CN106777805A - The offset frequency main spring cutting length method for designing of type progressive rate leaf spring such as the main spring formula of two-stage is non- - Google Patents

Abstract

The present invention relates to the offset frequency main spring cutting length method for designing of type progressive rate leaf spring such as the main spring formula of two-stage is non-, belong to suspension leaf spring technical field.The present invention can be according to each first and second grades of main springs and the structural parameters of auxiliary spring, elastic modelling quantity, U-bolts clamp away from, contact load, rigidity, rated load and the remaining tangent line camber design requirement value under rated load are clamped, on the basis of the design of initial tangential camber and curve form are calculated, using curved surface infinitesimal and principle of stacking, the cutting length to each first and second grades of main springs is designed.By model machine blanking processing experiment, the main spring formula of two-stage provided by the present invention is non-etc., and the offset frequency main spring cutting length method for designing of type progressive rate leaf spring is correct.Using the available accurately and reliably first and second grades of each cutting length design loads of main spring of the method, stock utilization can be improved, improve processing technology, improve production efficiency.

Description

The offset frequency main spring cutting length method for designing of type progressive rate leaf spring such as the main spring formula of two-stage is non-

Technical field

The present invention relates to the offset frequency type main spring of progressive rate leaf spring such as the main spring formula of vehicle suspension leaf spring, particularly two-stage is non- Cutting length method for designing.

Background technology

In order to further improve ride performance of the vehicle in the case of semi-load, can be by the master of former first-order gradient rigidity leaf spring Spring is split as the main spring formula progressive rate leaf spring of the main spring of two-stage, i.e. two-stage；Meanwhile, it is generally logical in order to ensure the stress intensity of main spring The main spring of the first order, the main spring in the second level and auxiliary spring initial tangential camber and two-stage gradual change gap are crossed, makes the main spring in the second level and auxiliary spring suitable When undertaking load in advance, so that the offset frequency type progressive rate leaf springs such as the main spring formula of the stress of the main spring of the first order, i.e. two-stage is non-are reduced, its In, each cutting length of the main spring of the first order and the second level of offset frequency type progressive rate leaf spring such as the main spring formula of two-stage is non-influences material Material utilization rate, processing technology and production efficiency.However, progressive rate by the offset frequency progressive rate leaf spring such as the main spring formula of two-stage is non-, Amount of deflection is calculated and curve form calculates the occupation of key issue, previously fails to provide the main spring formula of accurately and reliably two-stage always non-etc. The main spring cutting length method for designing of offset frequency type progressive rate leaf spring, it is thus impossible to meet Vehicle Industry fast development and suspension bullet Spring modernization CAD design requirement.With Vehicle Speed and its continuous improvement to ride comfort requirement, to progressive rate leaf spring Suspension proposes requirements at the higher level, therefore, it is necessary to set up the offset frequency type progressive rate plates such as a kind of accurate, reliable main spring formula of two-stage is non- The main spring cutting length method for designing of spring, is the cutting design and CAD software of the offset frequency type progressive rate leaf springs such as the main spring formula of two-stage is non- Reliable technical foundation is established in exploitation, meets fast-developing Vehicle Industry, vehicle ride performance and to progressive rate leaf spring Design requirement, improves the design level and stock utilization of the offset frequency type progressive rate leaf springs such as the main spring formula of two-stage is non-；Meanwhile, improve Processing technology, improve production efficiency.

The content of the invention

For defect present in above-mentioned prior art, the technical problems to be solved by the invention be to provide it is a kind of easy, The offset frequency main spring cutting length method for designing of type progressive rate leaf spring such as the reliable main spring formula of two-stage is non-, design cycle is as shown in Figure 1. The offset frequency type progressive rate leaf spring, one hemihedrism such as offset frequency type progressive rate leaf spring the is main spring formula of two-stage such as the main spring formula of two-stage is non-is non- Structure the main spring 2 of the main spring 1, second level of the first order and auxiliary spring 3 as shown in Fig. 2 be made up of.Using the main spring of two-stage, and by first The initial tangential camber H of the main main spring 2 of the spring 1, second level of level and auxiliary spring_gM10、H_gM20And H_gA0, in the main spring 1 of the first order and second level master Two-stage gradual change gap delta is provided between the main spring 2 of spring 2 and the second level and auxiliary spring 3_M12And δ_MA, travelled with improving the vehicle in the case of semi-load Ride comfort.In order to ensure meeting the main stress intensity design requirement of spring 1 of the first order, the main spring 2 in the second level and auxiliary spring 3 suitably undertake in advance Load, suspension gradual change load offset frequency is unequal, i.e., non-etc. offset frequency type progressive rate leaf spring.The half total span of progressive rate leaf spring Equal to the first half action length L of main spring_11T, U-bolts clamp away from half be L₀, width is b, and elastic modelling quantity is E.The The piece number of the main spring 1 of one-level is n₁, the thickness of each of the main spring of the first order is h_1i, half action length is L_1iT, half clamping length L_1i =L_1iT-L₀/ 2, i=1,2 ..., n₁.The piece number of the main spring 2 in the second level is n₂, the thickness of each of the main spring in the second level is h_2j, half work It is L with length_2jT, half clamping length L_2j=L_2jT-L₀/ 2, j=1,2 ..., n₂.The piece number of auxiliary spring 3 is m, the thickness that auxiliary spring is each It is h to spend_Ak, half action length is L_AkT, half clamping length L_Ak=L_AkT-L₀/ 2, k=1,2 ..., m.The main spring of the first order is clamped Stiffness K_M1, the compound clamping stiffness K of the main spring of the main spring of the first order and the second level_M2, the total compound clamping stiffness K of major-minor spring_MA.According to Each structural parameters of leaf spring, elastic modelling quantity, U-bolts is clamped away from each contact load, clamping rigidity at different levels, rated load And the remaining tangent line camber design requirement value under rated load, on the basis of curve form calculating, using curved surface infinitesimal and Principle of stacking, each cutting length of first and second grades of main springs of offset frequency type progressive rate leaf spring such as non-to the main spring formula of two-stage enters Row design.

In order to solve the above technical problems, the offset frequency type main spring of progressive rate leaf spring such as the main spring formula of two-stage provided by the present invention is non- Cutting length method for designing, it is characterised in that use following design procedure：

(1) the main spring initial tangential camber H of the first order of the offset frequency type progressive rate leaf spring such as the main spring formula of two-stage is non-_gM10Determination

Step A：First order gradual change is compound to clamp stiffness K_kwP1Calculating

Start contact load P according to the 1st time_k1, the 2nd beginning contact load P_k2, the main spring clamping stiffness K of the first order_M1, the The compound clamping stiffness K of the main spring of the main spring of one-level and the second level_M2, to load p in [P_k1,P_k2] scope when first order gradual change be combined Clamp stiffness K_kwP1Calculated, i.e.,

Step B：Second level gradual change is compound to clamp stiffness K_kwP2Calculating

Start contact load P according to the 2nd time_k2, the 2nd full contact load p_w2, the compound clamping rigidity of the main spring in the second level K_M2, the total compound clamping stiffness K of major-minor spring_MA, to load p in [P_k2,P_w2] scope when second level gradual change compound clamp rigidity K_kwP2Calculated, i.e.,

Step C：The main spring initial tangential camber H of the first order_gM10Determination

Stiffness K is clamped according to the main spring of the first order_M1, the total compound clamping stiffness K of major-minor spring_MA；1st beginning contact load P_k1, the 2nd beginning contact load P_k2, the 2nd full contact load p_w2, rated load P_N, in rated load P_NUnder residue cut Bank H high_gMsy, the K being calculated in step A_kwP1, the K being calculated in step B_kwP2, the offset frequency type such as non-to the main spring formula of two-stage The initial tangential camber H of the main spring of the first order of progressive rate leaf spring_gM10It is determined, i.e.,

(2) the main spring initial tangential camber H in the second level of the offset frequency type progressive rate leaf spring such as the main spring formula of two-stage is non-_gM20Really It is fixed：

I steps：The main spring tailpiece lower surface initial curvature radius R of the first order_M10Calculate

According to the main reed number n of the first order₁, the thickness h of each of the main spring of the first order_1i, i=1,2 ..., n₁；The main spring of the first order is first The half clamping length L of piece₁₁, the H that design is obtained in step (1)_gM10, to the main spring tailpiece lower surface initial curvature radius of the first order R_M10bCalculated, i.e.,

Ii steps：First of the main spring in second level upper surface initial curvature radius R_M20Calculate

According to the width b of the offset frequency type progressive rate leaf spring such as the main spring formula of two-stage is non-, elastic modulus E；The main reed number of the first order n₁, the thickness h of each of the main spring of the first order_i, i=1,2 ..., n₁, the half clamping length L of first of the main spring of the first order₁₁, open for the 1st time Beginning contact load P_k1, and the R being calculated in i steps_M10b, to first of the main spring in second level upper surface initial curvature radius R_M20aEnter Row is calculated, i.e.,

In formula, h_M1eIt is the root lap equivalent thickness of the main spring of the first order,

Iii steps：The main spring initial tangential camber H in the second level_gM20Determination

According to the second level auxiliary spring half clamping length L of first₂₁, the R that ii step values are calculated_M20a, to second level master Spring initial tangential camber H_gM20It is determined, i.e.,

(3) the first original state curve form of the main spring of the first order for the offset frequency type progressive rate leaf spring such as the main spring formula of two-stage is non- f_M1xCalculating：

A steps：The equivalent end points power F of first first of main spring_1eCalculating

According to the width b of the offset frequency type progressive rate leaf spring such as the main spring formula of two-stage is non-, elastic modulus E；First of the main spring of the first order Thickness h₁₁, the half clamping length L of first of the main spring of the first order₁₁, the H that design is obtained in step (1)_gM10, to the main spring of the first order The equivalent end points power F of first_1eCalculated, i.e.,

B step：The deformation coefficient G that first of the main spring of the first order is located at an arbitrary position_M1xCalculating

According to the width b of the offset frequency type progressive rate leaf spring such as the main spring formula of two-stage is non-, U-bolts clamp away from half L₀, bullet Property modulus E；The half clamping length L of first of the main spring of the first order₁₁, with apart from symmetrical centre L₀Position at/2 is the origin of coordinates, To the deformation coefficient G at first of the main spring of the first order at an arbitrary position x_M1xCalculated, i.e.,

Step c：First original state curve form f of the main spring of the first order_M1xCalculating

According to the first order main spring thickness h of first₁₁, the F being calculated in a steps_1e, the G being calculated in b step_M1x, With apart from leaf spring symmetrical centre L₀/ 2 position is the origin of coordinates, to the first order main spring initial surface shape f of first_M1xCarry out Calculate, i.e.,

(4) each design of cutting length of the main spring of the first order for the offset frequency type progressive rate leaf spring such as the main spring formula of two-stage is non-：

I steps：First cutting length L of the main spring of the first order_11CDesign

According to the central diameter d of first two ends hanger of the main spring of the first order_e, U-bolts clamp away from half L₀, the main spring head of the first order The half clamping length L of piece₁₁, it is curved surface infinitesimal length with Δ L, in 0~L₁₁In the range of be divided into N_1c=L₁₁L curved surface of/Δ is micro- Unit, according to the f being calculated in step (3)_M1xAnd x at an arbitrary position_jThe curved surface height f at place_M1xj, 0≤x_j≤L₁₁, j=1, 2,…,N_1c+ 1, using principle of stacking to the cutting length L of first of the main spring of the first order_11CIt is designed, i.e.,

II steps：The main spring of the first order other each cutting length L_1iCDesign

According to the central diameter d of first two ends hanger of the main spring of the first order_e, the main reed number n of the first order₁, the one of first of the main spring of the first order Half action length L_11T, other n₁- 1 half action length L of main spring_1iT, the L that the design of I steps is obtained_11C, to the main spring of the first order Other each cutting length L_1iCIt is designed, i=2 ..., n₁I.e.

L_1iC=L_11C-2πd_e-2(L_11T-L_1iT), i=2 ..., n₁；

(5) the first original state curve form of the main spring in the second level for the offset frequency type progressive rate leaf spring such as the main spring formula of two-stage is non- f_M2xCalculating：

1. step：The equivalent end points power F of first of the main spring in the second level_2eCalculating

According to the width b of the offset frequency type progressive rate leaf spring such as the main spring formula of two-stage is non-, elastic modulus E；First of the main spring in the second level Thickness

h₂₁, half clamping length L₂₁, the H that design is obtained in step (2)_gM20, to the main spring in the second level equivalent end points of first Power F_2eCalculated, i.e.,

2. step：The deformation coefficient G that first of the main spring in the second level is located at an arbitrary position_M2xCalculating

According to the width b of the offset frequency type progressive rate leaf spring such as the main spring formula of two-stage is non-, elastic modulus E；First of the main spring in the second level Half clamping length L₂₁, with apart from leaf spring symmetrical centre L₀/ 2 position is the origin of coordinates, in office to first of the main spring in the second level Deformation coefficient G at meaning position x_M2xCalculated, i.e.,

3. step：First original state curve form f of the main spring in the second level_M2xCalculating,

According to the main spring in the second level thickness h of first₂₁, first half clamping length L of the main spring in the second level₂₁, 1. calculated in step The F for obtaining_2e, the G being 2. calculated in step_M2x, with apart from leaf spring symmetrical centre L₀/ 2 position is the origin of coordinates, to second The main first initial surface shape f of spring of level_M2xCalculated, i.e.,

(6) design of the main spring cutting length in the second level of offset frequency type progressive rate leaf spring such as the main spring formula of two-stage is non-

1) step：First cutting length L of the main spring in the second level_21CDesign

U-bolts according to the offset frequency type progressive rate leaf spring such as the main spring formula of two-stage is non-clamp away from half L₀, second level master The half clamping length L of first of spring₂₁, it is curved surface infinitesimal length with Δ L, in 0~L₂₁In the range of be divided into N_2c=L₂₁/ Δ L is bent Face infinitesimal, the f being calculated in the 3. step according to step (4)_M2xAnd x at an arbitrary position_kThe curved surface height f at place_M2xk, 0≤x_k ≤L₂₁, k=1,2 ..., N_2c+ 1, using principle of stacking to first cutting length L of the main spring in the second level_21CIt is designed, i.e.,

2) step：The main spring in the second level other each cutting length L_2jCDesign

Piece number n according to the main spring in the second level₂, the half action length L of first of the main spring in the second level_21T, other each half Action length L_2iT, 1) and the L that obtains of step design_21C, to other each cutting length L of the main spring in the second level_2jCIt is designed, j= 2,…,n₂I.e.

L_2jC=L_21C-2(L_21T-L_2jT), j=2 ..., n₂。

The present invention has the advantage that than prior art

Due to the progressive rate by the offset frequency progressive rate leaf spring such as the main spring formula of two-stage is non-, amount of deflection is calculated and curve form is calculated The occupation of key issue, previously fails to provide the offset frequency type main springs of progressive rate leaf spring such as the main spring formula of accurate reliable two-stage is non-always Cutting length method for designing, it is thus impossible to meeting, Vehicle Industry is fast-developing and bearing spring modernizes CAD design requirement.This Invention can according to the structural parameters of each main spring of one-level, two grades of main springs and auxiliary spring, elastic modelling quantity, U-bolts clamp away from, it is at different levels Rigidity, each contact load, rated load and the remaining tangent line camber design requirement value under rated load are clamped, at the beginning of main spring On the basis of beginning tangent line camber is designed and initial surface shape is calculated, using curved surface infinitesimal and principle of stacking, to the main spring formula of two-stage Each cutting length of first and second grades of main springs of the offset frequency type progressive rate leaf spring such as non-is designed.Added by model machine blanking Work experimental test understands, the main spring cutting length design of offset frequency type progressive rate leaf spring such as the main spring formula of two-stage provided by the present invention is non- Method is correct, is each cutting length design of the main spring of the first order and the second level of the main spring formula level progressive rate leaf spring of two-stage There is provided reliable method for designing.Using the available accurately and reliably first and second grades of each cutting lengths of main spring of the method Design load, improves stock utilization, improves processing technology, improve production efficiency；At the same time it can also reduce design and test fee With quickening product development speed.

Brief description of the drawings

For a better understanding of the present invention, it is described further below in conjunction with the accompanying drawings.

Fig. 1 is the offset frequency type progressive rate leaf spring first design flow diagrams of cutting length of main spring such as the main spring formula of two-stage is non-；

Fig. 2 is the half symmetrical structure schematic diagram of the offset frequency progressive rate leaf springs such as the main spring formula of two-stage is non-；

Fig. 3 is the clamping stiffness K of the offset frequency progressive rate leaf spring such as the main spring formula of two-stage is non-of embodiment_PWith the change of load p Curve；

Fig. 4 is the deformation coefficient curve G of first of the main spring of the first order of embodiment_M1x；

Fig. 5 is the initial surface pattern curve f of first of the main spring of the first order of first of the main spring of the first order of embodiment_M1x；

Fig. 6 is the deformation coefficient curve G of first of the main spring in the second level of embodiment_M2x；

Fig. 7 is the initial surface pattern curve f of first of the main spring of the first order of first of the main spring in the second level of embodiment_M2x。

Specific embodiment

The present invention is described in further detail below by embodiment.

Embodiment：The width b=63mm of the offset frequency progressive rate leaf spring such as the main spring formula of certain two-stage is non-, U-bolts clamp away from Half L₀=50mm, elastic modulus E=200GPa.The main reed number n of the first order₁=2, the thickness h of each of the main spring of the first order₁₁=h₁₂ =8mm, half action length difference L_11T=525mm, L_12T=450mm；Half clamping length is respectively L₁₁=L_11T-L₀/ 2= 500mm, L₁₂=L_12T-L₀/ 2=425mm.The main reed number n in the second level₂=1, thickness h₂₁=8mm；Half action length L_21T= 350mm, half clamping length L₂₁=L_21T-L₀/ 2=325mm.Auxiliary spring piece number m=2, the thickness h that auxiliary spring is each_A1=h_A2= 13mm；The half action length of each of auxiliary spring is respectively L_A1T=250mm, L_A2T=150mm；The half clamping length of each of auxiliary spring Respectively L_A1=L_A1T-L₀/ 2=225mm, L_A2=L_A2T-L₀/ 2=125mm.The main spring of the first order clamps stiffness K_M1=51.4N/mm； The compound clamping stiffness K of the main spring of the first order and the main spring in the second level_M2=75.4N/mm, the total compound of major-minor spring clamps stiffness K_MA= 172.9N/mm.Start contact load P 1st time_k1=1850N, the 2nd beginning contact load P_k2=2600N, connects for the 2nd time completely Touch load p_w2=3680N.Rated load P_N=7227N, and in rated load P_NUnder remaining tangent line camber H_gMsy=26.1mm. According to each structural parameters of leaf spring, elastic modelling quantity, U-bolts clamp away from, it is clamping rigidity at different levels, each contact load, specified Load and the remaining tangent line camber design requirement value under rated load, the offset frequency type progressive rate plate such as non-to the main spring formula of the two-stage Each cutting length of first and second grades of main springs of spring is designed.

The main spring cutting length design side of offset frequency type progressive rate leaf spring such as the main spring formula of two-stage that present example is provided is non- Method, its design cycle are as shown in figure 1, specific design step is as follows：

(1) the main spring initial tangential camber H of the first order of the offset frequency type progressive rate leaf spring such as the main spring formula of two-stage is non-_gM10Set Meter：

Step A：First order gradual change is compound to clamp stiffness K_kwP1Calculating

Stiffness K is clamped according to the first main spring_M1=51.4N/mm, the compound clamping rigidity of the main spring of the main spring of the first order and the second level K_M2=75.4N/mm, the 1st beginning contact load P_k1=1850N, the 2nd beginning contact load P_k2=2600N, exists to load p [P_k1,P_k2] scope when first order gradual change compound clamp stiffness K_kwP1Calculated, i.e.,

Step B：Second level gradual change is compound to clamp stiffness K_kwP2Calculating

According to the compound clamping stiffness K of the main spring of the main spring of the first order and the second level_M2=75.4N/mm, the total compound folder of major-minor spring Tight stiffness K_MA=172.9N/mm, the 2nd beginning contact load P_k2=2600N, the 2nd full contact load p_w2=3680N is right Load p is in [P_k2,P_w2] when second level gradual change compound clamp stiffness K_kwP2Calculated, i.e.,

Using Matlab calculation procedures, the folder of the offset frequency type progressive rate leaf spring such as the main spring formula of the two-stage obtained by calculating is non- Tight stiffness K_PWith the change curve of load p, as shown in Figure 3.

Step C：The main spring initial tangential camber H of the first order_gM10Determination

Stiffness K is clamped according to the main spring of the first order_M1=51.4N/mm；The total compound of major-minor spring clamps stiffness K_MA=172.9N/ mm；Start contact load P 1st time_k1=1850N, the 2nd beginning contact load P_k2=2600N, the 2nd full contact load p_w2 =3680N, rated load P_N=7227N, in rated load P_NUnder remaining tangent line camber H_gMsy=26.1mm, step A and B are walked The K being calculated in rapid_kwP1And K_kwP2, the main spring of the first order of offset frequency type progressive rate leaf spring such as non-to the main spring formula of the two-stage just Beginning tangent line camber H_gM10It is determined, i.e.,

(2) the main spring initial tangential camber H in the second level of the offset frequency type progressive rate leaf spring such as the main spring formula of two-stage is non-_gM20Set Meter：

I steps：The main spring tailpiece lower surface initial curvature radius R of the first order_M10Calculate

According to the main reed number n of the first order₁=2, the thickness h of each of the main spring of the first order₁₁=h₂₁=8mm；The main spring of the first order is first The half clamping length L of piece₁₁=500mm, identified H in step (1)_gM10=103.7mm, to the main spring tailpiece following table of the first order Face initial curvature radius R_M10bCalculated, i.e.,

Ii steps：First of the main spring in second level upper surface initial curvature radius R_M20aCalculate

According to the width b=63mm of the offset frequency type progressive rate leaf spring such as the main spring formula of two-stage is non-, elastic modulus E=200GPa； The main reed number n of the first order₁=2, the thickness h of each of the main spring of the first order₁₁=h₁₂=8mm；The half of first of the main spring of the first order is clamped Length L₁₁=500mm, the 1st beginning contact load P_k1The R being calculated in=1850N, and i steps_M10b=1272.8mm is right First of the main spring in second level upper surface initial curvature radius R_M20aCalculated, i.e.,

In formula, h_M1eIt is the root lap equivalent thickness of the main spring of the first order,

Iii steps：The main spring initial tangential camber H in the second level_gM20Design

According to the second level auxiliary spring half clamping length L of first₂₁The R that=325mm, ii step value are calculated_M20a= 2812.7mm, spring initial tangential camber H main to the second level_gM20It is designed, i.e.,

(3) the first original state curve form of the main spring of the first order for the offset frequency type progressive rate leaf spring such as the main spring formula of two-stage is non- f_M1xCalculating：

A steps：The equivalent end points power F of the first first of main spring_1eCalculating

According to the width b=63mm of the offset frequency type progressive rate leaf spring such as the main spring formula of two-stage is non-, elastic modulus E=200GPa； The thickness h of first of the main spring of the first order₁₁=8mm, the half clamping length L of first of the main spring of the first order₁₁=500mm, in step (1) The H that design is obtained_gM10=103.7mm, to the main spring of the first order equivalent end points power F of first_1eCalculated, i.e.,

B step：The deformation coefficient G that first of the main spring of the first order is located at an arbitrary position_M1xCalculating

According to the width b=63mm of the offset frequency type progressive rate leaf spring such as the main spring formula of two-stage is non-, U-bolts clamp away from one Half L₀=50mm elastic modulus Es=200GPa；The half clamping length L of first of the main spring of the first order₁₁=500mm, with apart from leaf spring Symmetrical centre L₀/ 2 position is the origin of coordinates, to first deformation coefficient G for locating at an arbitrary position of the main spring of the first order_M1xCounted Calculate, i.e.,

When x changes in the range of 0~500mm, the deformation coefficient G of first of the main spring of the first order obtained by calculating_M1xWith position The change curve of x is put, as shown in Figure 4；Wherein, the deformation coefficient G at x=0 positions_M1x=0, in x=L₁₁At=500mm Deformation coefficient G_M1x=G_Mmax=3.968 × 10^-11m⁴/N；

Step c：First original state curve form f of the main spring of the first order_M1xCalculating

According to the first order main spring thickness h of first₁₁The F being calculated in=8mm, a step_1e=1338.5N, in b step The G being calculated_M1x, with apart from leaf spring symmetrical centre L₀/ 2 position is the origin of coordinates, to the main spring of the first order initial song of first Face shape f_M1xCalculated, i.e.,

When x changes in the range of 0~500mm, the initial surface shape of first of the main spring of the first order obtained by calculating is bent Line f_M1xAs shown in figure 5, wherein, end maximum curved surface is highly equal to the initial tangential camber of the main spring of the first order, i.e. f_M1xmax= H_gM10=103.7mm.

(4) the first design of cutting length of the main spring of the first order for the offset frequency type progressive rate leaf spring such as the main spring formula of two-stage is non-：

I steps：First cutting length L of the main spring of the first order_11CDesign

According to the central diameter d of first hanger of the main spring of the first order_e=60mm, U-bolts clamp away from half L₀=50mm, first The half clamping length L of main first of the spring of level₁₁=500mm, is curved surface infinitesimal length with Δ L=5mm, in 0~L₁₁In the range of divide It is N_1c=L₁₁L=100 curved surface infinitesimal of/Δ, the f being calculated in step (3)_M1xAnd x at an arbitrary position_jThe curved surface at place is highly f_M1xj, 0≤x_j≤L₁₁, j=1,2 ..., N_1c+ 1, using principle of stacking to the cutting length L of first of the main spring of the first order_11CSet Meter, i.e.,

II steps：The main spring of the first order other each cutting length L_1iCDesign

According to the central diameter d of first hanger of the main spring of the first order_e=60mm, the piece number n of the main spring of the first order₁=2, the main spring of the first order The half action length L of first_11T=500mm, the half action length L of the 2nd_12TThe L that the design of=450mm, I step is obtained_11C =1483.8mm, to the 2nd cutting length L of the main spring of the first order_12CIt is designed, i.e.,

L_12C=L_11C-2πd_e-2(L_11T-L_12T)=925.3.8mm.

(5) the first cutting length L of the main spring in the second level for the offset frequency type progressive rate leaf spring such as the main spring formula of two-stage is non-_M2CDesign：

1. step：The equivalent end points power F of first of the main spring in the second level_2eCalculating

According to the width b=63mm of the offset frequency type progressive rate leaf spring such as the main spring formula of two-stage is non-, elastic modulus E=200GPa； The thickness h of first of the main spring in the second level₂₁=8mm, half clamping length L₂₁The H that design is obtained in=325mm, step (2)_gM20= 18.8mm, to the main spring in the second level equivalent end points power F of first_2eCalculated, i.e.,

2. step：The deformation coefficient G that first of the main spring in the second level is located at an arbitrary position_M2xCalculating

According to the width b=63mm of the offset frequency type progressive rate leaf spring such as the main spring formula of two-stage is non-, U-bolts clamp away from one Half L₀=50mm, elastic modulus E=200Gpa；The half clamping length L of first of the main spring in the second level₂₁=325mm, with apart from leaf spring Symmetrical centre L₀/ 2 position is the origin of coordinates, to first deformation coefficient G for locating at an arbitrary position of the main spring in the second level_M2xCounted Calculate, i.e.,

When x is in 0~L₂₁In the range of when changing, the first deformation coefficient curve G of the main spring in the second level obtained by calculating_M2x, such as scheme Shown in 6；Wherein, the deformation coefficient G at x=0 positions_M2x=0, in x=L₂₁Deformation coefficient G at=325mm_M2x=G_M2max =1.09 × 10^-11m⁴/N；

3. step：First original state curve form f of the main spring in the second level_M2xCalculating,

According to the main spring in the second level thickness h of first₂₁=8mm, half clamping length L₂₁=325mm, 1. calculates in step The F for arriving_2e=883.25N, the G being 2. calculated in step_M2x, center L is claimed to leaf spring with distance₀/ 2 position is the origin of coordinates, To first initial surface shape f of the main spring in the second level_M2xCalculated, i.e.,

When x is in 0~L₂₁In the range of when changing, the first initial surface pattern curve f of the main spring in the second level obtained by calculating_M2x, As shown in fig. 7, wherein, end maximum curved surface is highly equal to the main spring initial tangential camber in the second level, i.e. f_M2xmax=H_gM20= 18.8mm。

(6) design of the main spring cutting length in the second level of offset frequency type progressive rate leaf spring such as the main spring formula of two-stage is non-：

1) step：First cutting length L of the main spring in the second level_21CDesign

According to the main spring in the second level half clamping length L of first₂₁=325mm, U-bolts clamp away from half L₀= 50mm, is curved surface infinitesimal length with Δ L=5mm, in 0~L₂₁In the range of be divided into N_2c=L₂₁L=65 curved surface infinitesimal of/Δ, according to The f being calculated in 3. step according to step (4)_M2xAnd x at an arbitrary position_kThe curved surface height f at place_M2xk, 0≤x_k≤L₂₁, k=1, 2,…,N_2c+ 1, using principle of stacking to first cutting length L of the main spring in the second level_M2cIt is designed, i.e.,

2) step：The main spring in the second level other each cutting length designs

Piece number n according to the main spring in the second level₂=1, therefore, it is designed without other each needs.

Tested by model machine blanking processing experiment, the offset frequency type gradual change such as the main spring formula of two-stage provided by the present invention is non-is firm The degree main spring cutting length method for designing of leaf spring is correct, is each first and second of the main spring formula level progressive rate leaf spring of two-stage The cutting length design of the main spring of level provides reliable method for designing.Using under the available accurately and reliably each main spring of the method Material Design of length value, can improve stock utilization, improve processing technology, improve production efficiency；Set at the same time it can also reduce generation Meter and testing expenses, accelerate product development speed.

Claims (1)

1. the offset frequency main spring cutting length method for designing of type progressive rate leaf spring such as the main spring formula of two-stage is non-, wherein, each leaf spring be with Center mounting hole symmetrical structure, install clamp away from half for U-bolts clamp away from half；By former first-order gradient rigidity The main spring of leaf spring splits and is designed as the main spring of two-stage, by the initial tangential camber and two-stage gradual change gap of the main spring of two-stage and auxiliary spring, Improve the vehicle ride performance in the case of semi-load；Meanwhile, in order to ensure meeting the main spring stress intensity design requirement of the first order, the Two grades of main springs and auxiliary spring suitably undertake load in advance, and the offset frequency being suspended under gradual change load is unequal, i.e. the main spring formula of two-stage is non-etc. Offset frequency type progressive rate leaf spring；According to each structural parameters of leaf spring, elastic modelling quantity, U-bolts is clamped away from each contact is carried Lotus, clamping rigidity at different levels, rated load and the remaining tangent line camber design requirement value under rated load, in main spring curve form On the basis of calculating, using curved surface infinitesimal and principle of stacking, the first of the offset frequency type progressive rate leaf spring such as non-to the main spring formula of two-stage Each cutting length of level and the main spring in the second level is designed, and specific design step is as follows：

(1) the main spring initial tangential camber H of the first order of the offset frequency type progressive rate leaf spring such as the main spring formula of two-stage is non-_gM10Determination

Step A：First order gradual change is compound to clamp stiffness K_kwP1Calculating

Start contact load P according to the 1st time_k1, the 2nd beginning contact load P_k2, the main spring clamping stiffness K of the first order_M1, the first order The compound clamping stiffness K of the main spring of main spring and the second level_M2, to load p in [P_k1,P_k2] scope when first order gradual change compound clamp Stiffness K_kwP1Calculated, i.e.,

$K_{kwP1}=\frac{P}{P_{k1}}{K}_{M1}+\frac{P-P_{k1}}{P_{k2}-P_{k1}}(K_{M2}-\frac{P_{k2}}{P_{k1}}{K}_{M1}),P\∈\[P_{k1},P_{k2}\];$

Step B：Second level gradual change is compound to clamp stiffness K_kwP2Calculating

Start contact load P according to the 2nd time_k2, the 2nd full contact load p_w2, the compound clamping stiffness K of the main spring in the second level_M2, The total compound of major-minor spring clamps stiffness K_MA, to load p in [P_k2,P_w2] scope when second level gradual change compound clamp stiffness K_kwP2 Calculated, i.e.,

$K_{kwP2}=\frac{P}{P_{k2}}{K}_{M2}+\frac{P-P_{k2}}{P_{w2}-P_{k2}}(K_{MA}-\frac{P_{w2}}{P_{k2}}{K}_{M2}),P\∈\[P_{k2},P_{w2}\];$

Step C：The main spring initial tangential camber H of the first order_gM10Determination

Stiffness K is clamped according to the main spring of the first order_M1, the total compound clamping stiffness K of major-minor spring_MA；Start contact load P 1st time_k1, the Start contact load P 2 times_k2, the 2nd full contact load p_w2, rated load P_N, in rated load P_NUnder remaining tangent line camber H_gMsy, the K being calculated in step A_kwP1, the K being calculated in step B_kwP2, the offset frequency type gradual change such as non-to the main spring formula of two-stage is firm Spend the initial tangential camber H of the main spring of the first order of leaf spring_gM10It is determined, i.e.,

$H_{gM10}=\frac{P_{k1}}{K_{M1}}+{\∫}_{P_{k1}}^{P_{k2}}\frac{dP}{K_{kwP1}}+{\∫}_{P_{k2}}^{P_{w2}}\frac{dP}{K_{kwP2}}+\frac{P_N-P_{w2}}{K_{MA}}+H_{gMsy};$

(2) the main spring initial tangential camber H in the second level of the offset frequency type progressive rate leaf spring such as the main spring formula of two-stage is non-_gM20Determination：

I steps：The main spring tailpiece lower surface initial curvature radius R of the first order_M10Calculate

According to the main reed number n of the first order₁, the thickness h of each of the main spring of the first order_1i, i=1,2 ..., n₁；First of the main spring of the first order Half clamping length L₁₁, the H that design is obtained in step (1)_gM10, spring tailpiece lower surface initial curvature radius R main to the first order_M10b Calculated, i.e.,

$R_{M10b}=\frac{{L_{11}}^2+H_{gM10}^2}{2H_{gM10}}+\underset{i=1}{\overset{n_1}{\Σ}}{h}_{1i};$

Ii steps：First of the main spring in second level upper surface initial curvature radius R_M20Calculate

According to the width b of the offset frequency type progressive rate leaf spring such as the main spring formula of two-stage is non-, elastic modulus E；The main reed number n of the first order₁, the The thickness h of each of the main spring of one-level_i, i=1,2 ..., n₁, the half clamping length L of first of the main spring of the first order₁₁, start to connect for the 1st time Touch load p_k1, and the R being calculated in i steps_M10b, to first of the main spring in second level upper surface initial curvature radius R_M20aCounted Calculate, i.e.,

$R_{M20a}=\frac{R_{M10b}{\mathrm{Ebh}}_{M1e}^3}{{\mathrm{Ebh}}_{M1e}^3-6R_{M10b}{P}_{k1}{L}_{11}};$

In formula, h_M1eIt is the root lap equivalent thickness of the main spring of the first order,

Iii steps：The main spring initial tangential camber H in the second level_gM20Determination

According to the second level auxiliary spring half clamping length L of first₂₁, the R that ii step values are calculated_M20a, at the beginning of the main spring in the second level Beginning tangent line camber H_gM20It is determined, i.e.,

$H_{gM20}=R_{M20a}-\sqrt{R_{M20a}^2-L_{21}^2};$

(3) the first original state curve form f of the main spring of the first order for the offset frequency type progressive rate leaf spring such as the main spring formula of two-stage is non-_M1x's Calculate：

A steps：The equivalent end points power F of first first of main spring_1eCalculating

According to the width b of the offset frequency type progressive rate leaf spring such as the main spring formula of two-stage is non-, elastic modulus E；The thickness of first of the main spring of the first order Degree h₁₁, the half clamping length L of first of the main spring of the first order₁₁, the H that design is obtained in step (1)_gM10, to first of the main spring of the first order Equivalent end points power F_1eCalculated, i.e.,

$F_{1e}=\frac{{\mathrm{Ebh}}_{11}^3{H}_{gM10}}{4L_{11}^3};$

B step：The deformation coefficient G that first of the main spring of the first order is located at an arbitrary position_M1xCalculating

According to the width b of the offset frequency type progressive rate leaf spring such as the main spring formula of two-stage is non-, U-bolts clamp away from half L₀, springform Amount E；The half clamping length L of first of the main spring of the first order₁₁, with apart from symmetrical centre L₀Position at/2 is the origin of coordinates, to the First of the main spring of one-level deformation coefficient G at an arbitrary position at x_M1xCalculated, i.e.,

$G_{M1x}=\frac{2\[{(L_{11}-x)}^3-3L_{11}^2(L_{11}-x)+2L_{11}^3\]}{Eb},0\≤x\≤L_{11};$

Step c：First original state curve form f of the main spring of the first order_M1xCalculating

According to the first order main spring thickness h of first₁₁, the F being calculated in a steps_1e, the G being calculated in b step_M1x, with away from From leaf spring symmetrical centre L₀/ 2 position is the origin of coordinates, to the first order main spring initial surface shape f of first_M1xCalculated, I.e.

$f_{M1x}=G_{M1x}\frac{F_{1e}}{h_{11}^3},0\≤x\≤L_{11};$

(4) each design of cutting length of the main spring of the first order for the offset frequency type progressive rate leaf spring such as the main spring formula of two-stage is non-：

I steps：First cutting length L of the main spring of the first order_11CDesign

According to the central diameter d of first two ends hanger of the main spring of the first order_e, U-bolts clamp away from half L₀, first of the main spring of the first order Half clamping length L₁₁, it is curved surface infinitesimal length with Δ L, in 0~L₁₁In the range of be divided into N_1c=L₁₁L curved surface infinitesimal of/Δ, According to the f being calculated in step (3)_M1xAnd x at an arbitrary position_jThe curved surface height f at place_M1xj, 0≤x_j≤L₁₁, j=1,2 ..., N_1c+ 1, using principle of stacking to the cutting length L of first of the main spring of the first order_11CIt is designed, i.e.,

$L_{11C}=2\underset{j=1}{\overset{N_{1c}}{\Σ}}\sqrt{{\mathrm{\ΔL}}^2+{(f_{M1x_{j+1}}-f_{M1x_j})}^2}+2{\mathrm{\πd}}_e+L_0;$

II steps：The main spring of the first order other each cutting length L_1iCDesign

According to the central diameter d of first two ends hanger of the main spring of the first order_e, the main reed number n of the first order₁, the half work of first of the main spring of the first order Use length L_11T, other n₁- 1 half action length L of main spring_1iT, the L that the design of I steps is obtained_11C, to the main spring of the first order other Each cutting length L_1iCIt is designed, i=2 ..., n₁I.e.

L_1iC=L_11C-2πd_e-2(L_11T-L_1iT), i=2 ..., n₁；

(5) the first original state curve form f of the main spring in the second level for the offset frequency type progressive rate leaf spring such as the main spring formula of two-stage is non-_M2x's Calculate：

1. step：The equivalent end points power F of first of the main spring in the second level_2eCalculating

According to the width b of the offset frequency type progressive rate leaf spring such as the main spring formula of two-stage is non-, elastic modulus E；The thickness of first of the main spring in the second level Degree h₂₁, half clamping length L₂₁, the H that design is obtained in step (2)_gM20, to the main spring in the second level equivalent end points power F of first_2eEnter Row is calculated, i.e.,

$F_{2e}=\frac{{\mathrm{Ebh}}_{21}^3{H}_{gM20}}{4L_{21}^3};$

2. step：The deformation coefficient G that first of the main spring in the second level is located at an arbitrary position_M2xCalculating

According to the width b of the offset frequency type progressive rate leaf spring such as the main spring formula of two-stage is non-, elastic modulus E；The one of first of the main spring in the second level Half clamping length L₂₁, with apart from leaf spring symmetrical centre L₀/ 2 position is the origin of coordinates, to first of the main spring in the second level in any position Put the deformation coefficient G at x_M2xCalculated, i.e.,

$G_{M2x}=\frac{2\[{(L_{21}-x)}^3-3L_{21}^2(L_{21}-x)+2L_{21}^3\]}{Eb},0\≤x\≤L_{21};$

3. step：First original state curve form f of the main spring in the second level_M2xCalculating,

According to the main spring in the second level thickness h of first₂₁, first half clamping length L of the main spring in the second level₂₁, 1. it is calculated in step F_2e, the G being 2. calculated in step_M2x, with apart from leaf spring symmetrical centre L₀/ 2 position is the origin of coordinates, to second level master First initial surface shape f of spring_M2xCalculated, i.e.,

$f_{M2x}=G_{M2x}\frac{F_{2e}}{h_{21}^3},0\≤x\≤L_{21};$

(6) design of the main spring cutting length in the second level of offset frequency type progressive rate leaf spring such as the main spring formula of two-stage is non-

1) step：First cutting length L of the main spring in the second level_21CDesign

U-bolts according to the offset frequency type progressive rate leaf spring such as the main spring formula of two-stage is non-clamp away from half L₀, the main spring head in the second level The half clamping length L of piece₂₁, it is curved surface infinitesimal length with Δ L, in 0~L₂₁In the range of be divided into N_2c=L₂₁L curved surface of/Δ is micro- Unit, the f being calculated in the 3. step according to step (4)_M2xAnd x at an arbitrary position_kThe curved surface at place is highly0≤x_k≤ L₂₁, k=1,2 ..., N_2c+ 1, using principle of stacking to first cutting length L of the main spring in the second level_21CIt is designed, i.e.,

$L_{21C}=2\underset{k=1}{\overset{N_{2c}}{\Σ}}\sqrt{{\mathrm{\ΔL}}^2+{(f_{M2x_{k+1}}-f_{M2x_k})}^2}+L_0;$

2) step：The main spring in the second level other each cutting length L_2jCDesign

Piece number n according to the main spring in the second level₂, the half action length L of first of the main spring in the second level_21T, the effect of other each half Length L_2iT, 1) and the L that obtains of step design_21C, to other each cutting length L of the main spring in the second level_2jCIt is designed, j=2 ..., n₂I.e.

L_2jC=L_21C-2(L_21T-L_2jT), j=2 ..., n₂。