CN105550483A - End-heterogeneous taper slanting leaf spring with variable cross-section - Google Patents

Abstract

The invention relates to a design method for an end-heterogeneous taper slanting leaf spring with variable cross-section, and belongs to the technical field of suspension leaf springs. Based on a mounting structure and rigidity design required values of the leaf spring, root thickness he of the equivalent single slanting leaf spring with variable cross-section is determined firstly, and based on allowable stress, the maximum allowable thickness [h2] of the taper slanting leaf spring with variable cross-section is determined; then, based on he and [h2], piece number N and the root thickness h2 of the taper slanting leaf spring with variable cross-section, and the thickness h1i and the length l1i of a straight section at an end of each piece are designed. It can be known from ANSYS simulation verification that accurate and reliable parameter design values of end-heterogeneous taper slanting leaf spring with variable cross-section can be obtained by utilizing the method, the product design level and performance can be improved, the spring weight and cost can be lowered, and the vehicle running smoothness can be improved; at the same time, the designing and testing expenses are further reduced, and the product developing speed is increased.

Description

The non-method for designing waiting the few sheet bias type variable-section steel sheet spring of structure in end

Technical field

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

Background technology

Compared with few sheet variable-section steel sheet spring superposes leaf spring with multi-disc, due to its reasonable stress, stress loading is tending towards balanced, and saves material, realizes vehicle lightweight, reduce wheel dynamic load, improve vehicle safety, also save fuel oil simultaneously, improve vehicle transport efficiency, therefore there is good economic benefit and social benefit, caused showing great attention to of vehicle expert.Due to the 1st its stressed complexity of few-leaf-spring, not only bear vertical load, also bear torsional load and longitudinal loading simultaneously, therefore, the end thickness of the 1st leaf spring designed by reality, usual more each than other partially thicker, namely in actual design with in producing, mostly adopts the non-few sheet variable-section steel sheet spring waiting structure in end.The variable cross section of current leaf spring mainly contains two types, and one is parabolic type, and another is bias type, wherein, and more reasonable than bias type of Parabolic stress loading.But, because parabolic type processing technology is complicated, need complexity, expensive process equipment, bias type variable-section steel sheet spring then processing technology is simple, only need simple equipment just can process, therefore, meeting under stress intensity condition, by the variable-section steel sheet spring of available bias type, replace Parabolic variable-section steel sheet spring.

Although previously, once someone gave the method for designing of few sheet bias type variable-section steel sheet spring, such as, Peng Mo, high army is once in " automobile engineering ", (the 14th volume) the 3rd phase in 1992, propose the design and calculation method of Varied section leaf spring, the method mainly designs for few sheet bias type variable-section steel sheet spring of the structures such as end, and its weak point to meet the non-designing requirement waiting few sheet bias type variable-section steel sheet spring of structure in end.For the non-few sheet bias type variable-section steel sheet spring waiting structure in end, due to by distortion, rigidity, the equivalent thickness theory of computation and fractionation design theory restriction, so far easy, accurate, reliable method for designing always is not yet provided, mostly ignore the non-impact waiting structure in end at present, by structure methods for designing such as ends, Approximate Design is carried out to the non-few sheet bias type variable-section steel sheet spring of structure that waits in end, therefore, is difficult to obtain parameter designing value accurately and reliably.Along with the development of computing machine and finite element emulation software, possessor once adopted ANSYS modeling and simulating method to the non-few sheet bias type variable-section steel sheet spring of structure that waits in end to the greatest extent at present, but the method only can carry out simulating, verifying to the distortion of leaf spring or rigidity providing actual design structure, accurate analytical design method formula can not be provided, more can not meet fast-developing and that suspension leaf spring modernization CAD design software the is developed requirement of vehicle.

Therefore, a kind of method for designing of few sheet bias type variable-section steel sheet spring of the structures such as end is non-accurately, reliably must be set up, meet Vehicle Industry fast development and the requirement to suspension Precise Design for Laminated Spring, improve design level, the product quality and performances of variable-section steel sheet spring, improve vehicle ride performance and security; Meanwhile, reduce design and testing expenses, accelerate product development speed.

Summary of the invention

For the defect existed in above-mentioned prior art, technical matters to be solved by this invention is to provide the method for designing of the few sheet bias type variable-section steel sheet spring of the structures such as a kind of easy, reliable end is non-, wherein, the non-variable cross section waiting the few sheet variable-section steel sheet spring of structure in end is bias type, namely be made up of root flat segments, oblique line section, end flat segments three sections, and each end flat segments is non-structure such as grade, the i.e. thickness of end flat segments of the 1st and length, be greater than other thickness of each and length, its design flow diagram, as shown in Figure 1; As shown in Figure 2, wherein, L is the half of its length to the structural representation of the half of the single-leaf spring of few sheet bias type variable-section steel sheet spring such as end structure such as non-grade, l ₃for the half of installing space, b is width, h ₂for root thickness, l _1i, h _1ibe respectively end thickness and the flat segments length of the i-th flat spring.

For solving the problems of the technologies described above, the non-method for designing waiting the few sheet bias type variable-section steel sheet spring of structure in end provided by the present invention, is characterized in that adopting following design procedure:

(1) the equivalent one-chip root thickness h of few sheet bias type variable-section steel sheet spring _ecalculating:

First, choose the end thickness of monolithic bias type variable-section steel sheet spring and the ratio of root thickness, namely end thickness is than β=0.55; Then, according to the half rigidity Design required value K of few sheet bias type variable-section steel sheet spring _m, half length L, width b, the half l of installing space ₃, oblique line root is to the distance l of spring end points ₂=L-l ₃, elastic modulus E, calculates the equivalent one-chip root thickness of the few sheet bias type variable-section steel sheet spring meeting rigidity requirement, namely

Wherein, $\begin{array}{c}{h}_e=\sqrt[3]{K_M{G}_{x-D}};\\ G_{x-D}=\frac{4}{Ed}(L^3-l_2^3)+\frac{6l_2^3{(\mathrm{\β}+1)}^2\[3(\mathrm{\β}-1)-2\ln \mathrm{\β}(1+\mathrm{\β})\]}{Eb}+\frac{4{\mathrm{\β}}^3{l}_2^3}{Eb};\end{array}$

(2) sheet number N and each root thickness h of sheet bias type variable-section steel sheet spring is lacked ₂design:

Step A: the maximum allowable thickness [h determining each flat spring root thickness ₂]:

According to the half length L of few sheet bias type variable-section steel sheet spring, width b, suffered half load p, safe allowable stress [σ], and the h calculated in step (1) _e, determine the maximum allowable thickness [h of each flat spring root thickness ₂], namely

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

Step B: leaf of spring number N and each root thickness h ₂design:

Choose the non-sheet number initial value N=2 waiting the few sheet bias type variable-section steel sheet spring of structure in end, wherein, N is the integer between 2 ~ 5; The root thickness of designed few sheet bias type variable-section steel sheet spring is equal, namely all equals h ₂; According to [the h determined in step A ₂], and the h calculated in step (1) _e, to the non-each root thickness h waiting the few sheet bias type variable-section steel sheet spring of structure in end ₂design, namely

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

If h ₂≤ [h ₂], then h ₂be the non-each root thickness design load waiting the few sheet bias type variable-section steel sheet spring of structure in end, corresponding N is the sheet number design load of few sheet bias type variable-section steel sheet spring;

If h ₂> [h ₂], then get the sheet number N=N+1 of leaf spring, return and continue to perform step B, to the root thickness h in increase by 1 situation ₂design, until work as h ₂≤ [h ₂] time, sheet number and each root thickness design of few sheet bias type variable-section steel sheet spring are complete;

(3) non-each end flat segments thickness of few sheet bias type variable-section steel sheet spring and the design of length waiting structure in end:

I step: according to designing the h obtained in step (2) ₂, determine that the end thickness of the 1st leaf spring compares β ₁, namely

${\mathrm{\β}}_1=\{\begin{array}{cc}0.65& ,h_2\∈\[5,10\]mm\\ 0.60& ,h_2\∈(10,15\]mm\\ 0.55& ,h_2\∈(15,20\]mm\\ 0.50& ,h_2\∈(20,25\]mm\\ 0.45& ,h_2\∈(25,30\]mm\\ 0.40& ,h_2\∈(30,35\]mm\end{array};$

According to the distance l of oblique line root to spring end points ₂, in step (2), design the h obtained ₂, and the end thickness of determined 1st leaf spring compares β ₁, determine the end flat segments thickness h of the 1st leaf spring ₁₁with length l ₁₁, be respectively

h ₁₁＝β ₁h ₂，

$l_{11}={\mathrm{\β}}_1^2{l}_2;$

II step: the end thickness according to the 1st flat spring determined in I step compares β ₁, the end thickness determined in step (1) is than β and h _e, and in step (2), design the leaf of spring number N and each root thickness h that obtain ₂, determine the 2nd, the 3rd ..., the end thickness ratio of N flat 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 3rd ..., the Thickness Ratio β of N flat spring ₂=β ₃=...=β _n, oblique line root is to the distance l of spring end points ₂, and in step (2), design the h obtained ₂, determine the 2nd, the 3rd ..., the end flat segments thickness of N flat spring and length, be respectively

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

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

(4) the non-each diverse location thickness h waiting few sheet bias type variable-section steel sheet spring of structure in end _ithe design of (x):

According to the half length L of few sheet bias type variable-section steel sheet spring, oblique line root is to the distance l of spring end points ₂, the end thickness of each flat spring determined in step (3) and flat segments length, and in step (2), design each flat spring root thickness h obtained ₂, take spring free end as true origin, the non-each diverse location x place thickness h waiting the few sheet bias type variable-section steel sheet spring of structure in end can be obtained _ithe design load of (x), namely

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

Wherein, i=1,2 ..., N.

The advantage that the present invention has than prior art

Wait few sheet bias type variable cross-section steel plates of structure because end is non-, its analytical calculation is very complicated, and therefore, home and abroad fails to provide reliable resolution design method always.Be mostly ignore the non-impact waiting structure in end at present, by structure methods for designing such as ends, Approximate Design carried out to the non-few sheet bias type variable-section steel sheet spring of structure that waits in end, therefore, is difficult to obtain parameter designing value accurately and reliably.Along with the development of computing machine and finite element emulation software, possessor once adopted ANSYS modeling and simulating method to the non-few sheet bias type variable-section steel sheet spring of structure that waits in end to the greatest extent at present, but the method only can carry out simulating, verifying to the distortion of leaf spring or rigidity providing actual design structure, accurate analytical design method formula can not be provided, more can not meet fast-developing and that suspension leaf spring modernization CAD design software the is developed requirement of vehicle.

The present invention is according to the design rigidity of leaf spring and mounting structure size, the Thickness Ratio β of oblique line section of selected equivalent one-chip bias type variable-section steel sheet spring, and the Leading Edge Deformation coefficient of bias type variable-section steel sheet spring, first, provide equivalent one-chip bias type variable-section steel sheet spring root thickness h _emethod for designing; Then, according to leaf spring load p and maximum permissible stress [σ], give few sheet bias type variable-section steel sheet spring root maximum allowable thickness [h ₂] method for designing; Subsequently, according to the root thickness h of equivalent one-chip leaf spring _e, utilize the equivalent thickness computing formula of superposition steel plate lap, give few sheet bias type variable-section steel sheet spring sheet number N and root thickness h ₂method for designing; Finally, according to the thickness design load β h of equivalent one-chip bias type variable-section steel sheet spring end flat segments _e, utilize the equivalent thickness computing formula of superposition steel plate lap, provide the non-each end flat segments thickness h waiting the few sheet bias type variable-section steel sheet spring of structure in end _1iwith length l _1imethod for designing.

By design example and ANSYS simulating, verifying known, the parameter designing value of few sheet bias type variable-section steel sheet spring of the structures such as the method can obtain accurately, reliable end is non-, wait for end is non-the design of the few sheet bias type variable-section steel sheet spring of structure to provide reliable method for designing, and establish reliable technical foundation for CAD software development.Utilize the method, design level, the product quality and performances 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; Meanwhile, also reduce design and testing expenses, accelerate product development speed.

Accompanying drawing explanation

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

Fig. 1 is the non-design flow diagram waiting the few sheet bias type variable-section steel sheet spring of structure in end;

Fig. 2 is the structural representation of the 1st flat spring of embodiment one;

Fig. 3 is the structural representation of the 2nd flat spring of embodiment one;

Fig. 4 is the non-deformation simulation cloud atlas waiting the few sheet bias type variable-section steel sheet spring of structure in end designed by embodiment one;

Fig. 5 is the structural representation of the 1st flat spring of embodiment two;

Fig. 6 is the structural representation of the 2nd flat spring of embodiment two;

Fig. 7 is the structural representation of the 3rd flat spring of embodiment two;

Fig. 8 is the non-deformation simulation cloud atlas waiting the few sheet bias type variable-section steel sheet spring of structure in end designed by embodiment two.

Specific embodiments

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

Embodiment one: certain end structure such as non-grade lacks the structural representation of the half of the single-leaf spring of sheet bias type variable-section steel sheet spring as shown in Figure 2, wherein, the half length L=575mm of each leaf spring, width b=60mm, the half l of installing space ₃=55mm, acts on the half load p=1200N of spring free end, elastic modulus E=200GPa, safe allowable stress [σ]=500MPa.The non-half rigidity Design required value K waiting the few sheet bias type variable-section steel sheet spring of structure of this vehicle end _m=24N/mm, designs the non-few sheet bias type variable-section steel sheet spring of structure that waits in this end.

The non-method for designing waiting the few sheet bias type variable-section steel sheet spring of structure in the end that example of the present invention provides, as shown in Figure 1, concrete steps are as follows for its design cycle:

(1) the equivalent one-chip root thickness h of few sheet bias type variable-section steel sheet spring _ecalculating:

First, choose the end thickness of monolithic bias type variable-section steel sheet spring and the ratio of root thickness, namely end thickness is than β=0.55; Then, according to the half rigidity Design required value K of few sheet bias type variable-section steel sheet spring _m=24N/mm, half length L=575mm, width b=60mm, the half l of installing space ₃=55mm, oblique line root is to the distance l of spring end points ₂=L-l ₃=520mm, elastic modulus E=200GPa, calculate the root thickness of the monolithic bias type variable-section steel sheet spring meeting rigidity requirement, namely

Wherein, $\begin{array}{c}{h}_e=\sqrt[3]{K_M{G}_{x-D}}=13.79mm;\\ G_{x-D}=\frac{4}{Ed}(L^3-l_2^3)+\frac{6l_2^3{(\mathrm{\β}+1)}^2\[3(\mathrm{\β}-1)-2\ln \mathrm{\β}(1+\mathrm{\β})\]}{Eb}+\frac{4{\mathrm{\β}}^3{l}_2^3}{Eb}=109.31{\mathrm{mm}}^4/N;\end{array}$

(2) sheet number N and each root thickness h of sheet bias type variable-section steel sheet spring is lacked ₂design:

Step A: the maximum allowable thickness [h determining each flat spring root thickness ₂]:

According to the half length L=575mm of few sheet bias type variable-section steel sheet spring, width b=60mm, suffered half load p=1200N, safe allowable stress [σ]=500MPa, and the h calculated in step (1) _e=13.79mm, determines the maximum allowable thickness [h of each flat spring root thickness ₂], namely

$\[h_2\]=\frac{{\mathrm{bh}}_e^3\[\mathrm{\σ}\]}{6PL}=19.00mm;$

Step B: leaf of spring number N and each flat spring root thickness h ₂design:

Choose the sheet number initial value N=2 of few sheet bias type variable-section steel sheet spring, wherein, N is the integer between 2 ~ 5; The root thickness of designed few sheet bias type variable-section steel sheet spring is equal, namely all equals h ₂; According to [h determined in step A ₂]=19.00mm, and the h that in step (1), calculating gained arrives _e=13.79mm, to the non-each root thickness h waiting the few sheet bias type variable-section steel sheet spring of structure in end ₂design, namely

$h_2=\frac{1}{\sqrt[3]{N}}{h}_e=10.95mm;$

Because h ₂≤ [h ₂], then the non-each root thickness design load h waiting the few sheet bias type variable-section steel sheet spring of structure in end ₂=10.95mm, the design sheet number N=2 of few sheet bias type variable-section steel sheet spring;

(3) non-each end flat segments thickness of few sheet bias type variable-section steel sheet spring and the design of length waiting structure in end:

I step: according to designing the h obtained in step (2) ₂=10.95mm, determines that the end thickness of the 1st flat spring compares β ₁, namely

β ₁＝0.60；

According to the distance l of oblique line root to spring end points ₂=520mm, designs the h obtained in step (2) ₂=10.95mm, and the end thickness of the 1st flat spring determined compares β ₁=0.60, determine the end thickness h of the 1st flat spring ₁₁with flat segments length l ₁₁, be respectively

h ₁₁＝β ₁h ₂＝6.57mm，

$l_{11}={\mathrm{\β}}_1^2{l}_2=187.20mm;$

II step: the end thickness according to the 1st flat spring determined in I step compares β ₁=0.60, the end thickness determined in step (1) is than β=0.55 and h _e=13.50mm, and in step (2), design the leaf of spring number N=2 and each root thickness h that obtain ₂=10.95mm, determines the Thickness Ratio of the 2nd leaf spring, namely

${\mathrm{\β}}_2=\sqrt[3]{\frac{{\mathrm{\β}}^3{h}_e^3-{\mathrm{\β}}_1^3{h}_2^3}{h_2^3(N-1)}}=0.49;$

According to the Thickness Ratio β of determined 2nd flat spring ₂=0.49, oblique line root is to the distance l of spring end points ₂=520mm, and in step (2), design the h obtained ₂=10.95mm, determines end flat segments thickness and the length of the 2nd flat spring, is respectively

$h_2=\sqrt[3]{\frac{{\mathrm{\β}}^3{h}_e^3-{\mathrm{\β}}_1^3{h}_2^3}{h_2^3(N-1)}}{h}_2=5.37mm,l_{12}={\left(\frac{{\mathrm{\β}}^3{h}_e^3-{\mathrm{\β}}_1^3{h}_2^3}{h_2^3(N-1)}\right)}^{\frac{2}{3}}{l}_2=124.85mm;$

(4) the non-thickness h of each flat spring at diverse location waiting few sheet bias type variable-section steel sheet spring of structure in end _ithe design of (x):

According to the half length L=575mm of few sheet bias type variable-section steel sheet spring, oblique line root is to the distance l of spring end points ₂=520mm, the end thickness h of the 1st flat spring determined in step (3) ₁₁=6.57mm and flat segments length l ₁₁the end thickness h of=187.20mm, the 2nd flat spring ₁₂=5.37mm and flat segments length l ₁₂=124.85mm, and in step (2), design each flat spring root thickness h obtained ₂=10.95mm take spring free end as true origin, can obtain non-the 1st, the 2nd thickness h at diverse location x place waiting the few sheet bias type variable-section steel sheet spring of structure in end ₁(x), h ₂x the design load of (), is respectively

$h_1\left(x\right)=\{\begin{array}{cc}6.57mm& x\∈\[0,187.20\]mm\\ 0.013x+4.11mm& x\∈(187.20,520\]mm\\ 10.95mm& x\∈(520,575\]mm\end{array},$

$h_2\left(x\right)=\{\begin{array}{cc}5.37mm& x\∈\[0,124.85\]mm\\ 0.014x+3.59mm& x\∈(124.85,520\]mm\\ 10.95mm& x\∈(520,575\]mm\end{array};$

Wherein, the 1st flat spring at the thickness at oblique line section diverse location x place in shown in table one; The thickness of 2nd flat spring at oblique line section diverse location x place is in shown in table two;

The thickness h of table one the 1st flat spring at oblique line section diverse location x place ₁(x)

Position x/ (mm)	520	502.20	467.20	432.20	397.20	362.20	327.20	292.20	257.20	222.20	187.20
												Thickness h 1(x)/(mm)	10.95	10.72	10.26	9.79	9.33	8.87	8.41	7.95	7.49	7.03	6.57

The thickness h of table two the 2nd flat spring at oblique line section diverse location x place ₂(x)

Position x/ (mm)	520	484.85	444.85	404.85	364.85	324.85	284.85	244.85	204.85	164.85	124.85
												Thickness h 2(x)/(mm)	10.95	10.45	9.89	9.32	8.76	8.19	7.63	7.06	6.50	5.93	5.37

Design the structural parameters of the 1st flat spring obtained, as shown in Figure 3; The structural parameters of the 2nd flat spring as shown in Figure 4.

Utilize ANSYS finite element emulation software, according to designing, the end obtained is non-waits the few sheet bias type variable-section steel sheet spring of structure, and other structural parameters of this spring and material characteristic parameter, set up ANSYS realistic model, grid division, and apply fixed constraint at the root of realistic model, centre-point load P=1200N is applied at free end, the distortion of the few sheet bias type variable-section steel sheet spring of structure is waited to carry out ANSYS emulation to end is non-, the deformation simulation cloud atlas obtained, as shown in Figure 5, wherein, this leaf spring is at the maximum deformation quantity f=49.57mm at end position place, therefore can the half rigidity of this leaf spring be K _m=P/f=24.21N/mm.

Known, the ANSYS simulating, verifying value K of this leaf spring half rigidity _m=24.21N/mm, with designing requirement value K _m=24N/mm matches, and relative deviation is only 0.88%; Result shows that the non-method for designing waiting the few sheet bias type variable-section steel sheet spring of structure in end that this invention provides is correct, and parameter designing value is accurately and reliably.

Embodiment two: certain end structure such as non-grade lacks the structural representation of the half of the single-leaf spring of sheet bias type variable-section steel sheet spring as shown in Figure 2, wherein, the half length L=600mm of each leaf spring, width b=60mm, the half l of installing space ₃=60mm, acts on the half load p=3000N of spring free end, elastic modulus E=200GPa, safe allowable stress [σ]=500MPa.The non-half rigidity Design required value K waiting the few sheet bias type variable-section steel sheet spring of structure of this vehicle end _m=46N/mm, designs the non-few sheet bias type variable-section steel sheet spring of structure that waits in this end.

The non-method for designing waiting the few sheet bias type variable-section steel sheet spring of structure in the end that example of the present invention provides, as shown in Figure 1, concrete steps are as follows for its design cycle:

(1) the equivalent one-chip root thickness h of few sheet bias type variable-section steel sheet spring _ecalculating:

First, choose the end thickness of equivalent one-chip bias type variable-section steel sheet spring and the ratio of root thickness, namely end thickness is than β=0.55; Then, according to the half rigidity Design required value K of few sheet bias type variable-section steel sheet spring _m=46N/mm, half length L=600mm, width b=60mm, the half l of installing space ₃=60mm, oblique line root is to the distance l of spring end points ₂=L-l ₃=540mm, elastic modulus E=200GPa, calculate the equivalent one-chip root thickness of the few sheet bias type variable-section steel sheet spring meeting rigidity requirement, namely

Wherein, $\begin{array}{c}{h}_e=\sqrt[3]{K_M{G}_{x-D}}=17.84mm;\\ G_{x-D}=\frac{4}{Eb}(L^3-l_2^3)+\frac{6l_2^3{(\mathrm{\β}+1)}^2\[3(\mathrm{\β}-1)-2\ln \mathrm{\β}(1+\mathrm{\β})\]}{Eb}+\frac{4{\mathrm{\β}}^3{l}_2^3}{Eb}=123.44{\mathrm{mm}}^4/N;\end{array}$

(2) sheet number N and each root thickness h of sheet bias type variable-section steel sheet spring is lacked ₂design:

Step A: the maximum allowable thickness [h determining each flat spring root thickness ₂]:

According to the half length L=600mm of few sheet bias type variable-section steel sheet spring, width b=60mm, suffered half load p=3000N, safe allowable stress [σ]=500MPa, and the h calculated in step (1) _e=17.84mm, determines the maximum allowable thickness [h of each flat spring root thickness ₂], namely

$\[h_2\]=\frac{{\mathrm{bh}}_e^3\[\mathrm{\σ}\]}{6PL}=15.77mm;$

Step B: leaf of spring number N and each flat spring root thickness h ₂design:

Choose the sheet number initial value N=2 of few sheet bias type variable-section steel sheet spring, wherein, N is the integer between 2 ~ 5; The root thickness of designed few sheet bias type variable-section steel sheet spring is equal, namely all equals h ₂; According to [the h determined in step A ₂]=15.77mm, and the h calculated in step (1) _e=17.84mm, to the non-root thickness h waiting each flat spring of the few sheet bias type variable-section steel sheet spring of structure in end ₂design, namely

$h_2=\frac{1}{\sqrt[3]{N}}{h}_e=14.16mm;$

Because h ₂≤ [h ₂], then the non-each root thickness design load h waiting the few sheet bias type variable-section steel sheet spring of structure in end ₂=14.16mm, leaf of spring number N=2;

(3) non-each end flat segments thickness of few sheet bias type variable-section steel sheet spring and the design of length waiting structure in end:

I step: according to designing the h obtained in step (2) ₂=14.16mm, determines that the end thickness of the 1st flat spring compares β ₁, namely

β ₁＝0.60；

According to the distance l of oblique line root to spring end points ₂=540mm, designs the h obtained in step (2) ₂=14.16mm, and the end thickness of the 1st flat spring determined compares β ₁=0.60, determine the end flat segments thickness h of the 1st flat spring ₁₁with length l ₁₁, be respectively

h ₁₁＝β ₁h ₂＝8.50mm，

$l_{11}={\mathrm{\β}}_1^2{l}_2=194.40mm;$

II step: the end thickness according to the 1st flat spring determined in I step compares β ₁=0.60, the end thickness determined in step (1) is than β=0.55 and h _e=17.84mm, and in step (2), design the leaf of spring number N=2 and each root thickness h that obtain ₂=14.16mm, determines the Thickness Ratio of the 2nd flat spring, namely

${\mathrm{\β}}_2=\sqrt[3]{\frac{{\mathrm{\β}}^3{h}_e^3-{\mathrm{\β}}_1^3{h}_2^3}{h_2^3(N-1)}}=0.49;$

According to the Thickness Ratio β of determined 2nd flat spring ₂=0.49, oblique line root is to the distance l of spring end points ₂=540mm, and in step (2), design the h obtained ₂=14.16mm, determines end flat segments thickness and the length of the 2nd flat spring, is respectively

$h_{12}=\sqrt[3]{\frac{{\mathrm{\β}}^3{h}_e^3-{\mathrm{\β}}_1^3{h}_2^3}{h_2^3(N-1)}}{h}_2=6.94mm{l}_{12}={\left(\frac{{\mathrm{\β}}^3{h}_e^3-{\mathrm{\β}}_1^3{h}_2^3}{h_2^3(N-1)}\right)}^{\frac{2}{3}}{l}_2=129.65mm;$

(4) the non-each diverse location thickness h waiting few sheet bias type variable-section steel sheet spring of structure in end _ithe design of (x):

According to the half length L=600mm of few sheet bias type variable-section steel sheet spring, oblique line root is to the distance l of spring end points ₂=540mm, the end thickness h of the 1st flat spring determined in step (3) ₁₁=8.50mm and flat segments length l ₁₁the end thickness h of=194.40mm, the 2nd flat spring ₁₂=6.94mm and flat segments length l ₁₂=129.65mm, and in step (2), design each flat spring root thickness h obtained ₂=14.16mm take spring free end as true origin, can obtain the non-thickness h waiting the 1st, the 2nd diverse location x place of the few sheet bias type variable-section steel sheet spring of structure in end ₁(x), h ₂x the design load of (), is respectively

$h\left(x\right)=\{\begin{array}{cc}8.50mm& x\∈\[0,194.40\]mm\\ 0.016x+5.31mm& x\∈(194.40,540\]mm\\ 14.16mm& x\∈(540,600\]mm\end{array},$

$h_2\left(x\right)=\{\begin{array}{cc}6.94mm& x\∈\[0,129.65\]mm\\ 0.018x+4.65mm& x\∈(129.65,540\]mm\\ 14.16mm& x\∈(540,600\]mm\end{array};$

Wherein, the 1st flat spring at the thickness at oblique line section diverse location x place, in shown in table three; 2nd flat spring at the thickness at oblique line section diverse location x place, in shown in table four;

The thickness h of table three the 1st flat spring at oblique line section diverse location x place ₁(x)

Position x/ (mm)	540	509.40	474.40	439.40	404.40	369.40	334.40	299.40	264.40	229.40	194.40
												Thickness h 1(x)/(mm)	14.16	13.66	13.09	12.51	11.94	11.37	10.79	10.22	9.65	9.07	8.50

The thickness h of table four the 2nd flat spring at oblique line section diverse location x place ₂(x)

Position x/ (mm)	540	507.65	465.65	423.65	381.65	339.65	297.65	255.65	213.65	171.65	129.65
												Thickness h 2(x)/(mm)	14.16	13.59	12.85	12.11	11.37	10.63	9.90	9.16	8.42	7.68	6.94

Design the structural parameters of the 1st flat spring obtained, as shown in Figure 6; The structural parameters of the 2nd flat spring, as shown in Figure 7.Utilize ANSYS finite element emulation software, according to designing, the end obtained is non-waits the few sheet bias type variable-section steel sheet spring of structure, and other structural parameters of this spring and material characteristic parameter, set up ANSYS realistic model, grid division, and apply fixed constraint at the root of realistic model, centre-point load P=3000N is applied at free end, the distortion of the few sheet bias type variable-section steel sheet spring of structure is waited to carry out ANSYS emulation to end is non-, the deformation simulation cloud atlas obtained, as shown in Figure 8, wherein, this leaf spring is at the maximum deformation quantity f=64.84mm at end position place, therefore, can the half rigidity simulating, verifying value of this leaf spring be K _m=P/f=46.27N/mm.

Known, 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 non-method for designing waiting the few sheet bias type variable-section steel sheet spring of structure in end that this invention provides is correct, and parameter designing value is accurately and reliably.

Claims (1)

1. the non-method for designing waiting the few sheet bias type variable-section steel sheet spring of structure in end, wherein, the non-variable cross section waiting the few sheet variable-section steel sheet spring of structure in end is bias type, namely be made up of root flat segments, oblique line section, end flat segments three sections, and each end flat segments is non-structure such as grade, the i.e. thickness of end flat segments of the 1st and length, be greater than other thickness of each and length, its specific design step is as follows:

(1) the equivalent one-chip root thickness h of few sheet bias type variable-section steel sheet spring _ecalculating:

First, choose the end thickness of monolithic bias type variable-section steel sheet spring and the ratio of root thickness, namely end thickness is than β=0.55; Then, according to the half rigidity Design required value K of few sheet bias type variable-section steel sheet spring _m, half length L, width b, the half l of installing space ₃, oblique line root is to the distance l of spring end points ₂=L-l ₃, elastic modulus E, calculates the equivalent one-chip root thickness of the few sheet bias type variable-section steel sheet spring meeting rigidity requirement, namely

Wherein, $\begin{array}{c}{h}_e=\sqrt[3]{K_M{G}_{x-D}};\\ G_{x-D}=\frac{4}{Eb}(L^3-l_2^3)+\frac{6l_2^3{(\mathrm{\β}+1)}^2\[3(\mathrm{\β}-1)-2\ln \mathrm{\β}(1+\mathrm{\β})\]}{Eb}+\frac{4{\mathrm{\β}}^3{l}_2^3}{Eb};\end{array}$

(2) sheet number N and each root thickness h of sheet bias type variable-section steel sheet spring is lacked ₂design:

Step A: the maximum allowable thickness [h determining each flat spring root thickness ₂]:

According to the half length L of few sheet bias type variable-section steel sheet spring, width b, suffered half load p, safe allowable stress [σ], and the h calculated in step (1) _e, determine the maximum allowable thickness [h of each flat spring root thickness ₂], namely

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

Step B: leaf of spring number N and each root thickness h ₂design:

Choose the non-sheet number initial value N=2 waiting the few sheet bias type variable-section steel sheet spring of structure in end, wherein, N is the integer between 2 ~ 5; The root thickness of designed few sheet bias type variable-section steel sheet spring is equal, namely all equals h ₂; According to [the h determined in step A ₂], and the h calculated in step (1) _e, to the non-each root thickness h waiting the few sheet bias type variable-section steel sheet spring of structure in end ₂design, namely

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

If h ₂≤ [h ₂], then h ₂be the non-each root thickness design load waiting the few sheet bias type variable-section steel sheet spring of structure in end, corresponding N is the sheet number design load of few sheet bias type variable-section steel sheet spring;

If h ₂> [h ₂], then get the sheet number N=N+1 of leaf spring, return and continue to perform step B, to the root thickness h in increase by 1 situation ₂design, until work as h ₂≤ [h ₂] time, sheet number and each root thickness design of few sheet bias type variable-section steel sheet spring are complete;

(3) non-each end flat segments thickness of few sheet bias type variable-section steel sheet spring and the design of length waiting structure in end:

I step: according to designing the h obtained in step (2) ₂, determine that the end thickness of the 1st leaf spring compares β ₁, namely

${\mathrm{\β}}_1=\left\{\begin{array}{cc}0.65,& h_2\∈\[5,10\]mm\\ 0.60,& h_2\∈(10,15\]mm\\ 0.55,& h_2\∈(15,20\]mm\\ 0.50,& h_2\∈(20,25\]mm\\ 0.45,& h_2\∈(25,30\]mm\\ 0.40,& h_2\∈(30,35\]mm\end{array}\right.;$

According to the distance l of oblique line root to spring end points ₂, in step (2), design the h obtained ₂, and the end thickness of determined 1st leaf spring compares β ₁, determine the end flat segments thickness h of the 1st leaf spring ₁₁with length l ₁₁, be respectively

h ₁₁＝β ₁h ₂，

$l_{11}={\mathrm{\β}}_1^2{l}_2;$

II step: the end thickness according to the 1st flat spring determined in I step compares β ₁, the end thickness determined in step (1) is than β and h _e, and in step (2), design the leaf of spring number N and each root thickness h that obtain ₂, determine the 2nd, the 3rd ..., the end thickness ratio of N flat 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 3rd ..., the Thickness Ratio β of N flat spring ₂=β ₃=...=β _n, oblique line root is to the distance l of spring end points ₂, and in step (2), design the h obtained ₂, determine the 2nd, the 3rd ..., the end flat segments thickness of N flat spring and length, be respectively

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

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

(4) the non-each diverse location thickness h waiting few sheet bias type variable-section steel sheet spring of structure in end _ithe design of (x):

According to the half length L of few sheet bias type variable-section steel sheet spring, oblique line root is to the distance l of spring end points ₂, the end thickness of each flat spring determined in step (3) and flat segments length, and in step (2), design each flat spring root thickness h obtained ₂, take spring free end as true origin, the non-each diverse location x place thickness h waiting the few sheet bias type variable-section steel sheet spring of structure in end can be obtained _ithe design load of (x), namely

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

Wherein, i=1,2 ..., N.