Air spring bladder skin dynamic stiffness acquisition method and system

Abstract

The present application relates to air spring dynamic stiffness estimation technical field, provide a kind of air spring bag skin dynamic stiffness acquisition method and system, wherein method includes: obtaining the effective area radius of air spring and, the structural parameters of bag skin's ear section and the material parameters of bag skin;Based on effective area radius, the structural parameters of ear section and the material parameters of bag skin, determine the dynamic stiffness value generated by curling of ear section;Based on the dynamic stiffness value generated by curling of ear section and preset correction coefficient, determine the dynamic stiffness value generated by structural deformation of bag skin.Based on directly measured parameters and air spring design structural parameters, to solve the defect that the dynamic stiffness generated by the structural deformation of bag skin of air spring cannot be effectively estimated in the prior art, the effective estimation of bag skin dynamic stiffness is realized, to make it possible for air spring dynamic stiffness to change nonlinearly with amplitude Modeling, and provide guidance for air spring bag skin structure material selection and forward design.

Description

Technical Field

[0001] This invention relates to the field of air spring dynamic stiffness estimation technology, and in particular to a method and system for obtaining the dynamic stiffness of the air spring bladder. Background Technology

[0002] Currently, vehicles primarily employ air suspension systems to improve vibration isolation performance. In addition to vibration isolation, another characteristic of air suspension systems is their ability to adjust vehicle height to best match the vehicle's dynamic behavior. For example, during high-speed driving, the vehicle height can be lowered to its minimum to reduce wind resistance; while during off-road driving, the chassis height can be raised to increase the vehicle's passability.

[0003] In electronically controlled air suspension systems, the most important actuator is the air spring, making accurate prediction of its dynamic behavior essential. However, current modeling of air spring dynamics faces numerous challenges, one of which is the inability to effectively estimate the dynamic stiffness of the air spring caused by the deformation of the bladder structure. This makes modeling the nonlinear variation of the air spring's dynamic stiffness with amplitude a difficult task. Summary of the Invention

[0004] This invention provides a method and system for obtaining the dynamic stiffness of the air spring's bladder, which solves the problem that the existing technology cannot effectively estimate the dynamic stiffness of air springs caused by the deformation of the bladder structure. It enables effective estimation of the bladder dynamic stiffness based on directly measured parameters and the air spring's design structural parameters, thereby making it possible to model the nonlinear variation of the air spring's dynamic stiffness with amplitude, and providing guidance for the selection of air spring bladder structure materials and forward design.

[0005] This invention also provides a method for obtaining the dynamic stiffness of the air spring's bladder, comprising:

[0006] Obtain the effective area radius of the air spring, the structural parameters of the flap section of the bladder, and the material parameters of the bladder; the flap section is the part of the bladder that is rolled up outside the piston of the air spring.

[0007] Based on the effective area radius, the structural parameters of the auricle segment, and the material parameters of the sac skin, the dynamic stiffness value of the auricle segment caused by curling is determined;

[0008] Based on the dynamic stiffness value generated by the curling of the auricle segment, the dynamic stiffness value generated by the structural deformation of the sac skin is determined.

[0009] According to the method for obtaining the dynamic stiffness of the air spring sheath of the present invention, determining the dynamic stiffness value of the sheath segment due to curling based on the effective area radius, the structural parameters of the sheath segment, and the material parameters of the sheath includes:

[0010] Based on the effective area radius and the material parameters of the bladder, the bending stiffness of the bladder is determined;

[0011] Based on the bending stiffness and the structural parameters of the drooping segment, the dynamic stiffness value of the drooping segment caused by curling is determined.

[0012] According to the method for obtaining the dynamic stiffness of the air spring bladder according to the present invention, the structural parameters of the lug segment include: the angle of the side of the bladder that is attached to the piston surface relative to the direction perpendicular to the horizontal plane. and the radius r of the said auricle segment;

[0013] The material parameters of the capsule skin include: the thickness t of the capsule skin; the thickness t of the intermediate layer of the capsule skin. f The intermediate layer of the capsule skin is a composite layer composed of rubber and cord in the capsule skin; the elastic modulus E of the cord is... f Volume fractions c f and the inclination angle α c The elastic modulus E of the rubber m .

[0014] According to the method for obtaining the dynamic stiffness of the air spring sheath of the present invention, determining the dynamic stiffness value of the sheath segment due to curling based on the effective area radius, the structural parameters of the sheath segment, and the material parameters of the sheath includes:

[0015] According to a first preset formula, based on the effective area radius, the structural parameters of the auricle segment, and the material parameters of the sac skin, the dynamic stiffness value of the auricle segment caused by curling is determined. The first preset formula includes:

[0016]

[0017] Among them, R eff The effective area radius of the air spring is given.

[0018] According to the method for obtaining the dynamic stiffness of the air spring's bladder according to the present invention, the first preset formula is constructed in the following manner:

[0019] Based on the strain relationship of off-axis tensile stress in composite material mechanics, the definition of bending stiffness is deformed to obtain an expression for the bending stiffness of the bladder skin expressed in terms of the effective area radius and the material parameters of the bladder skin.

[0020] Obtain the inward bending moment of the drooping segment along the meridian direction of the air spring at a preset angle position;

[0021] Based on the principle of minimum complementary energy, a first expression for the displacement of the drooping segment caused by the internal bending moment is derived.

[0022] Based on the expression for bending stiffness and the first expression for displacement, a second expression for displacement is obtained, which is expressed in terms of the effective area radius, the structural parameters of the auricle segment, and the material parameters of the bladder skin.

[0023] Based on the second expression for the displacement and the dynamic stiffness calculation formula, the first preset formula is obtained;

[0024] The expression for the bending stiffness is:

[0025]

[0026] Among them, E s I is the equivalent Young's modulus of the sac skin; I is the moment of inertia of the cross section of the drooping segment along the bending direction.

[0027] The first expression for the displacement is:

[0028]

[0029] Among them, u B P is the displacement caused by the internal bending moment; P is the vertical external force generated by the bladder skin.

[0030] The formula for calculating the dynamic stiffness is:

[0031]

[0032] Where K is the dynamic stiffness and u is the displacement.

[0033] According to the method for obtaining the dynamic stiffness of the air spring bladder according to the present invention, determining the dynamic stiffness value of the bladder due to structural deformation based on the dynamic stiffness value generated by the curling of the ear segment includes:

[0034] Based on the dynamic stiffness value of the auricle segment due to curling and the preset correction coefficient, the dynamic stiffness value of the sac skin due to structural deformation is determined.

[0035] The preset correction coefficient is determined based on the dynamic stiffness value of the auricle segment due to tension, the dynamic stiffness value of the auricle segment due to shear, and the dynamic stiffness value of the vertical segment of the sac skin due to tension. The vertical segment refers to the other parts of the sac skin besides the auricle segment.

[0036] According to the method for obtaining the dynamic stiffness of the air spring bladder of the present invention, the preset correction coefficient is determined based on the harmonic average relationship between the dynamic stiffness value of the drooping segment due to curling, the dynamic stiffness value of the drooping segment due to stretching, the dynamic stiffness value of the drooping segment due to shearing, and the dynamic stiffness value of the vertical segment of the bladder due to stretching.

[0037] According to the method for obtaining the dynamic stiffness of the air spring bladder of the present invention, the dynamic stiffness value of the drooping segment due to tension is determined based on the effective area radius, the structural parameters of the drooping segment, and the material parameters of the bladder according to the second preset formula.

[0038] According to the third preset formula, the dynamic stiffness value of the auricle segment caused by shear is determined based on the effective area radius, the structural parameters of the auricle segment, and the material parameters of the sac skin.

[0039] According to the fourth preset formula, the dynamic stiffness value of the vertical segment due to tension is determined based on the effective area radius and the material parameters of the bladder.

[0040] The second preset formula is:

[0041]

[0042] Among them, K t The value of the dynamic stiffness of the drooping segment due to tension; u x The displacement of the drooping segment due to stretching;

[0043] The third preset formula is:

[0044]

[0045] Among them, K s The value of the dynamic stiffness of the shear segment due to shearing; u s G represents the displacement of the auricle segment due to shearing; G is the shear modulus of the sac skin.

[0046] The fourth preset formula is:

[0047]

[0048] Among them, K P The value of the dynamic stiffness of the vertical segment due to tension; u P h is the displacement of the vertical segment caused by stretching; h is the height of the vertical segment.

[0049] According to the method for obtaining the dynamic stiffness of the air spring's bladder according to the present invention, the second preset formula is constructed in the following manner:

[0050] The tensile force equation is constructed at the preset angle position of the ear segment along the meridian direction of the air spring;

[0051] Based on the principle of minimum residual energy, and the relationship between the tensile force and internal stress on the auricle segment and the cross-sectional area of ​​the bladder skin perpendicular to the meridian direction, combined with the tensile force equation, an expression for the displacement of the auricle segment due to tension is obtained, expressed in terms of the effective area radius, the structural parameters of the auricle segment, and the material parameters of the bladder skin.

[0052] Based on the expression for the displacement caused by the stretching of the auricle segment, the second preset formula is obtained;

[0053] The third preset formula is constructed in the following way:

[0054] The equation for the internal shear force along the meridian direction of the air spring is constructed at a preset angle position on the drooping section.

[0055] Based on the principle of minimum residual energy, and the relationship between the shear force and internal stress of the auricle segment and the cross-sectional area of ​​the bladder skin perpendicular to the meridian direction, combined with the internal shear force equation, an expression for the displacement of the auricle segment caused by shear is obtained, expressed in terms of the effective area radius, the structural parameters of the auricle segment, and the material parameters of the bladder skin.

[0056] Based on the expression for the displacement of the auricle segment caused by shearing, the third preset formula is obtained;

[0057] The fourth preset formula is constructed in the following way:

[0058] Based on the principle of virtual work, and the relationship between the tensile force and internal stress on the vertical segment and the cross-sectional area of ​​the skin perpendicular to the meridian direction, an expression for the displacement of the vertical segment caused by the vertical external force is obtained, expressed in terms of the effective area radius and the material parameters of the skin.

[0059] Based on the expression for the displacement of the vertical segment caused by the vertical external force, the fourth preset formula is obtained.

[0060] The present invention also provides a system for obtaining the dynamic stiffness of the air spring's bladder, comprising:

[0061] The acquisition module is used to acquire the effective area radius of the air spring, the structural parameters of the flap section of the bladder, and the material parameters of the bladder; the flap section is the part of the bladder that is rolled up outside the piston of the air spring.

[0062] The first processing module is used to determine the dynamic stiffness value of the auricle segment caused by curling based on the effective area radius, the structural parameters of the auricle segment, and the material parameters of the sac skin.

[0063] The second processing module is used to determine the dynamic stiffness value of the sac skin due to structural deformation based on the dynamic stiffness value generated by the curling of the auricle segment.

[0064] The present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the method for obtaining the dynamic stiffness of the air spring bladder as described above.

[0065] The present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the method for obtaining the dynamic stiffness of the air spring bladder as described above.

[0066] This invention provides a method and system for obtaining the dynamic stiffness of an air spring's diaphragm. First, the effective area radius of the air spring, the structural parameters of the flap segment of the diaphragm, and the material parameters of the diaphragm are obtained. Then, based on the effective area radius, the structural parameters of the flap segment, and the material parameters of the diaphragm, the dynamic stiffness value of the flap segment due to curling is determined. Finally, based on the dynamic stiffness value of the flap segment due to curling, the dynamic stiffness value of the diaphragm due to structural deformation is determined. On the one hand, this achieves effective estimation of the dynamic stiffness caused by the structural deformation of the diaphragm, thus solving the modeling problem of the nonlinear variation of the dynamic stiffness of a diaphragm air spring with amplitude. On the other hand, by using the effective area radius of the air spring, the structural parameters of the flap segment of the diaphragm, and the material parameters of the diaphragm, the dynamic stiffness of the air spring caused by the structural deformation of the diaphragm is estimated. This allows the dynamic stiffness caused by the structural deformation of the diaphragm to be expressed based on the parameters of the air spring directly measured in experiments and the inherent parameters of the air spring in its structural design, thus providing effective guidance for the selection of air spring diaphragm structural materials and forward design. Attached Figure Description

[0067] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0068] Figure 1 This is a flowchart illustrating a method for obtaining the dynamic stiffness of the air spring's bladder according to an embodiment of the present invention.

[0069] Figure 2 This is a schematic diagram of a diaphragm air spring;

[0070] Figure 3 This is a schematic diagram of the air spring's bladder structure;

[0071] Figure 4 This is a diagram illustrating the force distribution principle of the sac skin;

[0072] Figure 5 This is a schematic diagram of the structure of the air suspension system test bench provided in an embodiment of the present invention;

[0073] Figure 6 This is the hysteresis characteristic curve of an air spring;

[0074] Figure 7 This is a comparison diagram of the theoretical dynamic stiffness and the experimental dynamic stiffness provided in the embodiments of the present invention;

[0075] Figure 8 This is a schematic diagram of the structure of an air spring bladder dynamic stiffness acquisition system provided in an embodiment of the present invention;

[0076] Figure 9 A schematic diagram of the structure of the electronic device provided by this invention;

[0077] Figure label:

[0078] 1: Vertical section; 2: Lug section; 3: Cover plate; 4: Piston; 5: Surface section; 6: Rubber layer; 7: Intermediate layer; 8: High-pressure air source; 9: High-pressure air pipe; 10: Pressure reducing valve; 11: Pressure sensor; 12: Air spring; 13: Actuator; 14: Force sensor; 15: Data acquisition equipment. Detailed Implementation

[0079] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0080] First, to facilitate understanding of the prediction method described in this invention, the air spring involved in this invention will be introduced. It should be noted that the technical solution of this invention pertains to a diaphragm air spring. A diaphragm air spring is a type of air spring that achieves overall expansion and contraction by placing a rubber diaphragm between a cover plate and a piston, and by deforming the diaphragm.

[0081] The following is combined with Figures 1 to 7 This invention describes a method for obtaining the dynamic stiffness of an air spring's bladder, executed using a computer or a combination of its software and / or hardware, such as... Figure 1 As shown, the method includes the following steps:

[0082] 101. Obtain the effective area radius of the air spring, the structural parameters of the flap section of the bladder, and the material parameters of the bladder; the flap section is the part of the bladder that is rolled up outside the piston of the air spring;

[0083] It is understandable that, such as Figure 2 As shown, the air spring's bladder mainly consists of a vertical section 1, a lug section 2, a surface section 5 that is in close contact with the cover plate 3 and the piston 4. When the height of the air spring changes, the bladder will generate corresponding dynamic stiffness due to the curling, shearing and stretching deformation of the bladder.

[0084] Specifically, the effective area of ​​an air spring transmits the air pressure within the spring to the surface of the contacting part in the form of force. Therefore, the deformation of the spring casing is related to the change in the effective area. It is known that the air pressure (internal pressure of the air spring) and the force transmitted to the surface of the part (load of the air spring) are both known quantities; therefore, the effective area of ​​the air spring can be determined. The radius of the effective area is the radius when the effective area is assumed to be circular; therefore, the radius of the effective area of ​​the air spring can also be determined.

[0085] Structural parameters are quantities that characterize the specific structure of an object, such as the tilt angle characterizing the shape of a triangular object, the radius characterizing the size of a circular object, etc. In the method for obtaining the dynamic stiffness of the air spring bladder provided in this embodiment of the invention, the structural parameters of the bladder are obtained, that is, parameters characterizing the specific shape of the bladder. Furthermore, the ease with which the bladder deforms is related to the structural parameters of the bladder.

[0086] Material parameters are quantities that characterize the material information of an object, such as the types and proportions of raw materials in concrete, or the material and thickness of a mobile phone case. In the method for obtaining the dynamic stiffness of the air spring's bladder provided in this embodiment of the invention, the material parameters of the bladder are obtained, that is, parameters characterizing the type of material in the bladder, as well as the thickness and distribution of each material. Similarly, it can be understood that the ease with which the bladder deforms is also related to its material parameters.

[0087] 102. Based on the effective area radius, the structural parameters of the auricle segment, and the material parameters of the sac skin, determine the dynamic stiffness value of the auricle segment caused by curling;

[0088] 103. Based on the dynamic stiffness value generated by the curling of the auricle segment, determine the dynamic stiffness value generated by the structural deformation of the sac skin.

[0089] Specifically, by obtaining the effective area radius of the air spring, the structural parameters of the flap segment, and the material parameters of the flap, the dynamic stiffness value of the flap segment due to curling is determined. Then, based on the dynamic stiffness value of the flap segment due to curling, the dynamic stiffness value of the flap due to structural deformation is determined. This achieves effective estimation of the dynamic stiffness value of the flap due to structural deformation using the effective area radius of the air spring and the inherent parameters of the flap, solving the modeling problem of nonlinear dynamic stiffness of membrane air springs with amplitude variation. Simultaneously, it allows the dynamic stiffness caused by flap structural deformation to be expressed based on the parameters of the air spring directly measured in experiments and the inherent parameters of the air spring in structural design, thus providing effective guidance for the selection of air spring flap structural materials and forward design.

[0090] More specifically, the dynamic stiffness value of the loop segment caused by curling is determined based on the effective area radius, the structural parameters of the loop segment, and the material parameters of the bladder. This makes each parameter characterizing the dynamic stiffness value of the loop segment caused by curling have a clear physical meaning and can be directly measured according to the design structure and experiments. This makes the method for obtaining the dynamic stiffness of the air spring bladder provided in this embodiment of the invention highly feasible.

[0091] As an embodiment of the present invention, determining the dynamic stiffness value of the auricle segment due to curling based on the effective area radius, the structural parameters of the auricle segment, and the material parameters of the sac includes:

[0092] Based on the effective area radius and the material parameters of the bladder, the bending stiffness of the bladder is determined;

[0093] Based on the bending stiffness and the structural parameters of the drooping segment, the dynamic stiffness value of the drooping segment caused by curling is determined.

[0094] It is understandable that the flexural stiffness of the skin refers to its ability to resist bending deformation. Therefore, it is directly related to the microstructure of the skin, i.e., the material used to make the skin, and has a direct impact on the dynamic stiffness value of the auricle segment caused by curling. At the same time, the structural parameters of the auricle segment of the skin mainly affect the skin's resistance to curling.

[0095] Specifically, the bending stiffness of the air spring is first determined based on the effective area radius of the air spring and the material parameters of the air spring skin. Then, based on the bending stiffness of the air spring skin and the structural parameters of the flap segment, the dynamic stiffness value of the flap segment caused by curling can be determined.

[0096] As an embodiment of the present invention, the structural parameters of the auricle segment include: the angle of the side of the bladder skin that adheres to the piston surface relative to the vertical horizontal plane. and the radius r of the said auricle segment;

[0097] The material parameters of the capsule skin include: the thickness t of the capsule skin; the thickness t of the intermediate layer of the capsule skin. f The intermediate layer of the capsule skin is a composite layer composed of rubber and cord in the capsule skin; the elastic modulus E of the cord is... f Volume fractions c f and the inclination angle α c The elastic modulus E of the rubber m .

[0098] Specifically, such as Figure 2 As shown, the angle of the side of the bladder that fits against the piston surface relative to the vertical horizontal plane. The angle of inclination of the piston is equal to that of the air spring, which is determined during the manufacturing process. The radius r of the lug section can also be obtained by measurement.

[0099] More specifically, for diaphragm air springs, such as Figure 3 As shown, its capsule structure consists of rubber layers 6 on the inner and outer sides, and a rubber-cord reinforced composite material 7 in the middle. Therefore, the thickness t of the capsule and the thickness t of the middle layer of the capsule are... f The elastic modulus E of the cord f Volume fractions c f and the inclination angle α c And the elastic modulus E of rubber m All of these can be determined during the design and manufacturing process of the air spring.

[0100] As an embodiment of the present invention, determining the dynamic stiffness value of the auricle segment due to curling based on the effective area radius, the structural parameters of the auricle segment, and the material parameters of the sac includes:

[0101] According to a first preset formula, based on the effective area radius, the structural parameters of the auricle segment, and the material parameters of the sac skin, the dynamic stiffness value of the auricle segment caused by curling is determined. The first preset formula includes:

[0102]

[0103] Among them, R eff The effective area radius of the air spring is given.

[0104] Specifically, as can be seen from the first preset formula, the method for obtaining the dynamic stiffness of the air spring bladder provided in this embodiment of the invention proposes an analytical expression for the dynamic stiffness of the air spring caused by the curling of the flap section, and further provides an analytical expression for the contribution of the additional dynamic stiffness of the air spring caused by the deformation of the rubber bladder structure, thereby solving the modeling problem of the nonlinear variation of the dynamic stiffness of the diaphragm air spring with amplitude.

[0105] More specifically, as shown in Formula 1, the dynamic stiffness value generated by the curling of the flap section, i.e., the dynamic stiffness of the bladder due to structural deformation, is positively correlated with the elastic modulus of the rubber material and cord, the cord angle, and the designed thickness of the bladder, and negatively correlated with the flap radius and piston tilt angle. Furthermore, all parameters involved in the formula can be obtained through experiments or direct measurement. Moreover, it is mainly based on the inherent parameters of the air spring, such as the bladder thickness, intermediate layer thickness, and piston tilt angle. This not only facilitates the determination of the additional dynamic stiffness of the air spring caused by the structural deformation of the rubber bladder, but also provides theoretical guidance for the selection and forward design of air spring bladder structural materials.

[0106] As an embodiment of the present invention, the first preset formula is constructed in the following manner:

[0107] Based on the strain relationship of off-axis tensile stress in composite material mechanics, the definition of bending stiffness is deformed to obtain an expression for the bending stiffness of the bladder skin expressed in terms of the effective area radius and the material parameters of the bladder skin.

[0108] Obtain the inward bending moment of the drooping segment along the meridian direction of the air spring at a preset angle position;

[0109] Based on the principle of minimum complementary energy, a first expression for the displacement of the drooping segment caused by the internal bending moment is derived.

[0110] Based on the expression for bending stiffness and the first expression for displacement, a second expression for displacement is obtained, which is expressed in terms of the effective area radius, the structural parameters of the auricle segment, and the material parameters of the bladder skin.

[0111] Based on the second expression for the displacement and the dynamic stiffness calculation formula, the first preset formula is obtained;

[0112] The expression for the bending stiffness is:

[0113]

[0114] Among them, E s I is the equivalent Young's modulus of the sac skin; I is the moment of inertia of the cross section of the drooping segment along the bending direction.

[0115] The first expression for the displacement is:

[0116]

[0117] Among them, u B P is the displacement caused by the internal bending moment; P is the vertical external force generated by the bladder skin.

[0118] The formula for calculating the dynamic stiffness is:

[0119]

[0120] Where K is the dynamic stiffness and u is the displacement.

[0121] Understandably, assuming the rubber material is isotropic and each layer is uniformly laid, the definition of flexural stiffness based on mechanics of materials is:

[0122] E s I=∫ A E z z 2 dA (5)

[0123] Where A is the cross-sectional area of ​​the air spring's longitudinal structure shell perpendicular to the air spring's meridian direction; E z Here, z represents the tensile modulus at position z; z is the distance from the neutral surface of the air spring, which is the middle surface when the air spring is considered as a single layer of composite material. The meridian direction of the air spring refers to the direction along the axial direction of the sphere when the air spring is considered as a sphere.

[0124] Specifically, according to the definition of the positive direction in composite material mechanics, the stress-strain relationship under off-axis tensile stress should satisfy:

[0125]

[0126] Where, σ x and σ y These represent the stresses along the x and y directions, respectively; τ xy The shear stress is along the xy direction; Equivalents are the stiffness representations in the stiffness matrix; ε x and ε y Strain along the x and y directions, respectively; γ xy Let x be the shear strain along the xy direction.

[0127] Furthermore, the strain of the air spring in the y-direction (latitude) is more pronounced than in other directions. Therefore, considering both physical meaning and practical considerations, all strains except those in the y-direction are small, meaning they are not on the same order of magnitude as the strain in the y-direction. We can then ignore the effect of Poisson's ratio and neglect the strain relative to Q. 11 If the other terms are small, then the expression for bending stiffness can be obtained as shown in Formula 2.

[0128] More specifically, the internal bending moment M of the drooping section at a preset angle θ along the meridian of the air spring p for:

[0129]

[0130] Then, using the principle of minimum complementary energy, the factor M can be derived through Equation 7. pThe resulting additional displacement u B The first expression is 3. Substituting formula 2 into formula 3, we can obtain the second expression for the displacement as shown in formula 8:

[0131]

[0132] It can be seen that, except for the vertical external force P generated by the sac skin, all the parameters in Formula 8 are parameters that can be obtained through experiments and directly measured.

[0133] Finally, substituting Formula 8 into Formula 4 for dynamic stiffness calculation yields the first preset formula.

[0134] As an embodiment of the present invention, determining the dynamic stiffness value of the scaly skin due to structural deformation based on the dynamic stiffness value generated by the curling of the auricle segment includes:

[0135] Based on the dynamic stiffness value of the auricle segment due to curling and the preset correction coefficient, the dynamic stiffness value of the sac skin due to structural deformation is determined.

[0136] The preset correction coefficient is determined based on the dynamic stiffness value of the auricle segment due to tension, the dynamic stiffness value of the auricle segment due to shear, and the dynamic stiffness value of the vertical segment of the sac skin due to tension. The vertical segment refers to the other parts of the sac skin besides the auricle segment.

[0137] Specifically, such as Figure 4 As shown, when the height of the air spring changes, the dynamic stiffness of the bladder skin is generated by the curling, shearing, and tensile deformation. Therefore, when determining the dynamic stiffness of the bladder skin due to structural deformation using the dynamic stiffness value generated by the curling of the flap segment, a preset correction coefficient β is determined based on the dynamic stiffness values ​​generated by the tension of the flap segment, the dynamic stiffness values ​​generated by the shearing of the flap segment, and the dynamic stiffness values ​​generated by the tension of the vertical segment of the bladder skin. c This can improve the accuracy of determining the dynamic stiffness of the sac skin due to structural deformation by using the dynamic stiffness value generated by the curling of the auricle segment.

[0138] As an embodiment of the present invention, the preset correction coefficient is determined based on the harmonic average relationship between the dynamic stiffness value of the auricle segment due to curling, the dynamic stiffness value of the auricle segment due to stretching, the dynamic stiffness value of the auricle segment due to shearing, and the dynamic stiffness value of the vertical segment of the cyst skin due to stretching.

[0139] Specifically, along the direction of the air spring's longitudinal section, the displacement of the flap segment due to curling, the displacement of the flap segment due to tension, the displacement of the flap segment due to shearing, and the displacement of the vertical segment of the air spring due to tension all exhibit a simple superposition relationship. Therefore, the dynamic stiffness value of the air spring due to structural deformation should satisfy the harmonic average relationship shown in Formula 9 below:

[0140]

[0141] Among them, K t This represents the dynamic stiffness value of the drooping segment due to tension; u x K represents the displacement of the auricle segment due to stretching; s u represents the dynamic stiffness of the shear segment due to shearing. s K represents the displacement of the auricle segment due to shearing. P The value of the dynamic stiffness of the vertical segment due to tension; u P This represents the displacement of the vertical segment due to stretching.

[0142] More specifically, when the preset correction coefficient β is determined based on the dynamic stiffness values ​​of the auricle segment due to tension, the dynamic stiffness values ​​of the auricle segment due to shear, and the dynamic stiffness values ​​of the vertical segment of the sac skin due to tension... c Subsequently, the dynamic stiffness value of the skin due to structural deformation is:

[0143]

[0144] As an embodiment of the present invention, the dynamic stiffness value of the auricle segment due to stretching is determined based on the effective area radius, the structural parameters of the auricle segment, and the material parameters of the sac skin, according to the second preset formula.

[0145] According to the third preset formula, the dynamic stiffness value of the auricle segment caused by shear is determined based on the effective area radius, the structural parameters of the auricle segment, and the material parameters of the sac skin.

[0146] According to the fourth preset formula, the dynamic stiffness value of the vertical segment due to tension is determined based on the effective area radius and the material parameters of the bladder.

[0147] The second preset formula is:

[0148]

[0149] The third preset formula is:

[0150]

[0151] Wherein, G is the shear modulus of the cystic membrane;

[0152] The fourth preset formula is:

[0153]

[0154] Where h is the height of the vertical segment.

[0155] Specifically, the thickness t of the skin is generally on the order of millimeters. As can be seen from Equations 11 to 13, the dynamic stiffness values ​​of the auricle segment due to tension, the auricle segment due to shear, and the vertical segment of the skin due to tension are all linear terms proportional to the skin thickness. However, as can be seen from Equation 1, the dynamic stiffness value of the auricle segment due to curling is a cubic term proportional to the skin thickness. Therefore, under the harmonic average relationship shown in Equation 9, the stiffness value of the skin due to structural deformation is mainly affected by the dynamic stiffness value of the auricle segment due to curling. By introducing a correction coefficient to replace the dynamic stiffness values ​​of the auricle segment due to tension, the auricle segment due to shear, and the vertical segment of the skin due to tension, the computational workload can be effectively reduced while ensuring computational accuracy, thereby improving the efficiency of stiffness value determination.

[0156] As an embodiment of the present invention, the second preset formula is constructed in the following manner:

[0157] The tensile force equation is constructed at the preset angle position of the ear segment along the meridian direction of the air spring;

[0158] Based on the principle of minimum residual energy, and the relationship between the tensile force and internal stress on the auricle segment and the cross-sectional area of ​​the bladder skin perpendicular to the meridian direction, combined with the tensile force equation, an expression for the displacement of the auricle segment due to tension is obtained, expressed in terms of the effective area radius, the structural parameters of the auricle segment, and the material parameters of the bladder skin.

[0159] Based on the expression for the displacement caused by the stretching of the auricle segment, the second preset formula is obtained;

[0160] The third preset formula is constructed in the following way:

[0161] The equation for the internal shear force along the meridian direction of the air spring is constructed at a preset angle position on the drooping section.

[0162] Based on the principle of minimum residual energy, and the relationship between the shear force and internal stress of the auricle segment and the cross-sectional area of ​​the bladder skin perpendicular to the meridian direction, combined with the internal shear force equation, an expression for the displacement of the auricle segment caused by shear is obtained, expressed in terms of the effective area radius, the structural parameters of the auricle segment, and the material parameters of the bladder skin.

[0163] Based on the expression for the displacement of the auricle segment caused by shearing, the third preset formula is obtained;

[0164] The fourth preset formula is constructed in the following way:

[0165] Based on the principle of virtual work, and the relationship between the tensile force and internal stress on the vertical segment and the cross-sectional area of ​​the skin perpendicular to the meridian direction, an expression for the displacement of the vertical segment caused by the vertical external force is obtained, expressed in terms of the effective area radius and the material parameters of the skin.

[0166] Based on the expression for the displacement of the vertical segment caused by the vertical external force, the fourth preset formula is obtained.

[0167] Specifically, the internal stress is the tensile internal stress generated by the tensile force of the air spring skin. At the preset angle θ position on the flap section, the equation for the tensile force along the meridian of the air spring is:

[0168] X p =P sinθ (14)

[0169] Meanwhile, the tensile force and internal stress σ of the ear segment along the meridian of the air spring satisfy the following relationship:

[0170]

[0171] Furthermore, based on the principle of minimum complementary energy, and neglecting the Poisson effect, the displacement u of the apron segment due to tension can be derived using Equations 14 and 15. x The expression:

[0172]

[0173] Then, based on formulas 16 and 4, the second preset formula can be obtained.

[0174] Similarly, at the preset angle θ position on the drooping section, the equation for the internal shear force along the meridian direction of the air spring is:

[0175] S p =P cosθ (17)

[0176] Based on the principle of minimum complementary energy, by deriving Equation 17, the displacement u of the shear segment caused by shear can be obtained. s The expression:

[0177]

[0178] Then, based on formulas 18 and 4, the third preset formula can be obtained.

[0179] Regarding the displacement of the vertical segment due to stretching, based on the principle of virtual work and the relationship between the tensile force and internal stress on the vertical segment, and the cross-sectional area of ​​the scabbard perpendicular to the meridian direction, we can obtain:

[0180]

[0181] Substituting formula 19 into formula 4 yields the fourth preset formula.

[0182] The following section uses an air suspension system test bench to verify the degree of agreement between the test dynamic stiffness of the air spring obtained through the indicator test and the dynamic stiffness value of the spring skin due to structural deformation obtained by the spring skin dynamic stiffness acquisition method based on the above embodiments of the present invention, i.e., the theoretical dynamic stiffness, as well as the degree of influence of the spring skin material on the dynamic stiffness of the spring.

[0183] The principle of the air suspension system test bench is as follows: Figure 5 As shown, gas from high-pressure gas source 8 passes through high-pressure gas pipe 9, pressure reducing valve 10, and pressure sensor 11 to connect to air spring 12; actuator 13 provides sinusoidal displacement excitation to air spring 12, and force sensor 14 detects the force generated by the excitation in air spring 12; the pressure reducing valve 10 controls the internal air pressure of air spring 12, and data from actuator 13 and force sensor 14 are collected by data acquisition device 15 and cross-compared with pressure sensor 11. Three air springs (sample 1, sample 2, and sample 3) with different designs and structures were selected for dynamometer tests on the experimental platform. The initial state data at the initial state of the test are shown in Table 1.

[0184] Table 1 Initial state of the experiment

[0185] Parameters / Units Value Parameters / Units Value <![CDATA[T0 / (K)]]> 298 <![CDATA[K b / (J / K)]]> 1.039 <![CDATA[A eff / (m 2 )]]> 0.01079 <![CDATA[z0 / (m)]]> 0.1303 <![CDATA[p b0 / (N / m 2 )]]> <![CDATA[9×10 5 ]]> <![CDATA[C V / (J / (K·kg))]]> 717.5 <![CDATA[V b0 / (m 3 )]]> <![CDATA[2.45×10 -3 ]]> κ / (1 / m) 6.6061 <![CDATA[m b0 / (kg)]]> 0.02578 A / (m) 0.026

[0186] It is understandable that the dynamic stiffness of an air spring consists of two parts: elastic dynamic stiffness and hysteresis loss, both of which are related to the high-pressure gas and the rubber bladder. Therefore, elastic dynamic stiffness includes: the dynamic stiffness generated by the rubber material (i.e., the stored dynamic stiffness of the air spring bladder at the current amplitude), the dynamic stiffness due to changes in effective area, and the gas-equivalent dynamic stiffness; hysteresis loss includes: the loss dynamic stiffness due to the hysteretic characteristics of the rubber material (i.e., the loss dynamic stiffness of the air spring bladder at the current amplitude) and the loss dynamic stiffness due to heat exchange between the solid and gas. It is known that, except for the dynamic stiffness generated by the air spring bladder, the others are independent of the amplitude. Therefore, the influence of the bladder on the dynamic stiffness of the spring can be studied based on the change in the air spring dynamic stiffness with amplitude.

[0187] Specifically, the elastic dynamic stiffness and hysteresis loss are respectively referred to as the real parts k. Re and the imaginary part k Im With the real part k Re The experimental dynamic stiffness and theoretical dynamic stiffness are compared.

[0188] Among them, the experimental dynamic stiffness of the real part is based on, for example, Figure 6 The indicated power curve of the air spring shown has hysteresis characteristics, and the calculation obtained from formula 20 is as follows:

[0189]

[0190] The experimental dynamic stiffness of specimens 1, 2, and 3 was obtained for amplitudes of 0.1 mm, 1 mm, and 10 mm, respectively. This was then compared with the theoretical dynamic stiffness of specimens 1, 2, and 3. The results are shown in Table 2 and... Figure 7 As shown, where, Figure 7 The curves shown correspond to the theoretical stiffness of specimen 1, specimen 2, and specimen 3 from top to bottom, respectively. Points close to each curve correspond to the experimental stiffness of specimen 1, specimen 2, and specimen 3 at three amplitudes, respectively.

[0191] Table 2 Stiffness Comparison

[0192]

[0193] It is evident that the relative error between the theoretical stiffness and the experimental stiffness for the three air springs with different designs and structures (samples 1, 2, and 3) is less than 4%. Furthermore, the dynamic stiffness varies significantly for different samples, i.e., air springs with different sheath materials. Therefore, by using the method for obtaining the dynamic stiffness of the air spring sheath provided in this embodiment of the invention, the dynamic stiffness value generated by the structural deformation of the sheath is added to the calculation of the total stiffness of the air spring. This improves the accuracy of the air spring stiffness calculation and has universality. Simultaneously, the additional stiffness generated by the sheath of the air spring is significant at low amplitudes, and the deflector moment has the greatest impact on it.

[0194] The following is combined with Figure 8 The present invention describes a system for obtaining the dynamic stiffness of the air spring's bladder. The system described below and the method described above can be referred to in correspondence.

[0195] like Figure 8 As shown, the present invention also provides a system for acquiring the dynamic stiffness of an air spring's bladder, comprising: an acquisition module 810, a first processing module 820, and a second processing module 830; wherein,

[0196] The acquisition module 810 is used to acquire the effective area radius of the air spring and the structural parameters of the flap section of the bladder; the flap section is the part of the bladder that is rolled up outside the piston of the air spring.

[0197] The first processing module 820 is used to determine the dynamic stiffness value of the auricle segment caused by curling based on the effective area radius, the structural parameters of the auricle segment, and the material parameters of the sac skin.

[0198] The second processing module 830 is used to determine the dynamic stiffness value of the sac skin due to structural deformation based on the dynamic stiffness value of the auricle segment caused by curling and a preset correction coefficient.

[0199] The air spring shell dynamic stiffness acquisition system provided in this invention first acquires the effective area radius of the air spring, the structural parameters of the flap segment of the shell, and the material parameters of the shell. Then, based on the effective area radius, the structural parameters of the flap segment, and the material parameters of the shell, it determines the dynamic stiffness value of the flap segment caused by curling. Finally, based on the dynamic stiffness value of the flap segment caused by curling, it determines the dynamic stiffness value of the shell caused by structural deformation. On the one hand, it achieves effective estimation of the dynamic stiffness caused by shell structural deformation, thereby solving the modeling problem of nonlinear dynamic stiffness of membrane air springs with amplitude variation. On the other hand, by using the effective area radius of the air spring, the structural parameters of the flap segment of the shell, and the material parameters of the shell, it achieves estimation of the dynamic stiffness of the air spring caused by shell structural deformation. This allows the dynamic stiffness caused by shell structural deformation to be expressed based on the parameters of the air spring directly measured in experiments and the inherent parameters of the air spring in structural design, thus providing effective guidance for the selection of air spring shell structural materials and forward design.

[0200] Preferably, the first processing module is specifically used to determine the bending stiffness of the skin based on the effective area radius and the material parameters of the skin; and to determine the dynamic stiffness value of the awl segment caused by curling based on the bending stiffness and the structural parameters of the awl segment.

[0201] Preferably, the structural parameters of the loparm segment include: the angle of the side of the bladder skin that adheres to the piston surface relative to the vertical horizontal plane. The radius r of the auricle segment; the material parameters of the capsule include: the thickness t of the capsule; the thickness t of the middle layer of the capsule. f The middle layer of the capsule skin is a composite layer composed of rubber and cord in the capsule skin;

[0202] The elastic modulus E of the cord f Volume fractions c f and the inclination angle α c The elastic modulus E of the rubber m .

[0203] Preferably, the first processing module is more specifically used to determine the dynamic stiffness value of the auricle segment caused by curling, based on the effective area radius, the structural parameters of the auricle segment, and the material parameters of the sac skin, according to the first preset formula shown in Formula 1.

[0204] Preferably, it also includes building modules;

[0205] The construction module is used to deform the definition of bending stiffness based on the strain relationship of off-axis tensile stress in composite material mechanics, to obtain the expression for the bending stiffness of the bladder skin as shown in Formula 2, which is expressed in terms of the effective area radius and the material parameters of the bladder skin; to obtain the internal bending moment of the ear segment along the meridian direction of the air spring at a preset angle position; based on the principle of minimum complementary energy, to derive the first expression for the displacement of the ear segment caused by the internal bending moment as shown in Formula 3; based on the expression for bending stiffness and the first expression for displacement, to obtain the second expression for displacement as shown in Formula 8, which is expressed in terms of the effective area radius, the structural parameters of the ear segment, and the material parameters of the bladder skin; and based on the second expression for displacement and the dynamic stiffness calculation formula as shown in Formula 4, to obtain the first preset formula.

[0206] Preferably, the second processing module is specifically used to determine the dynamic stiffness value of the capsule skin due to structural deformation based on the dynamic stiffness value of the auricle segment due to curling and a preset correction coefficient; the preset correction coefficient is determined based on the dynamic stiffness value of the auricle segment due to stretching, the dynamic stiffness value of the auricle segment due to shearing, and the dynamic stiffness value of the vertical segment of the capsule skin due to stretching, wherein the vertical segment is the other part of the capsule skin excluding the auricle segment.

[0207] Preferably, the second processing module is further configured to determine the preset correction coefficient based on the harmonic average relationship between the dynamic stiffness value of the auricle segment due to curling, the dynamic stiffness value of the auricle segment due to stretching, the dynamic stiffness value of the auricle segment due to shearing, and the dynamic stiffness value of the vertical segment of the sac skin due to stretching.

[0208] Preferably, the second processing module is further configured to determine the dynamic stiffness value of the auricle segment due to tension based on the effective area radius, the structural parameters of the auricle segment, and the material parameters of the sac skin according to the second preset formula shown in Formula 11; determine the dynamic stiffness value of the auricle segment due to shear based on the effective area radius, the structural parameters of the auricle segment, and the material parameters of the sac skin according to the third preset formula shown in Formula 12; and determine the dynamic stiffness value of the vertical segment due to tension based on the effective area radius and the material parameters of the sac skin according to the fourth preset formula shown in Formula 13.

[0209] Preferably, the construction module is further configured to construct a tensile force equation along the meridian direction of the air spring at a preset angle position of the droop segment; based on the principle of minimum complementary energy, and the relationship between the tensile force and internal stress on the droop segment, and the cross-sectional area of ​​the bladder perpendicular to the meridian direction, combined with the tensile force equation, to obtain an expression for the displacement of the droop segment due to tension, expressed in terms of the effective area radius, the structural parameters of the droop segment, and the material parameters of the bladder; based on the expression for the displacement of the droop segment due to tension, to obtain the second preset formula; construct an internal shear force equation along the meridian direction of the air spring at a preset angle position of the droop segment; based on the principle of minimum complementary energy, and the relationship between the shear force and internal stress on the droop segment, and the cross-sectional area of ​​the bladder perpendicular to the meridian direction, to obtain an expression for the displacement of the droop segment due to tension; based on the expression for the displacement of the droop segment due to tension, to obtain the second preset formula; to construct an internal shear force equation along the meridian direction of the air spring at a preset angle position of the droop segment; based on the principle of minimum complementary energy, and the relationship between the shear force and internal stress on the droop segment, and the cross-sectional area of ​​the bladder perpendicular to the meridian direction, to obtain an expression for the displacement of the droop segment due to tension; based on the relationship between the tensile force and internal stress on the droop segment, and the cross-sectional area of ​​the air spring perpendicular to the meridian direction, to obtain an expression for the displacement of the droop segment due to tension; based on the expression for the displacement of the droop segment due to tension; to construct an internal shear force equation along the meridian direction of the air spring at a preset angle position of the droop segment; based on the principle of minimum complementary energy, and the relationship between the tensile force and internal stress on the droop segment, and the cross-sectional area of ​​the air spring perpendicular to the meridian direction, to obtain an expression for the displacement of the droop segment The relationship between internal stress and the cross-sectional area of ​​the skin perpendicular to the meridian direction is used to derive an expression for the displacement of the awl segment due to shear, expressed in terms of the effective area radius, the structural parameters of the awl segment, and the material parameters of the skin. Based on this expression, the third preset formula is derived. Furthermore, based on the principle of virtual work and the relationship between the tensile force on the vertical segment, internal stress, and the cross-sectional area of ​​the skin perpendicular to the meridian direction, an expression for the displacement of the vertical segment due to the vertical external force is derived, expressed in terms of the effective area radius and the material parameters of the skin. Based on this expression, the fourth preset formula is derived.

[0210] Figure 9 An example is a schematic diagram of the physical structure of an electronic device, such as... Figure 9 As shown, the electronic device may include: a processor 910, a communication interface 920, a memory 930, and a communication bus 940, wherein the processor 910, the communication interface 920, and the memory 930 communicate with each other through the communication bus 940. The processor 910 uses the memory 930 to encode instructions to execute a method for obtaining the dynamic stiffness of the air spring's bladder. The method includes: obtaining the effective area radius of the air spring, the structural parameters of the bladder's flap segment, and the material parameters of the bladder; the flap segment is the portion of the bladder that is rolled up outside the piston of the air spring; determining the dynamic stiffness value of the flap segment due to its roll-up based on the effective area radius, the structural parameters of the flap segment, and the material parameters of the bladder; and determining the dynamic stiffness value of the bladder due to its structural deformation based on the dynamic stiffness value of the flap segment due to its roll-up and a preset correction coefficient.

[0211] Furthermore, when the aforementioned memory 930 instruction set can be 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 the present invention, or the part that contributes to the prior art, or a 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 several 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 described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0212] On the other hand, the present invention also provides a computer program product, which includes a computer program that can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer can execute the method for obtaining the dynamic stiffness of the air spring bladder provided by the above methods. The method includes: obtaining the effective area radius of the air spring, the structural parameters of the ear segment of the bladder, and the material parameters of the bladder; the ear segment is the part of the bladder that is rolled up outside the piston of the air spring; determining the dynamic stiffness value of the ear segment due to rolling based on the effective area radius, the structural parameters of the ear segment, and the material parameters of the bladder; and determining the dynamic stiffness value of the bladder due to structural deformation based on the dynamic stiffness value of the ear segment due to rolling and a preset correction coefficient.

[0213] In another aspect, the present invention also provides a non-transitory computer-readable storage medium storing a computer program thereon. When executed by a processor, the computer program implements the method for obtaining the dynamic stiffness of the air spring bladder provided by the above methods. The method includes: obtaining the effective area radius of the air spring, the structural parameters of the ear segment of the bladder, and the material parameters of the bladder; the ear segment is the part of the bladder that is rolled up outside the piston of the air spring; determining the dynamic stiffness value of the ear segment due to rolling based on the effective area radius, the structural parameters of the ear segment, and the material parameters of the bladder; and determining the dynamic stiffness value of the bladder due to structural deformation based on the dynamic stiffness value of the ear segment due to rolling and a preset correction coefficient.

[0214] The device embodiments described above are merely illustrative. The units described 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 modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0215] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, 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 can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0216] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for obtaining the dynamic stiffness of the air spring's bladder, characterized in that, include: Obtain the effective area radius of the air spring, the structural parameters of the flap segment of the bladder, and the material parameters of the bladder; The drooping section is the part of the bladder skin that is rolled up outside the piston of the air spring; Based on the effective area radius, the structural parameters of the auricle segment, and the material parameters of the sac skin, the dynamic stiffness value of the auricle segment caused by curling is determined; Based on the dynamic stiffness value of the auricle segment due to curling, the dynamic stiffness value of the sac skin due to structural deformation is determined. The structural parameters of the auricle segment include: the angle of the side of the bladder skin that adheres to the piston surface relative to the vertical horizontal plane. and the radius of the loparm segment r ; The material parameters of the capsule skin include: the thickness of the capsule skin. t The thickness of the middle layer of the cystic lining t f The middle layer of the capsule skin is a composite layer composed of rubber and cord in the capsule skin; the elastic modulus of the cord is... Volume fractions and tilt angle The elastic modulus of the rubber ; The determination of the dynamic stiffness value of the auricle segment due to curling, based on the effective area radius, the structural parameters of the auricle segment, and the material parameters of the sac skin, includes: According to a first preset formula, based on the effective area radius, the structural parameters of the auricle segment, and the material parameters of the sac skin, the dynamic stiffness value of the auricle segment caused by curling is determined. The first preset formula includes: ； in, R eff The effective area radius of the air spring is given.

2. The method for obtaining the dynamic stiffness of the air spring's bladder according to claim 1, characterized in that, The determination of the dynamic stiffness value of the auricle segment due to curling, based on the effective area radius, the structural parameters of the auricle segment, and the material parameters of the sac skin, includes: Based on the effective area radius and the material parameters of the bladder, the bending stiffness of the bladder is determined; Based on the bending stiffness and the structural parameters of the drooping segment, the dynamic stiffness value of the drooping segment caused by curling is determined.

3. The method for obtaining the dynamic stiffness of the air spring's bladder according to claim 2, characterized in that, The first preset formula is constructed in the following way: Based on the strain relationship of off-axis tensile stress in composite material mechanics, the definition of bending stiffness is deformed to obtain an expression for the bending stiffness of the bladder skin expressed in terms of the effective area radius and the material parameters of the bladder skin. Obtain the inward bending moment of the drooping segment along the meridian direction of the air spring at a preset angle position; Based on the principle of minimum complementary energy, a first expression for the displacement of the drooping segment caused by the internal bending moment is derived. Based on the expression for bending stiffness and the first expression for displacement, a second expression for displacement is obtained, which is expressed in terms of the effective area radius, the structural parameters of the auricle segment, and the material parameters of the bladder skin. Based on the second expression for the displacement and the dynamic stiffness calculation formula, the first preset formula is obtained; The expression for the bending stiffness is: ； in, E s The equivalent Young's modulus of the sac skin; I Let be the moment of inertia of the cross section of the drooping segment along the bending direction; The first expression for the displacement is: ； in, u B The displacement is caused by the internal bending moment; P The vertical external force generated by the said sac skin; The formula for calculating the dynamic stiffness is: ； in, K For dynamic stiffness, u For displacement.

4. The method for obtaining the dynamic stiffness of the air spring's bladder according to claim 3, characterized in that, The determination of the dynamic stiffness value of the sac skin due to structural deformation based on the dynamic stiffness value of the auricle segment due to curling includes: Based on the dynamic stiffness value of the auricle segment due to curling and the preset correction coefficient, the dynamic stiffness value of the sac skin due to structural deformation is determined. The preset correction coefficient is determined based on the dynamic stiffness value of the auricle segment due to tension, the dynamic stiffness value of the auricle segment due to shear, and the dynamic stiffness value of the vertical segment of the sac skin due to tension. The vertical segment refers to the other parts of the sac skin besides the auricle segment.

5. The method for obtaining the dynamic stiffness of the air spring's bladder according to claim 4, characterized in that, The preset correction coefficient is determined based on the harmonic average relationship between the dynamic stiffness values ​​of the auricle segment due to curling, the dynamic stiffness values ​​of the auricle segment due to stretching, the dynamic stiffness values ​​of the auricle segment due to shearing, and the dynamic stiffness values ​​of the vertical segment of the sac skin due to stretching.

6. The method for obtaining the dynamic stiffness of the air spring's bladder according to claim 5, characterized in that, According to the second preset formula, the dynamic stiffness value of the auricle segment due to tension is determined based on the effective area radius, the structural parameters of the auricle segment, and the material parameters of the sac skin. According to the third preset formula, the dynamic stiffness value of the auricle segment caused by shear is determined based on the effective area radius, the structural parameters of the auricle segment, and the material parameters of the sac skin. According to the fourth preset formula, the dynamic stiffness value of the vertical segment due to tension is determined based on the effective area radius and the material parameters of the bladder. The second preset formula is: ； in, K t The value of dynamic stiffness of the drooping segment due to tension; u x The displacement of the drooping segment due to stretching; The third preset formula is: ； in, K s This is the dynamic stiffness value of the shear segment caused by shearing. u s The displacement of the drooping segment caused by shearing; G The shear modulus of the cystic membrane; The fourth preset formula is: ； in, K P This is the dynamic stiffness value of the vertical segment due to tension. u P The displacement of the vertical segment due to stretching; h The height of the vertical segment.

7. The method for obtaining the dynamic stiffness of the air spring's bladder according to claim 6, characterized in that, The second preset formula is constructed in the following way: Construct the tensile force equation of the ear segment along the meridian direction of the air spring at a preset angle position; Based on the principle of minimum residual energy, and the relationship between the tensile force and internal stress on the auricle segment and the cross-sectional area of ​​the bladder skin perpendicular to the meridian direction, combined with the tensile force equation, an expression for the displacement of the auricle segment due to tension is obtained, expressed in terms of the effective area radius, the structural parameters of the auricle segment, and the material parameters of the bladder skin. Based on the expression for the displacement caused by the stretching of the auricle segment, the second preset formula is obtained; The third preset formula is constructed in the following way: Construct the internal shear force equation of the drooping segment at a preset angle position along the meridian direction of the air spring; Based on the principle of minimum residual energy, and the relationship between the shear force and internal stress of the auricle segment and the cross-sectional area of ​​the bladder skin perpendicular to the meridian direction, combined with the internal shear force equation, an expression for the displacement of the auricle segment caused by shear is obtained, expressed in terms of the effective area radius, the structural parameters of the auricle segment, and the material parameters of the bladder skin. Based on the expression for the displacement of the auricle segment caused by shearing, the third preset formula is obtained; The fourth preset formula is constructed in the following way: Based on the principle of virtual work, and the relationship between the tensile force and internal stress on the vertical segment and the cross-sectional area of ​​the skin perpendicular to the meridian direction, an expression for the displacement of the vertical segment caused by the vertical external force is obtained, expressed in terms of the effective area radius and the material parameters of the skin. Based on the expression for the displacement of the vertical segment caused by the vertical external force, the fourth preset formula is obtained.

8. A system for obtaining the dynamic stiffness of the air spring's bladder, characterized in that, include: The acquisition module is used to acquire the effective area radius of the air spring, the structural parameters of the flap segment of the bladder, and the material parameters of the bladder. The drooping section is the part of the bladder skin that is rolled up outside the piston of the air spring; The first processing module is used to determine the dynamic stiffness value of the auricle segment caused by curling based on the effective area radius, the structural parameters of the auricle segment, and the material parameters of the sac skin. The second processing module is used to determine the dynamic stiffness value of the sac skin due to structural deformation based on the dynamic stiffness value generated by the curling of the auricle segment. The structural parameters of the auricle segment include: the angle of the side of the bladder skin that adheres to the piston surface relative to the vertical horizontal plane. and the radius of the said auricle segment r ; The material parameters of the capsule skin include: the thickness of the capsule skin. t The thickness of the middle layer of the cystic lining t f The middle layer of the capsule skin is a composite layer composed of rubber and cord in the capsule skin; the elastic modulus of the cord is... Volume fractions and tilt angle The elastic modulus of the rubber ; The first processing module is specifically used for: According to a first preset formula, based on the effective area radius, the structural parameters of the auricle segment, and the material parameters of the sac skin, the dynamic stiffness value of the auricle segment caused by curling is determined. The first preset formula includes: ； in, R eff The effective area radius of the air spring is given.

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