Closed double-cavity air spring modeling method, device and equipment and readable storage medium
By dividing the air spring stiffness into two parts, thermodynamics and structural dynamics, and simplifying its representation and parameter analysis, the problem of the inability to effectively characterize the nonlinear stiffness of air springs in the existing technology is solved, achieving a balance between computational efficiency and accuracy, and is applicable to vehicle control.
Patent Information
- Application Number
- CN202610126764.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-01-29
- Publication Date
- 2026-05-15
AI Technical Summary
Existing air spring modeling methods cannot effectively characterize nonlinear stiffness characteristics while ensuring computational efficiency, resulting in an inability to accurately describe the mechanical properties of double-cavity closed air springs.
The stiffness of the air spring is divided into two parts: thermodynamic stiffness and structural dynamic stiffness. A simplified stiffness model is established by using constant and linear simplification and combining the measured values of the bench to perform parameter analysis.
A simplified stiffness model that accurately describes the nonlinear stiffness characteristics of air springs while simplifying calculations is achieved and is applicable to vehicle control.
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Figure CN122046537A_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of vehicle suspension control, specifically to a closed-type dual-cavity air spring modeling method, apparatus, device, and readable storage medium. Background Technology
[0002] As a core damping component, air springs are widely used in buses, trucks, and high-end passenger vehicles. The accurate modeling of their mechanical behavior is directly related to the comfort, handling stability, and safety of the entire vehicle. With the development of intelligent and lightweight vehicles, the industry has placed higher demands on air spring modeling: it must simultaneously meet the requirements of high-precision description (such as nonlinear stiffness and damping characteristics) and efficient calculation (adapting to real-time simulation of vehicle dynamics) to support vehicle design optimization, active suspension control, and the development of intelligent driving systems.
[0003] In existing technologies, air spring models can be broadly classified into three categories based on their modeling principles: The first is the physical parameter model, which mathematically describes each component of the air spring's physical model. However, due to the complexity of the modeling method and low computational efficiency, it is not suitable for dynamic analysis in vehicle control. The third method is the non-parametric method, which is a black-box model based on experimental data analysis. It extrapolates using physical prototypes and a large amount of experimental data. However, due to the high cost of testing, it can often only obtain data from some experimental conditions for extrapolation. The second is the equivalent parameterized model, which abstracts the air spring into mechanical components, such as equivalently considering it as a combination of damping, elastic, and friction components, and then models and describes it. This is currently the conventional method for vehicle dynamics simulation analysis.
[0004] However, while existing air spring modeling methods can guarantee computational efficiency using equivalent parameterized models, the extensive simplifications and equivalences prevent them from effectively characterizing the nonlinear stiffness characteristics of the air spring. These models often differ significantly from the performance of physical prototypes and fail to accurately describe the mechanical properties of double-cavity closed air springs. Therefore, existing technologies suffer from the technical problem of failing to effectively characterize the nonlinear stiffness characteristics of air springs while maintaining computational efficiency. Summary of the Invention
[0005] This application provides a closed-loop double-cavity air spring modeling method, apparatus, device, and readable storage medium, which can solve the technical problem in the prior art that it is impossible to effectively characterize the nonlinear stiffness characteristics of the air spring while ensuring computational efficiency.
[0006] In a first aspect, embodiments of this application provide a method for modeling a closed double-cavity air spring, including:
[0007] Obtain the operating parameters of the closed double-cavity air spring to be modeled, and construct the thermodynamic stiffness and structural dynamic stiffness of the air spring based on the operating parameters; The first simplified stiffness is obtained by simplifying the damping characteristics of the additional air chamber and air bladder in the thermodynamic stiffness of the air spring by constant expression. The second simplified stiffness is obtained by simplifying the effective area change characteristics in the dynamic stiffness of the air spring structure by linear expression. The simplified stiffness expression is determined based on the first and second simplified stiffness. External excitation is applied to the closed double-cavity air spring to be modeled by an actuator to obtain the measured values on the bench. Based on the measured values on the bench, the simplified stiffness expression is analyzed to obtain the simplified stiffness model of the closed double-cavity air spring to be modeled.
[0008] In conjunction with the first aspect, in one embodiment, the damping characteristics of the additional air chamber and air bladder in the thermodynamic stiffness of the air spring are simplified by constant representation to obtain a first simplified stiffness, including: Ignoring the damping characteristics of the connecting holes, the damping characteristics of the additional air chamber and air bladder are expressed as constants that do not change with height and effective area. The thermodynamic stiffness of the air spring is then expressed as an equivalent value to obtain the simplified thermodynamic stiffness. The mechanical transmission characteristics of the simplified thermodynamic stiffness are differentiated and Taylorized to obtain the first simplified stiffness in the form of the suspension height.
[0009] In conjunction with the first aspect, in one implementation, a second simplified stiffness is obtained by linearly simplifying the effective area variation characteristics in the dynamic stiffness of the air spring structure, including: The relationship between the effective area of the airbag and height is simplified to a linear relationship, and the dynamic stiffness of the air spring structure is equivalently expressed to obtain the second air spring stiffness.
[0010] In conjunction with the first aspect, in one implementation method, a simplified stiffness model for the closed double-cavity air spring to be modeled is obtained by parametric analysis of the simplified stiffness expression based on the measured values from the test bench, including: The theoretical analytical value is determined based on the excitation value corresponding to the external excitation and the simplified stiffness expression; The parameters in the simplified stiffness expression are treated as particles to be optimized. The optimization objective is to minimize the difference between the theoretical analytical value and the measured value on the bench. The optimal analytical value of each parameter is obtained by iterative optimization using the particle swarm optimization algorithm. Substituting the optimal analytical value into the simplified stiffness expression yields the simplified stiffness model.
[0011] In conjunction with the first aspect, in one embodiment, the operating parameters include the physical structural parameters of the additional air chamber, air bladder, and air tank of the closed double-cavity air spring to be modeled, as well as the gas pressure state parameters, suspension height parameters, and temperature parameters of the closed double-cavity air spring to be modeled in a charge-discharge cycle.
[0012] In conjunction with the first aspect, in one implementation method, the thermodynamic stiffness of the air spring and the structural dynamic stiffness of the air spring are constructed based on operating parameters, including: The internal gas mass is obtained by determining the mass of the gas during filling and discharging based on the operating parameters. Gravity balance analysis and pressure balance analysis were performed on the closed double-cavity air spring to be modeled, and a set of two-degree-of-freedom dynamic equations were obtained. Based on the two-degree-of-freedom dynamic equations and the internal gas mass, equivalent expressions for thermodynamic damping characteristics and structural dynamic transmission characteristics are made to obtain the thermodynamic stiffness and structural dynamic stiffness of the air spring.
[0013] In conjunction with the first aspect, in one implementation, equivalent representations of thermodynamic damping characteristics and structural dynamic transmission characteristics are performed to obtain the thermodynamic stiffness and structural dynamic stiffness of the air spring, including: The heat exchange process of the closed double-cavity air spring to be modeled is equivalent to the heat exchange between the air bag and the ambient air. The effect of the change in effective area on the volume of the air bag is ignored, and the thermodynamic stiffness of the air spring is established. The relationship between the change in effective area and stiffness can be equivalently expressed as the dynamic stiffness of an air spring structure.
[0014] Secondly, embodiments of this application provide a closed-loop double-cavity air spring modeling device, comprising: The air spring stiffness modeling module is used to obtain the operating parameters of the closed double-cavity air spring to be modeled, and to construct the air spring thermodynamic stiffness and air spring structural dynamic stiffness based on the operating parameters. The air spring stiffness simplification module is used to simplify the damping characteristics of the additional air chamber and air bladder in the thermodynamic stiffness of the air spring by constant expression to obtain the first simplified stiffness, and to simplify the effective area change characteristics in the dynamic stiffness of the air spring structure by linear expression to obtain the second simplified stiffness. The simplified stiffness expression is determined based on the first simplified stiffness and the second simplified stiffness. The parameter analysis module is used to apply external excitation to the closed double-cavity air spring to be modeled based on the actuator, obtain the test bench measured values, and perform parameter analysis on the simplified stiffness expression based on the test bench measured values to obtain the simplified stiffness model of the closed double-cavity air spring to be modeled.
[0015] Thirdly, embodiments of this application provide a closed double-cavity air spring modeling device, which includes a processor, a memory, and a closed double-cavity air spring modeling program stored in the memory and executable by the processor. When the closed double-cavity air spring modeling program is executed by the processor, it implements the steps of the closed double-cavity air spring modeling method as described above.
[0016] Fourthly, embodiments of this application provide a computer-readable storage medium storing a closed double-cavity air spring modeling program, wherein when the closed double-cavity air spring modeling program is executed by a processor, it implements the steps of the closed double-cavity air spring modeling method as described above.
[0017] The beneficial effects of the technical solutions provided in this application include: This application divides the air spring stiffness into two parts: air spring thermodynamic stiffness and air spring structural dynamic stiffness. This allows for the accurate description of the nonlinear stiffness characteristics of the air spring. Then, by simplifying the air spring thermodynamic stiffness with a constant representation and the air spring structural dynamic stiffness with a linear representation, the computational workload can be effectively reduced. Finally, by bench testing and analytical fitting of the parameters in the simplified stiffness expression, a simplified air spring stiffness model that can effectively characterize nonlinear stiffness characteristics, is computationally simple, and can be applied to vehicle control is obtained. Attached Figure Description
[0018] Figure 1 This is a flowchart illustrating an embodiment of the closed double-cavity air spring modeling method of this application; Figure 2 The thermodynamic stiffness and structural dynamic stiffness of the air spring are constructed according to the embodiments of this application; Figure 3 This is a detailed flowchart of step S203 in the embodiments of this application; Figure 4 This is a 1 / 4 scale dynamic model diagram of the vehicle according to an embodiment of this application; Figure 5 This is a mechanical model diagram of the dual-cavity closed air spring according to an embodiment of this application; Figure 6 This is a simplified flowchart illustrating the thermodynamic stiffness of an air spring according to an embodiment of this application. Figure 7 This is a simplified stiffness equivalent model and schematic diagram of an embodiment of this application; Figure 8 This is a schematic diagram illustrating the process of obtaining a simplified stiffness model through parameter parsing in an embodiment of this application. Figure 9 This is a schematic diagram of the functional modules of an embodiment of the closed double-cavity air spring modeling device of this application; Figure 10 This is a schematic diagram of the hardware structure of the closed double-cavity air spring modeling device involved in the embodiments of this application. Detailed Implementation
[0019] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present application, and not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present application.
[0020] To make the objectives, technical solutions, and advantages of this application clearer, the embodiments of this application will be described in further detail below with reference to the accompanying drawings.
[0021] In a first aspect, embodiments of this application provide a method for modeling a closed double-cavity air spring.
[0022] In one embodiment, reference is made to Figure 1 , Figure 1 This is a flowchart illustrating an embodiment of the closed double-cavity air spring modeling method of this application. Figure 1 As shown, the modeling method for a closed double-cavity air spring includes: S101. Obtain the working parameters of the closed double-cavity air spring to be modeled, and construct the thermodynamic stiffness and structural dynamic stiffness of the air spring based on the working parameters. S102. The damping characteristics of the additional air chamber and air bladder in the thermodynamic stiffness of the air spring are simplified by constant expression to obtain the first simplified stiffness. The effective area change characteristics in the dynamic stiffness of the air spring structure are simplified by linear expression to obtain the second simplified stiffness. The simplified stiffness expression is determined based on the first simplified stiffness and the second simplified stiffness. S103. Apply external excitation to the closed double-cavity air spring to be modeled based on the actuator, obtain the test bench measurement value, and perform parameter analysis on the simplified stiffness expression based on the test bench measurement value to obtain the simplified stiffness model of the closed double-cavity air spring to be modeled.
[0023] Specifically, in the closed double-cavity air spring modeling method, for the closed double-cavity air spring to be modeled, the embodiment converts its stiffness into two parts: one part is the part affected by thermodynamics and aerodynamics when the effective area remains unchanged; the other part is the part affected by the change in effective area on the dynamic stiffness.
[0024] In this embodiment, for the thermodynamic stiffness of the air spring under the influence of thermodynamics and aerodynamics when the effective area remains constant, the operating parameters of the closed double-cavity air spring to be modeled are first obtained, including the physical structural parameters of the additional air chamber, air bladder, and air tank, as well as the gas pressure state parameters and suspension height parameters of the closed double-cavity air spring to be modeled in one inflation / deflation cycle. Based on the obtained operating parameters, inflation / deflation cycle analysis and mass determination are performed to determine the internal gas mass of the air spring. Then, combining the operating parameters and the determined internal gas mass, a two-degree-of-freedom dynamic equation for the air spring is constructed, and further thermodynamic analysis is performed based on the established dynamic equation. In the thermodynamic analysis, the heat exchange of the air spring is equivalent to the heat exchange between the air bladder and the air, resulting in the thermodynamic equation. Then, the thermodynamic equation is simplified and Fourier transformed to obtain the frequency domain relationship between the additional air chamber and the suspension, thus obtaining the thermodynamic stiffness of the air spring influenced by thermodynamics and aerodynamics.
[0025] For the effect of changes in effective area on the dynamic stiffness of the air spring structure, the embodiment expresses the influence of effective area on the air spring stiffness as the dynamic stiffness of the air spring structure. As another branch of stiffness, the stiffness of the entire air spring is a parallel combination of the air spring thermodynamic stiffness and the air spring structural dynamic stiffness.
[0026] To enable rapid calculations in actual vehicle control and improve computational efficiency in practical vehicle control applications, the embodiment simplifies the stiffness representations of the two parts. For the air spring structure's dynamic stiffness, the embodiment simplifies the relationship between the effective area and height to a linear relationship, resulting in the simplified structural dynamic stiffness. For the air spring's thermodynamic stiffness, the embodiment ignores the damping characteristics of the connecting holes, representing the damping characteristics of the additional air chamber and airbag as constants independent of height and effective area. Then, differentiation and Taylor expansion are performed, and the mechanical transfer differential equation is Taylor-expanded into a first-order form of the suspension height, yielding the simplified thermodynamic stiffness. Finally, the two parts are combined to obtain the simplified stiffness parameter expression.
[0027] Finally, in this embodiment, an external excitation is applied using an electromagnetic actuator to obtain a map showing the relationship between the feedback load and the real-time displacement and frequency. This map serves as the measured value on the test bench. Based on the particle swarm optimization algorithm, the values of each parameter representing the relationship between stiffness and actual working conditions in the simplified stiffness parameter expression are solved. Finally, the obtained parameter values are substituted into the simplified stiffness parameter expression to obtain an accurate analytical expression for the air spring stiffness.
[0028] In this embodiment, by dividing the air spring stiffness into two parts, air spring thermodynamic stiffness and air spring structural dynamic stiffness, the nonlinear stiffness characteristics of the air spring can be accurately described first. Then, by simplifying the air spring thermodynamic stiffness with a constant representation and the air spring structural dynamic stiffness with a linear representation, the amount of calculation can be effectively simplified. Finally, by bench testing and analytical fitting of the parameters in the simplified stiffness expression, a simplified air spring stiffness model that can effectively characterize nonlinear stiffness characteristics, is easy to calculate, and can be applied to vehicle control is obtained.
[0029] Furthermore, in one embodiment, the operating parameters include the physical structural parameters of the additional air chamber, air bladder, and air tank of the closed double-cavity air spring to be modeled, as well as the gas pressure state parameters, suspension height parameters, and temperature parameters of the closed double-cavity air spring to be modeled in one inflation / deflation cycle.
[0030] Specifically, the operating parameters required in the embodiments include the physical structural parameters of the additional air chamber, air bladder, and air tank of the closed double-chamber air spring, such as the volume of the additional air chamber and air tank and the initial volume of the air bladder, as well as the initial suspension height and initial pressure of each part during one inflation / deflation cycle, the changes in suspension height and pressure of each part during the cycle, the temperature changes of each part, and the ambient temperature. Based on these operating parameters and the working principle of the closed double-chamber air spring, a mass determination is performed. After one inflation / deflation cycle, the internal gas mass can be determined, providing basic data for subsequent modeling.
[0031] Furthermore, in one embodiment, Figure 2 To construct the thermodynamic stiffness and structural dynamic stiffness of the air spring in the embodiments of this application, such as... Figure 2 As shown, the thermodynamic stiffness and structural dynamic stiffness of the air spring are constructed based on the operating parameters, including: S201. Based on the operating parameters, perform a fixed mass of filling and discharging gas to obtain the internal gas mass; S202. Perform gravity balance analysis and pressure balance analysis on the closed double-cavity air spring to be modeled to obtain a set of two-degree-of-freedom dynamic equations. S203. Based on the two-degree-of-freedom dynamic equations and the internal gas mass, equivalent expressions for thermodynamic damping characteristics and structural dynamic transmission characteristics are made to obtain the thermodynamic stiffness and structural dynamic stiffness of the air spring.
[0032] Furthermore, in one embodiment, Figure 3 This is a detailed flowchart of step S203 in an embodiment of this application, as shown below. Figure 3 As shown, equivalent representations of thermodynamic damping characteristics and structural dynamic transmission characteristics are performed to obtain the thermodynamic stiffness and structural dynamic stiffness of the air spring, including: S301. The heat exchange process of the closed double-cavity air spring to be modeled is equivalent to the heat exchange between the air bag and the ambient air. The effect of the change in effective area on the volume of the air bag is ignored, and the thermodynamic stiffness of the air spring is established. S302. The relationship between the effective area change and the stiffness transfer characteristics is equivalently expressed as the dynamic stiffness of the air spring structure.
[0033] Specifically, in the embodiments, Figure 4 This is a 1 / 4 scale dynamic model diagram of the vehicle according to an embodiment of this application, as shown below. Figure 4As shown, a 1 / 4 vehicle dynamics model is obtained by combining the three-degree-of-freedom 1 / 4 air suspension dynamics, where the air spring is considered an elastic element. Considering the height-adjustable nature of the air spring, it can remain in equilibrium at any initial position. Therefore, when modeling the dynamic parameters, the general methods of structural dynamics cannot be used to describe the dynamic equations using a static state caused by gravity as the initial position. In this case, in addition to considering gravity, the pressure balance of the air spring itself needs to be considered. A two-degree-of-freedom dynamic system is established, and its set of dynamic equations is as follows:
[0034] in, Indicates the load mass. This indicates the total mass of the air spring and the additional air chamber. Indicates the displacement of the unsprung position. Indicates the displacement of the spring position. Indicates the unsprung position velocity. Indicates the speed of the spring position. Indicates the acceleration at the unsprung position. Indicates the acceleration at the position on the spring. This represents the response load output by the air spring system. Indicates tire stiffness. Indicates the road surface input displacement. Indicates the road surface input speed. Indicates tire damping. This indicates the suspension damping coefficient. This indicates the air pressure in the airbag. Indicates ambient pressure. This indicates the effective cross-sectional area of the air spring airbag, with the vertical upward direction as the positive direction.
[0035] After constructing the two-degree-of-freedom dynamic system, during the thermodynamic stiffness analysis, the example first performs total differential on the dynamic equations, obtaining:
[0036] in, This indicates the pressure of the air bladder.
[0037] Then, by combining the dynamic equations and differential expressions, eliminating the mass of gas flowing through the throttling orifice, and further considering that the contact area between the air spring bladder and the outside is larger than that of the auxiliary air chamber, the heat exchange between the auxiliary air chamber and the outside is ignored, or it can be equivalent to the heat exchange between the air spring bladder and the air, resulting in:
[0038] in, Indicates the flow coefficient of the throttling orifice. This represents the initial equilibrium temperature of the system. Indicates the pressure ratio. Indicates the volume of the additional air chamber. This represents the first derivative of the additional chamber pressure with respect to time. This represents the first derivative of the airbag pressure with respect to time. This indicates the heat exchange coefficient between the airbag and the outside environment. Indicates the airbag temperature. Indicates the external ambient temperature. Represents the state constant of an ideal gas. This represents the specific heat ratio of the gas, with a value of 1.4.
[0039] Further assumptions are made regarding the temperature difference between the airbag and the ambient temperature, the coupling term between pressure and airbag velocity, and the reciprocal of the air suspension system's travel and the reciprocal of the original initial height:
[0040] in, Indicates the volume of the air bladder. Indicates the mass of gas in the airbag. This indicates the initial pressure of the airbag. This indicates the initial volume of the airbag. Indicates the initial gas mass of the airbag. This indicates the initial suspension height.
[0041] The further simplified differential relationship between the air spring parameters is as follows:
[0042] in, This indicates the specific heat capacity at constant volume.
[0043] Then, perform a Fourier transform on the time-domain signal in the above equation. Note the Fourier transform of the suspension travel: The following relationship can be obtained:
[0044] Eliminating the Fourier transform of the additional air chamber pressure, the frequency domain relationship between the additional air chamber and the suspension structure is obtained. The formula for calculating the total dynamic stiffness of the air spring with the additional air chamber can be expressed as:
[0045] Simplifying the above equation, we can obtain a physically meaningful stiffness formula, and then perform simple mathematical transformations:
[0046] in, To incentivize the frequency of park visits, It is the imaginary unit.
[0047]
[0048] Based on the above equivalence relationship, the air spring system can be regarded as the following three items connected in series: spring and damper Parallel systems, springs and damper At this point, the change in effective area and its impact on the equivalent dynamic stiffness are not considered, and the change in effective area has a negligible impact on the calculation of the airbag volume. The resulting air spring stiffness is solely the thermodynamic stiffness of the air spring.
[0049] Considering the direct impact of changes in effective area on stiffness, the embodiment further expresses the transmission characteristic relationship of changes in effective area on stiffness as equivalent to the dynamic stiffness of the air spring structure, assuming that the equivalent stiffness generated by changes in effective area is... Then we have:
[0050] in, This indicates the effect of changes in effective area on the mechanical transmission characteristics of an air spring.
[0051] Figure 5 This is an equivalent mechanical model diagram of a double-cavity closed air spring according to an embodiment of this application. Combining the stiffness of the two parts, the overall stiffness of the air spring can be expressed as follows: Figure 5 The dynamic stiffness of an air spring is thus defined in two parts: one part is the effect of thermodynamics and aerodynamics when the effective area remains constant; the other part is the effect of the effective area changing on the dynamic stiffness. (Air spring dynamic stiffness) The formula is described as follows:
[0052] In this embodiment, through aerodynamic and thermodynamic analysis, the equivalent damping characteristics generated by external heat exchange, the air chamber stiffness characteristics of the airbag, and the airbag damping characteristics are comprehensively considered to achieve high-precision modeling of the thermodynamic nonlinear characteristics of the air spring. Simultaneously, the influence of effective area variation on stiffness is considered, and the dynamic stiffness of the air spring structure is established. This embodiment divides the air spring stiffness into two parts: the air spring thermodynamic stiffness and the air spring structural dynamic stiffness, and provides explicit mathematical expressions for each component, accurately describing the nonlinear stiffness characteristics of the air spring.
[0053] Furthermore, in one embodiment, Figure 6 This is a simplified flowchart illustrating the thermodynamic stiffness of an air spring according to an embodiment of this application, as shown below. Figure 6 As shown, the damping characteristics of the additional air chamber and air bladder in the thermodynamic stiffness of the air spring are simplified by constant representation to obtain the first simplified stiffness, which includes: S601. Ignoring the damping characteristics of the connecting hole, the damping characteristics of the additional air chamber and air bladder are expressed as constants that do not change with height and effective area. The thermodynamic stiffness of the air spring is equivalently expressed to obtain the simplified thermodynamic stiffness. S602. Differentiate the mechanical transmission characteristics of the simplified thermodynamic stiffness and expand it into a first-order form of the suspension height using Taylor expansion to obtain the first simplified stiffness.
[0054] Furthermore, in one embodiment, a second simplified stiffness is obtained by linearly simplifying the effective area variation characteristics in the dynamic stiffness of the air spring structure, including: The relationship between the effective area of the airbag and height is simplified to a linear relationship, and the dynamic stiffness of the air spring structure is equivalently expressed to obtain the second air spring stiffness.
[0055] Specifically, to simplify the model for application in actual vehicle control, the embodiment simplifies both parts of the stiffness.
[0056] To establish a universally applicable simplified model, the embodiment incorporates the actual geometric parameters of the double-cavity air spring, the geometric dimensions between the additional air chamber and the air bladder, and further neglects the damping characteristics of the connecting hole. This yields the following more universal expression:
[0057] For the dynamic stiffness of the air spring structure The embodiment simplifies the change of effective area with height to a linear relationship, resulting in the following expression for the stiffness caused by the change in effective area:
[0058] in This applies to any empty spring equilibrium position and small amplitude conditions. It also considers damping as a constant independent of height and effective area. The elastic term is then... Considered as a change that does not change with the effective area, but is related to the pressure and chamber volume under the current state, we further obtain:
[0059] Figure 7 This is a simplified stiffness equivalent model and schematic diagram of an embodiment of this application, combined with Figure 7 Therefore, the dynamic stiffness of the double-cavity closed air spring in this embodiment can be expressed as follows: Figure 7 The form is given, and for this equation, the differential equation for the mechanical transmission characteristics is as follows:
[0060] Assumption Without changing the equation, it degenerates into a common linear model. In the example, performing a Taylor expansion to obtain a first-order form of the suspension height yields a nonlinear model, namely:
[0061] Thus, the simplified stiffness model not only characterizes the semilinear characteristics of the stiffness of the closed double-cavity air spring, but also simplifies the computation, enabling the stiffness model to be applied to actual vehicle control.
[0062] In this embodiment, by simplifying the thermodynamic stiffness of the air spring with a constant representation and simplifying the dynamic stiffness of the air spring structure with a linear representation, the computational workload can be simplified and the computational efficiency can be improved while retaining the nonlinear stiffness characteristics of the closed double-cavity air spring.
[0063] Furthermore, in one embodiment, Figure 8 This is a schematic diagram illustrating the process of obtaining a simplified stiffness model through parameter parsing in an embodiment of this application, as shown below. Figure 8 As shown, based on the measured values from the test bench, the simplified stiffness expression is parametrically analyzed to obtain the simplified stiffness model of the closed double-cavity air spring to be modeled, including: S801. Determine the theoretical analytical value based on the excitation value corresponding to the external excitation and the simplified stiffness expression; S802. Take each parameter in the simplified stiffness expression as a particle to be optimized, and take minimizing the difference between the theoretical analytical value and the actual measured value on the bench as the optimization objective. Perform particle swarm optimization to obtain the optimal analytical value of each parameter. S803. Substitute the optimal analytical value into the simplified stiffness expression to obtain the simplified stiffness model.
[0064] Specifically, in the preceding steps, the embodiment simplified the stiffness of the air spring. Although the parameters in the simplified stiffness expression can be initially calculated using the operating parameters of the closed double-cavity air spring, the original parameter representation and the simplified parameter representation are not completely equivalent (for example, ignoring some damping characteristics during the simplification process will lead to certain deviations). Therefore, it is necessary to further accurately fit the relational parameters in the simplified stiffness expression.
[0065] In the parameter fitting and solution process, the embodiment uses an electromagnetic actuator to apply external excitation and obtains a map diagram between the feedback load and the real-time displacement and frequency. The above problem can be transformed into the following optimization problem:
[0066] in, Represents the theoretical analytical value. This indicates the measured value of the test bench.
[0067] The embodiment can obtain a set of test bench measurements by customizing the loading conditions, and obtain the analytical formula for parametric modeling based on the measured values of the displacement sensor. In order to accurately fit the parameters, a particle swarm intelligence algorithm is used for fast solution.
[0068] In this embodiment, the particle swarm optimization algorithm is set up according to the following steps: Initialization process: Select the number of potential solutions N, i.e., the number of particles. Upper bound of the parameter to be determined Lower bound of the parameter to be determined Maximum number of iterations Fitness function ; .
[0069] Optimal position mutation handling: Three core dynamic parameters are introduced to explore the factors K, drug concentration E, and mutation probability M. The particle position update rule is as follows:
[0070]
[0071] in, This represents the exploratory decay rate, which is generally taken as a constant; in this example, a value of 6 is preferred. Indicates the current iteration number. This indicates the maximum number of iterations.
[0072] During the local search phase, the particle position update strategy is as follows: Wherein, This represents the position of the i-th particle in the j-th dimension at iteration t+1, i.e., the actual value. This represents the globally optimal position at the t-th iteration; parameter E represents the drug decay concentration exponent, and the modeling method is as follows:
[0073]
[0074]
[0075] in, Drug attenuation rate .
[0076] Then, using a mutation mechanism based on fitness normalization, the potential optimal solution location is locally refined, iterating as follows:
[0077] in, , and Three particles were randomly selected. Here, is the mutation scaling factor, representing the normalized fitness of the i-th particle, calculated as follows:
[0078] in, Indicates the worst global solution. This represents the globally optimal solution.
[0079] Integration phase: Introduce the mutation probability parameter M, which is modulated by time decay, and calculate it as follows:
[0080] in, Used to enhance the diversity of the initial population. To ensure that the basic level of variation is maintained during the development phase, the decay rate is determined by the time constant. Control is implemented to achieve a balance between global algorithm development and local exploration. During mutation, if the random number is less than M, a random number is selected and updated according to the following formula:
[0081] in, This indicates the randomly selected particle number. .
[0082] Repeat the above steps until the number of iterations reaches its maximum value, output the global optimal solution, and output the analytical values of each parameter. Finally, substitute the obtained parameter values into the simplified stiffness expression to obtain a simplified stiffness model that can characterize the nonlinear stiffness characteristics of the air spring and is easy to calculate.
[0083] In this embodiment, the particle swarm optimization algorithm is used to accurately fit the values of each parameter, eliminating the errors caused by the simplification process and further improving the accuracy of the dynamic stiffness modeling of the air spring.
[0084] Secondly, embodiments of this application also provide a closed-type double-cavity air spring modeling device.
[0085] In one embodiment, reference is made to Figure 9 , Figure 9 This is a functional module diagram of an embodiment of the closed double-cavity air spring modeling device of this application. Figure 9 As shown, the closed double-cavity air spring modeling device includes: The air spring stiffness modeling module 901 is used to obtain the working parameters of the closed double-cavity air spring to be modeled, and to construct the air spring thermodynamic stiffness and air spring structural dynamic stiffness based on the working parameters. The air spring stiffness simplification module 902 is used to simplify the damping characteristics of the additional air chamber and air bladder in the thermodynamic stiffness of the air spring by constant expression to obtain the first simplified stiffness, and to simplify the effective area change characteristics in the dynamic stiffness of the air spring structure by linear expression to obtain the second simplified stiffness. The simplified stiffness expression is determined based on the first simplified stiffness and the second simplified stiffness. The parameter analysis module 903 is used to apply external excitation to the closed double-cavity air spring to be modeled based on the actuator, obtain the test bench measured value, and perform parameter analysis on the simplified stiffness expression based on the test bench measured value to obtain the simplified stiffness model of the closed double-cavity air spring to be modeled.
[0086] Furthermore, in one embodiment, the air spring stiffness simplification module is used for: The first simplified stiffness is obtained by simplifying the damping characteristics of the additional air chamber and air bladder in the thermodynamic stiffness of the air spring using a constant expression, including: Ignoring the damping characteristics of the connecting holes, the damping characteristics of the additional air chamber and air bladder are expressed as constants that do not change with height and effective area. The thermodynamic stiffness of the air spring is then expressed as an equivalent value to obtain the simplified thermodynamic stiffness. The mechanical transmission characteristics of the simplified thermodynamic stiffness are differentiated and Taylorized to obtain the first simplified stiffness in the form of the suspension height.
[0087] Furthermore, in one embodiment, the air spring stiffness simplification module is used for: The relationship between the effective area of the airbag and height is simplified to a linear relationship, and the dynamic stiffness of the air spring structure is equivalently expressed to obtain the second air spring stiffness.
[0088] Furthermore, in one embodiment, the parameter parsing module is used for: The theoretical analytical value is determined based on the excitation value corresponding to the external excitation and the simplified stiffness expression; The parameters in the simplified stiffness expression are treated as particles to be optimized. The optimization objective is to minimize the difference between the theoretical analytical value and the measured value on the bench. The optimal analytical value of each parameter is obtained by iterative optimization using the particle swarm optimization algorithm. Substituting the optimal analytical value into the simplified stiffness expression yields the simplified stiffness model.
[0089] Furthermore, in one embodiment, the operating parameters in the air spring stiffness modeling module include the physical structural parameters of the additional air chamber, air bladder, and air tank of the closed double-cavity air spring to be modeled, as well as the gas pressure state parameters, suspension height parameters, and temperature parameters of the closed double-cavity air spring to be modeled in a charge-discharge cycle.
[0090] Furthermore, in one embodiment, the air spring stiffness modeling module is used for: The internal gas mass is obtained by determining the mass of the gas during filling and discharging based on the operating parameters. Gravity balance analysis and pressure balance analysis were performed on the closed double-cavity air spring to be modeled, and a set of two-degree-of-freedom dynamic equations were obtained. Based on the two-degree-of-freedom dynamic equations and the internal gas mass, equivalent expressions for thermodynamic damping characteristics and structural dynamic transmission characteristics are made to obtain the thermodynamic stiffness and structural dynamic stiffness of the air spring.
[0091] Furthermore, in one embodiment, the air spring stiffness modeling module is used for: The heat exchange process of the closed double-cavity air spring to be modeled is equivalent to the heat exchange between the air bag and the ambient air. The effect of the change in effective area on the volume of the air bag is ignored, and the thermodynamic stiffness of the air spring is established. The relationship between the change in effective area and stiffness can be equivalently expressed as the dynamic stiffness of an air spring structure.
[0092] The functions of each module in the above-mentioned closed double-cavity air spring modeling device correspond to the steps in the above-mentioned closed double-cavity air spring modeling method embodiment, and their functions and implementation processes will not be described in detail here.
[0093] Thirdly, this application provides a closed double-cavity air spring modeling device, which can be a personal computer (PC), laptop computer, server or other device with data processing capabilities.
[0094] Reference Figure 10 , Figure 10 This is a schematic diagram of the hardware structure of the closed-cavity double-cavity spring modeling device involved in the embodiments of this application. In the embodiments of this application, the closed-cavity double-cavity spring modeling device may include a processor, a memory, a communication interface, and a communication bus.
[0095] The communication bus can be of any type and is used to interconnect the processor, memory, and communication interface.
[0096] The communication interface includes input / output (I / O) interfaces, physical interfaces, and logical interfaces used for interconnecting components within the closed-cavity double-spring modeling device, as well as interfaces used for interconnecting the closed-cavity double-spring modeling device with other devices (such as other computing devices or user equipment). Physical interfaces can be Ethernet interfaces, fiber optic interfaces, ATM interfaces, etc.; user equipment can be displays, keyboards, etc.
[0097] Memory can be various types of storage media, such as random access memory (RAM), read-only memory (ROM), non-volatile RAM (NVRAM), flash memory, optical storage, hard disk, programmable ROM (PROM), erasable PROM (EPROM), electrically erasable PROM (EEPROM), etc.
[0098] The processor can be a general-purpose processor, which can call the closed-cavity double-cavity spring modeling program stored in memory and execute the closed-cavity double-cavity spring modeling method provided in the embodiments of this application. For example, the general-purpose processor can be a central processing unit (CPU). The method executed when the closed-cavity double-cavity spring modeling program is called can be referred to the various embodiments of the closed-cavity double-cavity spring modeling method of this application, and will not be repeated here.
[0099] Those skilled in the art will understand that Figure 10 The hardware structure shown does not constitute a limitation of this application and may include more or fewer components than shown, or combine certain components, or have different component arrangements.
[0100] Fourthly, embodiments of this application also provide a computer-readable storage medium.
[0101] The computer-readable storage medium of this application stores a closed double-cavity air spring modeling program, wherein when the closed double-cavity air spring modeling program is executed by a processor, it implements the steps of the closed double-cavity air spring modeling method as described above.
[0102] The method implemented when the closed double-cavity air spring modeling program is executed can be referred to in various embodiments of the closed double-cavity air spring modeling method of this application, and will not be repeated here.
[0103] It should be noted that the sequence numbers of the embodiments in this application are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.
[0104] The terms "comprising" and "having," and any variations thereof, in the specification, claims, and accompanying drawings of this application are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or apparatus that includes a series of steps or units is not limited to the listed steps or units, but may optionally include steps or units not listed, or may optionally include other steps or units inherent to such process, method, product, or apparatus. The terms "first," "second," and "third," etc., are used to distinguish different objects, etc., and do not indicate a sequence, nor do they limit "first," "second," and "third" to different types.
[0105] In the description of the embodiments of this application, terms such as "exemplary," "for example," or "for instance" are used to indicate examples, illustrations, or explanations. Any embodiment or design described as "exemplary," "for example," or "for instance" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or designs. Specifically, the use of terms such as "exemplary," "for example," or "for instance" is intended to present the relevant concepts in a concrete manner.
[0106] In the description of the embodiments of this application, unless otherwise stated, " / " means "or". For example, A / B can mean A or B. The "and / or" in the text is merely a description of the relationship between related objects, indicating that there can be three relationships. For example, A and / or B can mean: A exists alone, A and B exist simultaneously, and B exists alone. In addition, in the description of the embodiments of this application, "multiple" means two or more.
[0107] In some processes described in the embodiments of this application, multiple operations or steps are included in a specific order. However, it should be understood that these operations or steps may not be executed in the order they appear in the embodiments of this application, or they may be executed in parallel. The sequence number of the operation is only used to distinguish different operations, and the sequence number itself does not represent any execution order. In addition, these processes may include more or fewer operations, and these operations or steps may be executed sequentially or in parallel, and these operations or steps may be combined.
[0108] Through the above description of the embodiments, those skilled in the art can clearly understand that the methods of the above embodiments can be implemented by means of software plus necessary general-purpose hardware platforms. Of course, they can also be implemented by hardware, but in many cases the former is a better implementation method. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium (such as ROM / RAM, magnetic disk, optical disk) as described above, and includes several instructions to cause a terminal device to execute the methods of the various embodiments of this application.
[0109] The above are merely preferred embodiments of this application and do not limit the patent scope of this application. Any equivalent structural or procedural transformations made using the content of this application's specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of this application.
Claims
1. A method for modeling a closed double-cavity air spring, characterized in that, include: Obtain the operating parameters of the closed double-cavity air spring to be modeled, and construct the thermodynamic stiffness and structural dynamic stiffness of the air spring based on the operating parameters. The damping characteristics of the additional air chamber and air bladder in the thermodynamic stiffness of the air spring are simplified by constant representation to obtain the first simplified stiffness. The effective area change characteristics in the dynamic stiffness of the air spring structure are simplified by linear representation to obtain the second simplified stiffness. The simplified stiffness expression is determined based on the first simplified stiffness and the second simplified stiffness. An external excitation is applied to the closed double-cavity air spring to be modeled by an actuator to obtain the measured values on the test bench. Based on the measured values on the test bench, the simplified stiffness expression is analyzed to obtain the simplified stiffness model of the closed double-cavity air spring to be modeled.
2. The closed double-cavity air spring modeling method according to claim 1, characterized in that, The process of simplifying the damping characteristics of the additional air chamber and air bladder in the thermodynamic stiffness of the air spring using a constant representation to obtain the first simplified stiffness includes: Ignoring the damping characteristics of the connecting hole, the damping characteristics of the additional air chamber and air bladder are expressed as constants that do not change with height and effective area. The thermodynamic stiffness of the air spring is then expressed as an equivalent thermodynamic simplified stiffness. The mechanical transmission characteristics of the thermodynamic simplified stiffness are differentiated and Taylorized to obtain the first simplified stiffness in the form of the suspension height.
3. The closed double-cavity air spring modeling method according to claim 1, characterized in that, The method of simplifying the effective area variation characteristics in the dynamic stiffness of the air spring structure to obtain the second simplified stiffness includes: The relationship between the effective area of the airbag and height is simplified to a linear relationship, and the dynamic stiffness of the air spring structure is equivalently expressed to obtain the second air spring stiffness.
4. The closed double-cavity air spring modeling method according to claim 1, characterized in that, The simplified stiffness model of the closed double-cavity air spring to be modeled is obtained by parametric analysis of the simplified stiffness expression based on the measured values of the test bench, including: The theoretical analytical value is determined based on the excitation value corresponding to the external excitation and the simplified stiffness expression; The parameters in the simplified stiffness expression are taken as particles to be optimized. The optimization objective is to minimize the difference between the theoretical analytical value and the measured value on the test bench. The optimal analytical value of each parameter is obtained by iterative optimization using the particle swarm optimization algorithm. Substituting the optimal analytical value into the simplified stiffness expression yields the simplified stiffness model.
5. The closed double-cavity air spring modeling method according to claim 1, characterized in that, The operating parameters include the physical structural parameters of the additional air chamber, air bladder, and air tank of the closed double-cavity air spring to be modeled, as well as the gas pressure state parameters, suspension height parameters, and temperature parameters of the closed double-cavity air spring to be modeled in one inflation / deflation cycle.
6. The closed double-cavity air spring modeling method according to claim 1, characterized in that, The construction of the air spring thermodynamic stiffness and air spring structural dynamic stiffness based on the operating parameters includes: Based on the aforementioned operating parameters, the internal gas mass is obtained by performing a constant mass filling and discharging operation. Gravity balance analysis and pressure balance analysis were performed on the closed double-cavity air spring to be modeled, and a set of two-degree-of-freedom dynamic equations were obtained. Based on the two-degree-of-freedom dynamic equations and the internal gas mass, equivalent representations of thermodynamic damping characteristics and structural dynamic transmission characteristics are performed to obtain the thermodynamic stiffness and structural dynamic stiffness of the air spring.
7. The closed double-cavity air spring modeling method according to claim 6, characterized in that, The process of performing equivalent representations of thermodynamic damping characteristics and structural dynamic transmission characteristics yields the thermodynamic stiffness and structural dynamic stiffness of the air spring, including: The heat exchange process of the closed double-cavity air spring to be modeled is equivalent to the heat exchange between the air bag and the ambient air. The effect of the change in effective area on the volume of the air bag is ignored, and the thermodynamic stiffness of the air spring is established. The relationship between the change in effective area and stiffness can be equivalently expressed as the dynamic stiffness of an air spring structure.
8. A closed-type double-cavity air spring modeling device, characterized in that, include: The air spring stiffness modeling module is used to obtain the operating parameters of the closed double-cavity air spring to be modeled, and to construct the air spring thermodynamic stiffness and air spring structural dynamic stiffness based on the operating parameters. The air spring stiffness simplification module is used to simplify the damping characteristics of the additional air chamber and air bladder in the thermodynamic stiffness of the air spring by constant expression to obtain the first simplified stiffness, and to simplify the effective area change characteristics in the dynamic stiffness of the air spring structure by linear expression to obtain the second simplified stiffness. The simplified stiffness expression is determined based on the first simplified stiffness and the second simplified stiffness. The parameter parsing module is used to apply external excitation to the closed double-cavity air spring to be modeled based on the actuator, obtain the test bench measured value, and perform parameter parsing on the simplified stiffness expression based on the test bench measured value to obtain the simplified stiffness model of the closed double-cavity air spring to be modeled.
9. A closed-type double-cavity air spring modeling device, characterized in that, The closed double-cavity air spring modeling device includes a processor, a memory, and a closed double-cavity air spring modeling program stored in the memory and executable by the processor, wherein when the closed double-cavity air spring modeling program is executed by the processor, it implements the steps of the closed double-cavity air spring modeling method as described in any one of claims 1 to 7.
10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a closed double-cavity air spring modeling program, wherein when the closed double-cavity air spring modeling program is executed by a processor, it implements the steps of the closed double-cavity air spring modeling method as described in any one of claims 1 to 7.