CN105590009A - Auxiliary spring work load checking method of non end part contact type end part strengthened few-leaf main and auxiliary springs - Google Patents

Abstract

The invention relates to an auxiliary spring work load checking method of a non end part contact type end part strengthened few-leaf main and auxiliary springs belonging to the suspension steel plate spring technical field. According to the method of the invention, firstly, according to the structure size and the elastic modulus of each end part strengthened few-leaf cross-section variable main spring, the end point deformation coefficient Gx-Ei and the half rigidity KMi of each main spring, and the deformation coefficient Gx-BC at the contact point of the Nth main spring and an auxiliary spring on a parabolic segment can be determined; then, according to the half rigidity KMi of each main spring, the thickness h2 of a root straight section, the Gx-BC of the Nth main spring and a main and auxiliary spring interval Delta design value, the auxiliary spring work load of the non end part contact type end part strengthened few-leaf cross-section variable main and auxiliary springs is checked. Through the emulation proof, in adoption of the method of the invention, the accurate and reliable auxiliary spring work load checking value can be obtained; therefore, the design levels and performances of the few-leaf cross-section variable main and auxiliary springs and the smoothness of a vehicle are improved; moreover, the design and test cost is saved; and the product development speed is accelerated.

Description

The auxiliary spring of the few sheet major-minor spring of the non-end contact reinforcement end load checking method that works

Technical field

The present invention relates to vehicle suspension leaf spring, is that the auxiliary spring of the few sheet major-minor spring of non-end contact reinforcement end plays work especiallyUse load checking method.

Background technology

Due to its stressed complexity of the 1st main spring of variable cross-section, not only bear vertical load, also bear torsional load and longitudinal simultaneouslyLoad, therefore, thickness and the length of the end flat segments of the 1st actual designed main spring, be greater than other each main spring conventionallyThickness and the length of end flat segments, mostly adopt the non-main spring of few sheet variable cross-section that waits structure of end flat segments; Meanwhile, forStrengthen the intensity of main spring end, conventionally between main spring end flat segments and parabolic segment, add an oblique line section, adopt end to addThe main spring of few sheet variable cross-section of strong type. In addition, for meeting the designing requirement of major-minor spring different composite rigidity, conventionally adopt different pairsSpring length, namely auxiliary spring contact is different from the contact position of main spring, therefore, for variable cross-section major-minor spring, can be divided into end flatStraight section contacts two kinds that contact with parabolic segment, i.e. end contact and non-end contact. The work size of load of auxiliary spring isDetermined by the length of the structural parameters of each of main spring, material characteristic parameter, auxiliary spring and major-minor spring gap length, and shadowRing Vehicle Driving Cycle ride comfort. Then, due to the few sheet variable-section steel sheet spring of reinforcement end, to be out of shape at an arbitrary position calculating very multipleAssorted, the auxiliary spring of previously always failing to provide the few sheet variable cross-section major-minor spring of the non-end contact reinforcement end checking computations of load of workingMethod. Although previously once someone had provided the design and calculation method of few sheet parabolic type variable-section steel sheet spring, for example, Peng Mo,High army is once in " automobile engineering ", (the 14th volume) the 3rd phase in 1992, proposed the designing and calculating side of few sheet variable-section steel sheet springMethod, the method is mainly that its weak point is not for the designing and calculating of few sheet parabolic type variable-section steel sheet spring of the structures such as endCan meet the designing requirement of the non-few sheet variable cross-section major-minor spring that waits structure in end, more can not meet non-end contact reinforcement end fewThe work requirement of load checking computations of the auxiliary spring of sheet variable cross-section major-minor spring. Therefore, must set up a kind of accurate, reliable non-end connectsThe work Method for Checking of load of the auxiliary spring of the few sheet variable cross-section major-minor spring of touch reinforcement end, meet Vehicle Industry fast-developing andTo the work requirement of load checking computations of the design of few sheet variable cross-section major-minor spring and auxiliary spring, improve variable-section steel sheet spring design level,Product quality and performances, improve Vehicle Driving Cycle ride comfort and security; Meanwhile, reduce and design and develop and experimental test expense, addFast product development speed.

Summary of the invention

For the defect existing in above-mentioned prior art, technical problem to be solved by this invention is to provide a kind of easy, reliableThe auxiliary spring of the few sheet major-minor spring of the non-end contact reinforcement end load Method for Checking that works, checking computations flow chart as shown in Figure 1.Contact reinforcement end few sheet variable cross-section major-minor spring in non-end is symmetrical structure, and the half symmetrical structure of major-minor spring can be seen as outstandingArm beam, is root stiff end by symmetrical center line, by main spring end stress point and auxiliary spring contact see as respectively main spring end points andAuxiliary spring end points. The half symmetrical structure schematic diagram of the few sheet variable cross-section major-minor spring of non-end contact reinforcement end, as Fig. 2 instituteShow, wherein, comprising: main spring 1, root shim 2, auxiliary spring 3, end pad 4; The half length that main spring 1 is each is L,To be formed by four sections of root flat segments, parabolic segment, oblique line section, end flat segments; Oblique line section rises to add to tapered spring and pretendsWith; The thickness of every root flat segments is h₂, length is l₃, the root of parabolic segment is l to the distance of main spring end points₂, parabolicThe end thickness of line segment is h_1ip, i.e. the Thickness Ratio β of each parabolic segment_i＝h_1ip/h₂, the end of parabolic segment is to main spring end pointsApart from l_1ip, i=1,2 ..., N, the sheet number that N is main spring; End flat segments that main spring 1 the is each non-structure that waits, i.e. the 1st main springThe thickness of end flat segments and length, be greater than other thickness of each and length, and the thickness of each end flat segments and length are respectivelyFor h_1iAnd l_1i; The length of each oblique line section is Δ l, the Thickness Ratio γ=h of oblique line section_1i/h_1ip; Each root flat segments of main spring 1And and the root flat segments of auxiliary spring 3 between be provided with root shim 2, the end flat segments that main spring 1 is each is provided with end pad 4,The material of end pad 4 is carbon fibre composite, is used for reducing the frictional noise producing when spring is worked; The half of auxiliary spring is longDegree is L_A, auxiliary spring 3 contacts, end are l to the horizontal range of main spring 1 end points₀; The N sheet parabolic segment of main spring 1 is with secondaryBetween spring 3 contacts, be provided with certain major-minor spring gap delta, in the time that load is greater than auxiliary spring and works load, auxiliary spring and main spring parabolaIn section, certain point contacts. Structural parameters, elastic modelling quantity, auxiliary spring length, major-minor spring gap design value at each main spring giveUnder condition, the auxiliary spring of the few sheet major-minor spring of the non-end contact reinforcement end load that works is checked.

For solving the problems of the technologies described above, the auxiliary spring of the few sheet major-minor spring of non-end provided by the present invention contact reinforcement end plays workUse load checking method, it is characterized in that adopting following checking computations step:

(1) the end points deformation coefficient G of the each main spring of reinforcement end variable cross-section_x-EiCalculate:

According to the half length L of the main spring of reinforcement end variable cross-section, width b, elastic modulus E, the half l of installing space₃, oblique lineThe length Δ l of section, the root of parabolic segment is to the distance l of main spring end points₂＝L-l₃, the Thickness Ratio of the parabolic segment of the main spring of i sheetβ_i, wherein, i=1,2 ..., N, N is main reed number, the root of the main spring oblique line of i sheet section is to the distance of main spring end pointsl_1ip＝l₂β_i ², the end of the main spring oblique line of i sheet section is to the distance l of main spring end points_1i＝l_1ip-Δ l, the Thickness Ratio γ of oblique line section, to eachThe end points deformation coefficient G of the main spring of reinforcement end variable cross-section_x-EiCalculate,

$\begin{array}{c}{G}_{x-Ei}=\frac{4(L^3-l_2^3)}{Eb}-\frac{8l_2^{3/2}(l_{1ip}^{3/2}-l_2^{3/2})}{Eb}+\frac{4l_{1i}^3}{{\mathrm{Eb\γ}}^3{\mathrm{\β}}_i^3}+\frac{6\mathrm{\Δ}l(4l_{1i}^2\mathrm{\γ}-l_{1i}^2-3l_{1i}^2{\mathrm{\γ}}^2+3l_{1ip}^2{\mathrm{\γ}}^2-4l_{1ip}^2{\mathrm{\γ}}^3+l_{1ip}^2{\mathrm{\γ}}^4)}{{\mathrm{Eb\γ}}^2{\mathrm{\β}}_i^3{(\mathrm{\γ}-1)}^3}-\\ \frac{6\mathrm{\Δ}l(-2l_{1i}{l}_{1ip}\mathrm{\γ}+2l_{1i}^2{\mathrm{\γ}}^2\ln \mathrm{\γ}+2l_{1ip}^2{\mathrm{\γ}}^2\ln \mathrm{\γ}+2l_{1i}{l}_{1ip}{\mathrm{\γ}}^3-4l_{1i}{l}_{1ip}{\mathrm{\γ}}^2\ln \mathrm{\γ})}{{\mathrm{Eb\γ}}^2{\mathrm{\β}}_i^3{(\mathrm{\γ}-1)}^3},i=1,2,\mathrm{...},N;\end{array}$

The main spring of (2) N sheet reinforcement end variable cross-section is at the deformation coefficient G at parabolic segment and auxiliary spring contact point place_x-BCCalculate:

According to the half length L of the main spring of reinforcement end variable cross-section, width b, elastic modulus E, the root of parabolic segment is to main spring endThe distance l of point₂, the horizontal range l of auxiliary spring contact and main spring end points₀, to the main spring of N sheet reinforcement end variable cross-section at parabolaSection and the deformation coefficient G at auxiliary spring contact point place_x-BCCalculate,

$G_{x-BC}=\frac{2(2L^3-9l_2^2{l}_0-3L^2{l}_0+2l_2^3+8l_2^{3/2}{l}_0^{3/2})}{Eb};$

(3) the half stiffness K of the each main spring of reinforcement end variable cross-section_MiCalculate:

According to the thickness h of the root flat segments of the main spring of reinforcement end variable cross-section₂, and the end of the each main spring calculating in step (1)Deformation coefficient G_x-Ei, to the half stiffness K of the each main spring of reinforcement end variable cross-section_MiCalculate,

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

(4) auxiliary spring of the few main spring of sheet variable cross-section of the non-end contact reinforcement end load p that works_KChecking computations:

According to the thickness h of the root flat segments of the few main spring of sheet variable cross-section of reinforcement end₂, major-minor spring gap delta, calculates in step (2)The G obtaining_x-BC, and the K calculating in step (3)_Mi, to the auxiliary spring load p that works_KCalculate,

$P_K=\frac{2h_2^3\mathrm{\δ}\underset{i=1}{\overset{N}{\Σ}}{K}_{Mi}}{G_{x-BC}{K}_{MN}};$

In formula, K_MNBe the half rigidity of the main spring of N sheet.

The present invention has advantages of than prior art

Due to the few sheet variable-section steel sheet spring of reinforcement end, to be out of shape at an arbitrary position calculating very complicated, previously failed to provide alwaysThe work Method for Checking of load of the auxiliary spring of the few sheet major-minor spring of non-end contact reinforcement end. The present invention can be according to each endPhysical dimension, the elastic modelling quantity of the main spring of reinforced variable cross-section, first, determine the end points of the each main spring of reinforcement end variable cross-sectionDeformation coefficient G_x-EiWith half stiffness K_Mi, and the main spring of N sheet is at the deformation coefficient G at parabolic segment and auxiliary spring contact point place_x-BC; WithAfter, according to the thickness h of main spring root flat segments₂, the half stiffness K of each main spring_Mi, the main spring of N sheet is at parabolic segment and auxiliary springThe deformation coefficient G at contact point place_x-BC, the design load of major-minor spring gap delta, to the few sheet variable cross-section of non-end contact reinforcement endThe auxiliary spring of the major-minor spring load p that works_KCheck. Known by design example and ANSYS simulating, verifying, the method can obtainTo the auxiliary spring of the few sheet variable cross-section major-minor spring of accurate, the reliable non-end contact reinforcement end load p that works_KChecking computations value, forThe load checking computations of working of the auxiliary spring of the few sheet variable cross-section major-minor spring of non-end contact reinforcement end provide reliable Method for Checking,Can improve design level, the product quality and performances of vehicle suspension variable cross-section major-minor leaf spring, guarantee to meet auxiliary spring work carryThe designing requirement of lotus, improves ride performance, reduces bearing spring quality and cost, improves the conevying efficiency of vehicle; Meanwhile,Also reduce design and testing expenses, accelerate product development speed.

Brief description of the drawings

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

Fig. 1 is the work checking computations flow chart of load of the auxiliary spring of the few sheet variable cross-section major-minor spring of non-end contact reinforcement end;

Fig. 2 is the half symmetrical structure schematic diagram of the few sheet variable cross-section major-minor spring of non-end contact reinforcement end;

Fig. 3 is the deformation simulation cloud atlas of the few main spring of sheet variable cross-section of reinforcement end of embodiment mono-;

Fig. 4 is the deformation simulation cloud atlas of the few main spring of sheet variable cross-section of reinforcement end of embodiment bis-.

Specific embodiments

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

Embodiment mono-: the sheet of the few main spring of sheet variable cross-section of certain reinforcement end is counted N=2, wherein, the half length of each main springL=575mm, width b=60mm, elastic modulus E=200GPa, the thickness h of root flat segments₂=10.72mm, installing spaceHalf l₃=55mm, oblique line segment length Δ l=30mm, the root of parabolic segment is to the distance l of main spring end points₂＝L-l₃=520mm; The end thickness h of the parabolic segment of the 1st main spring_11p=5.9mm, the thickness of the parabolic segment of the 1st main springCompare β₁＝h_11p/h₂=0.55; The end thickness h of the thing line segment of the 2nd main spring_12p=4.7mm, the parabolic segment of the 2nd main springThickness Ratio β₂＝h_12p/h₂=0.44; The thickness h of the end flat segments of the 1st main spring₁₁=6.9mm, the end of the 2nd main spring is flatThe thickness h of straight section₁₂=5.5mm; Thickness Ratio γ=the h of each main spring oblique line section₁₁/h_11p＝h₁₂₁/h_12p=1.17. The half of auxiliary spring is longDegree L_A=375mm, the horizontal range l of auxiliary spring contact and main spring end points₀=200mm, between auxiliary spring contact and main spring parabolic segmentMajor-minor spring gap delta=19.37mm, the auxiliary spring of the few sheet variable cross-section major-minor spring of this non-end contact reinforcement end is worked and is carriedLotus checks.

The auxiliary spring of the few sheet major-minor spring of non-end contact reinforcement end that example of the present invention the provides load Method for Checking that works,Its checking computations flow process as shown in Figure 1, specifically checks step as follows:

(1) the end points deformation coefficient G of the each main spring of reinforcement end variable cross-section_x-EiCalculate:

According to the half length L=575mm of the main spring of reinforcement end variable cross-section, width b=60mm, elastic modulus E=200GPa, peaceThe half l of dress spacing₃=55mm, the length Δ l=30mm of oblique line section, the root of parabolic segment is to the distance of main spring end pointsl₂=520mm, the Thickness Ratio β of the parabolic segment of the 1st main spring₁The Thickness Ratio of the parabolic segment of the=0.55,2nd main springβ₂=0.44; The root of the 1st main spring oblique line section is to the distance l of main spring end points_11p=157.51mm, the 2nd main spring oblique line sectionRoot is to the distance l of main spring end points_12p=100.81mm, the end of the 1st main spring oblique line section is to the distance l of main spring end points₁₁＝127.51mm, the end of the 2nd main spring oblique line section is to the distance l of main spring end points₁₂=70.81mm; The Thickness Ratio of oblique line sectionγ=1.17; To the end points deformation coefficient G of the 1st main spring and the 2nd main spring_x-E1And G_x-E2Calculate respectively,

$\begin{array}{c}{G}_{x-E1}=\frac{4(L^3-l_2^3)}{Eb}-\frac{8l_2^{3/2}(l_{11p}^{3/2}-l_2^{3/2})}{Eb}+\frac{4l_{11}^3}{{\mathrm{Eb\γ}}^3{\mathrm{\β}}_1^3}+\frac{6\mathrm{\Δ}l(4l_{11}^2\mathrm{\γ}-l_{11}^2-3l_{11}^2{\mathrm{\γ}}^2+3l_{11p}^2{\mathrm{\γ}}^2-4l_{11p}^2{\mathrm{\γ}}^3+l_{11p}^2{\mathrm{\γ}}^4)}{{\mathrm{Eb\γ}}^2{\mathrm{\β}}_1^3{(\mathrm{\γ}-1)}^3}-\\ \frac{6\mathrm{\Δ}l(-2l_{11}{l}_{11p}\mathrm{\γ}+2l_{11}^2{\mathrm{\γ}}^2\ln \mathrm{\γ}+2l_{11p}^2{\mathrm{\γ}}^2\ln \mathrm{\γ}+2l_{11}{l}_{11p}{\mathrm{\γ}}^3-4l_{11}{l}_{11p}{\mathrm{\γ}}^2\ln \mathrm{\γ})}{{\mathrm{Eb\γ}}^2{\mathrm{\β}}_1^3{(\mathrm{\γ}-1)}^3}=100.16{\mathrm{mm}}^4/N;\end{array}$

$\begin{array}{c}{G}_{x-E2}=\frac{4(L^3-l_2^3)}{Eb}-\frac{8l_2^{3/2}(l_{12p}^{3/2}-l_2^{3/2})}{Eb}+\frac{4l_{12}^3}{{\mathrm{Eb\γ}}^3{\mathrm{\β}}_2^3}+\frac{6\mathrm{\Δ}l(4l_{12}^2\mathrm{\γ}-l_{12}^2-3l_{12}^2{\mathrm{\γ}}^2+3l_{12p}^2{\mathrm{\γ}}^2-4l_{12p}^2{\mathrm{\γ}}^3+l_{12p}^2{\mathrm{\γ}}^4)}{{\mathrm{Eb\γ}}^2{\mathrm{\β}}_2^3{(\mathrm{\γ}-1)}^3}-\\ \frac{6\mathrm{\Δ}l(-2l_{12}{l}_{12p}\mathrm{\γ}+2l_{12}^2{\mathrm{\γ}}^2\ln \mathrm{\γ}+2l_{12p}^2{\mathrm{\γ}}^2\ln \mathrm{\γ}+2l_{12}{l}_{12p}{\mathrm{\γ}}^3-4l_{12}{l}_{12p}{\mathrm{\γ}}^2\ln \mathrm{\γ})}{{\mathrm{Eb\γ}}^2{\mathrm{\β}}_2^3{(\mathrm{\γ}-1)}^3}=105.23{\mathrm{mm}}^4/N;\end{array}$

The main spring of (2) N sheet reinforcement end variable cross-section is at the deformation coefficient G at parabolic segment and auxiliary spring contact point place_x-BCCalculate:

According to the half length L=575mm of the main spring of reinforcement end variable cross-section, width b=60mm, elastic modulus E=200GPa, throwsThe root of thing line segment is to the distance l of main spring end points₂=520mm, the horizontal range l of auxiliary spring contact and main spring end points₀=200mm is rightThe 2nd main spring is at the deformation coefficient G at parabolic segment and auxiliary spring contact point place_x-BCCalculate,

$G_{x-BC}=\frac{2(2L^3-9l_2^2{l}_0-3L^2{l}_0+2l_2^3+8l_2^{3/2}{l}_0^{3/2})}{Eb}=40.78{\mathrm{mm}}^4/N;$

(3) the half stiffness K of the each main spring of reinforcement end variable cross-section_MiCalculate:

I step: according to the thickness h of the root flat segments of the main spring of reinforcement end variable cross-section₂=10.72mm, and calculate in step (1)The G arriving_x-E1＝100.16mm⁴/ N and G_x-E2＝105.23mm⁴/ N, to the half stiffness K of the 1st main spring and the 2nd main spring_M1And K_M2Calculate respectively,

$K_{M1}=\frac{h_2^3}{G_{x-E1}}=12.30N/\mathrm{mm},$

$K_{M2}=\frac{h_2^3}{G_{x-E2}}=11.71N/\mathrm{mm};$

(4) auxiliary spring of the few main spring of sheet variable cross-section of the non-end contact reinforcement end load p that works_KChecking computations:

According to the thickness h of the root flat segments of the main spring of reinforcement end variable cross-section₂=10.72mm, major-minor spring gap delta=19.37mm, stepSuddenly in (2), calculate the G that gained arrives_x-BC＝40.78mm⁴/ N, and in step (3), calculate to 1 and the 2nd main springHalf stiffness K_M1=12.30N/mm and K_M2=11.71N/mm, to the auxiliary spring load p that works_KCheck,

$P_K=\frac{2h_2^3\mathrm{\δ}\underset{i=1}{\overset{2}{\Σ}}{K}_{Mi}}{G_{x-BC}{K}_{M2}}=2400N.$

Utilize ANSYS finite element emulation software, according to main spring structure parameter and the material of the few sheet variable-section steel sheet spring of this reinforcement endMaterial characterisitic parameter, sets up ANSYS simulation model, grid division, and apply fixed constraint at the root of simulation model, leadingIt is P=1200N that spring end points applies the work half of load of auxiliary spring that checking computations obtain, to the few sheet Variable Section Steel of this reinforcement endANSYS emulation is carried out in the distortion of the main spring of flat spring, the deformation simulation cloud atlas obtaining, as shown in Figure 3, and wherein, this main springAt the deflection δ=19.52mm apart from end position 200mm place.

Known, in same load situation, the ANSYS simulating, verifying value δ=19.52mm of this main spring deflection, with major-minor spring gapDesign load δ=19.37mm matches, and relative deviation is only 0.77%; Result shows the non-end contact that this invention providesThe work Method for Checking of load of the auxiliary spring that few sheet variable cross-section major-minor spring is strengthened in end is correct.

Embodiment bis-: the sheet of the few main spring of sheet variable cross-section of certain reinforcement end is counted N=2, wherein, the half length of each main springL=600mm, width b=60mm, elastic modulus E=200GPa, the thickness h of root flat segments₂=13.87mm, installing spaceHalf l₃=60mm, the length Δ l=30mm of oblique line section, the root of parabolic segment is to the distance l of main spring end points₂＝L-l₃=540mm; The end thickness h of the parabolic segment of the 1st main spring_11p=7.63mm, the thickness of the parabolic segment of the 1st main springCompare β₁＝h_11p/h₂=0.55; The end thickness h of the parabolic segment of the 2nd main spring_12p=6.1mm, the parabolic segment of the 2nd main springThickness Ratio β₂=0.44; The end thickness h of the end flat segments of the 1st main spring₁₁=8.93mm, the end of the 2nd main spring is flatThe end thickness h of straight section₁₂=7.14mm; Thickness Ratio γ=the h of each main spring oblique line section₁₁/h_11p＝h₁₂/h_12p=1.17. One of auxiliary springHalf length L_A=370mm, the horizontal range l of auxiliary spring contact and main spring end points₀=230mm, auxiliary spring contact and main spring parabolic segmentBetween major-minor spring gap delta=22.41mm. To the auxiliary spring of the few sheet major-minor spring of this non-end contact reinforcement end load that worksCheck.

Adopt Method for Checking and the step identical with embodiment mono-, to the few sheet variable cross-section major-minor of this non-end contact reinforcement endThe auxiliary spring of the spring load that works checks, and specifically checks step as follows:

(1) the end points deformation coefficient G of the each main spring of reinforcement end variable cross-section_x-EiCalculate:

According to the half length L=600mm of the main spring of reinforcement end variable cross-section, width b=60mm, elastic modulus E=200GPa, peaceThe half l of dress spacing₃=60mm, the length Δ l=30mm of oblique line section, the root of parabolic segment is to the distance of main spring end pointsl₂=540mm; The Thickness Ratio β of the parabolic segment of the 1st main spring₁The Thickness Ratio of the parabolic segment of the=0.55,2nd main springβ₂=0.44; The root of the 1st main spring oblique line section is to the distance l of main spring end points_11p=163.41mm, the 2nd main spring oblique line sectionRoot is to the distance l of main spring end points_12p=104.45mm; The end of the 1st main spring oblique line section is to the distance of main spring end pointsl₁₁=133.41mm, the end of the 2nd main spring oblique line section is to the distance l of main spring end points₁₂=74.45mm; The oblique line of each main springThickness Ratio γ=1.17 of section; To the end points deformation coefficient G of the 1st main spring and the 2nd main spring_x-E1And G_x-E2Count respectivelyCalculate,

$\begin{array}{c}{G}_{x-E1}=\frac{4(L^3-l_2^3)}{Eb}-\frac{8l_2^{3/2}(l_{11p}^{3/2}-l_2^{3/2})}{Eb}+\frac{4l_{11}^3}{{\mathrm{Eb\γ}}^3{\mathrm{\β}}_1^3}+\frac{6\mathrm{\Δ}l(4l_{11}^2\mathrm{\γ}-l_{11}^2-3l_{11}^2{\mathrm{\γ}}^2+3l_{11p}^2{\mathrm{\γ}}^2-4l_{11p}^2{\mathrm{\γ}}^3+l_{11p}^2{\mathrm{\γ}}^4)}{{\mathrm{Eb\γ}}^2{\mathrm{\β}}_1^3{(\mathrm{\γ}-1)}^3}-\\ \frac{6\mathrm{\Δ}l(-2l_{11}{l}_{11p}\mathrm{\γ}+2l_{11}^2{\mathrm{\γ}}^2\ln \mathrm{\γ}+2l_{11p}^2{\mathrm{\γ}}^2\ln \mathrm{\γ}+2l_{11}{l}_{11p}{\mathrm{\γ}}^3-4l_{11}{l}_{11p}{\mathrm{\γ}}^2\ln \mathrm{\γ})}{{\mathrm{Eb\γ}}^2{\mathrm{\β}}_1^3{(\mathrm{\γ}-1)}^3}\\ =113.19{\mathrm{mm}}^4/N;\end{array}$

$\begin{array}{c}{G}_{x-E2}=\frac{4(L^3-l_2^3)}{Eb}-\frac{8l_2^{3/2}(l_{12p}^{3/2}-l_2^{3/2})}{Eb}+\frac{4l_{12}^3}{{\mathrm{Eb\γ}}^3{\mathrm{\β}}_2^3}+\frac{6\mathrm{\Δ}l(4l_{12}^2\mathrm{\γ}-l_{12}^2-3l_{12}^2{\mathrm{\γ}}^2+3l_{12p}^2{\mathrm{\γ}}^2-4l_{12p}^2{\mathrm{\γ}}^3+l_{12p}^2{\mathrm{\γ}}^4)}{{\mathrm{Eb\γ}}^2{\mathrm{\β}}_2^3{(\mathrm{\γ}-1)}^3}-\\ \frac{6\mathrm{\Δ}l(-2l_{12}{l}_{12p}\mathrm{\γ}+2l_{12}^2{\mathrm{\γ}}^2\ln \mathrm{\γ}+2l_{12p}^2{\mathrm{\γ}}^2\ln \mathrm{\γ}+2l_{12}{l}_{12p}{\mathrm{\γ}}^3-4l_{12}{l}_{12p}{\mathrm{\γ}}^2\ln \mathrm{\γ})}{{\mathrm{Eb\γ}}^2{\mathrm{\β}}_2^3{(\mathrm{\γ}-1)}^3}\\ =118.88{\mathrm{mm}}^4/N;\end{array}$

(2) the 2nd main springs of reinforcement end variable cross-section are at the deformation coefficient G at parabolic segment and auxiliary spring contact point place_x-BCCalculate:

According to the half length L=600mm of the main spring of reinforcement end variable cross-section, width b=60mm, elastic modulus E=200GPa, throwsThe root of thing line segment is to the distance l of main spring end points₂=540mm, the horizontal range l of auxiliary spring contact and main spring end points₀=230mm is rightThe 2nd main spring is at the deformation coefficient G at parabolic segment and auxiliary spring contact point place_x-BCCalculate,

$G_{x-BC}=\frac{2(2L^3-9l_2^2{l}_0-3L^2{l}_0+2l_2^3+8l_2^{3/2}{l}_0^{3/2})}{Eb}=40.85{\mathrm{mm}}^4/N;$

(3) the half stiffness K of the each main spring of reinforcement end variable cross-section_MiCalculate:

According to the thickness h of the root flat segments of the main spring of reinforcement end variable cross-section₂=13.87mm, and each of calculating in step (1)The end points deformation coefficient G of main spring_x-E1＝113.19mm⁴/ N and G_x-E2＝118.88mm⁴/ N, to the 1st main spring and the 2nd main springHalf stiffness K_M1And K_M2Calculate respectively,

$K_{M1}=\frac{h_2^3}{G_{x-E1}}=23.57N/mm,$

$K_{M2}=\frac{h_2^3}{G_{x-E2}}=22.45N/mm;$

(4) auxiliary spring of the few main spring of sheet variable cross-section of the non-end contact reinforcement end load p that works_KChecking computations:

According to the thickness h of the root flat segments of the main spring of reinforcement end variable cross-section₂=13.87mm, major-minor spring gap delta=22.41mm, stepSuddenly in (2), calculate the G that gained arrives_x-BC＝40.85mm⁴/ N, and the K calculating in step (3)_M1=23.57N/mm andK_M2=22.45N/mm, to the auxiliary spring of the few main spring of sheet variable cross-section of this non-end contact reinforcement end load p that works_KCarry outChecking computations,

$P_K=\frac{2h_2^3\mathrm{\δ}\underset{i=1}{\overset{2}{\Σ}}{K}_{Mi}}{G_{x-BC}{K}_{M2}}=6000N.$

Utilize ANSYS finite element emulation software, according to main spring structure parameter and the material of the few sheet variable-section steel sheet spring of this reinforcement endMaterial characterisitic parameter, sets up ANSYS simulation model, grid division, and apply fixed constraint at the root of simulation model, leadingThe work half of load of the auxiliary spring that spring end points applies checking computations gained is P=3000N, to the few sheet variable cross-section steel plates of this reinforcement endANSYS emulation is carried out in the distortion of the main spring of spring, the deformation simulation cloud atlas obtaining, and as shown in Figure 4, wherein, this main spring existsApart from the deflection δ=22.53mm at end position 230mm place.

Known, in same load situation, the ANSYS simulating, verifying value δ=22.53mm of this main spring deflection, with major-minor spring gapDesign load δ=22.41mm matches, and relative deviation is only 0.53%; Result shows the non-end contact that this invention providesThe auxiliary spring of the few sheet major-minor spring of the reinforcement end load checking method that works is correct, and load checking computations value is accurately and reliably.

Claims (1)

1. the auxiliary spring of the few sheet major-minor spring of the non-end contact reinforcement end load checking method that works, wherein, the few sheet of reinforcement endThe half symmetrical structure of the main spring of variable cross-section is made up of 4 sections of root flat segments, parabolic segment and end flat segments, and oblique line section is to masterSpring plays booster action; The non-structure that waits of end flat segments of each main spring, i.e. thickness and the length of the end flat segments of the 1st main spring,Be greater than thickness and the length of the end flat segments of other each main spring; Between auxiliary spring contact and main spring parabolic segment, be designed with certainMajor-minor spring gap; In each chip architecture parameter of main spring, elastic modelling quantity, auxiliary spring length, major-minor spring gap design value to stable conditionUnder, the auxiliary spring of the few sheet variable cross-section major-minor spring of the non-end contact reinforcement end load that works is checked to concrete checking computations stepRapid as follows:

(1) the end points deformation coefficient G of the each main spring of reinforcement end variable cross-section_x-EiCalculate:

According to the half length L of the main spring of reinforcement end variable cross-section, width b, elastic modulus E, the half l of installing space₃, oblique lineThe length Δ l of section, the root of parabolic segment is to the distance l of main spring end points₂＝L-l₃, the Thickness Ratio of the parabolic segment of the main spring of i sheetβ_i, wherein, i=1,2 ..., N, N is main reed number, the root of the main spring oblique line of i sheet section is to the distance of main spring end pointsl_1ip＝l₂β_i ², the end of the main spring oblique line of i sheet section is to the distance l of main spring end points_1i＝l_1ip-Δ l, the Thickness Ratio γ of oblique line section, to eachThe end points deformation coefficient G of the main spring of reinforcement end variable cross-section_x-EiCalculate,

$\begin{array}{c}{G}_{x-Ei}=\frac{4\left(L^3-l_2^3\right)}{Eb}-\frac{8l_2^{3/2}\left(l_{1ip}^{3/2}-l_2^{3/2}\right)}{Eb}+\frac{4l_{1i}^3}{{\mathrm{Eb\γ}}^3{\mathrm{\β}}_i^3}+\frac{6\mathrm{\Δ}l\left(4l_{1i}^2\mathrm{\γ}-l_{1i}^2-3l_{1i}^2{\mathrm{\γ}}^2+3l_{1ip}^2{\mathrm{\γ}}^2-4l_{1ip}^2{\mathrm{\γ}}^3+l_{1ip}^2{\mathrm{\γ}}^4\right)}{{\mathrm{Eb\γ}}^2{\mathrm{\β}}_i^3{\left(\mathrm{\γ}-1\right)}^3}-\\ \frac{6\mathrm{\Δ}l\left(-2l_{1i}{l}_{1ip}\mathrm{\γ}+2l_{1i}^2{\mathrm{\γ}}^2\ln \mathrm{\γ}+2l_{1ip}^2{\mathrm{\γ}}^2\ln \mathrm{\γ}+2l_{1i}{l}_{1ip}{\mathrm{\γ}}^3-4l_{1i}{l}_{1ip}{\mathrm{\γ}}^2\ln \mathrm{\γ}\right)}{{\mathrm{Eb\γ}}^2{\mathrm{\β}}_i^3{\left(\mathrm{\γ}-1\right)}^3},i=1,2,...,N;\end{array}$ The main spring of (2) N sheet reinforcement end variable cross-section is at the deformation coefficient G at parabolic segment and auxiliary spring contact point place_x-BCCalculate:

According to the half length L of the main spring of reinforcement end variable cross-section, width b, elastic modulus E, the root of parabolic segment is to main spring endThe distance l of point₂, the horizontal range l of auxiliary spring contact and main spring end points₀, to the main spring of N sheet reinforcement end variable cross-section at parabolaSection and the deformation coefficient G at auxiliary spring contact point place_x-BCCalculate,

$G_{x-BC}=\frac{2(2L^3-9l_2^2{l}_0-3L^2{l}_0+2l_2^3+8l_2^{3/2}{l}_0^{3/2})}{Eb};$

(3) the half stiffness K of the each main spring of reinforcement end variable cross-section_MiCalculate:

According to the thickness h of the root flat segments of the main spring of reinforcement end variable cross-section₂, and the end of the each main spring calculating in step (1)Deformation coefficient G_x-Ei, to the half stiffness K of the each main spring of reinforcement end variable cross-section_MiCalculate,

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

(4) auxiliary spring of the few main spring of sheet variable cross-section of the non-end contact reinforcement end load p that works_KChecking computations:

According to the thickness h of the root flat segments of the few main spring of sheet variable cross-section of reinforcement end₂, major-minor spring gap delta, calculates in step (2)The G obtaining_x-BC, and the K calculating in step (3)_Mi, to the auxiliary spring load p that works_KCalculate,

$P_K=\frac{2h_2^3\mathrm{\δ}\underset{i=1}{\overset{N}{\mathrm{\Σ}}}{K}_{Mi}}{G_{x-BC}{K}_{MN}};$

In formula, K_MNBe the half rigidity of the main spring of N sheet.