JP2862414B2 - End plate structure of pressure vessel - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a pressure vessel head plate structure, and more particularly to a pressure vessel head plate structure formed to have a minimum height.

[0002]

2. Description of the Related Art Conventionally, a structure as shown in FIG. 6 is widely used as a head plate structure of a pressure vessel. That is, a portion indicated by reference numeral 1 with respect to the body portion 4 formed of a cylindrical shell has a head plate structure, and the head plate structure 1 has a portion indicated by reference numeral 2 which is a part of a torus surface and a reference numeral 3 which is part of a spherical shell. It consists of a combination of parts indicated by. In general, the spherical shell does not generate a compressive membrane force in the circumferential direction with respect to the internal pressure. However, in order to reduce the height of the pressure vessel by effectively using a cylindrical part having excellent volumetric efficiency, such a spherical shell 3 is used. And the torus surface 2 are used. Torus surface 2 and spherical shell 3
At the junction (contact point) 5, the tangents of the torus surface 2 and the spherical shell 3 are smoothly connected. Similarly, the torus surface 2 and the trunk 4 are smoothly connected.

FIG. 7 shows a stress distribution in the circumferential direction when an internal pressure is applied to the above-mentioned conventional pressure vessel having a head plate structure. In FIG. 7, the horizontal axis represents the girth length measured from the top of the pressure vessel in the direction of arrow 7 in FIG. The vertical axis represents stress. The graph in FIG. 7A shows the circumferential stress on the inner surface of the shell, and the graph in FIG. 7B shows the circumferential stress on the outer surface. As can be seen from FIG. 7, a part of the compressive stress (−) is generated, but this is generated in the portion of the torus surface 2 in FIG. As described above, since the torus surface 2 generates a compressive stress with respect to the internal pressure unlike the spherical shell portion 3, it is necessary to consider the buckling strength with respect to this compressive force in this kind of conventional head plate structure.

FIG. 8 shows the magnitude 9 of the equivalent stress (Misesstress) along the meridian on the shell surface. High stress is generated near the joint 5 between the torus surface 2 and the spherical shell 3. This is due to the fact that the curvature radius of the two curved surfaces at the joint 5 is different, so that a bending moment for making the deformation continuous is generated. In an actual design, the thickness of the shell is determined in consideration of the peak stress and the buckling strength described above.

As described above, in the conventional head plate structure composed of the combination of the spherical shell 3 and the torus surface 2, the torus surface 2
Due to the characteristics described above, there is a danger of buckling due to a circumferential compressive stress due to the internal pressure, and a large bending stress is generated at the joint 5 between the spherical shell 3 and the torus surface 2 due to the discontinuity of the radius of curvature. The presence of a stress peak makes the allowable stress design strict. Furthermore, since a welding line exists near this peak, great care must be taken in designing fatigue strength. Therefore, it is conceivable that the end plate structure 1 is constituted by a single smooth curved surface instead of a combination of two curved surfaces. In such an example, if a curved surface (spheroid) obtained by rotating an ellipse having a specific aspect ratio B / A (see equation (2)) is used as a head plate, circumferential stress is regarded as tensile stress. Is known (see FIG. 9).

(Equation 2)

[0006]

However, when a curved surface obtained by rotating an ellipse having a specific aspect ratio as described above is used for the head plate structure of the pressure vessel, the height of the head plate structure becomes large. However, there is a problem that it is not desirable due to cost or structural restrictions. The present invention seeks to solve such a problem, and forms a single smooth curved surface such that the circumferential stress becomes 0 with respect to the internal pressure, that is, a surface obtained as a solution of a certain differential equation. By using as the shape of the head plate structure, the reliability of the head plate structure with respect to high stress due to bending moment, circumferential buckling, and fatigue strength is increased, and the height of the head plate structure is minimized. The purpose is to provide.

[0007]

SUMMARY OF THE INVENTION In order to achieve the above-mentioned object, the pressure vessel head plate structure of the present invention is formed such that the pressure vessel head plate has a single smooth curved surface obtained by rotating a curve. Then, the curve is represented by the above-mentioned [Equation 1], so that the height is minimized in the end plate structure in which the compressive film force is not generated in the circumferential direction with respect to the internal pressure. And

[0008]

In the above-described head plate structure of the pressure vessel of the present invention, the head plate is formed so as to have a single smooth curved surface obtained by rotating the curve represented by the above [Equation 1]. In addition, no compression film force is generated in the circumferential direction with respect to the internal pressure, and the height thereof is minimized.

[0009]

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a sectional view of a head plate structure of a pressure vessel according to an embodiment of the present invention; FIG. FIG. 3 is a front view of a pressure vessel employing the end plate structure, FIG. 4 is a model diagram for stress analysis of the pressure vessel, and FIG. 5 is a graph showing a result of the stress analysis. .

First, a process of deriving a curve as shown in FIG. 1 will be described below. The coordinate system used for the derivation is shown in FIG.
The reference numeral 10 in the figure indicates a curved surface that is an axis of rotational symmetry.
The curve when cut by a plane including 11 is shown. Also r
₁ of curvature of the curve radius, r ₂ is the distance to the point where the normal line of the curve intersects the rotation axis. And in the above coordinate system, FIG.
When the symbols in (a) are used, the relationship represented by the following [Equations 3 to 5] holds.

(Equation 3)

(Equation 4)

(Equation 5)

On the other hand, the external force acting on the shell element and the generated film force are as shown in FIG. 2B. When a balance equation is established using the symbols in FIG. 2B, the following [Equations 6 to 8] are obtained. ]
An expression is obtained. (See "Stress in Shells", 2nd edition, by W. Flüge, published by Springer)

(Equation 6)

(Equation 7)

(Equation 8)

When an internal pressure or an external pressure is applied, the film force distribution becomes axially symmetric. Therefore, the expression (7) is always satisfied, and the expression (6) is transformed into the expression (9).

(Equation 9) Then, the membrane force N _{φ in the} meridian direction is given by the following [Equation 10] from [Equation 3, 8, 9].

[Equation 10] C: Integral constant Now, substituting equation (3,5) into equation (10), internal pressure Pr = P
Considering only the above, N _φ is as follows.

[Equation 11] The force acting on the entire end plate structure is πa ² P, where a is the radius of the cylindrical portion. Therefore, the expression at the position of the boundary with the cylindrical portion (see [Expression 12]) is expressed by [Expression 13].

(Equation 12)

(Equation 13)

On the other hand, by substituting [Equation 12 and 14] into [Equation 11], [Equation 15] is obtained, but the integration constant C becomes 0 according to [Equation 13 and 15]. Therefore, [Equation 11] becomes the following [Equation 11]
16].

[Equation 14] r = a

(Equation 15)

(Equation 16)

Further, when [Equation 3, 5, 16] is substituted into [Equation 8] and transformed, it becomes [Equation 17].

[Equation 17] In order to _satisfy N _θ = 0, if an upwardly convex curve is targeted,
Since sinφ ≧ 0, it is necessary and sufficient to satisfy the following [Equation 18].

(Equation 18) When the differential equation of [Equation 18] is expressed by [Equation 12], [Equation 14]
Solving under the condition of the equation yields the following equation (19).

(Equation 19)

Note that 0 ≦ r ≦ a according to [Equation 19].
Then, the following differential equation of [Equation 20] is obtained from [Equation 4] and [Equation 19].

(Equation 20) Since r = 0 when Z = 0, the solution of the [Equation 20] becomes the following [Equation 21].

[Equation 21] (0 ≦ r ≦ a) In the curve Z (r) represented by the equation (21), the slope of the tangent is 0 at the vertex r = 0, and the slope is ∞ at the joint (r = a) with the cylindrical shell. It is smoothly connected at the joint.

Next, an example will be described in which a head plate structure formed by a curved surface obtained by rotating a curve represented by the equation (21) is employed. As shown in FIG. 3, in this example, the pressure vessel is composed of a cylindrical shell body 13, an upper head plate structure 12, and a lower head plate structure 14, and the head plate structure of the present invention is adopted for the upper head plate structure 12. . The pressure vessel is fixed on a base by a support structure 15. The dotted line in FIG. 3 indicates the end plate structure of the ellipsoidal rotator (see FIG. 9) in which the circumferential stress is changed to the tensile stress, the height of which is the minimum, and the minimum length and width thereof are shown. The ratio (ratio between the radius of the cylindrical shell and the height of the head plate) is expressed by the following [Equation 22]. On the other hand, since the aspect ratio of the head plate structure of the present invention is about 0.599 as shown in FIG. 1, its height is about 15% lower than that of the above-mentioned spheroid head plate structure.

[Equation 22]

Now, the result of the stress analysis when the internal pressure is applied to the head plate structure of the pressure vessel of the present invention as described above will be described below. "BOSOR" (a stress analysis program for an axisymmetric shell structure by the difference method) was used as the analysis code.
In the analysis model diagram shown in FIG. 4, members along the direction of arrow 16 indicate a head plate structure, members along the direction of arrow 17 indicate cylindrical portions,
The direction of arrow 18 indicates the direction of the horizontal axis of the graph in FIG. 5 (the direction of the girth length measured from the vertex of the end plate structure in the meridian direction), and each point on the curve is a mesh point. In FIG. 5, the vertical axis indicates the membrane force in the direction of the meridian (the direction of arrow 18) in the graph of FIG. 5A, and the vertical axis indicates the circumferential membrane force in the graph of FIG. As can be seen from the graph of FIG. 5B, the circumferential membrane force shows a value close to 0 over a wide range of the head plate. Although it has a positive value near the vertex where the condition of sin φ> 0 is broken, the possibility of buckling with respect to the internal pressure is extremely low. As described above, according to the present invention, the head plate structure that does not generate a compressive membrane force in the circumferential direction with respect to the internal pressure can be reduced in size as compared with the related art, so that effects such as a reduction in manufacturing cost can be obtained. .

[0018]

As described above in detail, according to the head plate structure of the pressure vessel of the present invention, the height of the head plate can be minimized under the condition that no compression film force is generated in the circumferential direction with respect to the internal pressure. Therefore, the effect that the manufacturing cost can be reduced can be obtained. Further, the effect that the installation space of the pressure vessel is reduced is obtained.

[Brief description of the drawings]

FIG. 1 is a partial view showing a cross-sectional shape of a main part of a head plate structure of a pressure vessel as one embodiment of the present invention.

FIG. 2 is an explanatory diagram showing a coordinate system used for deriving the shape of FIG. 1;

FIG. 3 is a front view of a pressure vessel employing the end plate structure of FIG.

FIG. 4 is a model diagram for stress analysis of the end plate structure of FIG. 1;

FIG. 5 is a graph showing a result of stress analysis of the head plate structure of FIG.

FIG. 6 is a sectional view of a head plate structure of a conventional pressure vessel.

FIG. 7 is a circumferential stress distribution diagram with respect to internal pressure of a head plate structure of a conventional pressure vessel.

FIG. 8 is an equivalent stress distribution diagram with respect to an internal pressure of a head plate structure of a conventional pressure vessel.

FIG. 9 is a cross-sectional shape diagram when the head plate structure of the pressure vessel is formed of a spheroid.

[Explanation of symbols]

10 Curve 11 Axisymmetric rotation axis 12 Upper end plate structure 13 Cylindrical shell body 14 Lower end plate structure 15 Support structure 16 End plate structure 17 Cylindrical portion 18 Girth length direction measured from the top of the end plate structure in the meridian direction

Claims (1)

(57) [Claims] 1. A head plate of a pressure vessel is formed so as to have a single smooth curved surface obtained by rotating a curve, and the curve is represented by the following equation, so that the pressure plate has a circumferential direction with respect to an internal pressure. An end plate structure for a pressure vessel, wherein the end plate structure has a minimum height among end plate structures that do not generate a compressive membrane force. (Equation 1) (0 ≦ r ≦ a) where r: distance from rotation axis a: radius of cylindrical part