CN104358867A - Elastic temperature difference prestress pressure container - Google Patents
Elastic temperature difference prestress pressure container Download PDFInfo
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- CN104358867A CN104358867A CN201410640932.2A CN201410640932A CN104358867A CN 104358867 A CN104358867 A CN 104358867A CN 201410640932 A CN201410640932 A CN 201410640932A CN 104358867 A CN104358867 A CN 104358867A
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F16—ENGINEERING ELEMENTS AND UNITS; GENERAL MEASURES FOR PRODUCING AND MAINTAINING EFFECTIVE FUNCTIONING OF MACHINES OR INSTALLATIONS; THERMAL INSULATION IN GENERAL
- F16J—PISTONS; CYLINDERS; SEALINGS
- F16J12/00—Pressure vessels in general
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Abstract
The invention provides an elastic temperature difference prestress pressure container, solving the technical problems of how to improve the bearing capability and the safety of a pressure container and the like. According to the pressure container, temperature difference stress generated by a temperature difference between inner and outer walls is used for counteracting a part of mechanical stress caused by operation inner pressure p and the stress distribution is reduced and homogenized, so that the bearing capability is enhanced; compared with a mechanical prestress method, the self-enhanced pressure container is safer, portable, reliable and economical and has a more flexible design. According to the technical scheme, the elastic temperature difference prestress pressure container has the characteristics that the limitation conditions for ensuring the safety (equivalent weight stress is lower than yield strength) and the economy (high bearing capability, small thickness and low cost) of the pressure container can be given, namely the constraint conditions which should be met among a diameter ratio k, a temperature difference dt, working pressure p, elasticity modulus E, coefficient of thermal expansion m, Poisson's ratio u and yield strength sy are given, so that the safe and economical technical scheme is formed. The minimal diameter ratio of the pressure container can reach k=ep/sy or the equation shown as the specification; the highest working pressure reaches p/sy=lnk or p/sy=(k2-1)/k2.
Description
Technical field
The present invention relates to a kind of elasticity temperature difference prestressed pressure container.
Background technique
Pressurized container is key, the special equipment of many industrial departments, is widely used in all trades and professions, as departments such as machinery, chemical industry, pharmacy, the energy, material, food, metallurgy, oil, building, Aeronautics and Astronautics, weapons.The main body overwhelming majority of pressurized container is cylinder, and when cylinder bears working pressure, the stress in its wall is very uneven, as shown in Figure of description 3.Container thickness is larger, and stress is more uneven.If press maximum stress design pressure container, its wall thickness can be made very large, and wall thickness greatly not only wastes material, resource, fund, increases cost, also has potential safety hazard.Must manage to reduce the stress in container wall, the intensity of container could be improved, save material, reduce costs, and improve the Security of pressurized container.The method reducing the stress in container wall has a lot, such as, before container comes into operation, larger mechanical pressure is applied to it, its internal layer portion of material is made to produce plastic deformation, outer section material is still elastic state, after removal mechanical pressure, just in container wall, produce mechanical prestress (residual stress): internal layer portion of material is pressure stress, outer section material is tensile stress.The stress that mechanical prestress and container operation pressure cause is superimposed can reduce stress.The present invention then utilizes the temperature difference of pressurized container inside and outside wall generation temperature difference prestressing force to reduce and the stress in homogenization pressures container, thus constructs a kind of elasticity temperature difference prestressed pressure container.The temperature difference is caused by the operational difference of container itself, or heats its inside and outside wall or cool and cause before container comes into operation.Temperature difference prestressed pressure container is more safer than mechanical prestress pressurized container, convenient, reliable, save, flexibly, because (1) produce prestressed method by temperature difference stress to there is not medium of exerting pressure, therefore not dangerous, do not need expensive hydraulic press etc. to exert pressure equipment yet; (2) control of the temperature difference is comparatively easy, and thus the size of temperature difference stress and uniformity thereof are easily guaranteed; (3) once temperature difference stress is excessive, owing to there is not pressure medium, therefore unlikelyly as mechanical stress, the catastrophic failures such as pressurized container blast are caused; (4) inventor studies discovery, the prestressed size of the temperature difference and the regularity of distribution and the temperature difference
dtbe closely connected, therefore, can change according to operational condition
dtto obtain different operational stresses induced states, visual cell structure optimization space is very large, and this just can obtain the design proposal of maneuverability.
Pressurized container is by machinery during pressure, and its most severe stress is the tensile stress of internal face; When internal pressure vessel walls surface temperature is higher than outer wall temperature, the distribution of its temperature difference stress is, most severe stress is the pressure stress of internal face.Therefore the present invention is to provide in interior pressure the technological scheme adding thermoelasticity temperature difference prestressed pressure container, so-called elasticity temperature difference prestressing force is namely under temperature difference stress independent role, and pressurized container is in elastic state.
The inefficacy of some pressure vessel material should be controlled by the 3rd theory of strength, and the inefficacy of some pressure vessel material should be controlled by fourth strength theory, and namely different materials should be controlled by different theory of strength.The invention provides the technological scheme of the elasticity temperature difference prestressed pressure container controlled by fourth strength theory.
Summary of the invention
The object of this invention is to provide a kind of elasticity temperature difference prestressed pressure container.
The technical solution adopted for the present invention to solve the technical problems is: construct a kind of elasticity temperature difference prestressed pressure container, it is characterized in that: the inside and outside wall of described pressurized container exists the temperature difference, and internal face temperature
t ihigher than outer wall temperature
t o, i.e. the temperature difference
dt=
t i-
t o>0; The temperature difference makes pressurized container wall produce temperature difference prestressing force, and total stress during pressurized container work is that temperature difference prestressing force and mechanical stress are superimposed; Described mechanical stress finger pressure container work pressure
pthe stress produced, described pressurized container working pressure
pfor interior pressure; Described internal pressure vessel walls radius surface is
r i, outer wall radius is
r o, footpath ratio is
k=
r o/
r i; Described pressurized container, under the effect of temperature difference prestressing force, is in elastic state, namely
dt≤
dt c,
dt cfor temperature difference prestressing force has just made internal pressure vessel walls face produce the temperature difference of surrender, be called critical temperature difference,
dt cby each technical parameter of pressurized container, the i.e. Young's modulus of material
e, material thermal expansion coefficient
m, material Poisson's ratio
u, material yield strength
s y, footpath ratio
kdetermine, specifically:
; Described pressure vessel technology parameter is retrained by following two correlations (1), (2):
(1) 3
b 2 p 2+ 3
abp t p+
a 2 p t 2-
s y 2≤ 0, namely
,
(2) 3
d 2 p 2-3
cdp t p+
c 2 p t 2-
s y 2≤ 0, namely
,
For determining footpath ratio
k, determine the temperature difference
dtpressurized container, its working pressure
pfeature be
p=min{
p 1,
p 2, for determining working pressure
p, determine the temperature difference
dtpressurized container, its footpath ratio
kfor the higher value of correlation (1), (2) gained, wherein
,
,
,
,
.The described temperature difference is caused by the operating temperature of pressurized container itself, or heats the inside and outside wall of pressurized container or cool and cause.For footpath ratio
kthe pressurized container of≤2.0542956825, its temperature difference
dtfor the optimum temperature difference
dt e, working pressure is
p=
p 1=
p 2, wherein
dt eby correlation
determine.The temperature difference
dtfor critical temperature difference
dt c, (1) is for footpath ratio
kthe pressurized container of≤2.0542956825, working pressure
pfor
; (2) for footpath ratio
kthe pressurized container of>=2.0542956825, working pressure
pfor
, or footpath ratio is
.Footpath ratio is
k, bear working pressure
ptime, inside and outside wall temperature difference
dtbe defined as
, or be defined as
, or be defined as
dt 1≤
dt≤
dt 2.
Beneficial effect of the present invention and advantage are: the inside and outside wall of container exists temperature difference, temperature difference prestressing force offsets the stress that caused by working pressure of a part, thus reduce and true stress in homogenizing container.Each technical parameter of container is limited to not only safely but also in economic scope, for making constructed pressurized container science, advanced person, to reach optimum efficiency, the invention provides the footpath ratio of constructed pressurized container
k, working pressure
p, material property factor is (as Young's modulus
e, thermal expansion coefficient
m, Poisson's ratio
u, yield strength
s y), the temperature difference
dtbetween the concrete technological scheme such as the constraint rule that should follow.Prestressed method is produced not only safe but also economical with temperature difference stress; The control of the temperature difference is easier to, therefore the size of temperature difference stress and uniformity thereof are easily guaranteed; Can obtain different operational stresses induced states according to operational condition, it is very large that structure of container optimizes space, can obtain the design proposal of maneuverability.
Accompanying drawing explanation
Fig. 1 is the cylindrical pressure vessel that inside and outside wall exists the temperature difference.
Fig. 2 is the distribution of elasticity temperature difference stress.
Fig. 3 is interior pressure
pthe mechanical stress caused.
Fig. 4 is temperature difference stress and the superposing of mechanical stress---total stress.
Fig. 5 is embodiment 2 total stress distribution map.
Fig. 6 is embodiment 4 total stress distribution map.
Fig. 7 is embodiment 5 total stress distribution map.
Fig. 8 is embodiment 6 total stress distribution map.
Embodiment
Provide the scientific basis constructing this pressurized container below, and provide enforcement example in conjunction with these theories.
The main body overwhelming majority of pressurized container is cylinder, if the inside and outside radius of cylindrical pressure vessel is respectively
r i,
r o, the symbol of subscripting i, o represents the value on inside and outside wall respectively; Inside and outside wall temperature is respectively
t i,
t o.The arbitrary radius of barrel is
rthe temperature at place is
t, see Figure of description 1.
By analysis, studying, there is the temperature difference in the inside and outside wall of cylindrical pressure vessel
dttime, in wall, (radius is at any point place
r) temperature difference stress be:
(1)
Wherein,
s r t,
s t t,
s z t-radial direction, hoop, axial temperature difference stress, MPa;
p t-thermal force, MPa,
;
ethe Young's modulus of-pressure vessel material, MPa;
mthe thermal expansion coefficient of-pressure vessel material, ° C
-1;
uthe Poisson's ratio of-pressure vessel material, dimensionless;
dtthe temperature difference of the inside and outside wall of-pressurized container, ° C,
dt=
t i-
t o;
kthe footpath ratio of-pressurized container, dimensionless,
k=
r o/
r i;
k r-
k r=
r o/
r, dimensionless;
x-relative position,
x=
r/
r i, dimensionless.
The inside and outside wall temperature difference stress of pressurized container is:
(2)
On the inside and outside wall of cylinder, axle, hoop temperature difference stress are equal.If
dt>0, heating namely, then
s z t<
s t t, namely
s r t<0; If
dt<0, i.e. external heat, then
s z t>
s t t, namely
s r t>0.No matter interior heating or external heat, internal face stress absolute value is greater than outer wall stress absolute value, and
s ri t=0, therefore, along with |
dt| increase, always internal face is first surrendered.
Example: the Young's modulus of general steel is
e=1.95 × 10
5mPa, Poisson's ratio is
u=0.3, thermal expansion coefficient is
m=1.2 × 10
-5° C
-1.If
dt=50 ° of C,
r i=200mm,
r o=500mm, namely
k=2.5, its temperature difference stress is as shown in Figure of description 2.
The equivalent stress of fourth strength theory (meter Sai Si yield condition) is
, when
s e=
s ytime, container inner wall face starts surrender, obtains the internal face initial yield temperature difference, be called critical temperature difference by formula (2)
dt c:
(3)
Wherein
s yfor the yield strength of pressure vessel material.
Thermal force when surrendering by formula (3) obtains internal face, is called critical heat load
p tc:
(4)
(wherein, internal pressure vessel elastic mechanical stress be
s r p,
s t p,
s z p-radial direction, hoop, axial mechanical stress, MPa)
、
、
(5)
If
p=150Mpa, to the container in example, by
pthe mechanical stress caused is as shown in Figure of description 3.
Visible, if the yield strength of this pressure vessel material is less than 310MPa, do not utilize temperature difference pressure stress to reduce the mechanical stress of pressurized container, just dangerous.
dtduring=50 ° of C, temperature difference stress superposes as shown in Figure of description 4 with mechanical stress.
Temperature difference stress is called total stress with superposing of mechanical stress, and when cylindrical pressure vessel is by interior pressure, total stress is
(6)
In formula,
s r,
s t,
s z-radial direction, hoop, axial total stress, MPa.
(7)
(8)
(9)
, as seen at-∞ <
xin <+ ∞, remove
p=
p toutward,
s t-
s rthere is no stationary point,
p<
p ttime,
s t-
s rdan Zeng;
p>
p ttime,
s t-
s rsingly subtract;
p=
p ttime,
s t-
s rfor constant
p t/ ln
k.
Outer wall,
x=
k:
(10)
(11)
(12)
Wherein
,
.
The equivalent stress of fourth strength theory (meter Sai Si yield condition)
, order
s e≤
s y?
3
b 2 p 2+3
abp t p+
a 2 p t 2-
s y 2≤0 (13)
Solved by formula (13)
p:
(14)
Solved by formula (13)
p t:
(15)
Namely
(15a)
time,
.
Internal face,
x=1:
(16)
(17)
(18)
Wherein
,
.
By fourth strength theory
?
3
d 2 p 2-3
cdp t p+
c 2 p t 2-
s y 2≤0 (19)
Solved by formula (19)
p
(20)
p t≤
p tctime, namely
dt≤
dt ctime,
p 10≤ 0.
Solved by formula (19)
p t
(21)
Namely
(21a)
time (without prestressed maximum flexibility load),
.
dtincrease,
p 2reduce, and
p 1increase;
dtreduce,
p 2increase, and
p 1reduce.In practical application, to a sizing ratio
k, a fixed difference difference
dt, get
p 1,
p 2little person as allowable load; Or to certain load
p, a fixed difference difference
dt, the large person of modus ponens (13), (19) gained is as footpath ratio
k.
Order
p 1=
p 2?
(22)
Can be obtained by formula (22) and make
p 1=
p 2the temperature difference
dt e, be called the optimum temperature difference.But
dt ecan not be greater than
dt c.If
k≤
k i,
dt e≤
dt c; If
k>=
k i,
dt e>=
dt c; Wherein
k i=2.0542956825.
When
dt=
dt c, namely
p t=
p tctime,
.
dt=
dt ctime, if
k≤
k i(corresponding
dt c=135.2732 ° of C), then
p 2≤
p 1,
dtbe reduced to suitable degree can make
p 1=
p 2; If
k>=
k i, then
p 1≤
p 2, except non-increasing
dt, but
dtcan not be greater than
dt c; If reduce
dt, then due to
dtreduce,
p 2increase, and
p 1reduce, thus make
p 2>
p 1.So,
k>=
k itime, always
p 1≤
p 2if,
dt<
dt c, then allowable load
p=
p 1; If get
dt=
dt c, then allowable load
or
(23)
The footpath ratio of embodiment 1 elasticity temperature difference prestressed pressure container
k=2.1(>
k i), (Young's modulus
e=1.95 × 10
5mPa, Poisson's ratio
u=0.3, thermal expansion coefficient
m=1.2 × 10
-5° C
-1, yield strength
s y=300MPa, lower same).Obtained by formula (3)
dt c=144.9011 ° of C, are obtained by formula (23)
p=
p 1=231.9728MPa.Obtained by formula (22)
dt e=149.9513 ° of C>
dt c, meaningless.Therefore, the technical parameter of this pressurized container is
k=2.1,
dt=
dt c=144.9011 ° of C,
pduring=231.9728MPa, not only safety (equivalent pressure is less than yield strength) but also the technique effect of economy (carrying maximum) can be obtained.
Embodiment 2
k=3>
k i(>
k i).Obtained by formula (3)
dt c=133.9696 ° of C, are obtained by formula (23)
p=
p 1=266.6667MPa, is obtained by formula (22)
dt e=218.1078 ° of C>
dt c.Therefore, the technical parameter of this pressurized container is
k=3,
dt=144.9011 ° of C,
pduring=231.9728MPa, not only safety but also economic technique effect can be obtained.The distribution of its total stress is as shown in Figure of description 5.
Embodiment 3
k=1.6(<
k i), obtained by formula (3)
dt c=155.4798 ° of C, are obtained by formula (23)
p=
p 2=80.0235MPa.Obtained by formula (22)
dt e=96.31247 ° of C<
dt c.
dt=
dt etime,
p=
p 1=
p 2=156.9785MPa.Therefore, the technical parameter of this pressurized container is
k=1.6,
dt=
dt e=96.31247 ° of C,
pduring=156.9785MPa, not only safety but also economic technique effect can be obtained.
If elasticity temperature difference prestressed pressure container footpath ratio is
k, need working pressure be born
p, then reference
dt 0,
dt 1,
dt 2,
dt cget the suitable temperature difference, get the lower temperature difference as far as possible.
The footpath ratio of embodiment 4 elasticity temperature difference prestressed pressure container
k=1.6(<
k i), need working pressure be born
p=130MPa.Obtained by formula (3)
dt c=155.4798 ° of C, are obtained by formula (21a)
dt 0=288.3432 ° of C,
dt 1=43.3471 ° of C, are obtained by formula (15a)
dt 2=117.5862 ° of C.The present gets
dt=70 ° of C.Namely the optimum technology parameter of this container is
k=1.6,
p=130MPa,
dt=70 ° of C.The distribution of its total stress is as shown in Figure of description 6.
Embodiment 5,
k=2.1>
k i,
p=220MPa.Obtained by formula (3)
dt c=144.9011 ° of C, are obtained by formula (21a)
dt 0=288.7934 ° of C,
dt 1=123.4736 ° of C, are obtained by formula (15a)
dt 2=155.5836 ° of C.The present gets
dt=130 ° of C.Namely the optimum technology parameter of this container is
k=2.1,
p=220MPa,
dt=130 ° of C.The distribution of its total stress is as shown in Figure of description 7.
Embodiment 6
k=2.5(>
k i),
p=250MPa.Obtained by formula (3)
dt c=139.181 ° of C, are obtained by formula (21a)
dt 0=278.3362 ° of C,
dt 1=135.8928 ° of C, are obtained by formula (15a)
dt 2=190.1005 ° of C.The present gets
dt=139 ° of C.Namely the optimum technology parameter of this container is
k=2.5,
p=250MPa,
dt=139 ° of C.The distribution of its total stress is as shown in Figure of description 8.
If elasticity temperature difference prestressed pressure container need bear working pressure
p, its inside and outside wall temperature difference is
dt, then footpath ratio is determined by formula (13), (19) by numerical radius
k, get larger
kas footpath ratio.
k>=
k itime, if right
dtunrestrictedly, then determined by formula (23)
k, then determined by formula (3)
dt c, with
dt cas the temperature difference.
Embodiment 7 elasticity temperature difference prestressed pressure container need bear working pressure
p=130MPa, its inside and outside wall temperature difference is
dt=150 ° of C.Determined by formula (13)
k=1.770509, determined by formula (19)
k=1.343435, the present gets
k=1.770509.If get
dt c=130 ° of C, are determined by formula (23)
k=1.328422<
k i, cast out.Therefore the optimum technology parameter of container is
k=1.770509,
p=130MPa,
dt=150 ° of C.
Embodiment 8
p=220MPa,
dt=130 ° of C.Determined by formula (13)
k=1.931518, determined by formula (19)
k=2.048803<
k i, the present gets
k=2.048803.If get
dt c=130 ° of C, are determined by formula (23)
k=1.936492<
k i, cast out.Therefore the optimum technology parameter of container is
k=2.048803,
p=220MPa,
dt=130 ° of C.
Embodiment 9
p=250MPa,
dt=110 ° of C.Determined by formula (13)
k=1.903431<
k i, determined by formula (19)
k=3.005172>
k i, the present gets
k=3.005172, therefore the technical parameter of container is
k=3.005172,
p=250MPa,
dt=110 ° of C.In addition,
pduring=250MPa, determined by formula (23)
k=2.44949>
k i.
kwhen=2.44949,
dt c=139.8116 ° of C.Therefore another technological scheme of intending bearing the container of 250MPa is
k=2.44949,
p=250MPa,
dt=139.8116 ° of C.This scheme is like better.
Claims (5)
1. an elasticity temperature difference prestressed pressure container, is characterized in that: the inside and outside wall of described pressurized container exists the temperature difference, and internal face temperature
t ihigher than outer wall temperature
t o, i.e. the temperature difference
dt=
t i-
t o>0; The temperature difference makes pressurized container wall produce temperature difference prestressing force, and total stress during pressurized container work is that temperature difference prestressing force and mechanical stress are superimposed; Described mechanical stress finger pressure container work pressure
pthe stress produced, described pressurized container working pressure
pfor interior pressure; Described internal pressure vessel walls radius surface is
r i, outer wall radius is
r o, footpath ratio is
k=
r o/
r i; Described pressurized container, under the effect of temperature difference prestressing force, is in elastic state, namely
dt≤
dt c,
dt cfor temperature difference prestressing force has just made internal pressure vessel walls face produce the temperature difference of surrender, be called critical temperature difference,
dt cby each technical parameter of pressurized container, the i.e. Young's modulus of material
e, material thermal expansion coefficient
m, material Poisson's ratio
u, material yield strength
s y, footpath ratio
kdetermine, specifically:
; Described pressure vessel technology parameter is retrained by following two correlations (1), (2):
(1) 3
b 2 p 2+ 3
abp t p+
a 2 p t 2-
s y 2≤ 0, namely
,
(2) 3
d 2 p 2-3
cdp t p+
c 2 p t 2-
s y 2≤ 0, namely
,
For determining footpath ratio
k, determine the temperature difference
dtpressurized container, its working pressure
pfeature be
p=min{
p 1,
p 2, for determining working pressure
p, determine the temperature difference
dtpressurized container, its footpath ratio
kfor the higher value of correlation (1), (2) gained,
Wherein
,
,
,
,
.
2. elasticity temperature difference prestressed pressure container according to claim 1, is characterized in that: the described temperature difference is caused by the operating temperature of pressurized container itself, or heats the inside and outside wall of pressurized container or cool and cause.
3. elasticity temperature difference prestressed pressure container according to claim 1, is characterized in that: for footpath ratio
kthe pressurized container of≤2.0542956825, its temperature difference
dtfor the optimum temperature difference
dt e, working pressure is
p=
p 1=
p 2, wherein
dt eby correlation
determine.
4. elasticity temperature difference prestressed pressure container according to claim 1, is characterized in that: the temperature difference
dtfor critical temperature difference
dt c, (1) is for footpath ratio
kthe pressurized container of≤2.0542956825, working pressure
pfor
; (2) for footpath ratio
kthe pressurized container of>=2.0542956825, working pressure
pfor
, or footpath ratio is
.
5. elasticity temperature difference prestressed pressure container according to claim 1, is characterized in that: footpath ratio is
k, bear working pressure
ptime, inside and outside wall temperature difference
dtbe defined as
, or be defined as
, or be defined as
dt 1≤
dt≤
dt 2.
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| CN105508600A (en) * | 2016-01-07 | 2016-04-20 | 湖南师范大学 | Low-temperature prestress internal-pressure internal-heating pressure vessel |
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| Title |
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| 朱瑞林: "自增强容器塑性区深度与承载能力剖析", 《化工装备技术》 * |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105508600A (en) * | 2016-01-07 | 2016-04-20 | 湖南师范大学 | Low-temperature prestress internal-pressure internal-heating pressure vessel |
Also Published As
| Publication number | Publication date |
|---|---|
| CN104358867B (en) | 2016-04-20 |
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