Stiffness calculation method, device and equipment of inverted cone type diaphragm air spring and medium

Abstract

The application discloses a rigidity calculation method, device, equipment and medium of an inverted cone type air bag, relates to the technical field of parameter design, and comprises the following steps: establishing a first mathematical model between the rigidity of the inverted cone type air bag and various state parameters; determining a conversion relationship between the various state parameters and various design parameters of the inverted cone type air bag; substituting the conversion relationship into the first mathematical model to obtain a second mathematical model between the rigidity and the various design parameters; determining the various design parameters corresponding to the various state parameters; and substituting the various design parameters into the second mathematical model to obtain the rigidity of the inverted cone type air bag. The first mathematical model for calculating the rigidity is converted through the conversion relationship between the state parameters and the design parameters of the inverted cone type air bag, and then the rigidity of the inverted cone type air bag is accurately calculated through the fixed parameters such as the design parameters and the second mathematical model obtained after conversion.

Description

Technical Field

[0001] This application relates to the field of parametric design technology, and in particular to a method, apparatus, equipment and medium for calculating the stiffness of an inverted conical diaphragm air spring. Background Technology

[0002] The inverted cone diaphragm air spring is a major type of diaphragm air spring, but currently there is no specific calculation method for its stiffness. The inverted cone diaphragm air spring is a high-performance elastic element with nonlinear stiffness characteristics, good vibration isolation and damping performance, and the ability to adjust vehicle height via airbag pressure. It is widely used in vibration isolation systems for automobiles, rail transportation, and industrial machinery. In practical engineering applications, the vertical stiffness of the inverted cone diaphragm air spring is often obtained through experimental testing, finite element analysis, equivalent mechanical models, and thermodynamic models, thus yielding its force-displacement characteristic curve.

[0003] However, current research methods still have many problems. Experimental testing methods require a lot of time and manpower and can only be applied to specific types of springs, lacking convenience and universality. The finite element method cannot quantitatively analyze the influence of parameters, resulting in a large workload, high cost, and lack of convenience. The "equivalent mechanical model" does not establish a direct relationship with the structural parameters of the air spring, which is not conducive to guiding the design of air springs. The method of combining thermodynamic models and geometric analysis has few studies on the widely used inverted conical diaphragm air springs. In addition, existing modeling methods all ignore the tensile deformation of inverted conical diaphragm air springs under the action of internal high-pressure gas. At the same time, most of the initial state parameters of inverted conical diaphragm air springs are obtained by establishing finite element models, without achieving complete analytical calculation. Summary of the Invention

[0004] The main objective of this application is to provide a method, apparatus, equipment, and medium for calculating the stiffness of an inverted conical diaphragm air spring, so as to accurately calculate the stiffness of the inverted conical diaphragm air spring.

[0005] To achieve the above objectives, one aspect of this application proposes a method for calculating the stiffness of an inverted conical diaphragm air spring, the method comprising the following steps:

[0006] A first mathematical model is established to establish the relationship between the stiffness and various state parameters of the inverted conical diaphragm air spring.

[0007] Determine the conversion relationship between each of the aforementioned state parameters and each of the design parameters of the inverted conical diaphragm air spring;

[0008] Substituting the transformation relationship into the first mathematical model, a second mathematical model is obtained between the stiffness and each of the design parameters;

[0009] Determine the design parameters corresponding to each of the aforementioned state parameters;

[0010] Substituting the design parameters into the second mathematical model, the stiffness of the inverted conical diaphragm air spring is obtained.

[0011] In some embodiments, establishing a first mathematical model relating the stiffness of the inverted conical diaphragm air spring to its various state parameters includes the following steps:

[0012] Based on the relationship between the external force and displacement of the upper cover plate of the inverted conical diaphragm air spring, a first mathematical model is established between the stiffness of the inverted conical diaphragm air spring and each of the state parameters.

[0013] The expression for the first mathematical model is:

[0014]

[0015] Wherein, C is the stiffness of the inverted conical diaphragm air spring; F is the external force on the upper cover plate; x is the displacement; γ is 1, indicating that under quasi-static tension and compression conditions, the thermodynamic process of the air inside the inverted conical diaphragm air spring is an isothermal process; P i P a These are the internal air pressure and external atmospheric pressure of the inverted cone diaphragm air spring, respectively; S w V These are the effective area, effective volume, rate of change of the effective area with displacement, and rate of change of the effective volume with displacement, respectively.

[0016] In some embodiments, determining the conversion relationship between the various state parameters and the various design parameters of the inverted conical diaphragm air spring includes the following steps:

[0017] A radial tensile force analysis of the air bladder of the inverted cone diaphragm air spring yields the force balance equation.

[0018] Geometric analysis of the airbag yields its geometric equation;

[0019] The transformation relationship between the state parameters and the design parameters is determined based on the force balance equation and the geometric equation.

[0020] In some embodiments, determining the design parameters corresponding to each of the state parameters includes the following steps:

[0021] Determine the effective area and effective volume of the inverted cone diaphragm air spring, as well as the rate of change of the effective area with displacement and the rate of change of the effective volume with displacement;

[0022] Establish a first mathematical relationship between the effective area, the effective volume, the rate of change of the effective area with displacement, the rate of change of the effective volume with displacement, and each of the state parameters;

[0023] Establish a second mathematical relationship between the internal air pressure of the inverted cone diaphragm air spring and the radial tensile deformation of the air bladder;

[0024] Substituting the second mathematical relationship into the first mathematical relationship, we obtain the third mathematical relationship between the effective area, the effective volume, the rate of change of the effective area with displacement, and the rate of change of the effective volume with displacement and each of the design parameters;

[0025] Substituting the effective area, the effective volume, the rate of change of the effective area with displacement, and the rate of change of the effective volume with displacement into the third mathematical relationship yields the various design parameters.

[0026] In some embodiments, determining the effective area of ​​the inverted conical diaphragm air spring includes the following steps:

[0027] Based on the working principle of the inverted conical diaphragm air spring, a stress analysis is performed on the inverted conical diaphragm air spring, and the relationship between the effective area and the state parameters is obtained as follows:

[0028] S w =πr e 2 ;

[0029] Among them, S w For the effective area, r e This is the distance from the point where the airbag separates from the top cover to the axis of symmetry.

[0030] Determining the rate of change of the effective volume of the inverted conical diaphragm air spring with respect to displacement includes the following steps:

[0031] The relationship between the rate of change of the effective area with displacement and the state parameters is determined as follows:

[0032]

[0033] in, The rate of change of the distance from the separation point of the airbag and the top cover to the axis of symmetry; The effective area is the rate of change with displacement.

[0034] In some embodiments, determining the effective volume of the inverted conical diaphragm air spring includes the following steps:

[0035] The internal volume of the inverted conical diaphragm air spring is decomposed into multiple regions of target shape;

[0036] The relationship between the effective volume and the state parameters, determined based on the regions of each target shape, is as follows:

[0037] V = V a +V b +V c -V d -V e -V f ;

[0038] Where V is the effective volume; V a V is the outer volume enclosed by the upper part of the airbag. b V is the outer volume enclosed by the middle part of the airbag; c V is the outer volume enclosed by the lower part of the airbag; d V is the inner volume enclosed by the top of the piston. e V is the inner volume enclosed by the middle of the piston; f The inner volume enclosed by the lower part of the airbag;

[0039] Determining the rate of change of the effective volume of the inverted conical diaphragm air spring with respect to displacement includes the following steps:

[0040] The relationship between the effective volume and the rate of change of displacement is determined as follows:

[0041]

[0042] Where x is the displacement.

[0043] In some embodiments, substituting the design parameters into the second mathematical model to obtain the stiffness of the inverted conical diaphragm air spring includes the following steps:

[0044] Substituting the airbag curtain angle and Young's modulus into the second mathematical model, the static stiffness of the inverted cone diaphragm air spring is obtained.

[0045] To achieve the above objectives, another aspect of this application provides a stiffness calculation device for an inverted conical diaphragm air spring, the device comprising:

[0046] The model building unit is used to establish the first mathematical model between the stiffness and various state parameters of the inverted cone diaphragm air spring.

[0047] A conversion relationship determination unit is used to determine the conversion relationship between each of the aforementioned state parameters and each of the design parameters of the inverted conical diaphragm air spring;

[0048] The model conversion unit is used to substitute the conversion relationship into the first mathematical model to obtain a second mathematical model relating the stiffness to each of the design parameters.

[0049] The design parameter determination unit is used to determine the design parameters corresponding to each of the state parameters;

[0050] The stiffness calculation unit is used to substitute the design parameters into the second mathematical model to obtain the stiffness of the inverted cone diaphragm air spring.

[0051] To achieve the above objectives, another aspect of this application provides an electronic device, which includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the above-described method.

[0052] To achieve the above objectives, another aspect of the embodiments of this application proposes a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described method.

[0053] The embodiments of this application include at least the following beneficial effects:

[0054] This application establishes a first mathematical model relating the stiffness of an inverted conical diaphragm air spring to its various state parameters; determines the conversion relationships between these state parameters and the various design parameters of the inverted conical diaphragm air spring; substitutes these conversion relationships into the first mathematical model to obtain a second mathematical model relating the stiffness to the various design parameters; determines the corresponding design parameters for each state parameter; and substitutes these design parameters into the second mathematical model to obtain the stiffness of the inverted conical diaphragm air spring. This application transforms the first mathematical model for calculating the stiffness of the inverted conical diaphragm air spring by using the conversion relationships between its state parameters and design parameters, and then accurately calculates the stiffness of the inverted conical diaphragm air spring using fixed parameters such as design parameters and the transformed second mathematical model. Attached Figure Description

[0055] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0056] Figure 1 A flowchart illustrating the stiffness calculation method for an inverted conical diaphragm air spring provided in this application embodiment;

[0057] Figure 2 A flowchart for calculating the static stiffness of an inverted cone diaphragm air spring with different cord angles, provided for embodiments of this application;

[0058] Figure 3 An example diagram of an inverted cone diaphragm air spring provided in the embodiments of this application;

[0059] Figure 4 An exploded view of the internal volume of the inverted conical diaphragm air spring provided in the embodiments of this application;

[0060] Figure 5 A simplified model schematic diagram of an inverted cone diaphragm air spring provided in an embodiment of this application;

[0061] Figure 6 Example diagram showing the static stiffness calculation results of the diaphragm air spring provided in the embodiments of this application;

[0062] Figure 7 A schematic diagram of the structure of the stiffness calculation device for the inverted cone diaphragm air spring provided in the embodiments of this application;

[0063] Figure 8 This is a schematic diagram of the hardware structure of an electronic device provided in an embodiment of this application. Detailed Implementation

[0064] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of this application and are not intended to limit it. In the following description, when referring to the accompanying drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with those of this application; they are merely examples of apparatuses and methods consistent with some aspects of the embodiments of this application as detailed in the appended claims.

[0065] It is understood that the terms “first,” “second,” etc., used in this application may be used herein to describe various concepts, but unless otherwise stated, these concepts are not limited by these terms. These terms are only used to distinguish one concept from another. For example, without departing from the scope of the embodiments of this application, first information may also be referred to as second information, and similarly, second information may also be referred to as first information. Depending on the context, the words “if,” “when,” or “in response to a determination” as used herein may be interpreted as “when…” or “when…” or “in response to a determination.”

[0066] As used in this application, the terms "at least one", "multiple", "each", "any", etc., "at least one" includes one, two or more, "multiple" includes two or more, "each" refers to each of the corresponding multiples, and "any" refers to any one of the multiples.

[0067] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used herein is for the purpose of describing embodiments of this application only and is not intended to limit this application.

[0068] This application provides a method, apparatus, device, and medium for calculating the stiffness of an inverted conical diaphragm air spring, relating to the field of parameter design technology. The method, apparatus, device, and medium for calculating the stiffness of an inverted conical diaphragm air spring provided in this application can be applied to terminals, servers, or software running on terminals or servers. In some embodiments, the terminal can be a smartphone, tablet, laptop, desktop computer, smart speaker, smartwatch, or vehicle terminal, but is not limited to these; the server can be configured as an independent physical server, a server cluster or distributed system composed of multiple physical servers, or a cloud server providing basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communication, middleware services, domain name services, security services, CDN, and big data and artificial intelligence platforms. The server can also be a node server in a blockchain network; the software can be an application implementing knowledge extraction methods, but is not limited to the above forms.

[0069] This application can be used in a wide variety of general-purpose or special-purpose computer system environments or configurations. Examples include: personal computers, server computers, handheld or portable devices, tablet devices, multiprocessor systems, microprocessor-based systems, set-top boxes, programmable consumer electronics, network PCs, minicomputers, mainframe computers, and distributed computing environments including any of the above systems or devices. This application can be described in the general context of computer-executable instructions executed by a computer, such as program modules. Generally, program modules include routines, programs, objects, components, data structures, etc., that perform specific tasks or implement specific abstract data types. This application can also be practiced in distributed computing environments where tasks are performed by remote processing devices connected via a communication network. In distributed computing environments, program modules can reside in local and remote computer storage media, including storage devices.

[0070] Reference Figure 1 This application provides a method for calculating the stiffness of an inverted conical diaphragm air spring. This method may include, but is not limited to, steps S100 to S140, as follows:

[0071] S100: Establish the first mathematical model relating the stiffness of the inverted conical diaphragm air spring to its various state parameters.

[0072] Furthermore, S100 may include S101:

[0073] S101: Based on the relationship between the external force and displacement of the upper cover plate of the inverted conical diaphragm air spring, establish the first mathematical model between the stiffness of the inverted conical diaphragm air spring and each of the state parameters.

[0074] The expression for the first mathematical model is:

[0075]

[0076] Wherein, C is the stiffness of the inverted conical diaphragm air spring; F is the external force on the upper cover plate; x is the displacement; γ is 1, indicating that under quasi-static tension and compression conditions, the thermodynamic process of the air inside the inverted conical diaphragm air spring is an isothermal process; P i P a These are the internal air pressure and external atmospheric pressure of the inverted cone diaphragm air spring, respectively; S w V These are the effective area, effective volume, rate of change of the effective area with displacement, and rate of change of the effective volume with displacement, respectively.

[0077] S110: Determine the conversion relationship between each of the stated state parameters and each of the design parameters of the inverted conical diaphragm air spring.

[0078] Furthermore, S110 may include S111 to S113:

[0079] S111: The force balance equation is obtained by performing radial tensile force analysis on the air bladder of the inverted cone diaphragm air spring.

[0080] S112: Perform geometric analysis on the airbag to obtain the geometric equation;

[0081] S113: Determine the conversion relationship between the state parameters and the design parameters based on the force balance equation and the geometric equation.

[0082] S120: Substitute the transformation relationship into the first mathematical model to obtain a second mathematical model relating the stiffness to each of the design parameters.

[0083] S130: Determine the design parameters corresponding to each of the state parameters.

[0084] Furthermore, S130 may include:

[0085] S131: Determine the effective area and effective volume of the inverted cone diaphragm air spring, as well as the rate of change of the effective area with displacement and the rate of change of the effective volume with displacement;

[0086] S132: Establish a first mathematical relationship between the effective area, the effective volume, the rate of change of the effective area with displacement, the rate of change of the effective volume with displacement, and each of the state parameters;

[0087] S133: Establish a second mathematical relationship between the internal air pressure of the inverted conical diaphragm air spring and the radial tensile deformation of the air bladder;

[0088] S133: Substitute the second mathematical relationship into the first mathematical relationship to obtain the third mathematical relationship between the effective area, the effective volume, the rate of change of the effective area with displacement, and the rate of change of the effective volume with displacement and each of the design parameters;

[0089] S134: Substitute the effective area, the effective volume, the rate of change of the effective area with displacement, and the rate of change of the effective volume with displacement into the third mathematical relationship to obtain the various design parameters.

[0090] As a further implementation, the step of determining the effective area and the rate of change of the effective area with displacement in S131 may include:

[0091] Based on the working principle of the inverted conical diaphragm air spring, a stress analysis is performed on the inverted conical diaphragm air spring, and the relationship between the effective area and the state parameters is obtained as follows:

[0092] S w =πr e 2 ;

[0093] Among them, S w For the effective area, r e This is the distance from the point where the airbag separates from the top cover to the axis of symmetry.

[0094] Determining the rate of change of the effective volume of the inverted conical diaphragm air spring with respect to displacement includes the following steps:

[0095] The relationship between the rate of change of the effective area with displacement and the state parameters is determined as follows:

[0096]

[0097] in, The rate of change of the distance from the separation point of the airbag and the top cover to the axis of symmetry; The effective area is the rate of change with displacement.

[0098] As another further implementation, the step of determining the effective volume and the rate of change of the effective volume with displacement in S131 may include:

[0099] The internal volume of the inverted conical diaphragm air spring is decomposed into multiple regions of target shape;

[0100] The relationship between the effective volume and the state parameters, determined based on the regions of each target shape, is as follows:

[0101] V = V a +V b +V c -V d -V e -V f ;

[0102] Where V is the effective volume; V a V is the outer volume enclosed by the upper part of the airbag. b V is the outer volume enclosed by the middle part of the airbag; c V is the outer volume enclosed by the lower part of the airbag; d V is the inner volume enclosed by the top of the piston. e V is the inner volume enclosed by the middle of the piston; f The inner volume enclosed by the lower part of the airbag;

[0103] Determining the rate of change of the effective volume of the inverted conical diaphragm air spring with respect to displacement includes the following steps:

[0104] The relationship between the effective volume and the rate of change of displacement is determined as follows:

[0105]

[0106] Where x is the displacement.

[0107] S140: Substitute the design parameters into the second mathematical model to obtain the stiffness of the inverted conical diaphragm air spring.

[0108] Furthermore, S140 may include S141:

[0109] S141: Substitute the airbag curtain angle and Young's modulus into the second mathematical model to obtain the static stiffness of the inverted cone diaphragm air spring.

[0110] The following section will provide a detailed introduction and explanation of the solutions in the embodiments of this application, using specific application examples.

[0111] Since there is currently no calculation model that incorporates designable parameters such as airbag cord angle and Young's modulus into the vertical stiffness, the calculation results of the static stiffness of the inverted cone diaphragm air spring are not accurate.

[0112] This embodiment aims to propose a method for calculating the vertical stiffness of an inverted cone diaphragm air spring that can reasonably describe the characteristics of the piston cone surface of the air spring, consider the airbag deformation, and introduce design parameters such as the airbag cord angle and Young's modulus.

[0113] This embodiment establishes a general calculation method for the static stiffness of an inverted conical diaphragm air spring based on geometric and mechanical analysis. A static stiffness model for the inverted conical diaphragm air spring is established based on thermodynamic principles. Functional expressions for the state parameters in the stiffness model are obtained through geometric and mechanical analysis. The geometric equations and force balance equations of the air spring bladder are obtained, and their simultaneous equations yield the conversion relationship between the state parameters and design parameters. Substituting this conversion relationship into the model using functional expressions establishes the functional relationship between the static stiffness of the inverted conical diaphragm air spring and the design parameters, thereby obtaining the force-displacement characteristics of the inverted conical diaphragm air spring.

[0114] The static stiffness calculation method for the inverted cone diaphragm air spring provided in this embodiment is faster, more efficient, more accurate, and simpler than the finite element analysis method used in the prior art, thus greatly saving the production cost of air springs.

[0115] Reference Figure 2 , Figure 2 This is a flowchart for calculating the static stiffness of an inverted cone diaphragm air spring applicable to different cord angles.

[0116] Specifically, this embodiment provides a method for calculating the static stiffness of an inverted conical diaphragm air spring, the method comprising the following steps:

[0117] Step (1), construct an inverted conical diaphragm air spring (an example of an inverted conical diaphragm air spring such as...) Figure 3 A mathematical model of the static stiffness and state parameters of the inverted conical diaphragm air spring (as shown) is established based on thermodynamic principles, revealing the mathematical relationship between the static stiffness and various state parameters:

[0118]

[0119] In the formula, C represents the static stiffness of the inverted conical diaphragm air spring, and γ represents the polytropic index. Under quasi-static tension and compression conditions, the thermodynamic process of the air inside the inverted conical diaphragm air spring can be considered as an isothermal process, in which case γ is taken as 1; P i P a These represent the internal air pressure and external atmospheric pressure of the inverted cone diaphragm air spring, respectively; S w V These are the effective area, volume, and rate of change of the inverted cone diaphragm air spring with respect to displacement.

[0120] Step (2): Obtain the effective area, effective volume, and corresponding rate of change of the inverted cone diaphragm air spring.

[0121] The effective area of ​​an inverted conical diaphragm air spring is an abstract equivalent concept. The effective area characterizes the load-bearing capacity F of the inverted conical diaphragm air spring under the action of internal air pressure P1.

[0122] Based on the working principle of the inverted conical diaphragm air spring, a force analysis is performed on the inverted conical diaphragm air spring to obtain the relationship between the external force F acting on the upper cover plate and the design parameters:

[0123] F=πr e 2 (P1-P a (2)

[0124] In the formula, F is the vertical net external force of the inverted cone diaphragm air spring, and r is the net external force. e The distance between the airbag and the top cover separation position and the axis of symmetry, P1, P a These refer to the internal air pressure of the inverted cone diaphragm air spring and the external air pressure of the air spring, respectively.

[0125] Therefore, the effective area S of the inverted cone diaphragm air spring w The expression is shown in the following formula;

[0126] S w =πr e 2 (3)

[0127] In the formula r e This is the distance between the point where the airbag separates from the top cover and the axis of symmetry.

[0128] Taking the derivative of the effective area with respect to the vertical displacement, we can obtain the expression for the rate of change of the effective area as follows:

[0129]

[0130] In the formula The rate of change of the distance between the airbag and the upper cover separation position and the axis of symmetry. This represents the effective area change rate of the inverted cone diaphragm air spring.

[0131] Among them, the effective area calculated by equations (3) and (4) and its rate of change with displacement are the state parameter vector X and its derivative. The function.

[0132] The internal volume of the inverted cone diaphragm air spring reflects the expansion and deformation characteristics of the air bladder under the action of internal air pressure P1. As shown in equation (1), the rate of change of volume with displacement reflects the change of internal air pressure with displacement. Figure 4As shown, by decomposing the internal volume of the inverted conical diaphragm air spring into several easily calculable target shapes, the total volume of the air chamber of the inverted conical diaphragm air spring can be obtained. The calculation formula is as follows:

[0133] V = V a +V b +V c -V d -V e -V f (5)

[0134] Among them, V a The outer volume enclosed by the upper part of the airbag, V b The outer volume enclosed by the middle of the airbag, V c V is the outer volume enclosed by the lower part of the airbag. d V is the inner volume enclosed by the top of the piston. e V is the inner volume enclosed by the middle of the piston. f It refers to the inner volume enclosed by the lower part of the airbag.

[0135] Based on the above formula, the effective volume is differentiated with respect to displacement to obtain the effective volume change rate:

[0136]

[0137] Among them, the volume calculated by equations (5) and (6) and its rate of change with displacement are the state parameter vector X and its derivative. The function.

[0138] Step (3) establishes the relationship between the internal air pressure of the inverted cone diaphragm air spring and the radial tensile deformation of the air bladder, and introduces the air bladder deformation of the inverted cone diaphragm air spring into the calculation model of the performance of the inverted cone diaphragm air spring, in order to prepare for the conversion of state parameters to design parameters.

[0139] The air bladder of an inverted cone diaphragm air spring consists of a cord layer that primarily bears the load and inner and outer rubber layers that provide sealing. Its Young's modulus E is mainly determined by the angle, number, and material of the cords. In the radial direction of the air bladder, the Young's modulus can be obtained by adding the equivalent modulus of the cord in that direction to the rubber modulus by a certain volume fraction.

[0140] Step (4): Based on the above derivation, the vertical stiffness calculation model of the inverted conical diaphragm air spring uses the state parameter vector and its derivative with respect to displacement x as variables. Since the state parameters change with working conditions such as working height, it is not conducive to design and optimization. Therefore, it is necessary to convert the changing state parameters and their derivatives into design parameters in the vector, and then express the vertical stiffness calculation model of the inverted conical diaphragm air spring as a functional relationship of design parameters.

[0141] Reference Figure 5 Establish a plane coordinate system XOY with the inverted conical diaphragm air spring in a static state, and mark the endpoints (O and O) of the upper and lower cover plates of the inverted conical diaphragm air spring. h Several contours reflecting the inverted conical diaphragm air spring and its geometric center O i (i=1, 2, 3, 4), N (i= 1, 2, 3, 4, 5), B i (i = 1, 2) are the key feature points, and the coordinates of each feature point on the plane coordinate system XOY are obtained.

[0142] Let the state parameter vector be X = [r1, r2, r3, α1, α2, α3, a, l]. T The design parameter vector is C = [h1, h2, h3, h4, b1, b2, S0, H]. T Where r1 is the radius of the arc of the upper part of the airbag, r2 is the radius of the arc of the middle part of the airbag, r3 is the radius of the arc of the lower part of the airbag, α1 is the arc angle of the upper part of the airbag, α2 is the arc angle of the middle part of the airbag and the horizontal line, α3 is the arc angle of the lower part of the airbag, α is the distance between the separation position of the airbag and the top cover and the axis of symmetry, l is the distance between the centers of the arcs of the upper and lower parts of the airbag, h1 is the thickness of the top cover, h2 is the height of the piston top, h3 is the height of the piston middle, h4 is the height of the piston bottom, b1 is the radius of the piston top, b2 is the radius of the piston bottom, S0 is the initial radial length of the airbag, and H is the working height of the air spring.

[0143] The force balance equation is obtained by radial tensile force analysis of the air bladder part of the inverted cone diaphragm air spring; the geometric equation is obtained by geometric analysis of the air bladder; by combining the force balance equation and the geometric equation of the inverted cone diaphragm air spring air bladder, the conversion relationship between the state parameters and design parameters of the inverted cone diaphragm air spring can be analyzed.

[0144] Step (5): Substitute the result of step (3) into the relationship in step (2) to obtain the functional relationship between the effective area, effective volume and its rate of change of the inverted cone diaphragm air spring and the design parameters.

[0145] Step (6): Substitute the result of step (4) into the mathematical model of step (1) to calculate the static stiffness of the inverted cone diaphragm air spring, which is related to the designable parameters such as the airbag curtain angle and Young's modulus.

[0146] Plot the force-displacement characteristic curve of the inverted cone diaphragm air spring with a cord angle of 35°, as follows: Figure 6 As shown, the results are compared with experimental test results. Figure 6The results show that the static stiffness calculation method for diaphragm air springs proposed in this embodiment can well describe the load-displacement characteristics of inverted conical diaphragm air springs under different working pressures, and it matches the experimental values. Furthermore, it has good applicability to diaphragm air springs with different cord angles.

[0147] Reference Figure 7 This application also provides a stiffness calculation device for an inverted conical diaphragm air spring, which can realize the above-described stiffness calculation method for an inverted conical diaphragm air spring. The device includes:

[0148] The model building unit is used to establish the first mathematical model between the stiffness and various state parameters of the inverted cone diaphragm air spring.

[0149] A conversion relationship determination unit is used to determine the conversion relationship between each of the aforementioned state parameters and each of the design parameters of the inverted conical diaphragm air spring;

[0150] The model conversion unit is used to substitute the conversion relationship into the first mathematical model to obtain a second mathematical model relating the stiffness to each of the design parameters.

[0151] The design parameter determination unit is used to determine the design parameters corresponding to each of the state parameters;

[0152] The stiffness calculation unit is used to substitute the design parameters into the second mathematical model to obtain the stiffness of the inverted cone diaphragm air spring.

[0153] It is understood that the content of the above method embodiments is applicable to the present device embodiments. The specific functions implemented by the present device embodiments are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0154] This application also provides an electronic device, which includes a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the above-described method for calculating the stiffness of an inverted conical diaphragm air spring. This electronic device can be any smart terminal, including tablet computers, in-vehicle computers, etc.

[0155] It is understood that the content of the above method embodiments is applicable to this device embodiment. The specific functions implemented by this device embodiment are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0156] Please see Figure 8 , Figure 8 The hardware structure of an electronic device according to another embodiment is illustrated. The electronic device includes:

[0157] The processor 801 can be implemented using a general-purpose CPU (Central Processing Unit), microprocessor, application-specific integrated circuit (ASIC), or one or more integrated circuits, and is used to execute relevant programs to implement the technical solutions provided in the embodiments of this application.

[0158] The memory 802 can be implemented as a read-only memory (ROM), static storage device, dynamic storage device, or random access memory (RAM). The memory 802 can store the operating system and other application programs. When the technical solutions provided in the embodiments of this specification are implemented through software or firmware, the relevant program code is stored in the memory 802 and is called and executed by the processor 801 to execute the stiffness calculation method for the inverted cone diaphragm air spring of this application embodiment.

[0159] The 803 input / output interface is used to implement information input and output.

[0160] The communication interface 804 is used to enable communication and interaction between this device and other devices. Communication can be achieved through wired means (such as USB, Ethernet cable, etc.) or wireless means (such as mobile network, WIFI, Bluetooth, etc.).

[0161] Bus 805 transmits information between various components of the device (e.g., processor 801, memory 802, input / output interface 803, and communication interface 804);

[0162] The processor 801, memory 802, input / output interface 803, and communication interface 804 are connected to each other within the device via bus 805.

[0163] This application also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described method for calculating the stiffness of an inverted conical diaphragm air spring.

[0164] It is understood that the content of the above method embodiments is applicable to this storage medium embodiment. The specific functions implemented in this storage medium embodiment are the same as those in the above method embodiments, and the beneficial effects achieved are also the same as those achieved in the above method embodiments.

[0165] Memory, as a non-transitory computer-readable storage medium, can be used to store non-transitory software programs and non-transitory computer-executable programs. Furthermore, memory may include high-speed random access memory, and may also include non-transitory memory, such as at least one disk storage device, flash memory device, or other non-transitory solid-state storage device. In some embodiments, memory may optionally include memory remotely located relative to the processor, and these remote memories can be connected to the processor via a network. Examples of such networks include, but are not limited to, the Internet, intranets, local area networks, mobile communication networks, and combinations thereof.

[0166] The embodiments described in this application are for the purpose of more clearly illustrating the technical solutions of the embodiments of this application, and do not constitute a limitation on the technical solutions provided by the embodiments of this application. As those skilled in the art will know, with the evolution of technology and the emergence of new application scenarios, the technical solutions provided by the embodiments of this application are also applicable to similar technical problems.

[0167] Those skilled in the art will understand that the technical solutions shown in the figures do not constitute a limitation on the embodiments of this application, and may include more or fewer steps than shown, or combine certain steps, or different steps.

[0168] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs.

[0169] Those skilled in the art will understand that all or some of the steps in the methods disclosed above, as well as the functional modules / units in the systems and devices, can be implemented as software, firmware, hardware, or suitable combinations thereof.

[0170] The terms “first,” “second,” “third,” “fourth,” etc. (if present) in the specification and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of this application described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms “comprising” and “having,” and any variations thereof, are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0171] It should be understood that in this application, "at least one (item)" means one or more, and "more than" means two or more. "And / or" is used to describe the relationship between related objects, indicating that three relationships can exist. For example, "A and / or B" can represent three cases: only A exists, only B exists, and both A and B exist simultaneously, where A and B can be singular or plural. The character " / " generally indicates that the preceding and following related objects are in an "or" relationship. "At least one (item) of the following" or similar expressions refer to any combination of these items, including any combination of single or plural items. For example, at least one (item) of a, b, or c can represent: a, b, c, "a and b", "a and c", "b and c", or "a and b and c", where a, b, and c can be single or multiple.

[0172] In the several embodiments provided in this application, it should be understood that the disclosed apparatus and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of the units described above is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between apparatuses or units may be electrical, mechanical, or other forms.

[0173] The units described above as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0174] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0175] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes multiple instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of this application. The aforementioned storage medium includes various media capable of storing programs, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0176] The preferred embodiments of the present application have been described above with reference to the accompanying drawings, but this does not limit the scope of the claims of the present application. Any modifications, equivalent substitutions, and improvements made by those skilled in the art without departing from the scope and substance of the embodiments of the present application shall be within the scope of the claims of the present application.

Claims

1. A method for calculating the stiffness of an inverted conical diaphragm air spring, characterized in that, The method includes the following steps: A first mathematical model is established to establish the relationship between the stiffness and various state parameters of the inverted conical diaphragm air spring. Determine the conversion relationship between each of the aforementioned state parameters and each of the design parameters of the inverted conical diaphragm air spring; Substituting the transformation relationship into the first mathematical model, a second mathematical model is obtained between the stiffness and each of the design parameters; Determine the design parameters corresponding to each of the aforementioned state parameters; Substituting the design parameters into the second mathematical model, the stiffness of the inverted conical diaphragm air spring is obtained; Determining the design parameters corresponding to each of the state parameters includes the following steps: Determine the effective area and effective volume of the inverted cone diaphragm air spring, as well as the rate of change of the effective area with displacement and the rate of change of the effective volume with displacement; Establish a first mathematical relationship between the effective area, the effective volume, the rate of change of the effective area with displacement, and the rate of change of the effective volume with displacement and other state parameters; Establish a second mathematical relationship between the internal air pressure of the inverted cone diaphragm air spring and the radial tensile deformation of the air bladder; Substituting the second mathematical relationship into the first mathematical relationship, we obtain the third mathematical relationship between the effective area, the effective volume, the rate of change of the effective area with displacement, and the rate of change of the effective volume with displacement and each of the design parameters. Substituting the effective area, the effective volume, the rate of change of the effective area with displacement, and the rate of change of the effective volume with displacement into the third mathematical relationship yields the various design parameters.

2. The method for calculating the stiffness of the inverted conical diaphragm air spring according to claim 1, characterized in that, The establishment of the first mathematical model relating the stiffness of the inverted conical diaphragm air spring to its various state parameters includes the following steps: Based on the relationship between the external force and displacement of the upper cover plate of the inverted conical diaphragm air spring, a first mathematical model is established between the stiffness of the inverted conical diaphragm air spring and each of the state parameters. The expression for the first mathematical model is: ； in, The stiffness of the inverted conical diaphragm air spring; The external force acting on the upper cover plate. For displacement; γ A value of 1 indicates that, under quasi-static tension and compression conditions, the thermodynamic process of the air inside the inverted cone diaphragm air spring is an isothermal process. P i , P a These refer to the internal air pressure and external atmospheric pressure of the inverted cone-shaped diaphragm air spring, respectively. S w , V , , These are the effective area, effective volume, rate of change of the effective area with displacement, and rate of change of the effective volume with displacement, respectively.

3. The method for calculating the stiffness of the inverted conical diaphragm air spring according to claim 1, characterized in that, Determining the conversion relationship between the various state parameters and the various design parameters of the inverted conical diaphragm air spring includes the following steps: A radial tensile force analysis of the air bladder of the inverted cone diaphragm air spring yields the force balance equation. Geometric analysis of the airbag yields its geometric equation; The transformation relationship between the state parameters and the design parameters is determined based on the force balance equation and the geometric equation.

4. The method for calculating the stiffness of the inverted conical diaphragm air spring according to claim 1, characterized in that, Determining the effective area of ​​the inverted conical diaphragm air spring includes the following steps: Based on the working principle of the inverted conical diaphragm air spring, a stress analysis was performed on the inverted conical diaphragm air spring, and the relationship between the effective area and other state parameters was obtained as follows: ； in, The effective area is... This is the distance from the point where the airbag separates from the top cover to the axis of symmetry. Determining the rate of change of the effective volume of the inverted conical diaphragm air spring with respect to displacement includes the following steps: The relationship between the rate of change of the effective area with respect to displacement and other state parameters is determined as follows: ； in, The rate of change of the distance from the separation point of the airbag and the top cover to the axis of symmetry; The effective area is the rate of change with displacement.

5. The method for calculating the stiffness of the inverted conical diaphragm air spring according to claim 1, characterized in that, Determining the effective volume of the inverted conical diaphragm air spring includes the following steps: The internal volume of the inverted conical diaphragm air spring is decomposed into multiple regions of target shape; The relationship between the effective volume and other state parameters is determined based on the regions of each target shape as follows: ； in, The effective volume; The outer volume enclosed by the upper part of the airbag; The outer volume enclosed by the middle part of the airbag; The outer volume enclosed by the lower part of the airbag; The inner volume enclosed by the top of the piston. The inner volume enclosed by the middle of the piston; The inner volume enclosed by the lower part of the airbag; Determining the rate of change of the effective volume of the inverted conical diaphragm air spring with respect to displacement includes the following steps: The relationship between the rate of change of the effective volume with displacement and other state parameters is determined as follows: ； in, For displacement.

6. The method for calculating the stiffness of the inverted conical diaphragm air spring according to any one of claims 1 to 5, characterized in that, The step of substituting the design parameters into the second mathematical model to obtain the stiffness of the inverted conical diaphragm air spring includes the following steps: Substituting the airbag curtain angle and Young's modulus into the second mathematical model, the static stiffness of the inverted cone diaphragm air spring is obtained.

7. A stiffness calculation device for an inverted conical diaphragm air spring, characterized in that, The device is applied to the stiffness calculation method for the inverted conical diaphragm air spring as described in claim 1, and the device comprises: The model building unit is used to establish the first mathematical model between the stiffness and various state parameters of the inverted cone diaphragm air spring. The conversion relationship determination unit is used to determine the conversion relationship between each of the state parameters and each of the design parameters of the inverted conical diaphragm air spring; The model conversion unit is used to substitute the conversion relationship into the first mathematical model to obtain a second mathematical model between the stiffness and each of the design parameters; The design parameter determination unit is used to determine the design parameters corresponding to each of the state parameters; The stiffness calculation unit is used to substitute the design parameters into the second mathematical model to obtain the stiffness of the inverted cone diaphragm air spring.

8. An electronic device, characterized in that, The electronic device includes a memory and a processor, the memory storing a computer program, and the processor executing the computer program to implement the method as described in any one of claims 1 to 6.

9. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the method as described in any one of claims 1 to 6.

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