CN105912757A - Method for checking strength of end contact type few-leaf parabola-shaped section-variable master and slave springs - Google Patents

Abstract

The invention relates to a method for checking the strength of end contact type few-leaf parabola-shaped section-variable master and slave springs, and belongs to the technical field of suspension steel plate springs. The method can check the stress strength of each of master springs and slave springs according to structure parameters, elasticity modulus, allowable stress, slave spring work load and the maximum load of each of the master springs and the slave springs of the end contact type few-leaf parabola-shaped section-variable master and slave springs. The embodiment and simulation verification show that the method for checking the strength of the end contact type few-leaf parabola-shaped section-variable master and slave springs is correct; and a check value of stress strength of each of the master springs and the slave springs is accurate and reliable. The method can improve and prolong the design level, the product quality, and the service life of the end contact type few-leaf parabola-shaped section-variable master and slave springs, improves the riding comfort of a vehicle, decreases design and testing expenses, and accelerates the product development speed.

Description

The strength check methods of the few sheet parabolic type variable cross-section major-minor spring of ends contact formula

Technical field

The present invention relates to the few sheet parabolic type variable cross-section major-minor spring of vehicle suspension leaf spring, particularly ends contact formula Strength check methods.

Background technology

In order to meet vehicle suspension light-weighted design requirement, the lightest card suspension leaf spring mostly uses few sheet parabolic Line variable cross-section major-minor spring.Owing to the stress of the 1st main spring of few sheet variable cross-section major-minor spring is complicated, it is subjected to vertical load, with Time also subject to torsional load and longitudinal loading, therefore, the thickness of the end flat segments of the 1st main spring designed by reality and length Degree, more than the thickness of end flat segments and the length of other each main spring, the most mostly uses the non-few sheet variable cross-section waiting structure in end Leaf spring, the requirement complicated to meet the 1st main spring stress.It addition, for the design requirement meeting different composite rigidity, logical Frequently with the auxiliary spring of different length, different according to connect from the main spring position of contact, auxiliary spring contact, few sheet parabola variable cross-section master Auxiliary spring can be divided into ends contact formula and non-ends contact formula.Sheet parabolic type variable cross-section major-minor spring few to end contact, works as load Lotus more than auxiliary spring work load time, auxiliary spring contact with in the flat segments of main spring end certain point contact and together with work time, wherein, The main spring of m sheet, in addition to by end points power, is also acted on by auxiliary spring contact support power in end flat segments.In order to meet the life-span And the requirement of Reliable Design, it is necessary to each stress of sheet parabolic type variable cross-section major-minor spring few to designed ends contact formula is strong Degree carries out calculation and check.Yet with the end flat segments structure such as non-grade of each of main spring, the length of auxiliary spring is unequal with main spring, main Each main spring and the calculating of the end points power of auxiliary spring after secondary contact are extremely complex, fail to provide ends contact formula few the most always Each main spring of sheet parabolic type variable cross-section major-minor spring and each auxiliary spring stress intensity check method.Therefore, it is necessary to set up one Accurately, the check method of the few sheet parabolic type variable cross-section major-minor spring stress intensity of reliable ends contact formula, meet Vehicle Industry The requirement of the des ign and strength checking of fast-developing and few sheet parabolic type variable cross-section major-minor spring, improves few sheet parabolic type change and cuts Design level, product quality and the service life of face major-minor spring and vehicle ride performance；Meanwhile, product design and test are reduced Expense, accelerates 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 strength check methods of the few sheet parabolic type variable cross-section major-minor spring of ends contact formula reliably, its design flow diagram, such as Fig. 1 institute Show.The few sheet parabolic type variable cross-section major-minor spring of ends contact formula is symmetrical structure, and it is different that the half of major and minor spring can regard length as Cantilever beam, the center of installing space regards the root of cantilever beam as, and the stress point of major and minor spring regards the end points of cantilever beam, major-minor spring as Half symmetrical structure schematic diagram, as in figure 2 it is shown, include: main spring 1, root shim 2, auxiliary spring 3, end pad 4, wherein, few sheet The half symmetrical structure of the main spring of parabolic type variable cross-section 1 and auxiliary spring 3 is by root flat segments, parabolic segment, end flat segments three sections Constitute；The a length of L of half of each of main spring 1_M, root flat segments thickness is h₂, half l of installing space₃；The end of each main spring Portion's flat segments is non-isomorphic, i.e. the thickness of the end flat segments of the 1st main spring and length, more than other thickness of each and length； Thickness and the length of each end flat segments are respectively h_1iAnd l_1i；The root of parabolic segment is l to the distance of main spring end points₂, throw The thickness of thing line segment compares β_i=h_1i/h₂.Between the root flat segments of main spring 1 and and the root flat segments of auxiliary spring 3 between, be provided with Root shim 2；Between the end flat segments of main spring 1, being provided with end pad 4, the material of end pad 4 is carbon fiber composite Material, in order to reduce frictional noise during spring works.The a length of L of half that auxiliary spring 3 is each_A, the end points of auxiliary spring 3 is to main spring 1 end The horizontal range of point is l₀；The thickness of the root flat segments of auxiliary spring is h_2A, thickness and the length of each auxiliary spring end flat segments are divided Wei h_A1jAnd l_A1j, the distance of the root of parabolic segment to auxiliary spring end points is l_2A, the thickness of each parabolic segment compares β_Aj=h_A1j/ h_2A.Vertical dimension between auxiliary spring contact and main spring end flat segments is major-minor spring gap delta；When load works load more than auxiliary spring Lotus, auxiliary spring contact contacts with certain point in the flat segments of main spring end, and end points power and the maximum stress of each of major-minor spring all differ. The structural parameters of each of major-minor spring, allowable stress, maximum load, auxiliary spring work load given in the case of, to ends contact The stress intensity of few each of the sheet parabolic type major-minor spring of formula is checked.

For solving above-mentioned technical problem, the few sheet parabolic type variable cross-section major-minor spring of ends contact formula provided by the present invention Strength check methods, it is characterised in that the following step of checking of employing:

(1) each main spring of the few sheet parabolic type variable cross-section major-minor spring of ends contact formula and the half of auxiliary spring clamp rigidimeter Calculate:

I step: the half clamping stiffness K of each main spring before the contact of major-minor spring_MiCalculate:

Half length L according to few sheet main spring of parabolic type variable cross-section_M, main reed number m, the root flat segments of each main spring Thickness h_2M, width b, elastic modulus E, half l of installing space₃, the root of main spring parabolic segment is to the distance of main spring end points l_2M=L_M-l₃, the thickness of the parabolic segment of i-th main spring compares β_i=h_1i/h_2M, wherein, i=1,2 ..., m, major-minor spring is contacted The half clamping stiffness K of each main spring before_MiCalculate, i.e.

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

In formula,

II step: the half clamping stiffness K of each main spring after the contact of major-minor spring_MAiCalculate:

Half length L according to few sheet main spring of parabolic type variable cross-section_M, main reed number m, the root flat segments of each main spring Thickness h_2M, width b, elastic modulus E, half l of installing space₃, the root of main spring parabolic segment is to the distance of main spring end points l_2M=L_M-l₃, the thickness of the parabolic segment of i-th main spring compares β_i, wherein, i=1,2 ..., m；Half length L of auxiliary spring_A, auxiliary spring Sheet number n, the thickness h of each auxiliary spring root flat segments_2A, auxiliary spring contact and horizontal range l of main spring end points₀=L_M-L_A, auxiliary spring is thrown The root of thing line segment is to distance l of auxiliary spring end points_2A=L_A-l₃, the thickness of the parabolic segment of jth sheet auxiliary spring compares β_Aj=h_A1j/h_2A, Wherein, j=1,2 ..., n, the half clamping stiffness K of each main spring after major-minor spring is contacted_MAiCalculate, i.e.

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

In formula,

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

$G_{x-DAj}=\frac{4\[l_{2A}^3(1-{\mathrm{\β}}_{Aj}^3)+{(L_A-l_3/2)}^3\]}{Eb},G_{x-DAT}=\frac{1}{\underset{j=1}{\overset{n}{\Σ}}\frac{1}{G_{x-DAj}}},j=1,2,...,n;$

$\begin{array}{c}{G}_{x-CD}=\frac{4{(L_M-l_3/2)}^3-6l_0{(L_M-l_3/2)}^2-4l_{2M}^3+6l_0{l}_{2M}^2}{Eb}+\frac{2{(l_0-l_{2M}{\mathrm{\β}}_m^2)}^2(2l_{2M}{\mathrm{\β}}_m^2+l_0)}{{\mathrm{Eb\β}}_m^3}-\\ \frac{8l_{2M}^2({\mathrm{\β}}_m-1)(l_{2M}-3l_0+l_{2m}{\mathrm{\β}}_m^2+l_{2M}{\mathrm{\β}}_m)}{Eb};\end{array}$

$\begin{array}{c}{G}_{x-D_{z}m}=\frac{4{(L_M-l_3/2)}^3-6l_0{(L_M-l_3/2)}^2-4l_{2M}^3+6l_0{l}_{2M}^2}{Eb}+\frac{2{(l_0-l_{2M}{\mathrm{\β}}_m^2)}^2(2l_{2M}{\mathrm{\β}}_m^2+l_0)}{{\mathrm{Eb\β}}_m^3}-\\ \frac{8l_{2M}^2({\mathrm{\β}}_m-1)(l_{2M}-3l_0+l_{2m}{\mathrm{\β}}_m^2+l_{2M}{\mathrm{\β}}_m)}{Eb},;\end{array}$

Wherein, β_mIt is m sheet master The thickness ratio of the parabolic segment of spring；

III step: the half clamping stiffness K of each auxiliary spring_AjCalculate:

Half length L according to few sheet parabolic type variable cross-section auxiliary spring_A, auxiliary spring sheet number n, the root flat segments of each auxiliary spring Thickness h_2A, width b, elastic modulus E, half l of installing space₃, the root of auxiliary spring parabolic segment is to the distance of auxiliary spring end points l_2A；The thickness of the parabolic segment of jth sheet auxiliary spring compares β_Aj, wherein, j=1,2 ..., n, the half of each auxiliary spring is clamped stiffness K_Aj Calculate, i.e.

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

In formula,

(2) ends contact formula lacks each main spring and the maximum end points power meter of auxiliary spring of sheet parabolic type variable cross-section major-minor spring Calculate:

I step: the maximum end points power of each main spring calculates:

Half according to maximum load suffered by the few sheet parabolic type variable cross-section major-minor spring of ends contact formula is the most single-ended maximum Load p_max, auxiliary spring works load p_K, main reed number m, calculated K in I step_Mi, and in II step obtained by calculating K_MAi, maximum end points power P to each main spring_imaxCalculate, i.e.

$P_{i\max }=\frac{K_{Mi}{P}_K}{2\underset{i=1}{\overset{m}{\Σ}}{K}_{Mi}}+\frac{K_{MAi}(2P_{\max }-P_K)}{2\underset{i=1}{\overset{m}{\Σ}}{K}_{MAi}},i=1,2,\mathrm{...},m;$

Ii step: the maximum end points power of each auxiliary spring calculates:

The most single-ended some maximum load P of half according to maximum load suffered by few sheet parabolic type variable cross-section major-minor spring_max, secondary Spring works load p_K；Main reed number m, the thickness h of each main spring root flat segments_2M；Auxiliary spring sheet number n, each auxiliary spring root is put down The thickness h of straight section_2A, calculated K in II step_MAi、G_x-CD、G_x-CDzAnd G_x-DAT, and calculated K in III step_Aj, Maximum end points power P to each auxiliary spring_AjmaxCalculate, i.e.

$P_{Ajmax}=\frac{K_{Aj}{K}_{MAm}{G}_{x-CD}{h}_{2A}^3(2P_{max}-P_K)}{2\underset{j=1}{\overset{n}{\Σ}}{K}_{Aj}\underset{i=1}{\overset{m}{\Σ}}{K}_{MAi}(G_{x-DAT}{h}_{2M}^3+G_{x-{\mathrm{CD}}_z}{h}_{2A}^3)},j=1,2,...,n;$

(3) each main spring of the few sheet parabolic type variable cross-section major-minor spring of ends contact formula and the maximum stress of auxiliary spring calculate:

Step A: the maximum stress of the front main spring of m-1 sheet calculates:

Half length L according to few sheet main spring of parabolic type variable cross-section_M, main reed number m, each main spring root flat segments Thickness h_2M, width b, half l of installing space₃, calculated P in i step_imax, the maximum stress of spring main to front m-1 is carried out Calculate, i.e.

${\mathrm{\σ}}_{imax}=\frac{6P_{imax}(L_M-l_3/2)}{{\mathrm{bh}}_{2M}^2},i=1,2,...,m-1;$

Step B: the maximum stress of the main spring of m sheet calculates:

The thickness h of the root flat segments according to few sheet main spring of parabolic type variable cross-section_2M, width b, the root of parabolic segment arrives Distance l of main spring end points_2M, the thickness of the parabolic segment of the main spring of m sheet compares β_m, auxiliary spring contact and the horizontal range of main spring end points l₀, calculated P in i step_mmax, calculated P in ii step_Ajmax, the maximum stress of spring main to m sheet is counted Calculate, i.e.

${\mathrm{\σ}}_{mmax}=\frac{6\[P_{mmax}{\mathrm{\β}}_m^2{l}_{2M}-\underset{j=1}{\overset{n}{\Σ}}{P}_{Ajmax}({\mathrm{\β}}_m^2{l}_{2M}-l_0)\]}{b{\left({\mathrm{\β}}_m{h}_{2M}\right)}^2};$

Step C: the maximum stress of each auxiliary spring calculates:

Half length L according to few sheet parabolic type variable cross-section auxiliary spring_A, auxiliary spring sheet number n, each auxiliary spring root flat segments Thickness h_2A, width b, half l of installing space₃, calculated P in ii step_Ajmax, the maximum stress of each auxiliary spring is carried out Calculate, i.e.

${\mathrm{\σ}}_{Ajmax}=\frac{6P_{Ajmax}(L_A-l_3/2)}{{\mathrm{bh}}_{2A}^2},j=1,2,...,n;$

(4) each main spring of the few sheet parabolic type variable cross-section major-minor spring of ends contact formula and the stress intensity of auxiliary spring are checked:

1. step: the stress intensity of the front main spring of m-1 sheet is checked:

Allowable stress [σ] according to leaf spring, and the maximum of each of the calculated front main spring of m-1 sheet in step A Stress, the stress intensity of each of the front main spring of m-1 sheet of sheet parabolic type variable cross-section major-minor spring few to end contact carries out school Core, it may be assumed that

If σ_imax> [σ], then i-th main spring, it is unsatisfactory for stress intensity requirement；

If σ_imax≤ [σ], then i-th main spring, meet stress intensity requirement, i=1, and 2 ..., m-1；

2. step: the stress intensity of the main spring of m sheet is checked:

Allowable stress [σ] according to leaf spring, and the maximum stress of the calculated main spring of m sheet, opposite end in step B The stress intensity of the main spring of m sheet of the few sheet parabolic type variable cross-section major-minor spring of portion's contact is checked, it may be assumed that

If σ_mmax> [σ], the then main spring of m sheet, it is unsatisfactory for stress intensity requirement；

If σ_mmax≤ [σ], the then main spring of m sheet, meets stress intensity requirement；

3. step: the stress intensity of each auxiliary spring is checked:

Allowable stress [σ] according to leaf spring, and the maximum stress of calculated each auxiliary spring, opposite end in step C The stress intensity of each auxiliary spring of the few sheet parabolic type variable cross-section major-minor spring of portion's contact is checked, it may be assumed that

If σ_Ajmax> [σ], then jth sheet auxiliary spring, it is unsatisfactory for stress intensity requirement；

If σ_Ajmax≤ [σ], then jth sheet auxiliary spring, meet stress intensity requirement, j=1, and 2 ..., n.

The present invention has the advantage that than prior art

Due to the non-structure that waits of the main spring end flat segments of the few sheet parabolic type variable cross-section major-minor spring of ends contact formula, and auxiliary spring Length is less than the length of main spring, and meanwhile, the main spring of m sheet, in addition to by end points power, is also propped up by auxiliary spring contact in end flat segments The effect of support force, therefore, the end points power of each main spring and auxiliary spring calculates extremely complex, fails to provide ends contact formula the most always The check method of few sheet parabolic type variable cross-section major-minor spring stress intensity.The present invention can be according to the few sheet parabolic type of ends contact formula Each main spring of variable cross-section major-minor spring and the structural parameters of auxiliary spring, elastic modelling quantity, allowable stress, auxiliary spring work load, major-minor The maximum load that spring is born, each main spring of sheet parabolic type variable cross-section major-minor spring few to end contact and the stress of auxiliary spring Intensity is checked.By checking example and ANSYS simulating, verifying, the few sheet parabolic of the ends contact formula that this invention is provided The strength check methods of line style variable cross-section major-minor spring is correct, and the maximum stress calculation and check value of each main spring and auxiliary spring is accurate The most reliably.Utilize the method can improve the few sheet parabolic type variable cross-section major-minor leaf spring of ends contact formula design level, Product quality and service life and vehicle ride performance；Meanwhile, also can reduce design and testing expenses, 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 flow chart of each stress intensity check of the few sheet parabolic type variable cross-section major-minor spring of ends contact formula；

Fig. 2 is the half symmetrical structure schematic diagram of the few sheet parabolic type variable cross-section major-minor spring of ends contact formula；

Fig. 3 is the maximum stress emulation cloud atlas of the 1st main spring of embodiment；

Fig. 4 is the maximum stress emulation cloud atlas of the 2nd main spring of embodiment；

Fig. 5 is the maximum stress emulation cloud atlas of 1 auxiliary spring of embodiment.

Specific embodiments

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

Embodiment: the main reed number m=2 of the few sheet parabolic type variable cross-section major-minor spring of certain contact, wherein, each main spring Half length L_M=575mm, width b=60mm, elastic modulus E=200GPa, allowable stress [σ]=700MPa, clipping room Away from half l₃=55mm, the root of the parabolic segment of each main spring is to distance l of main spring end points_2M=L_M-l₃=520mm, each The thickness h of the root flat segments of main spring_2M=11mm；The thickness h of the end flat segments of the 1st main spring₁₁=7mm, the 1st main spring The thickness of parabolic segment compare β₁=h₁₁/h_2M=0.64；The thickness h of the end flat segments of the 2nd main spring₁₂=6mm, the 2nd master The thickness of the parabolic segment of spring compares β₂=h₁₂/h_2M=0.55.Auxiliary spring sheet number n=1, half length L of this sheet auxiliary spring_A=525mm, Auxiliary spring contact and horizontal range l of main spring end points₀=50mm, the root of auxiliary spring parabolic segment is to distance l of auxiliary spring end points_2A= L_A-l₃=470mm；The thickness h of the root flat segments of auxiliary spring_2A=14mm, the thickness h of the end flat segments of auxiliary spring_A11=8mm, secondary The thickness of the parabolic segment of spring compares β_A1=h_A11/h_2A=0.57.It is provided with major-minor spring between auxiliary spring contact and main spring end flat segments Gap, when load works load more than auxiliary spring, auxiliary spring contact contacts with main spring certain point in the flat segments of end, and major-minor is common With working.The auxiliary spring of the few sheet parabolic type variable cross-section major-minor spring of this ends contact formula works load p_K=2400N, when being held The most single-ended some maximum load P of half by maximum load_maxDuring=3040N, sheet parabolic type Variable Section Steel few to this contact Each main spring of flat spring and the stress intensity of each auxiliary spring are checked.

The strength check methods of the few sheet parabolic type variable cross-section major-minor spring of the ends contact formula that present example is provided, its Calculation process is as it is shown in figure 1, specifically comprise the following steps that

(1) each main spring of the few sheet parabolic type variable cross-section major-minor spring of ends contact formula and the half of auxiliary spring clamp rigidimeter Calculate:

I step: the half clamping stiffness K of each main spring before the contact of major-minor spring_MiCalculate:

Half length L according to few sheet main spring of parabolic type variable cross-section_M=575mm, main reed number m=2, main spring root is put down The thickness h of straight section_2M=11mm, width b=60mm, elastic modulus E=200GPa, the root of main spring parabolic segment is to main spring end points Distance l_2M=520mm, the thickness of the parabolic segment of the 1st main spring compares β₁The thickness of the parabolic segment of the=0.64, the 2nd main spring Compare β₂=0.55, the 1st main spring before major-minor spring is contacted and the half clamping stiffness K of the 2nd main spring_M1And K_M2Carry out respectively Calculate, i.e.

$K_{M1}=\frac{h_{2M}^3}{G_{x-D1}}=14.87N/mm;$

$K_{M2}=\frac{h_{2M}^3}{G_{x-D2}}=14.16N/mm;$

In formula,

$G_{x-D2}=\frac{4\[l_{2M}^3(1-{\mathrm{\β}}_2^3)+L_M^3\]}{Eb}=93.97{\mathrm{mm}}^4/N;$

II step: the half clamping stiffness K of each main spring after the contact of major-minor spring_MAiCalculate:

Half length L according to few sheet main spring of parabolic type variable cross-section_M=575mm, main reed number m=2, main spring root is put down The thickness h of straight section_2M=11mm, width b=60mm, elastic modulus E=200GPa, the root of parabolic segment to main spring end points away from From l_2M=520mm, the thickness of the parabolic segment of the 1st main spring compares β₁The thickness of the parabolic segment of the=0.64, the 2nd main spring compares β₂ =0.55；Half length L of auxiliary spring_AHorizontal range l of=525mm, auxiliary spring contact and main spring end points₀=50mm, auxiliary spring sheet number n =1, the thickness h of the root flat segments of this sheet auxiliary spring_2A=14mm, the root of auxiliary spring parabolic segment is to distance l of auxiliary spring end points_2A =470mm, the thickness of the parabolic segment of this sheet auxiliary spring compares β_A1=0.57；To major-minor spring contact after the 1st main spring and the 2nd The half clamping stiffness K of main spring_MA1And K_MA2It is respectively calculated, i.e.

$K_{MA1}=\frac{h_{2M}^3}{G_{x-D1}}=14.87N/mm;$

$K_{MA2}=\frac{h_{2M}^3(G_{x-DAT}{h}_{2M}^3+G_{x-{\mathrm{CD}}_z}{h}_{2A}^3)}{G_{x-D2}(G_{x-DAT}{h}_{2M}^3+G_{x-{\mathrm{CD}}_z}{h}_{2A}^3)-G_{x-D_{z}2}{G}_{x-CD}{h}_{2A}^3}=40.15N/mm;$

In formula,

$G_{x-D2}=\frac{4\[l_{2M}^3(1-{\mathrm{\β}}_2^3)+L_M^3\]}{Eb}=93.97{\mathrm{mm}}^4/N;$

$G_{x-DAT}=\frac{\underset{j=1}{\overset{n}{\Σ}}4\[l_{2A}^3(1-{\mathrm{\β}}_{Aj}^3)+L_A^3\]}{Eb}=69.20{\mathrm{mm}}^4/N;$

$\begin{array}{c}{G}_{x-CD}=\frac{4L_M^3-6l_0{L}_M^2-4l_{2M}^3+6l_0{l}_{2M}^2}{Eb}+\frac{2{(l_0-l_{2M}{\mathrm{\β}}_2^2)}^2(2l_{2M}{\mathrm{\β}}_2^2+l_0)}{{\mathrm{Eb\β}}_2^3}-\frac{8l_{2M}^2({\mathrm{\β}}_2-1)(l_{2M}-3l_0+l_{2M}{\mathrm{\β}}_2^2+l_{2M}{\mathrm{\β}}_2)}{Eb}\\ =77.39{\mathrm{mm}}^4/N;\end{array}$

$\begin{array}{c}{G}_{x-D_{z}2}=\frac{4L_M^3-6l_0{L}_M^2-4l_{2M}^3+6l_0{l}_{2M}^2}{Eb}+\frac{2{(l_0-l_{2M}{\mathrm{\β}}_2^2)}^2(2l_{2M}{\mathrm{\β}}_2^2+l_0)}{{\mathrm{Eb\β}}_2^3}-\frac{8l_{2M}^2({\mathrm{\β}}_2-1)(l_{2M}-3l_0+l_{2M}{\mathrm{\β}}_2^2+l_{2M}{\mathrm{\β}}_2)}{Eb}\\ =77.39{\mathrm{mm}}^4/N;\end{array}$

$\begin{array}{c}{G}_{x-{\mathrm{CD}}_z}=\frac{4(L_M-l_{2M})(L_M^2-3L_M{l}_0+L_M{l}_{2M}+3l_0^2-3l_0{l}_{2M}+l_{2M}^2)}{Eb}-\frac{4{(l_0-l_{2M}{\mathrm{\β}}_2^2)}^3}{{\mathrm{Eb\β}}_2^3}-\\ \frac{12l_{2M}}{Eb}\[4l_0{l}_{2M}(1-{\mathrm{\β}}_2)+2l_0^2(1-\frac{1}{{\mathrm{\β}}_2})+\frac{2l_{2M}^2({\mathrm{\β}}_2^3-1)}{3}\]=64.91{\mathrm{mm}}^4/N;\end{array}$

III step: the half clamping stiffness K of each auxiliary spring_AjCalculate:

Half length L according to this sheet parabolic type variable cross-section auxiliary spring_A=525mm, auxiliary spring sheet number n=1, this sheet root is thick Degree h_2A=14mm, width b=60mm, elastic modulus E=200GPa, the root of this sheet auxiliary spring parabolic segment to auxiliary spring end points away from From l_2A=470mm, the thickness of the parabolic segment of auxiliary spring compares β_A1=0.57, the half of this sheet auxiliary spring is clamped stiffness K_A1Count Calculate, i.e.

$K_{A1}=\frac{h_{2A}^3}{G_{x-DA1}}=39.65N/mm;$

In formula,

(2) ends contact formula lacks each main spring and the maximum end points power meter of auxiliary spring of sheet parabolic type variable cross-section major-minor spring Calculate:

I step: the maximum end points power of each main spring calculates:

The most single-ended point of half according to maximum load suffered by the few sheet parabolic type variable cross-section major-minor spring of this ends contact formula is Big load p_max=3040N, auxiliary spring works load p_K=2400N, main reed number m=2, calculated K in I step_M1= 14.87N/mm and K_M2=14.16N/mm, and II step calculate obtained K_MA1=14.87N/mm and K_MA2=40.15N/ Mm, to the 1st main spring and maximum end points power P of the 2nd main spring_1maxAnd P_2maxIt is respectively calculated, i.e.

$P_{1max}=\frac{K_{M1}{P}_K}{2\underset{i=1}{\overset{m}{\Σ}}{K}_{Mi}}+\frac{K_{MA1}(2P_{max}-P_K)}{2\underset{i=1}{\overset{m}{\Σ}}{K}_{MAi}}=1142.30N;$

$P_{2max}=\frac{K_{M2}{P}_K}{2\underset{i=1}{\overset{2}{\Σ}}{K}_{Mi}}+\frac{K_{MA2}(2P_{max}-P_K)}{2\underset{i=1}{\overset{2}{\Σ}}{K}_{MAi}}=1897.70N;$

Ii step: the maximum end points power of each auxiliary spring calculates:

The most single-ended point of half according to maximum load suffered by the few sheet parabolic type variable cross-section major-minor spring of this ends contact formula is Big load p_max=3040N, auxiliary spring sheet number n=1, auxiliary spring works load p_K=2400N, main reed number m=2, each main spring root The thickness h of portion's flat segments_2M=11mm, the thickness h of this sheet auxiliary spring root flat segments_2A=14mm；Obtained by II step calculates K_MA1=14.87N/mm, K_MA2=40.15N/mm, G_x-CD=77.39mm⁴/N,G_x-CDz=64.91mm⁴/ N and G_x-DAT= 69.20mm⁴Calculated K in/N, and III step_A1=39.65N/mm, maximum end points power P to this sheet auxiliary spring_A1maxCarry out Calculate, i.e.

$P_{A1max}=\frac{K_{A1}{K}_{MA2}{G}_{x-CD}{h}_{2A}^3(2P_{max}-P_K)}{2\underset{j=1}{\overset{n}{\Σ}}{K}_{Aj}\underset{i=1}{\overset{m}{\Σ}}{K}_{MAi}(G_{x-DAT}{h}_{2M}^3+G_{x-{\mathrm{CD}}_z}{h}_{2A}^3)}=983.29N;$

(3) each main spring of the few sheet parabolic type variable cross-section major-minor spring of ends contact formula and the maximum stress of auxiliary spring calculate:

Step A: the maximum stress of the 1st main spring calculates:

Half length L according to few sheet main spring of parabolic type variable cross-section_M=575mm, the root flat segments of each main spring Thickness h_2M=11mm, width b=60mm, half l of installing space₃Calculated P in=55mm, i step_1max= 1142.30N, calculates, i.e. the maximum stress of the 1st main spring of parabolic type variable cross-section

${\mathrm{\σ}}_{1max}=\frac{6P_1(L_M-l_3/2)}{{\mathrm{bh}}_{2M}^2}=516.87MPa;$

Step B: the maximum stress of the 2nd main spring calculates:

The thickness h of the root flat segments according to each main spring_2M=11mm, width b=60mm, the root of main spring parabolic segment Distance l to main spring end points_2M=520mm, main reed number m=2, the thickness of the parabolic segment of the 2nd main spring compares β₂=0.55, secondary Horizontal range l of reed number n=1, auxiliary spring contact and main spring end points₀Calculated P in=50mm, i step_2max= Calculated P in 1897.70N, ii step_A1max=983.29N, the maximum stress to the 2nd main spring of parabolic type variable cross-section Calculate, i.e.

${\mathrm{\σ}}_{2max}=\frac{6\[P_{2max}{\mathrm{\β}}_2^2{l}_{2M}-\underset{j=1}{\overset{n}{\Σ}}{P}_{Ajmax}({\mathrm{\β}}_2^2{l}_{2M}-l_0)\]}{b{\left({\mathrm{\β}}_2{h}_{2M}\right)}^2}=529.54MPa;$

Step C: the maximum stress of each auxiliary spring calculates:

Half length L according to auxiliary spring_A=525mm, auxiliary spring sheet number n=1, the thickness h of the root flat segments of this sheet auxiliary spring_2A =14mm, width b=60mm, half l of installing space₃Calculated P in=55mm, ii step_A1max=983.29N is right The maximum stress of this sheet parabolic type variable cross-section auxiliary spring calculates, i.e.

${\mathrm{\σ}}_{A1max}=\frac{6P_{A1max}(L_A-l_3/2)}{{\mathrm{bh}}_{2A}^2}=249.58MPa;$

(4) each main spring of the few sheet parabolic type variable cross-section major-minor spring of ends contact formula and the stress intensity of auxiliary spring are checked:

1. step: the stress intensity of the 1st main spring is checked:

The maximum of calculated 1st main spring in allowable stress [σ] according to leaf spring=700MPa, and step A Stress σ_1max=516.87MPa, it is known that σ_1max≤ [σ], i.e. the 1st main spring disclosure satisfy that stress intensity requirement；

2. step: the stress intensity of the 2nd main spring is checked:

The maximum of calculated 2nd main spring in allowable stress [σ] according to leaf spring=700MPa, and step B Stress σ_2max=529.54MPa, it is known that σ_2max≤ [σ], i.e. the 2nd main spring disclosure satisfy that stress intensity requirement；

3. step: the stress intensity of auxiliary spring is checked:

In allowable stress [σ] according to leaf spring=700MPa, and step C, the maximum of this sheet auxiliary spring calculated should Power σ_A1max=249.58MPa, it is known that σ_A1max≤ [σ], i.e. this sheet auxiliary spring disclosure satisfy that stress intensity requirement.

Utilize ANSYS finite element emulation software, according to the major-minor spring structure of this few sheet parabolic type variable-section steel sheet spring Parameter and material characteristic parameter, set up the ANSYS phantom of half symmetrical structure major-minor spring, grid division, arrange auxiliary spring end Point contacts with main spring, and at the root applying fixed constraint of phantom, applies concentrfated load F=P at main spring end points_max-P_K/2 =1840N, is carried out the stress of this few sheet parabolic type variable cross-section major-minor spring each main spring in the clamp state and auxiliary spring ANSYS emulates, the maximum stress emulation cloud atlas of the 1st obtained main spring, as shown in Figure 3；The maximum stress of the 2nd main spring is imitated True cloud atlas, as shown in Figure 4；The maximum stress emulation cloud atlas of 1 auxiliary spring, as it is shown in figure 5, wherein, the 1st main spring is at clamping root Maximum stress σ_1max=200.26MPa, the 2nd main spring maximum stress at parabolic segment with end flat segments contact position σ_2max=253.69MPa, 1 auxiliary spring are at the maximum stress σ clamping root_A1max=237.72MPa.

Understand, in the case of same load, this leaf spring the 1st and the 2nd main spring and 1 auxiliary spring maximum stress ANSYS simulating, verifying value σ_1max=200.26MPa, σ_2max=253.69MPa, σ_A1max=237.72MPa, resolves with deformation respectively Value of calculation σ_1max=199.18MPa, σ_2max=251.69MPa, σ_A1max=235.78MPa, matches, and relative deviation is respectively 0.54%, 0.79%, 0.82%；Result shows the few sheet parabolic type variable cross-section major-minor spring of ends contact formula that this invention is provided Strength check methods be correct, the maximum stress calculation and check value of each main spring and auxiliary spring is accurately and reliably.

Claims (1)

1. the strength check methods of the few sheet parabolic type variable cross-section major-minor spring of ends contact formula, wherein, few sheet parabolic type change cuts The half symmetrical structure of face major-minor spring is made up of root flat segments, parabolic segment, end flat segments three sections；The end of each main spring The non-thickness waiting structure, i.e. the end flat segments of the 1st main spring of flat segments and length, more than the end flat segments of other each main spring Thickness and length；The length of auxiliary spring is less than the length of main spring, when load works load, auxiliary spring contact and main spring more than auxiliary spring In the flat segments of end, certain point contacts；After the contact of major-minor spring, the end points power of each major-minor spring differs, and contacts with auxiliary spring 1 main spring not only by end points power, but also acted on by auxiliary spring contact support power；Each chip architecture parameter, bullet at major-minor spring Property modulus, allowable stress, auxiliary spring work load, the born maximum load of major-minor spring given in the case of, few to end contact Each main spring of sheet parabolic type variable cross-section major-minor spring and the stress intensity of auxiliary spring are checked, and concrete check step is as follows:

(1) each main spring of the few sheet parabolic type variable cross-section major-minor spring of ends contact formula and the half clamping Rigidity Calculation of auxiliary spring:

I step: the half clamping stiffness K of each main spring before the contact of major-minor spring_MiCalculate:

Half length L according to few sheet main spring of parabolic type variable cross-section_M, main reed number m, the thickness of the root flat segments of each main spring Degree h_2M, width b, elastic modulus E, half l of installing space₃, the root of main spring parabolic segment is to distance l of main spring end points_2M= L_M-l₃, the thickness of the parabolic segment of i-th main spring compares β_i=h_1i/h_2M, wherein, i=1,2 ..., m, before contacting major-minor spring Each main spring half clamping stiffness K_MiCalculate, i.e.

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

In formula,

II step: the half clamping stiffness K of each main spring after the contact of major-minor spring_MAiCalculate:

Half length L according to few sheet main spring of parabolic type variable cross-section_M, main reed number m, the thickness of the root flat segments of each main spring Degree h_2M, width b, elastic modulus E, half l of installing space₃, the root of main spring parabolic segment is to distance l of main spring end points_2M= L_M-l₃, the thickness of the parabolic segment of i-th main spring compares β_i, wherein, i=1,2 ..., m；Half length L of auxiliary spring_A, auxiliary spring sheet number N, the thickness h of each auxiliary spring root flat segments_2A, auxiliary spring contact and horizontal range l of main spring end points₀=L_M-L_A, auxiliary spring parabola The root of section is to distance l of auxiliary spring end points_2A=L_A-l₃, the thickness of the parabolic segment of jth sheet auxiliary spring compares β_Aj=h_A1j/h_2A, wherein, J=1,2 ..., n, the half clamping stiffness K of each main spring after major-minor spring is contacted_MAiCalculate, i.e.

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

In formula,

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

$G_{x-DAj}=\frac{4\[l_{2A}^3\left(1-{\mathrm{\β}}_{Aj}^3\right)+{\left(L_A-l_3/2\right)}^3\]}{Eb},G_{x-DAT}=\frac{1}{\underset{j=1}{\overset{n}{\mathrm{\Σ}}}\frac{1}{G_{x-DAj}}},j=1,2,...,n;$

$\begin{array}{c}{G}_{x-CD}=\frac{4{\left(L_M-l_3/2\right)}^3-6l_0{\left(L_M-l_3/2\right)}^2-4l_{2M}^3+6l_0{l}_{2M}^2}{Eb}+\frac{2{\left(l_0-l_{2M}{\mathrm{\β}}_m^2\right)}^2\left(2l_{2M}{\mathrm{\β}}_m^2+l_0\right)}{{\mathrm{Eb\β}}_m^3}-\\ \frac{8l_{2M}^2\left({\mathrm{\β}}_m-1\right)\left(l_{2M}-3l_0+l_{2M}{\mathrm{\β}}_m^2+l_{2M}{\mathrm{\β}}_m\right)}{Eb};\end{array}$

$G_{x-D_{z}m}=\frac{4{(L_M-l_3/2)}^3-6l_0{(L_M-l_3/2)}^2-4l_{2M}^3+6l_0{l}_{2M}^2}{Eb}+\frac{2{(l_0-l_{2M}{\mathrm{\β}}_m^2)}^2(2l_{2M}{\mathrm{\β}}_m^2+l_0)}{{\mathrm{Eb\β}}_m^3}-$

$\frac{8l_{2M}^2({\mathrm{\β}}_m-1)(l_{2M}-3l_0+l_{2M}{\mathrm{\β}}_m^2+l_{2M}{\mathrm{\β}}_m)}{Eb},;$

Wherein, β_mIt it is the parabolic of the main spring of m sheet The thickness ratio of line segment；

III step: the half clamping stiffness K of each auxiliary spring_AjCalculate:

Half length L according to few sheet parabolic type variable cross-section auxiliary spring_A, auxiliary spring sheet number n, the thickness of the root flat segments of each auxiliary spring Degree h_2A, width b, elastic modulus E, half l of installing space₃, the root of auxiliary spring parabolic segment is to distance l of auxiliary spring end points_2A；The The thickness of the parabolic segment of j sheet auxiliary spring compares β_Aj, wherein, j=1,2 ..., n, the half of each auxiliary spring is clamped stiffness K_AjCarry out Calculate, i.e.

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

In formula,

(2) each main spring of the few sheet parabolic type variable cross-section major-minor spring of ends contact formula and the maximum end points power of auxiliary spring calculate:

I step: the maximum end points power of each main spring calculates:

The most single-ended some maximum load of half according to maximum load suffered by the few sheet parabolic type variable cross-section major-minor spring of ends contact formula P_max, auxiliary spring works load p_K, main reed number m, calculated K in I step_Mi, and II step calculates obtained K_MAi, Maximum end points power P to each main spring_imaxCalculate, i.e.

$P_{i\max }=\frac{K_{Mi}{P}_K}{2\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{K}_{Mi}}+\frac{K_{MAi}\left(2P_{\max }-P_K\right)}{2\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{K}_{MAi}},i=1,2,...,m;$

Ii step: the maximum end points power of each auxiliary spring calculates:

The most single-ended some maximum load P of half according to maximum load suffered by few sheet parabolic type variable cross-section major-minor spring_max, auxiliary spring rises Used load P_K；Main reed number m, the thickness h of each main spring root flat segments_2M；Auxiliary spring sheet number n, each auxiliary spring root flat segments Thickness h_2A, calculated K in II step_MAi、G_x-CD、G_x-CDzAnd G_x-DAT, and calculated K in III step_Aj, to respectively Maximum end points power P of sheet auxiliary spring_AjmaxCalculate, i.e.

$P_{Ajmax}=\frac{K_{Aj}{K}_{MAm}{G}_{x-CD}{h}_{2A}^3(2P_{max}-P_K)}{2\underset{j=1}{\overset{n}{\Σ}}{K}_{Aj}\underset{i=1}{\overset{m}{\Σ}}{K}_{MAi}(G_{x-DAT}{h}_{2M}^3+G_{x-{\mathrm{CD}}_z}{h}_{2A}^3)},j=1,2,...,n;$

(3) each main spring of the few sheet parabolic type variable cross-section major-minor spring of ends contact formula and the maximum stress of auxiliary spring calculate:

Step A: the maximum stress of the front main spring of m-1 sheet calculates:

Half length L according to few sheet main spring of parabolic type variable cross-section_M, main reed number m, the thickness of each main spring root flat segments h_2M, width b, half l of installing space₃, calculated P in i step_imax, the maximum stress of spring main to front m-1 is counted Calculate, i.e.

${\mathrm{\σ}}_{imax}=\frac{6P_{imax}(L_M-l_3/2)}{{\mathrm{bh}}_{2M}^2},i=1,2,...,m-1;$

Step B: the maximum stress of the main spring of m sheet calculates:

The thickness h of the root flat segments according to few sheet main spring of parabolic type variable cross-section_2M, width b, the root of parabolic segment is to main spring Distance l of end points_2M, the thickness of the parabolic segment of the main spring of m sheet compares β_m, auxiliary spring contact and horizontal range l of main spring end points₀, i walks Calculated P in Zhou_mmax, calculated P in ii step_Ajmax, the maximum stress of spring main to m sheet calculates, i.e.

${\mathrm{\σ}}_{mmax}=\frac{6\[P_{mmax}{\mathrm{\β}}_m^2{l}_{2M}-\underset{j=1}{\overset{n}{\mathrm{\Σ}}}{P}_{Ajmax}({\mathrm{\β}}_m^2{l}_{2M}-l_0)\]}{b{\left({\mathrm{\β}}_m{h}_{2M}\right)}^2};$

Step C: the maximum stress of each auxiliary spring calculates:

Half length L according to few sheet parabolic type variable cross-section auxiliary spring_A, auxiliary spring sheet number n, the thickness of each auxiliary spring root flat segments h_2A, width b, half l of installing space₃, calculated P in ii step_Ajmax, the maximum stress of each auxiliary spring is counted Calculate, i.e.

${\mathrm{\σ}}_{Ajmax}=\frac{6P_{Ajmax}(L_A-l_3/2)}{{\mathrm{bh}}_{2A}^2},j=1,2,...,n;$

(4) each main spring of the few sheet parabolic type variable cross-section major-minor spring of ends contact formula and the stress intensity of auxiliary spring are checked:

1. step: the stress intensity of the front main spring of m-1 sheet is checked:

Allowable stress [σ] according to leaf spring, and the maximum stress of each of the calculated front main spring of m-1 sheet in step A, The stress intensity of each of the front main spring of m-1 sheet of sheet parabolic type variable cross-section major-minor spring few to end contact is checked, it may be assumed that

If σ_imax> [σ], then i-th main spring, it is unsatisfactory for stress intensity requirement；

If σ_imax≤ [σ], then i-th main spring, meet stress intensity requirement, i=1, and 2 ..., m-1；

2. step: the stress intensity of the main spring of m sheet is checked:

Allowable stress [σ] according to leaf spring, and the maximum stress of the calculated main spring of m sheet in step B, connect end The stress intensity of the main spring of m sheet of the few sheet parabolic type variable cross-section major-minor spring of touch is checked, it may be assumed that

If σ_mmax> [σ], the then main spring of m sheet, it is unsatisfactory for stress intensity requirement；

If σ_mmax≤ [σ], the then main spring of m sheet, meets stress intensity requirement；

3. step: the stress intensity of each auxiliary spring is checked:

Allowable stress [σ] according to leaf spring, and the maximum stress of calculated each auxiliary spring in step C, connect end The stress intensity of each auxiliary spring of the few sheet parabolic type variable cross-section major-minor spring of touch is checked, it may be assumed that

If σ_Ajmax> [σ], then jth sheet auxiliary spring, it is unsatisfactory for stress intensity requirement；

If σ_Ajmax≤ [σ], then jth sheet auxiliary spring, meet stress intensity requirement, j=1, and 2 ..., n.