CN106650176A - Calculation method for deflection characteristics of non-equal offset frequency type three-level leaf spring with gradually changing stiffness - Google Patents

Abstract

The invention relates to a calculation method for deflection characteristics of a non-equal offset frequency type three-level leaf spring with the gradually changing stiffness, and belongs to the technical field of vehicle suspension leaf springs. The method comprises the steps that on the basis of structural parameters of main springs and auxiliary springs, u-bolt clamping distances, elasticity modulus and contact loads make contact with loads, on the basis of three-level gradually-changing composite clamping stiffness calculation, and deflection characteristics of the non-equal offset frequency type three-level leaf spring with the gradually changing stiffness under different loads are calculated. Model machine loading deflection tests show that the calculation method for deflection characteristics of the non-equal offset frequency type three-level leaf spring with the gradually changing stiffness is correct, and an important technical foundation is laid for design of the non-equal offset frequency type three-level leaf spring with the gradually changing stiffness and CAD software development, by means of the method, reliable deflection calculation values under different loads can be obtained, and the design level, quality and performance and vehicle riding comfort of the non-equal offset frequency type three-level leaf spring with the gradually changing stiffness are improved; meanwhile, the design and experiment cost is lowered, and the product development speed is increased.

Description

The computational methods of the offset frequency type three-level progressive rate leaf spring flexibility characteristics such as non-

Technical field

The present invention relates to vehicle suspension leaf spring, is especially the calculating of the offset frequency type three-level progressive rate leaf spring flexibility characteristics such as non- Method.

Background technology

In order to meet the vehicle ride performance under different loads, can be by the main spring of former first-order gradient rigidity leaf spring and pair Spring is split as respectively two-stage, i.e., using three-level progressive rate leaf spring；Meanwhile, in order to ensure the stress intensity of main spring, generally pass through Main spring and three-level auxiliary spring initial tangential camber and three-level gradual change gap, make three-level auxiliary spring suitably undertake load in advance, so as to reduce The stress of main spring, i.e., using the offset frequency type three-level progressive rate plate spring suspension brackets such as non-, wherein, the flexibility characteristics under different loads, Natural bow, dynamic deflection and offset frequency characteristic and vehicle ride performance and the safety of suspension are affected, meanwhile, leaf spring is in different loads Under flexibility characteristics calculate be also main spring and auxiliary spring initial tangential camber at different levels and three-level gradual change gap design premise.However, Due to the amount of deflection of the offset frequency type three-level progressive rate leaf spring such as non-, not only with the structure of each main spring and three-level auxiliary spring and bear load Lotus is relevant, but also it is relevant to step up rigidity with each contact load and gradual change, therefore, the offset frequency type three-level progressive rate leaf spring such as non- Amount of deflection calculate extremely complex, understand according to consulting reference materials, predecessor State is inside and outside not to provide always the offset frequency type three-level progressive rate such as non- The computational methods of leaf spring flexibility characteristics, it is impossible to meet the design and CAD software exploitation of the offset frequency type three-level progressive rate leaf spring such as non- Require.Progressive rate plate spring suspension brackets are proposed higher by the continuous improvement required with Vehicle Speed and its to ride comfort Require, therefore, it is necessary to set up a kind of accurate, the reliably offset frequency type three-level progressive rate leaf spring flexibility characteristics such as non-calculating side Method, is that reliable technical foundation is established in the offset frequency type three-level progressive rate leaf spring design such as non-and CAD software exploitation, meets vehicle row Industry fast development, vehicle ride performance and the design requirement to the offset frequency type three-level progressive rate leaf spring such as non-, improve product Design level, quality and performance and vehicle ride performance；Meanwhile, design and testing expenses are reduced, accelerate product development speed.

The content of the invention

For defect present in above-mentioned prior art, the technical problem to be solved be to provide it is a kind of easy, The computational methods of the reliable offset frequency type three-level progressive rate leaf spring flexibility characteristics such as non-, its calculation process is as shown in Figure 1.Three-level is gradually The half symmetrical structure of variation rigidity 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 What three-level auxiliary spring 4 was constituted, the half total span of leaf spring is equal to half action length L of first main spring_1T, U-bolts clamp away from Half be L₀, the width of leaf spring is b, and elastic modelling quantity is E, allowable stress [σ].Wherein, the piece number n pieces of main spring 1, each The thickness of main spring is h_i, half action length is L_iT, half clamping length L_i=L_iT-L₀/ 2, i=1,2 ..., n.First order pair The piece number of spring 2 is n₁, the thickness that first order auxiliary spring is each is h_A1j, half action length is 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 of each of second level auxiliary spring piece 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.By main spring and the initial tangential camber of auxiliary spring at different levels, main spring tailpiece lower surface and first upper surface of first order auxiliary spring it Between be provided with first order gradual change gap delta_MA1；Arrange between first upper surface of first order auxiliary spring tailpiece lower surface and second level auxiliary spring There is second level gap delta_A12；The third level is provided between first upper surface of second level auxiliary spring tailpiece lower surface and third level auxiliary spring gradually Varied clearance δ_A23；Start the traveling smooth-going of contact load, stress intensity, progressive rate, suspension offset frequency and vehicle for each time to meet leaf spring The design requirement of property.According to the structural parameters of each leaf spring, U-bolts is clamped away from, elastic modelling quantity, each contact load contact Load, steps up rigidity, main spring and is combined with auxiliary springs at different levels to step up rigidity and three-level gradual change is combined the base that steps up Rigidity Calculation in main spring On plinth, flexibility characteristics of the offset frequency type three-level progressive rate leaf spring such as non-under different loads are calculated.

To solve above-mentioned technical problem, the offset frequency type three-level progressive rate leaf spring flexibility characteristics such as non-provided by the present invention Computational methods, it is characterised in that using following calculation procedure：

(1) the equivalent thickness h of variant number overlay segment of the offset frequency type three-level progressive rate leaf spring such as non-_meCalculating：

According to main reed number n, the thickness h of each of main spring_i, i=1,2 ..., n；The piece number n of first order auxiliary spring₁, first order pair The thickness h that 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；Main spring and first order pair Piece number sum N of spring₁=n+n₁, piece number sum N of main spring and the first auxiliary spring and second level auxiliary spring₂=n+n₁+n₂, major-minor spring it is total Piece number N=n+n₁+n₂+n₃, the equivalent thickness h to variant number m overlay segment of the offset frequency type three-level progressive rate leaf spring such as non-_me's Calculated, m=1,2 ..., N, i.e.,：

(2) the clamping stiffness Ks at different levels of the offset frequency type three-level progressive rate leaf spring such as non-_M、K_MA1、K_MA2And K_MA3Calculate：

Step A：Main spring clamps stiffness K_MCalculating

According to the width b of the offset frequency three-level leaf spring with gradually changing stiffness such as non-, elastic modulus E；Main reed number n, each of main spring Half clamping length L_i, calculated h in i=1,2 ..., n, and step (1)_me, m=i=1,2 ..., n are pressed from both sides to main spring Tight stiffness K_MCalculated, i.e.,

Step B：The clamping complex stiffness K of main spring and first order auxiliary spring_MA1Calculating

According to the width b of the offset frequency three-level leaf spring with gradually changing stiffness such as non-, elastic modulus E；The piece number n of main spring, main spring is each Half clamping length L of piece_i, i=1,2 ..., n；First order auxiliary spring piece number n₁, the half clamping length of each of first order auxiliary spring L_A1j=L_n+j, j=1,2 ..., n₁；Piece number sum N of main spring and first order auxiliary spring₁=n+n₁, and in step (1) it is calculated h_me, m=1,2 ..., N₁, to main spring and the clamping complex stiffness K of first order auxiliary spring_MA1Calculated, i.e.,

Step C：Main spring and first order auxiliary spring and the clamping complex stiffness K of second level auxiliary spring_MA2Calculate

According to the width b of the offset frequency three-level leaf spring with gradually changing stiffness such as non-, elastic modulus E；Main reed number n, each of main spring Half clamping length L_i, i=1,2 ..., n；First order auxiliary spring piece number n₁, half clamping length L of each of first order auxiliary spring_A1j =L_n+j, j=1,2 ..., n₁；Second level auxiliary spring piece number n₂, the half clamping length of each of second level auxiliary springK= 1,2,…,n₂, piece number sum N of main spring and first order auxiliary spring and second level auxiliary spring₂=n+n₁+n₂, and calculate in step (1) The h for arriving_me, m=1,2 ..., N₂, to main spring and the clamping complex stiffness K of the first order and second level auxiliary spring_MA2Calculated, i.e.,

D steps：The total compound of major-minor spring clamps stiffness K_MA3Calculate

According to the width b of the offset frequency three-level leaf spring with gradually changing stiffness such as non-, elastic modulus E；The piece number n of main spring, main spring is each Half clamping length L of piece_i, i=1,2 ..., n；First order auxiliary spring piece number n₁, the half clamping length of each of first order auxiliary spring L_A1j=L_n+j, j=1,2 ..., n₁；Second level auxiliary spring piece number n₂, the half clamping length of each of second level auxiliary springk =1,2 ..., n₂, third level auxiliary spring piece number n₃, the half clamping length of each of third level auxiliary springL=1,2 ..., n₃, the total tablet number N=n+n of major-minor spring₁+n₂+n₃, and calculated h in step (1)_me, m=1,2 ..., N, to major-minor spring Total compound clamping stiffness K_MA3Calculated, i.e. i.e.

(3) the three-level gradual change of the offset frequency type three-level progressive rate leaf spring such as non-is compound clamps stiffness K_kwP1、K_kwP2And K_kwP3Meter Calculate：

I steps：First order gradual change is compound to clamp stiffness K_kwP1Calculating

According to the 1st beginning contact load P_k1, the 2nd beginning contact load P_k2, calculated K in step (2)_MWith K_MA1, to load p in [P_k1,P_k2] scope when the offset frequency type three-level progressive rate leaf spring such as non-first order gradual change it is compound clamp it is firm Degree K_kwP1Calculated, i.e.,

II steps：Second level gradual change is compound to clamp stiffness K_kwP2Calculating

According to the 2nd beginning contact load P_k2, the 3rd beginning contact load P_k3, calculated K in step (2)_MA1With K_MA2, to load p in [P_k2,P_k3] scope when the offset frequency type three-level progressive rate leaf spring such as non-second level gradual change it is compound clamp it is firm Degree K_kwP2Calculated, i.e.,

III steps：Third level gradual change is compound to clamp stiffness K_kwP2Calculating

According to the 3rd beginning contact load P_k3, the 3rd full contact load p_w3, calculated K in step (2)_MA2With K_MA3, to load p in [P_k3,P_w3] scope when the offset frequency type three-level progressive rate leaf spring such as non-third level gradual change it is compound clamp it is firm Degree K_kwP3Calculated, i.e.,

(4) amount of deflection f of the main spring leaf spring with gradually changing stiffness of three-level under different loads P_MCalculate：

According to the 1st beginning contact load P_k1, the 2nd beginning contact load P_k2, the 3rd beginning contact load P_k3, the 3rd Secondary full contact load p_w3, in step (2) in calculated K_MAnd K_MA3, in step (3) in calculated K_kwP1、 K_kwP2And K_kwP2, to amount of deflection f of the offset frequency type three-level progressive rate leaf spring such as non-under any load p_MCalculated, i.e.,

The present invention has the advantage that than prior art

Step up rigidity and three-level gradual change is compound steps up just because acceptor's spring steps up the compound of rigidity, main spring and auxiliary springs at different levels The restriction of the calculating of degree, the inside and outside calculating side for not providing the offset frequency type three-level progressive rate leaf spring flexibility characteristics such as non-always of predecessor State Method, it is impossible to which the design and CAD software exploitation for meeting the offset frequency type three-level progressive rate leaf spring such as non-is required.The present invention can be according to each The structural parameters of main spring and auxiliary spring at different levels, U-bolts is clamped away from, elastic modelling quantity, each contact load, to the offset frequency type such as non- Flexibility characteristics of the three-level progressive rate leaf spring under different loads are calculated.Tested by model machine load deflection, this The computational methods of bright the provided offset frequency type three-level progressive rate leaf spring flexibility characteristics such as non-are correct, are the offset frequency type three such as non- Important technical foundation has been established in the design of level progressive rate leaf spring and CAD software exploitation.It is available in difference using the method Amount of deflection value of calculation under load, improves design level, quality and performance and the vehicle of the offset frequency type three-level progressive rate leaf spring such as non- Ride performance；Meanwhile, design and testing expenses are reduced, accelerate product development speed.

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 calculation flow chart of the offset frequency type three-level progressive rate leaf spring flexibility characteristics such as non-；

Fig. 2 is the half symmetrical structure schematic diagram of the offset frequency type three-level progressive rate leaf spring such as non-；

Fig. 3 is the clamping stiffness K of the offset frequency type three-level progressive rate leaf spring such as non-of embodiment_PWith the change curve of load p；

Fig. 4 is amount of deflection f of the offset frequency type three-level progressive rate leaf spring such as non-of embodiment_MWith the change curve of load p.

Specific embodiment

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

Embodiment：The width b=63mm of certain offset frequency type three-level progressive rate leaf spring such as non-, 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 main spring Thickness h₁=h₂=8mm；The half action length of each main spring is L_1T=525mm, L_2T=450mm；Half clamping length is 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 is made It is L with length_A11T=350mm, half clamping length is L_A11=L₃=L_A11T-L₀/ 2=325mm.The piece number n of second level auxiliary spring₂ =1, thickness h_A21=13mm, half action length is L_A21T=250mm, half clamping length is L_A21=L₄=L_A11T-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 clamps length Spend for L_A31=L₅=L_A31T-L₀/ 2=125mm.1st beginning contact load P_k1=1810N, the 2nd beginning contact load P_k2 =2560N, the 3rd beginning contact load P_k3=3050N, the 3rd full contact load p_w3=3620N, rated load P_N= 7227N.According to the structural parameters of each leaf spring, U-bolts is clamped away from, elastic modelling quantity, each contact load contact load and volume Determine load, the flexibility characteristics of the offset frequency type three-level progressive rate leaf spring under different loads such as non-are calculated.

The computational methods of the offset frequency type three-level progressive rate leaf spring flexibility characteristics such as non-that present example is provided, its calculating Flow process is as shown in figure 1, concrete calculation procedure is as follows：

(1) the equivalent thickness h of variant number overlay segment of the offset frequency type three-level progressive rate leaf spring such as non-_meCalculating：

According to main reed number n=2, the thickness h of each main spring₁=h₂=8mm；The piece number n of first order auxiliary spring₁=1, thickness h_A11=8mm；The piece number n of second level auxiliary spring₂=1, thickness h_A21=13mm；The piece number n of third level auxiliary spring₃=1, thickness h_A31= 13mm；The total tablet number N=5 of major-minor spring, the equivalent thickness to variant number m overlay segment of the offset frequency type three-level progressive rate leaf spring such as non- Degree h_meCarrying out calculate, m=1,2 ..., N, i.e.,：

h_1e=h₁=8.0mm；

(2) the clamping stiffness Ks at different levels of the offset frequency type three-level progressive rate leaf spring such as non-_M、K_MA1、K_MA2And K_MA3Calculate：

Step A：The clamping stiffness K of main spring_MCalculate

According to the width b=63mm of the offset frequency three-level leaf spring with gradually changing stiffness such as non-, elastic modulus E=200GPa；Main spring Piece number n=2, half clamping length L of each main spring₁=500mm, L₂Calculated h in=425mm, and step (1)_1e =8.0mm, h_2e=10.1mm, the clamping stiffness K to main spring_MCalculated, i.e.,

Step B：The clamping complex stiffness K of main spring and first order auxiliary spring_MA1Calculate

According to the width b=63mm of the offset frequency three-level leaf spring with gradually changing stiffness such as non-, elastic modulus E=200GPa；Main spring Piece number n=2, half clamping length L of each of main spring₁=500mm, L₂=425m；First order auxiliary spring piece number n₁=1, the first order Half clamping length L of auxiliary spring_A11=L₃=325mm；Piece number sum N of main spring and first order auxiliary spring₁=n+n₁=3, and step (1) calculated h in_1e=8.0mm, h_2e=10.1mm, h_3e=11.5mm, m=1,2 ..., N₁, to the main spring of the first order with The clamping complex stiffness K of the main spring in the second level_MA1Calculated, i.e.,

Step C：Main spring and the first order and the clamping complex stiffness K of second level auxiliary spring_MA2Calculate

According to the width b=63mm of the offset frequency three-level leaf spring with gradually changing stiffness such as non-, elastic modulus E=200GPa；Main spring Piece number n=2, half clamping length L of each of main spring₁=500mm, L₂=425m；First order auxiliary spring piece number n₁=1, the first order Half clamping length L of auxiliary spring_A11=L₃=325mm；Second level auxiliary spring piece number n₂=1, the half clamping length of second level auxiliary spring L_A21=L₄=225mm, main spring and the first order, piece number sum N of second level auxiliary spring₂=n+n₁+n₂Calculate in=4, and step (1) The h for obtaining_1e=8.0mm, h_2e=10.1mm, h_3e=11.5mm, h_4e=15.5mm, m=1,2 ..., N₂, to main spring and first The clamping complex stiffness K of level and second level auxiliary spring_MA2Calculated, i.e.,

D steps：The total compound of major-minor spring clamps stiffness K_MA3Calculate

According to the width b=63mm of the offset frequency three-level leaf spring with gradually changing stiffness such as non-, elastic modulus E=200GPa；Main spring Piece number n=2, half clamping length L of each main spring₁=500mm, L₂=425m；First order auxiliary spring piece number n₁=1, first is secondary Half clamping length L of spring_A11=L₃=325mm；Second level auxiliary spring piece number n₂=1, half clamping length L of second level auxiliary spring_A21 =L₄=225mm；Third level auxiliary spring piece number n₃=1, half clamping length L of third level auxiliary spring_A31=L₅=125mm, major-minor spring Total tablet number N=5, and calculated h in step (1)_1e=8.0mm, h_2e=10.1mm, h_3e=11.5mm, h_4e= 15.5mm, h_5e=18.1mm, m=1,2 ..., N, to the total compound of major-minor spring stiffness K is clamped_MA3Calculated, i.e. i.e.

(3) the three-level gradual change of the offset frequency type three-level progressive rate leaf spring such as non-is compound clamps stiffness K_kwP1、K_kwP2And K_kwP3Meter Calculate：

I steps：First order gradual change is compound to clamp stiffness K_kwP1Calculating

According to the 1st beginning contact load P_k1=1810N, the 2nd beginning contact load P_k2=2560N, in step (2) Calculated K_M=51.4N/mm and K_MA1=75.4N/mm, to load p ∈ [P_k1,P_k2] scope when the offset frequency type three-level such as non- The gradual change of the first order of progressive rate leaf spring is compound to clamp stiffness K_kwP1Calculated, i.e.,

II steps：Second level gradual change is compound to clamp stiffness K_kwP2Calculating

According to the 2nd beginning contact load P_k2=2560N, the 3rd beginning contact load P_k3=3050N, in step (2) Calculated K_MA1=75.4N/mm, calculated K in step C_MA2=144.5N/mm, to load p ∈ [P_k2,P_k3] scope When the second level gradual change of the offset frequency type three-level progressive rate leaf spring such as non-compound clamp stiffness K_kwP2Calculated, i.e.,

III steps：Third level gradual change is compound to clamp stiffness K_kwP3Calculating

According to the 3rd beginning contact load P_k3=3050N, the 3rd full contact load p_w3=3620N, in step (2) Calculated K_MA2=144.5N/mm and K_MA3=172.9N/mm, to load p in [P_k3,P_w3] scope when the offset frequency type such as non- The third level gradual change of three-level progressive rate leaf spring is compound to clamp stiffness K_kwP3Calculated, i.e.,

Using Matlab calculation procedures, the clamping rigidity of the offset frequency type three-level progressive rate leaf spring such as this obtained by calculating is non- K_PWith load p change curve as shown in figure 3, wherein, work as load p<P_k1During=1810N, gradual change clamps stiffness K_P=K_M= 51.4N/mm, as load p=P_k2During=2560N, gradual change clamps stiffness K_P=K_MA1=75.4N/mm, as load p=P_k3= During 3050N, gradual change clamps stiffness K_P=K_MA2=144.5N/mm, works as load p>P_W3During=3620N, gradual change clamps stiffness K_P= K_MA3=172.9N/mm.

(4) amount of deflection f of the main spring leaf spring with gradually changing stiffness of three-level under different loads P_MCalculate：

According to the 1st beginning contact load P_k1=1810N, the 2nd beginning contact load P_k2=2560N, the 3rd beginning Contact load P_k3=3050N, the 3rd full contact load p_w3=3620N, rated load P_NCalculate in=7227N, step (2) The K for obtaining_M=51.4N/mm and K_MA3=172.9N/mm, calculated K in step (3)_kwP1、K_kwP2And K_kwP3, to one-level gradually Amount of deflection f of the variation rigidity leaf spring under load p_MCalculated, i.e.,

Using Matlab calculation procedures, amount of deflection f of the offset frequency type three-level progressive rate leaf spring such as this obtained by calculating is non-_MWith The change curve of load p as shown in figure 4, wherein, in P_k1=1810N, P_k2=2560N, P_k3=3050N, P_w3=3620N and P_N Amount of deflection under=7227N load is respectively f_Mk1=35.2mm, f_Mk2=47.2mm, f_Mk3=51.8mm, f_Mw3=55.4mm and f_MN =76.2mm.

Tested by model machine load deflection, the offset frequency type three-level progressive rate leaf spring amount of deflection such as non-provided by the present invention The computational methods of characteristic are correct, are that weight has been established in the offset frequency type three-level progressive rate leaf spring design such as non-and CAD software exploitation The technical foundation wanted.Using the available amount of deflection value of calculation under different loads of the method, the offset frequency type three-level such as non-is improved gradually The design level of variation rigidity leaf spring, quality and performance and vehicle ride performance；Meanwhile, design and testing expenses are reduced, accelerate Product development speed.

Claims (1)

1. computational methods of the offset frequency type three-level progressive rate leaf spring flexibility characteristics such as non-, wherein, each leaf spring is to be installed with center The symmetrical structure at hole center, install clamp away from half be U-bolts clamp away from half；By main spring and three-level auxiliary spring Initial tangential camber and three-level gradual change gap, meet leaf spring contact load, gradual change and are combined the design for clamping rigidity and stress intensity Require, i.e., non-etc. offset frequency type three-level progressive rate leaf spring；According to the structural parameters of each leaf spring, U-bolts is clamped away from elasticity Modulus, each contact load is firm to the offset frequency type three-level gradual change such as non-on the basis of clamping rigidity at different levels and progressive rate are calculated Flexibility characteristics of the degree leaf spring under different loads are calculated, and concrete calculation procedure is as follows：

(1) the equivalent thickness h of variant number overlay segment of the offset frequency type three-level progressive rate leaf spring such as non-_meCalculating：

According to main reed number n, 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 is each The thickness h of piece_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；Main spring and first order auxiliary spring Piece number sum N₁=n+n₁, piece number sum N of main spring and the first auxiliary spring and second level auxiliary spring₂=n+n₁+n₂, the total tablet number of major-minor spring N=n+n₁+n₂+n₃, the equivalent thickness h to variant number m overlay segment of the offset frequency type three-level progressive rate leaf spring such as non-_meCarrying out Calculate, m=1,2 ..., N, i.e.,：

$h_{me}=\left\{\begin{array}{cc}\sqrt[3]{\underset{i=`}{\overset{m}{\&Sigma;}}{h}_i^3},& 1\&le;m\&le;n\\ \sqrt[3]{\underset{i=`}{\overset{n}{\&Sigma;}}{h}_i^3+\underset{j=1`}{\overset{m-n}{\&Sigma;}}{h}_{A1j}^3},& n+1\&le;m\&le;N_1\\ \sqrt[3]{\underset{i=`}{\overset{n}{\&Sigma;}}{h}_i^3+\underset{j=1`}{\overset{n_1}{\&Sigma;}}{h}_{A1j}^3+\underset{k=1`}{\overset{m-N_1}{\&Sigma;}}{h}_{A2k}^3},& N_1+1\&le;m\&le;N_2\\ \sqrt[3]{\underset{i=`}{\overset{n}{\&Sigma;}}{h}_i^3+\underset{j=1`}{\overset{n_1}{\&Sigma;}}{h}_{A1j}^3+\underset{k=1`}{\overset{n_2}{\&Sigma;}}{h}_{A2k}^3+\underset{l=1`}{\overset{m-N_2}{\&Sigma;}}{h}_{A3l}^3},& N_2+1\&le;m\&le;N\end{array}\right.;$

(2) the clamping stiffness Ks at different levels of the offset frequency type three-level progressive rate leaf spring such as non-_M、K_MA1、K_MA2And K_MA3Calculate：

Step A：Main spring clamps stiffness K_MCalculating

According to the width b of the offset frequency three-level leaf spring with gradually changing stiffness such as non-, elastic modulus E；Main reed number n, the one of each of main spring Half clamping length L_i, calculated h in i=1,2 ..., n, and step (1)_me, m=i=1,2 ..., n are clamped firm to main spring Degree K_MCalculated, i.e.,

$K_M=\frac{bE}{2\&lsqb;\frac{{(L_1-L_2)}^3}{h_{1e}^3}+\underset{m=2}{\overset{m-1}{\&Sigma;}}\frac{{(L_1-L_{m+1})}^3-{(L_1-L_m)}^3}{h_{me}^3}+\frac{L_1^3-{(L_1-L_n)}^3}{h_{ne}^3}\&rsqb;};$

Step B：The clamping complex stiffness K of main spring and first order auxiliary spring_MA1Calculating

According to the width b of the offset frequency three-level leaf spring with gradually changing stiffness such as non-, elastic modulus E；The piece number n of main spring, each of main spring Half clamping length L_i, i=1,2 ..., n；First order auxiliary spring piece number n₁, half clamping length L of each of first order auxiliary spring_A1j= L_n+j, j=1,2 ..., n₁；Piece number sum N of main spring and first order auxiliary spring₁=n+n₁, and calculated h in step (1)_me, m =1,2 ..., N₁, to main spring and the clamping complex stiffness K of first order auxiliary spring_MA1Calculated, i.e.,

$K_{MA1}=\frac{bE}{2\&lsqb;\frac{{(L_1-L_2)}^3}{h_{1e}^3}+\underset{m=2}{\overset{N_1-1}{\&Sigma;}}\frac{{(L_1-L_{m+1})}^3-{(L_1-L_m)}^3}{h_{me}^3}+\frac{L_1^3-{(L_1-L_{N_1})}^3}{h_{N_{1}e}^3}\&rsqb;};$

Step C：Main spring and first order auxiliary spring and the clamping complex stiffness K of second level auxiliary spring_MA2Calculate

According to the width b of the offset frequency three-level leaf spring with gradually changing stiffness such as non-, elastic modulus E；Main reed number n, the one of each of main spring Half clamping length L_i, i=1,2 ..., n；First order auxiliary spring piece number n₁, half clamping length L of each of first order auxiliary spring_A1j= L_n+j, j=1,2 ..., n₁；Second level auxiliary spring piece number n₂, half clamping length L of each of second level auxiliary spring_A2k=L_N1+k, k=1, 2,…,n₂, piece number sum N of main spring and first order auxiliary spring and second level auxiliary spring₂=n+n₁+n₂, and be calculated in step (1) H_me, m=1,2 ..., N₂, to main spring and the clamping complex stiffness K of the first order and second level auxiliary spring_MA2Calculated, i.e.,

$K_{MA2}=\frac{bE}{2\&lsqb;\frac{{(L_1-L_2)}^3}{h_{1e}^3}+\underset{m=2}{\overset{N_2-1}{\&Sigma;}}\frac{{(L_1-L_{m+1})}^3-{(L_1-L_m)}^3}{h_{me}^3}+\frac{L_1^3-{(L_1-L_{N_2})}^3}{h_{N_{2}e}^3}\&rsqb;};$

D steps：The total compound of major-minor spring clamps stiffness K_MA3Calculate

According to the width b of the offset frequency three-level leaf spring with gradually changing stiffness such as non-, elastic modulus E；The piece number n of main spring, each of main spring Half clamping length L_i, i=1,2 ..., n；First order auxiliary spring piece number n₁, half clamping length L of each of first order auxiliary spring_A1j= L_n+j, j=1,2 ..., n₁；Second level auxiliary spring piece number n₂, half clamping length L of each of second level auxiliary spring_A2k=L_N1+k, k=1, 2,…,n₂, third level auxiliary spring piece number n₃, half clamping length L of each of third level auxiliary spring_A3l=L_N2+l, l=1,2 ..., n₃, it is main The total tablet number N=n+n of auxiliary spring₁+n₂+n₃, and calculated h in step (1)_me, m=1,2 ..., N, to the total compound of major-minor spring Clamp stiffness K_MA3Calculated, i.e. i.e.

$K_{MA3}=\frac{bE}{2\&lsqb;\frac{{(L_1-L_2)}^3}{h_{1e}^3}+\underset{m=2}{\overset{N-1}{\&Sigma;}}\frac{{(L_1-L_{m+1})}^3-{(L_1-L_m)}^3}{h_{me}^3}+\frac{L_1^3-{(L_1-L_N)}^3}{h_{Ne}^3}\&rsqb;};$

(3) the three-level gradual change of the offset frequency type three-level progressive rate leaf spring such as non-is compound clamps stiffness K_kwP1、K_kwP2And K_kwP3Calculating：

I steps：First order gradual change is compound to clamp stiffness K_kwP1Calculating

According to the 1st beginning contact load P_k1, the 2nd beginning contact load P_k2, calculated K in step (2)_MAnd K_MA1, it is right Load p is in [P_k1,P_k2] scope when the first order gradual change of the offset frequency type three-level progressive rate leaf spring such as non-compound clamp stiffness K_kwP1 Calculated, i.e.,

$K_{kwP1}=\frac{P}{P_{k1}}{K}_M+\frac{P-P_{k1}}{P_{k2}-p_{k1}}(K_{MA1}-\frac{P_{k2}}{P_{k1}}{K}_M),P\&Element;\&lsqb;P_{k1},P_{k2}\&rsqb;;$

II steps：Second level gradual change is compound to clamp stiffness K_kwP2Calculating

According to the 2nd beginning contact load P_k2, the 3rd beginning contact load P_k3, calculated K in step (2)_MA1And K_MA2, To load p in [P_k2,P_k3] scope when the second level gradual change of the offset frequency type three-level progressive rate leaf spring such as non-compound clamp rigidity K_kwP2Calculated, i.e.,

$K_{kwP2}=\frac{P}{P_{k2}}{K}_{MA1}+\frac{P-P_{k2}}{P_{k3}-P_{k2}}(K_{MA2}-\frac{P_{k3}}{P_{k2}}{K}_{MA1}),P\&Element;\&lsqb;P_{k2},P_{k3}\&rsqb;;$

III steps：Third level gradual change is compound to clamp stiffness K_kwP2Calculating

According to the 3rd beginning contact load P_k3, the 3rd full contact load p_w3, calculated K in step (2)_MA2And K_MA3, To load p in [P_k3,P_w3] scope when the third level gradual change of the offset frequency type three-level progressive rate leaf spring such as non-compound clamp rigidity K_kwP3Calculated, i.e.,

$K_{kwP3}=\frac{P}{P_{k3}}{K}_{MA2}+\frac{P-P_{k3}}{P_{w3}-P_{k3}}(K_{MA3}-\frac{P_{w3}}{P_{k3}}{K}_{MA2}),P\&Element;\&lsqb;P_{k3},P_{w3}\&rsqb;;$

(4) amount of deflection f of the main spring leaf spring with gradually changing stiffness of three-level under different loads P_MCalculate：

According to the 1st beginning contact load P_k1, the 2nd beginning contact load P_k2, the 3rd beginning contact load P_k3, the 3rd time complete Full connected load p_w3, in step (2) in calculated K_MAnd K_MA3, in step (3) in calculated K_kwP1、K_kwP2With K_kwP2, to amount of deflection f of the offset frequency type three-level progressive rate leaf spring such as non-under any load p_MCalculated, i.e.,

$f_M=\left\{\begin{array}{cc}\frac{P}{K_M},& P<P_{k1}\\ \frac{P_{k1}}{K_M}+{\&Integral;}_{P_{k1}}^P\frac{dP}{K_{kwP1}},& P_{k1}\&le;P<P_{k2}\\ \frac{P_{k1}}{K_M}+{\&Integral;}_{P_{k1}}^{P_{k2}}\frac{dP}{K_{kwP1}}+{\&Integral;}_{P_{k2}}^P\frac{dP}{K_{kwP2}},& P_{k2}\&le;P<P_{k3}\\ \frac{P_{k1}}{K_M}+{\&Integral;}_{P_{k1}}^{P_{k2}}\frac{dP}{K_{kwP1}}+{\&Integral;}_{P_{k2}}^{P_{w2}}\frac{dP}{K_{kwP2}}++{\&Integral;}_{P_{k3}}^P\frac{dP}{K_{kwP3}},& P_{k3}\&le;P\&le;P_{k3}\\ \frac{P_{k1}}{K_M}+{\&Integral;}_{P_{k1}}^{P_{k2}}\frac{dP}{K_{kwP1}}+{\&Integral;}_{P_{k2}}^{P_{w2}}\frac{dP}{K_{kwP2}}+{\&Integral;}_{P_{k3}}^{P_{w3}}\frac{dP}{K_{kwP3}}+\frac{P-P_{w3}}{K_{MA3}},& P_{w3}\&le;P\end{array}\right..$