CN105550487A - Method for designing few-leaf oblique line type variable-section main springs in gaps between oblique line segments and auxiliary spring - Google Patents

Abstract

The invention relates to a method for designing few-leaf oblique line type variable-section main springs in the gaps between oblique line segments and an auxiliary spring, and belongs to the technical field of suspension steel plate springs. According to the structural sizes and the elasticity moduli of the oblique line type variable-section main springs, the endpoint deformation coefficient Gx-Di of each main spring and the deformation coefficient Gx-BC of the Nth main spring at the contact point of the corresponding oblique line segment and the auxiliary spring are determined first; then, according to the required auxiliary spring acting load design value and the endpoint deformation coefficient Gx-Di of each main spring, endpoint force FN of the Nth main spring is obtained; then, according to the thickness h of the root straight section of the Nth main spring, the Gx-BC and the FN, main spring and auxiliary spring gaps between the oblique line segment of the main springs and the contact point of the auxiliary spring are designed. Through simulation verification, it can be known that the main and auxiliary spring gap design value meeting the auxiliary spring acting load requirement can be obtained by means of the method, and the product design level, product performance and vehicle smoothness are improved. Meanwhile, design and testing cost is reduced, and product development speed is increased.

Description

Few main spring of sheet bias type variable cross section is in the method for designing in oblique line section and auxiliary spring gap

Technical field

The present invention relates to vehicle suspension leaf spring, particularly less the main spring of sheet bias type variable cross section in the method for designing in oblique line section and auxiliary spring gap.

Background technology

Compared with few sheet variable-section steel sheet spring superposes leaf spring with multi-disc, there is reasonable stress, stress loading is tending towards balanced, and saves material, realizes vehicle lightweight, reduce wheel dynamic load, improve vehicle safety, also save fuel oil simultaneously, improve vehicle transport efficiency, there is good economic benefit and social benefit, and obtain extensive promotion and application abroad.For few sheet variable-section steel sheet spring, in order to meet the requirement of variation rigidity, usually major and minor spring is designed to, wherein, main spring is designed with certain gap connecting with auxiliary spring between position, contact and auxiliary spring, guarantee after being greater than certain load, major and minor spring contacts and cooperatively works, and meets the designing requirement of vehicle suspension to leaf spring rigidity.

Due to the 1st its stressed complexity of the main spring of few sheet variable cross section, not only bear vertical load, also bear torsional load and longitudinal loading simultaneously, therefore, the end thickness of the 1st leaf spring designed by reality, usual more each than other partially thicker, namely in actual design with in producing, mostly adopts the non-few sheet variable-section steel sheet spring waiting structure in end.At present less sheet variable-section steel sheet spring mainly contains two types, and one is parabolic type, and another is bias type, and wherein, Parabolic stress is equal stress, more reasonable than bias type of its stress loading.But due to the processing technology of parabolic type variable cross section complicated, need complexity, expensive process equipment, and the processing technology of bias type variable cross section is simple, only need simple equipment just can process, therefore, meeting under stress intensity condition, the variable-section steel sheet spring of elongated available bias type, replaces Parabolic variable-section steel sheet spring.For the major and minor spring of few sheet bias type variable cross section, also because auxiliary spring is different from the contact position of main spring, can be divided into and contact in end flat segments the major and minor leaf spring contacted with in oblique line section.Although previously, once someone gave the method for designing of few sheet bias type variable-section steel sheet spring, such as, Peng Mo, high army is once in " automobile engineering ", (the 14th volume) the 3rd phase in 1992, propose the design and calculation method of Varied section leaf spring, the method mainly designs for few sheet bias type variable-section steel sheet spring of the structures such as end, its weak point to meet the non-designing requirement of few sheet bias type variable-section steel sheet spring waiting structure in end, more can not lack the design of the main spring of sheet bias type variable cross section in the major and minor spring gap at oblique line section and auxiliary spring contact point place.For the non-gap design of the main spring of few sheet bias type variable cross section at oblique line section and auxiliary spring contact point place waiting structure in end, owing to being subject to the non-few main spring of sheet bias type variable cross section of structure that waits in end in the restriction of the distortion theory of computation of oblique line section, not yet provide easy, accurate, reliable method for designing always so far.Along with the development of computing machine and finite element emulation software, use up possessor at present once to the non-distortion of the main spring of few sheet bias type variable cross section in oblique line Duan Chu position waiting structure in end, adopt ANSYS modeling and simulating method, but the method only can carry out simulating, verifying to the distortion of leaf spring or rigidity providing actual design structure, accurate analytical design method formula can not be provided, more can not meet fast-developing and that suspension leaf spring modernization CAD design software the is developed requirement of vehicle.

Therefore, the main spring of few sheet bias type variable cross section must setting up a kind of structures such as end is non-accurately, is reliably in the method for designing in the major-minor spring gap at oblique line section and auxiliary spring contact point place, meet Vehicle Industry fast development and the requirement to suspension Precise Design for Laminated Spring, improve design level, the product quality and performances of variable-section steel sheet spring, improve vehicle ride performance and security; Meanwhile, reduce design and testing expenses, accelerate product development speed.

Summary of the invention

For the defect existed in above-mentioned prior art, technical matters to be solved by this invention be to provide a kind of easy, reliably less the main spring of sheet bias type variable cross section is in the method for designing in oblique line section and auxiliary spring gap, design flow diagram, as shown in Figure 1.Few sheet bias type variable cross section major-minor spring is symmetrical structure, and the half symmetrical structure of spring can regard semi-girder as, and namely symmetrical center line regards the root stiff end of half spring as, and main spring end stress point and auxiliary spring contact see main spring end points and auxiliary spring end points respectively as.The half structural representation of few sheet bias type variable cross section major-minor spring, as shown in Figure 2, wherein, comprising: main spring 1, root shim 2, auxiliary spring 3; End pad 4; The half length of each of main spring 1 is L, is made up of root flat segments, oblique line section, end flat segments three sections, and the thickness of every sheet root flat segments is h ₂, the half of installing space is l ₃, the root of oblique line section is to the distance l of main spring end points ₂=L-l ₃; The end flat segments of each of main spring 1 is non-waits structure, and namely the thickness of the end flat segments of the 1st main spring and length, be greater than other thickness of each and length, and thickness and the length of the end flat segments of each are respectively h _1iand l _1i; The Thickness Ratio β of each oblique line section _i=h _1i/ h ₂, i=1,2 ..., N, N are the sheet number of main spring, and N is the integer of 2 ~ 4; Each root flat segments of main spring 1 and and the root flat segments of auxiliary spring 3 between be provided with root shim 2, end pad 4 is provided with between each end flat segments of main spring 1, the material of end pad is carbon fibre composite, the frictional noise produced during in order to reduce spring works; The half length of auxiliary spring 3 is L _a, namely auxiliary spring contact is to the horizontal range l of main spring end points ₀=L-L _a; Be provided with certain major and minor spring gap delta between the oblique line section of the main spring of N sheet and the ends points of auxiliary spring 3, when load be greater than auxiliary spring work load time, in auxiliary spring and main spring oblique line section, certain point contacts.Work load under stable condition at each chip architecture parameter of main spring, material characteristic parameter, auxiliary spring length, auxiliary spring, the major-minor spring gap of the main spring of few sheet bias type variable cross section between oblique line section and auxiliary spring contact is designed.

For solving the problems of the technologies described above, few main spring of sheet bias type variable cross section provided by the present invention, in the method for designing in oblique line section and auxiliary spring gap, is characterized in that adopting following design procedure:

(1) the end points deformation coefficient G of each main spring of bias type variable cross section _x-Dicalculate:

According to the half length L of the main spring of few sheet bias type variable cross section, width b, elastic modulus E, the half l of installing space ₃, the root of oblique line section is to the distance l of main spring end points ₂=L-l ₃, the Thickness Ratio β of the oblique line section of i-th main spring _i, wherein, i=1,2 ..., N, N are main reed number, to the end points deformation coefficient G of each main spring _x-Dicalculate, namely

$G_{x-Di}=\frac{4}{Eb}(L^3-l_2^3)+\frac{6l_2^3{({\mathrm{\β}}_i+1)}^2\[3({\mathrm{\β}}_i-1)-2{\mathrm{ln\β}}_i(1+{\mathrm{\β}}_i)\]}{Eb}+\frac{4{\mathrm{\β}}_i^3{l}_2^3}{Eb},i=1,2,...,N;$

The main spring of (2) N sheet bias type variable cross section is at the deformation coefficient G at oblique line section and auxiliary spring contact point place _x-BCcalculate:

According to the half length L of the main spring of few sheet bias type variable cross section, width b, elastic modulus E, the root of oblique line section is to the distance l of main spring end points ₂, the Thickness Ratio β of the oblique line section of the main spring of N sheet _n, auxiliary spring contact is in the horizontal range l of main spring end points ₀, to the deformation coefficient G of the main spring of N sheet bias type variable cross section at oblique line section and auxiliary spring contact point place _x-BCcalculate, namely

$\begin{array}{c}{G}_{x-BC}=\frac{12l_2^3}{Eb}\[\frac{{\mathrm{\β}}_N(3{\mathrm{\β}}_N^2+7{\mathrm{\β}}_N+4)}{2}+{({\mathrm{\β}}_N+1)}^3\ln \frac{l_2({\mathrm{\β}}_N+1)}{l_0+l_2{\mathrm{\β}}_N}-\frac{l_2{\mathrm{\β}}_N(4l_0+3l_2{\mathrm{\β}}_N){({\mathrm{\β}}_N+1)}^3}{2{(l_0+l_2{\mathrm{\β}}_N)}^2}\]+\\ \frac{4L^3-6l_0{L}^2-4l_2^3+6l_0{l}_2^2}{Eb}-\frac{6l_2^2{l}_0(l_2-l_0)({\mathrm{\β}}_N+1)(2l_0+l_2{\mathrm{\β}}_N+{\mathrm{\β}}_N{l}_0)}{Eb{(l_0+l_2{\mathrm{\β}}_N)}^2};\end{array}$

(3) auxiliary spring works the end points power F of the main spring of N sheet bias type variable cross section under load _ncalculate:

I step: according to the thickness h of the root flat segments of the main spring of few sheet bias type variable cross section ₂, and the end points deformation coefficient G of each main spring calculated in step (1) _x-Di, determine the half stiffness K of each main spring of bias type variable cross section _mi, namely

$K_{Mi}=\frac{h_2^3}{G_{x-Di}},i=1,2,...,N;$

II step: to work the half of load and single-ended point load P and determined K in I step according to auxiliary spring _mi, the end points power F of the main spring of N sheet bias type variable cross section under load that auxiliary spring is worked _ncalculate, namely

$F_N=\frac{K_{MN}P}{\underset{i=1}{\overset{N}{\Σ}}{K}_{Mi}},i=1,2,...,N,$

In formula, K _mNbe the half rigidity of the main spring of N sheet bias type variable cross section;

(4) the few major-minor spring gap delta of the main spring of sheet bias type variable cross section between oblique line section and auxiliary spring contact designs:

According to the thickness h of the root flat segments of the main spring of bias type variable cross section ₂, the end points power F of the main spring of N sheet calculated in II step _n, and the G calculated in step (2) _x-BC, the major-minor spring gap delta of the main spring of few sheet bias type variable cross section between oblique line section and auxiliary spring contact is designed, namely

$\mathrm{\δ}=G_{x-BC}\frac{F_N}{h_2^3}.$

The advantage that the present invention has than prior art

Wait few sheet bias type variable-section steel sheet spring calculating at an arbitrary position of structure very complicated because end is non-, therefore, the resolution design method of sheet bias type variable-section steel sheet spring in the major-minor spring gap at oblique line section and auxiliary spring contact point place is failed to provide reliably less in home and abroad always.Along with the development of computing machine and finite element emulation software, possessor once adopted ANSYS modeling and simulating method to the non-major and minor spring gap of few sheet bias type variable cross section of structure of waiting, end to the greatest extent at present, but the method only can carry out simulating, verifying to the distortion of the leaf spring providing actual design structure, accurate analytical design method formula can not be provided, more can not meet fast-developing and that suspension leaf spring modernization CAD design software the is developed requirement of vehicle.

The present invention can according to each non-physical dimension, the elastic modulus waiting the main spring of bias type variable cross section of structure in end, first determine the deformation coefficient of each main spring of bias type variable cross section at endpoint location place, and the main spring of N is at the deformation coefficient at oblique line section and auxiliary spring contacting points position place; Then, by deformation coefficient and the Rigidity Calculation at each endpoint location place, the load that the main spring of N sheet bears at end points is obtained; Subsequently, according to the load that the obtained main spring of N sheet bears at end points, and the main spring of N is at the deformation coefficient at oblique line section and auxiliary spring contacting points position place, designs the major and minor spring gap of the main spring of few sheet bias type variable cross section at oblique line section and auxiliary spring contacting points position place.

By design example and ANSYS simulating, verifying known, the main spring of few sheet bias type variable cross section of the structures such as the method can obtain accurately, reliably end is non-is in the major and minor spring gap design value at oblique line section and auxiliary spring contacting points position place, wait the major and minor spring gap of few sheet bias type variable cross section root spring of structure to provide reliable method for designing for end is non-, and establish reliable technical foundation for CAD software development.Utilize the method, the design level of vehicle suspension variable-section steel sheet spring, product quality and performances can be improved, reduce bearing spring quality and cost, improve conevying efficiency and the driving safety of vehicle; Meanwhile, also reduce design and testing expenses, accelerate product development speed.

Accompanying drawing explanation

In order to understand the present invention better, be described further below in conjunction with accompanying drawing.

Fig. 1 is the main spring of few sheet bias type variable cross section in the design flow diagram in oblique line section and auxiliary spring gap;

Fig. 2 is the half symmetrical structure schematic diagram of the main spring of few sheet bias type variable cross section;

Fig. 3 is the deformation simulation cloud atlas of the main spring of few sheet bias type variable cross section of embodiment one;

Fig. 4 is the deformation simulation cloud atlas of the main spring of few sheet bias type variable cross section of embodiment two.

Specific embodiments

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

Embodiment one: the sheet number N=2 of the main spring of certain few sheet bias type variable cross section, wherein, the half length L=575mm of each main spring, width b=60mm, elastic modulus E=200GPa, root thickness h ₂=11mm, the half l of installing space ₃=55mm, the root of oblique line section is to the distance l of main spring end points ₂=L-l ₃=520mm; The thickness h of the end flat segments of the 1st main spring ₁₁=7mm, i.e. the Thickness Ratio β of the oblique line section of the 1st main spring ₁=h ₁₁/ h ₂=0.64; The thickness h of the end flat segments of the 2nd main spring ₁₂=6mm, i.e. the Thickness Ratio β of the oblique line section of the 2nd main spring ₂=h ₁₂/ h ₂=0.55; The half length L of auxiliary spring _a=355mm, auxiliary spring contact is to the horizontal range l of main spring end points ₀=L-L _a=220mm, auxiliary spring contact contacts with certain point in main spring oblique line section.Auxiliary spring required by design works load half P=1200N, designs this few sheet bias type variable-section steel sheet spring major-minor spring gap between oblique line section and auxiliary spring contact.

The main spring of few sheet bias type variable cross section that example of the present invention provides is in the method for designing in oblique line section and auxiliary spring gap, and as shown in Figure 1, concrete steps are as follows for its design cycle:

(1) the end points deformation coefficient G of each main spring of bias type variable cross section _x-Dicalculate:

According to the half length L=575mm of the main spring of few sheet bias type variable cross section, width b=60mm, elastic modulus E=200GPa, the half l of installing space ₃=55mm, the root of oblique line section is to the distance l of main spring end points ₂=520mm, the Thickness Ratio β of the oblique line section of the 1st main spring ₁the Thickness Ratio β of the oblique line section of the=0.64,2nd main spring ₂=0.55, to the end points deformation coefficient G of the 1st, the 2nd main spring _x-D1, G _x-D2calculate respectively, namely

$G_{x-D1}=\frac{4}{Eb}(L^3-l_2^3)+\frac{6l_2^3{({\mathrm{\β}}_1+1)}^2\[3({\mathrm{\β}}_1-1)-2{\mathrm{ln\β}}_1(1+{\mathrm{\β}}_1)\]}{Eb}+\frac{4{\mathrm{\β}}_1^3{l}_2^3}{Eb}=101.68{\mathrm{mm}}^4/N,$

$G_{x-D2}=\frac{4}{Eb}(L^3-l_2^3)+\frac{6l_2^3{({\mathrm{\β}}_2+1)}^2\[3({\mathrm{\β}}_2-1)-2{\mathrm{ln\β}}_2(1+{\mathrm{\β}}_2)\]}{Eb}+\frac{4{\mathrm{\β}}_2^3{l}_2^3}{Eb}=109.72{\mathrm{mm}}^4/N;$

(2) the 2nd main springs of bias type variable cross section are at the deformation coefficient G at oblique line section and auxiliary spring contact point place _x-BCcalculate:

According to the half length L=575mm of the main spring of few sheet bias type variable cross section, width b=60mm, elastic modulus E=200GPa, the root of oblique line section is to the distance l of main spring end points ₂=520mm, the Thickness Ratio β of the oblique line section of the 2nd main spring ₂=0.55, the horizontal range l of auxiliary spring contact and main spring end points ₀=220mm, to the deformation coefficient G of the 2nd main spring of bias type variable cross section at oblique line section and auxiliary spring contact point place _x-BCcalculate, namely

$\begin{array}{c}{G}_{x-BC}=\frac{12l_2^3}{Eb}\[\frac{{\mathrm{\β}}_2(3{\mathrm{\β}}_2^2+7{\mathrm{\β}}_2+4)}{2}+{({\mathrm{\β}}_2+1)}^3\ln \frac{l_2({\mathrm{\β}}_2+1)}{l_0+l_2{\mathrm{\β}}_2}-\frac{l_2{\mathrm{\β}}_2(4l_0+3l_2{\mathrm{\β}}_2){({\mathrm{\β}}_2+1)}^3}{2{(l_0+l_2{\mathrm{\β}}_2)}^2}\]+\\ \frac{4L^3-6l_0{L}^2-4l_2^3+6l_0{l}_2^2}{Eb}-\frac{6l_2^2{l}_0(l_2-l_0)({\mathrm{\β}}_2+1)(2l_0+l_2{\mathrm{\β}}_2+{\mathrm{\β}}_2{l}_0)}{Eb{(l_0+l_2{\mathrm{\β}}_2)}^2}=38.61{\mathrm{mm}}^4/N;\end{array}$

(3) auxiliary spring works the end points power F of the 2nd main spring of bias type variable cross section under load ₂calculate:

I step: according to the thickness h of the root flat segments of the main spring of few sheet bias type variable cross section ₂=11mm, and the G calculated in step (1) _x-D1=101.68mm ⁴/ N and G _x-D2=109.72mm ⁴/ N, determines the half stiffness K of the 1st, the 2nd main spring of bias type variable cross section _m1, K _m2, be respectively

$K_{M1}=\frac{h_2^3}{G_{x-D1}}=13.09N/mm,$

$K_{M2}=\frac{h_2^3}{G_{x-D2}}=12.13N/mm;$

II step: the auxiliary spring required by design works the half of load and single-ended point load P=1200N, and the half stiffness K of determined 1st main spring in I step _m1the half stiffness K of=13.09N/mm, the 2nd main spring _m2=12.13N/mm, the end points power F of the 2nd main spring of bias type variable cross section under load that auxiliary spring is worked ₂calculate, namely

$F_2=\frac{K_{M2}P}{\underset{i=1}{\overset{2}{\Σ}}{K}_{Mi}}=577.16N;$

(4) the few major-minor spring gap delta of the main spring of sheet bias type variable cross section between oblique line section and auxiliary spring contact designs:

According to the thickness h of the root flat segments of the main spring of bias type variable cross section ₂the stressed F of end points of the 2nd main spring calculated in=11mm, II step ₂=577.16N, and the G that in step (2), calculating gained arrives _x-BC=38.61mm ⁴/ N, designs the major-minor spring gap delta of the main spring of few sheet bias type variable cross section between oblique line section and auxiliary spring contact, namely

$\mathrm{\δ}=G_{x-BC}\frac{F_2}{h_2^3}=16.74mm.$

Utilize ANSYS finite element emulation software, according to each chip architecture parameter and the material characteristic parameter of the main spring of this few sheet bias type variable cross section, set up the ANSYS realistic model of the half symmetrical structure of few main spring of sheet bias type variable cross section, grid division, and apply fixed constraint at the root of realistic model, centre-point load P=1200N is applied at end points, ANSYS emulation is carried out to the distortion of the few main spring of sheet variable-section steel sheet spring of this bias type, the deformation simulation cloud atlas obtained, as shown in Figure 3, wherein, this main spring is at the deflection δ=16.89mm at distance end position 220mm place.

Known, under same load, the ANSYS simulating, verifying value δ=16.89mm of the main spring deflection of this leaf spring, match with major-minor spring gap design value δ=16.74mm, relative deviation is only 0.89%; Result shows that the main spring of few sheet bias type variable cross section that this invention provides is correct in the method for designing in oblique line section and auxiliary spring gap, and parameter designing value is accurately and reliably.

Embodiment two: the sheet number N=2 of the main spring of certain few sheet bias type variable cross section, wherein, the half length L=600mm of each main spring, width b=60mm, elastic modulus E=200GPa, the thickness h of root flat segments ₂=14mm, the half l of installing space ₃=60mm, the root of oblique line section is to the distance l of main spring end points ₂=L-l ₃=540mm; The thickness h of the end flat segments of the 1st main spring ₁₁=9mm, i.e. the Thickness Ratio β of the oblique line section of the 1st main spring ₁=h ₁₁/ h ₂=0.64; The thickness h of the end flat segments of the 2nd main spring ₁₂=8mm, i.e. the Thickness Ratio β of the oblique line section of the 2nd main spring ₂=h ₁₂/ h ₂=0.57; The half length L of auxiliary spring _a=340mm, the horizontal range l of auxiliary spring contact and main spring end points ₀=L-L _a=260mm, auxiliary spring contact contacts with certain point in main spring oblique line section.Auxiliary spring required by design works the half of load and single-ended point load P=3000N, designs the major-minor spring gap of the main spring of this few sheet bias type variable cross section between oblique line section and auxiliary spring contact.

Adopt the method for designing identical with embodiment one and step, design this few sheet bias type variable-section steel sheet spring major-minor spring gap between oblique line section and auxiliary spring contact, concrete steps are as follows:

(1) the end points deformation coefficient G of each main spring of bias type variable cross section _x-Dicalculate:

According to the half length L=600mm of the main spring of few sheet bias type variable cross section, width b=60mm, elastic modulus E=200GPa, the half l of installing space ₃=60mm, the root of oblique line section is to the distance l of main spring end points ₂=540mm, the Thickness Ratio β of the oblique line section of the 1st main spring ₁the Thickness Ratio β of the oblique line section of the=0.64,2nd main spring ₂=0.57, to the end points deformation coefficient G of the 1st, the 2nd main spring _x-D1, G _x-D2calculate respectively, namely

$G_{x-D1}=\frac{4}{Eb}(L^3-l_2^3)+\frac{6l_2^3{({\mathrm{\β}}_1+1)}^2\[3({\mathrm{\β}}_1-1)-2{\mathrm{ln\β}}_1(1+{\mathrm{\β}}_1)\]}{Eb}+\frac{4{\mathrm{\β}}_1^3{l}_2^3}{Eb}=114.27{\mathrm{mm}}^4/N,$

$G_{x-D2}=\frac{4}{Eb}(L^3-l_2^3)+\frac{6l_2^3{({\mathrm{\β}}_2+1)}^2\[3({\mathrm{\β}}_2-1)-2{\mathrm{ln\β}}_2(1+{\mathrm{\β}}_2)\]}{Eb}+\frac{4{\mathrm{\β}}_2^3{l}_2^3}{Eb}=121.28{\mathrm{mm}}^4/N;$

(2) the 2nd main springs are at the deformation coefficient G at oblique line section and auxiliary spring contact point place _x-BCcalculate:

According to the half length L=600mm of the main spring of few sheet bias type variable cross section, width b=60mm, elastic modulus E=200GPa, the root of oblique line section is to the distance l of main spring end points ₂=540mm, the Thickness Ratio β of the oblique line section of the 2nd main spring ₂=0.57, the horizontal range l of auxiliary spring contact and main spring end points ₀=260mm, to the deformation coefficient G of the 2nd main spring of bias type variable cross section at oblique line section and auxiliary spring contact point place _x-BCcalculate, namely

$\begin{array}{c}{G}_{x-BC}=\frac{12l_2^3}{Eb}\[\frac{{\mathrm{\β}}_2(3{\mathrm{\β}}_2^2+7{\mathrm{\β}}_2+4)}{2}+{({\mathrm{\β}}_2+1)}^3\ln \frac{l_2({\mathrm{\β}}_2+1)}{l_0+l_2{\mathrm{\β}}_2}-\frac{l_2{\mathrm{\β}}_2(4l_0+3l_2{\mathrm{\β}}_2){({\mathrm{\β}}_2+1)}^3}{2{(l_0+l_2{\mathrm{\β}}_2)}^2}\]+\\ \frac{4L^3-6l_0{L}^2-4l_2^3+6l_0{l}_2^2}{Eb}-\frac{6l_2^2{l}_0(l_2-l_0)({\mathrm{\β}}_2+1)(2l_0+l_2{\mathrm{\β}}_2+{\mathrm{\β}}_2{l}_0)}{Eb{(l_0+l_2{\mathrm{\β}}_2)}^2}=36.22{\mathrm{mm}}^4/N;\end{array}$

(3) auxiliary spring works the end points power F of the 2nd main spring of bias type variable cross section under load ₂calculate:

I step: according to the thickness h of the root flat segments of the main spring of few sheet bias type variable cross section ₂=14mm, and the G calculated in step (1) _x-D1=114.27mm ⁴/ N and G _x-D2=121.28mm ⁴/ N, determines the half stiffness K of the 1st, the 2nd main spring of bias type variable cross section _m1, K _m2, be respectively

$K_{M1}=\frac{h_2^3}{G_{x-D1}}=24.01N/mm,$

$K_{M2}=\frac{h_2^3}{G_{x-D2}}=22.63N/mm;$

II step: the auxiliary spring required by design works the half of load and single-ended point load P=3000N and determined K in I step _m1=24.01N/mm and K _m2=22.63N/mm, the end points power F of the 2nd main spring of bias type variable cross section under load that auxiliary spring is worked ₂calculate, namely

$F_2=\frac{K_{M2}P}{\underset{i=1}{\overset{2}{\Σ}}{K}_{Mi}}=1455.60N;$

(4) the few major-minor spring gap delta of the main spring of sheet bias type variable cross section between oblique line section and auxiliary spring contact designs:

According to the thickness h of the root flat segments of the main spring of bias type variable cross section ₂the F calculated in=14mm, II step ₂=1455.60N, and the G calculated in step (2) _x-BC=36.22mm ⁴/ N, designs the major-minor spring gap delta of the main spring of few sheet bias type variable cross section between oblique line section and auxiliary spring contact, namely

$\mathrm{\δ}=G_{x-BC}\frac{F_2}{h_2^3}=19.21mm.$

Utilize ANSYS finite element emulation software, according to structural parameters and the material characteristic parameter of each main spring of this few sheet bias type variable-section steel sheet spring, set up the ANSYS realistic model of the half symmetrical structure of few sheet bias type tapered spring, grid division, and apply fixed constraint at the root of realistic model, centre-point load P=3000N is applied at end points, ANSYS emulation is carried out to the distortion of the few main spring of sheet variable-section steel sheet spring of this bias type, the deformation simulation cloud atlas obtained, as shown in Figure 4, wherein, this main spring is at the deflection δ=19.19mm at distance end position 260mm place.

Known, under same load, the ANSYS simulating, verifying value δ=19.19mm of the main spring deflection of this leaf spring, match with major-minor spring gap design value δ=19.21mm, relative deviation is only 0.10%; Result shows that the main spring of few sheet bias type variable cross section that this invention provides is correct in the method for designing in oblique line section and auxiliary spring gap, and parameter designing value is accurately and reliably.

Claims (1)

1. few main spring of sheet bias type variable cross section is in the method for designing in oblique line section and auxiliary spring gap, wherein, the half symmetrical structure of few main spring of sheet bias type variable cross section is made up of root flat segments, oblique line section and end flat segments three sections, the end flat segments of each main spring is non-waits structure, namely the thickness of the end flat segments of the 1st main spring and length, be greater than other thickness of each and length; The main spring of N sheet is designed with certain major-minor spring gap between oblique line section and auxiliary spring contact, to work the designing requirement of load to meet auxiliary spring; Work load under stable condition at each chip architecture parameter of main spring, material characteristic parameter, auxiliary spring length, auxiliary spring, the major-minor spring gap of the main spring of few sheet bias type variable cross section between oblique line section and auxiliary spring contact designed, specific design step:

(1) the end points deformation coefficient G of each main spring of bias type variable cross section _x-Dicalculate:

According to the half length L of the main spring of few sheet bias type variable cross section, width b, elastic modulus E, the half l of installing space ₃, the root of oblique line section is to the distance l of main spring end points ₂=L-l ₃, the Thickness Ratio β of the oblique line section of i-th main spring _i, wherein, i=1,2 ..., N, N are main reed number, to the end points deformation coefficient G of each main spring _x-Dicalculate, namely

$G_{x-Di}=\frac{4}{Eb}\left(L^3-l_2^3\right)+\frac{6l_2^3{\left({\mathrm{\β}}_i+1\right)}^2\[3\left({\mathrm{\β}}_i-1\right)-2{\mathrm{ln\β}}_i\left(1+{\mathrm{\β}}_i\right)\]}{Eb}+\frac{4{\mathrm{\β}}_i^3{l}_2^3}{Eb},i=1,2,...,N;$

The main spring of (2) N sheet bias type variable cross section is at the deformation coefficient G at oblique line section and auxiliary spring contact point place _x-BCcalculate:

According to the half length L of the main spring of few sheet bias type variable cross section, width b, elastic modulus E, the root of oblique line section is to the distance l of main spring end points ₂, the Thickness Ratio β of the oblique line section of the main spring of N sheet _n, auxiliary spring contact is in the horizontal range l of main spring end points ₀, to the deformation coefficient G of the main spring of N sheet bias type variable cross section at oblique line section and auxiliary spring contact point place _x-BCcalculate, namely

$\begin{array}{c}{G}_{x-BC}=\frac{12l_2^3}{Eb}\[\frac{{\mathrm{\β}}_N(3{\mathrm{\β}}_N^2+7{\mathrm{\β}}_N+4)}{2}+{({\mathrm{\β}}_N+1)}^{3}ln\frac{l_2({\mathrm{\β}}_N+1)}{l_0+l_2{\mathrm{\β}}_N}-\frac{l_2{\mathrm{\β}}_N\left(4l_0+3l_2{\mathrm{\β}}_N\right){\left({\mathrm{\β}}_N+1\right)}^3}{2{\left(l_0+l_2{\mathrm{\β}}_N\right)}^2}\]+\\ \frac{4L^3-6l_0{L}^2-4l_2^3+6l_0{l}_2^2}{Eb}-\frac{6l_2^2{l}_0(l_2-l_0)({\mathrm{\β}}_N+1)(2l_0+l_2{\mathrm{\β}}_N+{\mathrm{\β}}_N{l}_0)}{Eb{(l_0+l_2{\mathrm{\β}}_N)}^2};\end{array}$

(3) auxiliary spring works the end points power F of the main spring of N sheet bias type variable cross section under load _ncalculate:

I step: according to the thickness h of the root flat segments of the main spring of few sheet bias type variable cross section ₂, and the end points deformation coefficient G of each main spring calculated in step (1) _x-Di, determine the half stiffness K of each main spring of bias type variable cross section _mi, namely

$K_{Mi}=\frac{h_2^3}{G_{x-Di}},i=1,2,...,N;$

II step: to work the half of load and single-ended point load P and determined K in I step according to auxiliary spring _mi, the end points power F of the main spring of N sheet bias type variable cross section under load that auxiliary spring is worked _ncalculate, namely

$F_N=\frac{K_{MN}P}{\underset{i=1}{\overset{N}{\Σ}}{K}_{Mi}},i=1,2,...,N,$

In formula, K _mNbe the half rigidity of the main spring of N sheet bias type variable cross section;

(4) the few major-minor spring gap delta of the main spring of sheet bias type variable cross section between oblique line section and auxiliary spring contact designs:

According to the thickness h of the root flat segments of the main spring of bias type variable cross section ₂, the end points power F of the main spring of N sheet calculated in II step _n, and the G calculated in step (2) _x-BC, the major-minor spring gap delta of the main spring of few sheet bias type variable cross section between oblique line section and auxiliary spring contact is designed, namely

$\mathrm{\δ}=G_{x-BC}\frac{F_N}{h_2^3}.$