CN106326605A - Computing method of deflection of non-end-contact type few-leaf parabolic main and auxiliary spring structure - Google Patents

Abstract

The invention relates to a computing method of deflection of a non-end-contact type few-leaf parabolic main and auxiliary spring structure and belongs to the technical field of suspension steel plate springs. According to the computing method, the main and auxiliary spring deflection of a non-end-contact type few-leaf parabolic tapered leaf spring can be designed according to structural parameters and elasticity modulus of the main and auxiliary spring structure. A model machine loading deformation experiment test indicates that the computing method of deflection of the non-end-contact type few-leaf parabolic main and auxiliary spring structure is correct, an accurate and reliable main and auxiliary spring deflection computation value can be obtained, and reliable technological base is established for camber height design of the non-end-contact type few-leaf parabolic main and auxiliary spring structure and development of CAD (computer aided design) software; with the adoption of the method, design level, quality and performance of a product and driving comfort of a vehicle can be improved, besides, cost of product design and experiment testing is reduced, and the product development is accelerated.

Description

The computational methods of the few sheet parabolic type major-minor spring amount of deflection of non-ends contact formula

Technical field

The present invention relates to vehicle suspension leaf spring, be the few sheet parabolic type major-minor spring amount of deflection of non-ends contact formula especially Computational methods.

Background technology

Along with vehicle energy saving, comfortableization, lightweight, the fast development of safe, few sheet variable-section steel sheet spring is because of tool Having lightweight, stock utilization is high, and without friction or rub little between sheet, vibration noise is low, and service life, the advantage such as length, was increasingly subject to Vehicle suspension expert, manufacturing enterprise and the highest attention of vehicle manufacturing enterprise, and obtained in vehicle suspension system extensively Application.Generally for meeting the design requirement of processing technique, stress intensity, rigidity and hanger thickness, can few sheet Variable Section Steel The different structure form such as flat spring is processed as that parabolic type, bias type, root be reinforced, reinforcement end, two ends are reinforced, and Owing to the stress of few sheet variable-section steel sheet spring the 1st flat spring is complex, it is subjected to vertical load, simultaneously also subject to torsion Load and longitudinal loading, therefore, the thickness of the end flat segments of the 1st flat spring designed by reality and length, each more than other The thickness of flat spring end flat segments and length, the most mostly use the non-few sheet variable-section steel sheet spring waiting structure in end, to meet The requirement that 1st flat spring stress is complicated, additionally, in order to meet the rigidity Design requirement under different loads, generally cut few sheet change Face leaf spring is designed as the few sheet parabolic type variable cross-section major-minor spring form of non-ends contact formula.But, due to non-ends contact Structure and the contact type of the few sheet parabolic type variable cross-section major-minor spring of formula are complicated, are analyzed calculating extremely difficult, according to institute to it Consult reference materials and understand, the most do not provided the meter of the few sheet parabolic type major-minor spring amount of deflection of reliable non-ends contact formula Calculation method, constrains the design of few sheet variable-section steel sheet spring major-minor spring tangent line camber.Along with Vehicle Speed and to flat Improving constantly of pliable requirement, has higher requirement to non-ends contact formula sheet parabolic type variable cross-section major-minor spring less, because of This, it is necessary to set up the computational methods of the few sheet parabolic type major-minor spring amount of deflection of a kind of non-ends contact formula accurate, reliable, for non-end Reliable technical foundation is established in the camber design of the few sheet parabolic type variable cross-section major-minor spring of portion's contact, meets Vehicle Industry quick The design requirement of the few sheet parabolic type variable cross-section major-minor spring of development, vehicle ride performance and non-ends contact formula, improves product Design level, quality and performance, meet the design requirement of vehicle ride performance；Meanwhile, reduce design and testing expenses, accelerate Product development speed.

Summary of the invention

For defect present in above-mentioned prior art, the technical problem to be solved be to provide a kind of easy, The computational methods of the few sheet parabolic type major-minor spring amount of deflection of reliable non-ends contact formula, its calculation flow chart, as shown in Figure 1.Non- The few sheet parabolic type variable cross-section major-minor spring of ends contact formula is symmetrical structure, and the half symmetrical structure of major-minor spring can see cantilever as Beam, i.e. symmetrical center line are the fixing end of root, and the end stress point of main spring and the contact of auxiliary spring are respectively as main spring end points and pair Spring end points, the structural representation of the major-minor spring of half symmetrical structure, as in figure 2 it is shown, including, main spring 1, root shim 2, secondary Spring 3, end pad 4.The main spring 1 a length of L of half of every_M, it is by root flat segments, parabolic segment and end flat segments three sections Being constituted, the thickness of the root flat segments of every main spring is h_2M, the half of every main spring installing space is l₃, every main spring Width is b；The non-thickness waiting structure, i.e. the end flat segments of the 1st main spring of end flat segments of each of main spring 1 and length, be more than Other thickness of each and length, thickness and the length of the end flat segments of each main spring are respectively h_1MiAnd l_1Mi, i=1, 2 ..., m, m are main reed number；The middle variable cross-section of every main spring is parabolic segment, the thickness ratio of the parabolic segment of each main spring For β_i=h_1Mi/h_2M, the distance of the root of the parabolic segment of every main spring to main spring end points is l_2M=L_M-l₃, the throwing of each main spring The end of thing line segment is to distance l of main spring end points_1Mi=l_2Mβ_i ²；Each root flat segments of main spring 1 and the root with auxiliary spring 3 are put down Being provided with root shim 2 between straight section, the end flat segments of each of main spring 1 is provided with end pad 4, and the material of end pad 4 is carbon Fibrous composite, is used for the frictional noise produced when reducing spring works；The auxiliary spring 3 a length of L of half of every_A, it is by root Portion's flat segments, parabolic segment and end flat segments three sections are constituted, and the thickness of the root flat segments of every auxiliary spring is h_2A, every pair The half of spring installing space is l₃, the width of every auxiliary spring is b；The thickness of the end flat segments of each auxiliary spring and length are respectively h_1AjAnd l_1Aj, j=1,2 ..., n, n are auxiliary spring sheet number；The middle variable cross-section of every auxiliary spring is parabolic segment, the throwing of each auxiliary spring The thickness of thing line segment is than for β_Aj=h_1Aj/h_2A, the distance of the root of the parabolic segment of every auxiliary spring to auxiliary spring end points is l_2A=L_A- l₃, the end of the parabolic segment of each auxiliary spring is to distance l of auxiliary spring end points_1Aj=l_2Aβ_Aj ²；The m sheet parabolic segment of main spring 1 with Major and minor spring gap delta it is provided with between the ends points of auxiliary spring 3；When load works load more than auxiliary spring, auxiliary spring and main spring parabolic In line segment, certain point contacts, and auxiliary spring is l with the distance of main spring contact point to main spring end points₀；After major-minor spring ends contact, main Each end stress of auxiliary spring differs, and the main spring contacted with auxiliary spring is in addition to by end points power, also bears at contact point The support force of auxiliary spring.In the case of the structural parameters of major-minor spring, elastic modelling quantity are given, sheet parabolic type few to non-ends contact formula The major-minor spring amount of deflection of variable-section steel sheet spring calculates.

For solving above-mentioned technical problem, the few sheet parabolic type major-minor spring amount of deflection of non-ends contact formula provided by the present invention Computational methods, it is characterised in that use step calculated below:

(1) calculating of the few sheet parabolic type leaf spring major and minor spring end points deformation coefficient of non-ends contact formula:

I step: the calculating of each main spring end points deformation coefficient under end points stressing conditions:

Half length L according to few sheet main spring of parabolic type variable-section steel sheet spring_M, width b, half l of installing space₃, Parabola root is to distance l of spring end points_2M, elastic modulus E, the thickness of the parabolic segment of i-th main spring compares β_i, wherein, i= 1,2 ..., m, m are main reed number, to the deformation coefficient G at end points of each main spring under end points stressing conditions_x-DiCount Calculate, i.e.

$G_{x-Di}=\frac{4\[l_{2M}^3(1-{\mathrm{\β}}_i^3)+{(L_M-l_3/2)}^3\]}{Eb};$

II step: the main spring of the m sheet calculating of deformation coefficient at auxiliary spring contact point under end points stressing conditions:

Half length L according to few sheet main spring of parabolic type variable-section steel sheet spring_M, width b, half l of installing space₃, Parabola root is to distance l of spring end points_2M, elastic modulus E, distance l of auxiliary spring and main spring contact point to main spring end points₀, right The main spring of m sheet under end points stressing conditions deformation coefficient G at parabolic segment with auxiliary spring contact point_x-BCCalculate, i.e.

$G_{x-BC}=\frac{2}{Eb}\[8l_{2M}^{3/2}{l}_0^{3/2}-(9l_{2M}^2+3{(L_M-l_3/2)}^2{l}_0+2l_{2M}^3+2{(L_M-l_3/2)}^3\];$

III step: the calculating of the m sheet main spring end points deformation coefficient under stressing conditions at major-minor spring contact point:

Half length L according to few sheet main spring of parabolic type variable-section steel sheet spring_M, width b, half l of installing space₃, Parabola root is to distance l of spring end points_2M, elastic modulus E, distance l of auxiliary spring and main spring contact point to main spring end points₀, right The main spring of m sheet under stressing conditions deformation coefficient G at endpoint location at major-minor spring contact point_x-DpmCalculate, i.e.

$G_{x-D_{p}m}=\frac{4}{bE}\[l_{2M}^3-6l_0{l}_{2M}^2+4l_{2M}^{3/2}{l}_0^{3/2}+{(L_M-l_3/2)}^3\];$

IV step: the main spring of the m sheet meter of deformation coefficient at auxiliary spring contact point under stressing conditions at major-minor spring contact point Calculate:

Half length L according to few sheet main spring of parabolic type variable-section steel sheet spring_M, width b, half l of installing space₃, Parabola root is to distance l of spring end points_2M, elastic modulus E, distance l of auxiliary spring and main spring contact point to main spring end points₀, right The main spring of m sheet under stressing conditions deformation coefficient G at parabolic segment with auxiliary spring contact point at major-minor spring contact point_x-BCpCarry out Calculate, i.e.

$\begin{array}{c}{G}_{x-{\mathrm{BC}}_p}=\frac{4}{Eb}\{(L_M-l_3/2-l_{2M})\[{(L_M-l_3/2)}^2-3(L_M-l_3/2)l_0+(L_M-l_3/2)l_{2M}+3l_0^2-3l_0{l}_{2M}+l_{2M}^2\]-\\ (6l_{2M}{l}_0^2-2l_{2M}^3-16l_0^{3/2}{l}_{2M}^{1/2}+12l_0{l}_{2M}^3)\};\end{array}$

V step: the calculating of each auxiliary spring end points deformation coefficient under end points stressing conditions:

Half length L according to few sheet parabolic type variable-section steel sheet spring auxiliary spring_A, width b, half l of installing space₃, Parabola root is to distance l of spring end points_2A, elastic modulus E, the thickness of the parabolic segment of jth sheet auxiliary spring compares β_Aj, wherein, j =1,2 ..., n, n are auxiliary spring sheet number, to the deformation coefficient G at endpoint location of each auxiliary spring under end points stressing conditions_x-DAjEnter Row calculates, i.e.

$G_{x-DAj}=\frac{4\[l_{2A}^3(1-{\mathrm{\β}}_{Aj}^3)+{(L_A-l_3/2)}^3\]}{Eb};$

Wherein, the deformation coefficient G after the superposition of n sheet auxiliary spring_x-DATFor

$G_{x-DAT}=\frac{1}{\underset{j=1}{\overset{n}{\Σ}}\frac{1}{G_{x-DAj}}};$

(2) calculating of each main spring clamping rigidity of the few sheet parabolic type leaf spring of non-ends contact formula:

Step A: each main spring clamping stiffness K before auxiliary spring contact_MiCalculating:

According to main spring root thickness h_2M, and calculated G in the I step of step (1)_x-Di, before determining auxiliary spring contact Each main spring half stiffness K in the clamp state_Mi, i.e.

$K_{Mi}=\frac{h_{2M}^3}{G_{x-Di}},i=1,2,...,m;$

Wherein, m is main reed number；

Step B: each main spring clamping stiffness K after auxiliary spring contact_MAiCalculating:

According to main spring root thickness h_2M, auxiliary spring root thickness h_2A, calculated G in the I step of step (1)_x-Di, II step Calculated G in Zhou_x-BC, calculated G in III step_x-Dpm, calculated G in IV step_x-BCp, and V step fall into a trap The G obtained_x-DAT, determine the half stiffness K in the clamp state of each main spring after the contact of major-minor spring_MAi, i.e.

$K_{MAi}=\left\{\begin{array}{cc}\frac{h_{2M}^3}{G_{x-Di}},& i=1,2,\mathrm{...},m-1\\ \frac{h_{2M}^3(G_{x-DAT}{h}_{2M}^3+G_{x-{\mathrm{BC}}_p}{h}_{2A}^3)}{G_{x-Dm}(G_{x-DAT}{h}_{2M}^3+G_{x-{\mathrm{BC}}_p}{h}_{2A}^3)-G_{x-D_{p}m}{G}_{x-BC}{h}_{2A}^3},& i=m\end{array}\right.;$

Wherein, m is main reed number；

(3) calculating of each auxiliary spring clamping rigidity of the few sheet parabolic type leaf spring of non-ends contact formula:

According to auxiliary spring root thickness h_2A, and calculated G in the V step of step (1)_x-DAj, determine that each auxiliary spring is at folder Half stiffness K under tight state_Aj, i.e.

$K_{Aj}=\frac{h_{2A}^3}{G_{x-DAj}},j=1,2,...,n;$

Wherein, n is auxiliary spring sheet number；

(4) calculating of the non-ends contact formula parabolic type leaf spring major and minor spring amount of deflection under different loads:

I step: half load p when auxiliary spring works_KCalculating:

According to main spring root thickness h_2M, major-minor spring gap delta at contact point, main reed number m, in the II step of step (1) Calculated G_x-BC, and the K determined in the step A of step (2)_Mi, determine half load p when auxiliary spring works_K, i.e.

$P_K=\frac{{\mathrm{\δh}}_{2M}^3\underset{i=1}{\overset{m}{\Σ}}{K}_{Mi}}{G_{x-BC}{K}_{Mm}};$

Ii step: main spring amount of deflection f under different loads_MCalculating:

Main reed number m, calculated P in i step according to few sheet parabolic type variable-section steel sheet spring_K, and step (2) K determined in step A_Mi, the K that determines in step B_MAi, to main spring amount of deflection f under different loads P_MCalculate, i.e.

$f_M=\left\{\begin{array}{cc}\frac{P}{\underset{i=1}{\overset{m}{\&Sigma;}}{K}_{Mi}},& 0\&le;P<P_k\\ \frac{P_K}{\underset{i=1}{\overset{m}{\&Sigma;}}{K}_{Mi}}+\frac{(P-P_K)}{\underset{i=1}{\overset{m}{\&Sigma;}}{K}_{{\mathrm{MA}}_i}},& P_k\&le;P\end{array}\right.;$

Iii step: auxiliary spring amount of deflection f under different loads_ACalculating:

Main spring root thickness h according to few sheet parabolic type variable-section steel sheet spring_2M, auxiliary spring root thickness h_2A, main reed Number m, auxiliary spring sheet number n, the P determined in i step_K, calculated G in the II step of step (1)_x-BC, IV step is calculated G_x-BCp, calculated G in V step_x-DAT, the K that determines in the step B of step (2)_MAi, and the K determined in step (3)_Aj, To auxiliary spring amount of deflection f under different loads P_ACalculate, i.e.

$f_A=\left\{\begin{array}{cc}0,& 0\&le;P<P_k\\ \frac{K_{MAm}{G}_{x-BC}{h}_{2A}^3(P-P_k)}{\underset{j=1}{\overset{n}{\&Sigma;}}{K}_{Aj}\underset{i=1}{\overset{m}{\&Sigma;}}{K}_{MAi}(G_{x-DAT}{h}_{2M}^3+G_{x-{\mathrm{BC}}_p}{h}_{2A}^3)},& P_k\&le;P\end{array}\right..$

The present invention has the advantage that than prior art

Owing to structure and the contact type of the few sheet parabolic type variable cross-section major-minor spring of non-ends contact formula are complicated, it is carried out Analytical calculation is extremely difficult, is understood according to consulting reference materials, and has not the most provided the few sheet of reliable non-ends contact formula The computational methods of parabolic type major-minor spring amount of deflection, constrain the design of few sheet variable-section steel sheet spring major-minor spring tangent line camber.This Invention can be according to the structural parameters of major-minor spring, elastic modelling quantity, sheet parabolic type variable-section steel sheet spring few to non-ends contact formula The amount of deflection of major-minor spring calculate.Tested by model machine deformation under load test, non-ends contact provided by the present invention The computational methods of the few sheet parabolic type major-minor spring amount of deflection of formula are correct, available major-minor spring amount of deflection value of calculation accurately and reliably, Reliable technology has been established in camber design and CAD software exploitation for the few sheet parabolic type variable cross-section major-minor spring of non-ends contact formula Basis；Meanwhile, utilize the method, product design level, product quality and vehicle ride performance can be improved；Meanwhile, also can drop Low design and experimental test expense, accelerate product development speed.

Accompanying drawing explanation

In order to be more fully understood that the present invention, it is described further below in conjunction with the accompanying drawings.

Fig. 1 is the calculation flow chart of the few sheet parabolic type major-minor spring amount of deflection of non-ends contact formula；

Fig. 2 is the structural representation of the half of the few sheet parabolic type variable cross-section major-minor spring of non-ends contact formula；

Main spring amount of deflection f under the different loads P of Fig. 3 embodiment_MThe curve of change；

Auxiliary spring amount of deflection f under the different loads P of Fig. 4 embodiment_AThe curve of change.

Specific embodiments

Below by embodiment, the present invention is described in further detail.

Embodiment: the few sheet parabolic type variable cross-section major-minor spring of certain non-ends contact formula is made up of 2 main springs and 1 auxiliary spring, The most main reed number m=2, auxiliary spring sheet number n=1, wherein, each main spring parameter is: half length L_M=575mm, width b= 60mm, the thickness h of root flat segments_2M=11mm, half l of installing space₃=55mm, the root of parabolic segment is to main spring end points Distance l_2M=L_M-l₃The thickness h of the end flat segments of=520mm, elastic modulus E=200GPa, a 1st main spring_1M1=7mm, The thickness of parabolic segment compares β₁=h_1M1/h_2MThe thickness h of the end flat segments of the=0.64, the 2nd main spring_1M2=6mm, parabolic segment Thickness compare β₂=h_1M2/h_2M=0.55；Auxiliary spring parameter is: half length L_A=375mm, width b=60mm, root flat segments Thickness h_2A=14mm, half l of installing space₃=55mm, the root of parabolic segment is to distance l of auxiliary spring end points_2A=L_A-l₃ =320mm, the thickness h of the end flat segments of the 1st auxiliary spring_1A1=8mm, the thickness of parabolic segment compares β_A1=h_1A1/h_2A= 0.57；Auxiliary spring is positioned at main spring parabolic segment with the contact point of main spring, and contact point is to distance l of main spring end points₀=200mm, Gap delta=15.48mm between major and minor spring.The major-minor of sheet parabolic type variable-section steel sheet spring few to this non-ends contact formula Spring amount of deflection calculates.

The computational methods of the few sheet parabolic type major-minor spring amount of deflection of the non-ends contact formula that present example is provided, it calculates Flow process is as it is shown in figure 1, specifically comprise the following steps that

(1) calculating of the few sheet parabolic type leaf spring major and minor spring end points deformation coefficient of non-ends contact formula:

I step: the calculating of each main spring end points deformation coefficient under end points stressing conditions:

Half length L according to few sheet main spring of parabolic type variable-section steel sheet spring_M=575mm, width b=60mm, peace Half l of dress spacing₃=55mm, parabola root is to distance l of spring end points_2M=520mm, elastic modulus E=200GPa, the The thickness of the parabolic segment of 1 main spring compares β₁The thickness of the parabolic segment of the=0.64, the 2nd main spring compares β₂=0.55, end points is subject to In the case of power the 1st, the 2nd main spring deformation coefficient G at end points_x-D1、G_x-D2Calculate, i.e.

$G_{x-D1}=\frac{4\&lsqb;l_{2M}^3(1-{\mathrm{\&beta;}}_1^3)+{(L_M-l_3/2)}^3\&rsqb;}{Eb}=89.29{\mathrm{mm}}^4/N;$

$G_{x-D2}=\frac{4\&lsqb;l_{2M}^3(1-{\mathrm{\&beta;}}_1^3)+{(L_M-l_3/2)}^3\&rsqb;}{Eb}=93.78{\mathrm{mm}}^4/N;$

II step: the 2nd main spring calculating of deformation coefficient at auxiliary spring contact point under end points stressing conditions:

Half length L according to few sheet main spring of parabolic type variable-section steel sheet spring_M=575mm, width b=60mm, peace Half l of dress spacing₃=55mm, parabola root is to distance l of spring end points_2M=520mm, elastic modulus E=200GPa, secondary Spring and main spring contact point are to distance l of main spring end points₀=200mm, to the 2nd main spring under end points stressing conditions in parabolic segment With the deformation coefficient G at auxiliary spring contact point_x-BCCalculate, i.e.

$G_{x-BC}=\frac{2}{Eb}\&lsqb;8l_{2M}^{3/2}{l}_0^{3/2}-(9l_{2M}^2+3{(L_M-l_3/2)}^2{l}_0+2l_{2M}^3+2{(L_M-l_3/2)}^3\&rsqb;=35.20{\mathrm{mm}}^4/N;$

III step: the calculating of the main spring end points deformation coefficient of the 2nd under stressing conditions at major-minor spring contact point:

Half length L according to few sheet main spring of parabolic type variable-section steel sheet spring_M=575mm, width b=60mm, peace Half l of dress spacing₃=55mm, parabola root is to distance l of spring end points_2M=520mm, elastic modulus E=200GPa, secondary Spring and main spring contact point are to distance l of main spring end points₀=200mm, to the 2nd main spring under stressing conditions at major-minor spring contact point Deformation coefficient G at endpoint location_x-Dp2Calculate, i.e.

$G_{x-D_{p}2}=\frac{4}{bE}\&lsqb;l_{2M}^3-6l_0{l}_{2M}^2+4l_{2M}^{3/2}{l}_0^{3/2}+{(L_M-l_3/2)}^3\&rsqb;=35.20{\mathrm{mm}}^4/N;$

IV step: the 2nd main spring meter of deformation coefficient at auxiliary spring contact point under stressing conditions at major-minor spring contact point Calculate:

Half length L according to few sheet main spring of parabolic type variable-section steel sheet spring_M=575mm, width b=60mm, peace Half l of dress spacing₃=55mm, parabola root is to distance l of spring end points_2M=520mm, elastic modulus E=200GPa, secondary Spring and main spring contact point are to distance l of main spring end points₀=200mm, to the 2nd main spring under stressing conditions at major-minor spring contact point Deformation coefficient G at parabolic segment with auxiliary spring contact point_x-BCpCalculate, i.e.

$\begin{array}{c}{G}_{x-{\mathrm{BC}}_p}=\frac{4}{Eb}\{(L_M-l_3/2-l_{2M})\&lsqb;{(L_M-l_3/2)}^2-3(L_M-l_3/2)l_0+(L_M-l_3/2)l_{2M}+3l_0^2-3l_0{l}_{2M}+l_{2M}^2\&rsqb;-\\ (6l_{2M}{l}_0^2-2l_{2M}^3-16l_0^{3/2}{l}_{2M}^{1/2}+12l_0{l}_{2M}^3)\}=17.76{\mathrm{mm}}^4/N;\end{array}$

V step: the calculating of each auxiliary spring end points deformation coefficient under end points stressing conditions:

Half length L according to few sheet parabolic type variable-section steel sheet spring auxiliary spring_A=375mm, width b=60mm, peace Half l of dress spacing₃=55mm, parabola root is to distance l of spring end points_2A=320mm, elastic modulus E=200GPa, the The thickness of the parabolic segment of 1 auxiliary spring compares β_A1=0.57, to the 1st auxiliary spring change at endpoint location under end points stressing conditions Shape coefficient G_x-DA1Calculate, i.e.

$G_{x-DA1}=\frac{4\&lsqb;l_{2A}^3(1-{\mathrm{\&beta;}}_{A1}^3)+{(L_A-l_3/2)}^3\&rsqb;}{Eb}=22.89{\mathrm{mm}}^4/N;$

Wherein, the deformation coefficient G after 1 auxiliary spring superposition_x-DATFor

$G_{x-DAT}=\frac{1}{\underset{j=1}{\overset{1}{\&Sigma;}}\frac{1}{G_{x-DAj}}}=22.89{\mathrm{mm}}^4/N;$

(2) calculating of each main spring clamping rigidity of the few sheet parabolic type leaf spring of non-ends contact formula:

Step A: each main spring clamping stiffness K before auxiliary spring contact_MiCalculating:

According to main spring root thickness h_2MCalculated G in=11mm, and the I step of step (1)_x-D1=89.29mm⁴/ N、G_x-D2=93.78mm⁴/ N, determines the 1st before auxiliary spring contact, the 2nd main spring half stiffness K in the clamp state_M1、 K_M2, i.e.

$K_{M1}=\frac{h_{2M}^3}{G_{x-D1}}=14.91N/mm;$

$K_{M2}=\frac{h_{2M}^3}{G_{x-D2}}=14.19N/mm;$

Step B: each main spring clamping stiffness K after auxiliary spring contact_MAiCalculating:

According to main spring root thickness h_2M=11mm, auxiliary spring root thickness h_2A=14mm, calculates in the I step of step (1) The G arrived_x-D1=89.29mm⁴/N、G_x-D2=93.78mm⁴Calculated G in/N, II step_x-BC=35.20mm⁴/ N, III walk Calculated G in Zhou_x-Dp2=35.20mm⁴Calculated G in/N, IV step_x-BCp=17.76mm⁴/ N and V step are fallen into a trap The G obtained_x-DAT=22.89mm⁴/ N, determines the 1st after the contact of major-minor spring, the 2nd main spring one in the clamp state Half stiffness K_MA1、K_MA2, i.e.

$K_{MA1}=\frac{h_{2M}^3}{G_{x-D1}}=14.91N/mm;$

$K_{MA2}=\frac{h_{2M}^3(G_{x-DAT}{h}_{2M}^3+G_{x-{\mathrm{BC}}_p}{h}_{2A}^3)}{G_{x-D2}(G_{x-DAT}{h}_{2M}^3+G_{x-{\mathrm{BC}}_p}{h}_{2A}^3)-G_{x-D_{p}2}{G}_{x-BC}{h}_{2A}^3}=26.17N/mm;$

(3) calculating of each auxiliary spring clamping rigidity of the few sheet parabolic type leaf spring of non-ends contact formula:

According to auxiliary spring root thickness h_2ACalculated G in=14mm, and the V step of step (1)_x-DA1=22.89mm⁴/ N, determines the 1st auxiliary spring half stiffness K in the clamp state_A1, i.e.

$K_{A1}=\frac{h_{2A}^3}{G_{x-DA1}}=119.88N/mm;$

(4) calculating of the few sheet parabolic type leaf spring major and minor spring amount of deflection of the non-ends contact formula under different loads:

I step: half load p when auxiliary spring works_KCalculating:

According to main spring root thickness h_2M=11mm, the major-minor spring gap delta=15.48mm at contact point, main reed number m=2, Calculated G in the II step of step (1)_x-BC=35.20mm⁴The K determined in/N, and the step A of step (2)_M1= 14.91N/mm、K_M2=14.19N/mm, determines half load p when auxiliary spring works_K, i.e.

$P_K=\frac{{\mathrm{\&delta;h}}_{2M}^3\underset{i=1}{\overset{2}{\&Sigma;}}{K}_{Mi}}{G_{x-BC}{K}_{M2}}=1200.40N;$

Ii step: main spring amount of deflection f under different loads_MCalculating:

Main reed number m=2, calculated P in i step according to few sheet parabolic type variable-section steel sheet spring_K= The K determined in 1200.40N, and the step A of step (2)_M1=14.91N/mm, K_M2=14.19N/mm, step B determine K_MA1=14.91N/mm, K_MA2=26.17N/mm, to main spring amount of deflection f under different loads P_MCalculate, i.e.

$f_M=\left\{\begin{array}{cc}\frac{P}{\underset{i=1}{\overset{2}{\&Sigma;}}{K}_{Mi}}=\frac{P}{29.10}mm,& 0\&le;P<1200.40N\\ \frac{P_K}{\underset{i=1}{\overset{2}{\&Sigma;}}{K}_{Mi}}+\frac{(P-P_K)}{\underset{i=1}{\overset{2}{\&Sigma;}}{K}_{MAi}}=41.25mm+\frac{P-1200.40}{41.08}mm,& 1200.40N\&le;P\end{array}\right.;$

Wherein, main spring amount of deflection f under different loads P_MThe curve of change is as shown in Figure 3；

Iii step: auxiliary spring amount of deflection f under different loads_ACalculating:

Main spring root thickness h according to few sheet parabolic type variable-section steel sheet spring_2M=11mm, auxiliary spring root thickness h_2A =14mm, main reed number m=2, auxiliary spring sheet number n=1, the P determined in i step_K=1200.40N, in the II step of step (1) Calculated G_x-BC=35.20mm⁴Calculated G in/N, IV step_x-BCp=17.76mm⁴/ N, V step are calculated G_x-DAT=22.89mm⁴/ N, the K determined in the step B of step (2)_MA1=14.91N/mm, K_MA2=26.17N/mm and step (3) K determined in_A1=119.88N/mm, to auxiliary spring amount of deflection f under different loads P_ACalculate, i.e.

$f_A=\left\{\begin{array}{cc}0,& 0\&le;P<1200.40N\\ \frac{K_{MA2}{G}_{x-CD}{h}_{2A}^3(P-P_k)}{\underset{j=1}{\overset{n}{\&Sigma;}}{K}_{Aj}\underset{i=1}{\overset{2}{\&Sigma;}}{K}_{MAi}(G_{x-DAT}{h}_{2M}^3+G_{x-{\mathrm{CD}}_z}{h}_{2A}^3)}=0.00648\&times;(P-1200.40)mm,& 1200.40N\&le;P\end{array}\right.;$

Wherein, auxiliary spring amount of deflection f under different loads P_AThe curve of change is as shown in Figure 4.

Being tested by prototype test, the amount of deflection value of calculation of major-minor spring is reliable, can meet non-ends contact formula few The calculating requirement of the major-minor spring amount of deflection of sheet parabolic type variable-section steel sheet spring, result shows that the non-end that this invention is provided connects The computational methods of the few sheet parabolic type major-minor spring amount of deflection of touch are correct.

Claims (1)

1. The computational methods of the few sheet parabolic type major-minor spring amount of deflection of the most non-ends contact formula, wherein, the few sheet parabolic of non-ends contact formula The half symmetrical structure of line style variable-section steel sheet spring is made up of root flat segments, parabolic segment and end flat segments 3 sections, each The end flat segments of main spring is non-isomorphic, i.e. the thickness of the end flat segments of the 1st main spring and length, more than other each Thickness and length, to meet the requirement of the 1st main spring complicated applied force；It is provided with certain between main spring parabolic segment and auxiliary spring contact Major-minor spring gap, works the design requirement of load meeting auxiliary spring；At the structural parameters of major-minor spring, elastic modelling quantity to stable condition Under, the amount of deflection of the major-minor spring of sheet parabolic type variable-section steel sheet spring few to non-ends contact formula calculates, and specific design walks Rapid as follows:

   (1) calculating of the few sheet parabolic type leaf spring major and minor spring end points deformation coefficient of non-ends contact formula:

   I step: the calculating of each main spring end points deformation coefficient under end points stressing conditions:

   Half length L according to few sheet main spring of parabolic type variable-section steel sheet spring_M, width b, half l of installing space₃, parabolic Line root is to distance l of spring end points_2M, elastic modulus E, the thickness of the parabolic segment of i-th main spring compares β_i, wherein, i=1, 2 ..., m, m are main reed number, to the deformation coefficient G at end points of each main spring under end points stressing conditions_x-DiCalculate, I.e.

   $G_{x-Di}=\frac{4\&lsqb;l_{2M}^3(1-{\mathrm{\&beta;}}_i^3)+{(L_M-l_3/2)}^3\&rsqb;}{Eb};$

   II step: the main spring of the m sheet calculating of deformation coefficient at auxiliary spring contact point under end points stressing conditions:

   Half length L according to few sheet main spring of parabolic type variable-section steel sheet spring_M, width b, half l of installing space₃, parabolic Line root is to distance l of spring end points_2M, elastic modulus E, distance l of auxiliary spring and main spring contact point to main spring end points₀, to end points The main spring of m sheet under stressing conditions deformation coefficient G at parabolic segment with auxiliary spring contact point_x-BCCalculate, i.e.

   $G_{x-BC}=\frac{2}{Eb}\&lsqb;8l_{2M}^{3/2}{l}_0^{3/2}-(9l_{2M}^2+3{\left(L_M-l_3/2\right)}^2{l}_0+2l_{2M}^3+2{(L_M-l_3/2)}^3\&rsqb;;$

   III step: the calculating of the m sheet main spring end points deformation coefficient under stressing conditions at major-minor spring contact point:

   Half length L according to few sheet main spring of parabolic type variable-section steel sheet spring_M, width b, half l of installing space₃, parabolic Line root is to distance l of spring end points_2M, elastic modulus E, distance l of auxiliary spring and main spring contact point to main spring end points₀, to major-minor The main spring of m sheet under stressing conditions deformation coefficient G at endpoint location at spring contact point_x-DpmCalculate, i.e.

   $G_{x-D_{p}m}=\frac{4}{bE}\&lsqb;l_{2M}^3-6l_0{l}_{2M}^2+4l_{2M}^{3/2}{l}_0^{3/2}+{(L_M-l_3/2)}^3\&rsqb;;$

   IV step: the main spring of the m sheet calculating of deformation coefficient at auxiliary spring contact point under stressing conditions at major-minor spring contact point:

   Half length L according to few sheet main spring of parabolic type variable-section steel sheet spring_M, width b, half l of installing space₃, parabolic Line root is to distance l of spring end points_2M, elastic modulus E, distance l of auxiliary spring and main spring contact point to main spring end points₀, to major-minor The main spring of m sheet under stressing conditions deformation coefficient G at parabolic segment with auxiliary spring contact point at spring contact point_x-BCpCount Calculate, i.e.

   $\begin{array}{c}{G}_{x-{\mathrm{BC}}_p}=\frac{4}{Eb}\{(L_M-l_3/2-l_{2M})\&lsqb;{(L_M-l_3/2)}^2-3(L_M-l_3/2)l_0+(L_M-l_3/2)l_{2M}+3l_0^2-3l_0{l}_{2M}+l_{2M}^2\&rsqb;-\\ (6l_{2M}{l}_0^2-2l_{2M}^3-16l_0^{3/2}{l}_{2M}^{1/2}+12l_0{l}_{2M}^3)\};\end{array}$

   V step: the calculating of each auxiliary spring end points deformation coefficient under end points stressing conditions:

   Half length L according to few sheet parabolic type variable-section steel sheet spring auxiliary spring_A, width b, half l of installing space₃, parabolic Line root is to distance l of spring end points_2A, elastic modulus E, the thickness of the parabolic segment of jth sheet auxiliary spring compares β_Aj, wherein, j=1, 2 ..., n, n are auxiliary spring sheet number, to the deformation coefficient G at endpoint location of each auxiliary spring under end points stressing conditions_x-DAjCount Calculate, i.e.

   $G_{x-DAj}=\frac{4\&lsqb;l_{2A}^3(1-{\mathrm{\&beta;}}_{Aj}^3)+{(L_A-l_3/2)}^3\&rsqb;}{Eb};$

   Wherein, the deformation coefficient G after the superposition of n sheet auxiliary spring_x-DATFor

   $G_{x-DAT}=\frac{1}{\underset{j=1}{\overset{n}{\&Sigma;}}\frac{1}{G_{x-DAj}}};$

   (2) calculating of each main spring clamping rigidity of the few sheet parabolic type leaf spring of non-ends contact formula:

   Step A: each main spring clamping stiffness K before auxiliary spring contact_MiCalculating:

   According to main spring root thickness h_2M, and calculated G in the I step of step (1)_x-Di, determine auxiliary spring contact before each The main spring of sheet half stiffness K in the clamp state_Mi, i.e.

   $K_{Mi}=\frac{h_{2M}^3}{G_{x-Di}},i=1,2,...,m;$

   Wherein, m is main reed number；

   Step B: each main spring clamping stiffness K after auxiliary spring contact_MAiCalculating:

   According to main spring root thickness h_2M, auxiliary spring root thickness h_2A, calculated G in the I step of step (1)_x-Di, in II step Calculated G_x-BC, calculated G in III step_x-Dpm, calculated G in IV step_x-BCp, and V step in calculate The G arrived_x-DAT, determine the half stiffness K in the clamp state of each main spring after the contact of major-minor spring_MAi, i.e.

   $K_{MAi}=\left\{\begin{array}{cc}\frac{h_{2M}^3}{G_{x-Di}},& i=1,2,...,m-1\\ \frac{h_{2M}^3(G_{x-DAT}{h}_{2M}^3+G_{x-{\mathrm{BC}}_p}{h}_{2A}^3)}{G_{x-Dm}(G_{x-DAT}{h}_{2M}^3+G_{x-{\mathrm{BC}}_p}{h}_{2A}^3)-G_{x-D_{p}m}{G}_{x-BC}{h}_{2A}^3},& i=m\end{array}\right.;$

   Wherein, m is main reed number；

   (3) calculating of each auxiliary spring clamping rigidity of the few sheet parabolic type leaf spring of non-ends contact formula:

   According to auxiliary spring root thickness h_2A, and calculated G in the V step of step (1)_x-DAj, determine that each auxiliary spring is at clamping shape Half stiffness K under state_Aj, i.e.

   $K_{Aj}=\frac{h_{2A}^3}{G_{x-DAj}},j=1,2,...,n;$

   Wherein, n is auxiliary spring sheet number；

   (4) calculating of the non-ends contact formula parabolic type leaf spring major and minor spring amount of deflection under different loads:

   I step: half load p when auxiliary spring works_KCalculating:

   According to main spring root thickness h_2M, major-minor spring gap delta at contact point, main reed number m, the II step of step (1) calculates The G obtained_x-BC, and the K determined in the step A of step (2)_Mi, determine half load p when auxiliary spring works_K, i.e.

   $P_K=\frac{{\mathrm{\&delta;h}}_{2M}^3\underset{i=1}{\overset{m}{\&Sigma;}}{K}_{Mi}}{G_{x-BC}{K}_{Mm}};$

   Ii step: main spring amount of deflection f under different loads_MCalculating:

   Main reed number m, calculated P in i step according to few sheet parabolic type variable-section steel sheet spring_K, and the A of step (2) The K determined in step_Mi, the K that determines in step B_MAi, to main spring amount of deflection f under different loads P_MCalculate, i.e.

   $f_M=\left\{\begin{array}{cc}\frac{P}{\underset{i=1}{\overset{m}{\&Sigma;}}{K}_{Mi}},& 0\&le;P<P_k\\ \frac{P_K}{\underset{i=1}{\overset{m}{\&Sigma;}}{K}_{Mi}}+\frac{(P-P_K)}{\underset{i=1}{\overset{m}{\&Sigma;}}{K}_{MAi}},& P_k\&le;P\end{array}\right.;$

   Iii step: auxiliary spring amount of deflection f under different loads_ACalculating:

   Main spring root thickness h according to few sheet parabolic type variable-section steel sheet spring_2M, auxiliary spring root thickness h_2A, main reed number m, Auxiliary spring sheet number n, the P determined in i step_K, calculated G in the II step of step (1)_x-BC, calculated in IV step G_x-BCp, calculated G in V step_x-DAT, the K that determines in the step B of step (2)_MAi, and the K determined in step (3)_Aj, right Auxiliary spring amount of deflection f under different loads P_ACalculate, i.e.

   $f_A=\left\{\begin{array}{cc}0,& 0\&le;P<P_k\\ \frac{K_{MAm}{G}_{x-BC}{h}_{2A}^3(P-P_K)}{\underset{j=1}{\overset{n}{\&Sigma;}}{K}_{Aj}\underset{i=1}{\overset{m}{\&Sigma;}}{K}_{MAi}(G_{x-DAT}{h}_{2M}^3+G_{x-{\mathrm{BC}}_p}{h}_{2A}^3)},& P_k\&le;P\end{array}\right..$