CN102563063A - Self-reinforcing pressure container based on safety design technical conditions - Google Patents

Abstract

The invention provides a self-reinforcing pressure container based on safety design technical conditions, and is used for improving the safety and the bearing capability of the container and solving the technical problems of the prior art that the calculation is complicated, inaccurate or not safe enough. The essentials of the technical scheme are as follows: the depth of a plastic region of the container is calculated according to the specification so that residual stress does not exceed sigma y and reverse yielding is not generated; and a bearing capability is calculated according to the specification so that the absolute value of sigma ej is less than or equal to the sigma y and the absolute value of sigma ei is less than or equal to the sigma y, wherein k is the diameter ratio, kj is the ratio of an elastic-plastic interface radius to an inner diameter, the sigma y is the yield strength, p is the inner pressure borne by the container, pe is the maximum elastic bearing capability of a non-self-reinforcing container, the sigma ej is the equivalent stress of the total stress of an elastic-plastic interface and the sigma ei is e equivalent stress of the total stress of an inner wall; when the k is less than the determined value, namely when the k is less than 2.024678965...., the container does not generate the reverse yielding after the self-reinforcing pressure is removed no matter how large the kj is.

Description

A kind of self-reinforcing pressure vessel based on the safety design technical specifications

Technical field

The present invention relates to a kind of self-reinforcing pressure vessel, belong to technical fields such as machine science technology, chemical engineering based on the safety design technical specifications.

Background technique

Pressurized container is the special equipment that is widely used in many industrial departments, and like departments such as machinery, chemical industry, pharmacy, the energy, material, food, metallurgy, oil, building, Aeronautics and Astronautics, weapons, the pressurized container theme partly is generally cylindrical shape.The self intensification technology is to improve the important of pressurized container bearing capacity and Security thereof and effective means.The self intensification technology of pressurized container is before manipulating, it to be carried out pressure treatment (institute's plus-pressure generally surpasses operation pressure), makes the surrender of cylindrical shell internal layer, produces plastic deformation, form the plastic zone, and skin still is an elastic state.Keep the release after a period of time of this pressure.Release rear cylinder body internal layer plasticity part is because of there being residual deformation can not return to original state; Original state is tried hard to return in outer elastic region; But receiving stopping of internal layer plastic zone residual deformation can not return to original state; Therefore bear stretching, form tensile stress, internal layer then produces pressure stress because receiving the compression that skin tries hard to restore.So just formed the pre-stressed state that a kind of internal layer pressurized skin is drawn.After pressing in container comes into operation and bears, prestressing force is superimposed with the interior stress that causes of pressing of operation, and the bigger inboard wall stress of stress is reduced, and the less outer wall stress of stress increases to some extent, and stress is tending towards even in the container wall thereby make.Can improve the bearing capacity of pressurized container thus.Self intensification that Here it is.

The key factor of self intensification technology is the plastic zone degree of depth, i.e. confirming of the elasticity of container and plastic zone interface radius, or superstrain degree

Confirm that wherein ε is the superstrain degree, r _i, r _j, r _oBe respectively inside radius, elastoplasticity interface radius and the outer radius of shell; K is the self-reinforcing pressure vessel outer radius and the ratio of inside radius, i.e. k=r _o/ r _ik _jBe self-reinforcing pressure vessel elasticity and the ratio of plastic zone interface radius with inside radius, i.e. k _j=r _j/ r _i(consulting Fig. 1).The superstrain degree not only has influence on the enforcement of self-reinforcing process; And have influence on residual stress behind the removal from strengthen pressure of self intensification container, bearing capacity or the like; The superstrain degree is too big; Be that the plastic zone degree of depth is too big, reverse yielding possibly appear in container behind the removal from strengthen pressure, and promptly compressive residual stress (or its equivalent stress) (absolute value) can surpass the ultimate strength value of container material; The superstrain degree is too little, and promptly the plastic zone degree of depth is too shallow, and bearing capacity is then not high.For k _jOr r _jOr ε confirm that existing techniques mainly contains 1) graphical solution; 2) by formula

Rough calculation; 3) some r are promptly supposed in trial and error method _j, depress r in prestressing force after the calculating self intensification is handled and the operation _jThe equivalent stress σ of the total stress (prestressing force and operational stresses induced sum) at place _Ej, ask for making σ _EjMinimum r _jCalculate.These methods or too rough (like the graphical solution and the estimation technique) can not reflect question essence again; Or too loaded down with trivial details (like trial and error method), can not reflect question essence.And can not overcome some disadvantages, like the reverse yielding problem, i.e. removal self intensification possibly can produce the secondary compression surrender because receiving excessive compression by internal layer after handling time institute's applied pressure.This is very disadvantageous.From the viewpoint of safety, economy, self-reinforcing pressure vessel should guarantee not produce reverse yielding, guarantees r again _jThe equivalent stress σ of the total stress at place _EjLess than yield strength σ _y, bearing capacity is improved.

Pressurized container is processed with the good material of plasticity mostly, and third and fourth theory of strength relatively is suitable for passing judgment on the inefficacy of plastic material.Discover that when pressing fourth strength theory, only for settled amount residual stress not enough, when the equivalent residual stress had just reached the yield limit of material, the hoop residual stress of cylinder inner wall face had surpassed the yield limit of material.This safety to pressurized container is unfavorable, in case of necessity, must the hoop residual stress of cylinder inner wall face be limited, and improves the bearing capacity of container simultaneously again as best one can.

The present invention takes the corresponding techniques scheme greatly to improve its bearing capacity to avoid the container inner wall face hoop excessive while of residual stress, to the self-reinforcing pressure vessel under the pressure situation in bearing according to the purpose of restriction internal face hoop residual stress.

Summary of the invention

The purpose of this invention is to provide a kind of self-reinforcing pressure vessel based on the safety design technical specifications.

The technical solution adopted for the present invention to solve the technical problems is: construct a kind of self-reinforcing pressure vessel based on the safety design technical specifications, the physical dimension of this kind pressurized container and bearing capacity confirm that by specific technological scheme specifically: its whole wall thickness does For k greater than by formula

The self-reinforcing pressure vessel of the value of confirming, its plastic zone degree of depth by formula ${2\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HSA00000644018300022.png,HSA00000644018300031.png"\; state="\{\{state\}\}">k</figure-callout>}}^2\mathrm{Ln}{k}_j^2-{2k}_j^2-\sqrt{3}{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HSA00000644018300022.png,HSA00000644018300031.png"\; state="\{\{state\}\}">k</figure-callout>}}^2+(2+\sqrt{3})=0$ Confirm that its bearing capacity does $\frac{p}{{\mathrm{\&sigma;}}_y}=\frac{2\sqrt{3}+3}{6}\frac{k^2-1}{{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HSA00000644018300022.png,HSA00000644018300031.png"\; state="\{\{state\}\}">k</figure-callout>}}^2}=(1+\frac{\sqrt{3}}{2})\frac{p_e}{{\mathrm{\&sigma;}}_y};$ R wherein _iBe the internal diameter of self-reinforcing pressure vessel, k is the self-reinforcing pressure vessel outer radius and the ratio of inside radius, plastic zone degree of depth k _jBe self-reinforcing pressure vessel elasticity and plastic zone interface radius r _jTo the ratio of inside radius, i.e. k _j=r _j/ r _i, σ _yBe the self-reinforcing pressure vessel YIELD STRENGTH, p is the interior pressure that self-reinforcing pressure vessel bore, p _eMaximum flexibility bearing capacity (initial yield load) for non-self-reinforcing pressure vessel.For k less than by formula

The self-reinforcing pressure vessel of the value of confirming, its plastic zone scope can be whole wall thickness, i.e. k _j=k.

Beneficial effect of the present invention and advantage are: the plastic zone depth calculation formula of self-reinforcing pressure vessel safety is provided, promptly

The thickness size (with k reflection) that this formula has been established container and the plastic zone degree of depth of safety are (with k _jReflection) function relation between has reflected the name of the game, and that has avoided that existing technology calculates is rough or loaded down with trivial details; Found the many maximum k values that can not produce reverse yielding deeply of the plastic zone degree of depth, promptly k equals by formula The value of confirming, that is k ≈ 2.024678965... (comprise by 2.024678965... and obtain approximate number) by certain rule; The formula of self-reinforcing pressure vessel bearing capacity is provided.Whole wall thickness with the self-reinforcing pressure vessel of technological scheme of the present invention structure can be minimized, and simultaneously, presses

The plastic zone degree of depth k that relation is confirmed _jSmaller, and the plastic zone degree of depth is little, help practicing thrift the expense when carrying out self intensification and handling, and bearing capacity is the maximum flexibility bearing capacity of non-self-reinforcing pressure vessel

Doubly.In addition, by technological scheme of the present invention, each all is no more than cylinder YIELD STRENGTH σ to residual stress and equivalent stress thereof in the whole barrel after self intensification is handled can to reach the assurance container _y, the technique effect of reverse yielding does not promptly take place.The interior pressure self-reinforcing pressure vessel of therefore being constructed with technological scheme provided by the present invention is a kind of safe and economic pressurized container.

Description of drawings

Fig. 1 is the autofrettaged cylinder of pressing in receiving.

Fig. 2 is k=3, k _jThree-dimensional relative residual stress in=1.5 o'clock barrels (σ '/σ _y) along relative position (r/r in the barrel _i) distribution.

Fig. 3 is k=3, k _jThree-dimensional relative residual stress in=1.748442 o'clock barrels (σ '/σ _y) along relative position (r/r in the barrel _i) distribution.

Fig. 4 is restriction internal face hoop residual stress σ _Ti' time k and k _jRelation.

Fig. 5 is restriction internal face hoop residual stress σ _TiThe bearing capacity figure in ' time.

Residual stress after improving when Fig. 6 is k=3 and the residual stress before equivalent stress and the improvement and the comparison of equivalent stress thereof.

Residual stress after improving when Fig. 7 is k=4 and the residual stress before equivalent stress and the improvement and the comparison of equivalent stress thereof.

Embodiment

Embodiment 1, can be confirmed the internal diameter r of pressurized container by technology Calculation _iContainer material decision back according to it with the load of bearing (p/ σ _y), by the bearing capacity calculating formula

Can confirm the footpath than k (by k=r _o/ r _iCan confirm external diameter r _o).After k confirms, by formula

Confirm the ratio of elastic-plastic district interface radius and inside radius, i.e. plastic zone degree of depth k _j, press k _j=r _j/ r _iCalculate safe r _jKey factor r _jJust can carry out self intensification after confirming has handled.Equation

The solution can be a) by explicitly

solving; or 2) using Excel software solution; or 3) in Figure 2 Zha take; or 4) the data provided in Table 1 Cha taken (in case of intermediate values available interpolation).

Annotate: this example focuses on key point of the present invention, so the existing design procedure of pressurized container is not had and needn't be described in detail.

Analyze below in conjunction with accompanying drawing, to prove foundation of the present invention.Shown in Figure 1 is a pressure container cylinder of pressing in receiving, and internal layer is the plastic zone, and skin is the elastic region, and the elastic-plastic interface radius is r _j

According to the existing theory of pressurized container, behind the removal from strengthen pressure, during based on fourth strength theory, the residual stress in the container wall is (with yield limit or claim intersity limitation σ _yThe ratio value representation):

The plastic zone:

$\frac{{{\mathrm{\&sigma;}}_z}^{\&prime;}}{{\mathrm{\&sigma;}}_y}=\frac{1}{\sqrt{3}}[\frac{k_j^2}{{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HSA00000644018300022.png,HSA00000644018300031.png"\; state="\{\{state\}\}">k</figure-callout>}}^2}+\ln \frac{{(r/r_i)}^2}{k_j^2}-(1-\frac{k_j^2}{{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HSA00000644018300022.png,HSA00000644018300031.png"\; state="\{\{state\}\}">k</figure-callout>}}^2}+\ln k_j^2)\frac{1}{k^2-1}]---\left(1\right)$

$\frac{{{\mathrm{\&sigma;}}_r}^{\&prime;}}{{\mathrm{\&sigma;}}_y}=\frac{1}{\sqrt{3}}[\frac{k_j^2}{k^2}-1+\ln \frac{{(r/r_i)}^2}{k_j^2}-(1-\frac{k_j^2}{{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HSA00000644018300022.png,HSA00000644018300031.png"\; state="\{\{state\}\}">k</figure-callout>}}^2}+\ln k_j^2)\frac{1}{k^2-1}(1-\frac{k^2}{{(r/r_i)}^2})]---\left(2\right)$

$\frac{{{\mathrm{\&sigma;}}_t}^{\&prime;}}{{\mathrm{\&sigma;}}_y}=\frac{1}{\sqrt{3}}[\frac{k_j^2}{{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HSA00000644018300022.png,HSA00000644018300031.png"\; state="\{\{state\}\}">k</figure-callout>}}^2}+1+\ln \frac{{(r/r_i)}^2}{k_j^2}-(1-\frac{k_j^2}{{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HSA00000644018300022.png,HSA00000644018300031.png"\; state="\{\{state\}\}">k</figure-callout>}}^2}+\ln k_j^2)\frac{1}{k^2-1}(1+\frac{k^2}{{(r/r_i)}^2})]---\left(3\right)$

Press fourth strength theory, the equivalent stress of residual stress is:

${{\mathrm{\&sigma;}}_e}^{\&prime;}=\sqrt{\frac{1}{2}[{({{\mathrm{\&sigma;}}_z}^{\&prime;}-{{\mathrm{\&sigma;}}_r}^{\&prime;})}^2+{({{\mathrm{\&sigma;}}_r}^{\&prime;}-{{\mathrm{\&sigma;}}_t}^{\&prime;})}^2+{({{\mathrm{\&sigma;}}_t}^{\&prime;}-{{\mathrm{\&sigma;}}_r}^{\&prime;})}^2]}$

The equivalent stress that formula (1)～(3) substitution following formula is got the plastic zone residual stress is:

$\frac{{{\mathrm{\&sigma;}}_e}^{\&prime;}}{{\mathrm{\&sigma;}}_y}=\frac{\sqrt{3}}{2}(\frac{{{\mathrm{\&sigma;}}_t}^{\&prime;}}{{\mathrm{\&sigma;}}_y}-\frac{{{\mathrm{\&sigma;}}_r}^{\&prime;}}{{\mathrm{\&sigma;}}_y})=1-\frac{k^2-{\mathrm{<figure-callout\; id="2"\; label="k\; j"\; filenames="HSA00000644018300022.png,HSA00000644018300031.png"\; state="\{\{state\}\}">k</figure-callout>}}_j^{}+{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HSA00000644018300022.png,HSA00000644018300031.png"\; state="\{\{state\}\}">k</figure-callout>}}^2\ln k_j^2}{(k^2-1){(r/r_i)}^2}---\left(4\right)$

The elastic region:

$\frac{{{\mathrm{\&sigma;}}_z}^{\&prime;}}{{\mathrm{\&sigma;}}_y}=\frac{1}{\sqrt{3}}[\frac{k_j^2}{k^2}-(1-\frac{k_j^2}{{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HSA00000644018300022.png,HSA00000644018300031.png"\; state="\{\{state\}\}">k</figure-callout>}}^2}+\ln k_j^2)\frac{1}{k^2-1}]---\left(5\right)$

$\frac{{{\mathrm{\&sigma;}}_r}^{\&prime;}}{{\mathrm{\&sigma;}}_y}=\frac{1}{\sqrt{3}}(1-\frac{k^2}{{(r/r_i)}^2})[\frac{k_j^2}{k^2}-(1-\frac{k_j^2}{{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HSA00000644018300022.png,HSA00000644018300031.png"\; state="\{\{state\}\}">k</figure-callout>}}^2}+\ln k_j^2)\frac{1}{k^2-1}]=(1-\frac{k^2}{{(r/r_i)}^2})\frac{{{\mathrm{\&sigma;}}_z}^{\&prime;}}{{\mathrm{\&sigma;}}_y}---\left(6\right)$

$\frac{{{\mathrm{\&sigma;}}_t}^{\&prime;}}{{\mathrm{\&sigma;}}_y}=\frac{1}{\sqrt{3}}(1+\frac{k^2}{{(r/r_i)}^2})[\frac{k_j^2}{k^2}-(1-\frac{k_j^2}{{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HSA00000644018300022.png,HSA00000644018300031.png"\; state="\{\{state\}\}">k</figure-callout>}}^2}+\ln k_j^2)\frac{1}{k^2-1}]=(1+\frac{k^2}{{(r/r_i)}^2})\frac{{{\mathrm{\&sigma;}}_z}^{\&prime;}}{{\mathrm{\&sigma;}}_y}---\left(7\right)$

Equivalent stress is: $\frac{{{\mathrm{\&sigma;}}_e}^{\&prime;}}{{\mathrm{\&sigma;}}_y}=\frac{\sqrt{3}}{2}(\frac{{{\mathrm{\&sigma;}}_t}^{\&prime;}}{{\mathrm{\&sigma;}}_y}-\frac{{{\mathrm{\&sigma;}}_r}^{\&prime;}}{{\mathrm{\&sigma;}}_y})=\frac{k^2(k_j^2-1-\mathrm{Ln}{k}_j^2)}{(k^2-1){(r/r_i)}^2}---\left(8\right)$

σ wherein _z'---axial residual stress, units MPa; σ _r'---residual stress radially, units MPa; σ _t'---circumferential residual stress, units MPa; R---the radius at place, arbitrfary point in the cylindrical wall, the m of unit; σ _e'---the equivalent residual stress, units MPa, indexing i representes the equivalent residual stress at internal face place, is designated as σ _Ei'/σ _y, indexing j representes the equivalent residual stress at elastic-plastic interface place, is designated as σ _Ej'/σ _y

At whole elastic region, σ _Ei'/σ _y＞0.At the internal face place of cylinder, r/r _i=1, the equivalent residual stress that is got here by formula (4) is:

$\frac{{{\mathrm{\&sigma;}}_{\mathrm{ei}}}^{\&prime;}}{{\mathrm{\&sigma;}}_y}=\frac{k_j^2-1-{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HSA00000644018300022.png,HSA00000644018300031.png"\; state="\{\{state\}\}">k</figure-callout>}}^2\ln k_j^2}{k^2-1}---\left(9\right)$

At the internal face place of cylinder, σ _Ei'/σ _yAlways negative.At the elastic-plastic interface place of cylinder, r/r _i=k _j, so formula (4) and (8) all become:

$0<\frac{{{\mathrm{\&sigma;}}_e}^{\&prime;}}{{\mathrm{\&sigma;}}_y}=\frac{{{\mathrm{\&sigma;}}_{\mathrm{ej}}}^{\&prime;}}{{\mathrm{\&sigma;}}_y}=\frac{k^2(k_j^2-1-\ln k_j^2)}{(k^2-1){\mathrm{<figure-callout\; id="2"\; label="k\; j"\; filenames="HSA00000644018300022.png,HSA00000644018300031.png"\; state="\{\{state\}\}">k</figure-callout>}}_j^{}}<1---\left(10\right)$

Order in formula (4) $1-\frac{k^2-{\mathrm{<figure-callout\; id="2"\; label="k\; j"\; filenames="HSA00000644018300022.png,HSA00000644018300031.png"\; state="\{\{state\}\}">k</figure-callout>}}_j^{}+{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HSA00000644018300022.png,HSA00000644018300031.png"\; state="\{\{state\}\}">k</figure-callout>}}^2\mathrm{Ln}{k}_j^2}{(k^2-1){(r/r_i)}^2}=0$

$\frac{r}{r_i}=\sqrt{\frac{k^2-{\mathrm{<figure-callout\; id="2"\; label="k\; j"\; filenames="HSA00000644018300022.png,HSA00000644018300031.png"\; state="\{\{state\}\}">k</figure-callout>}}_j^{}+{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HSA00000644018300022.png,HSA00000644018300031.png"\; state="\{\{state\}\}">k</figure-callout>}}^2\ln k_j^2}{k^2-1}}=\sqrt{\frac{{{\mathrm{\&sigma;}}_{\mathrm{ei}}}^{\&prime;}}{{\mathrm{\&sigma;}}_y}+1}<k_j---\left(11\right)$

On the other hand, to formula (1)～(3), make σ _z'=σ _r', σ _r'=σ _t' and σ _t'=σ _z' also must formula (11).In other words, plastic zone three-dimensional residual stress (σ _z', σ _r' and σ _t') congruence of curves meets at a bit, the abscissa of this point promptly is formula (11).

Get k=3, k _jBe respectively 1.5 and 1.748442, the relative residual stress in the cylindrical wall is (with yield limit σ _yThe ratio value representation) along relative position (r/r in the barrel _i) distribution like Fig. 2, shown in 3.Can know by Fig. 3, theoretical by top four's degree, k=3, k _j=1.748442 o'clock, at the absolute value of the relative equivalent residual stress at cylinder inner wall face place | σ _Ei'/σ _y| just reached 1, but the absolute value of relative hoop residual stress | σ _Ti'/σ _y| surpassed 1, this be because And the σ at internal face place _Ri'/σ _y=0, so work as | σ _Ei'/σ _y|=1 o'clock, | σ _Ti'/σ _y| must surpass 1.

So, tackle σ in case of necessity _Ti'/σ _yLimit.Order

Must be according to restriction σ _Ti'/σ _yPrinciple and maximum plastic zone degree of depth k under certain k of determining _j:

${2\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HSA00000644018300022.png,HSA00000644018300031.png"\; state="\{\{state\}\}">k</figure-callout>}}^2\mathrm{Ln}{k}_j^2-{2k}_j^2-\sqrt{3}{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HSA00000644018300022.png,HSA00000644018300031.png"\; state="\{\{state\}\}">k</figure-callout>}}^2+(2+\sqrt{3})=0$ Or $k=\sqrt{\frac{2(k_j^2-1)-\sqrt{3}}{\text{2ln}{k}_j^2-\sqrt{3}}}---\left(12\right)$

Know by formula (12),

Note is by the determined k of formula (12) _jBe k _Jt

In formula (12), make k _j=k gets:

$\frac{{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HSA00000644018300022.png,HSA00000644018300031.png"\; state="\{\{state\}\}">k</figure-callout>}}^2\ln k^2}{k^2-1}=\frac{2+\sqrt{3}}{2}---\left(13\right)$

Separating of formula (13) is k=2.024678965...=k _Ct, k _CtBe called critical footpath ratio, this means k≤k _CtThe time, no matter how dark the plastic zone is, even full surrender, i.e. k _j=k, when carrying out the self intensification processing, removal from strengthen pressure p _aReverse yielding can not take place in back cylinder; K＞k _CtThe time, if k _jGreater than by the determined value (k of formula (12) _j＞k _Jt), when carrying out the self intensification processing, removal from strengthen pressure p _aReverse yielding can take place in back cylinder.K in the formula (12) _jBe shown in Fig. 4, k≤k with the relation of k _CtThe time, plastic zone degree of depth k _jCalculate (look into and get), i.e. k by straight line od _j=k; K>=k _CtThe time, plastic zone degree of depth k _jCalculate (look into and get) by curve da, promptly calculate by formula (12).Practical application for ease is with k in the formula (12) _jList in table 1 with the numerical value of k.

Table 1 ${2\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HSA00000644018300022.png,HSA00000644018300031.png"\; state="\{\{state\}\}">k</figure-callout>}}^2\mathrm{Ln}{k}_j^2-{2k}_j^2-\sqrt{3}{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HSA00000644018300022.png,HSA00000644018300031.png"\; state="\{\{state\}\}">k</figure-callout>}}^2+(2+\sqrt{3})=0$ Numerical tables

Continuous table 1

Continuous table 1

According to pressurized container knowledge, the plastic zone degree of depth is k _jThe load (interior pressure) that can bear of cylinder be:

$\frac{p}{{\mathrm{\&sigma;}}_y}=\frac{2}{\sqrt{3}}\ln k_j+\frac{k^2-{\mathrm{<figure-callout\; id="2"\; label="k\; j"\; filenames="HSA00000644018300022.png,HSA00000644018300031.png"\; state="\{\{state\}\}">k</figure-callout>}}_j^{}}{\sqrt{3}{k}^2}---\left(14\right)$

Wherein p is the load that cylinder bore.Convolution (14) and (12) proper k _j=k _JtThe time, promptly when the plastic zone degree of depth by formula (12) when confirming, at condition σ _Ti'/σ _y=-1 (| σ _Ei'/σ _y|＜1) the following cylinder load of being born:

$\frac{p}{{\mathrm{\&sigma;}}_y}=\frac{\sqrt{3}+2}{2\sqrt{3}}\frac{k^2-1}{{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HSA00000644018300022.png,HSA00000644018300031.png"\; state="\{\{state\}\}">k</figure-callout>}}^2}=(1+\frac{\sqrt{3}}{2})\frac{p_e}{{\mathrm{\&sigma;}}_y}---\left(15\right)$

Therefore, at k＞k _CtSituation under, if need to satisfy | σ _Ti'/σ _y|≤1 (| σ _Ei'/σ _y|＜1), then the bearing capacity of autofrettaged cylinder is confirmed by formula (15).P/ σ _y, p _e/ σ _yBe shown in Fig. 5, wherein p _eInitial yield pressure (load) for non-autofrettaged cylinder.K>=k _CtThe time, bearing capacity is calculated (look into and get) by curve fb, promptly calculates by formula (15).

Work as k _j=k _Jt, i.e. k _jBy formula (12) when confirming, utilize formula (12) can formula (1)～(8) be put in order and residual stress and equivalent stress thereof after being improved:

$\frac{{{\mathrm{\&sigma;}}_z}^{\&prime;}}{{\mathrm{\&sigma;}}_y}=\frac{1}{\sqrt{3}}\ln {\left(\frac{r}{r_i}\right)}^2-\frac{1}{2}=\frac{1}{\sqrt{3}}\ln x^2-\frac{1}{2}---\left(1a\right)$

$\frac{{{\mathrm{\&sigma;}}_r}^{\&prime;}}{{\mathrm{\&sigma;}}_y}=\frac{1}{\sqrt{3}}(\ln x^2+\frac{2+\sqrt{3}}{2x^2}-\frac{2+\sqrt{3}}{2})---\left(2a\right)$

$\frac{{{\mathrm{\&sigma;}}_t}^{\&prime;}}{{\mathrm{\&sigma;}}_y}=\frac{1}{\sqrt{3}}(\ln x^2-\frac{2+\sqrt{3}}{2x^2}+\frac{2-\sqrt{3}}{2})---\left(3a\right)$

$\frac{{{\mathrm{\&sigma;}}_e}^{\&prime;}}{{\mathrm{\&sigma;}}_y}=1-\frac{\sqrt{3}+2}{2{(r/r_i)}^2}=1-\frac{\sqrt{3}+2}{2x^2}---\left(4a\right)$

$\frac{{{\mathrm{\&sigma;}}_z}^{\&prime;}}{{\mathrm{\&sigma;}}_y}=\frac{k_j^2-(\sqrt{3}+2)/2}{\sqrt{3}{k}^2}---\left(5a\right)$

$\frac{{{\mathrm{\&sigma;}}_r}^{\&prime;}}{{\mathrm{\&sigma;}}_y}=(1-\frac{k^2}{{(r/r_i)}^2})\frac{{{\mathrm{\&sigma;}}_z}^{\&prime;}}{{\mathrm{\&sigma;}}_y}=(1-\frac{k^2}{x^2})\frac{{{\mathrm{\&sigma;}}_z}^{\&prime;}}{{\mathrm{\&sigma;}}_y}---\left(6a\right)$

$\frac{{{\mathrm{\&sigma;}}_t}^{\&prime;}}{{\mathrm{\&sigma;}}_y}=(1+\frac{k^2}{{(r/r_i)}^2})\frac{{{\mathrm{\&sigma;}}_z}^{\&prime;}}{{\mathrm{\&sigma;}}_y}=(1+\frac{k^2}{x^2})\frac{{{\mathrm{\&sigma;}}_z}^{\&prime;}}{{\mathrm{\&sigma;}}_y}---\left(7a\right)$

$\frac{{{\mathrm{\&sigma;}}_e}^{\&prime;}}{{\mathrm{\&sigma;}}_y}=\frac{k_j^2-(\sqrt{3}+2)/2}{x^2}---\left(8a\right)$

X=r/r wherein _i

Residual stress before residual stress after the improvement and equivalent stress thereof and the improvement and equivalent stress thereof relatively see Fig. 6,7 (all representing to the residual stress and the relative value of the ratio of yield strength) with each.Obviously, residual stress and equivalent stress thereof after the improvement have reduced, and all in safety range, promptly all above yield strength.Among Fig. 6,7, residual stress after solid line is represented to improve and equivalent stress thereof (are r/r along barrel relative position x _i) distribution, wherein, a: σ _z'/σ _y, b: σ _r'/σ _y, c: σ _t'/σ _y, d: σ _e'/σ _yResidual stress and equivalent stress thereof before dotted line is represented to improve (are r/r along barrel relative position x _i) distribution, wherein, a ': σ _z'/σ _y, b ': σ _r'/σ _y, c ': σ _t'/σ _y, d ': σ _e'/σ _y

The theoretical foundation and the foundation of reference when certain law, relation and the data that obtain in the above analytic demonstration process, chart etc. can be used as the pressurized container engineering design also make theoretical each relationship between parameters of self intensification and Changing Pattern more clear, thorough and practical.

Claims (2)

1. self-reinforcing pressure vessel based on the safety design technical specifications is characterized in that: the physical dimension of this kind pressurized container and bearing capacity confirm that by specific technological scheme specifically: its whole wall thickness does For k greater than by formula

The self-reinforcing pressure vessel of the value of confirming, its plastic zone degree of depth by formula

Confirm that its bearing capacity does

R wherein _iBe the internal diameter of self-reinforcing pressure vessel, k is the self-reinforcing pressure vessel outer radius and the ratio of inside radius, plastic zone degree of depth k _jBe self-reinforcing pressure vessel elasticity and plastic zone interface radius r _jTo the ratio of inside radius, i.e. k _j=r _j/ r _i, σ _yBe the self-reinforcing pressure vessel YIELD STRENGTH, p is the interior pressure that self-reinforcing pressure vessel bore, p _eMaximum flexibility bearing capacity (initial yield load) for non-self-reinforcing pressure vessel.

2. the self-reinforcing pressure vessel based on the safety design technical specifications as claimed in claim 1 is characterized in that: for k less than by formula

The self-reinforcing pressure vessel of the value of confirming, its plastic zone scope can be whole wall thickness, i.e. k _j=k.

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