CN106838088A - The method for designing of high intensity three-level progressive rate leaf spring auxiliary spring tangent line camber at different levels - Google Patents

Abstract

The present invention relates to the method for designing of high intensity three-level progressive rate leaf spring auxiliary spring tangent line camber at different levels, belong to vehicle suspension leaf spring technical field.Can be according to each structural parameters of leaf spring, elastic modelling quantity, main spring clamps rigidity, the compound clamping rigidity of main spring and auxiliary springs at different levels, rated load and it is left cotangent bank high request value in rated load, high intensity three-level progressive rate leaf spring auxiliary spring initial tangential camber at different levels is designed.By prototype test, auxiliary spring initial tangential camber design loads at different levels are reliable, show that the method for designing of provided high intensity three-level progressive rate leaf spring auxiliary spring tangent line camber at different levels is correct, be that reliable technical foundation has been established in the design of high intensity three-level progressive rate leaf spring.Product design level, quality and performance can be improved using the method, it is ensured that meet the design requirement of three-level gradual change gap and suspension offset frequency, improve vehicle ride performance and security；Meanwhile, design and testing expenses are reduced, accelerate product development speed.

Description

The method for designing of high intensity three-level progressive rate leaf spring auxiliary spring tangent line camber at different levels

Technical field

The present invention relates to vehicle suspension leaf spring, particularly high intensity three-level progressive rate leaf spring auxiliary spring tangent line camber at different levels Method for designing.

Background technology

With the appearance of high strength steel plate material, high intensity three-level progressive rate leaf spring can be used, so as to meet in difference Suspension progressive rate and suspension offset frequency under load keep constant design requirement, further improve vehicle ride performance, its In, the initial tangential camber of auxiliary springs at different levels not only influences the three-level gradual change gap of high intensity three-level progressive rate leaf spring, contact to carry Lotus, gradual change contact stiffness, suspension offset frequency and vehicle ride performance, and influence maximum Root Stress, the specified load of major-minor spring Remaining tangent line camber and vehicle safety under lotus.The initial tangential camber of auxiliary springs at different levels is by main spring initial tangential camber Determined with each contact load required by design.Because the amount of deflection of high intensity three-level gradual change leaf spring calculates extremely complex, Structure and load not only with main spring and auxiliary spring at different levels is relevant, but also relevant with contact load size, therefore, according to being consulted reference materials Understand, not yet provide the design side of reliable high intensity three-level progressive rate leaf spring auxiliary spring tangent line camber at different levels both at home and abroad at present Method.With Vehicle Speed and its continuous improvement to ride comfort requirement, higher wanting is proposed to vehicle suspension system design Ask, therefore, it is necessary to set up a kind of accurate, reliable high intensity three-level progressive rate leaf spring auxiliary spring tangent line camber at different levels design side Method, is improved constantly and to high intensity three-level transition slab with meeting fast-developing Vehicle Industry, vehicle ride performance and security The design requirement of spring, it is ensured that leaf spring three-level gradual change gap, contact load and maximum spacing amount of deflection meet design requirement, improves product Design level, performance and quality and vehicle ride performance and security；Meanwhile, design and testing expenses are reduced, accelerate to produce Product development rate.

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 method for designing of reliable high intensity three-level progressive rate leaf spring auxiliary spring tangent line camber at different levels, its design cycle is as shown in Figure 1.It is high The half symmetrical structure of intensity three-level progressive rate leaf spring is as shown in Fig. 2 be by main spring 1, first order auxiliary spring 2 and second level auxiliary spring 3 and third level auxiliary spring 4 constituted, the half effect of the main spring of piece headed by the half total span of high intensity three-level progressive rate leaf spring Length L_1T, U-bolts clamp away from half be L₀, the width of leaf spring is b, and elastic modelling quantity is E.The piece number of main spring 1 is n, Wherein, the thickness of each of main spring is h_i, half action length L_iT, half clamping length L_i=L_iT-L₀/ 2, i=1,2 ..., n.The The piece number of one-level auxiliary spring 2 is n₁, the thickness that first order auxiliary spring is each is h_A1j, half action length L_A1jT, half clamping length L_A1j =L_A1jT-L₀/ 2, j=1,2 ..., n₁.The piece number of second level auxiliary spring 3 is n₂, the thickness that second level auxiliary spring is each is h_A2k, half Action length L_A2kT, half clamping length L_A2k=L_A2kT-L₀/ 2, k=1,2 ..., n₂.The piece number of third level auxiliary spring 4 is n₃, the 3rd The thickness of each of auxiliary spring of level is h_A3l, half action length L_A3lT, half clamping length L_A3l=L_A3lT-L₀/ 2, l=1,2 ..., n₃.The total tablet number N=n+n of high intensity three-level progressive rate leaf spring₁+n₂+n₃, three-level gradual change is provided between main spring and auxiliary spring at different levels Gap delta_MA1、δ_A12And δ_A23, i.e., it is provided with first-order gradient gap between first upper surface of the main spring lower surface of tailpiece and first order auxiliary spring δ_MA1；First order auxiliary spring tailpiece lower surface and second level auxiliary spring are provided with two grades of gradual change gap deltas between first upper surface_A12；The second level Auxiliary spring tailpiece lower surface and third level auxiliary spring are provided with three-level gradual change gap delta between first upper surface_A23.By main spring and pair at different levels Spring initial tangential camber and three-level gradual change gap, with meet leaf spring with gradually changing stiffness each contact load and progressive rate and The design requirement of suspension offset frequency.According to each structural parameters of leaf spring, elastic modelling quantity, main spring clamps rigidity and main spring and pairs at different levels The compound clamping rigidity of spring, each contact load, main spring residue tangent line camber design requirement under rated load, and rated load High intensity three-level progressive rate leaf spring auxiliary spring tangent line camber at different levels on the basis of the determination of main spring initial tangential camber, are entered by value Row design.

In order to solve the above technical problems, high intensity three-level progressive rate leaf spring auxiliary spring tangent line arcs at different levels provided by the present invention Method for designing high, it is characterised in that use following design procedure：

(1) the main spring of high intensity three-level progressive rate leaf spring and its lap equivalent thickness calculating with auxiliary springs at different levels：

Piece number n according to main spring, the thickness h of each of main spring_i, i=1,2 ..., n；The piece number n of first order auxiliary spring₁, the first order The thickness h that auxiliary spring is each_A1j, j=1,2 ..., n₁；The piece number n of second level auxiliary spring₂, the thickness h that second level auxiliary spring is each_A2k, k= 1,2,…,n₂；The piece number n of third level auxiliary spring₃, the thickness h that third level auxiliary spring is each_A3l, l=1,2 ..., n₃；To main spring overlapping portion Effect of grading thickness h_MeAnd the lap equivalent thickness h of main spring and the first order, the second level and third level auxiliary spring_MA1e、h_MA2eAnd h_MA3e It is respectively calculated, i.e.,

(2) the main spring initial tangential camber H of high intensity three-level progressive rate leaf spring_gM0Determination：

Stiffness K is clamped according to main spring_M, the compound clamping stiffness K of main spring and three-level auxiliary spring_MA1、K_MA2And K_MA3；1st beginning Contact load P_k1, the 2nd beginning contact load P_k2, the 3rd beginning contact load P_k3With the 3rd full contact load p_w3；It is specified Load p_NAnd the remaining tangent line camber H under rated load_gMsy, to the main spring initial tangential of high intensity three-level progressive rate leaf spring Camber H_gM0It is determined, i.e.,

(3) first order auxiliary spring tangent line camber H of high intensity three-level progressive rate leaf spring_gA10Design：

I steps：Main spring tailpiece lower surface initial curvature radius R_M0bCalculate

Piece number n according to main spring, the thickness h of each of main spring_i；The half clamping length L of first of main spring₁, institute in step (2) The H of determination_gM0, to main spring tailpiece lower surface initial curvature radius R_M0bCalculated, i.e.,

II steps：First radius of curvature R of upper surface of first order auxiliary spring_A10aCalculate

According to the width b of high intensity three-level progressive rate leaf spring, elastic modulus E；The first half clamping length L of main spring₁, Start contact load P 1st time_k1, the h being calculated in step (1)_Me, and the R being calculated in I steps_M0b, to first order pair First of spring upper surface initial curvature radius R_A10aCalculated, i.e.,

III steps：First order auxiliary spring initial tangential camber H_gA10Design

According to the first order auxiliary spring half clamping length L of first_A11, the R being calculated in II steps_A10a, to first order pair The initial tangential camber H of spring_gA10It is designed, i.e.,

(4) second level auxiliary spring initial tangential camber H of high intensity three-level progressive rate leaf spring_gA20Design：

A steps：First order auxiliary spring tailpiece lower surface initial curvature radius R_A10bCalculate

Piece number n according to first order auxiliary spring₁, the thickness h that first order auxiliary spring is each_A1j, j=1,2 ..., n₁, in step (3) The R being calculated_A10a, to first order auxiliary spring tailpiece lower surface initial curvature radius R_A10bCalculated, i.e.,

B step：First of second level auxiliary spring upper surface initial curvature radius R_A20aCalculating

According to the width b of high intensity three-level progressive rate leaf spring, elastic modulus E；The first half clamping length L of main spring₁, Start contact load P 1st time_k1, the 2nd beginning contact load P_k2, the h being calculated in step (1)_MA1e, and calculating in a steps The R for obtaining_A10b, to first of second level auxiliary spring upper surface initial curvature radius R_A20aCalculated, i.e.,

Step c：Second level auxiliary spring initial tangential camber H_gA20Design

According to the second level auxiliary spring half clamping length L of first_A21, the R being calculated in b step_A20a, to second level pair Spring initial tangential camber H_gA20It is designed, i.e.,

(5) third level auxiliary spring initial tangential camber H of high intensity three-level progressive rate leaf spring_gA30Design：

Step A：Second level auxiliary spring tailpiece lower surface initial curvature radius R_A20bCalculate

Piece number n according to second level auxiliary spring₂, the thickness h that second level auxiliary spring is each_A2k, k=1,2 ..., n₂, in step (4) The R being calculated_A20a, to second level auxiliary spring tailpiece lower surface initial curvature radius R_A20bCalculated, i.e.,

Step B：First of third level auxiliary spring upper surface initial curvature radius R_A30aCalculating

According to the width b of high intensity three-level progressive rate leaf spring, elastic modulus E；The first half clamping length L of main spring₁, Start contact load P 2nd time_k2, the 3rd beginning contact load P_k3, the h being calculated in step (1)_MA2e, and calculating in step A The R for obtaining_A20b, to first of third level auxiliary spring upper surface initial curvature radius R_A30aCalculated, i.e.,

Step C：Third level auxiliary spring initial tangential camber H_gA30Design

According to the third level auxiliary spring half clamping length L of first_A31, the R being calculated in step B_A30a, to third level pair Spring initial tangential camber H_gA30It is designed, i.e.,

The present invention has the advantage that than prior art

Because the amount of deflection of high intensity three-level gradual change leaf spring calculates extremely complex, understood according to consulting reference materials, one inside and outside predecessor State The straight method for designing for not providing high intensity three-level progressive rate leaf spring auxiliary spring tangent line camber at different levels.The present invention can be according to high intensity three Each of the main spring of level progressive rate leaf spring and the structural parameters of auxiliary spring, elastic modelling quantity, main spring clamp rigidity, main spring and auxiliary springs at different levels Compound clamping rigidity, each contact load, rated load and the remaining tangent line camber design requirement value under rated load, On the basis of main spring initial tangential camber determines, in the initial tangential camber to high intensity three-level progressive rate leaf spring auxiliary springs at different levels It is designed.Tested by prototype test, high intensity three-level progressive rate leaf spring provided by the present invention auxiliary springs at different levels are cut Bank method for designing high is correct, is that reliable technical foundation has been established in the design of high intensity three-level progressive rate leaf spring.Profit Product design level, quality and performance can be improved with the method, it is ensured that the design for meeting three-level gradual change gap and suspension offset frequency will Ask, improve vehicle ride performance and security；Meanwhile, design and testing expenses are 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 design flow diagram of high intensity three-level progressive rate leaf spring auxiliary spring tangent line camber at different levels；

Fig. 2 is the half symmetrical structure schematic diagram of high intensity three-level gradual change leaf spring；

Fig. 3 is the first order, the first half symmetrical structure in the second level and third level auxiliary spring obtained by the calculating of embodiment Initial surface pattern curve f_A1x、f_A2xAnd f_A3x。

Specific embodiment

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

Embodiment：The width b=63mm of certain high intensity three-level leaf spring with gradually changing stiffness, U-bolts clamp away from half L₀=50mm, elastic modulus E=200GPa.The total tablet number N=5 of major-minor spring, wherein, the piece number n=2 of main spring, each of main spring Thickness h₁=h₂=8mm；The half action length of each of main spring is respectively L_1T=525mm, L_2T=450mm；Half clamping length Respectively L₁=L_1T-L₀/ 2=500mm, L₂=L_2T-L₀/ 2=425mm.The piece number n of first order auxiliary spring₁=1, thickness h_A11= 8mm, half action length is L_A11T=350mm, half clamping length is L_A11=L₃=L_A11T-L₀/ 2=325mm.Second level pair The piece number n of spring₂=1, thickness h_A21=13mm, half action length is L_A21T=250mm, half clamping length is L_A21=L₄= L_A21T-L₀/ 2=225mm.The piece number n of third level auxiliary spring₃=1, thickness h_A31=13mm, half action length is L_A31T= 150mm, half clamping length is L_A31=L₅=L_A31T-L₀/ 2=125mm.Main spring clamps stiffness K_M=51.44N/mm, main spring with The compound clamping rigidity of first order level auxiliary spring, second level auxiliary spring and third level auxiliary spring is respectively K_MA1=75.41N/mm, K_MA2= 144.46N/mm and K_MA3=172.9N/mm.Start contact load P 1st time_k1=1966N, the 2nd beginning contact load P_k2= 2882N, the 3rd beginning contact load P_k3=5522N, the 3rd full contact load p_w3=6609N.Rated load P_N= 7227N, and the main spring residue tangent line camber required value H under rated load_gMsy=26mm.According to each structure ginseng of leaf spring The compound clamping rigidity of number, elastic modelling quantity, main spring clamping rigidity and main spring and auxiliary springs at different levels, each contact load, rated load, And main spring residue tangent line camber design requirement value under rated load, on the basis of the determination of main spring initial tangential camber, to the height Intensity three-level progressive rate leaf spring auxiliary spring tangent line camber at different levels are designed.

The method for designing of the high intensity three-level progressive rate leaf spring auxiliary spring tangent line camber at different levels that present example is provided, its Design cycle is as shown in figure 1, specific design step is as follows：

(1) the main spring of high intensity three-level progressive rate leaf spring and its with the root lap equivalent thickness of auxiliary springs at different levels Calculate：

Piece number n=2 according to main spring, the thickness h of each of main spring₁=h₂=8mm；First order auxiliary spring piece number n₁=1, thickness h_A11=8mm；Second level auxiliary spring piece number n₂=1, thickness h_A21=13mm；Third level auxiliary spring piece number n₃=1, thickness h_A31=13mm, To main spring root lap equivalent thickness h_Me, and main spring and first order auxiliary spring, second level auxiliary spring and third level auxiliary spring root Lap equivalent thickness h_MA1e、h_MA2eAnd h_MA3eIt is respectively calculated, i.e.,

(2) the main spring initial tangential camber H of high intensity three-level progressive rate leaf spring_gM0Determination：

Stiffness K is clamped according to main spring_M=51.44N/mm, main spring and first order level auxiliary spring, second level auxiliary spring and third level pair The compound clamping stiffness K of spring_MA1=75.41N/mm, K_MA2=144.46N/mm and K_MA3=172.9N/mm；Start contact for 1st time Load p_k1=1966N, the 2nd beginning contact load P_k2=2882N, the 3rd beginning contact load P_k3=5522N and the 3rd time complete Full connected load p_w3=6609N；Rated load P_N=the 7227N and remaining tangent line camber H under rated load_gMsy=26mm, To the main spring initial tangential camber H of the high intensity three-level progressive rate leaf spring_gM0It is determined, i.e.,

(3) first order auxiliary spring tangent line camber H of high intensity three-level progressive rate leaf spring_gA10Design：

I steps：Main spring tailpiece lower surface initial curvature radius R_M0bCalculate

Piece number n=2 according to main spring, the thickness h of each of main spring₁=h₂=8mm；The first half clamping length L of main spring₁ =500mm, identified H in step (2)_gM0=114.1mm, to main spring tailpiece lower surface initial curvature radius R_M0bCounted Calculate, i.e.,

II steps：First of first order auxiliary spring upper surface initial curvature radius R_A10aCalculate

According to the width b=63mm of high intensity three-level progressive rate leaf spring, elastic modulus E=200GPa；First main spring Half clamping length L₁=500mm, the 1st beginning contact load P_k1=1966N, the h being calculated in step (1)_Me= The R being calculated in 10.1mm, and I steps_M0b=1168.6mm, to first upper surface initial curvature radius of first order auxiliary spring R_A10aCalculated, i.e.,

III steps：First order auxiliary spring initial tangential camber H_gA10Design

According to the first order auxiliary spring half clamping length L of first_A11The R being calculated in=325mm, II step_A10a= 2508.9mm, to the initial tangential camber H of first order auxiliary spring_gA10It is designed, i.e.,

(4) second level auxiliary spring initial tangential camber H of high intensity three-level progressive rate leaf spring_gA20Design

A steps：First order auxiliary spring tailpiece lower surface initial curvature radius R_A10bCalculate

Piece number n according to first order auxiliary spring₁=1, thickness h_A11=8mm, the R being calculated in the II steps of step (3)_A10a =2508.9mm, to first order auxiliary spring tailpiece lower surface initial curvature radius R_A10bCalculated, i.e.,

B step：First of second level auxiliary spring upper surface initial curvature radius R_A20aCalculating

According to the width b=63mm of high intensity three-level progressive rate leaf spring, elastic modulus E=200GPa；First main spring Half clamping length L₁=500mm, the 1st beginning contact load P_k1=1966N, the 2nd beginning contact load P_k2=2882N, The h being calculated in step (1)_MA1eThe R being calculated in=11.5mm, and a steps_A10b=2516.9mm, to second level auxiliary spring First upper surface initial curvature radius R_A20aCalculated, i.e.,

Step c：Second level auxiliary spring initial tangential camber H_gA20Design

According to the second level auxiliary spring half clamping length L of first_A21=225mm, the R being calculated in b step_A20a= 3918.1mm, to second level auxiliary spring initial tangential camber H_gA20It is designed, i.e.,

(5) third level auxiliary spring initial tangential camber H of high intensity three-level progressive rate leaf spring_gA30Design

Step A：Second level auxiliary spring tailpiece lower surface initial curvature radius R_A20bCalculate

Piece number n according to second level auxiliary spring₂=1, thickness h_A21=13mm, the R being calculated in the b step of step (4)_A20a =3918.1mm, to second level auxiliary spring tailpiece lower surface initial curvature radius R_A20bCalculated, i.e.,

Step B：First of third level auxiliary spring upper surface initial curvature radius R_A30aCalculating

According to the width b=63mm of high intensity three-level progressive rate leaf spring, elastic modulus E=200GPa；First main spring Half clamping length L₁=500mm, the 2nd beginning contact load P_k2=2882N, the 3rd beginning contact load P_k3=5522N, The h being calculated in step (1)_MA2eThe R being calculated in=11.5mm, and step A_A20b=3931.1mm, to third level auxiliary spring First upper surface initial curvature radius R_A30aCalculated, i.e.,

Step C：Third level auxiliary spring initial tangential camber H_gA30Design

According to the third level auxiliary spring half clamping length L of first_A31=125mm, the R being calculated in step B_A30a= 11621.7mm, to third level auxiliary spring initial tangential camber H_gA30It is designed, i.e.,

Auxiliary springs at different levels obtained by the main spring initial tangential camber of the high intensity three-level progressive rate leaf spring and design just Beginning tangent line camber design load, is shown in Table 1.

The main spring initial tangential camber of the table 1 high intensity three-level leaf spring with gradually changing stiffness and the initial tangential of auxiliary spring at different levels Camber design load

				114.1	21.1	6.5	0.67

Using Matlab calculation procedures, the first order, second of the high intensity three-level progressive rate leaf spring obtained by calculating The initial surface pattern curve f of level and first hemihedrism clamping structure of third level auxiliary spring_A1x、f_A2xAnd f_A3x, as shown in Figure 3.

Tested by model machine load deflection, designed auxiliary spring initial tangential camber at different levels meet high intensity three-level gradually Become each contact load, progressive rate, a suspension offset frequency and the remaining tangent line camber design requirement under rated load of leaf spring Value.

Claims (1)

1. the method for designing of high intensity three-level progressive rate leaf spring auxiliary spring tangent line camber at different levels, wherein, leaf spring uses high strength steel Plate, each leaf spring with center mounting hole symmetrical structure, install clamp away from half for U-bolts clamp away from half；Leaf spring It is made up of main spring and three-level auxiliary spring, by the initial tangential camber and three-level gradual change gap of main spring and three-level auxiliary spring, it is ensured that meet The design requirement of leaf spring contact load, progressive rate, suspension offset frequency and vehicle ride performance, i.e. high intensity three-level progressive rate Leaf spring；According to each structural parameters of leaf spring, elastic modelling quantity, main spring clamps rigidity and main spring is firm with the compound clamping of auxiliary springs at different levels Degree, each contact load, rated load and the remaining tangent line camber under rated load, determine in main spring initial tangential camber On the basis of, high intensity three-level progressive rate leaf spring auxiliary spring tangent line camber at different levels are designed, specific design step is as follows：

(1) the main spring of high intensity three-level progressive rate leaf spring and its lap equivalent thickness calculating with auxiliary springs at different levels：

Piece number n according to main spring, the thickness h of each of main spring_i, i=1,2 ..., n；The piece number n of first order auxiliary spring₁, first order auxiliary spring The thickness h of each_A1j, j=1,2 ..., n₁；The piece number n of second level auxiliary spring₂, the thickness h that second level auxiliary spring is each_A2k, k=1, 2,…,n₂；The piece number n of third level auxiliary spring₃, the thickness h that third level auxiliary spring is each_A3l, l=1,2 ..., n₃；To main spring lap Equivalent thickness h_MeAnd the lap equivalent thickness h of main spring and the first order, the second level and third level auxiliary spring_MA1e、h_MA2eAnd h_MA3ePoint Do not calculated, i.e.,

$h_{Me}=\sqrt[3]{\underset{i=1}{\overset{n}{\Σ}}{h}_i^3};$

$h_{MA1e}=\sqrt[3]{h_{Me}^3+\underset{j=1}{\overset{n_1}{\Σ}}{h}_{A1j}^3};$

$h_{MA2e}=\sqrt[3]{h_{MA1e}^3+\underset{k=1}{\overset{n_2}{\Σ}}{h}_{A2k}^3};$

$h_{MA3e}=\sqrt[3]{h_{MA2e}^3+\underset{l=1}{\overset{n_3}{\Σ}}{h}_{A31}^3};$

(2) the main spring initial tangential camber H of high intensity three-level progressive rate leaf spring_gM0Determination：

Stiffness K is clamped according to main spring_M, the compound clamping stiffness K of main spring and three-level auxiliary spring_MA1、K_MA2And K_MA3；Start contact for 1st time Load p_k1, the 2nd beginning contact load P_k2, the 3rd beginning contact load P_k3With the 3rd full contact load p_w3；Rated load P_NAnd the remaining tangent line camber H under rated load_gMsy, to the main spring initial tangential camber of high intensity three-level progressive rate leaf spring H_gM0It is determined, i.e.,

$H_{gM0}=\frac{P_{k1}}{K_M}+\frac{P_{k1}}{K_M}\ln \left(\frac{P_{k2}}{P_{k1}}\right)+\frac{P_{k2}}{K_{MA1}}\ln \left(\frac{P_{k3}}{P_{k2}}\right)+\frac{P_{k3}}{K_{MA2}}\ln \left(\frac{P_{w3}}{P_{k3}}\right)+\frac{P_N-P_{w3}}{K_{MA3}}+H_{gMsy};$

(3) first order auxiliary spring tangent line camber H of high intensity three-level progressive rate leaf spring_gA10Design：

I steps：Main spring tailpiece lower surface initial curvature radius R_M0bCalculate

Piece number n according to main spring, the thickness h of each of main spring_i；The half clamping length L of first of main spring₁, determined in step (2) H_gM0, to main spring tailpiece lower surface initial curvature radius R_M0bCalculated, i.e.,

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

II steps：First radius of curvature R of upper surface of first order auxiliary spring_A10aCalculate

According to the width b of high intensity three-level progressive rate leaf spring, elastic modulus E；The first half clamping length L of main spring₁, the 1st time Start contact load P_k1, the h being calculated in step (1)_Me, and the R being calculated in I steps_M0b, to first of first order auxiliary spring Upper surface initial curvature radius R_A10aCalculated, i.e.,

$R_{A10a}=\frac{R_{M0b}{\mathrm{Ebh}}_{Me}^3}{{\mathrm{Ebh}}_{Me}^3-6R_{M0b}{P}_{k1}{L}_1};$

III steps：First order auxiliary spring initial tangential camber H_gA10Design

According to the first order auxiliary spring half clamping length L of first_A11, the R being calculated in II steps_A10a, to first order auxiliary spring Initial tangential camber H_gA10It is designed, i.e.,

$H_{gA10}=R_{A10a}-\sqrt{R_{A10a}^2-L_{A11}^2}.$

(4) second level auxiliary spring initial tangential camber H of high intensity three-level progressive rate leaf spring_gA20Design：

A steps：First order auxiliary spring tailpiece lower surface initial curvature radius R_A10bCalculate

Piece number n according to first order auxiliary spring₁, the thickness h that first order auxiliary spring is each_A1j, j=1,2 ..., n₁, calculated in step (3) The R for obtaining_A10a, to first order auxiliary spring tailpiece lower surface initial curvature radius R_A10bCalculated, i.e.,

$R_{A10b}=R_{A10a}+\underset{j=1}{\overset{n_1}{\Σ}}{h}_{A1j};$

B step：First of second level auxiliary spring upper surface initial curvature radius R_A20aCalculating

According to the width b of high intensity three-level progressive rate leaf spring, elastic modulus E；The first half clamping length L of main spring₁, the 1st time Start contact load P_k1, the 2nd beginning contact load P_k2, the h being calculated in step (1)_MA1e, and be calculated in a steps R_A10b, to first of second level auxiliary spring upper surface initial curvature radius R_A20aCalculated, i.e.,

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

Step c：Second level auxiliary spring initial tangential camber H_gA20Design

According to the second level auxiliary spring half clamping length L of first_A21, the R being calculated in b step_A20a, it is initial to second level auxiliary spring Tangent line camber H_gA20It is designed, i.e.,

$H_{gA20}=R_{A20a}-\sqrt{R_{A20a}^2-L_{A21}^2};$

(5) third level auxiliary spring initial tangential camber H of high intensity three-level progressive rate leaf spring_gA30Design：

Step A：Second level auxiliary spring tailpiece lower surface initial curvature radius R_A20bCalculate

Piece number n according to second level auxiliary spring₂, the thickness h that second level auxiliary spring is each_A2k, k=1,2 ..., n₂, calculated in step (4) The R for obtaining_A20a, to second level auxiliary spring tailpiece lower surface initial curvature radius R_A20bCalculated, i.e.,

$R_{A20b}=R_{A20a}+\underset{k=1}{\overset{n_2}{\Σ}}{h}_{A2k};$

Step B：First of third level auxiliary spring upper surface initial curvature radius R_A30aCalculating

According to the width b of high intensity three-level progressive rate leaf spring, elastic modulus E；The first half clamping length L of main spring₁, the 2nd time Start contact load P_k2, the 3rd beginning contact load P_k3, the h being calculated in step (1)_MA2e, and be calculated in step A R_A20b, to first of third level auxiliary spring upper surface initial curvature radius R_A30aCalculated, i.e.,

$R_{A30a}=\frac{R_{A20b}{\mathrm{Ebh}}_{MA2e}^3}{{\mathrm{Ebh}}_{MA2e}^3-6R_{A20b}(P_{k3}-P_{k3})L_1};$

Step C：Third level auxiliary spring initial tangential camber H_gA30Design

According to the third level auxiliary spring half clamping length L of first_A31, the R being calculated in step B_A30a, it is initial to third level auxiliary spring Tangent line camber H_gA30It is designed, i.e.,

$H_{gA30}=R_{A30a}-\sqrt{R_{A30a}^2-L_{A31}^2}.$