A method for calculating vertical isolation mechanical performance parameters of an air spring

Abstract

The present application relates to air spring shock isolation theory technical field, especially a kind of air spring vertical isolation mechanical performance parameter's calculation method.The method is by establishing the vertical stress model of air spring, the calculation method of the vertical bearing capacity of multi-parameter air spring and the vertical stiffness of multi-parameter air spring is obtained;Based on the biaxial stress state of air spring bag skin, the calculation formula of the related parameters in the vertical bearing capacity of multi-parameter air spring and the vertical stiffness of multi-parameter air spring;With the geometric deformation parameter of air spring into the calculation formula of related parameters for calculation;The related parameter value after calculation is substituted into the calculation method of air spring vertical bearing capacity, vertical stiffness and is calculated, obtains air spring vertical isolation mechanical performance parameter, and the calculation result is accurate, and the calculation efficiency is high.

Description

Technical Field

[0001] This invention relates to the field of air spring vibration isolation theory and technology, and in particular to a method for calculating the vertical vibration isolation mechanical performance parameters of an air spring. Background Technology

[0002] Base isolation involves placing a "soft" isolation layer between the lower foundation and the superstructure. This allows the natural vibration period of the structure to be extended through the large displacement of the isolation layer, reducing the input of seismic energy to the upper structure, decreasing the seismic response of the upper structure, and providing better safety assurance for the structure's seismic protection.

[0003] Currently, commonly used engineering seismic isolation bearings such as laminated rubber bearings, friction sliding bearings, and rolling friction sliding bearings have good horizontal seismic isolation effects, but they do not have vertical seismic isolation functions. Existing vertical seismic isolation devices mostly use disc springs and hydraulic devices connected in series, but due to the large stiffness of disc springs and the lag in the seismic isolation effect of hydraulic devices, the seismic isolation effect under vertical ground motion is not good.

[0004] Air springs possess excellent vibration isolation and noise reduction capabilities due to their small mass and low internal friction. Furthermore, their vertical stiffness and load-bearing capacity can be adjusted by regulating the internal pressure of the air chamber. Therefore, using air springs for vertical seismic isolation offers significant advantages. However, existing standards for air springs are lacking, and their vertical mechanical performance parameters still require experimental determination. This necessitates incorporating extensive test results during selection, hindering their practical application in engineering projects. Therefore, a theoretical calculation method for the vertical seismic isolation mechanical performance parameters of air springs is needed to facilitate their selection during the engineering design phase. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to propose a method for calculating the vertical seismic isolation mechanical performance parameters of an air spring. This method obtains relatively accurate vertical seismic isolation mechanical performance parameters by analyzing the stress and deformation characteristics of the air spring under vertical load.

[0006] The present invention adopts the following technical solution:

[0007] A method for calculating the vertical seismic isolation mechanical performance parameters of an air spring, the calculation steps are as follows:

[0008] Step 1: By establishing a vertical force model of the air spring, the calculation methods for the vertical bearing capacity and vertical stiffness of the air spring with multiple parameters are obtained.

[0009] Step 2: Based on the bidirectional stress state of the air spring bladder, establish calculation formulas for the relevant parameters in the multi-parameter vertical bearing capacity and multi-parameter vertical stiffness of the air spring in Step 1;

[0010] Step 3: Substitute the geometric deformation parameters of the air spring into the calculation formulas for the multi-parameter vertical bearing capacity and vertical stiffness of the air spring established in Step 2 to perform the calculation.

[0011] Step 4: Substitute the calculated relevant parameter values ​​into the calculation methods for the vertical bearing capacity and vertical stiffness of the air spring in Step 1 to obtain the vertical seismic isolation mechanical performance parameters of the air spring.

[0012] The method for calculating the vertical seismic isolation mechanical performance parameters of an air spring according to the present invention includes the following expression for the vertical bearing capacity of the multi-parameter air spring in step 1:

[0013] F V =pA eff

[0014] The internal gas pressure of the air spring is p, A eff This refers to the effective load-bearing area of ​​the air spring.

[0015] The vertical stiffness of the multi-parameter air spring is:

[0016]

[0017] V is the gas volume inside the air spring under operating conditions, p0 is the gas pressure under standard conditions, and V0 is the gas volume inside the air spring under standard conditions. a Where is atmospheric pressure, and n is the gas multivariate index.

[0018] The method for calculating the vertical vibration isolation mechanical performance parameters of an air spring according to the present invention, wherein the vertical bearing capacity and vertical stiffness of the air spring in step 2 are related to the air pressure, gas multi-element index, volume of the air spring, and effective bearing area.

[0019] The air pressure, gas multivariate index, and air spring volume are all known quantities. When calculating the effective bearing area of ​​the air spring, the air spring is cut along the section with the largest diameter. The formula for calculating the effective bearing area is as follows:

[0020]

[0021] s is the thickness of the air spring bladder, σ j Let be the stress along the meridian of the air spring's cross-section, R be the maximum outer diameter of the air spring, and p be the internal gas pressure of the air spring.

[0022] The calculation method for the vertical vibration isolation mechanical performance parameters of an air spring described in this invention uses the formula for calculating the effective bearing area of ​​the air spring device, which includes the known maximum outer diameter of the air spring, the thickness of the bladder, and the gas pressure.

[0023] For the unknown value σ j Calculation; Take a small element from the maximum diameter of the air spring bladder, and from the radial force equilibrium of the small element, we can obtain:

[0024]

[0025] r is the radius of the air spring arc, E j With E w These are the warp and weft elastic moduli of the air spring bladder, μ, respectively. j With μ w These are the Poisson's ratios in the longitudinal and latitudinal directions of the air spring bladder, respectively, k = R / r, ω = |Δr / ΔR|.

[0026] The present invention discloses a method for calculating the vertical vibration isolation mechanical performance parameters of an air spring.

[0027] The effective bearing area of ​​the air spring is obtained from the stress along the meridian of the spring's cross-section, and the calculation formula is as follows:

[0028]

[0029] The method for calculating the vertical vibration isolation mechanical performance parameters of an air spring according to the present invention includes the following steps for calculating the geometric deformation parameters of the air spring:

[0030] The calculation of the effective bearing area of ​​an air spring requires obtaining the maximum outer diameter R and the radius r of the arc during the deformation process of the air spring;

[0031] During normal use, in the elastic phase, the geometric relationships satisfied by the air spring bladder arc length, air spring maximum outer diameter R, air spring working height h, end sealing plate diameter a, arc angle θ, and air spring arc radius r are as follows:

[0032] l=2θr

[0033]

[0034]

[0035] The present invention discloses a method for calculating the vertical vibration isolation mechanical performance parameters of an air spring, wherein the effective bearing area A of the air spring device is... eff The vertical load-bearing capacity and vertical stiffness of the air spring can be calculated as follows:

[0036]

[0037]

[0038] α is the vertical shape factor, and its calculation formula is:

[0039] .

[0040] Beneficial effects

[0041] This invention addresses the practical use of bladder-type air springs, providing calculation models for their vertical bearing capacity and vertical stiffness based on their stress characteristics and relevant theories of air thermodynamics, thus laying the foundation for establishing a method for calculating their mechanical performance parameters.

[0042] The method for calculating the vertical seismic isolation mechanical performance parameters of air springs proposed in this invention is based on the calculation model of the vertical bearing capacity and vertical stiffness of air springs. By performing force analysis on its micro-elements and coordinating its deformation characteristics, the calculation formulas of relevant parameters in its calculation model are obtained, resulting in more accurate calculation results and higher calculation efficiency.

[0043] The method for calculating the vertical seismic isolation mechanical performance parameters of air springs proposed in this invention can also obtain the vertical seismic isolation mechanical performance parameters of air springs of different models and under different loads by changing the air springs and load conditions. Attached Figure Description

[0044] Figure 1 This is a schematic diagram of the air spring under stress, illustrating the calculation method for the vertical vibration isolation mechanical performance parameters of the air spring according to the present invention.

[0045] Figure 2 This is a schematic diagram of the air spring cross-section under stress, illustrating the calculation method for the vertical vibration isolation mechanical performance parameters of the air spring according to the present invention.

[0046] Figure 3 The method for calculating the vertical vibration isolation mechanical performance parameters of the air spring in this invention includes a micro-element force analysis of the air spring.

[0047] Figure 4 This is a schematic diagram of the air spring structure used in the calculation method of the vertical vibration isolation mechanical performance parameters of the air spring of the present invention.

[0048] Figure 5 The results are based on the vertical isolation theoretical calculations of the calculation method for the vertical isolation mechanical performance parameters of the air spring of this invention. Detailed Implementation

[0049] To make the objectives and technical solutions of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present 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 the present invention. All other embodiments obtained by those skilled in the art based on the described embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0050] The method for calculating the vertical vibration isolation mechanical performance parameters of the air spring of the present invention includes the following specific steps:

[0051] Step 1: By establishing a vertical force model of the air spring, we obtain the calculation methods for the vertical bearing capacity and vertical stiffness of the air spring with multiple parameters.

[0052] Figure 1 The diagram shows the forces acting on an air spring device, with internal gas pressure p and vertical bearing capacity F. V From the equilibrium of forces, we can obtain...

[0053] F V =pA eff (1)

[0054] In the formula, A eff This refers to the effective load-bearing area of ​​the air spring.

[0055] According to the ideal gas equation, assuming the gas inside the air spring is an ideal gas and its temperature is constant during loading, for the gas with pressure p in the air spring device under working conditions, we can obtain...

[0056] (2)

[0057] In the formula, V is the gas volume inside the air spring device under working conditions, p0 is the gas pressure under standard conditions, V0 is the gas volume inside the air spring device under standard conditions, and p a Where is atmospheric pressure, and n is the gas multivariate index.

[0058] From equation (2), the working pressure in the air spring device can be obtained as follows:

[0059] (3)

[0060] Assuming a vertical load F V If the air spring device is made to produce a vertical displacement dz, then the vertical stiffness can be expressed as:

[0061] (4)

[0062] Differentiating equation (3) with respect to z yields

[0063] (5)

[0064] Considering dV / dz = -Aeff, equation (5) can be simplified to

[0065] (6)

[0066] Substituting equation (6) into equation (4) yields

[0067] (7)

[0068] Step 2: Perform stress analysis on the micro-element of the air spring bladder based on the bidirectional stress state, and establish calculation formulas for relevant parameters in the multi-parameter vertical bearing capacity and multi-parameter vertical stiffness of the air spring.

[0069] Equation (7) shows that the vertical stiffness of the air spring device is related to the air pressure inside the air spring device, the change in the effective bearing area, the gas multivariate index, the volume of the air spring, and the effective bearing area. When calculating the effective bearing area of ​​the air spring device, the air spring can be cut along the section with the largest diameter, such as... Figure 2 As shown.

[0070] According to the principle of force balance, the load-bearing capacity of the air spring device is the air pressure at the maximum outer diameter minus the tension of the air spring bladder, which can be expressed as:

[0071] F V =pπR 2 -2πRsσ j (8)

[0072] In the formula, s is the thickness of the air spring bladder, and σ is the thickness of the air spring bladder. j R represents the stress along the meridian of the air spring's cross-section, and R is the maximum outer diameter of the air spring.

[0073] Dividing both sides of equation (8) by the gas pressure p, we get...

[0074] (9)

[0075] In the formula for calculating the effective bearing area of ​​the air spring device given in equation (9), the maximum outer diameter of the air spring, the thickness of the bladder, and the gas pressure are known. Only σ j Unknown. To further calculate σ j Take a tiny element from the maximum diameter of the air spring bladder, such as... Figure 3 As shown. dΦ and dφ are the latitudinal and longitudinal arc angles of the capsule element, respectively, and r is the radius of the air spring arc. Therefore, the latitudinal and longitudinal lengths of the element are RdΦ and Rdφ, respectively. According to the basic assumptions of thin film theory, the air spring capsule cannot transmit bending moment and out-of-plane shear force; therefore, it has only two principal stresses: dF j The resulting meridional stress σ j and by dF w The generated latitudinal stress σ w dF j and dF w The radial component dF j,r and dF w,r They are respectively

[0076] (10)

[0077] (11)

[0078] Since the radial and lateral arc angles corresponding to the infinitesimal element are very small, equations (10) and (11) can be simplified to:

[0079] (12)

[0080] (13)

[0081] Due to the presence of air pressure, a radial force dF exists on the inner surface of the micro-element. r for

[0082] dF r =pRrdΦdφ (14)

[0083] When the radially infinitesimal element is in equilibrium, we can obtain...

[0084] dF r =2dF j,r +2dF w,r (15)

[0085] Substituting equations (12), (13), and (14) into equation (15) yields...

[0086] (16)

[0087] Equation (16) can be simplified to

[0088] pRr=σ j Rs+σ w rs (17)

[0089] Within a limited vertical deformation range, the stress and strain of the air spring can be considered to obey Hooke's law. Therefore, the strain ε in the meridional and zonal directions... j , ε w The calculation formula is

[0090] (18)

[0091] (19)

[0092] In the formula, E j With E w These are the warp and weft elastic moduli of the air spring bladder, μ, respectively. j With μ w These are the Poisson's ratios in the longitudinal and latitudinal directions of the air spring bladder, respectively.

[0093] From equations (18) and (19), we can obtain

[0094] (20)

[0095] (twenty one)

[0096] Substituting equation (21) into equation (17) yields

[0097] (twenty two)

[0098] In the formula, k = R / r.

[0099] Step 3: Solve the relevant parameters in the calculation model of vertical bearing capacity and vertical stiffness of air spring based on the vertical deformation characteristics of air spring, and then obtain the vertical bearing capacity and vertical stiffness of air spring, thus obtaining the vertical seismic isolation mechanical performance parameters of air spring.

[0100] Substituting equation (22) into equation (9) yields

[0101] (twenty three)

[0102] During normal use, the air spring bladder is in its elastic stage. During deformation, the arc length l of the air spring bladder can be calculated using the following formula.

[0103] l=2θr (24)

[0104] The maximum outer diameter R of the air spring device, the working height h of the air spring, the diameter a of the end sealing plate, the arc angle θ, and the arc radius r satisfy the following geometric relationships.

[0105] (25)

[0106] (26)

[0107] When a, l, h, and s are known, numerical solutions for θ, r, and R can be obtained using equations (24), (25), and (26), and then the effective bearing area A of the air spring device can be calculated. eff Substituting equation (23) into equation (1), we can obtain the vertical bearing capacity of the air spring device as follows:

[0108] (27)

[0109] Due to dA eff / dz=αA eff Therefore, the vertical stiffness of the air spring device is

[0110] (28)

[0111] In the formula, α is the vertical shape coefficient, and its calculation formula is as follows:

[0112] (29)

[0113] In the formula, R eff The effective radius is the area corresponding to the effective area of ​​the air spring bag, and its calculation formula is: .

[0114] In summary, the vertical load-displacement curve and vertical stiffness of the three-dimensional seismic isolation bearing can be calculated from equations (27) and (28).

[0115] Example 1:

[0116] A schematic diagram of the air spring structure is shown below. Figure 4 As shown, the dimensional parameters are listed in Table 1.

[0117] Table 1 Parameters of Three-Dimensional Seismic Isolation Bearings

[0118]

[0119] Figure 5 The figure shows the load-displacement curve obtained by the calculation method of the vertical seismic isolation mechanical performance parameters of the air spring. It can be found that the vertical load-displacement curve of the three-dimensional seismic isolation bearing exhibits nonlinear characteristics. When compressed downward from the initial working height, the vertical stiffness gradually increases, and when stretched upward, the vertical stiffness gradually decreases.

[0120] This invention addresses the practical application of bladder-type air springs. Based on their stress characteristics and relevant theories of aerodynamics, it provides calculation models for their vertical bearing capacity and vertical stiffness, laying the foundation for establishing methods to calculate their mechanical performance parameters. Based on these calculation models, the invention analyzes the stress on the air spring's micro-elements and coordinates their deformation characteristics to obtain calculation formulas for relevant parameters within the model, resulting in more accurate and efficient calculations. Furthermore, this invention can also obtain vertical vibration isolation mechanical performance parameters for air springs of different models and under different loads by modifying the air spring and load conditions.

[0121] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for calculating the vertical vibration isolation mechanical performance parameters of an air spring, characterized in that: The calculation steps are as follows: Step 1: By establishing a vertical force model of the air spring, the calculation methods for the vertical bearing capacity and vertical stiffness of the air spring with multiple parameters are obtained. Step 2: Based on the bidirectional stress state of the air spring bladder, establish calculation formulas for the relevant parameters in the multi-parameter vertical bearing capacity and multi-parameter vertical stiffness of the air spring in Step 1; The vertical load-bearing capacity and vertical stiffness of the air spring are both related to the air pressure inside the air spring, the gas multi-element index, the volume of the air spring, and the effective load-bearing area. The air pressure, gas multivariate index, and air spring volume are all known quantities. When calculating the effective bearing area of ​​the air spring, the air spring is cut along the section with the largest diameter. The formula for calculating the effective bearing area is as follows: ， F V σ represents the vertical load-bearing capacity of the air spring, s represents the thickness of the air spring bladder, and σ represents the vertical load-bearing capacity of the air spring. j Let R be the stress along the meridian of the air spring cross section, R be the maximum outer diameter of the air spring, and p be the internal gas pressure of the air spring. The formula for calculating the effective load-bearing area of ​​the air spring device is known in terms of the maximum outer diameter of the air spring, the thickness of the bladder, and the gas pressure. For the unknown value σ j Calculation; Take a small element from the maximum diameter of the air spring bladder, and from the radial force equilibrium of the small element, we can obtain: ， r is the radius of the air spring arc, E j With E w These are the warp and weft elastic moduli of the air spring bladder, μ, respectively. j With μ w The Poisson's ratios for the air spring bladder in the longitudinal and latitudinal directions are respectively, k = R / r, ω = |Δr / ΔR|; The effective load-bearing area of ​​an air spring is obtained from the stress along the meridian of the spring's cross-section, and the calculation formula is as follows: ； Step 3: Substitute the geometric deformation parameters of the air spring into the calculation formulas for the multi-parameter vertical bearing capacity and vertical stiffness of the air spring established in Step 2 to perform the calculation. Step 4: Substitute the calculated relevant parameter values ​​into the calculation methods for the vertical bearing capacity and vertical stiffness of the air spring in Step 1 to obtain the vertical seismic isolation mechanical performance parameters of the air spring.

2. The method for calculating the vertical vibration isolation mechanical performance parameters of an air spring according to claim 1, characterized in that: The vertical bearing capacity of the multi-parameter air spring in step 1 is expressed by the following expression: F V =pA eff The internal gas pressure of the air spring is p, A eff This refers to the effective load-bearing area of ​​the air spring. The vertical stiffness of the multi-parameter air spring is: V is the gas volume inside the air spring under operating conditions, p0 is the gas pressure under standard conditions, and V0 is the gas volume inside the air spring under standard conditions. a Where is atmospheric pressure, and n is the gas multivariate index.

3. The method for calculating the vertical vibration isolation mechanical performance parameters of an air spring according to claim 1, characterized in that: The geometric deformation parameters of the air spring in step 3 are as follows: During normal use, in the elastic phase, the geometric relationships satisfied by the air spring bladder arc length l, the maximum outer diameter R of the air spring, the working height h of the air spring, the diameter a of the end sealing plate, the arc angle θ, and the arc radius r of the air spring are as follows: l=2θr ， ， l is the arc length of the air spring's bladder at its initial working height.

4. The method for calculating the vertical vibration isolation mechanical performance parameters of an air spring according to claim 1, characterized in that: The effective load-bearing area A of the air spring device eff The vertical load-bearing capacity and vertical stiffness of the air spring can be calculated as follows: ， ， α is the vertical shape factor, and its calculation formula is: ， R eff Let θ be the effective radius corresponding to the effective area of ​​the air spring capsule, and θ be the arc angle of the air spring arc radius r.

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