CN107895098B - Optimization design method for parabolic-arc-shaped end socket structure - Google Patents

Optimization design method for parabolic-arc-shaped end socket structure Download PDF

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CN107895098B
CN107895098B CN201711474495.1A CN201711474495A CN107895098B CN 107895098 B CN107895098 B CN 107895098B CN 201711474495 A CN201711474495 A CN 201711474495A CN 107895098 B CN107895098 B CN 107895098B
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parabolic
arc
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end socket
beta
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CN107895098A (en
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苏文献
陈嘉雯
李波
黄文彬
熊丽敏
季思园
凌一玮
赵婉瑄
李业勤
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University of Shanghai for Science and Technology
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Abstract

The invention provides an optimization design method of a parabolic-arc-shaped end socket structure, which comprises the following steps: firstly, setting characteristic parameters and initial design parameters of a parabolic-arc seal head; step two, establishing a two-dimensional geometric model according to the characteristic parameters and the initial design parameters; determining a function corresponding to the two-dimensional geometric model when the stress is minimum as a target function; step four, setting a variable range of the initial design parameters; step five, using finite element analysis software, setting constraints and loads to carry out optimization analysis on the initial design parameters to obtain stress strength values corresponding to the initial design parameters; step six, substituting the stress intensity value into the target function, judging whether the target function is converged and meets constraint conditions, if not, modifying the initial design parameters and returning to the step five; and step seven, obtaining the optimal design parameters when the target function is converged and meets the constraint conditions.

Description

Optimization design method for parabolic-arc-shaped end socket structure
Technical Field
The invention relates to an optimization design method, in particular to an optimization design method of a parabolic-arc-shaped end socket structure.
Background
The seal head is an important component of a pressure container, and seal heads in the national standard GB150 pressure container comprise an elliptical seal head, a disc seal head, a spherical cap seal head and a hemispherical seal head. The standard elliptical end socket with the ratio of the long axis to the short axis of 2 is recommended to be adopted, the comprehensive performance is good, and the application is most extensive; the spherical end socket is mostly used for pressure vessels with higher pressure, the stress distribution of the spherical end socket is good, but the manufacturing difficulty is higher; the disk-shaped sealing head consists of a middle spherical surface and a corner with a certain radius, the stress state of the disk-shaped sealing head is not as good as that of an elliptical sealing head, and the use is limited; the stress state of the spherical head is far inferior to that of the hemispherical head, but the spherical head is easy to form due to the shallow depth, and the spherical head is also applied to certain occasions.
In order to solve the problems, a structure of a parabolic-arc seal head is provided, but the shape of the seal head can be changed by slightly changing the parabola and the arc of the parabolic-arc seal head, and slight shape change has great influence on the pressure bearing performance. The existing design method is generally based on the classical mechanics theory and combines the experience of designers to carry out improved design on the structure of the parabola-arc-shaped end socket, and obviously, the design method cannot obtain the real optimal structure.
Disclosure of Invention
The invention is made to solve the above problems, and aims to provide an optimal design method for a parabolic-arc end socket structure.
The invention provides an optimization design method of a parabolic-arc end socket structure, which is characterized by comprising the following steps of: setting characteristic parameters and initial design parameters of a parabolic-arc-shaped end socket, wherein the characteristic parameters are the geometric size of a cylinder body, and the initial design parameters are coordinate values and curvature radius of a curvature center of the parabolic-arc-shaped end socket; step two, establishing a two-dimensional geometric model according to the characteristic parameters and the initial design parameters; determining a function corresponding to the two-dimensional geometric model when the stress is minimum as a target function; step four, setting a variable range of the initial design parameters; step five, using finite element analysis software, setting constraints and loads to carry out optimization analysis on the initial design parameters to obtain stress strength values corresponding to the initial design parameters; step six, substituting the stress intensity value into the target function, judging whether the target function is converged and meets constraint conditions, if not, modifying the initial design parameters and returning to the step five; step seven, when the objective function is converged and meets the constraint condition, obtaining the optimal design parameters, wherein the optimal design parameters are the coordinates (alpha and beta) of the curvature center C and the curvature radius R; and step eight, constructing the middle surface of the parabolic-arc-shaped end socket according to the coordinates (alpha and beta) of the curvature center C and the curvature radius R.
In the optimization design method of the parabolic-arc-shaped end socket structure provided by the invention, the method also has the following characteristics: wherein, the forming step of the middle surface is as follows: in the plane rectangular coordinate, making curve y ═ f (x) ═ Axn(A is more than 0, x is more than or equal to 0, n is more than 2 and less than or equal to 3), the coordinates of the curvature center C of one point M (1, A) on the curve are (alpha, beta), the curvature radius is R,
Figure BDA0001532548100000021
β＝A2(2n2-n)+1，
Figure BDA0001532548100000022
when n is more than 2 and A is more than 0,
Figure BDA0001532548100000023
let α be less than 0, then point C is on the left side of the y axis, point C is used as the center of a circle, R is used as the radius, the intersection line y of the M point is β at point O ═ β, the line y ═ β and the y axis intersect at point O ', O ' O ═ h, O ' O ═ R ═ β, y ═ β is used as the rotation axis, the curve formed by the parabola segment OM and the arc segment MO ″, and the middle plane OMO ″ of the seal head is obtained by rotating around the y ═ β axis.
In the optimization design method of the parabolic-arc-shaped end socket structure provided by the invention, the method also has the following characteristics: in the fifth step, the mathematical optimization model of the optimization analysis is as follows:
Figure BDA0001532548100000031
wherein f is the stress value of the parabola-arc seal head obtained by numerical calculation, alpha and betaR is the abscissa, ordinate and curvature radius of the center of curvature C of the parabolic-circular arc seal head, P is the internal pressure born by the seal head, sigma is the internal pressure born by the seal headmaxThe maximum stress value of the parabola-arc-shaped seal head.
In the optimization design method of the parabolic-arc-shaped end socket structure provided by the invention, the method also has the following characteristics: wherein, the initial conditions of the optimization analysis are the constraint of the parabola-arc-shaped end socket and the internal pressure.
Action and Effect of the invention
According to the optimization design method of the parabolic-arc-shaped end socket structure, due to the fact that finite element analysis software is adopted to conduct optimization design on the parabolic-arc-shaped end socket, numerical simulation and analysis are conducted on the pressure bearing performance of the end socket when the stress of the end socket is minimum, time and materials are saved compared with a traditional experiment, and an obtained design result is more accurate.
In addition, the parabola-arc-shaped end socket designed according to the optimized design method of the invention replaces the small arc with the parabola, and eliminates the sudden change of the first curvature and the second curvature between the transition section and the cylinder body and between the transition section and the middle arc, thereby reducing the local film stress and the secondary bending stress generated for satisfying the deformation coordination, improving the mechanical property and improving the limit load.
Drawings
Fig. 1 is a flow chart of a method for optimally designing a parabolic-circular arc-shaped end socket structure in an embodiment of the invention;
FIG. 2 is a schematic view of the structure of the middle surface of a parabolic-circular arc head in the embodiment of the invention; and
fig. 3 is a schematic structural diagram of a parabolic-circular arc head in an embodiment of the invention.
Detailed Description
In order to make the technical means, the creation characteristics, the achievement purposes and the effects of the invention easy to understand, the following embodiments of the attached drawings specifically describe the optimization design method of the parabolic-arc end socket structure of the invention.
Fig. 1 is a flowchart of an optimal design method of a parabolic-circular arc-shaped end socket structure in the embodiment of the invention.
As shown in fig. 1, the process of the optimization design method of the parabolic-arc head structure includes the following steps:
firstly, setting characteristic parameters and initial design parameters of the parabolic-arc seal head, wherein the characteristic parameters are the geometric size of the cylinder body, and the initial design parameters are coordinate values and curvature radius of the curvature center of the parabolic-arc seal head. In the embodiment, the end socket and the cylinder are both made of S30408, the design temperature is 300 ℃, the size of the end socket is 1600mm in inner diameter, 400mm in depth, 10mm in thickness, and the length of the cylinder connected with the end socket is 500 mm.
And step two, establishing a two-dimensional geometric model according to the characteristic parameters and the initial design parameters.
And step three, determining a corresponding function when the stress of the two-dimensional geometric model is minimum as an objective function.
And step four, setting the variable range of the initial design parameters.
And step five, carrying out mesh division by using finite element analysis software, wherein as the end socket structure meets the symmetry, only one side of the symmetry axis can be provided with constraint and the load can be used for carrying out optimization analysis on the initial design parameters to obtain the stress intensity value corresponding to the initial design parameters.
The initial conditions of the optimization analysis are constraint and internal pressure of the parabolic-arc seal head, and the mathematical optimization model of the optimization analysis is as follows:
Figure BDA0001532548100000051
wherein f is the stress value of the parabolic-arc seal head obtained by numerical calculation, alpha, beta and R are the abscissa value, the ordinate value and the curvature radius of the curvature center C of the parabolic-arc seal head, P is the internal pressure born by the seal head, and sigma is the internal pressure born by the seal headmaxThe maximum stress value of the parabola-arc-shaped seal head.
In this embodiment, the input material characteristics are: e is 1.76 multiplied by 105, mu is 0.31, an eight-node quadrilateral unit PLANE183 is selected, the stress distribution at the corner of the end socket is considered to be complex, the units are properly encrypted during division, uniform pressure is applied to the inner surfaces of the end socket and the cylinder, the symmetrical surface of the end socket is subjected to symmetrical constraint, and the lower end of the cylinder is subjected to axial fixing constraint. Dividing the seal head and the cylinder in the thickness direction by 5 parts, dividing the cylinder in the length direction by 300 parts, dividing the seal head by 400 parts, performing structure optimization analysis after constraint and loading, and calculating to obtain the stress strength value of the parabola-arc seal head.
And step six, substituting the stress intensity value obtained in the step five into the target function, judging whether the target function is converged, and if not, modifying the initial design parameters and returning to the step five.
And step seven, judging whether the target function meets the constraint condition, if not, modifying the initial design parameters and returning to the step five.
Step eight, when the objective function is converged and meets the constraint condition, obtaining the optimal design parameters, wherein the optimal design parameters are the coordinates (alpha and beta) of the curvature center C and the curvature radius R;
and step nine, constructing a middle surface of the parabolic-arc-shaped end socket according to the coordinates (alpha and beta) of the curvature center C and the curvature radius R.
Fig. 2 is a schematic structural view of a middle surface of a parabolic-circular arc-shaped end socket in an embodiment of the invention, and fig. 3 is a schematic structural view of the parabolic-circular arc-shaped end socket in the embodiment of the invention.
As shown in fig. 2 and 3, the intermediate surface is formed by the following steps:
in the plane rectangular coordinate, making curve y ═ f (x) ═ Axn(A is more than 0, x is more than or equal to 0, n is more than 2 and less than or equal to 3), the coordinates of the curvature center C of one point M (1, A) on the curve are (alpha, beta), the curvature radius is R,
Figure BDA0001532548100000061
β＝A2(2n2-n)+1，
Figure BDA0001532548100000062
when n is more than 2 and A is more than 0,
Figure BDA0001532548100000063
let alpha < 0, then point C is on the left side of the y-axisTaking the point C as a circle center, taking R as a radius, crossing the point M to form a circular arc intersection line y ═ beta at a point O ', intersecting the line y ═ beta and the y axis at a point O ', making O ' ═ h, O ' ═ R ═ beta, taking y ═ beta as a rotating shaft, and rotating around the y ═ beta axis to obtain a middle surface OMO ' of the seal head.
Effects and effects of the embodiments
According to the optimization design method of the parabolic-arc-shaped end socket structure in the embodiment, due to the fact that finite element analysis software is adopted to conduct optimization design on the parabolic-arc-shaped end socket, numerical simulation and analysis are conducted on the pressure bearing performance of the end socket when the stress of the end socket is minimum, time and materials are saved compared with a traditional experiment, and an obtained design result is more accurate.
In addition, the parabola-arc-shaped end socket designed according to the optimized design method of the invention replaces the small arc with the parabola, and eliminates the sudden change of the first curvature and the second curvature between the transition section and the cylinder body and between the transition section and the middle arc, thereby reducing the local film stress and the secondary bending stress generated for satisfying the deformation coordination, improving the mechanical property and improving the limit load.
The above embodiments are preferred examples of the present invention, and are not intended to limit the scope of the present invention.

Claims (3)

1. A method for optimally designing a parabolic-arc seal head structure is used for designing the parabolic-arc seal head, and is characterized by comprising the following steps of:
setting characteristic parameters and initial design parameters of a parabolic-arc-shaped end socket, wherein the characteristic parameters are the geometric size of a cylinder body, and the initial design parameters are coordinate values and curvature radius of a curvature center of the parabolic-arc-shaped end socket;
step two, establishing a two-dimensional geometric model according to the characteristic parameters and the initial design parameters;
determining a function corresponding to the two-dimensional geometric model when the stress is minimum as a target function;
step four, setting the variable range of the initial design parameters;
step five, using finite element analysis software, setting constraints and loads to carry out optimization analysis on the initial design parameters to obtain stress strength values corresponding to the initial design parameters;
substituting the stress intensity value into the target function, judging whether the target function is converged and meets constraint conditions, if not, modifying the initial design parameters and returning to the fifth step;
step seven, when the objective function is converged and meets constraint conditions, obtaining optimal design parameters, wherein the optimal design parameters are coordinates (alpha and beta) of a curvature center C and a curvature radius R;
step eight, constructing the middle surface of the parabolic-circular arc-shaped end socket according to the coordinates (alpha and beta) of the curvature center C and the curvature radius R,
in the fifth step, the mathematical optimization model of the optimization analysis is as follows:
Figure FDA0002831753980000011
wherein f is the stress value of the parabolic-arc seal head obtained by numerical calculation, alpha, beta and R are the abscissa value, the ordinate value and the curvature radius of the curvature center C of the parabolic-arc seal head, P is the internal pressure born by the seal head, and sigma is the internal pressure born by the seal headmaxThe maximum stress value of the parabola-arc-shaped seal head.
2. The optimization design method of the parabolic-circular arc-shaped end socket structure according to claim 1, characterized in that:
wherein the intermediate surface is formed by the following steps:
in the plane rectangular coordinate, making curve y ═ f (x) ═ Axn(A＞0,x≥0,2＜n≤3)，
The coordinates of the center of curvature C of a point M (1, A) on the curve are (alpha, beta), the radius of curvature is R,
Figure FDA0002831753980000021
β＝A2(2n2-n)+1，
Figure FDA0002831753980000022
when n is more than 2 and A is more than 0,
Figure FDA0002831753980000023
let alpha be less than 0, then the point C is on the left side of the y axis, the point C is taken as the center of a circle, R is taken as the radius, the line y which passes through the point M and is taken as the arc intersection is beta at the point O ', the line y which is beta and the y axis are intersected at the point O',
and (3) taking O ' (h) and O ' (r) beta, taking y-beta as a rotating shaft, and rotating around the y-beta shaft to obtain the middle surface OMO '.
3. The optimization design method of the parabolic-circular arc-shaped end socket structure according to claim 1, characterized in that:
in the fifth step, the initial conditions of the optimization analysis are the constraint of the parabolic-arc seal head and the internal pressure.
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