CN105760630A - Design method of end reinforcing taper leaf springs - Google Patents

Abstract

The invention relates to a design method of end reinforcing taper leaf springs, and belongs to the technical field of suspension leaf springs. The method comprises the following steps: firstly, determining the root thickness he of an equivalent single spring according to structural parameters, material characteristic parameters and rigidity design required values of a leaf spring, and determining the root maximum allowable thickness [h2] of the taper leaf spring according to allowable stress; then designing the quantity N and root thickness h2 of the end reinforcing taper leaf springs and structure parameters of the end of each spring according to he, [h2] and thickness ratio of an oblique line segment. ANSYS simulation verification shows that the method can obtain accurate and reliable parameter design values of the end reinforcing taper leaf springs, can improve the design level and performance of products, reduce the weight and cost of springs and improve the vehicle running smoothness; meanwhile, the method further reduces design and testing expenses, and accelerates the development rate of products.

Description

The method for designing of the few sheet variable-section steel sheet spring of reinforcement end

Technical field

The present invention relates to the method for designing of the few sheet variable-section steel sheet spring of vehicle suspension leaf spring, particularly reinforcement end.

Background technology

Variable-section steel sheet spring is compared with multi-disc superposition leaf spring, owing to its stress loading tends to balanced, and save material and cost, realize vehicle lightweight, reduce wheel dynamic load, improve vehicle safety, also save fuel oil simultaneously, improve vehicle transport efficiency, therefore there is good economic benefit and social benefit, caused showing great attention to of vehicle expert.For few sheet variable-section steel sheet spring, between end flat segments and parabolic segment, generally set up an oblique line section, namely the few sheet variable-section steel sheet spring of reinforcement end is adopted, so not only can reduce the stress of spring, improve its stress intensity, meanwhile, also can meet rigidity careful design value, but also the processing of parabola variable cross-section section can be easy to, improve processing technology.Although previously, once someone gave the method for designing of few sheet parabolic type variable-section steel sheet spring, such as, Peng not with high army once in " automobile engineering " the 14th volume the 3rd phase, propose the design and calculation method of Varied section leaf spring, the method can only to structures such as ends, and the few sheet parabolic type variable-section steel sheet spring for increasing oblique line strengthening segment is designed, its weak point is to meet the non-designing requirement waiting structure and the few sheet variable-section steel sheet spring with oblique line strengthening segment in end.

For the few sheet variable-section steel sheet spring of reinforcement end, owing to being subject to the theories of computation such as deformation, rigidity and equivalent thickness and the restriction splitting design theory, so far method for designing easy, accurate, reliable always is not yet provided, it is mostly ignore end to strengthen the impact of oblique line section at present, oblique line section is similar to the extension seeing end flat segments as, and think that the end of each such as is at the structure, the few sheet variable-section steel sheet spring of reinforcement end is carried out Approximate Design, it is therefore hard to obtain parameter designing value accurately and reliably.Emulation along with computer and finite element emulation software, once few sheet variable-section steel sheet spring of reinforcement end was adopted ANSYS modeling and simulating method despite people at present, but the deformation of reinforced few sheet variable-section steel sheet spring of given design structure or rigidity can only be carried out simulating, verifying by the method, it is not provided that accurate analytical design method formula, more can not meet vehicle fast development and the requirement to suspension leaf spring modernization CAD design software development.

Therefore, must be set up the method for designing of the few sheet variable-section steel sheet spring of a kind of reinforcement end accurate, reliable, meet Vehicle Industry fast development and the requirement to suspension Precise Design for Laminated Spring, improve the few design level of sheet variable-section steel sheet spring, product quality and performances, improve vehicle ride performance and safety；Meanwhile, reduce spring-mass and cost, reduce design and testing expenses, accelerate product development speed.

Summary of the invention

For the defect existed in above-mentioned prior art, the technical problem to be solved is to provide the method for designing of a kind of simplicity, the few sheet variable-section steel sheet spring of reliable reinforcement end.Described variable-section steel sheet spring includes at least two panels leaf spring, the symmetrical structure that every leaf spring is is axle center with central bolt mounting hole, the half symmetrical structure of few sheet variable-section steel sheet spring can regard cantilever beam as, namely using central bolt mounting hole centrage as the fixing end of the root of leaf spring, the end stress point of leaf spring is as end points, wherein, the half symmetrical structure schematic diagram of i-th, the half symmetrical structure of each leaf spring is made up of root flat segments, parabolic segment, oblique line section and end flat segments 4 sections；It is provided with an oblique line section between end flat segments and parabolic segment, booster action is played in the end of leaf spring；Each end flat segments is non-waits structure, and namely the thickness of the end flat segments of the 1st leaf spring and length are more than the thickness of other each leaf spring and length, the requirement complicated to meet the 1st spring end stress；Wherein, L is the half of its length, l₃For the half of installing space, h₂For the root flat segments thickness of each flat spring, l₂For the root of parabolic segment to the distance of spring end points；h_1ipBeing the end thickness of the i-th flat spring parabolic segment, namely the thickness of the i-th flat spring parabolic segment compares β_i=h_1ip/h₂；l_1ipIt it is the end distance to spring end points of the i-th flat spring parabolic segment；h_1i、l_1iThe respectively thickness of the end flat segments of the i-th flat spring and length；Preset the length Δ l of oblique line section, oblique line section thickness than γ, γ=h_1i/h_1ip.At the length of described variable-section steel sheet spring, width, installing space, rigidity Design required value, maximum load and allowable stress to, under stable condition, the reinforced few sheet variable-section steel sheet spring of root being designed.

For solving above-mentioned technical problem, the method for designing of the few sheet variable-section steel sheet spring of reinforcement end provided by the present invention, it is characterised in that adopt following design procedure:

(1) the equivalent one-chip root thickness h of few sheet variable-section steel sheet spring_eCalculating:

First, choosing the thickness of equivalent one-chip parabolic segment of few sheet variable-section steel sheet spring than β, wherein, the span of β is 0.5～0.55；Then, the half length L, half rigidity Design required value K according to the few sheet variable-section steel sheet spring of reinforcement end_M, width b, elastic modulus E, the length Δ l of default oblique line section, oblique line section thickness than γ, the half l of installing space₃, the root of parabolic segment is to the distance l of spring end points₂=L-l₃, the end of parabolic segment is to the distance l of spring end points_1p=β²l₂, the length l of end flat segments₁=l_1p-Δ l, the equivalent one-chip root thickness h to few sheet tapered spring_eIt is calculated, namely

$h_e=\sqrt[3]{K_M{G}_{x-E}};$

Wherein,

(2) the sheet number N and each leaf spring root thickness h of the few sheet variable-section steel sheet spring of reinforcement end₂Design:

Step A: determine the maximum allowable thickness [h of each leaf spring root thickness₂]:

Half length L according to the few sheet tapered spring of reinforcement end, width b, the half of suffered maximum load and single-ended point load P, allowable stress [σ], and calculated h in step (1)_e, it is determined that the maximum allowable thickness [h of each leaf spring root thickness₂], namely

$\[h_2\]=\frac{{\mathrm{bh}}_e^3\[\mathrm{\σ}\]}{6PL};$

Step B: tapered spring sheet number N and each leaf spring root thickness h₂Design:

Choosing the sheet number initial value N of the few sheet variable-section steel sheet spring of reinforcement end, wherein, N is the integer between 2～5；The root thickness of the few sheet variable-section steel sheet spring designed is equal, is namely equal to h₂；According to [the h determined in step A₂], and calculated h in step (1)_e, reinforcement end is lacked each leaf spring root thickness h of sheet variable-section steel sheet spring₂It is designed, namely

$h_2=\frac{1}{\sqrt[3]{N}}{h}_e;$

If h₂≤[h₂], then h₂Being each root thickness design load of the few sheet variable-section steel sheet spring of reinforcement end, corresponding leaf of spring number N is the design sheet number of the few sheet variable-section steel sheet spring of reinforcement end；

If h₂> [h₂], then take the sheet number N=N+1 of leaf spring, return and continue executing with step B, to the root thickness h increased in 1 situation₂It is designed, until working as h₂≤[h₂] time, sheet number and each root thickness design of the few sheet variable-section steel sheet spring of reinforcement end are complete；

(3) reinforcement end lacks the thickness of each spring end flat segments of sheet variable-section steel sheet spring and the design of length:

I step: the h obtained according to design in step (2)₂, it is determined that the thickness of the parabolic segment of the 1st leaf spring compares β₁, namely

${\mathrm{\β}}_1=\left\{\begin{array}{cc}0.60,& h_2\∈\[5,10\]mm\\ 0.55,& h_2\∈(10,15\]mm\\ 0.50,& h_2\∈(15,20\]mm\\ 0.45,& h_2\∈(20,25\]mm\\ 0.40,& h_2\∈(25,30\]mm\\ 0.35,& h_2\∈(30,35\]mm\end{array}\right.;$

Root according to parabolic segment is to the distance l of spring end points₂, the length Δ l of oblique line section, the thickness of oblique line section than γ, determined β₁, and the h that in step (2), design obtains₂, it is determined that the thickness h of the end flat segments of the 1st leaf spring₁₁With length l₁₁, respectively

h₁₁=β₁γh₂,

$l_{11}={\mathrm{\β}}_1^2{l}_2-\mathrm{\Δ}l;$

II step: according to β and the h determined in step (1)_e, the β that determines in I step₁, and N and the h that in step (2), design obtains₂, it is determined that the 2nd ..., the thickness ratio of the parabolic segment of N sheet leaf spring, namely

${\mathrm{\β}}_2={\mathrm{\β}}_3=...={\mathrm{\β}}_N=\sqrt[3]{\frac{{\mathrm{\β}}^3{h}_e^3-{\mathrm{\β}}_1^3{h}_2^3}{h_2^3(N-1)}};$

According to determined 2nd ..., the thickness of the parabolic segment of N sheet leaf spring compares β₂=β₃=...=β_N, the root of parabolic segment is to the distance l of spring end points₂, the length Δ l of oblique line section, the thickness of oblique line section is than γ, and the h that in step (2), design obtains₂, it is determined that the 2nd ..., the thickness of the end flat segments of N sheet leaf spring and length, respectively

$h_{12}=h_{13}=...=h_{1N}=\sqrt[3]{\frac{{\mathrm{\β}}^3{h}_e^3-{\mathrm{\β}}_1^3{h}_2^3}{h_2^3(N-1)}}{\mathrm{\γh}}_2,$

$l_{12}=l_{13}=...=l_{1N}={\left(\frac{{\mathrm{\β}}^3{h}_e^3-{\mathrm{\β}}_1^3{h}_2^3}{h_2^3(N-1)}\right)}^{\frac{2}{3}}{l}_2-\mathrm{\Δ}l;$

(4) each leaf spring diverse location thickness h of the few sheet variable-section steel sheet spring of reinforcement end_iThe design of (x):

Half length L according to the few sheet variable-section steel sheet spring of reinforcement end, the root of parabolic segment is to the distance l of spring end points₂, determined h in step (3)_1iAnd l_1i, and the h that in step (2), design is obtained₂, with spring end points for zero, reinforcement end is lacked each leaf spring various location thickness h of sheet variable-section steel sheet spring_iX () is designed, namely

$h_i\left(x\right)=\left\{\begin{array}{cc}{h}_{1i},& x\∈\[0,l_{1i}\]\\ \frac{{\mathrm{\β}}_i{h}_2-h_{1i}}{l_{1ip}-l_{1i}}x+\frac{h_{1i}{l}_{1ip}-{\mathrm{\β}}_i{h}_2{l}_{1i}}{l_{1ip}-l_{1i}},& x\∈(l_{1i},l_{1ip}\]\\ h_2\sqrt{\frac{x}{l_2}},& x\∈(l_{1ip},l_2\]\\ h_2,& x\∈(l_2,L\]\end{array}\right.;$

Wherein, l_1ip=β_i ²l₂, i=1,2 ..., N.

The present invention has the advantage that than prior art

Due to the deformation by the few sheet variable-section steel sheet spring of reinforcement end, the theories of computation such as rigidity, and lack sheet variable-section steel sheet spring equivalent thickness and split the restriction of design theory, so far not yet provide always easy, accurately, reliable method for designing, it is mostly ignore end to strengthen the impact of oblique line section at present, oblique line section is similar to the extension seeing end flat segments as, and think that the end of each such as is at the structure, the few sheet variable-section steel sheet spring of reinforcement end is carried out Approximate Design, therefore, hardly result in parameter designing value accurately and reliably, can not carry out the end of few sheet tapered spring strengthening design.Emulation along with computer and finite element emulation software, once few sheet variable-section steel sheet spring of reinforcement end was adopted ANSYS modeling and simulating method despite people at present, but the deformation of the few sheet variable-section steel sheet spring of the reinforcement end of given design structure or rigidity can only be carried out simulating, verifying by the method, it is not provided that accurate analytical design method formula, more can not meet vehicle fast development and the requirement to suspension leaf spring modernization CAD design software development.

The present invention is according to the design rigidity of leaf spring and mounting structure size, the end thickness of selected equivalent one-chip reinforcement end variable-section steel sheet spring compares β, the maximum gauge of oblique line section and the ratio γ of minimum thickness are strengthened in end, the length Δ l of oblique line section, and the Leading Edge Deformation coefficient of parabolic type variable-section steel sheet spring, first, to equivalent one-chip reinforcement end variable-section steel sheet spring root thickness h_eIt is designed；Then, according to the half P of leaf spring maximum load and allowable stress [σ], the root maximum allowable thickness [h to the few sheet variable-section steel sheet spring of reinforcement end₂] be calculated；Subsequently, the root thickness h according to the few sheet variable-section steel sheet spring of equivalent one-chip reinforcement end_e, utilize the equivalent thickness computing formula of superposition steel plate lap, the design sheet number N and each root thickness h to the few sheet variable-section steel sheet spring of reinforcement end₂It is designed；Finally, the design load β h according to the end flat segments thickness of the few sheet variable-section steel sheet spring of equivalent one-chip equivalence reinforcement end_e, utilize the equivalent thickness computing formula of superposition steel plate lap, the thickness h to each end flat segments of the few sheet variable-section steel sheet spring of reinforcement end_1iWith length l_1iBe designed.

By design example and ANSYS simulating, verifying, the method can obtain, and reinforcement end accurate, reliable lacks the parameter designing value of sheet variable-section steel sheet spring, provide reliable method for designing for the few sheet variable-section steel sheet spring of reinforcement end, and establish reliable technical foundation for the exploitation of variable-section steel sheet spring CAD software.Utilize the method, design level and the performance of the few sheet variable-section steel sheet spring of vehicle suspension can be improved, reduce bearing spring quality and cost, improve conevying efficiency and the driving safety of vehicle, and guaranteeing to meet under the premise that rigidity Design requires, improving the stress state of few flat spring；Meanwhile, also 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 accompanying drawing.

Fig. 1 is the design flow diagram of the few sheet variable-section steel sheet spring of reinforcement end；

Fig. 2 is the half symmetrical structure schematic diagram of the single-leaf spring of the few sheet variable-section steel sheet spring of reinforcement end；

Fig. 3 is the structural parameters figure of the 1st reinforcement end variable-section steel sheet spring designed by embodiment one；

Fig. 4 is the structural parameters figure of the 2nd reinforcement end variable-section steel sheet spring designed by embodiment one；

Fig. 5 is the deformation simulation cloud atlas of the few sheet variable-section steel sheet spring of reinforcement end designed by embodiment one；

Fig. 6 is the structural parameters figure of the 1st reinforcement end variable-section steel sheet spring designed by embodiment two；

Fig. 7 is the structural parameters figure of the 1st reinforcement end variable-section steel sheet spring designed by embodiment two；

Fig. 8 is the deformation simulation cloud atlas of the few sheet variable-section steel sheet spring of reinforcement end designed by embodiment two.

Specific embodiments

By the examples below the present invention is described in further detail.

Fig. 1 is the design flow diagram of the present invention, below in conjunction with embodiment, step is described in detail:

Embodiment one: the structural representation of the half of the single-leaf spring of the few sheet variable-section steel sheet spring of certain reinforcement end as in figure 2 it is shown, wherein, the half length L=575mm of each leaf spring, width b=60mm, elastic modulus E=200GPa, the half l of installing space₃=55mm, the thickness of oblique line section is than γ=1.17, the length Δ l=30mm of oblique line section, the half of the maximum load of leaf spring and single-ended point load P=1200N, allowable stress [σ]=500MPa.The half rigidity Design required value K of the few sheet variable-section steel sheet spring of this reinforcement end_M=24N/mm, is designed the few sheet variable-section steel sheet spring of this reinforcement end.

The method for designing of the few sheet variable-section steel sheet spring of the reinforcement end that present example provides, its design cycle is as it is shown in figure 1, specifically comprise the following steps that

(1) the equivalent one-chip root thickness h of the few sheet variable-section steel sheet spring of reinforcement end_eCalculating:

First, the parabola branch thickness of equivalent one-chip of the few sheet variable-section steel sheet spring of reinforcement end is chosen than β=0.50；Then, the half rigidity Design required value K according to the few sheet tapered spring of reinforcement end_M=24N/mm, half length L=575mm, width b=60mm, elastic modulus E=200GPa, the thickness of oblique line section is than γ=1.17, the length Δ l=30mm of oblique line section, the half l of installing space₃=55mm, the root of parabolic segment is to the distance l of spring end points₂=L-l₃=520mm, the end of parabolic segment is to the distance l of spring end points_1p=β²l₂=130mm, the length l of end flat segments₁=l_1p-Δ l=100mm, is calculated the root thickness of the equivalent one-chip reinforcement end variable-section steel sheet spring meeting rigidity requirement, namely

$h_e=\sqrt[3]{K_M{G}_{x-E}}=13.51mm;$

Wherein,

(2) the sheet number N and each root thickness h of the few sheet variable-section steel sheet spring of reinforcement end₂Design:

Step A: determine the maximum allowable thickness [h of each flat spring root thickness₂]:

Half length L=575mm according to the few sheet tapered spring of reinforcement end, width b=60mm, the half of maximum load and single-ended point load P=1200N, allowable stress [σ]=500MPa, and calculated h in step (1)_e=13.51mm, it is determined that the maximum allowable thickness [h of each tapered spring root thickness₂], namely

$\[h_2\]=\frac{{\mathrm{bh}}_e^3\[\mathrm{\σ}\]}{6PL}=17.87mm;$

Step B: tapered spring sheet number N and each root thickness h₂Design:

Choosing the initial value N=2 of the sheet number of the few sheet variable-section steel sheet spring of reinforcement end, wherein, N is the integer between 2～5；The root thickness of designed few sheet variable-section steel sheet spring is equal, is namely equal to h₂；According to [the h determined in step A₂]=17.87mm, and calculated h in step (1)_e=13.51mm, each root thickness h to the few sheet variable-section steel sheet spring of reinforcement end₂It is designed, namely

$h_2=\frac{1}{\sqrt[3]{N}}{h}_e=10.72mm;$

Because h₂≤[h₂], then the root thickness design load h of each flat spring of the few sheet variable-section steel sheet spring of reinforcement end₂=10.72mm, leaf of spring number N=2；

(3) reinforcement end lacks the thickness of each end flat segments of sheet variable-section steel sheet spring and the design of length:

I step: the h obtained according to design in step (2)₂=10.72mm, it is determined that the thickness of the 1st leaf spring parabolic segment compares β₁, namely

β₁=0.55；

Root according to parabolic segment is to the distance l of spring end points₂=520mm, the length Δ l=30mm of oblique line section, the thickness of oblique line section is than γ=1.17, the h that in step (2), design obtains₂=10.72mm, and the thickness of the parabolic segment of the determine the 1st tapered spring compares β₁=0.55, it is determined that the thickness h of the end flat segments of the 1st tapered spring₁₁With length l₁₁, respectively

h₁₁=β₁γh₂=6.90mm,

$l_{11}={\mathrm{\β}}_1^2{l}_2-\mathrm{\Δ}l=127.30mm;$

II step: according to the thickness of the parabolic segment of equivalent one-chip tapered spring determined in step (1) than β=0.50 and root thickness h_eThe β determined in=13.51mm, I step₁=0.55, and N=2 and the h that in step (2), design obtains₂=10.72mm, it is determined that the thickness ratio of the parabolic segment of the 2nd tapered spring, namely

${\mathrm{\β}}_2=\sqrt[3]{\frac{{\mathrm{\β}}^3{h}_e^3-{\mathrm{\β}}_1^3{h}_2^3}{h_2^3(N-1)}}=0.44;$

Thickness according to determined 2nd tapered spring parabolic segment compares β₂=0.44, the root of parabolic segment is to the distance l of spring end points₂=520mm, the length Δ l=30mm of oblique line section, the thickness of oblique line section is than γ=1.17, and the h that in step (2), design obtains₂=10.72mm, it is determined that the thickness of the end flat segments of the 2nd tapered spring and length, respectively

$h_{12}=\sqrt[3]{\frac{{\mathrm{\β}}^3{h}_e^3-{\mathrm{\β}}_1^3{h}_2^3}{h_2^3(N-1)}}{\mathrm{\γh}}_2=5.52mm,$

$l_{12}={\left(\frac{{\mathrm{\β}}^3{h}_e^3-{\mathrm{\β}}_1^3{h}_2^3}{h_2^3(N-1)}\right)}^{\frac{2}{3}}{l}_2-\mathrm{\Δ}l=70.67mm;$

(4) each diverse location thickness h of the few sheet variable-section steel sheet spring of reinforcement end_iThe design of (x):

Half length L=575mm according to the few sheet tapered spring of reinforcement end, the root of parabolic segment is to the distance l of spring end points₂=520mm, determined h in step (3)₁₁=6.90mm and l₁₁=127.30mm, h₁₂=5.52mm and l₁₂=70.67mm, and the h that in step (2), design is obtained₂=10.72mm, the diverse location thickness h with leaf spring end points for zero, to the few sheet variable-section steel sheet spring of two panels reinforcement end₁(x)、h₂X () is designed value respectively, namely

$h_1\left(x\right)=\left\{\begin{array}{cc}6.90mm,& x\∈\[0,127.30\]mm\\ (-33.47x+11.16)mm,& x\∈(127.30,157.30\]mm\\ 10.72\×\sqrt{\frac{x}{520}}mm,& x\∈(157.30,520\]mm\\ 10.72mm,& x\∈(520,575\]mm\end{array}\right.,$

$h_2\left(x\right)=\left\{\begin{array}{cc}5.52mm,& x\∈\[0,70.67\]mm\\ (-26.77x+7.41)mm,& x\∈(70.67,100.67\]mm\\ 10.72\×\sqrt{\frac{x}{520}}mm,& x\∈(100.67,520\]mm\\ 10.72mm,& x\∈(520,575\]mm\end{array}\right.;$

Wherein, the 1st tapered spring is in the thickness h of oblique line section and parabolic segment diverse location x place₁X (), shown in Table one；2nd tapered spring is in the thickness h of oblique line section and parabolic segment diverse location x place₂X (), shown in Table two；

The 1st tapered spring of table 1 is in the thickness h of oblique line section and parabolic segment diverse location x place₁(x)

Position x/ (mm)	520	487.30	447.30	407.30	367.30	327.30	287.30	247.30	207.30	167.30	127.30
												Thickness h1(x)/(mm)	10.72	10.38	9.94	9.49	9.01	8.50	7.97	7.39	6.77	6.08	6.90

The 2nd tapered spring of table 2 is in the thickness h of oblique line section and parabolic segment diverse location x place₂(x)

Position x/ (mm)	520	475.67	430.67	385.67	340.67	295.67	250.67	205.67	160.67	115.67	70.67
												Thickness h2(x)/(mm)	10.72	10.25	9.76	9.23	8.68	8.08	7.44	6.74	5.96	5.06	5.52

Design the structural parameters of obtained the 1st slice reinforcement end variable-section steel sheet spring, as shown in Figure 3；The structural parameters of the 2nd reinforcement end variable-section steel sheet spring, as shown in Figure 4.

Utilize ANSYS finite element emulation software, according to the structural parameters and the material characteristic parameter that design the few sheet variable-section steel sheet spring of the reinforcement end obtained, set up ANSYS phantom, grid division, and at the root applying fixed constraint of phantom, concentrfated load P=1200N is applied at end points, the deformation of the few sheet variable-section steel sheet spring of reinforcement end is carried out ANSYS emulation, obtained deformation simulation cloud atlas, as shown in Figure 5, wherein, this leaf spring at the maximum deformation quantity f=49.58mm at end position place, can the half rigidity of this leaf spring be therefore K_M=P/f=24.20N/mm.

It can be seen that the ANSYS simulating, verifying value K of this leaf spring half rigidity_M=24.20N/mm, with designing requirement value K_M=24N/mm matches, and relative deviation is only 0.83%；Result shows that the method for designing of the few sheet variable-section steel sheet spring of reinforcement end that this invention provides is correct, and parameter designing value is accurately and reliably.

Embodiment two: the half symmetrical structure schematic diagram of the single-leaf spring of the few sheet variable-section steel sheet spring of certain reinforcement end, as in figure 2 it is shown, wherein, the half length L=600mm of each leaf spring, width b=60mm, elastic modulus E=200GPa, the half l of installing space₃=60mm, the thickness of oblique line section is than γ=1.17, the length Δ l=30mm of oblique line section, the half of leaf spring maximum load and single-ended point load P=3000N, allowable stress [σ]=500MPa.The half rigidity Design required value K of the few sheet variable-section steel sheet spring of this reinforcement end_M=46N/mm, is designed the few sheet variable-section steel sheet spring of this reinforcement end.

Present example is adopted the method for designing identical with embodiment one and step, and specific design step is as follows:

(1) the equivalent one-chip root thickness h of the few sheet variable-section steel sheet spring of reinforcement end_eCalculating:

First, the thickness of parabolic segment of the equivalent one-chip tapered spring of the few sheet variable-section steel sheet spring of reinforcement end is chosen than β=0.50；Then, the half rigidity Design required value K according to the few sheet tapered spring of reinforcement end_M=46N/mm, half length L=600mm, width b=60mm, elastic modulus E=200GPa, the thickness of oblique line section is than γ=1.17, the length Δ l=30mm of oblique line section, the half l of installing space₃=60mm, the root of parabolic segment is to the distance l of spring end points₂=L-l₃=540mm, the end of parabolic segment is to the distance l of spring end points_1p=β²l₂=135mm, the length l of end flat segments₁=l_1p-Δ l=105mm, is calculated the root thickness of the equivalent one-chip tapered spring meeting rigidity requirement, namely

$h_e=\sqrt[3]{K_M{G}_{x-E}}=17.48mm;$

Wherein,

(2) the sheet number N and each root thickness h of the few sheet variable-section steel sheet spring of reinforcement end₂Design:

Step A: determine the maximum allowable thickness [h of each tapered spring root thickness₂]:

Half length L=600mm according to the few sheet variable-section steel sheet spring of reinforcement end, width b=60mm, the half of suffered maximum load and single-ended point load P=3000N, allowable stress [σ]=500MPa, and step (1) calculates obtained h_e=17.48mm, it is determined that the maximum allowable thickness [h of each tapered spring root thickness₂], namely

$\[h_2\]=\frac{{\mathrm{bh}}_e^3\[\mathrm{\σ}\]}{6PL}=14.84mm;$

Step B: the sheet number N and each root thickness h of variable-section steel sheet spring₂Design:

Choosing the sheet number initial value N=2 of the few sheet variable-section steel sheet spring of reinforcement end, wherein, N is the integer between 2～5；According to [the h determined in step A₂]=14.84mm, and calculated h in step (1)_e=17.48mm, each root thickness h to the few sheet variable-section steel sheet spring of reinforcement end₂It is designed, namely

$h_2=\frac{1}{\sqrt[3]{N}}{h}_e=13.87mm;$

Because h₂≤[h₂], then each root thickness design load h of the few sheet variable-section steel sheet spring of reinforcement end₂=13.87mm, leaf of spring number N=2；

(3) reinforcement end lacks the thickness of each end flat segments of sheet variable-section steel sheet spring and the design of length:

I step: the h obtained according to design in step (2)₂=13.87mm, it is determined that the thickness of the parabolic segment of the 1st tapered spring compares β₁, namely

β₁=0.55；

Root according to parabolic segment is to the distance l of spring end points₂=540mm, the length Δ l=30mm of oblique line section, the thickness of oblique line section is than γ=1.17, the h that in step (2), design obtains₂=13.87mm and β₁=0.55, it is determined that the thickness h of the end flat segments of the 1st tapered spring₁₁With length l₁₁, respectively

h₁₁=β₁γh₂=8.93mm,

$l_{11}={\mathrm{\β}}_1^2{l}_2-\mathrm{\Δ}l=133.35mm;$

II step: according to determined β=0.50 and h in step (1)_eDetermined β in=17.48mm, I step₁=0.55, and N=2 and the h that in step (2), design obtains₂=13.87mm, it is determined that the thickness ratio of the parabolic segment of the 2nd tapered spring, namely

${\mathrm{\β}}_2=\sqrt[3]{\frac{{\mathrm{\β}}^3{h}_e^3-{\mathrm{\β}}_1^3{h}_2^3}{h_2^3(N-1)}}=0.44;$

The thickness of the parabolic segment according to determined 2nd tapered spring compares β₂=0.44, the root of parabolic segment is to the distance l of spring end points₂=540mm, the length Δ l=30mm of oblique line section, the thickness of oblique line section is than γ=1.17, and the h that in step (2), design obtains₂=13.87mm, it is determined that the thickness of the end flat segments of the 2nd tapered spring and length, respectively

$h_{12}=\sqrt[3]{\frac{{\mathrm{\β}}^3{h}_e^3-{\mathrm{\β}}_1^3{h}_2^3}{h_2^3(N-1)}}{\mathrm{\γh}}_2=7.14mm,$

$l_{12}={\left(\frac{{\mathrm{\β}}^3{h}_e^3-{\mathrm{\β}}_1^3{h}_2^3}{h_2^3(N-1)}\right)}^{\frac{2}{3}}{l}_2-\mathrm{\Δ}l=74.54mm;$

(4) each diverse location thickness h of the few sheet variable-section steel sheet spring of reinforcement end_iThe design of (x):

Half length L=600mm according to the few sheet variable-section steel sheet spring of reinforcement end, the root of parabolic segment is to the distance l of spring end points₂=540mm, the h determined in step (3)₁₁=8.93mm and l₁₁=133.35mm, h₁₂=7.14mm and l₁₂=74.54mm, and the h that in step (2), design is obtained₂=13.87mm, with spring end points for zero, can obtain designed two panels reinforcement end variable-section steel sheet spring, in diverse location thickness h₁(x)、h₂The design load of (x), respectively

$h_1\left(x\right)=\left\{\begin{array}{cc}8.93mm,& x\∈\[0,133.35\]mm\\ (-43.38x+14.72)mm,& x\∈(133.35,163.35\]mm\\ 13.87\×\sqrt{\frac{x}{540}}mm,& x\∈(163.35,540\]mm\\ 13.87mm,& x\∈(540,600\]mm\end{array}\right.,$

$h_2\left(x\right)=\left\{\begin{array}{cc}7.14mm,& x\∈\[0,74.54\]mm\\ (-34.57x+9.72)mm,& x\∈(74.54,104.54\]mm\\ 13.87\×\sqrt{\frac{x}{540}}mm,& x\∈(104.54,540\]mm\\ 13.87mm,& x\∈(540,600\]mm\end{array}\right.;$

Wherein, the 1st tapered spring is in the thickness h of oblique line section and parabolic segment diverse location x place₁X (), shown in Table three；2nd tapered spring is in the thickness h of oblique line section and parabolic segment diverse location x place₂X (), shown in Table four；

The 1st tapered spring of table 3 is in the thickness h of oblique line section and parabolic segment diverse location x place₁(x)

Position x/ (mm)	540	538.35	493.35	448.35	403.35	358.35	313.35	268.35	223.35	178.35	133.35
												Thickness h1(x)/(mm)	13.87	13.85	13.26	12.64	11.99	11.30	10.57	9.78	8.92	7.97	8.93

The 2nd tapered spring of table 4 is in the thickness h of oblique line section and parabolic segment diverse location x place₂(x)

Position x/ (mm)	540	524.54	474.54	424.54	374.54	324.54	274.54	224.54	174.54	124.54	74.54
												Thickness h2(x)/(mm)	13.87	13.67	13.00	12.30	11.55	10.75	9.89	8.94	7.89	6.66	7.14

Design the structural parameters of obtained the 1st slice reinforcement end variable-section steel sheet spring, as shown in Figure 6；The structural parameters of the 2nd reinforcement end variable-section steel sheet spring, as shown in Figure 7.

Utilize ANSYS finite element emulation software, according to the structural parameters and the material characteristic parameter that design the few sheet variable-section steel sheet spring of the reinforcement end obtained, set up ANSYS phantom, grid division, and at the root applying fixed constraint of phantom, concentrfated load P=3000N is applied at end points, the deformation of the few sheet variable-section steel sheet spring of this reinforcement end is carried out ANSYS emulation, obtained deformation simulation cloud atlas, as shown in Figure 8, wherein, this leaf spring is at the maximum deformation quantity f=64.84mm at end points place, namely the half rigidity value of the few sheet variable-section steel sheet spring of this reinforcement end is K_M=P/f=46.27N/mm.

It can be seen that the ANSYS simulating, verifying value K of this leaf spring half rigidity_M=46.27N/mm, with designing requirement value K_M=46N/mm matches, and relative deviation is only 0.59%；Result shows that the method for designing of the few sheet variable-section steel sheet spring of reinforcement end that this invention provides is correct, and parameter designing value is accurately and reliably.

Claims (1)

1. the method for designing of the few sheet variable-section steel sheet spring of reinforcement end, described variable-section steel sheet spring includes at least two panels leaf spring, the symmetrical structure that every leaf spring is is axle center with central bolt mounting hole, the half symmetrical structure of the centre bore side of leaf spring is made up of root flat segments, parabolic segment, oblique line section and end flat segments 4 sections；It is provided with oblique line section between end flat segments and parabolic segment, booster action is played in the end of leaf spring；Each spring end flat segments is non-waits structure, and namely the thickness of the end flat segments of the 1st leaf spring and length are more than the thickness of other each leaf spring and length, the requirement complicated to meet the 1st spring end stress；At the length of described variable-section steel sheet spring, width, installing space, rigidity Design required value, maximum load and allowable stress to, under stable condition, the reinforced few sheet variable-section steel sheet spring of root being designed, specific design step is as follows:

(1) the equivalent one-chip root thickness h of few sheet variable-section steel sheet spring_eCalculating:

First, choosing the thickness of equivalent one-chip parabolic segment of few sheet variable-section steel sheet spring than β, wherein, the span of β is 0.5～0.55；Then, the half length L according to few sheet variable-section steel sheet spring, the half l of installing space₃, half rigidity Design required value K_M, width b, elastic modulus E；The length Δ l of oblique line section, the thickness of oblique line section preset compare γ；The root of parabolic segment is to the distance l of spring end points₂=L-l₃, the end of parabolic segment is to the distance l of spring end points_1p=β²l₂, the length l of end flat segments₁=l_1p-Δ l, the equivalent one-chip root thickness h to few sheet tapered spring_eIt is calculated, namely

$h_e=\sqrt[3]{K_M{G}_{x-E}};$

Wherein,

(2) the sheet number N and each leaf spring root thickness h of the few sheet variable-section steel sheet spring of reinforcement end₂Design:

Step A: determine the maximum allowable thickness [h of each tapered spring root thickness₂]:

Half length L according to the few sheet tapered spring of reinforcement end, width b, the half of suffered maximum load and single-ended point load P, allowable stress [σ], and calculated h in step (1)_e, it is determined that the maximum allowable thickness [h of each leaf spring root thickness₂], namely

$\[h_2\]=\frac{{\mathrm{bh}}_e^3\[\mathrm{\σ}\]}{6PL};$

Step B: tapered spring sheet number N and each leaf spring root thickness h₂Design:

Choosing the sheet number initial value N of the few sheet variable-section steel sheet spring of reinforcement end, wherein, N is the integer between 2～5；The root thickness of the few sheet variable-section steel sheet spring designed is equal, is namely equal to h₂；According to [the h determined in step A₂], and calculated h in step (1)_e, reinforcement end is lacked each leaf spring root thickness h of sheet variable-section steel sheet spring₂It is designed, namely

$h_2=\frac{1}{\sqrt[3]{N}}{h}_e;$

If h₂≤[h₂], then h₂Being each root thickness design load of the few sheet variable-section steel sheet spring of reinforcement end, corresponding sheet number N is the design sheet number of the few sheet variable-section steel sheet spring of reinforcement end；

If h₂> [h₂], then take the sheet number N=N+1 of leaf spring, return and continue executing with step B, to the root thickness h increased in 1 situation₂It is designed, until working as h₂≤[h₂] time, the sheet number N and each root thickness h of the few sheet variable-section steel sheet spring of reinforcement end₂Design complete；

(3) reinforcement end lacks the thickness of each spring end flat segments of sheet variable-section steel sheet spring and the design of length:

I step: the h obtained according to design in step (2)₂, it is determined that the thickness of the parabolic segment of the 1st leaf spring compares β₁, namely

${\mathrm{\β}}_1=\left\{\begin{array}{cc}0.60,& h_2\∈\[5,10\]mm\\ 0.55,& h_2\∈(10,15\]mm\\ 0.50,& h_2\∈(15,20\]mm\\ 0.45,& h_2\∈(20,25\]mm\\ 0.40,& h_2\∈(25,30\]mm\\ 0.35,& h_2\∈(30,35\]mm\end{array}\right.;$

Root according to parabolic segment is to the distance l of spring end points₂, the length Δ l of oblique line section, the thickness of oblique line section than γ, determined β₁, and the h that in step (2), design obtains₂, it is determined that the thickness h of the end flat segments of the 1st leaf spring₁₁With length l₁₁, respectively

h₁₁=β₁γh₂,

$l_{11}={\mathrm{\β}}_1^2{l}_2-\mathrm{\Δ}l;$

II step: according to β and the h determined in step (1)_e, the β that determines in I step₁, and N and the h that in step (2), design obtains₂, it is determined that the 2nd ..., the thickness ratio of the parabolic segment of N sheet leaf spring, namely

${\mathrm{\β}}_2={\mathrm{\β}}_3=...={\mathrm{\β}}_N=\sqrt[3]{\frac{{\mathrm{\β}}^3{h}_e^3-{\mathrm{\β}}_1^3{h}_2^3}{h_2^3(N-1)}};$

According to determined 2nd ..., the thickness of the parabolic segment of N sheet leaf spring compares β₂=β₃=...=β_N, the root of parabolic segment is to the distance l of spring end points₂, the length Δ l of oblique line section, the thickness of oblique line section is than γ, and the h that in step (2), design obtains₂, it is determined that the 2nd ..., the thickness of the end flat segments of N sheet leaf spring and length, respectively

$h_{12}=h_{13}=...=h_{1N}=\sqrt[3]{\frac{{\mathrm{\β}}^3{h}_e^3-{\mathrm{\β}}_1^3{h}_2^3}{h_2^3(N-1)}}{\mathrm{\γh}}_2,$

$l_{12}=l_{13}=...=l_{1N}={\left(\frac{{\mathrm{\β}}^3{h}_e^3-{\mathrm{\β}}_1^3{h}_2^3}{h_2^3(N-1)}\right)}^{\frac{2}{3}}{l}_2-\mathrm{\Δ}l;$

(4) each leaf spring diverse location thickness h of the few sheet variable-section steel sheet spring of reinforcement end_iThe design of (x):

Half length L according to the few sheet variable-section steel sheet spring of reinforcement end, the root of parabolic segment is to the distance l of spring end points₂, determined h in step (3)_1iAnd l_1i, and the h that in step (2), design is obtained₂, with spring end points for zero, reinforcement end is lacked the thickness h at each leaf spring diverse location x place of sheet variable-section steel sheet spring_iX () is designed, namely

$h_i\left(x\right)=\left\{\begin{array}{cc}{h}_{1i},& x\∈\[0,l_{1i}\]\\ \frac{{\mathrm{\β}}_i{h}_2-h_{1i}}{l_{1ip}-l_{1i}}x+\frac{h_{1i}{l}_{1ip}-{\mathrm{\β}}_i{h}_2{l}_{1i}}{l_{1ip}-l_{1i}},& x\∈(l_{1i},l_{1ip}\]\\ h_2\sqrt{\frac{x}{l_2}},& x\∈(l_{1ip},l_2\]\\ h_2,& x\∈(l_2,L\]\end{array}\right.;$

Wherein, l_1ip=β_i ²l₂, i=1,2 ..., N.