CN105868494A - Method for designing thicknesses of roots of non-end-contact few-leaf parabola type auxiliary springs - Google Patents

Abstract

The invention relates to a method for designing the thicknesses of roots of non-end-contact few-leaf parabola type auxiliary springs, and belongs to the technical field of steel plate springs of suspensions. The method includes that the thicknesses of straight sections of the roots of the various auxiliary springs can be designed according to design required values of structural parameters of various main springs of non-end-contact few-leaf parabola type variable-section main and auxiliary spring combinations, elastic modulus, the lengths and the leaf numbers of the auxiliary springs, the thicknesses ratios of parabola sections of the auxiliary springs and the complex stiffness of the main and auxiliary spring combinations. The method has the advantages that as known from living examples and ANSYS simulation verification, the method for designing the thicknesses of the roots of the non-end-contact few-leaf parabola type auxiliary springs is correct, accurate and reliable design values of the thicknesses of the straight sections of the roots of the auxiliary springs can be obtained by the aid of the method, accordingly, requirements on design required values of the complex stiffness of suspensions can be assuredly met, and the performance of products and the riding comfort of vehicles can be improved; the design and test costs can be reduced, and the product development speed can be increased.

Description

The method for designing of the few sheet parabolic type auxiliary spring root thickness of non-ends contact formula

Technical field

The present invention relates to vehicle suspension leaf spring, be the design of the few sheet parabolic type auxiliary spring root thickness of non-ends contact formula especially Method.

Background technology

Owing to the stress of the 1st main spring of few sheet variable cross-section major-minor spring is complicated, it is subjected to vertical load, simultaneously also subject to torsional load And longitudinal loading, therefore, the thickness of the end flat segments of the 1st main spring designed by reality and length, more than his each main spring The thickness of end flat segments and length, the most mostly use the non-few sheet variable-section steel sheet spring waiting structure in end, to meet the 1st The requirement that main spring stress is complicated.It addition, for the design requirement meeting different composite rigidity, generally use the pair of different length Spring, i.e. auxiliary spring contact are the most different from the position that main spring contacts, and therefore, can be divided into end flat segments contact and non-ends contact Formula two kinds, wherein, in the case of identical auxiliary spring root thickness, the complex stiffness of non-ends contact formula, contact less than end flat segments The complex stiffness of formula.When the contact of major-minor spring works together, the main spring of m sheet is in addition to by end points power, also by auxiliary spring contact The effect of support force, causes the deformation of few sheet variable cross-section major-minor spring and internal force to calculate extremely complex.Answering of few sheet variable cross-section major-minor spring Close rigidity, vehicle ride performance is had material impact, therefore, it is necessary to straight to the auxiliary spring root of few sheet variable cross-section major-minor spring The thickness of section carries out careful design, to guarantee to meet the design requirement of complex stiffness.But, owing to the end flat segments of main spring is non- Deng the length of structure, major-minor spring, unequal, the deformation of major-minor spring and internal force analysis calculate extremely complex, therefore, connect for non-end The few sheet parabolic type variable cross-section auxiliary spring root flat segments thickness of touch, fails to provide reliable method for designing the most always.Although first Before once someone gave the design and calculation method of few sheet variable-section steel sheet spring, such as, Peng Mo, high army is once in " automobile work Journey ", (volume 14) the 3rd phase in 1992, it is proposed that the design and calculation method of variable-section steel sheet spring, it is primarily directed to end Being designed Deng few sheet parabolic type variable-section steel sheet spring of structure and calculate, its weak point can not meet the few sheet of non-ends contact formula Parabolic type variable cross-section major-minor spring and the design requirement of auxiliary spring root thickness.Project planner, is mostly to ignore major-minor spring at present The impact of Length discrepancy, directly carries out Approximate Design by the method for designing of main spring to auxiliary spring root thickness, therefore it is difficult to obtain reliably Auxiliary spring root thickness design load, it is impossible to meet the careful design requirement of the few sheet parabolic type variable cross-section major-minor spring of ends contact formula. Therefore, it is necessary to set up the design side of the few sheet parabolic type variable cross-section auxiliary spring root thickness of a kind of non-ends contact formula accurate, reliable Method, to meet Vehicle Industry fast development and the requirement to few sheet parabolic type variable cross-section major-minor Precise Design for Laminated Spring, improves The few design level of sheet parabolic type variable cross-section major-minor spring, product quality and performances, it is ensured that meet the design of major-minor spring complex stiffness Requirement, improves vehicle ride performance；Meanwhile, reduce 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 method for designing of the few sheet parabolic type auxiliary spring root thickness of non-ends contact formula, its design flow diagram, as shown in Figure 1.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, including, main spring 1, root shim 2, auxiliary spring 3, end pad 4, between the root flat segments of each of main spring 1 and straight with the root of auxiliary spring 3 Being provided with root shim 2 between Duan, be provided with end pad 4 between the end flat segments of main spring 1, the material of end pad is that carbon is fine Dimension composite, to reduce frictional noise produced by spring works.The a length of L of half of each main spring_M, it is to be put down by root Straight section, parabolic segment and end flat segments three sections are constituted, and the thickness of the root flat segments of each main spring is h_2M, installing space Half be l₃；The non-thickness waiting structure, i.e. the end flat segments of the 1st main spring of end flat segments of each main spring and length, greatly The thickness of end flat segments and length, the thickness of the end flat segments of each main spring and length in other each main spring are respectively h_1iAnd l_1i, i=1,2 ..., m, m are the sheet number of few main spring of sheet variable cross-section；Middle variable cross-section is parabolic segment, each parabolic segment Thickness 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.The half of each auxiliary spring is long Degree is L_A, auxiliary spring sheet number is n, and the structure of each auxiliary spring is identical, and wherein, auxiliary spring width is equal to main spring width, i.e. auxiliary spring width For b, auxiliary spring contact is l with the horizontal range of main spring end points₀=L_M-L_A, the thickness h of auxiliary spring root flat segments_2AFor to be designed Value, thickness and the length of the end flat segments of jth sheet auxiliary spring are respectively h_A1jAnd l_A1j, and h_A11=h_A1j...=h_A1n, l_A11=l_A1j...=l_A1n, thickness and the length of the end flat segments of the most each auxiliary spring are equal；The thickness ratio of auxiliary spring parabolic segment is β_A, wherein, β_A=h_A1j/h_A2, j=1,2 ..., n, n are the sheet number of auxiliary spring.It is provided with one between auxiliary spring contact and main spring parabolic segment Fixed major-minor spring gap delta, after load works load more than auxiliary spring, auxiliary spring contact contacts with certain point in main spring parabolic segment And concur, to meet major-minor spring complex stiffness and auxiliary spring works the design requirement of load, wherein, major-minor spring compound Rigidity, not only the structural parameters of each with main spring are relevant, but also with auxiliary spring sheet number, auxiliary spring length and auxiliary spring root flat segments Thickness is relevant.At the structural parameters of each main spring, elastic modelling quantity, auxiliary spring length, the thickness ratio of auxiliary spring parabolic segment, auxiliary spring sheet In the case of number and major-minor spring complex stiffness design required value, the auxiliary spring root of sheet variable cross-section major-minor spring few to non-ends contact formula is put down Straight section thickness is designed.

For solving above-mentioned technical problem, the design of the few sheet parabolic type auxiliary spring root thickness of non-ends contact formula provided by the present invention Method, it is characterised in that use following design procedure:

(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, wherein, 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, 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, main reed number m, under end points stressing conditions M sheet main spring deformation coefficient G at parabolic segment and auxiliary spring contact point_x-BCCalculate, i.e.

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

(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-section steel sheet spring_M, width b, elastic modulus E, main spring parabolic segment Root to distance l of main spring end points_2M, auxiliary spring contact and horizontal range l of main spring end points₀, main reed number m, to major-minor spring The main spring of m sheet under stressing conditions deformation coefficient G at endpoint location at contact point_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 main spring of m sheet under major-minor spring contact point stressing conditions is at the deformation coefficient G of parabolic segment Yu auxiliary spring contact point_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, main reed number m, at major-minor spring contact point The main spring of m sheet under stressing conditions 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) total end points deformation coefficient G of the n sheet superposition auxiliary spring under end points stressing conditions_x-DATCalculate:

Half length L according to few sheet parabolic type variable cross-section auxiliary spring_A, auxiliary spring sheet number n, width b, elastic modulus E, auxiliary spring parabolic The root of line segment is to distance l of main spring end points_2A, the thickness of the parabolic segment of each auxiliary spring compares β_A, total to n sheet superposition auxiliary spring End points deformation coefficient G_x-DATCalculate, i.e.

$G_{x-DAT}=\frac{4\[l_{2A}^3(1-{\mathrm{\β}}_A^3)+L_A^3\]}{nEb};$

(6) the auxiliary spring root flat segments thickness h of the few sheet parabolic type major-minor spring of non-ends contact formula_2ADesign:

Complex stiffness design required value K according to major-minor spring_MAT, main reed number m, the thickness h of the root flat segments of each main spring_2M, 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 the G obtained by the middle calculating of step (5)_x-DAT, sheet parabolic type few to non-ends contact formula The auxiliary spring root flat segments thickness h of variable cross-section major-minor spring_2AIt is designed, i.e.

$h_{2A}=\sqrt[3]{\frac{(K_{MAT}-\underset{i=1}{\overset{m-1}{\Σ}}\frac{2h_{2M}^3}{G_{x-Di}})G_{x-Dm}{G}_{x-DAT}-2G_{x-DAT}{h}_{2M}^6}{(K_{MAT}-\underset{i=1}{\overset{m-1}{\Σ}}\frac{2h_{2M}^3}{G_{x-Di}})(G_{x-D_{p}m}{G}_{x-BC}-G_{x-Dm}{G}_{x-{\mathrm{BC}}_p})+2G_{x-{\mathrm{BC}}_p}{h}_{2M}^3}}.$

The present invention has the advantage that than prior art

Waiting structure owing to the end flat segments of main spring is non-, meanwhile, major-minor spring length is unequal, and the main spring of m sheet is except by end points power Outside, also being acted on by auxiliary spring contact support power, the deformation of few sheet variable cross-section major-minor spring and the analytical calculation of internal force are extremely complex, Therefore, fail to provide the method for designing of the few sheet variable cross-section auxiliary spring root thickness of non-ends contact formula the most always.The present invention can basis The structural parameters of each main spring, elastic modelling quantity, auxiliary spring length, auxiliary spring sheet number, the thickness ratio of auxiliary spring parabolic segment and major-minor spring Complex stiffness design required value given in the case of, each root of sheet parabolic type variable cross-section auxiliary spring few to end contact is straight The thickness of section is designed.By design example and ANSYS simulating, verifying, utilize the method available accurately, reliable The design load of the few sheet variable cross-section auxiliary spring root thickness of non-ends contact formula, secondary for the few sheet parabolic type variable cross-section of non-ends contact formula The design of spring root thickness provides reliable method for designing, and is the few sheet parabolic type variable cross-section major-minor spring of non-ends contact formula Reliable technical foundation has been established in CAD software exploitation.Utilize the method can improve the design water of few sheet variable cross-section major-minor leaf spring Flat, product quality and performances, it is ensured that meet the suspension design requirement to major-minor spring complex stiffness, improve vehicle ride performance； Meanwhile, also can reduce bearing spring quality and cost, reduce design and testing expenses, accelerate product development speed.

Accompanying drawing explanation

In order to be more fully understood that the present invention, it is described further below in conjunction with the accompanying drawings.

Fig. 1 is the design flow diagram of the auxiliary spring root thickness of the few sheet parabolic type variable cross-section major-minor spring of non-ends contact formula；

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

Fig. 3 is the ANSYS deformation simulation cloud atlas of the few sheet parabolic type variable cross-section major-minor spring of non-ends contact formula of embodiment one；

Fig. 4 is the ANSYS deformation simulation cloud atlas of the few sheet parabolic type variable cross-section major-minor spring of non-ends contact formula of embodiment two.

Specific embodiments

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

Embodiment one: the width b=60mm of the few sheet parabolic type variable-section steel sheet spring of certain non-ends contact formula, installing space Half l₃=55mm, elastic modulus E=200GPa；Wherein, main reed number m=2, half length L of main spring_M=575mm, The parabolical root of main spring is to distance l of main spring end points_2M=L_M-l₃=520mm；The thickness of the root flat segments of each main spring h_2M=11mm, the thickness h of the end flat segments of the 1st main spring₁₁=7mm, the thickness ratio of the parabolic segment of the 1st main spring β₁=h₁₁/h_2MThe thickness h of the end flat segments of the=0.64, the 2nd main spring₁₂=6mm, the thickness of the parabolic segment of the 2nd main spring Compare β₂=h₁₂/h_2M=0.55.Auxiliary spring sheet number n=1, half length L of auxiliary spring_AThe water of=375mm, auxiliary spring contact and main spring end points Flat distance l₀=L_M-L_A=200mm, the root of auxiliary spring parabolic segment is to distance l of auxiliary spring end points_2A=L_A-l₃=320mm, auxiliary spring The thickness of parabolic segment compare β_A=0.57, the complex stiffness design required value K of major-minor spring_MAT=76.42N/mm.According to each The structural parameters of main spring, auxiliary spring length and sheet number, elastic modelling quantity and major-minor spring complex stiffness design required value, connect this non-end The auxiliary spring root thickness of the few sheet parabolic type variable cross-section major-minor spring of touch is designed.

The method for designing of the few sheet parabolic type auxiliary spring root thickness of the non-ends contact formula that present example is provided, its design cycle As it is shown in figure 1, specific design step 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=575mm, width b=60mm, elastic modelling quantity E=200GPa, the parabolical root of main spring is to distance l of main spring end points_2M=520mm, main reed number m=2, wherein, the 1st The thickness of the parabolic segment of the main spring of sheet compares β₁The thickness of the parabolic segment of the=0.64, the 2nd main spring compares β₂=0.55, to end points stress In the case of the 1st main spring 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 G of the main spring of m sheet under major-minor spring contact point stressing conditions_x-Dp2Calculate:

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 Number G_x-Dp2Calculate, 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) 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=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 main spring under major-minor spring contact point stressing conditions parabolic segment with Deformation coefficient G at auxiliary spring contact point_x-BCpCalculate, 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) total end points deformation coefficient G of the n sheet superposition auxiliary spring under end points stressing conditions_x-DATCalculate:

Half length L according to few sheet parabolic type variable cross-section auxiliary spring_A=375mm, width b=60mm, elastic modelling quantity E=200GPa, the root of auxiliary spring parabolic segment is to distance l of auxiliary spring end points_2A=320mm, the thickness of the parabolic segment of this sheet auxiliary spring Degree compares β_A=0.57, auxiliary spring sheet number n=1, the deformation coefficient G to this sheet auxiliary spring end points of n sheet superposition auxiliary spring_x-DATCount Calculate, i.e.

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

(6) the auxiliary spring root flat segments thickness h of the few sheet parabolic type major-minor spring of non-ends contact formula_2ADesign:

Complex stiffness design required value K according to major-minor spring_MAT=76.42N/mm, main reed number m=2, the root of each main spring is straight The thickness h of section_2M=11mm, the G obtained by calculating in step (1)_x-D1=98.16mm⁴/ N and G_x-D2=102.63mm⁴/ N, step Suddenly calculated G in (2)_x-BC=40.77mm⁴/ N, calculated G in step (3)_x-Dp2=40.77mm⁴/ N, in step (4) Calculated G_x-BCp=21.35mm⁴G obtained by calculating in/N, and step (5)_x-DAT=26.46mm⁴/ N, to this non-end Auxiliary spring root thickness h of the few sheet parabolic type variable cross-section major-minor spring of contact_2AIt is designed, i.e.

$h_{2A}=\sqrt[3]{\frac{(K_{MAT}-\underset{i=1}{\overset{m-1}{\Σ}}\frac{2h_{2M}^3}{G_{x-Di}})G_{x-Dm}{G}_{x-DAT}{h}_{2M}^3-2G_{x-DAT}{h}_{2M}^6}{(K_{MAT}-\underset{i=1}{\overset{m-1}{\Σ}}\frac{2h_{2M}^3}{G_{x-Di}})(G_{x-D_{p}m}{G}_{x-BC}-G_{x-Dm}{G}_{x-{\mathrm{BC}}_p})+2G_{x-{\mathrm{BC}}_p}{h}_{2M}^3}}=14mm.$

Utilize ANSYS finite element emulation software, according to the structural parameters of the few sheet parabolic type variable cross-section major-minor spring of this non-ends contact formula And material characteristic parameter, and auxiliary spring root thickness h that design obtains_2A=14mm, sets up half symmetrical structure major-minor spring ANSYS phantom, grid division, auxiliary spring end points is set and contacts with main spring, and fixing about in the root applying of phantom Bundle, applies concentrfated load F=1840N, the deformation to the major-minor spring of this few sheet parabolic type variable-section steel sheet spring at main spring end points Carry out ANSYS emulation, the ANSYS deformation simulation cloud atlas of obtained major-minor spring, as it is shown on figure 3, wherein, major-minor spring Maximum deformation quantity f at endpoint location_DSmax=48.00mm.Understand, the complex stiffness emulation of this non-ends contact formula major-minor spring Validation value K_MAT=2F/f_DSmax=76.67N/mm.

Understand, complex stiffness simulating, verifying value K of this major-minor spring_MAT=76.67N/mm, with design required value K_MAT=76.42N/mm Matching, relative deviation is only 0.33%；Result shows the few sheet parabolic type variable cross-section of non-ends contact formula that this invention is provided The method for designing of auxiliary spring root thickness is correct, and auxiliary spring root flat segments thickness design load is accurate, reliable.

Embodiment two: the width b=60mm of the few sheet parabolic type variable-section steel sheet spring of certain non-ends contact formula, installing space Half l₃=60mm, elastic modulus E=200GPa, wherein, main reed number m=2, half length L of main spring_M=600mm, The thickness h of the root flat segments of each main spring_2M=12mm, the root of main spring parabolic segment is to distance l of main spring end points_2M=L_M- l₃=540mm；The end flat segments thickness h of the 1st main spring₁₁=8mm, the thickness ratio of the parabolic segment of the 1st main spring β₁=h₁₁/h_2MThe end flat segments thickness h of the=0.67, the 2nd main spring₁₂=7mm, the thickness ratio of the parabolic segment of the 2nd main spring β₂=h₁₂/h_2M=0.58.Auxiliary spring sheet number n=1, half length L of auxiliary spring_AThe level of=410mm, auxiliary spring contact and main spring end points Distance l₀=L_M-L_A=190mm, the root of auxiliary spring parabolic segment is to distance l of auxiliary spring end points_2A=L_A-l₃=350mm, auxiliary spring is thrown The thickness of thing line segment compares β_A=0.62.The complex stiffness design required value K of this major-minor spring_MAT=83.44N/mm, according to each master Being combined of the structural parameters of spring, elastic modelling quantity, auxiliary spring length, auxiliary spring sheet number, the thickness ratio of auxiliary spring parabolic segment and major-minor spring Rigidity Design required value, the auxiliary spring root thickness of sheet parabolic type variable cross-section major-minor spring few to this non-ends contact formula is designed.

Use the method for designing identical with embodiment one and step, sheet parabolic type variable cross-section major-minor spring few to this non-ends contact formula Auxiliary spring root thickness be designed, specific design step 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=600mm, 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=540mm, 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=0.67, the 2nd main spring compares β₂=0.58, 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}=108.70{\mathrm{mm}}^4/N,$

$G_{x-D2}=\frac{4\[l_{2M}^3(1-{\mathrm{\β}}_2^3)+L_M^3\]}{Eb}=114.25{\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=600mm, 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=540mm, auxiliary spring contact and main spring end points Flat distance l₀=190mm, 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}\[8l_{2M}^{3/2}{l}_0^{3/2}-(9l_{2M}^2+3L_M^2)l_0+2l_{2M}^3+2L_M^3\]=51.00{\mathrm{mm}}^4/N;$

(3) the end points deformation coefficient G of the main spring of m sheet under major-minor spring contact point stressing conditions_x-Dp2Calculate:

Half length L according to few sheet main spring of parabolic type variable cross-section_M=600mm, 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=540mm, auxiliary spring contact and main spring end points Flat distance l₀=190mm, main reed number m=2, to the 2nd main spring under major-minor spring contact point stressing conditions at endpoint location Deformation coefficient G_x-Dp2Calculate, i.e.

$G_{x-D_{p}2}=\frac{4}{bE}(l_{2M}^3-6l_0{l}_{2M}^2+4l_{2M}^{3/2}{l}_0^{3/2}+L_M^3)=51.00{\mathrm{mm}}^4/N;$

(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=600mm, 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=540mm, auxiliary spring contact and main spring end points Flat distance l₀=190mm, main reed number m=2, to the 2nd main spring under major-minor spring contact point stressing conditions parabolic segment with Deformation coefficient G at auxiliary spring contact point_x-BCpCalculate, i.e.

$\begin{array}{c}{G}_{x-{\mathrm{BC}}_p}=\frac{4}{Eb}\[(L_M-l_{2M})(L_M^2-3L_M{l}_0+L_M{l}_{2M}+3l_0^2-3l_0{l}_{2M}+l_{2M}^2)-(6l_{2M}{l}_0^2-2l_{2M}^3-16l_0^{3/2}{l}_{2M}^{1/2}+12l_0{l}_{2M}^3)\]\\ =28.33{\mathrm{mm}}^4/N;\end{array}$

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

Half length L according to few sheet parabolic type variable cross-section auxiliary spring_A=410mm, width b=60mm, elastic modelling quantity E=200GPa, the root of auxiliary spring parabolic segment is to distance l of auxiliary spring end points_2A=L_A-l₃=350mm, the thickness of the parabolic segment of auxiliary spring Degree compares β_A=0.62, auxiliary spring sheet number n=1, the total end points deformation coefficient G to n sheet auxiliary spring_x-DATCalculate, i.e.

$G_{x-DAT}=\frac{4\[l_{2A}^3(1-{\mathrm{\β}}_A^3)+L_A^3\]}{nEb}=33.86{\mathrm{mm}}^4/N;$

(6) the auxiliary spring root flat segments thickness h of the few sheet parabolic type major-minor spring of non-ends contact formula_2ADesign:

Complex stiffness design required value K according to major-minor spring_MAT=83.44N/mm, main reed number m=2, the root of each main spring is straight The thickness h of section_2M=12mm, calculated G in step (1)_x-D1=108.70mm⁴/ N and G_x-D2=114.25mm⁴/ N, step Suddenly calculated G in (2)_x-BC=51.00mm⁴/ N, calculated G in step (3)_x-Dp2=51.00mm⁴/ N, in step (4) Calculated G_x-BCp=28.33mm⁴G obtained by calculating in/N, and step (5)_x-DAT=33.86mm⁴/ N, to this non-end The auxiliary spring root flat segments thickness h of the few sheet parabolic type variable cross-section major-minor spring of contact_2AIt is designed, i.e.

$h_{2A}=\sqrt[3]{\frac{(K_{MAT}-\underset{i=1}{\overset{m-1}{\Σ}}\frac{2h_{2M}^3}{G_{x-Di}})G_{x-Dm}{G}_{x-DAT}{h}_{2M}^3-2G_{x-DAT}{h}_{2M}^6}{(K_{MAT}-\underset{i=1}{\overset{m-1}{\Σ}}\frac{2h_{2M}^3}{G_{x-Di}})(G_{x-D_{p}m}{G}_{x-BC}-G_{x-Dm}{G}_{x-{\mathrm{BC}}_p})+2G_{x-{\mathrm{BC}}_p}{h}_{2M}^3}}=13mm.$

Utilize ANSYS finite element emulation software, according to structural parameters and the material behavior ginseng of this few sheet parabolic type variable cross-section major-minor spring Number, and auxiliary spring root thickness h that design obtains_2A=13mm, the ANSYS setting up half symmetrical structure major-minor spring emulate mould Type, grid division, auxiliary spring end points is set and contacts with main spring, and at the root applying fixed constraint of phantom, at main spring end points Apply concentrfated load F=2000N, the deformation of the major-minor spring of this few sheet parabolic type variable-section steel sheet spring is carried out ANSYS and imitates Very, the ANSYS deformation simulation cloud atlas of obtained major-minor spring, as shown in Figure 4, wherein, major-minor spring is at endpoint location Maximum deformation quantity f_DSmax=47.50mm.Understand, the few sheet parabolic type variable cross-section major-minor spring complex stiffness of this non-ends contact formula Simulating, verifying value K_MAT=2F/f_DSmax=84.21N/mm.

Understand, this major-minor spring complex stiffness simulating, verifying value K_MAT=84.21N/mm, with design required value K_MAT=83.44N/mm phase Coincideing, relative deviation is only 0.91%；Result shows that the few sheet parabolic type variable cross-section of non-ends contact formula that this invention is provided is secondary The method for designing of spring root thickness is correct, and auxiliary spring root flat segments thickness design load is accurate, reliable.

Claims (1)

1. The most non-ends contact formula lacks the method for designing of sheet parabolic type auxiliary spring root thickness wherein, few sheet parabolic type variable cross-section major-minor steel The half symmetrical structure of flat spring is to be made up of root flat segments, parabolic segment and end flat segments three sections, wherein, and each main spring End flat segments non-wait the thickness of structure, i.e. the end flat segments of the 1st main spring and length, put down more than other each main spring end The thickness of straight section and length；Auxiliary spring length is less than main spring length, and when load auxiliary spring works load, auxiliary spring contact is thrown with main spring In thing line segment, certain point contacts, to meet the complex stiffness design requirement of few sheet parabolic type variable cross-section major-minor spring；At each main spring Structural parameters, auxiliary spring length and sheet number, elastic modelling quantity and major-minor spring complex stiffness design required value given in the case of, to non-end The auxiliary spring root flat segments thickness of the few sheet parabolic type major-minor spring of portion's contact is designed, and specific design step 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, wherein, 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, 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, main reed number m, under end points stressing conditions M sheet main spring deformation coefficient G at parabolic segment and auxiliary spring contact point_x-BCCalculate, i.e.

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

   (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-section steel sheet spring_M, width b, elastic modulus E, main spring parabolic segment Root to distance l of main spring end points_2M, auxiliary spring contact and horizontal range l of main spring end points₀, main reed number m, to major-minor spring The main spring of m sheet under stressing conditions deformation coefficient G at endpoint location at contact point_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 main spring of m sheet under major-minor spring contact point stressing conditions is at the deformation coefficient G of parabolic segment Yu auxiliary spring contact point_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, main reed number m, at major-minor spring contact point The main spring of m sheet under stressing conditions deformation coefficient G at parabolic segment with auxiliary spring contact point_x-BCpCalculate, i.e.

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

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

   Half length L according to few sheet parabolic type variable cross-section auxiliary spring_A, auxiliary spring sheet number n, width b, elastic modulus E, auxiliary spring parabolic The root of line segment is to distance l of main spring end points_2A, the thickness of the parabolic segment of each auxiliary spring compares β_A, total to n sheet superposition auxiliary spring End points deformation coefficient G_x-DATCalculate, i.e.

   $G_{x-DAT}=\frac{4\[l_{2A}^3(1-{\mathrm{\β}}_A^3)+L_A^3\]}{nEb};$

   (6) the auxiliary spring root flat segments thickness h of the few sheet parabolic type major-minor spring of non-ends contact formula_2ADesign:

   Complex stiffness design required value K according to major-minor spring_MAT, main reed number m, the thickness h of the root flat segments of each main spring_2M, 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 the G obtained by the middle calculating of step (5)_x-DAT, sheet parabolic type few to non-ends contact formula The auxiliary spring root flat segments thickness h of variable cross-section major-minor spring_2AIt is designed, i.e.

   $h_{2A}=\sqrt[3]{\frac{(K_{MAT}-\underset{i=1}{\overset{m-1}{\Σ}}\frac{2h_{2M}^3}{G_{x-Di}})G_{x-Dm}{G}_{x-DAT}{h}_{2M}^3-2G_{x-DAT}{h}_{2M}^6}{(K_{MAT}-\underset{i=1}{\overset{m-1}{\Σ}}\frac{2h_{2M}^3}{G_{x-Di}})(G_{x-D_{p}m}{G}_{x-BC}-G_{x-Dm}{G}_{x-{\mathrm{BC}}_p})+2G_{x-{\mathrm{BC}}_p}{h}_{2M}^3}}.$