CN106372371A - End part contact type few-leaf parabolic primary and secondary spring deflection calculating method - Google Patents

Abstract

The invention relates to an end part contact type few-leaf parabolic primary and secondary spring deflection calculating method, and belongs to the technical field of suspension leaf springs. According to the end part contact type few-leaf parabolic primary and secondary spring deflection calculating method, the deflection of a primary spring and a secondary spring of an end part contact type few-leaf parabolic variable cross section leaf spring can be designed according to structural parameters and elasticity modulus of the primary spring and the secondary spring. Through a prototype load deformation experiment test, the end part contact type few-leaf parabolic primary and secondary spring deflection calculating method provided by the invention is correct, an accurate and reliable primary and secondary spring deflection calculation value can be obtained, and a reliable technical foundation is laid for the arc height design of end part contact type few-leaf parabolic primary and secondary springs and CAD software development. By utilizing the method, the product design level, quality and performance, and vehicle driving smoothness can be improved; meanwhile, the product design and the experiment test cost are reduced; the product development speed is increased.

Description

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

Technical field

The present invention relates to the meter of the few piece parabolic type major-minor spring amount of deflection of vehicle suspension leaf spring, particularly ends contact formula Calculation method.

Background technology

With vehicle energy saving, comfortableization, lightweight, safe fast development, few piece variable-section steel sheet spring is because of tool Have lightweight, stock utilization is high, no rub between piece or friction is little, vibration noise is low, the advantages of long service life, be increasingly subject to The highest attention of vehicle suspension expert, manufacturing enterprise and vehicle manufacture enterprise, and obtained in vehicle suspension system extensively Application.Generally for the design requirement meeting processing technique, stress intensity, rigidity and hanger thickness, piece Variable Section Steel can will be lacked 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 Because the stress of few piece 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, reality designed by the thickness of end flat segments of the 1st flat spring and length, each more than other The thickness of flat spring end flat segments and length, mostly adopt the non-few piece variable-section steel sheet spring waiting structure in end, to meet The complicated requirement of 1st flat spring stress, additionally, requiring to meet the rigidity Design under different loads, generally will lack piece change and cutting Face leaf spring is designed as the few piece parabolic type variable cross-section major-minor spring form of ends contact formula.However, because ends contact formula is few The structure of piece parabolic type variable cross-section major-minor spring and contact type are complicated, it are analyzed calculate extremely difficult, according to looked into money Material understands, has not provided the calculating side of the few piece parabolic type major-minor spring amount of deflection of reliable ends contact formula at present both at home and abroad always Method, constrains the design of few piece variable-section steel sheet spring major-minor spring tangent line camber.With Vehicle Speed and its to ride comfort The continuous improvement requiring, to end contact, few piece parabolic type variable cross-section major-minor spring is put forward higher requirement, therefore, it is necessary to Set up a kind of computational methods of the few piece parabolic type major-minor spring amount of deflection of accurate, reliable ends contact formula, be that ends contact formula is few Reliable technical foundation is established in the camber design of piece parabolic type variable cross-section major-minor spring, meets Vehicle Industry fast development, vehicle Ride performance and the design requirement of the few piece parabolic type variable cross-section major-minor spring of ends contact formula, improve product design level, matter Amount and performance, meet the design requirement of vehicle ride performance；Meanwhile, reduce design and testing expenses, accelerate product development speed Degree.

Content of the invention

For defect present in above-mentioned prior art, the technical problem to be solved be provide a kind of easy, The reliably computational methods of the few piece parabolic type major-minor spring amount of deflection of ends contact formula, its calculation flow chart, as shown in Figure 1.End The few piece parabolic type variable cross-section major-minor spring of contact is symmetrical structure, and the half symmetrical structure of major-minor spring can see cantilever beam as, I.e. symmetrical center line is root fixing end, and the end stress point of main spring and the contact of auxiliary spring are respectively as main spring end points and auxiliary spring end Point, the structural representation of the major-minor spring of half symmetrical structure, as shown in Fig. 2 including, main spring 1, root shim 2, auxiliary spring 3, End pad 4.The half length of main spring 1 every is l_m, it is by root flat segments, parabolic segment and three sections of institute's structures of end flat segments Become, the thickness of the root flat segments of every main spring is h_2m, the half of every main spring installing space is l₃, the width of every main spring is b；The end flat segments of each of main spring 1 are non-to wait structure, i.e. the thickness of end flat segments of the 1st main spring and length is each more than other The thickness of piece and length, the thickness of end flat segments of each main spring and length 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, and the thickness of the parabolic segment of each main spring ratio is for β_i=h_1mi/ h_2m, the distance of root to the main spring end points of the parabolic segment of every main spring is l_2m=l_m-l₃, the end of the parabolic segment of each main spring Portion is to main spring end points apart from l_1mi=l_2mβ_i ²；Each root flat segments of main spring 1 and setting and the root flat segments of auxiliary spring 3 between There is a root shim 2, the end flat segments of each of main spring 1 are provided with end pad 4, and the material of end pad 4 is carbon fiber composite Material, for reducing the frictional noise being produced during spring works；The half length of auxiliary spring 3 every is l_a, it is by root flat segments, throwing Thing line segment and three sections of end flat segments are constituted, and the thickness of the root flat segments of every auxiliary spring is h_2a, every auxiliary spring installing space Half be l₃, the width of every auxiliary spring is b；The thickness of end flat segments of each auxiliary spring and length are respectively h_1ajAnd l_1aj, j =1,2 ..., n, n are auxiliary spring piece number；The middle variable cross-section of every auxiliary spring is parabolic segment, the thickness of the parabolic segment of each auxiliary spring Degree ratio is β_aj=h_1aj/h_2a, the distance of root to the auxiliary spring end points of the parabolic segment of every auxiliary spring is l_2a=l_a-l₃, each auxiliary spring Parabolic segment end to auxiliary spring end points distanceThe m piece end flat segments of main spring 1 and the end of auxiliary spring 3 It is provided with major and minor spring gap delta between contact；When load works load more than auxiliary spring, in auxiliary spring and main spring end flat segments 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, each of major-minor spring End stress differs, and the main spring contacting with auxiliary spring, in addition to by end points power, also bears propping up of auxiliary spring at contact point Support force.In the case of the structural parameters of major-minor spring, elastic modelling quantity give, few piece parabolic type variable cross-section steel plates to end contact The major-minor spring amount of deflection of spring is calculated.

For solving above-mentioned technical problem, the meter of the few piece parabolic type major-minor spring amount of deflection of ends contact formula provided by the present invention Calculation method is it is characterised in that adopt following calculation procedure:

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

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

Half length l according to the main spring of few piece parabolic type variable-section steel sheet spring_m, width b, half l of installing space₃, Parabola root is to spring end points apart from l_2m, elastic modelling quantity e, the thickness of the parabolic segment of i-th main spring compares β_i, wherein, i= Reed number based on 1,2 ..., m, m, to deformation coefficient g at end points for each main spring under end points stressing conditions_x-diCounted Calculate, that is,

$g_{x-di}=\frac{4\[l_{2m}^3(1-{\mathrm{\β}}_i^3)+{(l_m-l_3/2)}^3\]}{eb};$

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

Half length l according to the main spring of few piece parabolic type variable-section steel sheet spring_m, width b, half l of installing space₃, Parabola root is to spring end points apart from l_2m, elastic modelling quantity e, the thickness of the parabolic segment of the main spring of m piece compares β_m, auxiliary spring and master Spring contact point is to main spring end points apart from l₀, the main spring of m piece under end points stressing conditions is contacted with auxiliary spring in end flat segments Deformation coefficient g at point_x-cdCalculated, that is,

$\begin{array}{c}{g}_{x-cd}=\frac{4{(l_m-l_3/2)}^3-6l_0{(l_m-l_3/2)}^2-4l_{2m}^3+6l_0{l}_{2m}^2}{eb}+\frac{2{(l_0-l_{2m}{\mathrm{\β}}_m^2)}^2(2l_{2m}{\mathrm{\β}}_m^2+l_0)}{{\mathrm{eb\β}}_m^3}-\\ \frac{8l_{2m}^2({\mathrm{\β}}_m-1)(l_{2m}-3l_0+l_{2m}{\mathrm{\β}}_m^2+l_{2m}{\mathrm{\β}}_m)}{eb};\end{array}$

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

Half length l according to the main spring of few piece parabolic type variable-section steel sheet spring_m, width b, half l of installing space₃, Parabola root is to spring end points apart from l_2m, elastic modelling quantity e, the thickness of the parabolic segment of the main spring of m piece compares β_m, auxiliary spring and master Spring contact point is to main spring end points apart from l₀, to the main spring of m piece under stressing conditions at major-minor spring contact point at endpoint location Deformation coefficient g_x-dzmCalculated, that is,

$\begin{array}{c}{g}_{x-d_{z}m}=\frac{4{(l_m-l_3/2)}^3-6l_0{(l_m-l_3/2)}^2-4l_{2m}^3+6l_0{l}_{2m}^2}{eb}+\frac{2{(l_0-l_{2m}{\mathrm{\β}}_m^2)}^2(2l_{2m}{\mathrm{\β}}_m^2+l_0)}{{\mathrm{eb\β}}_m^3}-\\ \frac{8l_{2m}^2({\mathrm{\β}}_m-1)(l_{2m}-3l_0+l_{2m}{\mathrm{\β}}_m^2+l_{2m}{\mathrm{\β}}_m)}{eb};\end{array}$

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

Half length l according to the main spring of few piece parabolic type variable-section steel sheet spring_m, width b, half l of installing space₃, Parabola root is to spring end points apart from l_2m, elastic modelling quantity e, the thickness of the parabolic segment of the main spring of m piece compares β_m, auxiliary spring and master Spring contact point is to main spring end points apart from l₀, to the main spring of m piece under stressing conditions at major-minor spring contact point in end flat segments With the deformation coefficient g at auxiliary spring contact point_x-cdzCalculated, that is,

$\begin{array}{c}{g}_{x-{\mathrm{cd}}_z}=\frac{4(l_m-l_3/2-l_{2m})\[{(l_m-l_3/2)}^2-3(l_m-l_3/2)l_0+(l_m-l_3/2)l_{2m}+3l_0^2-3l_0{l}_{2m}+l_{2m}^2\]}{eb}-\\ \frac{4{(l_0-l_{2m}{\mathrm{\β}}_m^2)}^3}{{\mathrm{eb\β}}_m^3}-\frac{12l_{2m}}{eb}\[4l_0{l}_{2m}(1-{\mathrm{\β}}_m)+2l_0^2(1-\frac{1}{{\mathrm{\β}}_m})+\frac{2l_{2m}^2({\mathrm{\β}}_m^3-1)}{3}\];\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 piece parabolic type variable-section steel sheet spring auxiliary spring_a, width b, half l of installing space₃, Parabola root is to spring end points apart from l_2a, elastic modelling quantity e, the thickness of the parabolic segment of jth piece auxiliary spring compares β_aj, wherein, j =1,2 ..., n, n are auxiliary spring piece number, to deformation coefficient g at endpoint location for each auxiliary spring under end points stressing conditions_x-dajEnter Row calculates, that is,

$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 piece auxiliary spring_x-datFor

$g_{x-dat}=\frac{1}{\underset{j=1}{\overset{n}{\σ}}\frac{1}{g_{x-daj}}};$

(2) calculating of ends contact formula few each of piece parabolic type leaf spring main spring clamping rigidity:

A step: each main spring before auxiliary spring contact clamps rigidity k_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 rigidity k in the clamp state_mi, that is,

$k_{mi}=\frac{h_{2m}^3}{g_{x-di}},i=1,2,...,m;$

Wherein, reed number based on m；

B step: each main spring after auxiliary spring contact clamps rigidity k_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 rapid_x-cd, calculated g in iii step_x-dzm, calculated g in iv step_x-cdz, and v step fall into a trap The g obtaining_x-dat, determine each main spring half rigidity k in the clamp state after the contact of major-minor spring_mai, that is,

$k_{mai}=\left\{\begin{array}{cc}\frac{h_{2m}^3}{g_{x-di}},& i=1,2,...,m-1\\ \frac{h_{2m}^3(g_{x-dat}{h}_{2m}^3+g_{x-{\mathrm{cd}}_z}{h}_{2a}^3)}{g_{x-dm}(g_{x-dat}{h}_{2m}^3+g_{x-{\mathrm{cd}}_z}{h}_{2a}^3)-g_{x-d_{z}m}{g}_{x-cd}{h}_{2a}^3},& i=m\end{array}\right.;$

Wherein, reed number based on m；

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

According to auxiliary spring root thickness h_2a, and calculated g in the v step of step (1)_x-daj, determine each auxiliary spring in folder Half rigidity k under tight state_aj, that is,

$k_{aj}=\frac{h_{2a}^3}{g_{x-daj}},j=1,2,...,n;$

Wherein, n is auxiliary spring piece number；

(4) calculating of the few major and minor spring amount of deflection of piece parabolic type leaf spring of the ends contact formula 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-cd, and the k determining in a step of step (2)_mi, half load p when determining that auxiliary spring works_k, that is,

$p_k=\frac{{\mathrm{\δh}}_{2m}^3\underset{i=1}{\overset{m}{\σ}}{k}_{mi}}{g_{x-cd}{k}_{mm}};$

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

Main reed number m, calculated p in i step according to few piece parabolic type variable-section steel sheet spring_k, and step (2) k determining in a step_mi, the k that determines in b step_mai, to main spring amount of deflection f under different loads p_mCalculated, that is,

$f_m=\left\{\begin{array}{cc}\frac{p}{\underset{i=1}{\overset{m}{\&sigma;}}{k}_{mi}},& 0\&le;p<p_k\\ \frac{p_k}{\underset{i=1}{\overset{m}{\&sigma;}}{k}_{mi}}+\frac{(p-p_k)}{\underset{i=1}{\overset{m}{\&sigma;}}{k}_{mai}},& p_k\&le;p\end{array}\right.;$

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

Main spring root thickness h according to few piece parabolic type variable-section steel sheet spring_2m, auxiliary spring root thickness h_2a, main reed Number m, auxiliary spring piece number n, the p determining in i step_k, calculated g in the ii step of step (1)_x-cd, be calculated in iv step G_x-cdz, calculated g in v step_x-dat, the k of determination in the b step of step (2)_mai, and the k determining in step (3)_aj, To auxiliary spring amount of deflection f under different loads p_aCalculated, that is,

$f_a=\left\{\begin{array}{cc}0,& 0\&le;p<p_k\\ \frac{k_{mam}{g}_{x-cd}{h}_{2a}^3(p-p_k)}{\underset{j=1}{\overset{n}{\&sigma;}}{k}_{aj}\underset{i=1}{\overset{m}{\&sigma;}}{k}_{mai}(g_{x-dat}{h}_{2m}^3+g_{x-{\mathrm{cd}}_z}{h}_{2a}^3)},& p_k\&le;p\end{array}\right..$

The present invention has the advantage that than prior art

Because the structure of the few piece parabolic type variable cross-section major-minor spring of ends contact formula and contact type are complicated, it is carried out point Analysis calculating is extremely difficult, is understood according to consulting reference materials, and has not provided the few piece parabolic of reliable ends contact formula at present both at home and abroad always The computational methods of line style major-minor spring amount of deflection, constrain the design of few piece variable-section steel sheet spring major-minor spring tangent line camber.The present invention Can be according to the structural parameters of major-minor spring, elastic modelling quantity, the major-minor to the few piece parabolic type variable-section steel sheet spring of end contact The amount of deflection of spring is calculated.Tested by model machine deformation under load test, the few piece of ends contact formula provided by the present invention is thrown The computational methods of thing line style major-minor spring amount of deflection are correct, can get accurately and reliably major-minor spring amount of deflection value of calculation, are that end connects Reliable technical foundation has been established in the camber design of the few piece parabolic type variable cross-section major-minor spring of touch and cad software development；Meanwhile, Using the method, product design level, product quality and vehicle ride performance can be improved；Meanwhile, also can reduce design and try Test testing expense, accelerate product development speed.

Brief description

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 few piece parabolic type major-minor spring amount of deflection of ends contact formula；

Fig. 2 is the structural representation of the half of the few piece parabolic type variable cross-section major-minor spring of 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 piece parabolic type variable cross-section major-minor spring of certain ends contact formula is made up of 2 main springs and 1 auxiliary spring, that is, Main reed number m=2, auxiliary spring piece 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 to main spring end points away from From l_2m=l_m-l₃The thickness h of the end flat segments of=520mm, elastic modelling quantity e=200gpa, a 1st main spring_1m1=7mm, parabolic The thickness of line segment compares β₁=h_1m1/h_2mThe thickness h of the end flat segments of the=0.64, the 2nd main spring_1m2=6mm, the thickness of parabolic segment Degree compares β₂=h_1m2/h_2m=0.55；Auxiliary spring parameter is: half length l_a=525mm, width b=60mm, the thickness of root flat segments Degree h_2a=14mm, half l of installing space₃=55mm, the root of parabolic segment is to auxiliary spring end points apart from l_2a=l_a-l₃= 470mm, 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； The contact point of auxiliary spring and main spring is located in the flat segments of main spring end, and contact point to main spring end points apart from l₀=50mm, major and minor Gap delta=34.04mm between spring.The major-minor spring amount of deflection of the few piece parabolic type variable-section steel sheet spring of this ends contact formula is entered Row calculates.

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

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

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

Half length l according to the main spring of few piece parabolic type variable-section steel sheet spring_m=575mm, width b=60mm, peace Half l of dress spacing₃=55mm, parabola root is to spring end points apart from l_2m=520mm, elastic modelling quantity 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 The 1st in the case of power, the 2nd main spring deformation coefficient g at end points_x-d1、g_x-d2Calculated, that is,

$g_{x-d1}=\frac{4\&lsqb;l_{2m}^3(1-{\mathrm{\&beta;}}_1^3)+{(l_m-l_3/2)}^3\&rsqb;}{eb}=89.29{\mathrm{mm}}^4/n;$

$g_{x-d2}=\frac{4\&lsqb;l_{2m}^3(1-{\mathrm{\&beta;}}_1^3)+{(l_m-l_3/2)}^3\&rsqb;}{eb}=93.78{\mathrm{mm}}^4/n;$

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

Half length l according to the main spring of few piece parabolic type variable-section steel sheet spring_m=575mm, width b=60mm, peace Half l of dress spacing₃=55mm, parabola root is to spring end points apart from l_2m=520mm, elastic modelling quantity e=200gpa, the The thickness of the parabolic segment of 2 main springs compares β₂=0.55, auxiliary spring and main spring contact point are to main spring end points apart from l₀=50mm is right Deformation coefficient g at end flat segments with auxiliary spring contact point for the 2nd main spring under end points stressing conditions_x-cdCalculated, that is,

$\begin{array}{c}{g}_{x-cd}=\frac{4{(l_m-l_3/2)}^3-6l_0{(l_m-l_3/2)}^2-4l_{2m}^3+6l_0{l}_{2m}^2}{eb}+\frac{2{(l_0-l_{2m}{\mathrm{\&beta;}}_2^2)}^2(2l_{2m}{\mathrm{\&beta;}}_2^2+l_0)}{{\mathrm{eb\&beta;}}_2^3}-\\ \frac{8l_{2m}^2({\mathrm{\&beta;}}_2-1)(l_{2m}-3l_0+l_{2m}{\mathrm{\&beta;}}_2^2+l_{2m}{\mathrm{\&beta;}}_2)}{eb}=77.28{\mathrm{mm}}^4/n;\end{array}$

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

Half length l according to the main spring of few piece parabolic type variable-section steel sheet spring_m=575mm, width b=60mm, peace Half l of dress spacing₃=55mm, parabola root is to spring end points apart from l_2m=520mm, elastic modelling quantity e=200gpa, the The thickness of the parabolic segment of 2 main springs compares β₂=0.55, auxiliary spring and main spring contact point are to main spring end points apart from l₀=50mm is right Deformation coefficient g at endpoint location for the 2nd main spring under stressing conditions at major-minor spring contact point_x-dz2Calculated, that is,

$\begin{array}{c}{g}_{x-d_{z}2}=\frac{4{(l_m-l_3/2)}^3-6l_0{(l_m-l_3/2)}^2-4l_{2m}^3+6l_0{l}_{2m}^2}{eb}+\frac{2{(l_0-l_{2m}{\mathrm{\&beta;}}_2^2)}^2(2l_{2m}{\mathrm{\&beta;}}_2^2+l_0)}{{\mathrm{eb\&beta;}}_2^3}-\\ \frac{8l_{2m}^2({\mathrm{\&beta;}}_2-1)(l_{2m}-3l_0+l_{2m}{\mathrm{\&beta;}}_2^2+l_{2m}{\mathrm{\&beta;}}_2)}{eb}=77.28{\mathrm{mm}}^4/n;\end{array}$

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

Half length l according to the main spring of few piece parabolic type variable-section steel sheet spring_m=575mm, width b=60mm, peace Half l of dress spacing₃=55mm, parabola root is to spring end points apart from l_2m=520mm, elastic modelling quantity e=200gpa, the The thickness of the parabolic segment of 2 main springs compares β₂=0.55, auxiliary spring and main spring contact point are to main spring end points apart from l₀=50mm is right Deformation coefficient g at end flat segments with auxiliary spring contact point for the 2nd main spring under stressing conditions at major-minor spring contact point_x-cdzEnter Row calculates, that is,

$\begin{array}{c}{g}_{x-{\mathrm{cd}}_z}=\frac{4(l_m-l_3/2-l_{2m})\&lsqb;{(l_m-l_3/2)}^2-3(l_m-l_3/2)l_0+(l_m-l_3/2)l_{2m}+3l_0^2-3l_0{l}_{2m}+l_{2m}^2\&rsqb;}{eb}-\\ \frac{4{(l_0-l_{2m}{\mathrm{\&beta;}}_2^2)}^3}{{\mathrm{eb\&beta;}}_2^3}-\frac{12l_{2m}}{eb}\&lsqb;4l_0{l}_{2m}(1-{\mathrm{\&beta;}}_2)+2l_0^2(1-\frac{1}{{\mathrm{\&beta;}}_2})+\frac{2l_{2m}^2({\mathrm{\&beta;}}_2^3-1)}{3}\&rsqb;=64.85{\mathrm{mm}}^4/n;\end{array}$

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

Half length l according to few piece parabolic type variable-section steel sheet spring auxiliary spring_a=525mm, width b=60mm, peace Half l of dress spacing₃=55mm, parabola root is to spring end points apart from l_2a=470mm, elastic modelling quantity e=200gpa, the The thickness of the parabolic segment of 1 auxiliary spring compares β_a1=0.57, to the 1st change at endpoint location for the auxiliary spring under end points stressing conditions Shape coefficient g_x-da1Calculated, that is,

$g_{x-da1}=\frac{4\&lsqb;l_{2a}^3(1-{\mathrm{\&beta;}}_{a1}^3)+{(l_a-l_3/2)}^3\&rsqb;}{eb}=69.24{\mathrm{mm}}^4/n;$

Wherein, the deformation coefficient g after 1 auxiliary spring superposition_x-datFor

$g_{x-dat}=\frac{1}{\underset{j=1}{\overset{1}{\&sigma;}}\frac{1}{g_{x-daj}}}=69.24{\mathrm{mm}}^4/n;$

(2) calculating of ends contact formula few each of piece parabolic type leaf spring main spring clamping rigidity:

A step: each main spring before auxiliary spring contact clamps rigidity k_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, the 2nd main spring half rigidity k in the clamp state before auxiliary spring contact_m1、 k_m2, that is,

$k_{m1}=\frac{h_{2m}^3}{g_{x-d1}}=14.91n/mm;$

$k_{m2}=\frac{h_{2m}^3}{g_{x-d2}}=14.19n/mm;$

B step: each main spring after auxiliary spring contact clamps rigidity k_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 arriving_x-d1=89.29mm⁴/n、g_x-d2=93.78mm⁴Calculated g in/n, ii step_x-cd=77.28mm⁴/ n, iii walk Calculated g in rapid_x-dz2=77.28mm⁴Calculated g in/n, iv step_x-cdz=64.85mm⁴/ n and v step are fallen into a trap The g obtaining_x-dat=69.24mm⁴/ n, determine after the contact of major-minor spring the 1st, the 2nd main spring in the clamp state one Half rigidity k_ma1、k_ma2, that is,

$k_{ma1}=\frac{h_{2m}^3}{g_{x-d1}}=14.91n/mm;$

$k_{ma2}=\frac{h_{2m}^3(g_{x-dat}{h}_{2m}^3+g_{x-{\mathrm{cd}}_z}{h}_{2a}^3)}{g_{x-d2}(g_{x-dat}{h}_{2m}^3+g_{x-{\mathrm{cd}}_z}{h}_{2a}^3)-g_{x-d_{z}2}{g}_{x-cd}{h}_{2a}^3}=40.20n/mm;$

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

According to auxiliary spring root thickness h_2aCalculated g in=14mm, and the v step of step (1)_x-da1=69.24mm⁴/ N, determines the 1st auxiliary spring half rigidity k in the clamp state_a1, that is,

$k_{a1}=\frac{h_{2a}^3}{g_{x-da1}}=39.63n/mm;$

(4) calculating of the few major and minor spring amount of deflection of piece parabolic type leaf spring of the 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=34.04mm at contact point, main reed number m=2, Calculated g in the ii step of step (1)_x-cd=77.28mm⁴The k determining in/n, and a step of step (2)_m1= 14.91n/mm、k_m2=14.19n/mm, half load p when determining that auxiliary spring works_k, that is,

$p_k=\frac{{\mathrm{\&delta;h}}_{2m}^3\underset{i=1}{\overset{2}{\&sigma;}}{k}_{mi}}{g_{x-cd}{k}_{m2}}=1202.30n;$

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 piece parabolic type variable-section steel sheet spring_k= The k determining in 1202.30n, and a step of step (2)_m1=14.91n/mm, k_m2Determine in=14.19n/mm, b step k_ma1=14.91n/mm, k_ma2=40.20n/mm, to main spring amount of deflection f under different loads p_mCalculated, that is,

$f_m=\left\{\begin{array}{cc}\frac{p}{\underset{i=1}{\overset{2}{\&sigma;}}{k}_{mi}}=\frac{p}{29.10}mm,& 0\&le;p<1202.30n\\ \frac{p_k}{\underset{i=1}{\overset{2}{\&sigma;}}{k}_{mi}}+\frac{(p-p_k)}{\underset{i=1}{\overset{2}{\&sigma;}}{k}_{mai}}=41.32mm+\frac{p-1202.30}{55.11}mm,& 1202.30n\&le;p\end{array}\right.;$

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 piece parabolic type variable-section steel sheet spring_2m=11mm, auxiliary spring root thickness h_2a =14mm, main reed number m=2, auxiliary spring piece number n=1, the p determining in i step_k=1202.30n, in the ii step of step (1) Calculated g_x-cd=77.28mm⁴Calculated g in/n, iv step_x-cdz=64.85mm⁴It is calculated in/n, v step G_x-dat=69.24mm⁴/ n, the k determining in the b step of step (2)_ma1=14.91n/mm, k_ma2=40.20n/mm and step (3) k determining in_a1=39.63n/mm, to auxiliary spring amount of deflection f under different loads p_aCalculated, that is,

$f_a=\left\{\begin{array}{cc}0,& 0\&le;p<1202.30n\\ \frac{k_{ma2}{g}_{x-cd}{h}_{2a}^3(p-p_k)}{\underset{j=1}{\overset{1}{\&sigma;}}{k}_{aj}\underset{i=1}{\overset{2}{\&sigma;}}{k}_{mai}(g_{x-dat}{h}_{2m}^3+g_{x-{\mathrm{cd}}_z}{h}_{2a}^3)}=0.01445\&times;(p-1202.30)mm,& 1202.30n\&le;p\end{array}\right.;$

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

Tested by prototype test, the amount of deflection value of calculation of major-minor spring is reliable, the few piece of ends contact formula can be met The calculating of the major-minor spring amount of deflection of parabolic type variable-section steel sheet spring requires, and result shows the ends contact formula that this invention is provided The computational methods of few piece parabolic type major-minor spring amount of deflection are correct.

Claims (1)

1. the computational methods of the few piece parabolic type major-minor spring amount of deflection of ends contact formula, wherein, the few piece parabolic type of ends contact formula The half symmetrical structure of variable-section steel sheet spring is made up of root flat segments, parabolic segment and 3 sections of end flat segments, each main spring End flat segments be non-isomorphic, i.e. the thickness of end flat segments of the 1st main spring and length, more than other thickness of each And length, to meet the requirement of the 1st main spring complicated applied force；It is provided with certain master between main spring end flat segments and auxiliary spring contact Auxiliary spring gap, is worked the design requirement of load with meeting auxiliary spring；Give situation in the structural parameters of major-minor spring, elastic modelling quantity Under, the amount of deflection of the major-minor spring of the few piece parabolic type variable-section steel sheet spring of end contact is calculated, specific design step As follows:

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

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

Half length l according to the main spring of few piece parabolic type variable-section steel sheet spring_m, width b, half l of installing space₃, parabolic Line root is to spring end points apart from l_2m, elastic modelling quantity e, the thickness of the parabolic segment of i-th main spring compares β_i, wherein, i=1, Reed number based on 2 ..., m, m, to deformation coefficient g at end points for each main spring under end points stressing conditions_x-diCalculated, 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 calculating of the m piece main spring deformation coefficient at auxiliary spring contact point under end points stressing conditions:

Half length l according to the main spring of few piece parabolic type variable-section steel sheet spring_m, width b, half l of installing space₃, parabolic Line root is to spring end points apart from l_2m, elastic modelling quantity e, the thickness of the parabolic segment of the main spring of m piece compares β_m, auxiliary spring connect with main spring Contact is to main spring end points apart from l₀, to the main spring of m piece under end points stressing conditions at end flat segments with auxiliary spring contact point Deformation coefficient g_x-cdCalculated, that is,

$\begin{array}{c}{g}_{x-cd}=\frac{4{(l_m-l_3/2)}^3-6l_0{(l_m-l_3/2)}^2-4l_{2m}^3+6l_0{l}_{2m}^2}{eb}+\frac{2{(l_0-l_{2m}{\mathrm{\&beta;}}_m^2)}^2(2l_{2m}{\mathrm{\&beta;}}_m^2+l_0)}{{\mathrm{eb\&beta;}}_m^3}-\\ \frac{8l_{2m}^2({\mathrm{\&beta;}}_m-1)(l_{2m}-3l_0+l_{2m}{\mathrm{\&beta;}}_m^2+l_{2m}{\mathrm{\&beta;}}_m)}{eb}\end{array};$

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

Half length l according to the main spring of few piece parabolic type variable-section steel sheet spring_m, width b, half l of installing space₃, parabolic Line root is to spring end points apart from l_2m, elastic modelling quantity e, the thickness of the parabolic segment of the main spring of m piece compares β_m, auxiliary spring connect with main spring Contact is to main spring end points apart from l₀, to change at endpoint location for the main spring of m piece under stressing conditions at major-minor spring contact point Shape coefficient g_x-dzmCalculated, that is,

$\begin{array}{c}{g}_{x-d_{z}m}=\frac{4{(l_m-l_3/2)}^3-6l_0{(l_m-l_3/2)}^2-4l_{2m}^3+6l_0{l}_{2m}^2}{eb}+\frac{2{(l_0-l_{2m}{\mathrm{\&beta;}}_m^2)}^2(2l_{2m}{\mathrm{\&beta;}}_m^2+l_0)}{{\mathrm{eb\&beta;}}_m^3}-\\ \frac{8l_{2m}^2({\mathrm{\&beta;}}_m-1)(l_{2m}-3l_0+l_{2m}{\mathrm{\&beta;}}_m^2+l_{2m}{\mathrm{\&beta;}}_m)}{eb}\end{array};$

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

Half length l according to the main spring of few piece parabolic type variable-section steel sheet spring_m, width b, half l of installing space₃, parabolic Line root is to spring end points apart from l_2m, elastic modelling quantity e, the thickness of the parabolic segment of the main spring of m piece compares β_m, auxiliary spring connect with main spring Contact is to main spring end points apart from l₀, to the main spring of m piece under stressing conditions at major-minor spring contact point in end flat segments and pair Deformation coefficient g at spring contact point_x-cdzCalculated, that is,

$\begin{array}{c}{g}_{x-{\mathrm{cd}}_z}=\frac{4(l_m-l_3/2-l_{2m})\&lsqb;{(l_m-l_3/2)}^2-3(l_m-l_3/2)l_0+(l_m-l_3/2)l_{2m}+3l_0^2-3l_0{l}_{2m}+l_{2m}^2\&rsqb;}{eb}-\\ \frac{4{(l_0-l_{2m}{\mathrm{\&beta;}}_m^2)}^3}{{\mathrm{eb\&beta;}}_m^3}-\frac{12l_{2m}}{eb}\&lsqb;4l_0{l}_{2m}(1-{\mathrm{\&beta;}}_m)+2l_0^2(1-\frac{1}{{\mathrm{\&beta;}}_m})+\frac{2l_{2m}^2({\mathrm{\&beta;}}_m^3-1)}{3}\&rsqb;\end{array};$

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

Half length l according to few piece parabolic type variable-section steel sheet spring auxiliary spring_a, width b, half l of installing space₃, parabolic Line root is to spring end points apart from l_2a, elastic modelling quantity e, the thickness of the parabolic segment of jth piece auxiliary spring compares β_aj, wherein, j=1, 2 ..., n, n are auxiliary spring piece number, to deformation coefficient g at endpoint location for each auxiliary spring under end points stressing conditions_x-dajCounted Calculate, that is,

$g_{x-daj}=\frac{4\&lsqb;l_{2a}^3(1-{\mathrm{\&beta;}}_{aj}^3)+{(l_a-l_3/2)}^3\&rsqb;}{eb};$

Wherein, the deformation coefficient g after the superposition of n piece auxiliary spring_x-datFor

$g_{x-dat}=\frac{1}{\underset{j=1}{\overset{n}{\&sigma;}}\frac{1}{g_{x-daj}}};$

(2) calculating of ends contact formula few each of piece parabolic type leaf spring main spring clamping rigidity:

A step: each main spring before auxiliary spring contact clamps rigidity k_miCalculating:

According to main spring root thickness h_2m, and calculated g in the i step of step (1)_x-di, determine each before auxiliary spring contact The main spring of piece half rigidity k in the clamp state_mi, that is,

$k_{mi}=\frac{h_{2m}^3}{g_{x-di}},i=1,2,...,m;$

Wherein, reed number based on m；

B step: each main spring after auxiliary spring contact clamps rigidity k_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-cd, calculated g in iii step_x-dzm, calculated g in iv step_x-cdz, and v step in calculate The g arriving_x-dat, determine each main spring half rigidity k in the clamp state after the contact of major-minor spring_mai, that is,

$k_{mai}=\left\{\begin{array}{cc}\frac{h_{2m}^3}{g_{x-di}},& i=1,2,...,m-1\\ \frac{h_{2m}^3(g_{x-dat}{h}_{2m}^3+g_{x-{\mathrm{cd}}_z}{h}_{2a}^3)}{g_{x-dm}(g_{x-dat}{h}_{2m}^3+g_{x-{\mathrm{cd}}_z}{h}_{2a}^3)-g_{x-d_{z}m}{g}_{x-cd}{h}_{2a}^3},& i=m\end{array}\right.;$

Wherein, reed number based on m；

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

According to auxiliary spring root thickness h_2a, and calculated g in the v step of step (1)_x-daj, determine each auxiliary spring in clamping shape Half rigidity k under state_aj, that is,

$k_{aj}=\frac{h_{2a}^3}{g_{x-daj}},j=1,2,...,n;$

Wherein, n is auxiliary spring piece number；

(4) calculating of the few major and minor spring amount of deflection of piece parabolic type leaf spring of the ends contact formula 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, calculate in the ii step of step (1) The g obtaining_x-cd, and the k determining in a step of step (2)_mi, half load p when determining that auxiliary spring works_k, that is,

$p_k=\frac{{\mathrm{\&delta;h}}_{2m}^3\underset{i=1}{\overset{m}{\&sigma;}}{k}_{mi}}{g_{x-cd}{k}_{mm}};$

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

Main reed number m, calculated p in i step according to few piece parabolic type variable-section steel sheet spring_k, and a of step (2) The k determining in step_mi, the k that determines in b step_mai, to main spring amount of deflection f under different loads p_mCalculated, that is,

$f_m=\left\{\begin{array}{cc}\frac{p}{\underset{i=1}{\overset{m}{\&sigma;}}{k}_{mi}},& 0\&le;p<p_k\\ \frac{p_k}{\underset{i=1}{\overset{m}{\&sigma;}}{k}_{mi}}+\frac{(p-p_k)}{\underset{i=1}{\overset{m}{\&sigma;}}{k}_{mai}},& p_k\&le;p\end{array}\right.;$

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

Main spring root thickness h according to few piece parabolic type variable-section steel sheet spring_2m, auxiliary spring root thickness h_2a, main reed number m, Auxiliary spring piece number n, the p determining in i step_k, calculated g in the ii step of step (1)_x-cd, calculated in iv step g_x-cdz, calculated g in v step_x-dat, the k of determination in the b step of step (2)_mai, and the k determining in step (3)_aj, right Auxiliary spring amount of deflection f under different loads p_aCalculated, that is,

$f_a=\left\{\begin{array}{cc}0,& 0\&le;p<p_k\\ \frac{k_{mam}{g}_{x-cd}{h}_{2a}^3(p-p_k)}{\underset{j=1}{\overset{n}{\mathrm{\&sigma;}}}{k}_{aj}\underset{i=1}{\overset{m}{\mathrm{\&sigma;}}}{k}_{mai}(g_{x-dat}{h}_{2m}^3+g_{x-{\mathrm{cd}}_z}{h}_{2a}^3)},& p_k\&le;p\end{array}\right..$