CN106682359A - Calculation method for deflection of main spring of two-stage auxiliary spring type non-constant frequency variable grade rigidity leaf spring - Google Patents

Abstract

The invention relates to a calculation method for deflection of a main spring of a two-stage auxiliary spring type non-constant frequency variable grade rigidity leaf spring, and belongs to the technical field of suspension plate springs. According to the calculation method, the deflection of the main spring of the two-stage auxiliary spring type non-constant frequency variable grade rigidity leaf spring under various loadings can be calculated according to the structural parameters, modulus of elasticity, U-bolt clamping distance, specified load, and contact load of every time of each main spring and auxiliary spring. A prototype load deflection test result shows that the calculation method for deflection of the main spring of the two-stage auxiliary spring type non-constant frequency variable grade rigidity leaf spring is correct, which lays the groundwork for reliable design of the two-stage auxiliary spring type non-constant frequency variable grade rigidity leaf spring and CAD software development. Using the method can obtain an accurate and reliable main spring deflection calculation value under different loads, and improve product design level, quality and performance, and vehicle ride comfort and safety; meanwhile, the costs of design and test are reduced, and the rate of product development is increased.

Description

The computational methods of the offset frequency main spring amount of deflection of type progressive rate leaf spring such as two-stage auxiliary spring formula is non-

Technical field

The present invention relates to the offset frequency type main spring of progressive rate leaf spring such as vehicle suspension leaf spring, particularly two-stage auxiliary spring formula be non- The computational methods of amount of deflection.

Background technology

In order to improve the design requirement of ride performance of the vehicle under rated load, can be firm using two-stage auxiliary spring formula gradual change Degree leaf spring, simultaneously as the restriction of acceptor's spring intensity, generally by main spring initial tangential camber, first order auxiliary spring and the second level Auxiliary spring initial tangential camber and two-stage gradual change gap, make auxiliary spring suitably undertake load in advance, so as to reduce main spring stress, i.e., two Level auxiliary spring formula uses the offset frequency type progressive rate plate spring suspension brackets such as non-, wherein, the main spring amount of deflection under different loads, influence leaf spring is gradually Variation rigidity, the natural bow of suspension and dynamic deflection and offset frequency, vehicle ride performance and security, and it is also system that main spring amount of deflection is calculated The key issue that about two-stage auxiliary spring formula progressive rate leaf spring is designed.However, due to the offset frequency type progressive rate such as two-stage auxiliary spring formula is non- Main spring amount of deflection of the leaf spring in progressive formation calculates extremely complex, each chip architecture parameter not only with main spring and auxiliary spring, main spring folder Tight rigidity, main spring are relevant but also relevant with contact load with the compound clamping rigidity of auxiliary springs at different levels.Can according to consulting reference materials Know, previously failed to provide the computational methods of the offset frequency main spring amounts of deflection of type progressive rate leaf spring such as two-stage auxiliary spring formula is non-always, be mostly Using prototype test method of testing, main spring amount of deflection is determined, it is thus impossible to meet Vehicle Industry fast development and suspension bullet Spring suspension modernizes the requirement of CAD design and software development.With Vehicle Speed and its constantly carrying to ride comfort requirement Progressive rate plate spring suspension brackets are proposed requirements at the higher level by height, therefore, it is necessary to it is non-to set up a kind of accurate, reliable two-stage auxiliary spring formula It is the offset frequency type progressive rate leaf springs such as two-stage auxiliary spring formula is non-design etc. the computational methods of the offset frequency main spring amount of deflection of type progressive rate leaf spring And reliable technical foundation is established in art CAD software exploitation, Vehicle Industry fast-developing, vehicle ride performance and right are met The design requirement of progressive rate leaf spring, improves design level, the product matter of the offset frequency type progressive rate leaf springs such as two-stage auxiliary spring formula is non- Amount and performance and vehicle ride performance and security；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 problems to be solved by the invention be to provide it is a kind of easy, The computational methods of the offset frequency main spring amount of deflection of type progressive rate leaf spring such as reliable two-stage auxiliary spring formula is non-, calculation process is as shown in Figure 1.Two The half symmetrical structure of the level offset frequency type progressive rate leaf spring such as auxiliary spring formula is non-is as shown in Fig. 2 be by main spring 1, the and of first order auxiliary spring 2 Second level auxiliary spring 3 is constituted.Using two-stage auxiliary spring, it is provided between main spring and first order auxiliary spring and first order auxiliary spring and second level auxiliary spring Two-stage gradual change gap delta_MA1And δ_A12, to improve the vehicle ride performance under rated load；It is strong in order to ensure meeting main spring stress Degree design requirement, first order auxiliary spring and second level auxiliary spring suitably undertake load in advance, and suspension gradual change load offset frequency is unequal, will Leaf spring is designed as the offset frequency type progressive rate leaf spring such as non-.The half total span of leaf spring is equal to the first half action length of main spring L_1T, U-bolts clamp away from half be L₀, width is b, and elastic modelling quantity is E.The piece number of main spring 1 is n, each main spring of main spring Thickness is h_i, half action length is L_iT, half clamping length L_i=L_iT-L₀/ 2, i=1,2 ..., n.First order auxiliary spring piece number It is m₁, the thickness that first order auxiliary spring is each is h_A1j=h_n+j, half action length is L_A1jT, half clamping length L_A1j=L_n+j= L_A1jT-L₀/ 2, j=1,2 ..., m₁.Second level auxiliary spring piece number is m₂, wherein, the thickness that second level auxiliary spring is each is h_A2k= h_n+m1+k, half action length is L_A2kT, half clamping length L_A2k=L_n+m1+k=L_A2kT-L₀/ 2, k=1,2 ..., m₂.Major-minor spring Total tablet number N=n+m₁+m₂.By main spring and first order auxiliary spring and second level auxiliary spring initial tangential camber, it is ensured that meet the 1st time Start contact load P_k1, start contact load P the 2nd time_k2, completely attach to load p the 2nd time_w2, progressive rate K_kwP1And K_kwP2Set Meter is required.The calculating of the main spring amount of deflection under different loads is that the key for restricting the design of two-stage auxiliary spring formula progressive rate leaf spring is asked Topic.Structural parameters, elastic modelling quantity according to each main spring and auxiliary spring, U-bolts are clamped away from, rated load and each contact load In the case of lotus is given, main spring amount of deflection of the offset frequency type progressive rate leaf spring such as non-to two-stage auxiliary spring formula under different loads is counted Calculate.

In order to solve the above technical problems, the offset frequency type main spring of progressive rate leaf spring such as two-stage auxiliary spring formula provided by the present invention is non- The computational methods of amount of deflection, it is characterised in that use following calculation procedure：

(1) the equivalent thickness h of the variant number overlay segment of offset frequency type progressive rate leaf spring such as two-stage auxiliary spring formula is non-_leMeter Calculate：

According to main reed number n, wherein, each thickness h of main spring_i, i=1,2 ..., n；First order auxiliary spring piece number m₁, first Each thickness h of level auxiliary spring_A1j, j=1,2 ..., m₁；Second level auxiliary spring piece number m₂, each thickness h of second level auxiliary spring_A2k, k= 1,2,...,m₂；The total tablet number N=n+m of major-minor spring₁+m₂, the offset frequency type progressive rate leaf spring such as non-to two-stage auxiliary spring formula it is variant The equivalent thickness h of piece number l overlay segments_leCalculated, l=1,2 ..., N, i.e.,

(2) the clamping stiffness Ks at different levels of the offset frequency type progressive rate leaf spring such as two-stage auxiliary spring formula is non-_M、K_MA1And K_MA2Calculating：

I steps：The clamping stiffness K of main spring_MCalculate

According to the width b of the offset frequency type progressive rate leaf spring such as two-stage auxiliary spring formula is non-, elastic modulus E；Main reed number n, each The half clamping length L of main spring_i, and the different piece number overlay segments being calculated in step (1) equivalent thickness h_le, l=i=1, 2,...,n；Stiffness K is clamped to main spring_MCalculated, i.e.,

II steps：The compound clamping stiffness K of main spring and first order auxiliary spring_MA1Calculate

According to the width b of the offset frequency type progressive rate leaf spring such as two-stage auxiliary spring formula is non-, elastic modulus E；Main reed number n, each The half clamping length L of main spring_i, i=1,2 ..., n；First order auxiliary spring piece number m₁, the half that first order auxiliary spring is each is clamped to be grown It is L to spend_A1j=L_n+j, j=1,2 ..., m₁；The piece number sum N of main spring and first order auxiliary spring₁=n+m₁, and calculating in step (1) The equivalent thickness h of the different piece number overlay segments for obtaining_le, l=1,2 ..., N₁；It is firm with the compound clamping of first order auxiliary spring to main spring Degree K_MA1Calculated, i.e.,

III steps：Major-minor spring is always combined and clamps stiffness K_MA2Calculate

According to the width b of the offset frequency type progressive rate leaf spring such as two-stage auxiliary spring formula is non-, elastic modulus E；Main reed number n, each The half clamping length L of main spring_i, i=1,2 ..., n；First order auxiliary spring piece number m₁, the half that first order auxiliary spring is each is clamped to be grown It is L to spend_A1j=L_n+j, j=1,2 ..., m₁；Second level auxiliary spring piece number m₂, the half clamping length L of second level auxiliary spring_A2k, k=1, 2,...,m₂；The total tablet number N=n+m of major-minor spring₁+m₂, and the leaf spring with gradually changing stiffness being calculated in step (1) is not respectively With the equivalent thickness h of piece number overlay segment_le, l=1,2 ..., N, to total clamping complex stiffness K of major-minor spring_MA2Calculated, i.e. I.e.

(3) the two-stage gradual change of the offset frequency type progressive rate leaf spring such as two-stage auxiliary spring formula is non-clamps stiffness K_kwp1And K_kwp2Calculating：

Step A：First order gradual change clamps stiffness K_kwp1Calculating

Start contact load P according to the 1st time_k1, the 2nd beginning contact load P_k2, the K being calculated in step (2)_MWith K_MA1, to load p in [P_k1,P_k1] scope when first order gradual change clamp stiffness K_kwP1Calculated, i.e.,

Step B：Second level gradual change clamps stiffness K_kwp2Calculating

Start contact load P according to the 2nd time_k2, the 2nd full contact load p_w2, the K being calculated in step (2)_MA1With K_MA2, to load p in [P_k2,P_w2] in the range of when second level gradual change clamp stiffness K_kwP2Calculated, i.e.,

(4) the main spring amount of deflection f of the offset frequency type progressive rate leaf spring under different loads P such as two-stage auxiliary spring formula is non-_MCalculate：

Start contact load P according to the 1st time_k1, the 2nd beginning contact load P_k2, the 2nd full contact load p_w2, it is specified Load p_N, the K being calculated in step (2)_MAnd K_MA2, the K being calculated in step (3)_kwP1And K_kwP2, it is non-to two-stage auxiliary spring formula Etc. amount of deflection f of the offset frequency type progressive rate leaf spring under different loads P_MCalculated, i.e.,

The present invention has the advantage that than prior art

Because two-stage auxiliary spring formula is non-etc., amount of deflection of the offset frequency type progressive rate leaf spring in progressive formation is extremely complex, according to being looked into Data understands, previously fails to provide the computational methods of the offset frequency main spring amounts of deflection of type progressive rate leaf spring such as two-stage auxiliary spring formula is non-always, Mostly it is to utilize testing method, its flexibility characteristics is determined, it is thus impossible to it is fast-developing and outstanding to meet Vehicle Industry Frame spring suspension modernizes the requirement of CAD design and software development.The present invention can according to the structural parameters of each main spring and auxiliary spring, Elastic modelling quantity, U-bolts clamp away from, rated load and each contact load it is given in the case of, clamp rigidity, main spring in main spring Rigidity, the major-minor spring of clamping compound with first order auxiliary spring is always combined on the basis of clamping rigidity and the calculating of two-stage progressive rate, to two Auxiliary spring formula is non-etc. that main spring amount of deflection of the offset frequency type progressive rate leaf spring under different loads is calculated for level.By model machine load deflection And stiffness test result understands, the meter of the offset frequency main spring amount of deflection of type progressive rate leaf spring such as two-stage auxiliary spring formula provided by the present invention is non- Calculation method is correct, is the design of initial tangential camber and CAD software of the offset frequency type progressive rate leaf springs such as two-stage auxiliary spring formula is non- Reliable technical foundation has been established in exploitation.Using the available accurately and reliably two-stage auxiliary spring formula of the method is non-etc., offset frequency type gradual change is firm Degree amount of deflection calculated value of the leaf spring under different loads, can improve the design water of the offset frequency type progressive rate leaf springs such as two-stage auxiliary spring formula is non- Flat, quality and performance and vehicle ride performance and security；Meanwhile, design and experimental test expense can be also reduced, accelerate to produce Product development rate.

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 calculation flow chart of the offset frequency main spring amounts of deflection of type progressive rate leaf spring such as two-stage auxiliary spring formula is non-；

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

Fig. 3 is the ANSYS deformation simulation cloud atlas of the main spring clamping rigidity checking of embodiment one；

Fig. 4 is the ANSYS deformation simulation cloud atlas of the main spring with the compound clamping rigidity checking of first order auxiliary spring of embodiment one；

Fig. 5 is that the major-minor spring of embodiment one is always combined the ANSYS deformation simulation cloud atlas for clamping rigidity checking；

Fig. 6 is the offset frequency type progressive rate leaf spring such as two-stage auxiliary spring formula is non-of embodiment one in 0~P_NIn the range of main spring scratch Degree f_MWith load p change curve.

Specific embodiment

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

Embodiment：The width b=63mm of the offset frequency type progressive rate leaf spring such as certain two-stage auxiliary spring formula is non-, U-bolts clamp away from Half L₀=50mm, elastic modulus E=200GPa, allowable stress [σ]=430MPa.The total tablet number of major-minor spring is N=5, its In, main reed number n=3 pieces, each thickness h of main spring₁=h₂=h₃=8mm, half action length is respectively L_1T=525mm, L_2T=450mm, L_3T=350mm；The half clamping length of each main spring is respectively L₁=L_1T-L₀/ 2=500mm, L₂=L_2T-L₀/ 2=425mm, L₃=L_3T-L₀/ 2=325mm.The piece number m of first order auxiliary spring₁=1, thickness h_A11=h₄=13mm, half effect Length is L_A11T=250mm, half clamping length is L_A11=L₄=L_A11T-L₀/ 2=225mm.The piece number m of second level auxiliary spring₂= 1, thickness h_A21=h₅=13mm, half action length is L_A21T=150mm, half clamping length is L_A12=L₅=L_A21T-L₀/2 =125mm.First order gradual change gap between first upper surface of first order auxiliary spring and main spring tailpiece lower surface is δ_MA1, the second level Second level gradual change gap between first upper surface of auxiliary spring and first order auxiliary spring tailpiece lower surface is δ_A12.Start contact for 1st time to carry Lotus P_k1=1888N, the 2nd beginning contact load P_k2=2641N, the 2nd full contact load p_w2=3694N, rated load P_N =7227N.Each main spring and the first order and the structural parameters of second level auxiliary spring, springform according to the leaf spring with gradually changing stiffness Measure, contact load, rated load, the main spring of the offset frequency type progressive rate leaf spring under different loads such as non-to the two-stage auxiliary spring formula is scratched Degree is calculated.

The computational methods of the offset frequency main spring amount of deflection of type progressive rate leaf spring such as two-stage auxiliary spring formula that present example is provided is non-, Its calculation process is as shown in figure 1, specific calculation procedure is as follows：

(1) the equivalent thickness h of the variant number overlay segment of offset frequency type progressive rate leaf spring such as two-stage auxiliary spring formula is non-_leMeter Calculate：

According to main reed number n=3, each thickness h of main spring₁=h₂=h₃=8mm；First order auxiliary spring piece number m₁=1, the Each thickness h of one-level auxiliary spring_A11=13mm；Second level auxiliary spring piece number m₂=1, the thickness h that second level auxiliary spring is each_A21=13mm, The total tablet number N=n+m of major-minor spring₁+m₂=5, variant number of the offset frequency type progressive rate leaf spring such as non-to two-stage auxiliary spring formula is overlapped The equivalent thickness h of section_leCalculated, l=1,2 ..., N, i.e.,

h_1e=h₁=8.0mm；

(2) the clamping stiffness Ks at different levels of the offset frequency type progressive rate leaf spring such as two-stage auxiliary spring formula is non-_M、K_MA1And K_MA2Calculating：

I steps：The clamping stiffness K of main spring_MCalculate

According to the width b=63mm of the offset frequency type progressive rate leaf spring such as two-stage auxiliary spring formula is non-, elastic modulus E=200GPa； Main reed number n=3, each half clamping length L of main spring₁=500mm, L₂=425mm, L₃=425mm, and step (1) is fallen into a trap The h for obtaining_1e=8.0mm, h_2e=10.1mm and h_3e=11.5mm, l=i=1,2 ..., n；Stiffness K is clamped to main spring_MEnter Row is calculated, i.e.,

According to each thickness and half clamping length, elastic modulus E of main spring, a hemihedrism clamping structure is set up ANSYS simulation models, a concentrated force F=1330N is applied in main spring end points, carries out ANSYS deformation simulations and rigidity checking, emulation The main spring ANSYS deformation simulation cloud atlas for obtaining, as shown in figure 3, wherein, end maximum defluxion f_Mmax=34.984mm, therefore, it is main Spring clamps rigidity ANSYS simulating, verifying values K_M=2F/f_Mmax=76.034N/mm, with calculated value K_M=75.44N/mm's is relatively inclined Difference is only 0.84%, as a result shows that main spring clamps stiffness K_MCalculated value be accurately and reliably.

II steps：The compound clamping stiffness K of main spring and first order auxiliary spring_MA1Calculate

According to the width b=63mm of the offset frequency type progressive rate leaf spring such as two-stage auxiliary spring formula is non-, elastic modulus E=200GPa； Main reed number n=3, each half clamping length L of main spring₁=500mm, L₂=425mm, L₃=325mm；First order auxiliary spring piece Number m₁=1, the half clamping length of first order auxiliary spring is L_A11=L₄=225mm；The piece number sum N of main spring and first order auxiliary spring₁ =n+m₁The h being calculated in=4, and step (1)_1e=8.0mm, h_2e=10.1mm, h_3e=11.5mm, h_4e=15.5mm, l =1,2 ..., N₁；To main spring and the compound clamping stiffness K of first order auxiliary spring_MA1Calculated, i.e.,

According to main spring and each thickness and half clamping length, elastic modulus E of first order auxiliary spring, hemihedrism folder is set up The ANSYS simulation models of locking structure, a concentrated force F=1550N is applied in main spring end points, carries out ANSYS deformation simulations and rigidity Checking, main spring and the ANSYS deformation simulation cloud atlas of first order auxiliary spring that emulation is obtained, as shown in figure 4, wherein, main spring end points is most Large deflection f_Mmax=21.74mm, therefore, the compound clamping rigidity ANSYS simulating, verifying values K of main spring and first order auxiliary spring_MA1= 2F/f_Mmax=142.59N/mm, with calculated value K_MThe relative deviation of=144.5N/mm is only 1.32%, as a result shows main spring and The compound clamping stiffness K of one-level auxiliary spring_MACalculated value be accurately and reliably.

III steps：Major-minor spring is always combined and clamps stiffness K_MA2Calculate

According to the width b=63mm of the offset frequency type progressive rate leaf spring such as two-stage auxiliary spring formula is non-, elastic modulus E=200GPa； Main reed number n=3, each half clamping length L of main spring₁=500mm, L₂=425mm, L₃=325mm；First order auxiliary spring piece Number m₁=1, the half clamping length of first order auxiliary spring is L_A11=L₄=225mm；Second level auxiliary spring piece number m₂=1, second level pair The half clamping length L of spring_A21=L₅=125mm, the total tablet number N=n+m of major-minor spring₁+m₂It is calculated in=5, and step (1) H_1e=8.0mm, h_2e=10.1mm, h_3e=11.5mm, h_4e=15.5mm, h_5e=18.1mm, the total clamping to major-minor spring is answered Close stiffness K_MA2Calculated, i.e. i.e.

The thickness and half clamping length, elastic modulus E of each according to main spring and the first order and second level auxiliary spring, sets up The ANSYS simulation models of one hemihedrism clamping structure, a concentrated force F=4000N is applied in main spring end points, and the 2nd time is connect completely Major-minor spring after touching carries out ANSYS deformation simulations and rigidity checking, the ANSYS deformation simulation cloud atlas that emulation is obtained, such as Fig. 5 institutes Show, wherein, main spring end points maximum defluxion f_MA2max=45.44mm, therefore, the total compound clamping rigidity ANSYS emulation of major-minor spring is tested Card value K_MA2=2F/f_MA2max=176.05N/mm, with calculated value K_MA1The relative deviation of=172.9N/mm is only 1.82%, as a result Show that the total compound of major-minor spring clamps stiffness K_MA2Calculated value be accurately and reliably.

(3) the two-stage gradual change of the offset frequency type progressive rate leaf spring such as two-stage auxiliary spring formula is non-clamps stiffness K_kwp1And K_kwp2Calculating：

Step A：First order gradual change clamps stiffness K_kwp1Calculating

Start contact load P according to the 1st time_k1=1888N, the 2nd beginning contact load P_k2=2641N, in step (2) The K being calculated_M=75.4N/mm and K_MA1=144.5N/mm, to load p in [P_k1,P_k1] scope when first order gradual change clamp Stiffness K_kwP1Calculated, i.e.,

Step B：Second level gradual change clamps stiffness K_kwp2Calculating

Start contact load P according to the 2nd time_k2=2641N, the 2nd full contact load p_w2=3694N, in step (2) The K being calculated_MA1=144.5N/mm and K_MA2=172.9N/mm, to load p in [P_k2,P_w2] in the range of when the second level gradually Become and clamp stiffness K_kwP2Calculated, i.e.,

(4) the main spring amount of deflection f of the offset frequency type progressive rate leaf spring under different loads P such as two-stage auxiliary spring formula is non-_MCalculate：

Start contact load P according to the 1st time_k1=1888N, the 2nd beginning contact load P_k2=2641N, the 2nd time completely Contact load P_w2=3694N, rated load P_N=7227N, the K being calculated in step (2)_M=75.4N/mm and K_MA2= 172.9N/mm, the K being calculated in step (3)_kwP1And K_kwP2, the offset frequency type progressive rate leaf spring such as non-to two-stage auxiliary spring formula is not With the main spring amount of deflection f under load_MCalculated, i.e.,

Using Matlab calculation procedures, the offset frequency type progressive rate leaf spring such as the two-stage auxiliary spring formula obtained by calculating is non-is not With the main spring amount of deflection f under load_MWith the change curve of load p, as shown in fig. 6, wherein, the leaf spring with gradually changing stiffness is the 1st Secondary beginning contact load P_k1=1888N, the 2nd beginning contact load P_k2=2641N, the 2nd full contact load p_w2= 3694N and rated load P_NMain spring amount of deflection under=7227N is respectively f_Mk1=25mm, f_Mk2=32.1mm, f_Mw2=38.8mm and f_MN=59.2mm.

By model machine load deflection experimental test, the calculated value of the main spring amount of deflection under different loads is surveyed with experiment Examination value matches, and shows the calculating side of the offset frequency main spring amounts of deflection of type progressive rate leaf spring such as two-stage auxiliary spring formula provided by the present invention is non- Method is correct, is the design of initial tangential camber and CAD software exploitation of the offset frequency type progressive rate leaf springs such as two-stage auxiliary spring formula is non- Reliable technical foundation is established.Using the offset frequency type progressive rate plate such as the available accurately and reliably two-stage auxiliary spring formula of the method is non- Amount of deflection calculated value of the spring under different loads, can improve the design levels of offset frequency type progressive rate leaf spring such as two-stage auxiliary spring formula is non-, Quality and performance and vehicle ride performance and security；Meanwhile, design and experimental test expense can be also reduced, accelerate product and open Hair speed.

Claims (1)

1. the computational methods of the offset frequency main spring amount of deflection of type progressive rate leaf spring such as two-stage auxiliary spring formula is non-, wherein, each leaf spring is with center Mounting hole symmetrical structure, install clamp away from half for U-bolts clamp away from half；Auxiliary spring is designed as two-stage auxiliary spring, Between main spring and first order auxiliary spring, two-stage gradual change gap delta is provided with and first order auxiliary spring and second level auxiliary spring between_MA1And δ_A12, To improve the vehicle ride performance under rated load；In order to ensure meeting main spring stress intensity design requirement, make the first order Auxiliary spring and second level auxiliary spring suitably undertake load in advance, and the offset frequency being suspended under gradual change load is unequal, i.e., non-etc. offset frequency type is gradually Variation rigidity leaf spring；Clamped away from, each contact load, to two-stage according to each structural parameters of leaf spring, elastic modelling quantity, U-bolts Auxiliary spring formula is non-etc., and main spring amount of deflection of the offset frequency type progressive rate leaf spring under different loads is calculated, and specific calculation procedure is as follows：

(1) the equivalent thickness h of the variant number overlay segment of offset frequency type progressive rate leaf spring such as two-stage auxiliary spring formula is non-_leCalculate：

According to main reed number n, wherein, each thickness h of main spring_i, i=1,2 ..., n；First order auxiliary spring piece number m₁, first order pair Each thickness h of spring_A1j, j=1,2 ..., m₁；Second level auxiliary spring piece number m₂, each thickness h of second level auxiliary spring_A2k, k=1, 2,...,m₂；The total tablet number N=n+m of major-minor spring₁+m₂, variant of the offset frequency type progressive rate leaf spring such as non-to two-stage auxiliary spring formula The equivalent thickness h of number l overlay segments_leCalculated, l=1,2 ..., N, i.e.,

$h_{le}=\left\{\begin{array}{cc}\sqrt[3]{\underset{i=1}{\overset{l}{\Σ}}{h}_i^3},& 1\≤l\≤n\\ \sqrt[3]{\underset{i=1}{\overset{n}{\Σ}}{h}_i^3+\underset{j=1}{\overset{l-n}{\Σ}}{h}_{A1j}^3},& n+1\≤l\≤n+m_1\\ \sqrt[3]{\underset{i=1}{\overset{n}{\Σ}}{h}_i^3+\underset{j=1}{\overset{m_1}{\Σ}}{h}_{A1j}^3+\underset{k=1}{\overset{l-n-m_1}{\Σ}}{h}_{A1k}^3},& n+m_1+1\≤l\≤N\end{array}\right.;$

(2) the clamping stiffness Ks at different levels of the offset frequency type progressive rate leaf spring such as two-stage auxiliary spring formula is non-_M、K_MA1And K_MA2Calculating：

I steps：The clamping stiffness K of main spring_MCalculate

According to the width b of the offset frequency type progressive rate leaf spring such as two-stage auxiliary spring formula is non-, elastic modulus E；Main reed number n, each main spring Half clamping length L_i, and the different piece number overlay segments being calculated in step (1) equivalent thickness h_le, l=i=1, 2,...,n；Stiffness K is clamped to main spring_MCalculated, i.e.,

$K_M=\frac{bE}{2\[\frac{{(L_1-L_2)}^3}{h_{1e}^3}+\underset{l=2}{\overset{n-1}{\Σ}}\frac{{(L_1-L_{l+1})}^3-{(L_1-L_l)}^3}{h_{le}^3}+\frac{L_1^3-{(L_1-L_n)}^3}{h_{ne}^3}\]}$

II steps：The compound clamping stiffness K of main spring and first order auxiliary spring_MA1Calculate

According to the width b of the offset frequency type progressive rate leaf spring such as two-stage auxiliary spring formula is non-, elastic modulus E；Main reed number n, each main spring Half clamping length L_i, i=1,2 ..., n；First order auxiliary spring piece number m₁, the half clamping length of each of first order auxiliary spring is L_A1j=L_n+j, j=1,2 ..., m₁；The piece number sum N of main spring and first order auxiliary spring₁=n+m₁, and be calculated in step (1) Different piece number overlay segments equivalent thickness h_le, l=1,2 ..., N₁；To main spring and the compound clamping rigidity of first order auxiliary spring K_MA1Calculated, i.e.,

$K_{MA1}=\frac{bE}{2\[\frac{{(L_1-L_2)}^3}{h_{1e}^3}+\underset{l=2}{\overset{N_1-1}{\Σ}}\frac{{(L_1-L_{l+1})}^3-{(L_1-L_l)}^3}{h_{le}^3}+\frac{L_1^3-{(L_1-L_{N_1})}^3}{h_{N_{1}e}^3}\]};$

III steps：Major-minor spring is always combined and clamps stiffness K_MA2Calculate

According to the width b of the offset frequency type progressive rate leaf spring such as two-stage auxiliary spring formula is non-, elastic modulus E；Main reed number n, each main spring Half clamping length L_i, i=1,2 ..., n；First order auxiliary spring piece number m₁, the half clamping length of each of first order auxiliary spring is L_A1j=L_n+j, j=1,2 ..., m₁；Second level auxiliary spring piece number m₂, the half clamping length L of second level auxiliary spring_A2k, k=1, 2,...,m₂；The total tablet number N=n+m of major-minor spring₁+m₂, and the leaf spring with gradually changing stiffness being calculated in step (1) is not respectively With the equivalent thickness h of piece number overlay segment_le, l=1,2 ..., N, to total clamping complex stiffness K of major-minor spring_MA2Calculated, i.e. I.e.

$K_{MA2}=\frac{bE}{2\[\frac{{(L_1-L_2)}^3}{h_{1e}^3}+\underset{l=2}{\overset{N-1}{\Σ}}\frac{{(L_1-L_{l+1})}^3-{(L_1-L_l)}^3}{h_{le}^3}+\frac{L_1^3-{(L_1-L_N)}^3}{h_{Ne}^3}\]};$

(3) the two-stage gradual change of the offset frequency type progressive rate leaf spring such as two-stage auxiliary spring formula is non-clamps stiffness K_kwp1And K_kwp2Calculating：

Step A：First order gradual change clamps stiffness K_kwp1Calculating

Start contact load P according to the 1st time_k1, the 2nd beginning contact load P_k2, the K being calculated in step (2)_MAnd K_MA1, it is right Load p is in [P_k1,P_k1] scope when first order gradual change clamp stiffness K_kwP1Calculated, 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\∈\[P_{k1},P_{k1}\];$

Step B：Second level gradual change clamps stiffness K_kwp2Calculating

Start contact load P according to the 2nd time_k2, the 2nd full contact load p_w2, the K being calculated in step (2)_MA1And K_MA2, To load p in [P_k2,P_w2] in the range of when second level gradual change clamp stiffness K_kwP2Calculated, i.e.,

$K_{kwP2}=\frac{P}{P_{k2}}{K}_{MA1}+\frac{P-P_{k2}}{P_{w2}-P_{k2}}(K_{MA2}-\frac{P_{w2}}{P_{k2}}{K}_{MA1}),P\∈\[P_{k2},P_{w2}\];$

(4) the main spring amount of deflection f of the offset frequency type progressive rate leaf spring under different loads P such as two-stage auxiliary spring formula is non-_MCalculate：

Start contact load P according to the 1st time_k1, the 2nd beginning contact load P_k2, the 2nd full contact load p_w2, rated load P_N, the K being calculated in step (2)_MAnd K_MA2, the K being calculated in step (3)_kwP1And K_kwP2, it is inclined to the non-grade of two-stage auxiliary spring formula Amount of deflection f of the frequency type progressive rate leaf spring under different loads P_MCalculated, i.e.,

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