Variable cross-section leaf spring design method

Abstract

This invention discloses a design method for variable cross-section leaf springs, belonging to the technical field of leaf springs. It solves the defect in existing technologies where the stiffness and stress of traditional leaf springs differ significantly from the actual manufactured product. The method includes the following steps: S1: Dividing the leaf spring structure into a straight section L0, a root transition section L1-L0, a constant stress section L2-L1, an extension section L3-L2, an end transition section L4-L3, and an end constant thickness section L-L4; S2: Obtaining basic parameters; S3: Calculating the fillet radius r. x and moment of inertia I x S4: Obtain the calculation formula for the thickness at each point, and calculate the thickness of the raw material and the thickness of the root transition section L1-L0; S5: Obtain the calculation formulas for the thicknesses at each point of L2, L3, L4 and the end thickness h5, and the thicknesses of the extension section L3-L2 and the end transition section L4-L3; S6: Obtain the calculation formula for the thickness at each position of the leaf spring; S7: Calculate the stiffness of the leaf spring. This invention is mainly used for designing leaf springs.

Description

Technical Field

[0001] This invention belongs to the field of leaf spring technology, and more specifically, relates to a design method for variable cross-section leaf springs. Background Technology

[0002] As users demand higher levels of comfort from commercial vehicle manufacturers, OEMs are placing increasingly higher demands on the precision of leaf spring stress and stiffness. Traditional design methods, which inherently contain errors that cannot be eliminated, are no longer sufficient to meet the increasingly stringent requirements of OEMs.

[0003] Currently, in the industry, the design process for variable cross-section steel leaf springs using constant stress involves keeping the width 'b' constant while gradually changing the thickness value according to the constant stress requirements. For mathematical simplicity, the leaf spring cross-section is simplified to a pure rectangle, such as... Figure 6 As shown. For a leaf spring designed in this way, the stress σ at a certain cross section X of the constant stress segment is... x Thickness h x Width b, effective distance L x The mathematical relationship between σ and its applied load P is σ x =6PL x / bh x 2 This relationship perfectly matches the mathematical description of a parabola, hence the industry also refers to variable cross-section leaf springs as parabolic leaf springs. However, in reality, the cross-section of a leaf spring is not... Figure 6 The rectangle shown is not a pure rectangle, but rather divided into different types based on the raw materials, such as... Figure 2 and Figure 3 The two cross sections are shown. Due to neglecting the influence of fillet radius, the stiffness and stress of the leaf springs designed using the original design method differ significantly from those of the products actually manufactured. It is necessary to determine a correction coefficient through repeated experiments to modify the design scheme. This process relies heavily on design and production experience, resulting in different design schemes from different designers and manufacturers. Product consistency is difficult to guarantee, and it is also difficult to meet the current requirements of OEMs for the stiffness accuracy of leaf springs. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to overcome the shortcomings of the prior art and provide a design method for variable cross-section steel leaf springs. The variable cross-section steel leaf springs designed using this method have extremely small deviations in stress and stiffness values ​​from the actual product, and their accuracy is improved by more than 10%, thus ensuring the high accuracy requirements of the OEM for steel leaf springs to the greatest extent.

[0005] To achieve the above objectives, the present invention employs the following technical solution:

[0006] A method for designing variable cross-section steel leaf springs includes the following steps:

[0007] S1: The structure of the leaf spring is divided into straight section L0, root transition section L1-L0, equal stress section L2-L1, extension section L3-L2, end transition section L4-L3, and end equal thickness section L-L4.

[0008] S2: Obtain basic parameters, including load P, leaf spring width b, effective length L, and straight section L0. Determine the stress σ of the constant stress section based on the leaf spring material and application environment. x =σ;

[0009] S3: Calculate the fillet radius r x and moment of inertia I x ;

[0010] S4: Obtain the calculation formula for the thickness of each point, and calculate the thickness of the raw material (i.e., the thickness of the straight section L0) and the thickness of the root transition section L1-L0.

[0011] S5: Obtain the thicknesses of L2, L3, L4 and the end thickness h5, and the calculation formulas for the thicknesses of each point in the extension section L3-L2 and the end transition section L4-L3;

[0012] S6: Calculation formula for obtaining the thickness of the leaf spring at various locations;

[0013] S7: Calculate the stiffness of the leaf spring.

[0014] Preferably, when the leaf spring cross-section is an oblong hole shape, the fillet radius r x The calculation formula is:

[0015] (1)

[0016] Moment of inertia I x The calculation formula is:

[0017] (2)

[0018] Where, r x For the fillet of the cross section, h x The thickness is the cross-sectional thickness.

[0019] Preferably, according to the bending stress formula Therefore, the formula for calculating the thickness at each point is:

[0020] (3)

[0021] Wherein, formula (3) is about h x The cubic equation has discontinuous solutions, therefore L x Calculate the thickness sequentially at intervals within the range of 0-L, and the set of solutions represents the precise thickness at each point; let L... xSubstituting =0 into formula (3) to solve, the result obtained is rounded up according to the raw material specifications to obtain the raw material thickness h0;

[0022] Based on the capacity of the leaf spring production equipment, determine L1, and substitute it into formula (3) to obtain the thickness h1 at this point. The formula for calculating the thickness of each point in the root transition section L1-L0 is as follows:

[0023] (L0≤L) x ≤L1)(4)

[0024] Among them, L x By calculating sequentially at certain intervals within the range [L0, L1], the set of points in the L1-L0 segment can be obtained.

[0025] Preferably, based on the capacity of the leaf spring production equipment, L2, L3, L4 and the end thickness h5 are obtained sequentially. The calculation formulas for the thicknesses of each point in the extension section L3-L2 and the end transition section L4-L3 are as follows:

[0026] (5)

[0027] (6)

[0028] Preferably, the formula for calculating the thickness of the leaf spring at various locations is as follows:

[0029] (7)

[0030] The precise thickness of the variable cross-section steel leaf spring at each position can be obtained by calculating sequentially at certain intervals according to formula (7).

[0031] According to Mohr's law in mechanics of materials, the deformation of each segment under load P can be calculated using the following formula:

[0032] (8)

[0033] Total deformation The calculation formula is:

[0034] (9)

[0035] Total stiffness of leaf springs K The calculation formula is:

[0036] (10)

[0037] Where n is the number of intervals in the calculation of the thickness of the equal stress section, and m is the number of leaf springs.

[0038] Preferably, when the cross-section of the leaf spring is a rounded rectangle, the radius r of the leaf spring is...x The calculation formula is:

[0039] (11)

[0040] Moment of inertia I x The calculation formula is:

[0041] (12)

[0042] Where k is the correction coefficient obtained from actual measurement, r x For the fillet of the cross section, h x r0 is the cross-sectional thickness, r0 is the fillet radius of the raw material cross-section, and h0 is the cross-sectional thickness of the raw material.

[0043] Preferably, according to the formula Roughly estimate the thickness of the raw material, round the result upwards, and determine the fillet radius r0 based on the raw material specifications on the market.

[0044] According to the bending stress formula Therefore, the formula for calculating the thickness of each point in the equal stress segment L2-L1 is:

[0045] (13)

[0046] Based on the capacity of the leaf spring production equipment, determine L1, and substitute it into formula (12) to obtain the thickness h1 at this point. The formula for calculating the thickness of each point within the root transition section L1-L0 is as follows:

[0047] (L0≤L) x ≤L1)(14)

[0048] Among them, L x By calculating the points in the L0-L1 range at certain intervals, the set of points in this segment can be obtained.

[0049] Preferably, based on the capacity of the leaf spring production equipment, L2, L3, L4 and the end thickness h5 are obtained sequentially. The calculation formulas for the thicknesses of each point in the extension section L3-L2 and the end transition section L4-L3 are as follows:

[0050] (15)

[0051] (16)

[0052] Preferably, the formula for calculating the thickness of the leaf spring at various locations is as follows:

[0053] (17)

[0054] The precise thickness of the variable cross-section steel leaf spring at each position can be obtained by calculating sequentially at certain intervals according to formula (17).

[0055] Preferably, according to Mohr's law in mechanics of materials, the deformation of each segment under load P can be calculated, and the calculation formula is as follows:

[0056]

[0057] Total deformation The calculation formula is:

[0058] (18)

[0059] Total stiffness of leaf springs K The calculation formula is:

[0060] (19)

[0061] Where n is the number of intervals in the calculation of the thickness of the equal stress section, and m is the number of leaf springs.

[0062] Compared with the prior art, the beneficial effects of the present invention are:

[0063] 1. This invention proposes two more precise design methods for variable cross-section leaf springs, one with an oblong hole shape and the other with rounded corners, for two different types of leaf spring raw materials. These methods fully consider the variation in thickness during the constant stress section, and the effect of the rounded corner radius (r) on the design. x The gradual effect of stress σ x Thickness h x Width b, effective distance L x The fillet radius r is introduced into the calculation formula of the load P. x This makes the calculation formula more accurate, and the stiffness calculation formula of the steel leaf spring designed in this way is also more accurate than the existing design methods.

[0064] 2. The design method for variable cross-section steel leaf springs in this invention is more in line with actual production. The stress and stiffness values ​​of the variable cross-section steel leaf springs designed using this method deviate very little from those of the actual products, improving the accuracy by more than 10%, thus maximizing the guarantee of the high accuracy requirements of the OEM for steel leaf springs.

[0065] 3. The variable cross-section steel leaf spring design method proposed in this patent is applicable to all variable cross-section steel leaf springs. Precise design can be completed simply by adjusting the corresponding parameters according to the drawings. Attached Figure Description

[0066] Figure 1 This is a schematic diagram of the segmented structure of the present invention;

[0067] Figure 2 This is a schematic diagram of the structure of the steel leaf spring in this invention when the cross-section is in the shape of an oblong hole;

[0068] Figure 3 This is a schematic diagram of the structure of the leaf spring in this invention when the cross-section is a rounded rectangle;

[0069] Figure 4 This is a schematic diagram showing the structural parameters of the front leaf spring section in this invention;

[0070] Figure 5 This is a schematic diagram showing the structural parameters of the rear section of the leaf spring in this invention;

[0071] Figure 6 This is a schematic diagram of a steel leaf spring with a rectangular cross-section. Detailed Implementation

[0072] The present invention will be further described below through specific embodiments and in conjunction with the accompanying drawings.

[0073] Example 1:

[0074] A method for designing variable cross-section steel leaf springs includes the following steps:

[0075] S1: In the design of leaf spring thickness, the loading requirements and production process of the leaf spring are considered, such as... Figure 1 As shown, the structure of the leaf spring is divided into a straight section L0, a root transition section L1-L0, a constant stress section L2-L1, an extension section L3-L2, an end transition section L4-L3, and an end constant thickness section L-L4. The mathematical description of the thickness of each section is different.

[0076] S2: Obtain basic parameters, including load P, leaf spring width b, effective length L, and straight section L0. Determine the stress σ of the constant stress section based on the leaf spring material and application environment. x =σ;

[0077] S3: Calculate the fillet radius r x and moment of inertia I x ;

[0078] S4: Obtain the calculation formula for the thickness of each point, and calculate the thickness of the raw material (i.e., the thickness of the straight section L0) and the thickness of the root transition section L1-L0.

[0079] S5: Obtain the thicknesses of L2, L3, L4 and the end thickness h5, and the calculation formulas for the thicknesses of each point in the extension section L3-L2 and the end transition section L4-L3;

[0080] S6: Calculation formula for obtaining the thickness of the leaf spring at various locations;

[0081] S7: Calculate the stiffness of the leaf spring.

[0082] Example 2:

[0083] A design method for variable cross-section steel leaf springs, where the leaf spring cross-section is an oblong hole shape, such as... Figure 2 As shown, in step S3, the fillet r x The calculation formula is:

[0084] (1)

[0085] In step S3, the moment of inertia I x The calculation formula is:

[0086] (2)

[0087] Where, r x For the fillet of the cross section, h x The thickness is the cross-sectional thickness.

[0088] According to the bending stress formula

[0089] Therefore, the formula for calculating the thickness at each point in step S4 is:

[0090] (3)

[0091] Wherein, formula (3) is about h x The cubic equation has discontinuous solutions, therefore L x Calculate the thickness sequentially at intervals within the range of 0-L, and the set of solutions represents the precise thickness at each point; let L... x Substituting =0 into formula (3) to solve, the result obtained is rounded up according to the raw material specifications to obtain the raw material thickness h0;

[0092] Based on the capacity of the leaf spring production equipment, determine L1, and substitute it into formula (3) to obtain the thickness h1 at this point. The formula for calculating the thickness of each point in the root transition section L1-L0 is as follows:

[0093] (L0≤L) x ≤L1)(4)

[0094] Among them, L x By calculating sequentially at certain intervals within the range [L0, L1], the set of points in the L1-L0 segment can be obtained.

[0095] Based on the capacity of the leaf spring production equipment, in step S5, L2, L3, L4, and the end thickness h5 are obtained sequentially. The calculation formulas for the thicknesses of each point in the extension section L3-L2 and the end transition section L4-L3 are as follows:

[0096] (5)

[0097] (6)

[0098] In step S6, the formula for calculating the thickness of the leaf spring at various locations is as follows:

[0099] (7)

[0100] The precise thickness of the variable cross-section steel leaf spring at each position can be obtained by calculating sequentially at certain intervals according to formula (7).

[0101] In step S7, according to Mohr's law of materials, the deformation of each segment under load P can be calculated, and the calculation formula is as follows:

[0102] (8)

[0103] Total deformation The calculation formula is:

[0104] (9)

[0105] Total stiffness of leaf springs K The calculation formula is:

[0106] (10)

[0107] Where n is the number of intervals in the calculation of the thickness of the equal stress section, and m is the number of leaf springs. The other parts are the same as in Example 1.

[0108] Example 3:

[0109] A design method for variable cross-section leaf springs, where the leaf spring cross-section is a rounded rectangle, such as... Figure 3 As shown, in step S3, the fillet radius r of the leaf spring is... x The calculation formula is:

[0110] (11)

[0111] Moment of inertia I x The calculation formula is:

[0112] (12)

[0113] Where k is the correction coefficient obtained from actual measurement, r x For the fillet of the cross section, h x r0 is the cross-sectional thickness, r0 is the fillet radius of the raw material cross-section, and h0 is the cross-sectional thickness of the raw material.

[0114] According to the formula Roughly estimate the thickness of the raw material, round the result upwards, and determine the fillet radius r0 based on the raw material specifications on the market.

[0115] In step S4, according to the bending stress formula Therefore, the formula for calculating the thickness of each point in the equal stress segment L2-L1 is:

[0116] (13)

[0117] Based on the capacity of the leaf spring production equipment, determine L1, and substitute it into formula (12) to obtain the thickness h1 at this point. The formula for calculating the thickness of each point within the root transition section L1-L0 is as follows:

[0118] (L0≤L) x ≤L1)(14)

[0119] Among them, L x By calculating the points in the L0-L1 range at certain intervals, the set of points in this segment can be obtained.

[0120] Based on the capacity of the leaf spring production equipment, in step S5, L2, L3, L4, and the end thickness h5 are obtained sequentially. The calculation formulas for the thicknesses of each point in the extension section L3-L2 and the end transition section L4-L3 are as follows:

[0121] (15)

[0122] (16)

[0123] In step S6, the formula for calculating the thickness of the leaf spring at various locations is as follows:

[0124] (17)

[0125] The precise thickness of the variable cross-section steel leaf spring at each position can be obtained by calculating sequentially at certain intervals according to formula (17).

[0126] In step S7, according to Mohr's law of materials, the deformation of each segment under load P can be calculated, and the calculation formula is as follows:

[0127]

[0128] Total deformation The calculation formula is:

[0129] (18)

[0130] Total stiffness of leaf springs K The calculation formula is:

[0131] (19)

[0132] Where n is the number of intervals in the calculation of the thickness of the equal stress section, and m is the number of leaf springs. The other parts are the same as in Example 1.

[0133] Example 4:

[0134] like Figure 4 The diagram shows the parameters of a certain front leaf spring. According to the drawing requirements, the following steps are performed according to the design method of Example 2:

[0135] In step S2, the basic parameters are obtained:

[0136] Load: P = 7962.5 N

[0137] Width: b=90mm

[0138] Straight section: L0 = 90mm

[0139] Effective length: L=925mm

[0140] Stress in the constant stress section: σ = 680 MPa.

[0141] Assuming the leaf spring raw material thickness is no more than 30mm, using a circular arc material with a waist-shaped hole cross-section, and designing according to Example 2, with a fillet radius r... x Moment of inertia I x The calculation formulas for the thickness of each point in the equal stress section L2-L1 satisfy formulas (1), (2) and (3) in Example 2;

[0142] In step S4, L x Substituting =0 into formula (3), we obtain the raw material thickness as 28.6mm. After rounding up, we get h0=29mm, which means the raw material thickness is 29mm.

[0143] In step S4, based on the capacity of the leaf spring production equipment, L1=130 is determined, and it is substituted into formula (3) to obtain the thickness h1=26.58mm. The thickness of each point in the root transition section L1-L0 is shown in Table 1:

[0144] Table 1

[0145]

[0146] In steps S5 and S6, based on the capacity of the leaf spring production equipment, L2=690mm, L3=720mm, L4=800mm and end thickness h5=20mm are determined sequentially. Substituting these parameters into formulas (5), (6), and (7), the thicknesses (partial) of the variable cross-section leaf springs are obtained as shown in Table 2.

[0147] Table 2

[0148]

[0149] Note: After the second L2, the thickness is 14mm.

[0150] In step S7, calculations are performed according to formulas (8), (9), and (10).

[0151] First piece of overall deformation:

[0152] The stiffness of the first piece is:

[0153] The second piece undergoes total deformation:

[0154] The stiffness of the second piece is:

[0155] Therefore, the total stiffness of this variable cross-section steel leaf spring is 266 N / mm.

[0156] If the spring stiffness does not meet the requirements specified in the drawings, change the stress and repeat steps S2-S4.

[0157] Example 5:

[0158] like Figure 5 The diagram shows the parameters of a certain rear leaf spring. According to the drawing requirements, the following steps are performed according to the design method of Example 3:

[0159] In step S2, the basic parameters are obtained:

[0160] Load: P = 12576.67 N

[0161] Width: b=90mm

[0162] Straight section: L0 = 140mm

[0163] Effective length: L=700mm

[0164] Stress in the constant stress section: σ = 500 MPa

[0165] Using a rectangular material with rounded corners, the design follows Example 3, with the corner radius r... x Moment of inertia I x The calculation formulas for the thickness of each point in the equal stress section L2-L1 satisfy formulas (11), (12) and (13) in Example 3.

[0166] In step S4, by formula The rough estimate of the raw material thickness is 34.26mm. Based on the raw material specifications, the result is rounded up to 35mm, that is, the raw material thickness is 35mm, and the fillet radius r0 is set to 12mm.

[0167] In step S4, based on the capacity of the leaf spring production equipment, L1=230 is determined, and it is substituted into formula (12) to obtain the thickness h1=28.34mm. The thickness of each point in the root transition section L1-L0 is shown in Table 3:

[0168] Table 3

[0169]

[0170] In steps S5 and S6, based on the capacity of the leaf spring production equipment, L2=549mm, L3=L4=L =700mm and end thickness h5=16mm are determined sequentially. Substituting these parameters into formulas (15), (16), and (17), the thickness of the variable cross-section steel leaf spring (partial) is calculated as shown in Table 4.

[0171] Table 4

[0172]

[0173] In step S7, the deformation of each segment under load P is calculated according to formulas (18) and (19).

[0174] The first piece is in total deformation. for:

[0175] Total stiffness of leaf springs K for:

[0176] If the spring stiffness does not meet the requirements specified in the drawings, change the stress and repeat steps S2-S4.

Claims

1. A design method for a variable cross-section steel leaf spring, characterized in that: Includes the following steps: S1: The structure of the leaf spring is divided into straight section L0, root transition section L1-L0, equal stress section L2-L1, extension section L3-L2, end transition section L4-L3, and end equal thickness section L-L4. S2: Obtain basic parameters, including load P, leaf spring width b, effective length L, and straight section L0. Determine the stress σ of the constant stress section based on the leaf spring material and application environment. x =σ; S3: Calculate the fillet radius r x and moment of inertia I x ; S4: Obtain the calculation formula for the thickness of each point, and calculate the thickness of the raw material, namely the thickness of the straight section L0 and the thickness of the root transition section L1-L0. S5: Obtain the thicknesses of L2, L3, L4 and the end thickness h5, and the calculation formulas for the thicknesses of each point in the extension section L3-L2 and the end transition section L4-L3; S6: Calculation formula for obtaining the thickness of the leaf spring at various locations; S7: Calculate the stiffness of the leaf spring; When the cross-section of the leaf spring is a waist-shaped hole, the fillet radius r x The calculation formula is: （1） Moment of inertia I x The calculation formula is: （2） Where, r x For the fillet of the cross section, h x For cross-sectional thickness; The formula for calculating the thickness of a leaf spring at various locations is as follows: （7） The precise thickness of the variable cross-section steel leaf spring at each position can be obtained by calculating sequentially at certain intervals according to formula (7). According to Mohr's law in mechanics of materials, the deformation of each segment under load P can be calculated using the following formula: （8） Total deformation The calculation formula is: （9） Total stiffness of leaf springs K The calculation formula is: （10） Where m is the number of leaf springs; When the cross-section of the leaf spring is a rounded rectangle, the fillet radius of the leaf spring is r. x The calculation formula is: （11） Moment of inertia I x The calculation formula is: （12） Where k is the correction coefficient obtained from actual measurement, r x For the fillet of the cross section, h x Where r is the cross-sectional thickness, r0 is the fillet radius of the raw material cross-section, and h0 is the cross-sectional thickness of the raw material. The formula for calculating the thickness of a leaf spring at various locations is as follows: （17） The precise thickness of the variable cross-section steel leaf spring at each position can be obtained by calculating sequentially at certain intervals according to formula (17). According to Mohr's law in mechanics of materials, the deformation of each segment under load P can be calculated using the following formula: Total deformation The calculation formula is: （18） Total stiffness of leaf springs K The calculation formula is: （19） Where m is the number of leaf springs.

2. The design method for variable cross-section steel leaf springs according to claim 1, characterized in that: According to the bending stress formula Therefore, the formula for calculating the thickness at each point is: （3） Wherein, formula (3) is about h x The cubic equation has discontinuous solutions, therefore L x Calculate the thickness sequentially at intervals within the range of 0-L, and the set of solutions represents the precise thickness at each point; let L... x Substituting =0 into formula (3) to solve, the result obtained is rounded up according to the raw material specifications to obtain the raw material thickness h0; Based on the capacity of the leaf spring production equipment, determine L1, and substitute it into formula (3) to obtain the thickness h1 at this point. The formula for calculating the thickness of each point in the root transition section L1-L0 is as follows: (L0≤L x ≤L1)(4) Among them, L x By calculating sequentially at certain intervals within the range [L0, L1], the set of points in the L1-L0 segment can be obtained.

3. The design method for variable cross-section steel leaf springs according to claim 2, characterized in that: Based on the production capacity of the leaf spring manufacturing equipment, the thicknesses of L2, L3, L4, and the end thickness are obtained sequentially. The calculation formulas for the thicknesses of each point in the extension section L3-L2 and the end transition section L4-L3 are as follows: （5） （6）。 4. The design method for variable cross-section steel leaf springs according to claim 3, characterized in that: According to the formula Roughly estimate the thickness of the raw material, round the result upwards, and determine the fillet radius r0 based on the raw material specifications on the market. According to the bending stress formula Therefore, the formula for calculating the thickness of each point in the equal stress segment L2-L1 is: （13） Based on the capacity of the leaf spring production equipment, determine L1, and substitute it into formula (12) to obtain the thickness h1 at this point. The formula for calculating the thickness of each point within the root transition section L1-L0 is as follows: (L0≤L x ≤L1)(14) Among them, L x By calculating the points in the L0-L1 range at certain intervals, the set of points in this segment can be obtained.

5. The design method for variable cross-section steel leaf springs according to claim 4, characterized in that: Based on the production capacity of the leaf spring manufacturing equipment, the thicknesses of L2, L3, L4, and the end thickness are obtained sequentially. The calculation formulas for the thicknesses of each point in the extension section L3-L2 and the end transition section L4-L3 are as follows: （15） （16）。

Images