CN105912795A - Non-end contact type few-leaf parabola main-auxiliary spring endpoint force determining method - Google Patents

Abstract

The invention relates to a non-end contact type few-leaf parabola main-auxiliary spring endpoint force determining method, and belongs to the suspension rack steel plate spring technical field; according to structure parameters, elasticity modulus, main-auxiliary spring gaps and main-auxiliary spring bearing loads of each main spring and each auxiliary spring of the non-end contact type few-leaf parabola variable cross-section main-auxiliary spring, the novel method can use the relations between deformation, rigidity and load of each main-auxiliary spring to respectively determine end point force of each main spring and each auxiliary spring; through embodiments and ANSYS emulation proof, the method can obtain accurate and reliable end point force determined values of each main spring and auxiliary spring of the non-end contact type few-leaf parabola variable cross-section main-auxiliary spring, thus providing reliable technical basis for the design, rigidity calculation and stress intensity check of the non-end contact type few-leaf parabola variable cross-section main-auxiliary spring, improving product design level and performance, improving vehicle driving smoothness, reducing design and test cost, and accelerating product develop speed.

Description

The determination method of the few sheet parabolic type major-minor spring end points power of non-ends contact formula

Technical field

The present invention relates to vehicle suspension leaf spring, be the determination of the few sheet parabolic type major-minor spring end points power of non-ends contact formula especially Method.

Background technology

In order to meet the vehicle suspension variation rigidity design requirement under different loads, the few major and minor spring of sheet variable cross-section of employing, wherein, Certain major-minor spring gap it is designed with, it is ensured that after the load that works more than auxiliary spring, major and minor spring between auxiliary spring contact and main spring Cooperation, to meet the design requirement of complex stiffness.The stress of the 1st main spring of few sheet variable cross-section major-minor spring is complicated, not only Bearing vertical load, simultaneously also subject to torsional load and longitudinal loading, therefore, the end of the 1st main spring designed by reality is put down The thickness of straight section and length, more than the thickness of end flat segments and the length of other each main spring, the most mostly use that end is non-waits structure Few sheet variable-section steel sheet spring, the requirement complicated to meet the 1st main spring stress.It addition, in order to meet different composite rigidity Design requirement, generally use the auxiliary spring of different length, i.e. auxiliary spring contact is the most different from the position that main spring contacts, therefore, can It is divided into end flat segments contact and non-ends contact formula two kinds.The computational problem of few sheet variable cross-section major-minor spring end points power, is restriction The key issue that few sheet variable cross-section major-minor spring design, Rigidity Calculation, stress intensity are checked.Sheet parabola few to non-ends contact formula Type major-minor spring, when load more than auxiliary spring work load time, auxiliary spring contact with in main spring parabolic segment certain point contact and together with work When making, the main spring of m sheet, in addition to by end points power, is also acted on by auxiliary spring contact support power in parabolic segment, therefore, non- The calculating of the few sheet variable cross-section major-minor spring end points power of ends contact formula is extremely complex, fails to provide the meter of major-minor spring end points power the most always Calculation method.Project planner, is mostly the impact ignoring major-minor spring Length discrepancy at present, and direct basis main spring rigidity and auxiliary spring are firm Degree, carries out approximate calculation to the end points power of main spring and auxiliary spring, cuts it is thus impossible to meet the few sheet parabolic type change of non-ends contact formula The careful design of face major-minor spring and the requirement of analytical calculation.Therefore, it is necessary to it is few to set up a kind of non-ends contact formula accurate, reliable The computational methods of sheet parabolic type variable cross-section major-minor spring end points power, meet Vehicle Industry fast development and cut the change of few sheet parabolic type The requirement that face major-minor Precise Design for Laminated Spring, Rigidity Calculation and stress intensity are checked, improves few sheet parabolic type variable cross-section major-minor The design level of spring, product quality and performances and vehicle ride performance；Meanwhile, reduce product 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 is to provide a kind of easy, reliably The determination method of the few sheet parabolic type major-minor spring end points power of non-ends contact formula, its flow process determined is as shown in Figure 1.Few sheet parabolic The half symmetrical structure of line style variable cross-section major-minor spring can see Cantilever Beams of Variable Cross Section as, symmetrical center line will see half spring as The fixing end of root, see main spring end stress point and auxiliary spring ends points as main spring end points and auxiliary spring end points respectively；Non-end The half symmetrical structure schematic diagram of the few sheet parabolic type variable cross-section major-minor spring of contact, as in figure 2 it is shown, include, main spring 1, root Portion's pad 2, auxiliary spring 3, end pad 4.The a length of L of half of each of main spring 1_M, it is by root flat segments, parabolic segment Constituted with end flat segments three sections.Between the root flat segments of each of main spring 1 and and the root flat segments of auxiliary spring 3 between be provided with Root shim 2, is provided with end pad 4 between the end flat segments of main spring 1, and the material of end pad is carbon fiber composite Material, to reduce frictional noise produced by spring works, the width of major-minor spring is b, and the half of installing space is l₃, springform Amount is E.Main reed number is m, and the thickness of the root flat segments of each main spring is h_2M；The end flat segments of each main spring is non-etc. Structure, the thickness of the end flat segments of i.e. the 1st and length, more than the thickness of end flat segments and the length of other each main spring, Thickness and the length of the end flat segments of each main spring are respectively h_1iAnd l_1i, i=1,2 ..., m；Middle variable cross-section is parabolic segment, The thickness of each parabolic segment is than for β_i=h_1i/h_2M, the distance of the root of parabolic segment to main spring end points is l_2M=L_M-l₃.Auxiliary spring Sheet number is n, a length of L of half of auxiliary spring_A, auxiliary spring contact is l with the horizontal range of main spring end points₀=L_M-L_A；Each auxiliary spring Root flat segments thickness is h_2A, thickness and the length of the end flat segments of each auxiliary spring are respectively h_A1jAnd l_A1j, each auxiliary spring is thrown The thickness of thing line segment compares β_Aj=h_1j/h_2A, j=1,2 .., n；It is provided with between certain major-minor spring between auxiliary spring contact and main spring parabolic segment Gap δ, after load works load more than auxiliary spring, auxiliary spring contact contacts with certain point in main spring parabolic segment and jointly acts as With, to meet the design requirement of major-minor spring complex stiffness.At the structural parameters of each main spring, the structural parameters of each auxiliary spring, bullet Property modulus, major-minor spring gap and major-minor spring institute loaded given in the case of, sheet variable cross-section major-minor spring few to non-ends contact formula The end points power of each main spring and each auxiliary spring is determined.

For solving above-mentioned technical problem, the determination of the few sheet parabolic type major-minor spring end points power of non-ends contact formula provided by the present invention Method, it is characterised in that employing following steps:

(1) the end points deformation coefficient G of each main spring of parabolic type variable cross-section under end points stressing conditions_x-DiCalculate:

Half length L according to few sheet main spring of parabolic type variable cross-section_M, width b, elastic modulus E, the root of main spring parabolic segment arrives Distance l of main spring end points_2M, main reed number m, wherein, the thickness of the parabolic segment of i-th main spring compares β_i, i=1,2 ..., M, the end points deformation coefficient G to each main spring under end points stressing conditions_x-DiCalculate, i.e.

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

(2) the deformation coefficient G at parabolic segment with auxiliary spring contact point of the main spring of m sheet under end points stressing conditions_x-BCCalculate:

Half length L according to few sheet main spring of parabolic type variable cross-section_M, width b, elastic modulus E, half l of installing space₃, main Reed number m, the root of main spring parabolic segment is to distance l of main spring end points_2M, auxiliary spring contact and the horizontal range of main spring end points l₀, to the deformation coefficient G at parabolic segment with auxiliary spring contact point of the main spring of m sheet under end points stressing conditions_x-BCCount Calculate, i.e.

$G_{x-BC}=\frac{2}{Eb}\[8l_{2M}^{3/2}{l}_0^{3/2}-(9l_{2M}^2+3L_M^2)l_0+2l_{2M}^3+2L_M^3\];$

(3) the end points deformation coefficient of the main spring of m sheet under major-minor spring contact point stressing conditionsCalculate:

Half length L according to few sheet main spring of parabolic type variable cross-section_M, width b, elastic modulus E, main reed number m, main spring parabolic The root of line segment is to horizontal range l of the distance of main spring end points, auxiliary spring contact and main spring end points₀, to major-minor spring contact point stress feelings The end points deformation coefficient of the main spring of m sheet under conditionCalculate, i.e.

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

(4) deformation coefficient at parabolic segment with auxiliary spring contact point of the main spring of m sheet under major-minor spring contact point stressing conditionsMeter Calculate:

Half length L according to few sheet main spring of parabolic type variable cross-section_M, width b, elastic modulus E, the root of main spring parabolic segment arrives Distance l of main spring end points_2M, auxiliary spring contact and horizontal range l of main spring end points₀, under major-minor spring contact point stressing conditions M sheet main spring deformation coefficient at parabolic segment with auxiliary spring contact pointCalculate, i.e.

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

(5) the end points deformation coefficient G of each auxiliary spring under end points stressing conditions_x-DAjAnd total end points deformation coefficient of n sheet superposition auxiliary spring G_x-DATCalculating:

Half length L according to few sheet parabolic type variable cross-section auxiliary spring_A, width b, elastic modulus E, the root of auxiliary spring parabolic segment arrives Distance l of main spring end points_2A, auxiliary spring sheet number n, wherein, the thickness of the parabolic segment of jth sheet auxiliary spring compares β_Aj, j=1,2 ..., N, the end points deformation coefficient G to each auxiliary spring under end points stressing conditions_x-DAjCalculate, i.e.

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

End points deformation coefficient G according to each auxiliary spring_x-DAj, total end points deformation coefficient G to n sheet superposition auxiliary spring_x-DATFor

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

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

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

According to main reed number m, the thickness h of the root flat segments of each main spring_2M, and calculated G in step (1)_x-Di, to major-minor The half stiffness K of each main spring before spring contact_MiCalculate, i.e.

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

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

According to main reed number m, the thickness h of the root flat segments of each main spring_2M, the thickness h of the root flat segments of each auxiliary spring_2A, G obtained by calculating in step (1)_x-Di, calculated G in step (2)_x-BC, calculated in step (3)Step Suddenly calculated in (4)And calculated G in step (5)_x-DAT, each parabolic type after major-minor spring is contacted The half stiffness K of the main spring of variable cross-section_MAiIt is respectively calculated, i.e.

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

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

According to auxiliary spring sheet number n, the thickness h of the root flat segments of each auxiliary spring_2A, and calculated G in step (5)_x-DAj, to each The half stiffness K of auxiliary spring_AjCalculate, i.e.

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

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

I step: auxiliary spring works load p_KCalculating:

According to main reed number m, the thickness h of the root flat segments of each main spring_2M, calculated K in I step_Mi, step (2) is fallen into a trap The main spring of m sheet under end points stressing conditions obtained deformation coefficient G at parabolic segment with auxiliary spring contact point_x-BC, and Major-minor spring gap delta, work load p to auxiliary spring_KCalculate, i.e.

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

Ii step: end points power P of each main spring_iDetermine:

According to the half the most single-ended point load P that few sheet parabolic type variable cross-section major-minor spring is loaded, main reed number m, i step is fallen into a trap The P obtained_K, calculated K in I step_Mi, and II step calculates obtained K_MAi, determine the end of each main spring Point power P_i, i.e.

$P_i=\left\{\begin{array}{cc}\frac{K_{Mi}P}{\underset{i=1}{\overset{m}{\Σ}}{K}_{Mi}},& P\≤P_K/2,i=1,2,...m\\ \frac{K_{Mi}{P}_K}{2\underset{i=1}{\overset{m}{\Σ}}{K}_{Mi}}+\frac{K_{MAi}(2P-P_K)}{2\underset{i=1}{\overset{m}{\Σ}}{K}_{MAi}},& P>P_K/2,i=1,2,...m\end{array}\right.;$

Wherein, as P≤P_KWhen/2, P_iFor when load works load less than auxiliary spring, major-minor spring works feelings not in contact with, the most main spring The end points power of each main spring under condition；Work as P > P_KWhen/2, P_iFor when load works load more than auxiliary spring, major-minor spring connects Touch, major-minor spring concur in the case of the end points power of each main spring；

Iii step: end points power P of each auxiliary spring_AjDetermine:

According to the half the most single-ended point load P that few sheet parabolic type variable cross-section major-minor spring is loaded, wherein, P > P_K/2；Main reed number M, the thickness h of each main spring root flat segments_2M, auxiliary spring sheet number n, the thickness h of each auxiliary spring root flat segments_2A；I step In calculated P_K, calculated G in step (2)_x-BC, calculated in step (4)And step (5) falls into a trap The G obtained_x-DAT, II step calculates obtained K_MAi, and calculated K in III step_Aj, determine each auxiliary spring End points power P_Aj, i.e.

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

The present invention has the advantage that than prior art

Waiting structure owing to the end flat segments of each main spring is non-, meanwhile, auxiliary spring length is unequal with main spring length, and when load is more than Auxiliary spring work load time, the main spring of m sheet, in addition to by end points power, is also made by auxiliary spring contact support power in parabolic segment With, therefore, each main spring of the few sheet parabolic type variable cross-section major-minor spring of non-ends contact formula and the analytical calculation of auxiliary spring end points power are non- The most complicated, fail to provide the few sheet parabolic type variable cross-section major-minor spring end points power of non-ends contact formula accurate, reliable the most always Determine method.The present invention can the structural parameters of each main spring, the structural parameters of each auxiliary spring, elastic modelling quantity, major-minor spring gap, And major-minor spring institute is loaded, accurately calculates the end points power of each main spring and each auxiliary spring respectively.By design example and ANSYS simulating, verifying understands, and utilizes the method to can get the few sheet variable cross-section major-minor spring of non-ends contact formula accurate, reliable Each main spring and the end points force value of auxiliary spring, for the few sheet parabolic type variable cross-section major-minor spring design of non-ends contact formula, rigidity checking, Stress intensity is checked and is provided technical foundation.Utilize the method can improve the few sheet variable cross-section major-minor leaf spring of non-ends contact formula Design level, product quality and performances and vehicle ride performance；Meanwhile, also can reduce design and testing expenses, accelerate product Development rate.

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 determination flow chart of the few sheet parabolic type major-minor spring end points power of non-ends contact formula；

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

Fig. 3 is the ANSYS deformation simulation cloud atlas of the 1st main spring of parabolic type variable cross-section of embodiment one；

Fig. 4 is the ANSYS deformation simulation cloud atlas of the 2nd main spring of parabolic type variable cross-section of embodiment one；

Fig. 5 is the ANSYS deformation simulation cloud atlas of 1 parabolic type variable cross-section auxiliary spring of embodiment one.

Specific embodiments

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

Embodiment: the width b=60mm of the few sheet parabolic type variable cross-section major-minor spring of certain non-ends contact formula, elastic modelling quantity E=200GPa, half l of installing space₃=55mm；Wherein, main reed number m=2, the half length of main spring L_M=575mm, the thickness h of the root flat segments of each main spring_2M=11mm, the root of parabolic segment is to the distance of main spring end points l_2M=L_M-l₃=520mm；The thickness h of the end flat segments of the 1st main spring₁₁=7mm, the thickness of the parabolic segment of the 1st main spring Degree compares β₁=h₁₁/h_2M=0.64；The thickness h of the end flat segments of the 2nd main spring₁₂=6mm, the parabolic segment of the 2nd main spring Thickness compares β₂=h₁₂/h_2M=0.55.Auxiliary spring sheet number n=1, half length L of auxiliary spring_A=375mm, auxiliary spring contact and main spring end points Horizontal range l₀=L-L_A=200mm；The thickness h of auxiliary spring root flat segments_2A=14mm, the thickness of end flat segments h_A11=8mm, the thickness of the parabolic segment of auxiliary spring compares β_A1=h_A11/h_2A=0.57.Major-minor spring gap delta=17.97mm, when load is big When auxiliary spring works load, auxiliary spring contact contacts with certain point in main spring parabolic segment.When the few sheet parabolic of this non-ends contact formula During line style variable cross-section major-minor spring half single-ended point load P=3040N loaded, sheet parabola few to this non-ends contact formula Each main spring of type variable cross-section major-minor spring and the end points power of each auxiliary spring are determined.

The determination method of the few sheet parabolic type major-minor spring end points power of the non-ends contact formula that present example is provided, its stream determined Journey is as it is shown in figure 1, specifically comprise the following steps that

(1) the end points deformation coefficient G of each main spring of parabolic type variable cross-section under end points stressing conditions_x-DiCalculate:

Half length L according to few sheet main spring of parabolic type variable cross-section_M=575mm, width b=60mm, elastic modelling quantity E=200GPa, the root of main spring parabolic segment is to distance l of main spring end points_2M=520mm, main reed number m=2, wherein, 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 main spring in the case of power and the end points deformation coefficient G of the 2nd main spring_x-D1And G_x-D2It is respectively calculated, i.e.

$G_{x-D1}=\frac{4\[l_{2M}^3(1-{\mathrm{\β}}_1^3)+L_M^3\]}{Eb}=98.16{\mathrm{mm}}^4/N,$

$G_{x-D2}=\frac{4\[l_{2M}^3(1-{\mathrm{\β}}_2^3)+L_M^3\]}{Eb}=102.63{\mathrm{mm}}^4/N;$

(2) the deformation coefficient G at parabolic segment with auxiliary spring contact point of the main spring of m sheet under end points stressing conditions_x-BCCalculate:

Half length L according to few sheet main spring of parabolic type variable cross-section_M=575mm, width b=60mm, elastic modelling quantity E=200GPa, the root of main spring parabolic segment is to distance l of main spring end points_2MThe water of=520mm, auxiliary spring contact and main spring end points Flat distance l₀=200mm, main reed number m=2, contact with auxiliary spring in parabolic segment the 2nd main spring under end points stressing conditions Deformation coefficient G at Dian_x-BCCalculate, i.e.

$G_{x-BC}=\frac{2}{Eb}\[8l_{2M}^{3/2}{l}_0^{3/2}-(9l_{2M}^2+3L_M^2)l_0+2l_{2M}^3+2L_M^3\]=40.77{\mathrm{mm}}^4/N;$

(3) the end points deformation coefficient of the main spring of m sheet under major-minor spring contact point stressing conditionsCalculating:

Half length L according to few sheet main spring of parabolic type variable cross-section_M=575mm, width b=60mm, elastic modelling quantity E=200GPa, the root of main spring parabolic segment is to distance l of main spring end points_2MThe water of=520mm, auxiliary spring contact and main spring end points Flat distance l₀=200mm, main reed number m=2, deform system to the end points of the 2nd main spring under major-minor spring contact point stressing conditions NumberCalculate, i.e.

$G_{x-D_{p}2}=\frac{4}{bE}(l_{2M}^3-6l_0{l}_{2M}^2+4l_{2M}^{3/2}{l}_0^{3/2}+L_M^3)=40.77{\mathrm{mm}}^4/N;$

(4) deformation coefficient at parabolic segment with auxiliary spring contact point of the main spring of m sheet under major-minor spring contact point stressing conditionsMeter Calculate:

Half length L according to few sheet main spring of parabolic type variable cross-section_M=575mm, width b=60mm, elastic modelling quantity E=200GPa, the root of main spring parabolic segment is to distance l of main spring end points_2MThe water of=520mm, auxiliary spring contact and main spring end points Flat distance l₀=200mm, main reed number m=2, to the 2nd parabolic type variable cross-section master under major-minor spring contact point stressing conditions Spring deformation coefficient at parabolic segment with auxiliary spring contact pointCalculate, i.e.

$\begin{array}{c}{G}_{x-{\mathrm{BC}}_p}=\frac{4}{Eb}\[(L_M-l_{2M})(L_M^2-3L_M{l}_0+L_M{l}_{2M}+3l_0^2-3l_0{l}_{2M}+l_{2M}^2)-(6l_{2M}{l}_0^2-2l_{2M}^3-16l_0^{3/2}{l}_{2M}^{1/2}+12l_0{l}_{2M}^3)\]\\ =21.35{\mathrm{mm}}^4/N;\end{array}$

(5) the end points deformation coefficient G of each auxiliary spring under end points stressing conditions_x-DAjAnd total end points deformation coefficient of n sheet superposition auxiliary spring G_x-DATCalculating:

Half length L according to few sheet parabolic type variable cross-section auxiliary spring_A=375mm, the sheet number n=1 of auxiliary spring, width b=60mm, bullet Property modulus E=200GPa, half l of installing space₃=55mm, the root of auxiliary spring parabolic segment is to distance l of main spring end points_2A= 320mm, the thickness of the parabolic segment of auxiliary spring compares β_A1=0.57, the end points deformation coefficient to this sheet auxiliary spring under end points stressing conditions G_x-DA1Calculate, i.e.

$G_{x-DA1}=\frac{4\[l_{2A}^3(1-{\mathrm{\β}}_{A1}^3)+L_A^3\]}{Eb}=26.46{\mathrm{mm}}^4/N;$

This auxiliary spring sheet number n=1, therefore, total end points deformation coefficient G of n sheet superposition auxiliary spring_x-DAT, deform equal to the end points of this sheet auxiliary spring Coefficient, i.e.

$G_{x-DAT}=\frac{1}{\underset{j=1}{\overset{n}{\Σ}}\frac{1}{G_{x-DAj}}}=G_{x-DA1}=26.46{\mathrm{mm}}^4/N;$

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

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

According to main reed number m=2, the thickness h of the root flat segments of each main spring_2M=11mm, in step (1) the calculated 1st The end points deformation coefficient G of the main spring of sheet and the 2nd main spring_x-D1=98.16mm⁴/ N and G_x-D2=102.63mm⁴/ N, can be to major-minor spring The 1st main spring before contact and the half stiffness K of the 2nd main spring_M1And K_M2It is respectively calculated, i.e.

$K_{M1}=\frac{h_{2M}^3}{G_{x-D1}}=13.56N/mm;$

$K_{M2}=\frac{h_{2M}^3}{G_{x-D2}}=12.97N/mm;$

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

According to main reed number m=2, the root flat segments thickness h of each main spring_2M=11mm, the thickness of the root flat segments of this sheet auxiliary spring Degree h_2A=14mm, calculated G in step (1)_x-D1=98.16mm⁴/ N and G_x-D2=102.63mm⁴/ N, step (2) is fallen into a trap The G obtained_x-BC=40.77mm⁴/ N, calculated in step (3)Step is calculated in (4) 'sAnd calculated G in step (5)_x-DAT=26.46mm⁴/ N, the after major-minor spring is contacted 1 main spring and the half stiffness K of the 2nd main spring_MA1And K_MA2It is respectively calculated, i.e.

$K_{MA1}=\frac{h_{2M}^3}{G_{x-D1}}=13.56N/mm;$

$K_{MA2}=\frac{h_{2M}^3(G_{x-DAT}{h}_{2M}^3+G_{x-{\mathrm{BC}}_p}{h}_{2A}^3)}{G_{x-D2}(G_{x-DAT}{h}_{2M}^3+G_{x-{\mathrm{BC}}_p}{h}_{2A}^3)-G_{x-D_{p}2}{G}_{x-BC}{h}_{2A}^3}=24.65N/mm;$

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

According to auxiliary spring sheet number n=1, the thickness h of the root flat segments of this sheet auxiliary spring_2AObtained by=14mm, and step (5) calculate G_x-DA1=26.46mm⁴/ N, the half stiffness K to this sheet parabolic type variable cross-section auxiliary spring_A1Calculate, i.e.

$K_{A1}=\frac{h_{2A}^3}{G_{x-DA1}}=103.70N/mm;$

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

I step: auxiliary spring works load p_KCalculating:

According to main reed number m=2, the root flat segments thickness h of each main spring_2MIn=11mm, I step calculated K_M1=13.56N/mm and K_M2=12.97N/mm, calculated G in step (2)_x-BC=40.77mm⁴/ N, and major-minor spring Gap delta=17.97mm, work load p to auxiliary spring_KCalculate, i.e.

$P_K=\frac{2{\mathrm{\δh}}_{2M}^3\underset{i=1}{\overset{m}{\Σ}}{K}_{Mi}}{G_{x-BC}{K}_{M2}}=2400N;$

Ii step: end points power P of each main spring_iDetermine:

According to the half the most single-ended point load P=3040N that few sheet parabolic type variable cross-section major-minor spring is loaded, main reed number m=2, i Calculated P in step_KCalculated K in=2400N, I step_M1=13.56N/mm and K_M2=12.97N/mm, and II step calculates obtained K_MA1=13.56N/mm and K_MA2=24.65N/mm, to the 1st main spring and the 2nd main spring End points power P₁And P₂It is determined respectively, i.e.

$P_1=\frac{K_{M1}{P}_K}{2\underset{i=1}{\overset{m}{\Σ}}{K}_{Mi}}+\frac{K_{MA1}(2P-P_K)}{2\underset{i=1}{\overset{m}{\Σ}}{K}_{MAi}}=1266.30N;$

$P_2=\frac{K_{M2}{P}_K}{2\underset{i=1}{\overset{m}{\Σ}}{K}_{Mi}}+\frac{K_{MA2}(2P-P_K)}{2\underset{i=1}{\overset{m}{\Σ}}{K}_{MAi}}=1773.70N;$

Iii step: end points power P of each auxiliary spring_AjDetermine:

According to half the most single-ended point load P=3040N, main reed number m=2 that few sheet parabolic type variable cross-section major-minor spring is loaded, The root flat segments thickness h of each main spring_2M=11mm, auxiliary spring sheet number n=1, the root flat segments thickness of this sheet auxiliary spring h_2ACalculated P in=14mm, i step_K=2400N, calculated G in step (2)_x-BC=40.77mm⁴/ N, step (4) in calculatedAnd calculated G in step (5)_x-DAT=26.46mm⁴In/N, II step K obtained by calculating_MA1=13.56N/mm and K_MA2In=24.65N/mm, and III step calculated K_A1=103.70N/mm, to this sheet auxiliary spring end points power P_A1Calculate, i.e.

$P_{A1}=\frac{K_{A1}{K}_{MA2}{G}_{x-BC}{h}_{2A}^3(2P-P_K)}{2\underset{j=1}{\overset{n}{\Σ}}{K}_{Aj}\underset{i=1}{\overset{m}{\Σ}}{K}_{MAi}(G_{x-DAT}{h}_{2M}^3+G_{x-{\mathrm{BC}}_p}{h}_{2A}^3)}=1415.70N.$

Utilize ANSYS finite element emulation software, according to major-minor spring structure parameter and the material of this few sheet parabolic type variable-section steel sheet spring Material characterisitic parameter, sets up the ANSYS phantom of half symmetrical structure major-minor spring, grid division, arranges auxiliary spring end points and master Spring contacts, and at the root applying fixed constraint of phantom, applies concentrfated load F=P-at major-minor spring end points P_K/ 2=1840N, the deformation to the major-minor spring of this few sheet parabolic type variable-section steel sheet spring carries out ANSYS emulation, obtained The ANSYS deformation simulation cloud atlas of the 1st main spring, as shown in Figure 3；The ANSYS deformation simulation cloud of the 2nd main spring Figure, as shown in Figure 4；The ANSYS deformation simulation cloud atlas of the 1st auxiliary spring, as it is shown in figure 5, wherein, the 1st main spring exists Maximum deformation quantity f at endpoint location_MA1=48.00mm, the 2nd main spring maximum deformation quantity at endpoint location f_MA2=48.00mm, the 1st auxiliary spring maximum deformation quantity f at endpoint location_A1=13.69mm.

Understand, in the case of same load, the 1st main spring of the few sheet parabolic type major-minor spring of this non-ends contact formula and the 2nd main spring And ANSYS simulating, verifying value f of the maximum distortion of 1 auxiliary spring_MA1=48.00mm, f_MA2=48.00mm, f_A1=13.69mm, respectively with deformation analytical Calculation value

$f_{MA1}=K_{MA1}{G}_{x-D1}(P-P_K/2)/\left(h_{2M}^3\underset{i=1}{\overset{m}{\Σ}}{K}_{MAi}\right)=48.16mm,$

$f_{MA2}=K_{MA2}{G}_{x-D2}(P-P_K/2)/\left(h_{2M}^3\underset{i=1}{\overset{m}{\Σ}}{K}_{MAi}\right)-G_{x-D_{z}2}{P}_{A1}/h_{2M}^3=48.16mm,$

$f_{A1}=G_{x-DA1}{P}_{A1}/h_{2A}^3=13.65mm,$

Matching, relative deviation is respectively 0.33%, 0.33%, 0.29%；Result shows that the non-ends contact formula that this invention is provided is few The determination method of sheet parabolic type major-minor spring end points power is correct, determines each obtained main spring and the end points power of each auxiliary spring Value is accurate, reliable.

Claims (1)

1. The determination method of the few sheet parabolic type major-minor spring end points power of the most non-ends contact formula, wherein, few sheet parabolic type variable cross-section major-minor The half symmetrical structure of spring is made up of root flat segments, parabolic segment, end flat segments three sections, and the end of each main spring is non-same The thickness of structure, i.e. the end flat segments of the 1st main spring and length, more than the thickness of end flat segments and the length of other each main spring Degree；Auxiliary spring length is less than main spring length, is provided with major-minor spring gap between auxiliary spring contact and main spring parabolic segment；When load is more than pair Spring work load time, in auxiliary spring contact and main spring parabolic segment, certain point contacts, and major-minor spring concurs；When major-minor spring connects After Chuing, the end points power of each major-minor spring differs, and the 1 main spring contacted with auxiliary spring is in addition to by end points power, is also subject to The effect of auxiliary spring contact support power；Each chip architecture parameter, elastic modelling quantity, major-minor spring gap and born load at major-minor spring In the case of Gei Ding, each slice main spring of sheet parabolic type major-minor spring few to non-ends contact formula and the end points power of each auxiliary spring are counted Calculating, concrete calculation procedure is as follows:

   (1) the end points deformation coefficient G of each main spring of parabolic type variable cross-section under end points stressing conditions_x-DiCalculate:

   Half length L according to few sheet main spring of parabolic type variable cross-section_M, width b, elastic modulus E, the root of main spring parabolic segment arrives Distance l of main spring end points_2M, main reed number m, wherein, the thickness of the parabolic segment of i-th main spring compares β_i, i=1,2 ..., M, the end points deformation coefficient G to each main spring under end points stressing conditions_x-DiCalculate, i.e.

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

   (2) the deformation coefficient G at parabolic segment with auxiliary spring contact point of the main spring of m sheet under end points stressing conditions_x-BCCalculate:

   Half length L according to few sheet main spring of parabolic type variable cross-section_M, width b, elastic modulus E, half l of installing space₃, main Reed number m, the root of main spring parabolic segment is to distance l of main spring end points_2M, auxiliary spring contact and the horizontal range of main spring end points l₀, to the deformation coefficient G at parabolic segment with auxiliary spring contact point of the main spring of m sheet under end points stressing conditions_x-BCCount Calculate, i.e.

   $G_{x-BC}=\frac{2}{Eb}\[8l_{2M}^{3/2}{l}_0^{3/2}-(9l_{2M}^2+3L_M^2)l_0+2l_{2M}^3+2L_M^3\];$

   (3) the end points deformation coefficient G of the main spring of m sheet under major-minor spring contact point stressing conditions_x-DpmCalculate:

   Half length L according to few sheet main spring of parabolic type variable cross-section_M, width b, elastic modulus E, main reed number m, main spring parabolic The root of line segment is to horizontal range l of the distance of main spring end points, auxiliary spring contact and main spring end points₀, to major-minor spring contact point stress feelings The end points deformation coefficient G of the main spring of m sheet under condition_x-DpmCalculate, i.e.

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

   (4) the deformation coefficient G at parabolic segment with auxiliary spring contact point of the main spring of m sheet under major-minor spring contact point stressing conditions_x-BCpMeter Calculate:

   Half length L according to few sheet main spring of parabolic type variable cross-section_M, width b, elastic modulus E, the root of main spring parabolic segment arrives Distance l of main spring end points_2M, auxiliary spring contact and horizontal range l of main spring end points₀, under major-minor spring contact point stressing conditions M sheet main spring deformation coefficient G at parabolic segment with auxiliary spring contact point_x-BCpCalculate, i.e.

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

   (5) the end points deformation coefficient G of each auxiliary spring under end points stressing conditions_x-DAjAnd total end points deformation coefficient of n sheet superposition auxiliary spring G_x-DATCalculating:

   Half length L according to few sheet parabolic type variable cross-section auxiliary spring_A, width b, elastic modulus E, the root of auxiliary spring parabolic segment arrives Distance l of main spring end points_2A, auxiliary spring sheet number n, wherein, the thickness of the parabolic segment of jth sheet auxiliary spring compares β_Aj, j=1,2 ..., N, the end points deformation coefficient G to each auxiliary spring under end points stressing conditions_x-DAjCalculate, i.e.

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

   End points deformation coefficient G according to each auxiliary spring_x-DAj, total end points deformation coefficient G to n sheet superposition auxiliary spring_x-DATFor

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

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

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

   According to main reed number m, the thickness h of the root flat segments of each main spring_2M, and calculated G in step (1)_x-Di, to major-minor The half stiffness K of each main spring before spring contact_MiCalculate, i.e.

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

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

   According to main reed number m, the thickness h of the root flat segments of each main spring_2M, the thickness h of the root flat segments of each auxiliary spring_2A, G obtained by calculating in step (1)_x-Di, calculated G in step (2)_x-BC, calculated G in step (3)_x-Dpm, step Suddenly calculated G in (4)_x-BCp, and calculated G in step (5)_x-DAT, each parabolic type after major-minor spring is contacted The half stiffness K of the main spring of variable cross-section_MAiIt is respectively calculated, i.e.

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

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

   According to auxiliary spring sheet number n, the thickness h of the root flat segments of each auxiliary spring_2A, and calculated G in step (5)_x-DAj, to each The half stiffness K of auxiliary spring_AjCalculate, i.e.

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

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

   I step: auxiliary spring works load p_KCalculating:

   According to main reed number m, the thickness h of the root flat segments of each main spring_2M, calculated K in I step_Mi, step (2) is fallen into a trap The main spring of m sheet under end points stressing conditions obtained deformation coefficient G at parabolic segment with auxiliary spring contact point_x-BC, and Major-minor spring gap delta, work load p to auxiliary spring_KCalculate, i.e.

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

   Ii step: end points power P of each main spring_iDetermine:

   According to the half the most single-ended point load P that few sheet parabolic type variable cross-section major-minor spring is loaded, main reed number m, i step is fallen into a trap The P obtained_K, calculated K in I step_Mi, and II step calculates obtained K_MAi, determine the end of each main spring Point power P_i, i.e.

   $P_i=\left\{\begin{array}{cc}\frac{K_{Mi}P}{\underset{i=1}{\overset{m}{\Σ}}{K}_{Mi}},& P\≤P_K/2,i=1,2,\mathrm{...}m\\ \frac{K_{Mi}{P}_K}{2\underset{i=1}{\overset{m}{\Σ}}{K}_{Mi}}+\frac{K_{MAi}(2P-P_K)}{2\underset{i=1}{\overset{m}{\Σ}}{K}_{MAi}},& P>P_K/2,i=1,2,\mathrm{...}m\end{array}\right.;$

   Wherein, as P≤P_KWhen/2, P_iFor when load works load less than auxiliary spring, major-minor spring works feelings not in contact with, the most main spring The end points power of each main spring under condition；Work as P > P_KWhen/2, P_iFor when load works load more than auxiliary spring, major-minor spring connects Touch, major-minor spring concur in the case of the end points power of each main spring；

   Iii step: end points power P of each auxiliary spring_AjDetermine:

   According to the half the most single-ended point load P that few sheet parabolic type variable cross-section major-minor spring is loaded, wherein, P > P_K/2；Main reed number M, the thickness h of each main spring root flat segments_2M, auxiliary spring sheet number n, the thickness h of each auxiliary spring root flat segments_2A；I step In calculated P_K, calculated G in step (2)_x-BC, calculated G in step (4)_x-BCp, and step (5) falls into a trap The G obtained_x-DAT, II step calculates obtained K_MAi, and calculated K in III step_Aj, determine each auxiliary spring End points power P_Aj, i.e.

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