A method for analyzing dynamic characteristics of an air spring
By constructing a dual time-domain and frequency-domain model of the air spring, the problem of insufficient calculation accuracy in the low-frequency band of the air spring is solved, and high-precision dynamic characteristic analysis is achieved, which is applicable to the design of suspension systems for commercial vehicles and new energy passenger vehicles.
Patent Information
- Application Number
- CN202610725542.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-05-25
- Publication Date
- 2026-06-23
AI Technical Summary
The mathematical model for the dynamic characteristics of air springs across the entire frequency range in the existing technology has insufficient calculation accuracy in the low-frequency range of 0-1 Hz, which makes it difficult to meet the design requirements of automotive suspension systems.
A dual time-domain and frequency-domain model of an air spring is constructed. The relationship between effective area and volume change is identified through a quasi-static test method. Friction force is fitted by a friction model, and a differential equation for air pressure change is established. The first-order Taylor expansion method is used for linearization. A complex dynamic stiffness model is superimposed to achieve parameter identification and modeling.
It improves the calculation accuracy in the 0-1 Hz low-frequency band, meets the 0.4 Hz test requirements of the GB/T 13061-2017 national standard, and is suitable for the low-frequency comfort design of suspension systems in commercial vehicles and new energy passenger vehicles, shortening the R&D cycle and reducing design costs.
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Figure CN122263549A_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the field of automotive shock absorber technology, specifically a method for analyzing the dynamic characteristics of air springs. Background Technology
[0002] The automotive suspension system is a key subsystem affecting vehicle driving performance. Its main functions include isolating vibrations caused by road surface unevenness and transmitting loads between the wheels and the vehicle body. Air springs, due to their advantages of height adjustability, low natural frequency, and low noise levels, have been widely used in commercial vehicle suspension systems. In recent years, the requirements for driving range in new energy vehicles have continued to increase. The technological need to utilize air springs to achieve vehicle height adjustment to reduce wind resistance and optimize energy consumption has become increasingly urgent. This has driven a significant increase in the application of air springs in the new energy passenger vehicle sector.
[0003] To meet the requirements of air springs in vehicle suspension system engineering applications, accurate mathematical models are needed to characterize their dynamic characteristics. The dynamic characteristics of air springs are influenced by various factors such as air pressure, amplitude, and frequency, exhibiting significant nonlinearity. Notably, in the 0-3Hz low-frequency range, the dynamic characteristics of air springs have a significant impact on overall vehicle ride comfort. The national standard GB / T 13061-2017, "Technical Specification for Air Springs for Commercial Vehicle Air Suspension," explicitly stipulates that the dynamic characteristics of air springs should be tested using vertical vibration excitation at a frequency of 0.4 Hz. This standard further confirms the importance of low-frequency dynamic characteristics for air spring engineering applications. Therefore, the dynamic characteristics of air springs across the entire frequency range, especially in the 0-1 Hz low-frequency range, have significant engineering value for suspension system design. However, existing mathematical models for the dynamic characteristics of air springs across the entire frequency range still lack sufficient calculation accuracy in the 0-1 Hz low-frequency range, making it difficult to meet the actual needs of automotive suspension system design. Summary of the Invention
[0004] To address the aforementioned issues, the invention aims to provide a method for analyzing the dynamic characteristics of air springs. This method establishes time-domain and frequency-domain models of air springs to predict their dynamic characteristics across the entire frequency range, including the 0-1 Hz low-frequency band, which is helpful for optimizing the design of air spring structural parameters.
[0005] To achieve the above objectives, the technical solution of the invention is a method for analyzing the dynamic characteristics of an air spring, comprising the following steps; Step 1: Use the quasi-static test method to identify the relationship between the effective area and volume of the air spring and the displacement, and use the friction model to fit the friction force formula; Step 2: Establish the differential equation for the change in air pressure inside the air spring; Step 3: Based on the differential equation of the internal air pressure change of the air spring, the heat transfer coefficient in the differential equation is identified by experimental method; Step 4: Substitute the identified heat transfer coefficient into the differential equation of internal air pressure change to obtain the time-domain model of the internal air pressure of the air spring. Step 5: According to the formula Establish an air spring air pressure unit The time-domain variation results are given, where P and Pa are the internal air pressure and atmospheric pressure of the air spring, respectively, and Ae is the effective area of the air spring, according to the formula... Establish a time-domain model of the total response force F acting on the air spring, where For friction force units; Step 6: Apply the differential equations and formulas for the aforementioned air pressure. After linearization using the first-order Taylor expansion method, according to the formula... Establish the complex dynamic stiffness of the air spring pneumatic pressure unit ,in This represents the Laplace transform, where s is the Laplace complex variable. Angular frequency; Step 7: Superimpose the complex kinetic stiffness of the air pressure unit and the friction unit to establish the total complex kinetic stiffness of the air spring. ,in The complex kinetic stiffness caused by friction. For complex motion stiffness The real part, For complex motion stiffness The imaginary part; Step 8: Based on the calculated total complex dynamic stiffness of the air spring, the dynamic stiffness of the air spring is obtained as follows: The hysteresis angle of the air spring is ,in, Let be the dynamic stiffness of the air spring. The hysteresis angle of the air spring.
[0006] Furthermore, the relationship between the effective area and volume and displacement in step 1 is identified by the finite element model.
[0007] Furthermore, the friction model in step 1 can be either the Berg friction model or the Coulomb friction model.
[0008] Furthermore, the differential equation for the change in air pressure inside the air spring in step 2 is: ; Where P is the internal air pressure of the air spring. Let be the gas constant of air. It is the specific heat capacity at constant volume. It is the volume of the air chamber. It is the derivative of the air chamber volume with respect to the displacement x. It is the derivative of displacement x with respect to time. Where M is the heat transfer coefficient and M is the mass of the gas inside the air spring. For ambient temperature, Let be the gas constant of air.
[0009] Furthermore, the heat transfer coefficient parameter identification method in step 3 uses sinusoidal displacement excitation dynamic test data and utilizes the relationship between the measured air pressure fluctuation amplitude and the heat transfer coefficient for identification.
[0010] Furthermore, the expression for the complex motion stiffness of the air spring pneumatic unit in step 6 is as follows: ; ; ; in, The change in stiffness is caused by the change in effective area. The change in stiffness is caused by the change in volume. The adiabatic index, To be related to the heat transfer coefficient The relevant time constant, and are the complex dynamic stiffnesses, respectively. The real and imaginary parts.
[0011] This invention constructs a dual time-domain and frequency-domain model of an air spring, coupled with precise parameter identification and linearization modeling methods. Combined with high-fit experimental comparison results verified by attached figures, it possesses the following core beneficial effects: 1. Breakthrough in low-frequency precision, meeting engineering standards. It precisely addresses the pain point of insufficient calculation accuracy of existing models in the 0-1Hz ultra-low frequency band, matches the 0.4Hz test requirements of the GB / T13061-2017 national standard, and perfectly adapts to the low-frequency comfort design needs of commercial vehicles and new energy passenger vehicles.
[0012] 2. Predictable dynamic characteristics across the entire frequency band It can accurately simulate the force-displacement time-domain response of air springs under arbitrary excitation frequency and amplitude, and accurately calculate dynamic stiffness and hysteresis angular frequency domain characteristics, covering the engineering simulation needs of the entire frequency band.
[0013] 3. The parameter identification method is reliable and universal. It pioneered a heat transfer coefficient identification method (sinusoidal displacement excitation + third-order polynomial fitting, goodness of fit R²≥0.99), with high parameter identification accuracy; the effective area / volume can be identified through experiments or finite element dual-path identification, and the friction force is compatible with multiple models such as Berg and Coulomb, adapting to different test conditions.
[0014] 4. The modeling logic is rigorous and the engineering practicality is strong. After linearization using a first-order Taylor expansion, the complex dynamic stiffness modeling is simple and efficient. Even after neglecting the viscoelastic properties of the bladder skin, the model still closely matches the experimental data with small calculation errors, and can be directly used for the optimization design of air spring structural parameters.
[0015] 5. The model system is complete, supporting suspension research and development. Simultaneously establish time-domain models of air pressure, air pressure / total force, and complex dynamic stiffness / dynamic stiffness / hysteresis angular frequency domain models to form a complete analysis closed loop, shortening the R&D cycle of the suspension system and reducing design costs. Attached Figure Description
[0016] The invention will now be further described with reference to the accompanying drawings.
[0017] Figure 1 This is a flowchart of the present invention.
[0018] Figure 2 A schematic diagram illustrating the dynamic characteristics of an air spring provided in an embodiment of the present invention.
[0019] Figure 3 This is a schematic diagram illustrating the relationship between the air pressure fluctuation amplitude and the heat transfer coefficient calculated using a third-order polynomial fitting of the internal air pressure differential equation of an air spring, according to an embodiment of the present invention.
[0020] Figure 4 This is a schematic diagram of a method for calculating the pressure fluctuation amplitude using experimentally obtained internal pressure time-domain data, according to an embodiment of the present invention.
[0021] Figure 5 This is a schematic diagram illustrating the verification of the identified heat transfer coefficient in an example of the present invention.
[0022] Figure 6 This is a schematic diagram comparing the calculated and experimental results of the air spring force and displacement curves at a frequency of 0.01 Hz, as an example of the present invention.
[0023] Figure 7 This is a schematic diagram comparing the calculated and experimental results of the air spring force and displacement curves at a frequency of 0.04 Hz, as an example of the present invention.
[0024] Figure 8 This is a schematic diagram comparing the calculated and experimental results of the air spring force and displacement curves at a frequency of 0.16 Hz, as an example of the present invention.
[0025] Figure 9 This is a schematic diagram comparing the calculated and experimental results of the air spring force and displacement curves at a frequency of 1 Hz, as an example of the present invention.
[0026] Figure 10This is a schematic diagram comparing the dynamic stiffness calculation and experimental results of the air spring in this invention example.
[0027] Figure 11 This is a schematic diagram comparing the calculation and experimental results of the hysteresis angle of the air spring in this invention example. Detailed Implementation
[0028] like Figure 1-11 As shown, a method for analyzing the dynamic characteristics of an air spring includes the following steps.
[0029] Step 1: Use the quasi-static test method to identify the relationship between the effective area and volume of the air spring and the displacement, and use the friction model to fit the friction force formula; In an embodiment of the present invention, the relationship between effective area and volume and displacement is obtained by fitting quasi-static experimental data with a quadratic polynomial, as follows: ; ; ; ; in: and These are the effective area and volume, respectively. The coefficients of the effective area polynomial for fitting. These are the coefficients of the fitted volume polynomial. The relationship between effective area and volume and displacement is identified by the finite element model; In an embodiment of the present invention, frictional force F f The Berg friction model is used for fitting, and the formula is as follows: ; in, This is a reference state and will be updated in real time when the displacement direction changes; This represents the maximum frictional force amplitude. The displacement corresponding to the friction force reaching half of the maximum friction force when the reference state is (0,0) can be found in Section 4.1 of "Mats Berg. A non-linear rubber springmodel for rail vehicle dynamics analysis[J]. Vehicle System Dynamics,1998.".
[0030] Step 2: Establish the differential equation for the change in air pressure inside the air spring; In an embodiment of the present invention, a schematic diagram of the dynamic characteristics modeling of the air spring is shown below. Figure 2 As shown, taking a closed system composed of internal gas as the research object, based on the law of conservation of heat, we obtain: ; in, It is the increase in heat exchanged with the outside world (positive when heat enters the air spring chamber). It is the increase in the thermodynamic energy of the internal gas; It is the increase in volumetric work (positive when the air spring is stretched). State parameters of the gas inside the air spring P , V and T It satisfies the ideal gas law, and its expression is: ; in, P This refers to the internal air pressure of the air spring. V For the volume of the air spring, M 0 represents the mass of the gas inside the air spring. Let be the gas constant of air. T The temperature of the gas inside the air spring; Based on the two formulas above, the differential equation for the internal gas pressure is derived as follows: ; Where P is the internal air pressure of the air spring. Let be the gas constant of air. It is the specific heat capacity at constant volume. It is the volume of the air chamber. It is the derivative of the air chamber volume with respect to the displacement x. It is the derivative of displacement x with respect to time. Where M is the heat transfer coefficient and M is the mass of the gas inside the air spring. For ambient temperature, Let be the gas constant of air.
[0031] Step 3: Based on the differential equation of the internal air pressure change of the air spring, the heat transfer coefficient in the differential equation is identified by experimental method to obtain its parameter value; Under steady-state conditions, the internal air pressure has a period of . A periodic function, whose expression is assumed to be: ; in, yes P The average value, The period is T The fluctuation term; Substituting the above expression into the differential equation for internal gas pressure, and selecting low frequency (frequency range: 0.02-0.2 Hz) and low amplitude (amplitude range: 5-10 mm) operating conditions, we can obtain: ; According to the above formula, when the amplitude of the fluctuation term is... Much smaller than the average When, satisfy And the amplitude of the fluctuation term (Unit: Pa) and heat transfer coefficient There is a one-to-one correspondence between the units (W / K), in order to establish and The mathematical expression for the heat transfer coefficient Discrete values are taken in the range of 0.1-2 W / K at intervals of 0.1 W / K, and these values are substituted into the differential equation for the internal gas pressure to perform differential equation calculations, resulting in the following: and The discrete data points were then fitted using a third-order polynomial with the least squares method, and the goodness of fit R0 was determined. 2 It should exceed 0.95. The formula for fitting a third-order polynomial is: ; The fitting result of this embodiment is as follows: Figure 3 As shown, the fitted curve matches the discrete data points well, and the goodness of fit R0 is high. 2 The fitting formula is as follows: (The formula is not provided in the original text.) ; The average air pressure was obtained based on the test data of the internal air pressure. and fluctuation amplitude The method is as follows Figure 4 As shown, the fluctuation amplitude obtained from the internal air pressure test data is... Substituting into the above fitting formula, the heat transfer coefficient of the air spring can be solved. The identified heat transfer coefficients are substituted into the differential equation for the internal gas pressure to verify the accuracy of the identified parameters, such as... Figure 5 As shown.
[0032] Step 4: Substitute the identified heat transfer coefficient into the differential equation of internal air pressure change to establish a time-domain model of the internal air pressure of the air spring.
[0033] Step 5: Establish air pressure F p and air spring response force F The time-domain model; air pressure F pThe calculation formula is: ; Total Response Force of Air Spring F for: ; like Figure 6 and Figure 7 The figure shows a comparison between the calculated and experimental results of the air spring force versus displacement curves under displacement excitation at frequencies of 0.01 and 0.16 Hz and amplitudes of 10, 20, and 30 mm, as per this embodiment. As can be seen from the figure, the calculated results agree well with the experimental results. This demonstrates the effectiveness of the proposed air spring time-domain model and heat transfer coefficient identification method, laying the foundation for establishing an air spring frequency model.
[0034] Step 6: Apply air pressure F P The time-domain model is linearized, and a complex stiffness model of the air spring air pressure element is established. Since the complex dynamic stiffness modeling needs to be based on the linear system assumption, the air spring approximately satisfies the linear system assumption under the initial working height and small displacement conditions. Under the small displacement conditions, the time-domain model of the air spring is linearized. The linearization steps are as follows. First, the volume linearization of the differential equation for the internal air pressure of the air spring yields the following result: ; ; Secondly, the initial working height position of the air spring is the static equilibrium position, at which time the internal air pressure of the air spring is... ,volume Since this position is in static equilibrium, it satisfies the pressure change rate. rate of change of displacement Taking the static equilibrium position as the initial point, at the initial point At the given position, the above formula is expanded using a first-order Taylor series, as follows: ; ; ; in, For function exist Gradient of position; As a higher-order infinitesimal, based on the small displacement assumption, The changes were relatively small. Approaching 0, Since higher-order infinitesimals are approximately zero, they can be ignored, and the pressure differential equation is linearized as follows: ; Finally, eliminate The following linearized equations are obtained: ; Similarly, performing a Taylor expansion on the gas pressure formula in step 5 yields the following linearized equation: ; Taking the Laplace transform of the two linearized equations above, we get: ; ; eliminate The following transfer function can be obtained: ; ; ; ; in, The change in stiffness is caused by the change in effective area. The change in stiffness is caused by the change in volume. The adiabatic index, To be related to the heat transfer coefficient Regarding the time constant, the dynamic stiffness of an air spring is usually represented by a frequency domain diagram. Substituting into the above formula, the complex dynamic stiffness of the air pressure element can be obtained. The expression is: ; ; in, and Complex dynamic stiffness The real and imaginary parts.
[0035] Step 7: Establish the overall complex stiffness model of the air spring by superimposing the complex stiffness of the air pressure unit and the friction unit; The total complex kinetic stiffness of the air spring is: ; in, The complex dynamic stiffness of the friction element can be calculated from the corresponding friction model.
[0036] Step 8: Establish a frequency domain model of the dynamic stiffness and hysteresis angle of the air spring; Based on the above formula for calculating the total complex dynamic stiffness of an air spring, the dynamic stiffness of the air spring is... for: ; Hysteresis angle of air spring for: ; like Figure 8 and Figure 9 The figure shows the calculated and experimental results of the dynamic stiffness and hysteresis angle of the air spring under displacement excitation with amplitudes of 0.1 mm and 1.0 mm in this embodiment. The comparison results show that the calculated results are in good agreement with the experimental results in the ultra-low frequency range of 0.01-1 Hz. However, there are differences between the calculated and experimental results after the frequency exceeds 1 Hz. This is because the influence of the viscoelastic properties of the air spring bladder was ignored in the process of establishing the dynamic characteristic model of the air spring. However, the difference between the calculated results and the experimental results of this method is small, and it can predict the dynamic characteristics of the air spring relatively accurately, which is helpful for the optimization design of the structural parameters of the air spring.
[0037] The above description is merely an illustrative embodiment of the invention and is not intended to limit the scope of the invention. Any equivalent changes and modifications made by those skilled in the art without departing from the concept and principles of the invention should fall within the scope of protection of the invention.
Claims
1. A method for analyzing the dynamic characteristics of an air spring, characterized in that, Includes the following steps, Step 1: Use the quasi-static test method to identify the relationship between the effective area and volume of the air spring and the displacement, and use the friction model to fit the friction force formula; Step 2: Establish the differential equation for the change in air pressure inside the air spring; Step 3: Based on the differential equation of the internal air pressure change of the air spring, the heat transfer coefficient in the differential equation is identified by experimental method; Step 4: Substitute the identified heat transfer coefficient into the differential equation of internal air pressure change to obtain the time-domain model of the internal air pressure of the air spring. Step 5: According to the formula Establish an air spring air pressure unit The time-domain variation results are given, where P and Pa are the internal air pressure and atmospheric pressure of the air spring, respectively, and Ae is the effective area of the air spring, according to the formula... Establish a time-domain model of the total response force F acting on the air spring, where For friction force units; Step 6: Apply the differential equations and formulas for the aforementioned air pressure. After linearization using the first-order Taylor expansion method, according to the formula... Establish the complex dynamic stiffness of the air spring pneumatic pressure unit ,in This represents the Laplace transform, where s is the Laplace complex variable. Angular frequency; Step 7: Superimpose the complex kinetic stiffness of the air pressure unit and the friction unit to establish the total complex kinetic stiffness of the air spring. ,in The complex kinetic stiffness caused by friction. For complex motion stiffness The real part, For complex motion stiffness The imaginary part; Step 8: Based on the calculated total complex dynamic stiffness of the air spring, the dynamic stiffness of the air spring is obtained as follows: The hysteresis angle of the air spring is ,in, Let be the dynamic stiffness of the air spring. The hysteresis angle of the air spring.
2. The method for analyzing the dynamic characteristics of an air spring according to claim 1, characterized in that: The relationship between the effective area and volume and displacement in step 1 is identified by the finite element model.
3. The method for analyzing the dynamic characteristics of an air spring according to claim 1, characterized in that: In step 1, the friction model can be fitted by the Berg friction model or the Coulomb friction model.
4. The method for analyzing the dynamic characteristics of an air spring according to claim 1, characterized in that: The differential equation for the change in air pressure inside the air spring in step 2 is as follows: ； Where P is the internal air pressure of the air spring. Let be the gas constant of air. It is the specific heat capacity at constant volume. It is the volume of the air chamber. It is the derivative of the air chamber volume with respect to the displacement x. It is the derivative of displacement x with respect to time. Where M is the heat transfer coefficient and M is the mass of the gas inside the air spring. For ambient temperature, Let be the gas constant of air.
5. The method for analyzing the dynamic characteristics of an air spring according to claim 1, characterized in that: The method for identifying the heat transfer coefficient parameter in step 3 is to use sinusoidal displacement excitation dynamic test data and to identify it by utilizing the relationship between the measured air pressure fluctuation amplitude and the heat transfer coefficient.
6. The method for analyzing the dynamic characteristics of an air spring according to claim 1, characterized in that: The expression for the complex motion stiffness of the air spring pneumatic unit in step 6 is: ； ； ； in, The change in stiffness is caused by the change in effective area. The change in stiffness is caused by the change in volume. The adiabatic index, To be related to the heat transfer coefficient The relevant time constant, and Complex dynamic stiffness The real and imaginary parts.