CN112287486B - Performance prediction method for non-mould free bulging process of cylindrical shell of submersible - Google Patents
Performance prediction method for non-mould free bulging process of cylindrical shell of submersible Download PDFInfo
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Abstract
The invention discloses a performance prediction method for a model-free bulging process of a cylindrical shell of a submersible, which is used for designing and calculating the change rules of an axial curvature radius, a circumferential curvature radius, a surface area, a midpoint thickness, midpoint equivalent strain, an internal volume, bulging pressure and midpoint equivalent stress in the model-free bulging process and providing theoretical data support for the design and optimization of the model-free bulging process parameters of the cylindrical shell of the submersible.
Description
Technical Field
The invention belongs to the technical field of plastic processing of plate shells, and particularly relates to a mould-free bulging process for a cylindrical shell of a submersible.
Background
The submersible is an important device for ocean exploration and development, the pressure-resistant shell is a key part and a buoyancy unit of the submersible, and the pressure-resistant shell can ensure that internal equipment is not damaged and safety of staff is ensured in the submersible submerging process, and meanwhile positive buoyancy is provided. The cylindrical shell is a basic pressure-bearing unit of the pressure-resistant shell, and has the advantages of high space utilization rate, good hydrodynamic characteristics, convenient design and calculation and the like.
However, the cylindrical shell ultimate bearing capacity is very sensitive to initial geometric imperfections, resulting in reduced safety. By applying internal pressure to the cylindrical shell, the cylindrical shell is free of mold bulging, so that the oversized initial geometric defect can be eliminated, the yield strength of materials can be increased, the mechanical properties of the shell are balanced, the ultimate bearing capacity of the cylindrical shell is improved, the safety of the shell is improved, and meanwhile, the internal space is also increased. However, the industry still lacks a method of predicting performance of a cylindrical shell mold-less free bulging process.
Disclosure of Invention
In order to solve the technical problems mentioned in the background art, the invention provides a performance prediction method for a model-free bulging process of a cylindrical shell of a submersible.
In order to achieve the technical purpose, the technical scheme of the invention is as follows:
a performance prediction method for a model-free bulging process of a cylindrical shell of a submersible comprises the following steps:
(1) Designing a calculation formula of the axial curvature radius and the circumferential curvature radius of the cylindrical shell, and substituting the bulging amount into the calculation formula to obtain the course of the change of the axial curvature radius and the circumferential curvature radius of the cylindrical shell along with the bulging amount;
(2) Designing a calculation formula of the surface area of the cylindrical shell, and substituting the bulging amount into the calculation formula to obtain the process of the change of the surface area of the cylindrical shell along with the bulging amount;
(3) Designing a calculation formula of the thickness of the midpoint of the cylindrical shell, and substituting the bulging amount into the calculation formula to obtain the process that the thickness of the midpoint of the cylindrical shell changes along with the bulging amount;
(4) Designing a calculation formula of the internal volume of the cylindrical shell, and substituting the bulging amount into the calculation formula to obtain the course of the change of the internal volume of the cylindrical shell along with the bulging amount;
(5) Designing a calculation formula of the equivalent strain of the midpoint of the cylindrical shell, and substituting the bulging amount into the calculation formula to obtain the process of the equivalent strain of the midpoint of the cylindrical shell along with the change of the bulging amount;
(6) Designing a calculation formula of the bulging pressure of the cylindrical shell, and substituting the bulging amount into the calculation formula to obtain the process of the bulging pressure of the cylindrical shell along with the change of the bulging amount;
(7) And designing a calculation formula of the equivalent stress at the midpoint of the cylindrical shell, and substituting the bulging amount into the calculation formula to obtain the process of the change of the equivalent stress at the midpoint of the cylindrical shell along with the bulging amount.
Further, in step (1), the calculation formula of the axial curvature radius and the circumferential curvature radius of the cylindrical shell is as follows:
in the above, R 1 Is the axial curvature radius, R 2 Is circumferential curvature radius, h is bulging amount, and l is cylindrical shellHalf of height, r 0 Is the initial outer circular radius of the cylindrical shell.
Further, in step (2), the calculation formula of the cylindrical shell surface area is as follows:
in the above, y is a bulging curve, x is the vertical displacement of the middle point of the cylindrical shell, S is the bulging surface area of the cylindrical shell, and y' 2 Representing the square of the y derivative.
Further, in step (3), the calculation formula of the thickness of the midpoint of the cylindrical shell is as follows:
in the above formula, t is the thickness of the middle point of the cylindrical shell, and t 0 For the initial thickness, k is the thickness coefficient.
Further, the expression of the thickness coefficient k is as follows:
k＝2.79154E-06h 3 -2.92802E-04h 2 -1.39745E-04h+1
in the above formula, E is the elastic modulus.
Further, in step (4), the calculation formula of the internal volume of the cylindrical shell is as follows:
in the above, V 0 The cylinder shell is characterized in that the cylinder shell is in volume, V is the cylinder shell volume, V' is the cylinder shell inner volume, and x is the cylinder shell midpoint vertical displacement.
Further, in step (5), the calculation formula of the equivalent strain at the midpoint of the cylindrical shell is as follows:
in the above, ε t For normal strain ε θ For the purpose of axial strain,for circumferential strain, ε eq Is the equivalent strain.
Further, in step (6), the calculation formula of the cylindrical shell bulging pressure is as follows:
in the above, sigma y For material yield strength, E 1 And p is the bulging pressure of the cylindrical shell and is the material strength coefficient.
Further, in step (7), the calculation formula of the equivalent stress at the midpoint of the cylindrical shell is as follows:
in the above-mentioned method, the step of,is circumferential stress, sigma θ Is the axial stress, sigma eq Is equivalent stress.
Further, in steps (1) - (7), the bulging amount is valued in the range of percentage of the bulging radius.
The beneficial effects brought by adopting the technical scheme are that:
the invention designs and calculates the change rule of the axial curvature radius, the circumferential curvature radius, the surface area, the midpoint thickness, the midpoint equivalent strain, the internal volume, the bulging pressure and the midpoint equivalent stress in the non-mould free bulging process, and provides theoretical data support for the design and optimization of the non-mould free bulging process parameters of the cylindrical shell of the submersible. The prediction formula of the cylindrical shell non-mould free bulging performance can be popularized to the prediction of the cylindrical shell non-mould free bulging performance of other materials or fields.
Drawings
FIG. 1 is a flow chart of the overall method of the present invention;
FIG. 2 is a schematic view of a cylindrical shell mold-less free bulging structure;
FIG. 3 shows the bulging amount h and the axial radius of curvature R 1 Radius of curvature R in circumferential direction 2 Is a graph of (2);
FIG. 4 is a graph of bulging amount h versus cylindrical shell bulging surface area S;
FIG. 5 is a graph of bulging amount h versus thickness t at the midpoint of cylindrical shell bulging;
FIG. 6 is a graph of bulging amount h versus cylindrical shell bulging volume V';
FIG. 7 shows the equivalent strain ε between the bulging amount h and the bulging midpoint of the cylindrical shell eq Is a graph of (2);
FIG. 8 is a graph of bulging amount h versus cylindrical shell bulging pressure p;
FIG. 9 shows the equivalent stress sigma between the bulging amount h and the bulging midpoint of the cylindrical shell eq Is a graph of (2);
fig. 10 is a schematic diagram of the cylinder shell mold-less free bulging pressurization.
Detailed Description
The technical scheme of the present invention will be described in detail below with reference to the accompanying drawings.
The present invention will be further described in detail with reference to a flowchart of a method for predicting the free bulging performance of a cylindrical shell without a die shown in fig. 1. The dimensional parameters of the cylindrical shell of the example are shown in table 1, the shell bulging structure is shown in fig. 2, the shell material is stainless steel, and the material parameters are shown in table 2. The concrete implementation process adopts an analytic solution method, is realized by operation, and verifies the correctness of the analytic method through bulging tests of three physical column shells.
TABLE 1 nominal size of cylindrical shells
| Parameters (parameters) | Value (mm) |
| Cylindrical shell size | |
| Outer circle radius (r) 0 ) | 51 |
| Height (2 l) | 100 |
| Initial thickness (t) 0 ) | 0.9 |
| Thick plate size | |
| Radius (r) 0 ) | 51 |
| Thickness (T) | 16 |
TABLE 2 elastoplasticity parameters of Standard stainless Steel Material samples
| Material sample | σ y (MPa) | E 1 (GPa) | E(GPa) | μ |
| C1 | 288.5 | 1310.6 | 214.4 | 0.27 |
| C2 | 286.2 | 1307.2 | 208.1 | 0.28 |
| C3 | 279.1 | 1298.1 | 195.5 | 0.29 |
| average | 284.6 | 1305.3 | 206.0 | 0.28 |
σ y =yield strength; e (E) 1 =intensity coefficient; e = modulus of elasticity; μ=poisson ratio
Step one (S1): the axial curvature radius and the circumferential curvature radius of the cylindrical shell are calculated according to the following formula:
wherein: r is R 1 Is an axial radius of curvature，R 2 And h is the bulging amount, and h is the circumferential curvature radius.
The specific operation is as follows:
a. substituting half-cylinder height l=50mm into axial radius of curvature R 1 The analytical equation of the axial radius of the cylindrical shell along with the change of the bulging amount is obtained, namely:
b. radius r of initial outer circle of cylindrical shell 0 =51mm substitution into the circumferential radius of curvature R 2 The analytical equation of the circumferential radius of the cylindrical shell along with the change of the bulging amount is obtained, namely: r is R 2 ＝h+51；
c. Substituting bulging amount h (1-30 mm) into axial curvature radius R 1 And a circumferential radius of curvature R 2 The analytical equation is solved and in the commercial software Origin, the axial and circumferential radii of curvature of the cylindrical shell are output as a function of the bulging amount, i.e., the bulging radius-bulging amount curve, as shown in FIG. 3
Step two (S2): the surface area of the cylindrical shell is calculated as follows:
wherein: y is the horizontal displacement of the cylindrical shell, x is the vertical displacement of the midpoint of the cylindrical shell, and S is the bulging surface area of the cylindrical shell.
The specific operation is as follows:
a. based on the axial curvature radius R obtained in the first step 1 Circumferential displacement x of midpoint of cylindrical shell, initial outer circle radius r 0 Substituting 50mm into the calculation formula of the bulging radius r to obtain an analytical equation of the bulging radius of the cylindrical shell along with the change of the bulging amount, namely:
b. substituting the bulging radius y formula into a calculation formula of the bulging surface area S of the cylindrical shell to obtain an analytical equation of the bulging surface area of the cylindrical shell along with the change of the bulging amount, namely:
c. substituting the bulging amount h (1-30 mm) into the cylindrical shell bulging surface area S analytical equation and outputting the history of the cylindrical shell surface area as a function of the bulging amount, i.e., the bulging surface area-bulging amount curve, in the commercial software Origin, as shown in fig. 4.
Step three (S3): the thickness of the midpoint of the cylindrical shell is calculated as follows:
where k is a thickness coefficient and the expression is k= 2.79154E-06h 3 -2.92802E-04h 2 1.39745E-04h+1, t is the thickness of the midpoint of the cylindrical shell.
The specific operation is as follows:
a. based on the cylindrical shell bulging radius r, the thickness coefficient k and the initial outer circular radius r of the cylindrical shell obtained in the step two 0 Initial thickness t =51 mm 0 Substituting 0.9mm into a calculation formula of the bulging midpoint thickness t to obtain an analytical equation of the cylindrical shell midpoint thickness along with the bulging amount, namely:
b. substituting the thickness coefficient k expression and the bulging amount h (1-30 mm) into a cylinder shell midpoint thickness t analytical equation to solve and in a commercial software Origin, outputting a history of the cylinder shell midpoint thickness t along with the bulging amount change, namely a midpoint thickness-bulging amount curve, as shown in fig. 5.
Step four (S4): the internal volume of the cylindrical shell is calculated as follows:
wherein V is 0 The cylinder shell is characterized in that the cylinder shell is in volume, V is the cylinder shell volume, V' is the cylinder shell inner volume, and x is the cylinder shell midpoint vertical displacement.
The specific operation is as follows:
a. in the initial state, the bulging amount h is zero, the circumferential rate pi, the semi-column height l=50mm, and the initial outer circle radius r of the cylindrical shell 0 Initial thickness t of cylindrical shell =51mm 0 Substituting 0.9mm into the cylindrical shell volume analytical equation to obtain the shell volume V in the initial state 0 The method comprises the following steps:
b. based on the axial curvature radius R obtained in the first step 1 Substituting the midpoint circumferential displacement x of the calculated thickness t of the middle point of the cylindrical shell into a calculation formula of the bulging internal volume V' of the cylindrical shell to obtain an analytical equation of the bulging internal volume of the cylindrical shell along with the change of the bulging amount, namely:
c. based on the axial curvature radius R obtained in the first step 1 And thirdly, substituting the solution of the mid-point thickness t of the cylindrical shell along with the bulging amount h (1-30 mm) and the circumferential rate pi into an analytical equation of the bulging inner volume V 'of the cylindrical shell to solve, and outputting the process of the bulging inner volume V' of the cylindrical shell along with the bulging amount change in a commercial software Origin, namely an inner volume-bulging amount curve, as shown in fig. 6.
Step five (S5): the equivalent strain at the midpoint of the cylindrical shell is calculated as follows:
wherein ε t For normal strain ε θ For axial stressThe quality of the product is changed,for circumferential strain, ε eq Is the equivalent strain.
The specific operation is as follows:
a. the cylindrical shell is isotropic throughout the bulging process. The sum of the normal strain, the circumferential strain and the latitudinal strain at the same point is zero, so that the normal strain epsilon can be used t And circumferential strain ε θ Representing weft strainNamely:
b. will be strained in circumferential direction epsilon θ And strain in weft directionSubstituting the equivalent strain epsilon of the midpoint of the cylindrical shell eq The analytical equation of the equivalent strain of the middle point of the cylindrical shell along with the change of the bulging amount is obtained by a calculation formula, namely:
c. based on the bulging radius r obtained in the second step, the solution of the midpoint thickness t obtained in the third step along with the bulging amount h (1-30 mm) is substituted into the equivalent strain epsilon of the midpoint of the cylindrical shell eq Solving a calculation formula and outputting equivalent strain epsilon at the midpoint of the cylindrical shell in a commercial software Origin eq The history of the change in the bulging amount, i.e., the midpoint equivalent strain-bulging amount curve, is shown in fig. 7.
Step six (S6): the cylindrical shell bulging pressure is calculated as follows:
wherein sigma y For material yield strength, E 1 And p is the bulging pressure of the cylindrical shell and is the material strength coefficient.
The specific operation is as follows:
a. based on the axial curvature radius R obtained in the first step 1 And a circumferential radius of curvature R 2 The midpoint equivalent strain epsilon obtained in the step five eq Coefficient of material strength E 1 Substituting the analytic equation of the cylindrical shell bulging pressure to obtain the analytic equation of the cylindrical shell bulging pressure along with the change of bulging amount, namely:
b. the bulging amount h (1-30 mm), the yield strength sigma of the cylindrical shell y Substituting the thickness coefficient k into a cylindrical shell bulging pressure p calculation formula along with the solution of the bulging quantity h (1-30 mm) to solve;
c. in the commercial software Origin, the history of the cylindrical shell bulging pressure p as a function of the bulging amount, i.e., the bulging pressure-bulging amount curve, is output as shown in fig. 8.
Step seven (S7): calculating the equivalent stress of the midpoint of the cylindrical shell, wherein the formula is as follows:
wherein,is circumferential stress, sigma θ Is the axial stress, sigma eq Is equivalent stress.
The specific operation is as follows:
a. circumferential stress of cylindrical shellAxial stress sigma of cylindrical shell θ Substituting equivalent stress sigma eq The analytical equation of the equivalent stress of the cylindrical shell along with the change of the bulging amount is obtained by a calculation formula, namely:
b. based on the axial curvature radius R of the cylindrical shell obtained in the step one 1 Radius of curvature R in circumferential direction 2 The thickness t of the middle point of the cylindrical shell calculated in the step three, and the bulging pressure p of the cylindrical shell calculated in the step six are substituted into the equivalent stress sigma along with the solution of the bulging quantity h (1-30 mm) eq A calculation formula is adopted to obtain a solution of the equivalent stress of the cylindrical shell along with the change of bulging quantity;
c. in the commercial software Origin, the equivalent stress σ at the midpoint of the cylindrical shell is output eq The history of the change in the bulging amount, i.e., the midpoint equivalent stress-bulging amount curve, is shown in fig. 9.
To verify the correctness of the above numerical calculation method, three stainless steel cylindrical shells were processed according to the parameters of table 1, and bulging pressures of 8.5MPa, 10.5MPa, and 12MPa were applied, respectively, as shown in fig. 10. The outer surface area and the inner volume data under three bulging pressures were measured using a three-dimensional scanner as shown in fig. 4 and 6, respectively; wall thickness data at three bulging pressures were measured using a non-destructive thickness gauge, as shown in fig. 5. As can be seen from fig. 4, 5, 6 and 8, the analysis results and the test results have good consistency, which proves the correctness of the method of the invention.
The embodiments are only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited by the embodiments, and any modification made on the basis of the technical scheme according to the technical idea of the present invention falls within the protection scope of the present invention.
Claims (3)
1. The performance prediction method for the model-free bulging process of the cylindrical shell of the submersible is characterized by comprising the following steps of:
(1) Designing a calculation formula of the axial curvature radius and the circumferential curvature radius of the cylindrical shell, and substituting the bulging amount into the calculation formula to obtain the course of the change of the axial curvature radius and the circumferential curvature radius of the cylindrical shell along with the bulging amount;
(2) Designing a calculation formula of the surface area of the cylindrical shell, and substituting the bulging amount into the calculation formula to obtain the process of the change of the surface area of the cylindrical shell along with the bulging amount;
(3) Designing a calculation formula of the thickness of the midpoint of the cylindrical shell, and substituting the bulging amount into the calculation formula to obtain the process that the thickness of the midpoint of the cylindrical shell changes along with the bulging amount;
(4) Designing a calculation formula of the internal volume of the cylindrical shell, and substituting the bulging amount into the calculation formula to obtain the course of the change of the internal volume of the cylindrical shell along with the bulging amount;
(5) Designing a calculation formula of the equivalent strain of the midpoint of the cylindrical shell, and substituting the bulging amount into the calculation formula to obtain the process of the equivalent strain of the midpoint of the cylindrical shell along with the change of the bulging amount;
(6) Designing a calculation formula of the bulging pressure of the cylindrical shell, and substituting the bulging amount into the calculation formula to obtain the process of the bulging pressure of the cylindrical shell along with the change of the bulging amount;
(7) Designing a calculation formula of the equivalent stress at the midpoint of the cylindrical shell, and substituting the bulging amount into the calculation formula to obtain the course of the equivalent stress at the midpoint of the cylindrical shell along with the change of the bulging amount;
in step (1), the calculation formula of the axial curvature radius and the circumferential curvature radius of the cylindrical shell is as follows:
in the above, R 1 Is the axial curvature radius, R 2 Is the circumferential curvature radius, h is the bulging amount, l is half the height of the cylindrical shell, r 0 The initial outer circle radius of the cylindrical shell;
in step (2), the cylindrical shell surface area is calculated as follows:
in the above, y is a bulging curve, x is a vertical displacement of the midpoint of the cylindrical shell, S is a bulging surface area of the cylindrical shell,representing the square of the y derivative;
in step (3), the thickness of the midpoint of the cylindrical shell is calculated as follows:
in the above formula, t is the thickness of the middle point of the cylindrical shell, and t 0 The initial thickness, k is the thickness coefficient;
in step (4), the calculation formula of the cylindrical shell internal volume is as follows:
in the above, V 0 The device is characterized in that the device is a cylindrical shell body, V is the cylindrical shell body, V' is the cylindrical shell inner volume, and x is the vertical displacement of the midpoint of the cylindrical shell;
in step (5), the calculation formula of the equivalent strain at the midpoint of the cylindrical shell is as follows:
in the above, ε t For normal strain ε θ For the purpose of axial strain,for circumferential strain, ε eq Is equivalent strain;
in step (6), the cylindrical shell bulging pressure is calculated as follows:
in the above, sigma y For material yield strength, E 1 Is the material strength coefficient, p is a circleColumn shell bulging pressure;
in step (7), the calculation formula of the equivalent stress at the midpoint of the cylindrical shell is as follows:
in the above-mentioned method, the step of,is circumferential stress, sigma θ Is the axial stress, sigma eq Is equivalent stress.
2. The method for predicting the performance of a process of modular free bulging of a cylindrical shell of a submersible according to claim 1, wherein the thickness coefficient k is expressed as follows:
k＝2.79154E-06h 3 -2.92802E-04h 2 -1.39745E-04h+1
in the above formula, E is the elastic modulus.
3. The method of predicting the performance of a model-free bulging process for a cylindrical shell of a submersible according to any one of claims 1 to 2, wherein in steps (1) to (7), the bulging amount is taken to be a percentage of the bulging radius.
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| JP2002275535A (en) * | 2001-03-15 | 2002-09-25 | Kawasaki Steel Corp | Method for producing steel pipe for hydroforming having strain aging property |
| JP2011027484A (en) * | 2009-07-23 | 2011-02-10 | Tokyo Electric Power Co Inc:The | Method and program for calculating ratchet strain |
| CN103048203A (en) * | 2013-01-23 | 2013-04-17 | 哈尔滨工业大学 | Wall thickness linear model-based pipe mechanical property hydro-bugling testing method |
| CN103698220A (en) * | 2013-12-24 | 2014-04-02 | 南京航空航天大学 | Adaptive test method for pipe formation performance based on parabolic model |
| CN104634665A (en) * | 2014-09-12 | 2015-05-20 | 北京航空航天大学 | Pipe liquid filling bulging test method and device |
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Patent Citations (5)
| Publication number | Priority date | Publication date | Assignee | Title |
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| JP2002275535A (en) * | 2001-03-15 | 2002-09-25 | Kawasaki Steel Corp | Method for producing steel pipe for hydroforming having strain aging property |
| JP2011027484A (en) * | 2009-07-23 | 2011-02-10 | Tokyo Electric Power Co Inc:The | Method and program for calculating ratchet strain |
| CN103048203A (en) * | 2013-01-23 | 2013-04-17 | 哈尔滨工业大学 | Wall thickness linear model-based pipe mechanical property hydro-bugling testing method |
| CN103698220A (en) * | 2013-12-24 | 2014-04-02 | 南京航空航天大学 | Adaptive test method for pipe formation performance based on parabolic model |
| CN104634665A (en) * | 2014-09-12 | 2015-05-20 | 北京航空航天大学 | Pipe liquid filling bulging test method and device |
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