical equilibrium principle, thermodynamic equation of state, law of conservation of energy and gas volume partitioning theory of diaphragm air spring, establish a dynamic stiffness calculation model for diaphragm air spring to accurately describe the relationship between the design parameters, vibration frequency and dynamic stiffness of diaphragm air spring.

[0024] 2) Establish a vehicle dynamics model and combine it with a dynamic stiffness calculation model to construct a joint simulation model;

[0025] 3) Use a co-simulation model to perform simulation analysis on the whole vehicle, and determine the target range of the dynamic stiffness of the air spring and the setting range of the relative compression stroke based on the target requirements of the whole vehicle performance.

[0026] 4) Determine the range of values ​​for various design parameters of the diaphragm air spring based on the suspension's ultimate compression stroke range, the allowable space requirements and load-bearing requirements of the diaphragm air spring;

[0027] 5) Based on the target range of dynamic stiffness of the diaphragm air spring and the range of design parameters, the dynamic stiffness calculation model is used to iteratively calculate the feasibility of the schemes, and several diaphragm air spring manufacturing schemes with dynamic stiffness values ​​within the target range are obtained.

[0028] 6) Based on the spatial arrangement constraints of the air spring, the motion clearance is checked, and multiple diaphragm air spring manufacturing schemes that can guide production are selected from various diaphragm air spring manufacturing schemes.

[0029] 7) Import multiple diaphragm air spring manufacturing schemes that can guide production into the joint simulation model for simulation analysis, and take the manufacturing scheme that can optimize the performance of the whole vehicle as the final design scheme of the diaphragm air spring.

[0030] Preferably, in step 1), the method for establishing the dynamic stiffness calculation model specifically includes:

[0031] 1-1) Perform a force analysis on the air spring to determine the mathematical relationship between the dynamic restoring force and the relative compression stroke of the air spring;

[0032] 1-2) Take the derivative of the dynamic restoring force and define the derivative as the dynamic stiffness of the air spring;

[0033] 1-3) Based on the internal structural parameters of the air spring, determine the mathematical relationship between the effective cross-sectional area and the rate of change of the effective cross-sectional area and the relative compression stroke of the air spring, respectively;

[0034] 1-4) Based on the thermodynamic equation of state and the theory of gas volume partitioning, the mathematical relationship between the gas pressure inside the air spring and the relative compression stroke of the air spring is obtained;

[0035] 1-5) Based on the principle of energy conservation and the thermodynamic equation of state, the mathematical relationship between the rate of change of gas pressure inside the air spring and the relative compression stroke of the air spring is obtained;

[0036] 1-6) Based on the mathematical relationships in steps 1-1) to 1-5), determine the mathematical relationship between the dynamic stiffness of the air spring and the relative compression stroke, and obtain the dynamic stiffness calculation model of the diaphragm air spring.

[0037] Preferably, in step 1-1), a force analysis is performed on the air spring, and the mathematical relationship between the dynamic restoring force of the air spring and the relative compression stroke is as follows:

[0038] F d (z)=P(z)·A e (z)-P d ·A e (z)

[0039] In the formula, F d (z) represents the dynamic restoring force F acting on the air spring. d The functional relationship between P and the relative compression stroke z of the air spring d Let P(z) be the atmospheric pressure, and P(z) be the gas pressure inside the air spring when the relative compression stroke of the air spring is equal to z. e (z) is the effective cross-sectional area of ​​the main air chamber of the air spring when the relative compression stroke of the air spring is equal to z.

[0040] Preferably, in step 1-2), the derivative of the dynamic restoring force is calculated, and this derivative is defined as the dynamic stiffness of the air spring, as follows:

[0041]

[0042] F d (z)=(P(z)-P d A e (z)

[0043] In the formula, K d F is the dynamic stiffness of the air spring. d (z) represents the dynamic restoring force F acting on the air spring. d The functional relationship between the relative compression stroke z of the air spring and the air spring is given by: P(z) is the gas pressure inside the air spring when the relative compression stroke is equal to z, and P′(z) is the first derivative of P(z). d At atmospheric pressure, A e(z) is the effective cross-sectional area of ​​the main air chamber of the air spring when the relative compression stroke of the air spring is equal to z, A' e (z) is A e The first derivative of (z), where z is the relative compression stroke of the air spring.

[0044] Preferably, in steps 1-3), based on the internal structural parameters of the air spring, the mathematical relationships between the effective cross-sectional area, the rate of change of the effective cross-sectional area, and the relative compression stroke of the air spring are as follows:

[0045] A e (z)=π·[R e (z)] 2

[0046] In the formula, A e (z) is the effective cross-sectional area of ​​the main air chamber of the air spring when the relative compression stroke of the air spring is equal to z, π is pi, and R e (z) is the effective radius of the main air chamber of the air spring when the relative compression stroke of the air spring is equal to z;

[0047] A' e (z)=2π·R e (z)·R' e (z)

[0048] In the formula, A' e (z) represents the rate of change of the effective cross-sectional area of ​​the main air chamber of the air spring when the relative compression stroke of the air spring is equal to z, where π is pi and R is the ratio of π / 2 to π / 2. e (z) is the effective radius of the main air chamber of the air spring when the relative compression stroke of the air spring is equal to z, R' e (z) is R e The first derivative of (z);

[0049]

[0050] In the formula, R e (z) is the effective radius of the main air chamber of the air spring when the relative compression stroke of the air spring is equal to z, and R0 is the inner radius of the metal casing. s (z / 2) is the piston radius when the relative compression stroke of the air spring is equal to z, R s ′(z / 2) is R s The first derivative of (z / 2).

[0051] Preferably, in steps 1-4), the process of determining the mathematical relationship between the internal gas pressure of the air spring and the relative compression stroke of the air spring based on the thermodynamic equation of state and the gas volume partitioning theory specifically includes:

[0052] 1-4-1) Based on geometric characteristics, the internal volume of the main air chamber of the air spring is decomposed into multiple regular geometric units. The structural parameters such as the piston shape are transformed into volume change functions. By superimposing the volumes of each unit, the mathematical relationship between the total volume of the main air chamber of the air spring and the relative compression stroke z of the air spring is obtained as follows:

[0053]

[0054] R c =R0-R e (z)

[0055]

[0056] In the formula, V(z) is the total volume of the main chamber of the air spring when the relative compression stroke of the air spring is equal to z; V1(z) is the volume of the cylinder V1 when the relative compression stroke of the air spring is equal to z; V2(z) is the volume of the convex circular arc rotating body V2 when the relative compression stroke of the air spring is equal to z; V3(z) is the volume of the standard rotating body V3 when the relative compression stroke of the air spring is equal to z; V4(z) is the volume of the concave circular arc rotating body V4 when the relative compression stroke of the air spring is equal to z; π is pi; R0 is the inner radius of the metal casing; H is the distance between the upper end face of the piston and the top of the air spring when the relative compression stroke of the air spring is equal to 0; i is the perpendicular distance between the lowest point of the contact surface between the rubber air bladder and the piston and the upper end face of the piston when the relative compression stroke of the air spring is equal to 0; z is the relative compression stroke of the air spring; R c R is the difference between the inner radius of the metal casing and the effective radius of the air spring. e (z) is the effective radius of the main air chamber of the air spring when the relative compression stroke of the air spring is equal to z, R s (h) is the piston radius function. Let z be the piston radius when the relative compression stroke of the air spring is equal to z. for The first derivative;

[0057] 1-4-2) Using the thermodynamic equation of state, calculate the gas pressure inside the air spring when the relative compression stroke of the air spring is equal to z:

[0058]

[0059] In the formula, P(z) is the gas pressure inside the air spring when the relative compression stroke of the air spring is equal to z; P(0) is the gas pressure inside the air spring when the relative compression stroke of the air spring is equal to 0; V(z) is the total volume of the air spring chamber when the relative compression stroke of the air spring is equal to z; V(0) is the total volume of the air spring chamber when the relative compression stroke of the air spring is equal to 0; C p C is the specific heat capacity at constant pressure. vHere, π is the specific heat capacity at constant volume, R0 is the inner radius of the metal casing, H is the distance between the upper end face of the piston and the top of the air spring when the relative compression stroke of the air spring is 0, i is the vertical distance between the lowest point of the contact surface between the rubber bladder and the piston and the upper end face of the piston when the relative compression stroke of the air spring is 0, and z is the relative compression stroke of the air spring. c R is the difference between the inner radius of the metal casing and the effective radius of the air spring. e (z) is the effective radius of the main air chamber of the air spring when the relative compression stroke of the air spring is equal to z, R s (h) is the piston radius function.

[0060] Preferably, in steps 1-5), the process of obtaining the mathematical relationship between the rate of change of gas pressure inside the air spring and the relative compression stroke of the air spring based on the principle of energy conservation and the gas law specifically includes:

[0061] 1-5-1) During the dynamic motion of the air spring, considering the changes in the internal energy of the gas, the compression work, and the heat exchange, an energy conservation equation is established as follows:

[0062] -KS[T(z)-T(0)]dt-P(z)dV(z)=C v m0dT(z)

[0063] In the formula, K is the heat exchange coefficient, S is the heat dissipation area between the air spring and the outside, T(z) is the internal temperature of the air spring chamber when the relative compression stroke of the air spring is equal to z, T(0) is the internal temperature of the air spring chamber when the relative compression stroke of the air spring is equal to 0, t is time, P(z) is the gas pressure inside the air spring when the relative compression stroke of the air spring is equal to z, V(z) is the total volume of the air spring chamber when the relative compression stroke of the air spring is equal to z, and C v Here, m is the specific heat capacity at constant volume, and m0 is the mass of the gas inside the air spring.

[0064] 1-5-2) Based on the principle of air pressure balance and combined with the energy conservation equation, the frequency domain expression is obtained as follows:

[0065]

[0066] In the formula, P′(z) is the first derivative of P(z), P(ω) is the expression of P(z) after Fourier transform, P(z) is the gas pressure inside the air spring when the relative compression stroke of the air spring is equal to z, and z(π) is... After Fourier transform, P(0) represents the gas pressure inside the air spring when the relative compression stroke is 0, and A e(z) is the effective cross-sectional area of ​​the main air chamber of the air spring when the relative compression stroke of the air spring is equal to z, V(0) is the total volume of the air spring chamber when the relative compression stroke of the air spring is equal to 0, K is the heat exchange coefficient, R is the gas constant, and C v Where S is the specific heat capacity at constant volume, S is the heat dissipation area between the air spring and the outside, m0 is the mass of the gas inside the air spring, j is the imaginary unit, and ω is the angular frequency of vibration.

[0067] Preferably, the dynamic stiffness calculation model for the diaphragm air spring is as follows:

[0068]

[0069]

[0070] R c =R0-R e (z)

[0071] In the formula, K d Let be the dynamic stiffness of the air spring, π be pi, P(0) be the gas pressure inside the air spring when the relative compression stroke is 0, V(0) be the total volume of the air spring chamber when the relative compression stroke is 0, and C be the dynamic stiffness of the air spring. p C is the specific heat capacity at constant pressure. v For constant volume specific heat capacity, R0 is the inner radius of the metal casing, H is the distance between the upper end face of the piston and the top of the air spring when the relative compression stroke of the air spring is equal to 0, i is the vertical distance between the lowest point of the contact surface between the rubber bladder and the piston and the upper end face of the piston when the relative compression stroke of the air spring is equal to 0, z is the relative compression stroke of the air spring, R c R is the difference between the inner radius of the metal casing and the effective radius of the air spring. e (z) is the effective radius of the main air chamber of the air spring when the relative compression stroke of the air spring is equal to z, R s (h) is the piston radius function, P d Atmospheric pressure. Let z be the piston radius when the air spring's compression stroke is z. for The first derivative, R″ s (z / 2) is R s The second derivative of (z / 2), R is the gas constant, ρ is the gas density inside the air spring, and P d Where is atmospheric pressure, K is the heat exchange coefficient, S is the heat dissipation area between the air spring and the outside world, j is the imaginary unit, and ω is the angular frequency of vibration.

[0072] Preferably, the design parameters include: when the relative compression stroke is zero, the internal gas pressure, total volume, and effective cross-sectional area of ​​the air spring; the distance between the upper end face of the piston and the top of the air spring; the vertical distance between the lowest point of the contact surface between the rubber airbag and the piston and the upper end face of the piston; as well as the external shape of the piston, the inner radius of the metal casing, the thickness of the airbag, and the cord angle.

[0073] The beneficial effects of this invention are as follows:

[0074] ① Traditional methods rely on static stiffness theoretical calculation models or finite element calculations, deriving dynamic stiffness by multiplying static stiffness by the dynamic-to-static ratio, and then achieving the design goal through prototype fabrication, testing, and repeated iterations. This process is cumbersome and time-consuming. In contrast, this invention establishes a precise mathematical relationship between dynamic stiffness and air spring design parameters and vibration frequency through mathematical analysis. It directly designs based on spatial layout and dynamic stiffness targets, omitting complex iterative processes, significantly shortening the design cycle, and thus significantly improving design efficiency. The target dynamic stiffness can be directly obtained through forward design of the air spring structure.

[0075] ② This invention is designed based on mathematical relationships, which can accurately control the relationship between dynamic stiffness and various parameters. The dynamic stiffness of the manufactured air spring can be strictly controlled within the allowable error range, so that the actual product is highly consistent with the design target. Through actual experiments, the error between the dynamic stiffness results obtained by experiments and theory and the dynamic stiffness target required by the design is less than 5%.

[0076] ③ Traditional methods suffer from long design cycles, low accuracy, and require repeated iterations, leading to a significant increase in prototype manufacturing, testing costs, and time costs. In contrast, this invention, with its efficient and precise design process, reduces unnecessary duplication of work and resource waste. It obtains parameters such as effective cross-sectional area, effective cross-sectional area change rate, and internal pressure change rate without requiring prototype testing. This overcomes the limitation of traditional parameter identification methods, which are only applicable to specific test prototypes (i.e., no re-identification is required when the design changes), greatly reducing the production and design costs of air springs and effectively enhancing the product's competitiveness in the market.

[0077] ④ The clearly defined mathematical relationships in this invention can intuitively reflect the influence of changes in various parameters on dynamic stiffness, providing designers with clear design ideas and directions, effectively improving the scientificity and rationality of the design. It can not only provide strong theoretical guidance for air spring design, but also directly use the obtained mathematical model for vehicle handling, steering and ride comfort performance simulation. This allows the target range of dynamic stiffness of the air spring that meets the requirements to be determined in the early stage of vehicle performance design, greatly shortening the development cycle of the vehicle and air spring and reducing R&D costs.

[0078] Definitions:

[0079] The principle of mechanical equilibrium: The core condition for mechanical equilibrium is that the net force acting on an object is zero (in a state of rest or uniform linear motion). When an object is subjected to pressure, in order to maintain equilibrium, this pressure needs to satisfy the equilibrium relationship of "equal in magnitude and opposite in direction" with other forces (such as gravity, support force, etc.). This pressure is F = PS, where F represents pressure (unit: Newton, N), which is the force acting perpendicularly on the surface of the object; P represents pressure (unit: Pascal, Pa, i.e., N / m). 2 ), which is "pressure per unit area", reflects the effect of pressure; S represents the area of ​​force application (unit: square meters, m²). 2 ), which is the surface area under pressure.

[0080] Dynamic stiffness: The ratio of the force required per unit deformation to the unit deformation during the dynamic deformation of an air spring is called dynamic stiffness.

[0081] Dynamic-to-static ratio: The ratio of the dynamic stiffness to the static stiffness of an air spring, reflecting the degree of difference in stiffness characteristics of the air spring under dynamic and static loads.

[0082] Relative compression stroke: Once the air spring is installed in the predetermined position, the piston will be subjected to a certain external pressure (this pressure is usually called the design load), causing the air spring to be in the design load state. Taking the piston position at this time as the relative zero point, when the piston is subjected to additional dynamic pressure F in the installation position... d Then, the displacement of the piston from the initial position (relative to zero) to the final position, i.e., the relative compression stroke (Note: the additional external dynamic pressure F on the piston). d (excluding the design load of the air spring);

[0083] Effective radius of air spring: such as Figure 2 As shown, the actual working plane of the main air chamber is a circle, and the radius of this circle is the effective radius of the main air chamber of the air spring. That is, the square of the effective radius of the main air chamber of the air spring multiplied by pi equals the effective cross-sectional area of ​​the main air chamber of the air spring.

[0084] Effective cross-sectional area of ​​air spring: such as Figure 2 As shown, the effective cross-sectional area A of the main air chamber of the air spring is... e The area of ​​the actual working plane of the main air chamber is perpendicular to the force direction of the piston. The actual working plane of the main air chamber is essentially an artificially defined force-bearing plane inside a rubber bladder. The piston experiences additional external pressure F. c It equals the effective cross-sectional area of ​​the main air chamber of the air spring multiplied by the pressure of the air spring (the difference between the internal pressure of the main air chamber of the air spring and the atmospheric pressure).

[0085] Vehicle dynamics model: This refers to a computational model that uses mathematical equations to describe the overall motion of a vehicle. It simulates the vehicle's motion response (position, velocity, acceleration, attitude changes, etc.) under various operating conditions (acceleration, braking, turning, bumpy road surfaces, etc.) when subjected to forces and torques, and is widely used in automotive design, simulation, and control algorithm development. Attached Figure Description

[0086] Figure 1 This is a flowchart of the present invention;

[0087] Figure 2 This is a schematic diagram of the effective cross-sectional area of ​​the air spring in an embodiment of the present invention;

[0088] Figure 3 This is a schematic diagram defining the coordinate axes of the piston shape function of the air spring in an embodiment of the present invention;

[0089] Figure 4 This is a schematic diagram of the volume division of the air spring in an embodiment of the present invention;

[0090] Figure 5 This is a schematic diagram of the vehicle dynamics model according to an embodiment of the present invention;

[0091] Figure 6 This is a schematic diagram of the co-simulation model of an embodiment of the present invention. Detailed Implementation

[0092] like Figures 1 to 6 As shown, a method for designing the dynamic stiffness of a diaphragm air spring includes the following steps:

[0093] 1) Based on the mechanical equilibrium principle, thermodynamic equation of state, law of conservation of energy and gas volume partitioning theory of diaphragm air spring, establish a dynamic stiffness calculation model for diaphragm air spring to accurately describe the relationship between the design parameters, vibration frequency and dynamic stiffness of diaphragm air spring.

[0094] In this embodiment, the method for establishing the dynamic stiffness calculation model specifically includes:

[0095] 1-1) Perform a force analysis on the air spring to determine the mathematical relationship between the dynamic restoring force and the relative compression stroke of the air spring, as follows:

[0096] F d (z)=P(z)·A e (z)-P d ·A e (z)

[0097] In the formula, F d (z) represents the dynamic restoring force F acting on the air spring. d The functional relationship between P and the relative compression stroke z of the air springd Let P(z) be the atmospheric pressure, and P(z) be the gas pressure inside the air spring when the relative compression stroke of the air spring is equal to z. e (z) is the effective cross-sectional area of ​​the main air chamber of the air spring when the relative compression stroke of the air spring is equal to z;

[0098] 1-2) Take the derivative of the dynamic restoring force and define this derivative as the dynamic stiffness of the air spring, as follows:

[0099]

[0100] F d (z)=(P(z)-P d A e (z)

[0101] In the formula, K d F is the dynamic stiffness of the air spring. d (z) represents the dynamic restoring force F acting on the air spring. d The functional relationship between the relative compression stroke z of the air spring and the air spring is given by: P(z) is the gas pressure inside the air spring when the relative compression stroke is equal to z, and P′(z) is the first derivative of P(z). d At atmospheric pressure, A e (z) is the effective cross-sectional area of ​​the main air chamber of the air spring when the relative compression stroke of the air spring is equal to z, A' e (z) is A e The first derivative of (z), where z is the relative compression stroke of the air spring;

[0102] 1-3) Based on the internal structural parameters of the air spring, determine the mathematical relationships between the effective cross-sectional area, the rate of change of the effective cross-sectional area, and the relative compression stroke of the air spring, as follows:

[0103] 1-3-1) Mathematical relationship between effective cross-sectional area and relative compression stroke of air spring:

[0104] A e (z)=π·[R e (z)] 2

[0105] In the formula, A e (z) is the effective cross-sectional area of ​​the main air chamber of the air spring when the relative compression stroke of the air spring is equal to z, π is pi, and R e (z) is the effective radius of the main air chamber of the air spring when the relative compression stroke of the air spring is equal to z;

[0106] 1-3-2) Mathematical relationship between effective cross-sectional area change rate and relative compression stroke of air spring:

[0107] A'e (z)=2π·R e (z)·R' e (z)

[0108] In the formula, A' e (z) represents the rate of change of the effective cross-sectional area of ​​the main air chamber of the air spring when the relative compression stroke of the air spring is equal to z, where π is pi and R is the ratio of π / 2 to π / 2. e (z) is the effective radius of the main air chamber of the air spring when the relative compression stroke of the air spring is equal to z, R' e (z) is R e The first derivative of (z);

[0109] 1-3-3) When the relative compression stroke of the air spring is equal to z, the effective radius R of the main air chamber of the air spring is... e (z):

[0110]

[0111] In the formula, R e (z) is the effective radius of the main air chamber of the air spring when the relative compression stroke of the air spring is equal to z, and R0 is the inner radius of the metal casing. s (z / 2) is the piston radius when the relative compression stroke of the air spring is equal to z, R s ′(z / 2) is R s The first derivative of (z / 2), R s (z / 2) and R s The two parameters, z′ and z / 2, are strongly correlated with the external shape of the piston.

[0112] 1-4) Based on the thermodynamic equation of state and the theory of gas volume partitioning, the mathematical relationship between the gas pressure inside the air spring and the relative compression stroke of the air spring is obtained as follows:

[0113] 1-4-1) Based on geometric characteristics, the internal volume of the main air chamber of the air spring is decomposed into multiple regular geometric units (i.e., gas volume partitioning theory). Structural parameters such as piston shape are transformed into volume change functions. By superimposing the volumes of each unit, the relationship between the total volume of the main air chamber of the air spring and the relative compression stroke z is obtained. In other words, in this embodiment, the internal volume of the main air chamber of a single-chamber air spring is decomposed into a cylinder V1, a convex circular arc rotating body V2, a standard rotating body V3, and a concave circular arc rotating body V4. The mathematical relationship between the total volume of the main air chamber of the air spring and the relative compression stroke z of the air spring is as follows:

[0114]

[0115] R c =R0-R e (z)

[0116]

[0117] In the formula, V(z) is the total volume of the main chamber of the air spring when the relative compression stroke of the air spring is equal to z; V1(z) is the volume of the cylinder V1 when the relative compression stroke of the air spring is equal to z; V2(z) is the volume of the convex circular arc rotating body V2 when the relative compression stroke of the air spring is equal to z; V3(z) is the volume of the standard rotating body V3 when the relative compression stroke of the air spring is equal to z; V4(z) is the volume of the concave circular arc rotating body V4 when the relative compression stroke of the air spring is equal to z; π is pi; R0 is the inner radius of the metal casing; H is the distance between the upper end face of the piston and the top of the air spring when the relative compression stroke of the air spring is equal to 0; i is the perpendicular distance between the lowest point of the contact surface between the rubber air bladder and the piston and the upper end face of the piston when the relative compression stroke of the air spring is equal to 0; z is the relative compression stroke of the air spring; R c R is the difference between the inner radius of the metal casing and the effective radius of the air spring. e (z) is the effective radius of the main air chamber of the air spring when the relative compression stroke of the air spring is equal to z, R s (h) is the piston radius function. Let z be the piston radius when the relative compression stroke of the air spring is equal to z. for The first derivative;

[0118] 1-4-2) Using the thermodynamic equation of state, the mathematical relationship between the gas pressure inside the air spring and the relative compression stroke z of the air spring is obtained:

[0119]

[0120] In this embodiment, the mathematical relationship between the gas pressure inside the air spring and the relative compression stroke z of the air spring is expressed by the following mathematical expression:

[0121]

[0122] In the formula, P(z) is the gas pressure inside the air spring when the relative compression stroke of the air spring is equal to z; P(0) is the gas pressure inside the air spring when the relative compression stroke of the air spring is equal to 0; V(z) is the total volume of the air spring chamber when the relative compression stroke of the air spring is equal to z; V(0) is the total volume of the air spring chamber when the relative compression stroke of the air spring is equal to 0; C p C is the specific heat capacity at constant pressure. vHere, π is the specific heat capacity at constant volume, R0 is the inner radius of the metal casing, H is the distance between the upper end face of the piston and the top of the air spring when the relative compression stroke of the air spring is 0, i is the vertical distance between the lowest point of the contact surface between the rubber bladder and the piston and the upper end face of the piston when the relative compression stroke of the air spring is 0, and z is the relative compression stroke of the air spring. c R is the difference between the inner radius of the metal casing and the effective radius of the air spring. e (z) is the effective radius of the main air chamber of the air spring when the relative compression stroke of the air spring is equal to z, R s (h) is the piston radius function.

[0123] 1-5) Based on the principle of energy conservation and the thermodynamic equation of state, the mathematical relationship between the rate of change of gas pressure inside the air spring and the relative compression stroke of the air spring is obtained, specifically including:

[0124] 1-5-1) During the dynamic motion of the air spring, considering the changes in the internal energy of the gas, the compression work, and the heat exchange, an energy conservation equation is established as follows:

[0125] -KS[T(z)-T(0)]dt-P(z)dV(z)=C v m0dT(z)

[0126] In the formula, K is the heat exchange coefficient, S is the heat dissipation area between the air spring and the outside, T(z) is the internal temperature of the air spring chamber when the relative compression stroke of the air spring is equal to z, T(0) is the internal temperature of the air spring chamber when the relative compression stroke of the air spring is equal to 0, t is time, P(z) is the gas pressure inside the air spring when the relative compression stroke of the air spring is equal to z, V(z) is the total volume of the air spring chamber when the relative compression stroke of the air spring is equal to z, and C v Here, m is the specific heat capacity at constant volume, and m0 is the mass of the gas inside the air spring.

[0127] 1-5-2) Based on the principle of air pressure balance and combined with the energy conservation equation, the frequency domain expression is obtained as follows:

[0128] 1-5-2-1) In the micro-displacement, we have have:

[0129]

[0130] 1-5-2-2) By performing a Fourier transform and ignoring the constant term, we can obtain:

[0131]

[0132] In the formula, P(ω) and z(ω) are respectively P(z), The expression after Fourier transform.

[0133] (1-5-2-3) Finally, the mathematical relationship between the rate of change of gas pressure inside the air spring and the relative compression stroke of the air spring can be obtained, as shown below:

[0134]

[0135] In the formula, P′(z) is the first derivative of P(z), P(ω) is the expression of P(z) after Fourier transform, P(z) is the gas pressure inside the air spring when the relative compression stroke of the air spring is equal to z, and z(π) is... After Fourier transform, P(0) represents the gas pressure inside the air spring when the relative compression stroke is 0, and A e (z) is the effective cross-sectional area of ​​the main air chamber of the air spring when the relative compression stroke of the air spring is equal to z, V(0) is the total volume of the air spring chamber when the relative compression stroke of the air spring is equal to 0, K is the heat exchange coefficient, R is the gas constant, and C v Where S is the specific heat capacity at constant volume, S is the heat dissipation area between the air spring and the outside, m0 is the mass of the gas inside the air spring, j is the imaginary unit, and ω is the angular frequency of vibration.

[0136] 1-6) Based on the mathematical relationships established in steps 1-1) to 1-5), the mathematical relationship between the dynamic stiffness of the air spring and its relative compression stroke is determined, resulting in the dynamic stiffness calculation model for the diaphragm air spring. In other words, the dynamic stiffness mechanical relationship expression for the single-cavity air spring in this embodiment is as follows:

[0137]

[0138]

[0139] R c =R0-R e (z)

[0140] In the formula, K d Let be the dynamic stiffness of the air spring, π be pi, P(0) be the gas pressure inside the air spring when the relative compression stroke is 0, V(0) be the total volume of the air spring chamber when the relative compression stroke is 0, and C be the dynamic stiffness of the air spring. p C is the specific heat capacity at constant pressure. v For constant volume specific heat capacity, R0 is the inner radius of the metal casing, H is the distance between the upper end face of the piston and the top of the air spring when the relative compression stroke of the air spring is equal to 0, i is the vertical distance between the lowest point of the contact surface between the rubber bladder and the piston and the upper end face of the piston when the relative compression stroke of the air spring is equal to 0, z is the relative compression stroke of the air spring, R c R is the difference between the inner radius of the metal casing and the effective radius of the air spring. e(z) is the effective radius of the main air chamber of the air spring when the relative compression stroke of the air spring is equal to z, R s (h) is the piston radius function, P d Atmospheric pressure. Let z be the piston radius when the air spring's compression stroke is z. for The first derivative, R″ s (z / 2) is R s The second derivative of (z / 2), R is the gas constant, ρ is the gas density inside the air spring, and P d Where is atmospheric pressure, K is the heat exchange coefficient, S is the heat dissipation area between the air spring and the outside world, j is the imaginary unit, and ω is the angular frequency of vibration.

[0141] In the dynamic stiffness calculation model described above, the vibration angular frequency ω is actually used to represent the vibration frequency f, because the vibration frequency f can be represented by the vibration angular frequency ω (i.e., ω = 2πf, where ω is the vibration angular frequency, π is pi, and f is the vibration frequency). Therefore, the dynamic stiffness calculation model described above can accurately describe the mathematical relationship between the design parameters of the diaphragm air spring, the vibration frequency, and the dynamic stiffness.

[0142] 2) Establish a vehicle dynamics model and combine it with the dynamic stiffness calculation model to construct a joint simulation model (i.e., "vehicle dynamics-air spring dynamic stiffness calculation model", which is used to represent the relationship between various vehicle dynamics parameters, air spring dynamic stiffness, and the design parameters and vibration frequency of the diaphragm air spring).

[0143] Essentially, this involves constructing a co-simulation model of the entire vehicle, including air springs. This model can simulate the structure and operating state of a real car, accurately reflecting the function of the air springs within the vehicle and providing a reliable virtual platform for subsequent simulation analysis. The construction of the co-simulation model is as follows: Figure 6 As shown, the methods for establishing this co-simulation model include:

[0144] 2-1) In MATLAB software, construct the dynamic stiffness calculation model of the whole vehicle dynamics model and the single-cavity air spring respectively;

[0145] 2-2) Clarify the input and output parameters of the air spring module and dynamic stiffness calculation model in the vehicle dynamics model: The input parameter of the dynamic stiffness calculation model is the relative compression stroke of the air spring, and the output parameter is the dynamic restoring force of the air spring.

[0146] The input parameter of the air spring module in the vehicle dynamics model is the dynamic restoring force of the air spring. After the vehicle dynamics calculation, the output parameter of the module is the relative compression stroke of the air spring.

[0147] (2-3) Connect the output parameters of the dynamic stiffness calculation model to the input parameter interface of the air spring module in the vehicle dynamics model, and connect the input parameters of the dynamic stiffness calculation model to the output parameter interface of the air spring module in the vehicle dynamics model. Through the above signal connection, the construction of the co-simulation model is completed.

[0148] 3) Use the co-simulation model to perform a simulation analysis on the vehicle, and determine the target range of the dynamic stiffness of the air spring and the setting range of the compression stroke according to the target requirements of the vehicle performance.

[0149] That is, use the co-simulation model to perform a simulation analysis on the handling stability performance, steering performance, and ride comfort performance of the vehicle, and determine the target range of the dynamic stiffness of the air spring and the setting range of the relative compression stroke according to the target requirements of the vehicle performance, as follows:

[0150] 3-1) Set the simulation conditions and virtual road surface

[0151] According to the test method of the vehicle performance indicators, set the simulation conditions for the above co-simulation model, such as steady-state circular driving conditions, full throttle acceleration conditions, extreme braking conditions, sine sweep conditions, steering center feeling conditions, etc., to comprehensively test the handling stability performance and steering performance of the vehicle; at the same time, set virtual road surfaces with different characteristics, such as roads with different roughness, speed bump roads, etc., to test the ride comfort performance of the vehicle.

[0152] 3-2) Conduct a simulation analysis

[0153] Run the co-simulation model, and under the set simulation conditions and virtual road surface, perform a simulation analysis on the handling stability performance, steering performance, and ride comfort performance of the vehicle to obtain the simulation values of various vehicle performance indicators, such as the understeer degree, roll gradient, pitch gradient, natural frequency of yaw rate, root mean square value of primary pitch acceleration, root mean square value of primary pitch acceleration, root mean square value of body vertical vibration acceleration, shimmy, etc. shown in Table 1.

[0154] 3-3) Determine the parameter range

[0155] Compare the vehicle performance indicator values related to the dynamic stiffness of the air spring obtained from the simulation with the pre-set target range. If all the indicator values fall within the target range, it is determined that the vehicle performance corresponding to the current air spring parameters is qualified. Based on the qualified simulation results, determine the maximum / minimum target value of the dynamic stiffness of the air spring and the maximum / minimum setting value of the relative compression stroke.

[0156] Table 1

[0157]

[0158]

[0159] Finally, the target ranges for each parameter of the front suspension air spring determined in this embodiment are shown in Table 2:

[0160] Table 2

[0161] Target range for air spring dynamic stiffness (1Hz) Relative compression stroke setting range 52-55 N / mm ±50mm

[0162] In other words, the target range of dynamic stiffness of the air spring at a vibration frequency of 1Hz, as determined in this embodiment, is 52-55 N / mm, and the set range of relative compression stroke is ±50 mm.

[0163] 4) Determine the range of values ​​for various design parameters of the diaphragm air spring based on the suspension's limit compression stroke range, the allowable space requirements for the diaphragm air spring (i.e., the size of the installation space reserved for the air spring), and the load requirements.

[0164] In this embodiment, the design parameters of the diaphragm air spring include: when the relative compression stroke of the air spring is equal to 0: the internal gas pressure P(0), total volume V(0), and effective cross-sectional area A of the air spring. e (0), the distance H between the upper end face of the piston and the top of the air spring, the vertical distance i between the lowest point of the contact surface between the rubber air bladder and the piston and the upper end face of the piston; the initial value R of the piston radius function. s (0), piston radius function R s (h) is used to indicate the external shape of the piston; the inner radius R0 of the metal casing; the thickness of the air bladder; the angle of the cord, etc.

[0165] 4-1) Determine the range of values ​​for the inner radius R0 of the metal casing and related parameters based on the allowable space requirements of the air spring.

[0166] It is known that the air springs of this suspension can be installed with a maximum diameter ≤160mm and an installation height ≤380mm; the limit compression stroke is ±80mm.

[0167] (1) The air spring is equipped with a dust cover. Space needs to be left for the dust cover. Therefore, the inner radius of the metal protective cylinder is set to be 65-70mm.

[0168] (2) There is also a moving bladder between the piston and the metal casing, so the initial value of the piston radius function R is set to 0 when the relative compression stroke of the air spring is equal to 0. s (0) The value range is 45-55mm;

[0169] (3) The piston radius function is set to be (0,R) s Ten typical curves with (0) as the origin;

[0170] (4) Based on the parameters determined in steps (1)-(2), set the effective cross-sectional area A of the air spring when the relative compression stroke is equal to 0.e (0) is 7854-12272mm 2 ;

[0171] (5) According to the limit compression stroke range of the suspension, when the relative compression stroke of the air spring is equal to 0, the vertical distance i between the lowest point of the contact surface between the rubber airbag and the piston and the upper end surface of the piston is 60-80mm.

[0172] (6) Based on the installation height and the limit compression stroke range of the suspension, the distance H between the upper end face of the piston and the top of the air spring when the relative compression stroke of the air spring is equal to 0 is set to be 150-200mm.

[0173] (7) Based on the parameters determined in steps (1), (2), (5), and (6), the total volume V(0) when the relative compression stroke of the air spring is equal to 0 is set to a range of 1.9-3.0L.

[0174] 4-2) Based on the air spring load requirements and related parameters, set the range of values ​​for the internal gas pressure P(0) when the relative compression stroke of the air spring is equal to 0;

[0175] Given that the required load capacity of the air spring is 9800-10000N, because the internal gas pressure P(0) when the relative compression stroke of the air spring is equal to 0 and the effective cross-sectional area A e The product of (0) equals the bearing capacity. Based on design experience, the range of the internal gas pressure P(0) when the relative compression stroke of the air spring is equal to 0 is set to 0.82-1.10MPa.

[0176] The cord angle affects the lateral and longitudinal stiffness of the air spring. Considering its impact on performance within the allowable space constraints, the cord angle is set to a range of 30°-40°. The airbag thickness is related to the manufacturing process and the durability of the air spring, and its range is set to 2-3mm.

[0177] 4-3) The final range of design parameters

[0178] Considering both suspension load-bearing requirements and allowable space requirements, the value ranges for various design parameters of the diaphragm air spring are as follows:

[0179] (1) The range of the inner radius R0 of the metal casing is 65-70mm;

[0180] (2) When the relative compression stroke of the air spring is equal to 0:

[0181] The internal gas pressure P(0) ranges from 0.82 to 1.10 MPa.

[0182] Total volume V(0) ranges from 1.9 to 3.0 L;

[0183] Effective cross-sectional area A e (0) Value range: 7854-12272mm 2 ;

[0184] The distance H between the upper end face of the piston and the top of the air spring ranges from 150 to 200 mm.

[0185] The vertical distance i between the lowest point of the contact surface between the rubber airbag and the piston and the upper end face of the piston is 60-80mm.

[0186] Initial value R of piston radius function s (0) Value range: 45-55mm;

[0187] Piston radius function R s (h): 10 typical curves;

[0188] (3) Airbag thickness: 2-3mm;

[0189] (4) Cord angle: 30°-40°;

[0190] 5) Based on the target range of dynamic stiffness and the range of design parameters for diaphragm air springs, the feasibility of the schemes is iteratively calculated using a dynamic stiffness calculation model, resulting in several diaphragm air spring manufacturing schemes with dynamic stiffness values ​​within the target range, as shown in Table 3:

[0191] Table 3

[0192]

[0193]

[0194] 6) Based on the spatial arrangement constraints of the air springs, the motion clearance was checked, and several diaphragm air spring manufacturing schemes that could guide production were selected from various diaphragm air spring manufacturing schemes, as shown in Table 4:

[0195] Table 4

[0196]

[0197] 7) Import the multiple diaphragm air spring manufacturing schemes shown in Table 5 that can guide production into the joint simulation model for simulation analysis, and take the manufacturing scheme that can make the vehicle performance optimal as the final design scheme of the diaphragm air spring.

[0198] Table 5

[0199]

[0200]

[0201] By comparing the simulation results, Scheme 2 was finally selected as the final dynamic stiffness design scheme.

[0202] In other words, multiple diaphragm air spring manufacturing schemes that can guide production are imported into a co-simulation model to conduct simulation analysis on the vehicle's handling stability, steering performance, and ride comfort. The scheme that optimizes the overall vehicle performance is then identified, and this scheme is taken as the final design scheme for the diaphragm air spring. The dynamic stiffness of the air spring corresponding to this final design scheme is the optimal dynamic stiffness that satisfies the overall vehicle performance, thus completing the dynamic stiffness design of the air spring.

[0203] Experiments have shown that air springs manufactured using this invention not only have dynamic stiffness that fully meets the requirements of vehicle manufacturers, but also significantly improve production efficiency (by more than 50% compared to traditional methods) and reduce production costs (by more than 30% compared to traditional methods).

[0204] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications made to the present invention by those skilled in the art without departing from the spirit of the present invention shall fall within the protection scope of the present invention.

Claims

1. A method for designing the dynamic stiffness of a diaphragm air spring, characterized in that, Includes the following steps: 1) Based on the mechanical equilibrium principle, thermodynamic equation of state, law of conservation of energy and gas volume partitioning theory of diaphragm air spring, establish a dynamic stiffness calculation model for diaphragm air spring to accurately describe the relationship between the design parameters, vibration frequency and dynamic stiffness of diaphragm air spring. 2) Establish a vehicle dynamics model and combine it with a dynamic stiffness calculation model to construct a joint simulation model; 3) Use a co-simulation model to perform simulation analysis on the whole vehicle, and determine the target range of the dynamic stiffness of the air spring and the setting range of the relative compression stroke based on the target requirements of the whole vehicle performance. 4) Determine the range of values ​​for various design parameters of the diaphragm air spring based on the suspension's ultimate compression stroke range, the allowable space requirements and load-bearing requirements of the diaphragm air spring; 5) Based on the target range of dynamic stiffness of the diaphragm air spring and the range of design parameters, the dynamic stiffness calculation model is used to iteratively calculate the feasibility of the schemes, and several diaphragm air spring manufacturing schemes with dynamic stiffness values ​​within the target range are obtained. 6) Based on the spatial arrangement constraints of the air spring, the motion clearance is checked, and multiple diaphragm air spring manufacturing schemes that can guide production are selected from various diaphragm air spring manufacturing schemes. 7) Import multiple diaphragm air spring manufacturing schemes that can guide production into the joint simulation model for simulation analysis, and take the manufacturing scheme that can optimize the performance of the whole vehicle as the final design scheme of the diaphragm air spring.

2. The design method according to claim 1, characterized in that, In step 1), the method for establishing the dynamic stiffness calculation model specifically includes: 1-1) Perform a force analysis on the air spring to determine the mathematical relationship between the dynamic restoring force and the relative compression stroke of the air spring; 1-2) Take the derivative of the dynamic restoring force and define the derivative as the dynamic stiffness of the air spring; 1-3) Based on the internal structural parameters of the air spring, determine the mathematical relationship between the effective cross-sectional area and the rate of change of the effective cross-sectional area and the relative compression stroke of the air spring, respectively; 1-4) Based on the thermodynamic equation of state and the theory of gas volume partitioning, the mathematical relationship between the gas pressure inside the air spring and the relative compression stroke of the air spring is obtained; 1-5) Based on the principle of energy conservation and the thermodynamic equation of state, the mathematical relationship between the rate of change of gas pressure inside the air spring and the relative compression stroke of the air spring is obtained; 1-6) Based on the mathematical relationships in steps 1-1) to 1-5), determine the mathematical relationship between the dynamic stiffness of the air spring and the relative compression stroke, and obtain the dynamic stiffness calculation model of the diaphragm air spring.

3. The design method according to claim 2, characterized in that, In step 1-1), a force analysis was performed on the air spring, and the mathematical relationship between the dynamic restoring force and the relative compression stroke of the air spring was obtained as follows: F d (z)=P(z)·A e (z)-P d ·A e (z) In the formula, F d (z) represents the dynamic restoring force F acting on the air spring. d The functional relationship between P and the relative compression stroke z of the air spring d Let P(z) be the atmospheric pressure, and P(z) be the gas pressure inside the air spring when the relative compression stroke of the air spring is equal to z. e (z) is the effective cross-sectional area of ​​the main air chamber of the air spring when the relative compression stroke of the air spring is equal to z.

4. The design method according to claim 2, characterized in that, In steps 1-2), the derivative of the dynamic restoring force is calculated, and this derivative is defined as the dynamic stiffness of the air spring, as follows: F d (z)=(P(z)-P d )A e (z) In the formula, K d F is the dynamic stiffness of the air spring. d (z) represents the dynamic restoring force F acting on the air spring. d The functional relationship between the relative compression stroke z of the air spring and the air spring is given by: P(z) is the gas pressure inside the air spring when the relative compression stroke is equal to z, and P′(z) is the first derivative of P(z). d At atmospheric pressure, A e (z) is the effective cross-sectional area of ​​the main air chamber of the air spring when the relative compression stroke of the air spring is equal to z, A' e (z) is A e The first derivative of (z), where z is the relative compression stroke of the air spring.

5. The design method according to claim 2, characterized in that, In steps 1-3), based on the internal structural parameters of the air spring, the mathematical relationships between the effective cross-sectional area, the rate of change of the effective cross-sectional area, and the relative compression stroke of the air spring are as follows: AND e (z)=π·[R e (With)] 2 In the formula, A e (z) is the effective cross-sectional area of ​​the main air chamber of the air spring when the relative compression stroke of the air spring is equal to z, π is pi, and R e (z) is the effective radius of the main air chamber of the air spring when the relative compression stroke of the air spring is equal to z; A’ e (z)=2π·R e (z)·R’ e (z) In the formula, A' e (z) represents the rate of change of the effective cross-sectional area of ​​the main air chamber of the air spring when the relative compression stroke of the air spring is equal to z, where π is pi and R is the ratio of π / 2 to π / 2. e (z) is the effective radius of the main air chamber of the air spring when the relative compression stroke of the air spring is equal to z, R' e (z) is R e The first derivative of (z); In the formula, R e (z) is the effective radius of the main air chamber of the air spring when the relative compression stroke of the air spring is equal to z, and R0 is the inner radius of the metal casing. s (z / 2) is the piston radius when the relative compression stroke of the air spring is equal to z, R s ′(z / 2) is R s The first derivative of (z / 2).

6. The design method according to claim 2, characterized in that, Steps 1-4) involve determining the mathematical relationship between the internal gas pressure of the air spring and the relative compression stroke of the air spring based on the thermodynamic equation of state and the theory of gas volume partitioning. This process specifically includes: 1-4-1) Based on geometric characteristics, the internal volume of the main air chamber of the air spring is decomposed into multiple regular geometric units. The structural parameters such as the piston shape are transformed into volume change functions. By superimposing the volumes of each unit, the mathematical relationship between the total volume of the main air chamber of the air spring and the relative compression stroke z of the air spring is obtained as follows: R c =R0-R e (z) In the formula, V(z) is the total volume of the main chamber of the air spring when the relative compression stroke of the air spring is equal to z; V1(z) is the volume of the cylinder V1 when the relative compression stroke of the air spring is equal to z; V2(z) is the volume of the convex circular arc rotating body V2 when the relative compression stroke of the air spring is equal to z; V3(z) is the volume of the standard rotating body V3 when the relative compression stroke of the air spring is equal to z; V4(z) is the volume of the concave circular arc rotating body V4 when the relative compression stroke of the air spring is equal to z; π is pi; R0 is the inner radius of the metal casing; H is the distance between the upper end face of the piston and the top of the air spring when the relative compression stroke of the air spring is equal to 0; i is the perpendicular distance between the lowest point of the contact surface between the rubber air bladder and the piston and the upper end face of the piston when the relative compression stroke of the air spring is equal to 0; z is the relative compression stroke of the air spring; R c R is the difference between the inner radius of the metal casing and the effective radius of the air spring. e (z) is the effective radius of the main air chamber of the air spring when the relative compression stroke of the air spring is equal to z, R s (h) is the piston radius function. Let z be the piston radius when the relative compression stroke of the air spring is equal to z. for The first derivative; 1-4-2) Using the thermodynamic equation of state, calculate the gas pressure inside the air spring when the relative compression stroke of the air spring is equal to z: In the formula, P(z) is the gas pressure inside the air spring when the relative compression stroke of the air spring is equal to z; P(0) is the gas pressure inside the air spring when the relative compression stroke of the air spring is equal to 0; V(z) is the total volume of the air spring chamber when the relative compression stroke of the air spring is equal to z; V(0) is the total volume of the air spring chamber when the relative compression stroke of the air spring is equal to 0; C p C is the specific heat capacity at constant pressure. v Here, π is the specific heat capacity at constant volume, R0 is the inner radius of the metal casing, H is the distance between the upper end face of the piston and the top of the air spring when the relative compression stroke of the air spring is 0, i is the vertical distance between the lowest point of the contact surface between the rubber bladder and the piston and the upper end face of the piston when the relative compression stroke of the air spring is 0, and z is the relative compression stroke of the air spring. c R is the difference between the inner radius of the metal casing and the effective radius of the air spring. e (z) is the effective radius of the main air chamber of the air spring when the relative compression stroke of the air spring is equal to z, R s (h) is the piston radius function.

7. The design method according to claim 2, characterized in that, Steps 1-5) involve obtaining the mathematical relationship between the rate of change of gas pressure inside the air spring and the relative compression stroke of the air spring, based on the principle of energy conservation and the gas law. This process specifically includes: 1-5-1) During the dynamic motion of the air spring, considering the changes in the internal energy of the gas, the compression work, and the heat exchange, an energy conservation equation is established as follows: -KS[T(z)-T(0)]dt-P(z)dV(z)=C v m0dT(z) In the formula, K is the heat exchange coefficient, S is the heat dissipation area between the air spring and the outside, T(z) is the internal temperature of the air spring chamber when the relative compression stroke of the air spring is equal to z, T(0) is the internal temperature of the air spring chamber when the relative compression stroke of the air spring is equal to 0, t is time, P(z) is the gas pressure inside the air spring when the relative compression stroke of the air spring is equal to z, V(z) is the total volume of the air spring chamber when the relative compression stroke of the air spring is equal to z, and C v Here, m is the specific heat capacity at constant volume, and m0 is the mass of the gas inside the air spring. 1-5-2) Based on the principle of air pressure balance and combined with the energy conservation equation, the frequency domain expression is obtained as follows: In the formula, P′(z) is the first derivative of P(z), P(ω) is the expression of P(z) after Fourier transform, P(z) is the gas pressure inside the air spring when the relative compression stroke of the air spring is equal to z, and z(ω) is... After Fourier transform, P(0) represents the gas pressure inside the air spring when the relative compression stroke is 0, and A e (z) is the effective cross-sectional area of ​​the main air chamber of the air spring when the relative compression stroke of the air spring is equal to z, V(0) is the total volume of the air spring chamber when the relative compression stroke of the air spring is equal to 0, K is the heat exchange coefficient, R is the gas constant, and C v Where S is the specific heat capacity at constant volume, S is the heat dissipation area between the air spring and the outside, m0 is the mass of the gas inside the air spring, j is the imaginary unit, and ω is the angular frequency of vibration.

8. The design method according to claim 1 or 2, characterized in that, The dynamic stiffness calculation model for the diaphragm air spring is as follows: R c =R0-R e (z) In the formula, K d Let be the dynamic stiffness of the air spring, π be pi, P(0) be the gas pressure inside the air spring when the relative compression stroke is 0, V(0) be the total volume of the air spring chamber when the relative compression stroke is 0, and C be the dynamic stiffness of the air spring. p C is the specific heat capacity at constant pressure. v For constant volume specific heat capacity, R0 is the inner radius of the metal casing, H is the distance between the upper end face of the piston and the top of the air spring when the relative compression stroke of the air spring is equal to 0, i is the vertical distance between the lowest point of the contact surface between the rubber bladder and the piston and the upper end face of the piston when the relative compression stroke of the air spring is equal to 0, z is the relative compression stroke of the air spring, R c R is the difference between the inner radius of the metal casing and the effective radius of the air spring. e (z) is the effective radius of the main air chamber of the air spring when the relative compression stroke of the air spring is equal to z, R s (h) is the piston radius function, P d Atmospheric pressure. Let z be the piston radius when the air spring's compression stroke is z. for The first derivative, R″ s (z / 2) is R s The second derivative of (z / 2), R is the gas constant, ρ is the gas density inside the air spring, and P d Where is atmospheric pressure, K is the heat exchange coefficient, S is the heat dissipation area between the air spring and the outside world, j is the imaginary unit, and ω is the angular frequency of vibration.

9. The design method according to claim 1, characterized in that, The design parameters include: when the relative compression stroke is zero, the internal gas pressure, total volume, and effective cross-sectional area of ​​the air spring; the distance between the upper end face of the piston and the top of the air spring; the vertical distance between the lowest point of the contact surface between the rubber airbag and the piston and the upper end face of the piston; as well as the external shape of the piston, the inner radius of the metal casing, the thickness of the airbag, and the cord angle.

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