CN105138806A - Method for checking intensity of unequal-thickness annular valve plate of hydro-pneumatic spring - Google Patents

Abstract

The invention relates to a method for checking the intensity of an unequal-thickness annular valve plate of a hydro-pneumatic spring, belonging to the technical field of hydro-pneumatic suspensions. The method provided by the invention has the beneficial effects that the maximum compound stress of the unequal-thickness annular valve plate can be accurately and analytically computed according to the structure parameters and material property parameters of the unequal-thickness annular valve plate of the hydro-pneumatic spring, thus accurately checking the stress intensity of the unequal-thickness annular valve plate of the hydro-pneumatic spring; through comparison with ANSYS simulation results, the intensity checking method can be known to be accurate and reliable and provides a reliable method for checking the stress intensity of the unequal-thickness annular valve plate under uniformly distributed pressure for realizing modern CAD (computer-aided design) of the hydro-pneumatic spring and checking of the stress intensity of the unequal-thickness annular valve plate; the design level, quality and properties of the hydro-pneumatic spring can be improved, the design and experimental expenses of the hydro-pneumatic spring can be reduced and the requirement of the design life of the hydro-pneumatic spring can be met under the premise of ensuring the requirement of characteristic design by utilizing the method.

Description

Hydro-pneumatic spring not uniform thickness annular valve block strength check methods

Technical field

The present invention relates to hydro-pneumatic spring, particularly hydro-pneumatic spring not uniform thickness annular valve block strength check methods.

Background technology

For hydro-pneumatic spring not uniform thickness annular valve block stress intensity check, predecessor State is inside and outside not accurately, reliable method, mostly utilize finite element emulation software, to the not uniform thickness annular valve block under setting pressure, carry out numerical simulation by setting up solid model maximum compound stress is checked, but need to set up solid model and accurate analytical formula and computing method can not be provided, the slow and calculated value of the method computing velocity and actually have certain difference.Along with the fast development of auto industry and improving constantly of travel speed, to hydro-pneumatic spring and not uniform thickness annular valve block design have higher requirement, currently utilize finite element emulation software, carry out emulation by the intensity of solid modelling to not uniform thickness annular valve block to check, lack accurate analytical formula, the fast development of modern automobile industry and the requirement of hydro-pneumatic spring modernization CAD design can not be met.Therefore, in order to meet hydro-pneumatic spring and not uniform thickness annular valve block modernization CAD design and the stress intensity requirement of checking, must set up accurately, the strength check methods of hydro-pneumatic spring not uniform thickness annular valve block reliably.

Summary of the invention

For the defect existed in above-mentioned prior art, technical matters to be solved by this invention be to provide a kind of accurately, the strength check methods of hydro-pneumatic spring not uniform thickness annular valve block reliably, its calculation flow chart is as shown in Figure 1; Uniform thickness annular valve block mechanical model is not as shown in Figure 2 for hydro-pneumatic spring.

For solving the problems of the technologies described above, hydro-pneumatic spring provided by the present invention not uniform thickness annular valve block strength check methods, it is characterized in that adopting following calculation procedure:

(1) the constant term X of the not maximum compound stress coefficient formation of uniform thickness annular valve block is determined ₁and X ₂:

According to the elastic modulus E of not uniform thickness annular valve block, Poisson ratio μ, Varying-thickness radius r _t, effective inner circle radius r _a, exradius r _b, set up the secular equation of the constant term that the not maximum compound stress coefficient of uniform thickness annular valve block is formed, that is:

$X_1{r}_a^2-\frac{3(1-{\mathrm{\μ}}^2)r_a^2}{4E}(r_a^2-4r_b^2{\mathrm{lnr}}_a+2r_b^2)+X_2=0;$

$\frac{85r_b^2}{96}+\frac{{\mathrm{Er}}_t^3(11+3\sqrt{17})}{72(1-{\mathrm{\μ}}^2)}{r}_b^{\sqrt{17}/2-5/2}{Y}_2+\frac{{\mathrm{Er}}_t^3(11-3\sqrt{17})}{72(1-{\mathrm{\μ}}^2)}{r}_b^{-\sqrt{17}/2-5/2}{Y}_1=0;$

$X_1{r}_t^2+X_2-\frac{3(1-{\mathrm{\μ}}^2)}{4{\mathrm{Er}}_t}(r_t^2-4r_b^2\ln r_t+2r_b^2)-Y_1{r}_t^{5/2-\sqrt{17}/2}-Y_2{r}_t^{5/2+\sqrt{17}/2}+\frac{3(1-{\mathrm{\μ}}^2)r_t^2}{8E}(r_t^2-8r_b^2)=0;$

$\begin{array}{c}\frac{19r_t^2}{96}-\frac{13r_b^2}{12}+\frac{E}{9(1-{\mathrm{\μ}}^2)}{X}_1-\frac{E}{18(1-{\mathrm{\μ}}^2)r^2}{X}_2-\frac{5r_t^2}{24}+\frac{r_b^2\ln r_t}{3}+\frac{r_b^2}{12}\\ -\frac{E(11+3\sqrt{17})}{72(1-{\mathrm{\μ}}^2)}{r}_t^{\sqrt{17}/2+1/2}{Y}_2-\frac{E(11-3\sqrt{17})}{72(1-{\mathrm{\μ}}^2)}{r}_t^{-\sqrt{17}/2+1}{Y}_1=0;\end{array}$

Utilize Matlab program, solve above-mentioned about X ₁, X ₂, Y ₁and Y ₂the system of equations of four equations composition, try to achieve the constant term X that the not maximum compound stress coefficient of uniform thickness annular valve block is formed ₁and X ₂;

(2) the maximum compound stress coefficient G of not uniform thickness annular valve block is determined _{c σ max}:

According to hydro-pneumatic spring not uniform thickness annular valve block elastic modulus E, effective inner circle radius r _a, exradius r _b, and the constant term X that step (1) the maximum compound stress coefficient of not uniform thickness annular valve block of trying to achieve is formed ₁and X ₂, determine the maximum compound stress coefficient G of not uniform thickness annular valve block _{c σ max}, that is:

$G_{C\mathrm{\σ}max}=\sqrt{K_{\mathrm{\σ}rmax}^2+K_{\mathrm{\σ}\mathrm{\θ}max}^2-K_{\mathrm{\σ}rmax}{K}_{\mathrm{\σ}\mathrm{\θ}max}};$

In formula, $K_{\mathrm{\σ}\mathrm{\θ}max}=\frac{3{\mathrm{EX}}_2}{16r_a^2}-\frac{3{\mathrm{EX}}_2}{16r_a}+\frac{3r_a^2}{8}+\frac{r_a^3}{8}-\frac{r_b^2}{4}-\frac{3{\mathrm{EX}}_1}{16}-\frac{r_b^2\ln r_a}{2}-\frac{r_b^2{r}_a\ln r_a}{2}+\frac{r_a{r}_b^2}{4}-\frac{3{\mathrm{EX}}_1{r}_a}{16},$

$K_{\mathrm{\σ}rmax}=\frac{3{\mathrm{EX}}_2}{8r_a^2}-2r_b^2\ln r_a+\frac{5r_a^2}{4}-\frac{r_b^2}{2}-\frac{3{\mathrm{EX}}_1}{4};$

(3) the maximum compound stress σ of not uniform thickness annular valve block is calculated _cmax:

According to the thickness h of the equal thickness part of not uniform thickness annular valve block ₀, suffered well-distributed pressure p, and the G that step (2) is tried to achieve _{c σ max}, calculate the maximum compound stress σ of not uniform thickness annular valve block _cmax, that is:

${\mathrm{\σ}}_{Cmax}=G_{C\mathrm{\σ}max}\frac{p}{h_0^2};$

(4) uniform thickness annular valve block stress intensity is not checked:

According to the permissible stress [σ] of not uniform thickness annular valve block, and the σ that step (3) is tried to achieve _cmax, counter stress intensity is checked, if i.e.: σ _cmax> [σ], then uniform thickness annular valve block is not discontented with sufficient stress intensity requirement; If σ _cmax< [σ], then uniform thickness annular valve block can not meet stress intensity requirement.

The advantage that the present invention has than prior art:

For hydro-pneumatic spring not uniform thickness annular valve block stress intensity check, predecessor State is inside and outside without accurate, reliable computing method, mostly utilize finite element emulation software, to the not uniform thickness annular valve block under setting pressure, carry out numerical simulation by setting up solid model maximum compound stress is checked, but need to set up solid model and accurate analytical formula and computing method can not be provided, the method computing velocity is slow and calculated value has certain difference with actual, can not meet the fast development of modern automobile industry and the requirement of hydro-pneumatic spring modernization CAD design.

Hydro-pneumatic spring provided by the invention not uniform thickness annular valve block strength check methods, can according to the hydro-pneumatic spring not uniform thickness annular structural parameters of valve block and material property parameter, accurate fast calculating is carried out to the maximum compound stress of not uniform thickness annular valve block, thus the stress intensity of hydro-pneumatic spring not uniform thickness annular valve block is checked accurately.By more known with ANSYS simulation result, this strength check methods is reliable and result of calculation is accurate, to design and the stress intensity of not uniform thickness annular valve block is checked for realizing hydro-pneumatic spring modernization CAD, providing the not uniform thickness annular stress intensity check method of valve block under well-distributed pressure; Utilize the method can improve design level, the quality and performance of hydro-pneumatic spring, reduce design and the testing expenses of hydro-pneumatic spring, guaranteeing, under the prerequisite that hydro-pneumatic spring characteristics design requires, to meet the requirement of hydro-pneumatic spring designed life.

Accompanying drawing explanation

Be described further below in conjunction with accompanying drawing to understand the present invention better.

Fig. 1 is the process flow diagram of strength check methods of hydro-pneumatic spring not uniform thickness annular valve block;

Fig. 2 is hydro-pneumatic spring not uniform thickness annular valve block mechanical model figure;

Fig. 3 be hydro-pneumatic spring not uniform thickness annular valve block stress simulation cloud atlas.

Specific embodiments

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

Certain special vehicle hydro-pneumatic spring have employed not uniform thickness annular valve block, elastic modulus E=200GPa, Poisson ratio μ=1/3, the thickness h of its equal thickness part ₀=0.3mm, Varying-thickness radius r _t=7.3mm, effective inner circle radius r _a=5.0mm, exradius r _b=8.5mm, permissible stress [σ]=2000MPa.Valve block radius [5.0,8.5] mm interval applies well-distributed pressure p=3.0MPa, the stress intensity of not uniform thickness annular valve block is checked.

The strength check methods of the hydro-pneumatic spring that example of the present invention provides not uniform thickness annular valve block, its calculation flow chart as shown in Figure 1, hydro-pneumatic spring not uniform thickness annular valve block mechanical model as shown in Figure 2, concrete steps are as follows:

(1) the constant term X of the not maximum compound stress coefficient formation of uniform thickness annular valve block is determined ₁and X ₂:

According to the elastic modulus E=200GPa of not uniform thickness annular valve block, Poisson ratio μ=1/3, Varying-thickness radius r _t=7.3mm, effective inner circle radius r _a=5.0mm, exradius r _b=8.5mm, sets up the secular equation of the constant term that the not maximum compound stress coefficient of uniform thickness annular valve block is formed, that is:

$X_1{r}_a^2-\frac{3(1-{\mathrm{\&mu;}}^2)r_a^2}{4E}(r_a^2-4r_b^2{\mathrm{lnr}}_a+2r_b^2)+X_2=0;$

$\frac{85r_b^2}{96}+\frac{{\mathrm{Er}}_t^3(11+3\sqrt{17})}{72(1-{\mathrm{\&mu;}}^2)}{r}_b^{\sqrt{17}/2-5/2}{Y}_2+\frac{{\mathrm{Er}}_t^3(11-3\sqrt{17})}{72(1-{\mathrm{\&mu;}}^2)}{r}_b^{-\sqrt{17}/2-5/2}{Y}_1=0;$

$X_1{r}_t^2+X_2-\frac{3(1-{\mathrm{\&mu;}}^2)}{4{\mathrm{Er}}_t}(r_t^2-4r_b^2\ln r_t+2r_b^2)-Y_1{r}_t^{5/2-\sqrt{17}/2}-Y_2{r}_t^{5/2+\sqrt{17}/2}+\frac{3(1-{\mathrm{\&mu;}}^2)r_t^2}{8E}(r_t^2-8r_b^2)=0;$

$\begin{array}{c}\frac{19r_t^2}{96}-\frac{13r_b^2}{12}+\frac{E}{9(1-{\mathrm{\&mu;}}^2)}{X}_1-\frac{E}{18(1-{\mathrm{\&mu;}}^2)r^2}{X}_2-\frac{5r_t^2}{24}+\frac{r_b^2\ln r_t}{3}+\frac{r_b^2}{12}\\ -\frac{E(11+3\sqrt{17})}{72(1-{\mathrm{\&mu;}}^2)}{r}_t^{\sqrt{17}/2+1/2}{Y}_2-\frac{E(11-3\sqrt{17})}{72(1-{\mathrm{\&mu;}}^2)}{r}_t^{-\sqrt{17}/2+1}{Y}_1=0;\end{array}$

Utilize Matlab program, solve above-mentioned about X ₁, X ₂, Y ₁and Y ₂the system of equations of four equations composition, try to achieve the constant term X that the not maximum compound stress coefficient of uniform thickness annular valve block is formed ₁=5.059 × 10 ^-15and X ₂=1.526 × 10 ^-20;

(2) the maximum compound stress coefficient G of not uniform thickness annular valve block is determined _{c σ max}:

According to hydro-pneumatic spring not uniform thickness annular valve block elastic modulus E=200GPa, effective inner circle radius r _a=5.0mm, exradius r _b=8.5mm, and the constant term X that step (1) the maximum compound stress coefficient of not uniform thickness annular valve block of trying to achieve is formed ₁=5.059 ^-15and X ₂=1.526 ^-20, determine the maximum compound stress coefficient G of not uniform thickness annular valve block _{c σ max}, that is:

$G_{C\mathrm{\&sigma;}max}=\sqrt{K_{\mathrm{\&sigma;}rmax}^2+K_{\mathrm{\&sigma;}\mathrm{\&theta;}max}^2-K_{\mathrm{\&sigma;}rmax}{K}_{\mathrm{\&sigma;}\mathrm{\&theta;}max}}=4.20459\&times;{10}^{-11}{m}^2;$

In formula, $\begin{array}{c}{K}_{\mathrm{\&sigma;}\mathrm{\&theta;}max}=\frac{3{\mathrm{EX}}_2}{16r_a^2}-\frac{3{\mathrm{EX}}_2}{16r_a}+\frac{3r_a^2}{8}+\frac{r_a^3}{8}-\frac{r_b^2}{4}-\frac{3{\mathrm{EX}}_1}{16}-\frac{r_b^2\ln r_a}{2}-\frac{r_b^2{r}_a\ln r_a}{2}+\frac{r_a{r}_b^2}{4}-\frac{3{\mathrm{EX}}_1{r}_a}{16}\\ =1.58919\&times;{10}^{-11}{m}^2,\end{array}$

$K_{\mathrm{\&sigma;}rmax}=\frac{3{\mathrm{EX}}_2}{8r_a^2}-2r_b^2\ln r_a+\frac{5r_a^2}{4}-\frac{r_b^2}{2}-\frac{3{\mathrm{EX}}_1}{4}=4.76756\&times;{10}^{-11}{m}^2;$

(3) the maximum compound stress σ of not uniform thickness annular valve block is calculated _cmax:

According to the thickness h of the equal thickness part of not uniform thickness annular valve block ₀=0.3mm, well-distributed pressure p=3.0MPa, and the G that step (2) is tried to achieve _{c σ max}=4.20459 × 10 ^-11m ², calculate the maximum compound stress σ of not uniform thickness annular valve block _cmax, that is:

${\mathrm{\&sigma;}}_{Cmax}=G_{C\mathrm{\&sigma;}max}\frac{p}{h_0^2}=1401.53\&times;{10}^{6}Pa=1401.53MPa;$

(4) uniform thickness annular valve block stress intensity is not checked:

According to permissible stress [the σ]=2000MPa of not uniform thickness annular valve block, and the σ that step (3) is tried to achieve _cmax=1401.53MPa, known, σ _cmax< [σ], namely uniform thickness annular valve block can not meet stress intensity requirement.

According to the not uniform thickness annular valve block of the hydro-pneumatic spring in embodiment, elastic modulus E=200GPa, Poisson ratio μ=1/3, the thickness h of its equal thickness part ₀=0.3mm, Varying-thickness radius r _t=7.3mm, effective inner circle radius r _a=5.0mm, exradius r _b=8.5mm, suffered well-distributed pressure is p=3.0MPa, utilize ANSYS finite element analysis software Modling model, its boundary condition is consistent with the mechanical model of Fig. 2, to model partition grid in units of 0.1mm, radius [5.0,8.5] mm interval applies well-distributed pressure 3.0MPa, static numerical simulation analysis is carried out to valve block, obtains the stress simulation cloud atlas of not uniform thickness annular valve block as shown in Figure 3.

From simulation result Fig. 3, under well-distributed pressure p=3.0MPa, the maximum compound stress simulation value of uniform thickness annular valve block is not 1390MPa, and the maximum compound stress 1401.53MPa calculated with utilizing this strength check methods matches, and relative deviation is only 0.79%.Result shows, the hydro-pneumatic spring set up not uniform thickness annular valve block strength check methods be correct.

Claims (1)

1. hydro-pneumatic spring not uniform thickness annular valve block strength check methods, its concrete calculation procedure is as follows:

(1) the constant term X of the not maximum compound stress coefficient formation of uniform thickness annular valve block is determined ₁and X ₂:

According to the elastic modulus E of not uniform thickness annular valve block, Poisson ratio μ, Varying-thickness radius r _t, effective inner circle radius r _a, exradius r _b, set up the secular equation of the constant term that the not maximum compound stress coefficient of uniform thickness annular valve block is formed, that is:

$X_1{r}_a^2-\frac{3(1-{\mathrm{\&mu;}}^2)r_a^2}{4E}(r_a^2-4r_b^2{\mathrm{lnr}}_a+2r_b^2)+X_2=0;$

$\frac{85r_b^2}{96}+\frac{{\mathrm{Er}}_t^3(11+3\sqrt{17})}{72(1-{\mathrm{\&mu;}}^2)}{r}_b^{\sqrt{17}/2-5/2}{Y}_2+\frac{{\mathrm{Er}}_t^3(11-3\sqrt{17})}{72(1-{\mathrm{\&mu;}}^2)}{r}_b^{-\sqrt{17}/2-5/2}{Y}_1=0;$

$X_1{r}_t^2+X_2-\frac{3(1-{\mathrm{\&mu;}}^2)}{4{\mathrm{Er}}_t}(r_t^2-4r_b^2{\mathrm{lnr}}_t+2r_b^2)-Y_1{r}_t^{5/2-\sqrt{17}/2}-Y_2{r}_t^{5/2+\sqrt{17}/2}+\frac{3(1-{\mathrm{\&mu;}}^2)r_t^2}{8E}(r_t^2-8r_b^2)=0;$

$\begin{array}{c}\frac{19r_t^2}{96}-\frac{13r_b^2}{12}+\frac{E}{9(1-{\mathrm{\&mu;}}^2)}{X}_1-\frac{E}{18(1-{\mathrm{\&mu;}}^2)r^2}{X}_2-\frac{5r_t^2}{24}+\frac{r_b^2{\mathrm{lnr}}_t}{3}+\frac{r_b^2}{12}\\ -\frac{E(11+3\sqrt{17})}{72(1-{\mathrm{\&mu;}}^2)}{r}_t^{\sqrt{17}/2+1/2}{Y}_2-\frac{E(11-3\sqrt{17})}{72(1-{\mathrm{\&mu;}}^2)}{r}_t^{-\sqrt{17}/2+1}{Y}_1=0\end{array};$

Utilize Matlab program, solve above-mentioned about X ₁, X ₂, Y ₁and Y ₂the system of equations of four equations composition, try to achieve the constant term X that the not maximum compound stress coefficient of uniform thickness annular valve block is formed ₁and X ₂;

(2) the maximum compound stress coefficient G of not uniform thickness annular valve block is determined _{c σ max}:

According to hydro-pneumatic spring not uniform thickness annular valve block elastic modulus E, effective inner circle radius r _a, exradius r _b, and the constant term X that step (1) the maximum compound stress coefficient of not uniform thickness annular valve block of trying to achieve is formed ₁and X ₂, determine the maximum compound stress coefficient G of not uniform thickness annular valve block _{c σ max}, that is:

$G_{C\mathrm{\&sigma;}max}=\sqrt{K_{\mathrm{\&sigma;}rmax}^2+K_{\mathrm{\&sigma;}\mathrm{\&theta;}max}^2-K_{\mathrm{\&sigma;}rmax}{K}_{\mathrm{\&sigma;}\mathrm{\&theta;}max}};$

In formula, $K_{\mathrm{\&sigma;}\mathrm{\&theta;}max}=\frac{3{\mathrm{EX}}_2}{16r_a^2}-\frac{3{\mathrm{EX}}_2}{16r_a}+\frac{3r_a^2}{8}+\frac{r_a^3}{8}-\frac{r_b^2}{4}-\frac{3{\mathrm{EX}}_1}{16}-\frac{r_b^2{\mathrm{lnr}}_a}{2}-\frac{r_b^2{r}_a{\mathrm{lnr}}_a}{2}+\frac{r_a{r}_b^2}{4}-\frac{3{\mathrm{EX}}_1{r}_a}{16},$

$K_{\mathrm{\&sigma;}rmax}=\frac{3{\mathrm{EX}}_2}{8r_a^2}-2r_b^2{\mathrm{lnr}}_a+\frac{5r_a^2}{4}-\frac{r_b^2}{2}-\frac{3{\mathrm{EX}}_1}{4};$

(3) the maximum compound stress σ of not uniform thickness annular valve block is calculated _cmax:

According to the thickness h of the equal thickness part of not uniform thickness annular valve block ₀, suffered well-distributed pressure p, and the G that step (2) is tried to achieve _{c σ max}, calculate the maximum compound stress σ of not uniform thickness annular valve block _cmax, that is:

${\mathrm{\&sigma;}}_{Cmax}=G_{C\mathrm{\&sigma;}max}\frac{p}{h_0^2};$

(4) uniform thickness annular valve block stress intensity is not checked:

According to the permissible stress [σ] of not uniform thickness annular valve block, and the σ that step (3) is tried to achieve _cmax, counter stress intensity is checked, if i.e.: σ _cmax> [σ], then uniform thickness annular valve block is not discontented with sufficient stress intensity requirement; If σ _cmax< [σ], then uniform thickness annular valve block can not meet stress intensity requirement.