CN106709204A - Simulation computation method of deflection characteristics of high-duty two-leveled alterable stiffness leaf spring - Google Patents

Abstract

The invention relates to a simulation computation method of deflection characteristics of high-duty two-leveled alterable stiffness leaf spring, which belongs to vehicle suspension leaf spring technology field. According to the structure parameters of each main spring and each auxiliary spring, elastic modulus, load rating, the initial tangent arc height design value of the main spring, and the initial tangent arc height design value of the first level auxiliary spring and the second level auxiliary spring, the method can conduct the simulation computation to the deflection characteristics of high-duty two-leveled alterable stiffness leaf spring in different loads. The simulation and prototype testing can prove that the method is right. Utilizing the method, we can get an accurate and reliable simulation computation value of deflection characteristics. It is guaranteed that the initial tangent arc height of the leaf spring and the tangent arc height in load rating and the maximum deflection can meet design requirements. The simulation computation method of deflection characteristics of high-duty two-leveled alterable stiffness leaf spring has the advantages of improving the design, quality and performance of productions, and reducing design and testing expenses and accelerates product development speed.

Description

The simulation calculation method of the flexibility characteristics of high intensity two-stage progressive rate leaf spring

Technical field

The present invention relates to vehicle suspension leaf spring, particularly the emulation meter of the flexibility characteristics of high intensity two-stage progressive rate leaf spring Algorithm.

Background technology

With the appearance of high strength steel plate material, vehicle suspension can use high intensity two-stage progressive rate leaf spring, so as to enter The vehicle ride performance and suspension gradual change offset frequency that one step is met under different loads keep constant design requirement, wherein, gradually Flexibility characteristics of the variation rigidity leaf spring under different loads, not only influence the traveling smooth-going of leaf spring progressive rate, suspension offset frequency and vehicle Property, but also make the remaining tangent line camber and maximum spacing amount of deflection design influenceed under leaf spring initial tangential camber, rated load Simulating, verifying.Structural parameters and load due to main spring amount of deflection not only with main spring and one-level auxiliary spring and two grades of auxiliary springs are relevant, also with Each time contact load is relevant, and contact length and progressive rate in gradual change contact process all changes with load, therefore, The main spring amount of deflection of high intensity two-stage progressive rate leaf spring calculates extremely complex.And for give design structure high intensity two-stage gradually The flexibility characteristics simulation calculation of variation rigidity leaf spring, in addition to the restriction that acceptor's spring amount of deflection is calculated, is also emulated by contact load and counted The restriction of this key issue is calculated, is understood according to consulting reference materials, predecessor State is inside and outside not to provide high intensity two-stage progressive rate plate always The simulation calculation method of the flexibility characteristics of spring.With Vehicle Speed and its continuous improvement to ride comfort requirement, to high intensity The design of two-stage progressive rate plate spring suspension system proposes requirements at the higher level, therefore, it is necessary to set up a kind of accurate, reliable high intensity The simulation calculation method of the flexibility characteristics of two-stage progressive rate leaf spring, meet Vehicle Industry fast-developing, vehicle ride performance and Security and its design to high intensity two-stage progressive rate leaf spring and the requirement of characteristic Simulation, the design level of raising product, Quality and vehicle ride performance and security；Meanwhile, design and testing expenses can be also reduced, accelerate product development speed.

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 simulation calculation method of the flexibility characteristics of reliable high intensity two-stage progressive rate leaf spring, design flow diagram, as shown in Figure 1.Deng partially Each leaf spring of frequency two-stage progressive rate leaf spring uses high-strength steel sheet, and width is b, and elastic modelling quantity is E, each leaf spring in Symmetrical structure centered on heart bolt mounting hole, its install clamp away from half L₀For U-bolts clamp away from half L₀；High intensity The half symmetrical structure of two-stage progressive rate leaf spring is as shown in Fig. 2 by main spring 1, first order auxiliary spring 2 and the structure of second level auxiliary spring 3 Into, wherein, the piece number of main spring 1 is n, and the thickness of each of main spring is h_i, half action length is L_iT, half clamping length is L_i= L_iT-L₀/ 2, i=1,2 ..., n.The piece number of first order auxiliary spring 2 is m₁, the thickness that first order auxiliary spring is each is h_A1j, half effect Length is L_A1jT, half clamping length is L_A1j=L_AjT-L₀/ 2, j=1,2 ..., m₁.The piece number of second level auxiliary spring 3 is m₂, second The thickness of each of auxiliary spring of level is h_A2k, half action length is L_A2kT, half clamping length is L_A2k=L_A2kT-L₀/ 2, k=1, 2,…,m₂.First order gradual change gap between first upper surface of main spring tailpiece lower surface and first order auxiliary spring, in first order pair Second level gradual change gap between first upper surface of spring tailpiece lower surface and second level auxiliary spring.Main spring, first order auxiliary spring and second Level auxiliary spring is provided with initial tangential camber H_gM0、H_gA10And H_gA20, it is ensured that first order gradual change gap and second level gradual change gap meet the 1st It is secondary to start contact load, the 2nd beginning contact load and completely attach to gradual change offset frequency and the rated loads such as load, suspension the 2nd time It is left cotangent bank design requirement high.According to each structural parameters of leaf spring, elastic modelling quantity, rated load, main spring and at different levels Flexibility characteristics of the high intensity two-stage progressive rate leaf spring under different loads are carried out emulation meter by the initial tangential camber of auxiliary spring Calculate.

In order to solve the above technical problems, the flexibility characteristics of high intensity two-stage progressive rate leaf spring provided by the present invention is imitative True calculating method, it is characterised in that use following simulation calculation step：

(1) the initial curvature radius on the upper and lower surface in first order gradual change gap of high intensity two-stage progressive rate leaf spring is imitative It is true to calculate：

I steps：Main spring tailpiece lower surface initial curvature radius R_M0bCalculating

Initial tangential camber H according to main spring_gM0, the piece number n of main spring, the thickness h of each of main spring_i, i=1,2 ..., n are main The half clamping length L of first of spring₁, to main spring tailpiece lower surface initial curvature radius R_M0bSimulation calculation is carried out, i.e.,

II steps：First of first order auxiliary spring upper surface initial curvature radius R_A10aSimulation calculation

According to the first order auxiliary spring half clamping length L of first_A11, the initial tangential camber H of first order auxiliary spring_gA10, to First of one-level auxiliary spring upper surface initial curvature radius R_A10aEmulated, i.e.,

(2) the initial curvature radius on the upper and lower surface in second level gradual change gap of high intensity two-stage progressive rate leaf spring is imitative It is true to calculate：

Step A：First order auxiliary spring tailpiece lower surface initial curvature radius R_A10bSimulation calculation

Piece number m according to first order auxiliary spring₁, the thickness h that first order auxiliary spring is each_A1j, j=1,2 ... m₁, and step (1) R in II steps obtained by simulation calculation_A10a, to first order auxiliary spring tailpiece lower surface initial curvature radius R_A10bCarry out emulation meter Calculate, i.e.,

Step B：First of second level auxiliary spring upper surface initial curvature radius R_A20aSimulation calculation

According to the second level auxiliary spring half clamping length L of first_A21, the initial tangential camber H of second level auxiliary spring_gA20, to First upper table radius of curvature R of two grades of auxiliary springs_A20aSimulation calculation is carried out, i.e.,

(3) the 1st time of high intensity two-stage progressive rate leaf spring starts contact load P_k1Simulation calculation：

According to the width b of high intensity two-stage progressive rate leaf spring, elastic modulus E；The half of first of main spring clamps span length's degree L₁, the piece number n of main spring, the thickness h of each of main spring_i, i=1,2 ..., n, the R that simulation calculation is obtained in the I steps of step (1)_M0b, The R that simulation calculation is obtained in II steps_A10a, contact load P is started to the 1st time_k1Simulation calculation is carried out, i.e.,

In formula, h_MeIt is the equivalent thickness of main spring root lap,

(4) the 2nd time of high intensity two-stage progressive rate leaf spring starts contact load P_k2Simulation calculation：

According to the width b of high intensity two-stage leaf spring with gradually changing stiffness, elastic modulus E；The half of first main spring clamp across Length L₁；The piece number m of first order auxiliary spring₁, the thickness h that first order auxiliary spring is each_A1j, j=1,2 ..., m₁；Emulation meter in step (2) R obtained by calculating_A10bAnd R_A20a, resulting P in step (3)_k1And h_Me, to the 2nd beginning P_k2Simulation calculation is carried out, i.e.,

In formula, h_MA1eIt is main spring and the equivalent thickness of the root lap of first order auxiliary spring,

(5) the 2nd full contact load p of high intensity two-stage progressive rate leaf spring_w2Simulation calculation：

According to main spring and the compound clamping stiffness K of first order auxiliary spring_MA1, the total compound clamping stiffness K of major-minor spring_MA2, step (4) P that simulation calculation is obtained in_k2, to the 2nd full contact load p_w2Simulation calculation is carried out, i.e.,

(6) simulation calculation of flexibility characteristics of the high intensity two-stage progressive rate leaf spring under different loads：

Clamping stiffness K according to main spring_M, the compound clamping stiffness K of main spring and first order auxiliary spring_MA1, major-minor spring it is total compound Clamp stiffness K_MA2, rated load P_N, and the P that simulation calculation is obtained in step (3)~(5)_k1、P_k2And P_w2, reciprocity gradual change offset frequency Flexibility characteristics of the two-stage progressive rate leaf spring under different loads P carry out simulation calculation, i.e.,

The present invention has the advantage that than prior art

The restriction of key issue is calculated due to contact load simulation calculation and main spring amount of deflection, predecessor State is inside and outside not to be provided always The simulation calculation method of the flexibility characteristics of high intensity two-stage progressive rate leaf spring.The present invention can be according to each of main spring and the structure of auxiliary spring Parameter, elastic modelling quantity, rated load, main spring initial tangential camber, the first order and the initial camber design load of second level auxiliary spring, first Simulation calculation is carried out to contact load, then, on this basis, using amount of deflection analytical Calculation Mathematical Modeling, to high intensity two-stage The flexibility characteristics under different loads of progressive rate leaf spring carry out simulation calculation.By simulation calculation and prototype test, The simulation calculation method of the flexibility characteristics of high intensity two-stage progressive rate leaf spring provided by the present invention is correct, and it is accurate to can obtain The reliable amount of deflection simulation calculation value under specified load, is the checking of high intensity two-stage progressive rate leaf spring characteristic Simulation, there is provided Reliable technical foundation.The residue under contact load, initial tangential camber, the rated load of leaf spring is can ensure that using the method Tangent line camber and maximum spacing amount of deflection meet design requirement, improve product design level, quality and vehicle ride performance and Security；Meanwhile, design and testing expenses can be also reduced, accelerate 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 simulation calculation flow process figure of the flexibility characteristics of high intensity two-stage progressive rate leaf spring；

Fig. 2 is the half symmetrical structure schematic diagram of high intensity two-stage progressive rate leaf spring；

Fig. 3 is that the load deflexion characteristic of the high intensity two-stage progressive rate leaf spring obtained by the simulation calculation of embodiment is bent Line.

Specific embodiment

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

Embodiment：The width b=63mm of certain high intensity two-stage progressive rate leaf spring, U-bolts clamp away from half L₀= 50mm, elastic modulus E=200GPa.The total tablet number of major-minor spring is N=5, wherein, main reed number n=2 pieces, the thickness of each of main spring Degree h₁=h₂=8mm, the half action length of each of main spring is respectively L_1T=525mm, L_2T=450mm；Half clamping length point Wei not L₁=L_1T-L₀/ 2=500mm, L₂=L_2T-L₀/ 2=425mm；The initial tangential camber H of main spring_gM0=112.2mm.First The piece number m of level auxiliary spring₁=1, thickness h_A11=11mm, half action length is L_A11T=360mm, half clamping length L_A11= L_A11T-L₀/ 2=335mm；The initial tangential camber H of first order auxiliary spring_gA10=22.8mm.The piece number m of second level auxiliary spring₂=2, The thickness h that second level auxiliary spring is each_A21=h_A22=11mm, half action length L_A21T=250mm, L_A22T=155mm；Half is pressed from both sides Tight length L_A21=L_A21T-L₀/ 2=225mm, L_A22=L_A22T-L₀/ 2=130mm, the initial tangential camber H of second level auxiliary spring_gA20 =4.4mm.Rated load P_N=7227N, the main spring residue tangent line camber design requirement value H under rated load_gMsy= 26.1mm.Main spring clamps stiffness K_MThe compound clamping stiffness K of=51.44N/mm, main spring and first order auxiliary spring_MA1=112.56N/ Mm, the total compound of major-minor spring clamps stiffness K_MA2=181.86N/mm.According to each structural parameters of leaf spring, elastic modelling quantity is specified The initial tangential camber of load, main spring and auxiliary spring at different levels, to high intensity two-stage progressive rate leaf spring the scratching under different loads Degree characteristic carries out simulation calculation.

The simulation calculation method of the flexibility characteristics of the high intensity two-stage progressive rate leaf spring that present example is provided, its emulation Calculation process is as shown in figure 1, specific simulation calculation step is as follows：

(1) the initial curvature radius on the upper and lower surface in first order gradual change gap of high intensity two-stage progressive rate leaf spring is imitative It is true to calculate：

I steps：Main spring tailpiece lower surface initial curvature radius R_M0bSimulation calculation

According to main spring initial tangential camber H_gM0=112.2mm, the piece number n=2 of main spring, the thickness h of each of main spring₁=h₂= 8mm, the half clamping length L of first of main spring₁=500mm, to main spring tailpiece lower surface initial curvature radius R_M0bCarry out emulation meter Calculate, i.e.,

II steps：First of first order auxiliary spring upper surface initial curvature radius R_A10aSimulation calculation

According to the first order auxiliary spring half clamping length L of first_A11=335mm, first order auxiliary spring initial tangential camber H_gA10 =22.8mm, to first of first order auxiliary spring upper surface initial curvature radius R_A10aSimulation calculation is carried out, i.e.,

(2) the initial curvature radius on the upper and lower surface in second level gradual change gap of high intensity two-stage progressive rate leaf spring is imitative It is true to calculate：

Step A：First order auxiliary spring tailpiece lower surface initial curvature radius R_A10bSimulation calculation

Piece number m according to first order auxiliary spring₁=1, thickness h_A11Simulation calculation institute in=13mm, and the II steps of step (1) The R for obtaining_A10a=2786.1mm, to first order auxiliary spring tailpiece lower surface initial curvature radius R_A10bSimulation calculation is carried out, i.e.,

R_A10b=R_A10a+h_A11=2483.5mm；

Step B：First of second level auxiliary spring upper surface initial curvature radius R_A20aSimulation calculation

According to the second level auxiliary spring half clamping length L of first_A21=L₄=225mm, the initial tangential arc of second level auxiliary spring H high_gA20=4.4mm, to first upper table radius of curvature R of second level auxiliary spring_A20aSimulation calculation is carried out, i.e.,

(3) the 1st time of high intensity two-stage progressive rate leaf spring starts contact load P_k1Simulation calculation：

According to the width b=63mm of high intensity two-stage progressive rate leaf spring, elastic modulus E=200GPa；First of main spring Half clamps span length's degree L₁=500mm, the piece number n=2 of main spring, the thickness h of each of main spring₁=h₂=8mm, the I steps of step (1) The R that simulation calculation is obtained in rapid_M0bThe R that simulation calculation is obtained in=1186mm, II step_A10a=2472.5mm, opens the 1st time Beginning contact load P_k1Simulation calculation is carried out, i.e.,

In formula, h_MeIt is the equivalent thickness of main spring root lap,

(4) the 2nd time of high intensity two-stage progressive rate leaf spring starts contact load P_k2Simulation calculation：

According to the width b=63mm of high intensity two-stage leaf spring with gradually changing stiffness, elastic modulus E=200Gpa；First master The half of spring clamps span length's degree L₁=500mm；The piece number m of first order auxiliary spring₁=1, thickness h_A11Calculated in=11mm, step (2) Resulting R_A10b=2483.5mm and R_A20a=5755mm, resulting P in step (3)_k1=1886.3N and h_Me= 10.1mm, contact load P is started to the 2nd time_k2Simulation calculation is carried out, i.e.,

In formula, h_MA1eIt is main spring and the equivalent thickness of the root lap of first order auxiliary spring,(5) the 2nd full contact load p of high intensity two-stage progressive rate leaf spring_w2Emulation Calculate：

According to main spring and the compound clamping stiffness K of first order auxiliary spring_MA1=112.56N/mm, the total compound of major-minor spring is clamped Stiffness K_MA2=181.86N/mm, the P that simulation calculation is obtained in step (4)_k2=4150.3N, to the 2nd full contact load p_w2 Simulation calculation is carried out, i.e.,

Compared with design requirement value and prototype test test value by simulation calculation value, the 1st time start contact load, Start contact load P 2nd time_k2With the 2nd full contact load p_w2Checking computations value be respectively P_k1=1886.3N, P_k2= 4150.3N、P_w2=6705.7N, with former contact load design load P_k1=1888N, P_k2=4133N, P_w2=6678N matches, absolutely - 1.7N ,+17.3N ,+27.7N are respectively to deviation, the major-minor spring camber of the high intensity two-stage progressive rate leaf spring are illustrated and is connect Tactile load is reliable, meets the design requirement of the gradual change such as suspension offset frequency and contact load.

(6) simulation calculation of flexibility characteristics of the high intensity two-stage progressive rate leaf spring under different loads：

Stiffness K is clamped according to main spring_MThe compound clamping stiffness K of=51.44N/mm, main spring and first order auxiliary spring_MA1= 112.56N/mm, the total compound of major-minor spring clamps stiffness K_MA2=181.86N/mm, rated load P_N=7227N, step (3)~ The P that simulation calculation is obtained in step (5)_k1=1886.3N, P_k2=4150.3N and P_w2=6705.7N, to the high intensity two-stage gradually Flexibility characteristics of the variation rigidity leaf spring under different loads carry out simulation calculation, i.e.,

Using Matlab calculation procedures, the load deflexion of the high intensity two-stage progressive rate leaf spring obtained by simulation calculation Characteristic curve, as shown in figure 3, wherein, in P_k1Main spring amount of deflection f under=1886.3N_Mk1=36.7mm, in P_k2Under=4150.3N Main spring amount of deflection f_Mk2=65.6mm, in P_w2Main spring amount of deflection f under=6705.7N_Mw2=83.3mm, in P_NMaster under=7227N Spring amount of deflection f_MN=86.1mm.By the initial tangential camber H of the main spring_gM0=112.2mm, and main spring amount of deflection simulation calculation value f_MN= 86.1mm, it is known that, the design that the high intensity two-stage progressive rate leaf spring meets the main spring residue tangent line camber under rated load will Evaluation H_gMsy=H_gM0-f_MN=26.1mm, meets design requirement.

Verified by model machine load deflection experimental test, high intensity two-stage progressive rate leaf spring provided by the present invention The simulation calculation method of flexibility characteristics be correct, amount of deflection simulation calculation value and experimental test validation value phase under specified load It coincide, for the flexibility characteristics emulation of high intensity two-stage progressive rate leaf spring provides reliable technical method.Can using the method Ensure that the remaining tangent line camber under contact load, initial tangential camber, the rated load of leaf spring and maximum spacing amount of deflection meet to set Meter requirement, improves design level, quality and vehicle ride performance and the security of product；Meanwhile, reduce design and test fee With quickening product development speed.

Claims (1)

1. the simulation calculation method of the flexibility characteristics of high intensity two-stage progressive rate leaf spring, wherein, leaf spring uses high-strength steel sheet, respectively Piece leaf spring be with center mounting hole symmetrical structure, install clamp away from half for U-bolts clamp away from half；Leaf spring by Main spring and two-stage auxiliary spring are constituted, by the initial tangential camber and two-stage gradual change gap of main spring and two-stage auxiliary spring, it is ensured that leaf spring is full Sufficient contact load, progressive rate and suspension offset frequency keep constant requirement, that is, wait gradual change offset frequency type high intensity two-stage progressive rate Leaf spring；According to each structural parameters of leaf spring, elastic modelling quantity, rated load, the initial tangential camber of main spring and auxiliary spring at different levels, On the basis of contact load simulation calculation, flexibility characteristics of the high intensity two-stage progressive rate leaf spring under different loads are imitated True to calculate, specific simulation calculation step is as follows：

(1) the emulation meter of the initial curvature radius on the upper and lower surface in first order gradual change gap of high intensity two-stage progressive rate leaf spring Calculate：

I steps：Main spring tailpiece lower surface initial curvature radius R_M0bCalculating

Initial tangential camber H according to main spring_gM0, the piece number n of main spring, the thickness h of each of main spring_i, i=1,2 ..., n, main spring head The half clamping length L of piece₁, to main spring tailpiece lower surface initial curvature radius R_M0bSimulation calculation is carried out, i.e.,

$R_{M0b}=\frac{{L_1}^2+H_{gM0}^2}{2H_{gM0}}+\underset{i=1}{\overset{n}{\Σ}}{h}_i;$

II steps：First of first order auxiliary spring upper surface initial curvature radius R_A10aSimulation calculation

According to the first order auxiliary spring half clamping length L of first_A11, the initial tangential camber H of first order auxiliary spring_gA10, to the first order First of auxiliary spring upper surface initial curvature radius R_A10aEmulated, i.e.,

$R_{A10a}=\frac{L_{A11}^2+H_{gA10}^2}{2H_{gA10}};$

(2) the emulation meter of the initial curvature radius on the upper and lower surface in second level gradual change gap of high intensity two-stage progressive rate leaf spring Calculate：

Step A：First order auxiliary spring tailpiece lower surface initial curvature radius R_A10bSimulation calculation

Piece number m according to first order auxiliary spring₁, the thickness h that first order auxiliary spring is each_A1j, j=1,2 ... m₁, and step (1) II step R in rapid obtained by simulation calculation_A10a, to first order auxiliary spring tailpiece lower surface initial curvature radius R_A10bSimulation calculation is carried out, i.e.,

$R_{A10b}=R_{A10a}+\underset{j=1}{\overset{m_1}{\Σ}}{h}_{A1j};$

Step B：First of second level auxiliary spring upper surface initial curvature radius R_A20aSimulation calculation

According to the second level auxiliary spring half clamping length L of first_A21, the initial tangential camber H of second level auxiliary spring_gA20, to the second level First upper table radius of curvature R of auxiliary spring_A20aSimulation calculation is carried out, i.e.,

$R_{A20a}=\frac{L_{A21}^2+H_{gA20}^2}{2H_{gA20}};$

(3) the 1st time of high intensity two-stage progressive rate leaf spring starts contact load P_k1Simulation calculation：

According to the width b of high intensity two-stage progressive rate leaf spring, elastic modulus E；The half of first of main spring clamps span length's degree L₁, it is main The piece number n of spring, the thickness h of each of main spring_i, i=1,2 ..., n, the R that simulation calculation is obtained in the I steps of step (1)_M0b, II steps The R that simulation calculation is obtained in rapid_A10a, contact load P is started to the 1st time_k1Simulation calculation is carried out, i.e.,

$P_{k1}=\frac{{\mathrm{Ebh}}_{Me}^3(R_{A10a}-R_{M0b})}{6L_1{R}_{M0b}{R}_{A10a}};$

In formula, h_MeIt is the equivalent thickness of main spring root lap,

(4) the 2nd time of high intensity two-stage progressive rate leaf spring starts contact load P_k2Simulation calculation：

According to the width b of high intensity two-stage leaf spring with gradually changing stiffness, elastic modulus E；The first half of main spring clamps span length's degree L₁；The piece number m of first order auxiliary spring₁, the thickness h that first order auxiliary spring is each_A1j, j=1,2 ..., m₁；Simulation calculation institute in step (2) The R for obtaining_A10bAnd R_A20a, resulting P in step (3)_k1And h_Me, to the 2nd beginning P_k2Simulation calculation is carried out, i.e.,

$P_{k2}=P_{k1}+\frac{{\mathrm{Ebh}}_{MA1e}^3(R_{A20a}-R_{A10b})}{6L_1{R}_{A10b}{R}_{A20a}};$

In formula, h_MA1eIt is main spring and the equivalent thickness of the root lap of first order auxiliary spring,

(5) the 2nd full contact load p of high intensity two-stage progressive rate leaf spring_w2Simulation calculation：

According to main spring and the compound clamping stiffness K of first order auxiliary spring_MA1, the total compound clamping stiffness K of major-minor spring_MA2, in step (4) The P that simulation calculation is obtained_k2, to the 2nd full contact load p_w2Simulation calculation is carried out, i.e.,

$P_{w2}=P_{k2}\frac{K_{MA2}}{K_{MA1}};$

(6) simulation calculation of flexibility characteristics of the high intensity two-stage progressive rate leaf spring under different loads：

Clamping stiffness K according to main spring_M, the compound clamping stiffness K of main spring and first order auxiliary spring_MA1, the total compound clamping of major-minor spring Stiffness K_MA2, rated load P_N, and the P that simulation calculation is obtained in step (3)~(5)_k1、P_k2And P_w2, reciprocity gradual change offset frequency two-stage Flexibility characteristics of the progressive rate leaf spring under different loads P carry out simulation calculation, i.e.,

$f_M=\left\{\begin{array}{cc}\frac{P}{K_M},& 0\&le;P<P_{k1}\\ \frac{P_{k1}}{K_M}+\frac{P_{k1}}{K_M}\ln \left(\frac{P}{P_{k1}}\right),& P_{k1}\&le;P<P_{k2}\\ \frac{P_{k1}}{K_M}+\frac{P_{k1}}{K_M}\ln \left(\frac{P_{k2}}{K_{k1}}\right)+\frac{P_{k2}}{K_{MA1}}\ln \left(\frac{P}{P_{k2}}\right),& P_{k2}\&le;P<P_{w2}\\ \frac{P_{k1}}{K_M}+\frac{P_{k1}}{K_M}\ln \left(\frac{P_{k2}}{P_{k1}}\right)+\frac{P_{k2}}{K_{MA1}}\ln \left(\frac{P_{w2}}{P_{k2}}\right)+\frac{P-P_{w2}}{K_{MA2}},& P_{k2}\&le;P\&le;P_N\end{array}\right..$