WO2023092876A1 - Variable-thickness seal head and design method thereof - Google Patents

Abstract

A variable-thickness seal head and a design method thereof. The variable-thickness seal head comprises: a ball head (1) which is provided with a first thinning area (11) and a first thickening area (12); a ring portion (2), comprising a second thickening area (21) and a second thinning area (22); and a cylinder body (3), comprising a third thinning area (31). The design method comprises: selecting a variable-thickness seal head, and determining a thickening range and a thinning range of the variable-thickness seal head; calculating a surface area of the variable-thickness seal head, a surface area of the thinning area, and a surface area of the thickening area; on the basis of the fact that the total volume of the variable-thickness seal head under different thickening coefficients is equal to the total volume of the seal head before deformation, determining a thickness t1 of the thinning area and a thickness t2 of the thickening area; establishing a variable-thickness seal head simulation model; drawing a variable-thickness coefficient δ-load coefficient k graph, and selecting a beneficial variable-thickness interval; fitting a variable-thickness coefficient δ-load coefficient k functional equation; and determining a variable-thickness seal head limit load prediction model under different variable-thickness coefficients δ. According to the variable-thickness seal head, the problem of stress concentration can be solved, and the limit load is improved; according to the design method, the calculation amount can be reduced.

Description

A thickening head and its design method technical field

The invention relates to the field of mechanical structure design, in particular to a thickening head and a design method thereof.

Background technique

The pressure shell is the most important structural unit of the submersible. Its structural design must meet the ultimate strength requirements, have good mechanical properties, and space utilization in the shell; High efficiency and good bearing capacity have been widely used, and compared with spherical heads and elliptical heads, dished heads have better machinability and low production cost. The structure of the existing dish-shaped head is shown in Figure 1. The existing dish-shaped head includes a ball head 100, a ring part 200 and a cylinder 300. The ball head 100 is located at the upper position of the existing dish-shaped head. The ring part 200 is Located in the middle of the existing disc-shaped head, the cylinder 300 is located at the lower part of the existing disc-shaped head, and the existing butterfly-shaped head has the same uniform thickness at the ball head 100, the ring part 200 and the cylinder 300 . However, due to the discontinuous curvature in the radial direction, the dished head is prone to nonlinear buckling, and its buckling performance is very easily affected by thickness, geometry, material and defects. For thickened heads due to curvature discontinuity As for the problem of the stress concentration generated, especially the stress concentration of the ring part, which reduces its compressive capacity, it is now necessary to provide a thickened head and a design method thereof.

Contents of the invention

Purpose of the invention: To provide a thickened head and its design method, which can solve the problem of reduced compressive capacity of the existing head due to the stress concentration caused by the discontinuous curvature, and can calculate the ultimate load of the thickened head.

Technical solution: a thickened head with a central axis, the thickened head includes a ball head bent downward, a ring connected to the end of the ball and extending outward along the direction of bending of the ball, and a ring connected to the ring The bottom end of the ball head extends vertically downward; there is a top at the middle of the ball head, and there is a joint at the connection between the ball head and the ring; the ball head includes a first thinned area, connected to the first thinned The end of the thin zone and extends to the first thickened zone of the knuckle, the ring includes a second thickened zone connected to the knuckle, an annular ring connected to the second thickened zone and extending to the junction of the ring and the barrel In the thinning zone, the cylinder body includes a third thinning zone extending from the connection between the ring portion and the cylinder body to the bottom end of the cylinder body; wherein, the radial thicknesses of the first thickening zone and the second thickening zone are equal and Both are set to t2, the radial thicknesses of the first thinning zone, the second thinning zone, and the third thinning zone are equal and are all set to t1, and the thickening coefficient δ of the thickening head is set, t ₁ =t ₂ *δ.

Further, in the section of the thickening head along its central axis, the arc length of the first thickening zone is L1, the arc length of the second thickening zone is s1, and the arc length of the outer ring surface of the ring is s, where s1 is less than s, and L1 is less than s.

Further, the outer surfaces of the first thinned region, the first thickened region, the second thickened region, the second thinned region, and the third thinned region are smoothly connected in series; the first thickened region and the second thickened region The inner surface of the second thinned area is smoothly connected with the inner surface of the third thinned area; Concave setting along the radial direction.

Further, the value range of the thickness variation coefficient δ is 0.2 to 1; when the thickness variation coefficient δ is equal to 1, the thickened head is a uniform thickness head.

Further, the thickened head is a stainless steel structural part, and the material properties of the thickened head include: elastic modulus E, yield strength σ _y and Poisson's ratio μ.

The beneficial effect of the thickened head of the present invention is: compared with the existing butterfly head, the thickened head overcomes the stress concentration of the existing butterfly head, that is, the head before deformation due to the discontinuous curvature problem, the ultimate load of the thickened head is effectively improved, and thus the compressive capacity of the thickened head is effectively improved.

The present invention also provides a design method applied to the thickened head as described above, the design method comprising the following steps:

(01), select an existing butterfly head as the head before deformation, determine the thickening range and thinning range of the thickening head relative to the thickening of the head before deformation: in the thickening head along its central axis In the cross-section in the direction, select the arc length L1 of the first thickening zone of the thickening head, the arc length s1 of the second thickening zone, and the arc length of the outer ring surface of the ring part is s, where s1 is less than s, and L1 less than s; set the radial thicknesses of the first thickened zone and the second thickened zone to be t ₂ , and the radial thicknesses of the first thinned zone, the second thinned zone and the third thinned zone to be t ₁ ;Calculate the thickening coefficient of the thickening head as δ, where t ₁ =t ₂ *δ;

(02), select the distance D between the outer surfaces of the cylinder as the diameter of the thickening head, the radius R of the spherical surface of the ball, the height H of the cylinder, and the arc length of the spherical surface extending from the joint to the top L, the radius r of the ring; calculate the surface area S _total of the thickened head, the surface area of the thinned area of the thickened head S _thin , and the surface area of the thickened area S _thick of the thickened head, respectively:

S _thick = S _total - S _thin ;

(03) Based on the fact that the total volume of the thickening head under different thickness coefficients δ is equal to the total volume of the head under the uniform thickness t before deformation, according to S _total , S _thick , and S _thin obtained in step (02), determine The radial thickness t ₁ of the thinned area and the radial thickness t ₂ of the thickened area of the thickened head under different thickness coefficients δ;

(04) Obtain the material properties of the thickened head including: elastic modulus E, yield strength σ _y and Poisson's ratio μ, and establish a simulation model of the thickened head; use the simulation model to draw the thickness coefficient δ-load coefficient k diagram , where the load coefficient k is the ratio of the ultimate load of the thickened head to the ultimate load of the equal-thickness head; according to the diagram of the variable thickness coefficient δ-load coefficient k, the load coefficient k is selected to be greater than 1 and the load coefficient k increases with the increase of the variable thickness coefficient δ The value range of the corresponding thickening coefficient δ when the value of the value is reduced, and as a beneficial thickening interval; fitting the functional equation of the thickening coefficient δ-load coefficient k under the beneficial thickening interval;

(05) Use the function equation of the thickening coefficient δ-load coefficient k in step (04) to obtain the load coefficient k, and obtain the ultimate load of the head under the uniform thickness t before deformation, and determine the different deformation in the beneficial thickening interval The prediction model for the ultimate load of the thickened head under the thickness factor δ is:

Further, in step (01), the value range of the thickening coefficient δ is selected to be 0.2 to 1.

Further, in step (03), record the total volume V1 of the thickening head under different thickness coefficients δ, record the total volume V2 of the head before deformation under a uniform thickness t, V1=V2; and V1, V2 respectively satisfy the following formulas:

V1＝S _thick *t ₂ +S _thin *t ₁ ＝S _thick *t ₂ +S _thin *t ₂ *δ;

V2 = S _total *t.

Further, in step (04), according to the thickening coefficient δ-load coefficient k diagram, the value range of the corresponding thickening coefficient δ when the load coefficient k is greater than 1 is selected as the effective thickening interval.

Further, in step (04), the step of using the simulation model to draw the thickness coefficient δ-load coefficient k diagram includes: using the simulation model to obtain a plurality of ultimate loads of the thickness coefficient δ, and obtaining the load when the thickness coefficient δ=1 Ultimate load, calculate a plurality of load coefficients under the multiple thickness coefficients respectively, and in the Cartesian coordinate system with the thickness coefficient as the horizontal axis and the load coefficient as the vertical axis, calibrate the load coefficients under the multiple thickness coefficients The position of the coordinate point formed by the load coefficient of , in order to draw the thickening coefficient δ-load coefficient k diagram.

Beneficial effects: the design method of the thickened head, based on the total volume of the thickened head being equal to the total volume of the head before deformation, calculates the surface area of the thickened head, the surface area of the thinned area, and the surface area of the thickened area, And obtain the uniform thickness of the head before deformation, so as to determine the thickness of the thickening area and the thickness of the thinning area of the thickening head under the thickening coefficient. The thickening head obtained by using this design method can reduce the existing thickening The stress concentration phenomenon of the head due to the discontinuity of the geometric curvature can effectively improve the ultimate load of the thickened head; use the simulation model to obtain the ultimate load and load coefficient under multiple thickness coefficients, and draw the thickness coefficient-load coefficient Figure, determine the value range of the thickness coefficient as the beneficial thickness interval, and fit the function equation of the thickness coefficient-load coefficient under the beneficial thickness interval; and the function equation based on the simulation results that is based on the thickness coefficient-load coefficient , and then propose a thickened head limit load prediction model, which can calculate the ultimate load of the thickened head under any thickness coefficient δ in the beneficial thickening interval; by applying the formula obtained by the thickened head limit load prediction model Compared with the numerical solution obtained by the simulation model, the results of the two are consistent, which verifies the correctness of the ultimate load prediction model of the thickened head; compared with the results of the ultimate load calculated by selecting discrete point values in the simulation model, the The prediction model for the ultimate load of the thick head can be used for the ultimate load of the thickened head under any thickness coefficient δ, so that the calculation results can be reduced, and the calculation amount can be effectively reduced.

Description of drawings

Fig. 1 is the structural representation of existing butterfly head under uniform thickness;

Fig. 2 is a partial structural schematic diagram of a thickening head of the present invention;

Fig. 3 is a schematic flow chart of a design method of a thickening head of the present invention;

Fig. 4 is a schematic structural view of the thickening head in the first embodiment;

Fig. 5 is a schematic diagram of the thickness coefficient δ-load coefficient k in the first embodiment;

Fig. 6 is a solution comparison diagram of the thickened head limit load prediction model and the simulation model in the first embodiment;

Fig. 7 is a schematic structural view of the thickened head in the second embodiment;

Fig. 8 is a schematic diagram of the thickness coefficient δ-load coefficient k in the second embodiment;

Fig. 9 is a solution comparison diagram of the thickened head limit load prediction model and the simulation model in the second embodiment;

Fig. 10 is a schematic structural view of a thickening head in the third embodiment;

Fig. 11 is a schematic diagram of the thickness coefficient δ-load coefficient k in the third embodiment three;

Fig. 12 is a comparison diagram of solutions of the thickened head limit load prediction model and the simulation model in the third embodiment.

Detailed ways

The technical solutions provided by the present invention will be described in detail below in conjunction with the accompanying drawings.

As shown in Figure 2, the thickened head has a central axis 01, and the thickened head includes a ball head 1 bent downward, connected to the end of the ball head 1 and facing outward along the bending direction of the ball head 1 An extended ring part 2, and a cylinder body 3 connected to the bottom end of the ring part 2 and extending vertically downward. The thickened head is an integrally formed symmetrical structure, the ball head 1 is located at the upper part of the thickened head, the ring part 2 is located at the middle of the thickened head, and the cylinder 3 is located at the lower part of the thickened head. The middle position of the ball head 1 has a top 4 and the top 4 is located at the highest point of the whole device and also on the central axis 01 ; The inner surface of the ball head 1 has a first thinned area 11, a first thickened area 12 connected to the first thinned area 11 and extending to the joint part 5; the inner surface of the ring part 2 has a second thickened area connected to the joint part 5 The thickening zone 21, the second thinning zone 22 connected to the second thickening zone 21 and extending to the connection between the ring part 2 and the cylinder body 3; The third thinning zone 31 extending to the bottom end of the barrel 3 .

That is, from the end of the first thinned region 11, there are a first thickened region 12, a second thickened region 21, a second thinned region 22, and a third thinned region 31 in series, and the first thickened region 12, The second thickened area 21, the second thinned area 22, and the third thinned area 31 are all rotationally symmetrical structures around the central axis 01, the top 4 is located in the middle of the first thinned area 11, and the joint part 5 is located between the first thickened region 12 and the second thickened region 21 .

The outer surfaces of the first thinned region 11, the first thickened region 12, the second thickened region 21, the second thinned region 22, and the third thinned region 31 are smoothly connected in series; the first thickened region 12 It is smoothly connected with the inner surface of the second thickened region 21; the second thinned region 22 is smoothly connected with the inner surface of the third thinned region 31; the first thinned region 11, the second thinned region 22, and the third thinned region The inner surface of the zone 31 is radially concave relative to the second thickened zone 21 . The thickened head is a stainless steel structure, and the material properties of the thickened head include: elastic modulus E, yield strength σ _y and Poisson's ratio μ.

As shown in Figure 2, in the half section of the thickening head along the direction of the central axis 01, the arc length of the first thickening zone 12 is set as L1, and the arc length of the second thickening zone 21 is s1, The arc length of the outer ring surface of the ring part 2 is s, and the thickened head meets the following conditions: s1 is less than s, and L1 is less than s.

Moreover, the radial thicknesses of the first thickened region 12 and the second thickened region 21 are both t ₂ , and the diameters of the first thinned region 11, each second thinned region 22, and each third thinned region 31 are The thickness in both directions is t ₁ ; the thickening coefficient δ of the thickening head satisfies: t ₁ =t ₂ *δ.

In this embodiment, the thickness coefficient δ of the thickened head ranges from 0.2 to 1. When the thickening coefficient δ is equal to 1, the thickening head is a uniform thickness head.

The thickened head provided by the present invention, compared with the existing butterfly head, that is, the head before deformation, the thickened head overcomes the problem of stress concentration caused by the discontinuous curvature of the existing butterfly head, The ultimate load of the thickened head is effectively improved, so that the compressive capacity of the thickened head is effectively improved.

The present invention also provides a design method for a thickened head, as shown in Figure 2 and Figure 3, the design method specifically includes the following steps:

(01), select an existing butterfly head as the head before deformation, determine the thickening range and thinning range of the thickened head relative to the thickened head before deformation: in the thickened head along the central axis 01 In the half section in the direction, the arc length L1 of the first thickening zone 12 is selected, the arc length s1 of the second thickening zone 21 of the thickening head is selected, and the arc length of the outer ring surface of the ring part 2 is s, Where s1 is less than or equal to s, and L1 is less than or equal to s; the radial thicknesses of the first thickened region 12 and the second thickened region 21 are set to be t ₂ , and the first thinned region 11, the second thinned region 22, The radial thickness of the third thinning zone 31 is t ₁ ; the calculation of the thickening coefficient δ of the thickening head is: t ₁ =t ₂ *δ (1);

In this step (01), the existing butterfly head as shown in Figure 1 is selected, and the uniform thickness of the existing butterfly head before the deformation is selected as t;

As shown in Figure 2, the thickened part of the thickened head has two regions. The first region is the region covered by the arc length L1 extending from the joint part 5 to the direction of the top 4, which is the second region. A thickened area 12; the second area is the area covered by the arc length s1 extending from the joint part 5 to the connection between the ring part 2 and the column 3, that is, the second thickened area 21;

In this embodiment, the value range of the variable thickness coefficient δ is 0.2 to 1, and when δ=1, the thickened head is a traditional equal-thickness head.

(02), choose the lateral distance D between the outer surfaces of the cylinder body 3 and use it as the diameter of the thickening head, the radius R of the outer spherical surface of the ball head 1, the height H of the cylindrical body 3, and the outer spherical surface of the ball head 1 from the joint The arc length L from the part 5 to the top 4, the radius r of the ring part 2; calculate the surface area S _total of the thickened head, the surface area of the thinned area S _thin of the thickened head, and the surface area of the thickened area S _thic of the thickened head, respectively for:

S _thick = S _total - S _thin (4);

Wherein obtained by step (02), in the cross-section of the thickening head along the central axis 01, the arc length L1 of the thickening zone on the ball head in the radial direction; 5 to the arc length s of the cylinder 3; the arc length s1 of the thickened area on the ring in the radial direction;

The dimensions of the relevant parameters D, R, H, L, r, s, L1, s1, _t2 , and _t1 of the thickened head in this embodiment are shown in Figure 2; and, the head before deformation That is, the selected relevant parameters D, R, H, L, r, and s of the existing butterfly head as shown in FIG. 1 are all consistent with those shown in FIG. 2 .

S _total is the surface area of the dish-shaped head obtained from formula (2); S _thin is the area of the thinned area obtained from formula (3) and brought into formula (4) to obtain the surface of the thickened area.

(03) Based on the fact that the total volume of the thickening head under different thickness coefficients δ is equal to the total volume of the head under the uniform thickness t before deformation, according to S _total , S _thick , and S _thin obtained in step (02), determine The radial thickness t ₁ of the thinned area and the radial thickness t ₂ of the thickened area of the thickened head under different thickness coefficients δ;

Among them, record the total volume V1 of the variable-thickness head under different thickness coefficients δ, record the total volume V2 of the head before deformation under the uniform thickness t, V1=V2; and V1 and V2 respectively satisfy the following formulas:

V1＝S _thick *t ₂ +S _thin *t ₁ ＝S _thick *t ₂ +S _thin *t ₂ *δ (5);

V2＝S _total *t (6);

(04) Obtain the elastic modulus E, yield strength σ _y and Poisson's ratio μ of the thickened head, and establish a thickened head simulation model; use the simulation model to draw a diagram of the thickness coefficient δ-load coefficient k, where the load coefficient k is the ratio of the limit load of the thickened head to the limit load of the equal-thickness head; according to the diagram of the variable thickness coefficient δ-load coefficient k, the load coefficient k is selected to be greater than 1 and the value of the load coefficient k decreases with the increase of the thickness coefficient δ The value range of the corresponding thickening coefficient δ, and as a beneficial thickening interval; fitting the functional equation of the thickening coefficient δ-load coefficient k under the beneficial thickening interval;

In this step (04), the finite element calculation model of the thickened head is established, and shell elements, fixed boundaries, and uniform external pressure are used for modeling, and the number of shell elements is at least 40,000.

In the step of obtaining the beneficial thickening interval in this step (04), it further includes: according to the thickening coefficient δ-load coefficient k figure, selecting the value range of the corresponding thickening coefficient δ when the load coefficient k is greater than 1, as the effective thickening interval.

In this step (04), the step of using the simulation model to draw the diagram of the thickness coefficient δ-load coefficient k includes: using the simulation model to obtain the ultimate load of multiple thickness coefficients δ, and obtaining the ultimate load when the thickness coefficient δ=1 , respectively calculate a plurality of load coefficients under the multiple thickness coefficients, and in the Cartesian coordinate system with the thickness coefficient as the horizontal axis and the load coefficient as the vertical axis, calibrate the load under the multiple thickness coefficients The position of the coordinate point formed by the coefficient is used to draw the diagram of thickness change coefficient δ-load coefficient k.

In the step of obtaining the ultimate load of multiple thickness coefficients δ, and obtaining the ultimate load when the thickness coefficient δ=1, it also includes: using the Riks method, setting the maximum increment number, the initial arc length increment, the maximum and minimum arc length, etc. Calculation parameters, wherein the maximum increment number is generally taken as 250-300; the initial arc length increment is generally taken as 0.01 and the maximum arc length is generally taken as 0.1; the minimum arc length is generally taken as 1* ^10-50 ;

In the process of fitting the functional equation of the thickening coefficient δ-load coefficient k under the beneficial thickening interval, the results of the load coefficient k less than 1 need to be discarded;

(05) Utilize the function equation of the thickening coefficient δ-load coefficient k in step (04) to obtain the load coefficient k, and obtain the ultimate load of the head under uniform thickness t before deformation, and determine the prediction of the ultimate load of the thickened head The model is:

where k is the load factor obtained from step (04).

The ultimate load of the head under the uniform thickness t before deformation is obtained from the buckling strength formula of the dished head under the uniform thickness t; The multiplication of the buckling strength formula of the front _disc -shaped head under uniform thickness is obtained; The radius at the spherical surface; r is the radius of the ring; D is the overall diameter of the head; H is the height of the cylinder, and the above relevant parameters can be obtained in steps (01) to (04).

In this step (05), the ultimate load of the thickened head under different thickness coefficients is obtained by using the thickened head limit load prediction model; the formula solution obtained by the thickened head limit load prediction model and the simulation model are obtained The results of the two are consistent, which verifies the correctness of the prediction model for the ultimate load of the thickened head in predicting the ultimate load of the thickened head under different thickness coefficients δ in the beneficial thickening interval. Moreover, the ultimate load of the thickened head under any thickness coefficient δ can be obtained by using the prediction model of the ultimate load of the thickened head, thereby effectively reducing the amount of calculation.

The thickened head and its design method of the present invention will be described below in combination with the first embodiment, the second embodiment, and the third embodiment.

As shown in Fig. 4, Fig. 7 and Fig. 10, the thickening heads provided by the first embodiment, the second embodiment and the third embodiment all include a first thinned area 11, and the end of the first thinned area 11 The first thickened region 12, the second thickened region 21, the second thinned region 22, and the third thinned region 31 are sequentially connected in series. Wherein, the first thickened area 12 expands along the joint part 5 to the top 4 , and the second thickened area 21 expands along the joint part 5 to the connecting part between the ring part 2 and the barrel 3 .

First embodiment:

A method for designing a thickened head is provided, which specifically includes the following steps:

(101), select an existing butterfly head as the head before deformation, determine the thickening range and thinning range of the thickening head relative to the thickening head before deformation: in the thickening head along its central axis In the half section or the whole section in the direction of 01, the arc length L1 of the first thickening zone 12 of the thickening head, the arc length s1 of the second thickening zone 21, and the arc length of the outer ring surface of the ring part 2 are selected. The length is s, where s1 is less than or equal to s, and L1 is less than or equal to s; the radial thicknesses of the first thickened region 12 and the second thickened region 21 are set to be equal and both are t ₂ , the first thinned region 11, the second thickened region The radial thicknesses of the second thinning zone 22 and the third thinning zone 31 are equal and both are t ₁ ; the thickness coefficient δ of the thickening head is calculated as: t ₁ =t ₂ *δ (1);

In this step (101), select the existing butterfly-shaped head as shown in Figure 1, and select the uniform thickness of the existing butterfly-shaped head before deformation as t;

As shown in Figure 4, the specific area of the thickening part of the thickened dish-shaped head is shown in Figure 4. A uniform-thickness dish-shaped head with a diameter of D=304 (mm) and a thickness of t=1.85 (mm) is selected. The shaped head is made of 304 stainless steel.

In this first embodiment, the thickened portion of the thickened head is selected as the entire annulus, that is, the arc length s1=s of the second thickened region 21, and the arc length L1=0 of the first thickened region, then the second thickened region 21 has an arc length L1=0. The arc length of the second thinning zone is 0;

Set the thickness of the thickening zone as t ₂ , and the thickness of the thinning zone as t ₁ , and use formula (1) to calculate the thickness coefficient δ.

In the first embodiment, the value range of the variable thickness coefficient δ is selected from 0.2 to 1, and when δ=1, the thickened head is a traditional equal-thickness head. The arc lengths of heads under different thickness coefficients δ are shown in Table 1:

Table 1 Arc length of head under different thickness coefficient δ

(102), select the distance D of the outer surface of the cylinder body 3 and use it as the diameter of the thickening head, the radius R of the outer spherical surface of the ball head 1, the height H of the cylinder body 3, and the outer spherical surface of the ball head 1 extending from the joint part 5 The arc length L to the top 4 and the radius r of the ring part 2; the surface area S _total of the thickened head, the surface area of the thinned area S _thin of the thickened head, and the surface area of the thickened area S _thick of the thickened head are calculated as :

S _thick = S _total - S _thin (4);

The dimensions of the relevant parameters D, R, H, L, r, s, L1, s1, _t2 , and _t1 of the thickened head in this embodiment are shown in Figure 4; and, the head before deformation That is, the relevant parameters D, R, H, L, r, and s of the selected existing butterfly head shown in Figure 1 are all consistent with those shown in Figure 4, and the specific dimensions are not indicated in Figure 1.

In this first embodiment, select size: R=302 (mm); D=304 (mm); r=32 (mm); H=20 (mm); L=139.087 (mm); s=35.527 ( mm), substituting it into the formula (2), the surface area S _total of the head can be obtained as:

Substituting in the formula (3), the calculated thinning zone surface area S _thin in this embodiment is:

The surface area S _{thick of} the thickening zone of the thickening head is calculated by formula (4):

In the first embodiment, r=32 (mm); D=304 (mm); s=35.527 (mm) is substituted into the above formula to calculate the surface area of the thickening zone in this embodiment:

(103) Based on the fact that the total volume of the thickened head under different thickness coefficients δ is equal to the total volume of the head under the uniform thickness t before deformation, according to S _total , S _thick , and S _thin obtained in step (102), determine The radial thickness t ₁ of the thinned area and the radial thickness t ₂ of the thickened area of the thickened head under different thickness coefficients δ;

Record the total volume V1 of the variable-thickness head under different thickness coefficients δ, record the total volume V2 of the head under the uniform thickness t before deformation, V1=V2; and V1 and V2 respectively satisfy the following formulas:

V1＝S _thick *t ₂ +S _thin *t ₁ ＝S _thick *t ₂ +S _thin *t ₂ *δ (5);

V2＝S _total *t (6);

Specifically, substituting the surface area S _{thick of} the thickened region and the surface area S _{thin of} the thinned region into (5),

V1＝S _thick *t ₂ +S _thin *t ₂ *δ＝32533.760*t ₂ +78768.976*t ₂ *δ;

Substituting the total surface area S _{total of} the head and the uniform thickness t of the head before deformation into (6), we can get:

V2＝S _total *t＝111360.1*1.85＝206016.1(mm ³ );

Substituting the obtained V2=V1=206016.1 (mm ³ ) into the formula (5), the thickness t ₁ of the thinned area and the thickness t ₂ of the thickened area can be obtained under different thickness coefficients δ, as shown in Table 2;

Table 2: Thickness t ₁ of the thinned zone and thickness t ₂ of the thickened zone under different thickness coefficients δ

(104) Obtain the elastic modulus E, yield strength σ _y and Poisson's ratio μ of the thickened head, and establish a thickened head simulation model; use the simulation model to draw a diagram of the thickness coefficient δ-load coefficient k, where the load coefficient k is the ratio of the limit load of the thickened head to the limit load of the equal-thickness head; according to the diagram of the variable thickness coefficient δ-load coefficient k, the load coefficient k is selected to be greater than 1 and the value of the load coefficient k decreases with the increase of the thickness coefficient δ The value range of the corresponding thickening coefficient δ, and as a beneficial thickening interval; fitting the functional equation of the thickening coefficient δ-load coefficient k under the beneficial thickening interval;

In this step (105), the step of using the simulation model to determine the ultimate load of the thickened head includes: using the Riks method, setting calculation parameters such as the maximum increment number, the initial arc length increment, and the maximum and minimum arc lengths, wherein the maximum increment number Generally, it is taken as 250-300; the initial arc length increment is generally taken as 0.01 and the maximum arc length is generally taken as 0.1; the minimum arc length is generally taken as 1*10 ^-50 ;

In this step (104), the finite element calculation model of the variable-thickness head is established, using shell elements, fully fixed boundary conditions on the bottom edge, and uniform external pressure for modeling, in which there are at least 40,000 shell elements. The material properties of the thickened head are shown in Table 3:

Table 3 Material properties of thickening heads

In this step (104), use the simulation model to draw the thickness coefficient δ-load coefficient k figure as shown in Figure 5, and use the simulation model to draw the step of the thickness coefficient δ-load coefficient k figure comprising: using the simulation model to obtain a plurality of variables The ultimate load of the thickness coefficient δ, the ultimate load when obtaining the thickness coefficient δ=1, respectively calculate a plurality of load coefficients under the multiple thickness coefficients, and take the thickness coefficient as the horizontal axis and the load coefficient as the vertical In the Cartesian coordinate system of the axis, calibrate the position of the coordinate point formed by the load coefficients under multiple thickness coefficients, so as to draw the thickness coefficient δ-load coefficient k diagram;

In this step (104), it can be seen from Figure 5 that under this thickening scheme, when the thickness coefficient δ is 0.5 to 0.95, the buckling resistance of the thickened head is obviously better than that of the ordinary uniform thickness dished head, that is, the deformation For the front head, it is further preferable to select the value range of the thickening coefficient δ corresponding to when the load coefficient k is greater than 1 as the effective thickening range, and the thickening coefficient δ takes 0.7 to 0.95 as the beneficial thickening range of this scheme , where the load coefficient is the ratio of the limit load of the variable-thickness head to the limit load of the equal-thickness head, and the thickness-variation coefficient of the equal-thickness head is δ=1.

Further, discarding the results of the load coefficient k less than 1, the function equation of fitting the thickening coefficient δ-load coefficient k under the beneficial thickening interval is:

k=-1.94698*(δ-0.77528) ² -0.27534*δ+1.36192;

(105) Use the function equation of the thickening coefficient δ-load coefficient k in step (104) to obtain the load coefficient k, and obtain the ultimate load of the head under the uniform thickness t before deformation, and determine the different deformations in the beneficial thickening interval The prediction model for the ultimate load of the thickened head under the thickness factor δ is:

Among them, _σy is the yield strength of the head material, E is the elastic modulus of the head material, R is the radius of the spherical surface; r is the radius of the ring; D is the overall diameter of the head; H is the height of the column, The above relevant parameters can be obtained in steps (101) to (104);

The thickened head ultimate load prediction model is obtained by multiplying the thickness coefficient δ-load coefficient k with the buckling strength formula of the dished head before deformation under uniform thickness proposed by WANGER, and the above parameters are substituted into the formula (7 )Available:

Substituting the size parameters and the thickness coefficient δ used in this embodiment into the above formula to obtain the ultimate load of the thickened head under different thickness coefficients δ, and the solution of the formula for the ultimate load obtained through the ultimate load prediction model of the thickened head Compared with the numerical solution of the ultimate load calculated by the simulation model, as shown in Figure 6, the results of the two are very close, which verifies that the prediction model for the ultimate load of the thickened head is used to calculate the thickness of the thickened seal under different thickness coefficients δ. The correctness of the ultimate load of the head; and the ultimate load of the thickened head under any thickness coefficient δ in the beneficial thickening interval can be obtained by using the ultimate load prediction model of the thickened head, which is compared with the calculation of the discrete point value of the simulation model The result of the ultimate load of the thickened head can effectively reduce the amount of calculation.

Second embodiment:

A method for designing a thickened head is provided, which specifically includes the following steps:

(201) Select an existing butterfly head as the head before deformation, and determine the thickening range and thinning range of the thickened head relative to the thickened head before deformation: in the thickened head along its central axis 01 In the cross-section in the direction, select the arc length L1 of the first thickening zone 12 of the thickening head, the arc length s1 of the second thickening zone 21, and the arc length of the outer ring surface of the ring part 2 is s, wherein s1 is less than or equal to s, and L1 is less than or equal to s; set the radial thickness of each first thickened region 12 and second thickened region 21 to be t ₂ , the first thinned region 11, the second thinned region 22, the third thinned region The radial thickness of the thinned area 31 is t ₁ ; the thickness coefficient δ of the thickened head is calculated as: t ₁ =t ₂ *δ (1);

In this step (201), the existing butterfly head as shown in Figure 1 is selected, and the uniform thickness of the existing butterfly head before deformation is selected as t;

The specific area of the thickening part in the second embodiment is shown in Figure 7. The head is made of a dished head with a diameter of 304 (mm) and a thickness of 1.85 (mm). The dished head is made of 304 stainless steel. , the thickened part of the thickened head extends from the joint part 5 to the junction of the ring part 2 and the column 3 and the top 4 respectively, and the radial arc length is

The region, that is, the arc length of the second thickened region 21

The arc length of the first thickening zone 12

Thus s1=L1;

In the second embodiment, the value range of the variable thickness coefficient δ is 0.2 to 1. When δ=1, the thickened head is a traditional equal-thickness head, and the thickness of the thickened head under different thickness coefficients δ The arc length of the head is shown in Table 4

Table 4 Arc length of head under different thickness coefficient δ

(202) Determine the surface area S _{total of} the thickening head, the surface area S _{thin of} the thinning area, and the surface area S _{thick of} the thickening area:

The dimensions of the relevant parameters D, R, H, L, r, s, L1, s1, _t2 , and _t1 of the thickening head in this embodiment are shown in Figure 7; and, the head before deformation That is, the relevant parameters D, R, H, L, r, and s of the selected existing butterfly head shown in Figure 1 are all consistent with those shown in Figure 7, and the specific dimensions are not indicated in Figure 1.

The second embodiment selects part of the same size as the first embodiment, and the size parameters include:

R＝302(mm); D＝304(mm); r＝32(mm); H＝20(mm); L＝139.087(mm); Head surface area S _total =111360.1 (mm ² ), the same as the first embodiment;

Further selection size: R=302(mm); r=32(mm); D=304(mm); H=20(mm); s=35.527(mm); L=139.087(mm);

Bringing it into formula (3), the surface area S _{thin of} the thinning zone in the embodiment is obtained as:

The surface area S _{thick of} the thickening zone of the thickening head is calculated by formula (4):

S _thick = 111360.1-81512.1 = 29847.97 (mm ² );

(203) Based on the total volume of the thickening head under different thickness coefficients δ and the total volume of the head before deformation under uniform thickness t, according to S _total , S _thick , S _thin obtained in step (02), determine The radial thickness t ₁ of the thinned area and the radial thickness t ₂ of the thickened area of the thickened head under different thickness coefficients δ;

Substitute the surface area S _{thick of} the thickening zone and the surface area S _{thin of} the thinning zone into (5),

V1＝S _thick *t ₂ +S _thin *t ₂ *δ＝29847.97*t ₂ +81512.1*t ₂ *δ;

Substituting the uniform thickness t of the disc-shaped head before deformation and the surface area S _total of the head into formula (6) to obtain:

V2＝S _toaal *t＝111360.1*1.85＝206016.1(mm ³ );

Substituting the obtained V2=206016.1(mm ³ )=V1 into the formula (5), it can be obtained: 29847.97*t ₂ +81512.1*t ₂ *δ=206016.1, that is, the thickness of the thinning zone under different thickness coefficients t ₁ , the radial thickness t ₂ of the thickening zone, as shown in Table 5;

Table 5: Thickness t ₁ of the thinned zone and thickness t ₂ of the thickened zone under different thickness coefficients δ

(204) Establish a thickening head simulation model; obtain the elastic modulus E, yield strength σ _y and Poisson's ratio μ of the thickening head; use the simulation model to draw a thickening coefficient δ-load coefficient k diagram, wherein the load coefficient k is the ratio of the limit load of the thickened head to the limit load of the equal-thickness head; according to the diagram of the variable thickness coefficient δ-load coefficient k, the load coefficient k is selected to be greater than 1 and the value of the load coefficient k decreases with the increase of the thickness coefficient δ The value range of the corresponding thickening coefficient δ, and as a beneficial thickening interval; fitting the functional equation of the thickening coefficient δ-load coefficient k under the beneficial thickening interval;

In the (204) step, the second embodiment utilizes the simulation model to determine the step of the thickened head limit load is the same as the first embodiment;

The second embodiment uses the simulation model to draw a diagram of the thickness coefficient δ-load coefficient k as shown in Figure 8. From Figure 8, it can be seen that under this thickening scheme, when the thickness coefficient δ is 0.3 to 0.95, the thickening head The anti-buckling ability of the head is significantly better than that of the ordinary uniform dished head, that is, the head before deformation. When the thickness coefficient δ is 0.3 to 0.95, it is the effective thickening range of the scheme, and when the thickness coefficient δ is 0.5 to 0.95, it is the scheme. Beneficial thickening interval;

The results of the load coefficient k less than 1 are discarded, and the function equation of the fitting thickness coefficient δ-load coefficient k is:

k＝-11.18407*δ ⁴ +28.80854*δ ³ -27.14766*δ ² +10.87057*δ-0.36657;

(205) Utilize the function equation of the thickening coefficient δ-load coefficient k in step (204) to obtain the load coefficient k, and obtain the ultimate load of the head under the uniform thickness t before deformation, and determine the different variables in the beneficial thickening interval The prediction model for the ultimate load of the thickened head under the thickness factor δ is:

Substitute the dimensional parameters and thickening coefficient δ used in this embodiment into the above formula and compare it with the numerical solution using the simulation model. As shown in Figure 9, the prediction model for the ultimate load of the thickened head is very close to the numerical solution of the simulation model , and compared with the results of the limit load calculated by selecting multiple discrete point values in the simulation model, the thickened head limit load prediction model can be used for the limit load, thereby reducing the calculation result.

third embodiment;

A method for designing a thickened head is provided, which specifically includes the following steps:

(301), select an existing butterfly head as the head before deformation, determine the thickening and thinning range of the thickening head relative to the thickening of the head before deformation;

The difference from the parameters of the first embodiment and the second embodiment is that the thickened part of the thickened head includes: an area with an arc length s1=s extending from the joint part 5 to the junction of the ring part 2 and the column 3 , and the arc length extending from the joint 5 to the top 4

Area;

Set the radial thickness of the thickening zone as t ₂ , and the radial thickness of the thinning zone as t ₁ , and use the formula (1) to calculate the thickness coefficient δ, which satisfies the formula: t ₁ =t ₂ *δ(5);

In this step (301), the existing butterfly head as shown in Figure 1 is selected, and the uniform thickness of the existing butterfly head before deformation is selected as t;

Wherein the value range of δ in the third embodiment is 0.2 to 1, when δ=1, the thickened head is the traditional equal-thickness head; the head arc of the thickened head under different thickness coefficients δ As shown in Table (6):

Table 6 Arc length of head under different thickness coefficient δ

(302), determine the surface area S _{total of} the thickening head, the surface area S _thin of the thinning area, and the surface area S _thick of the thickening area:

In the section of the thickened head along its central axis 01, the relevant parameters D, R, H, L, r, s, L1, s1, _t2 , _t1 of the thickened head in this embodiment Dimensions are shown in Figure 10; and, the relevant parameters D, R, H, L, r, and s of the existing butterfly head selected as shown in Figure 1 before the deformation are all the same as The dimensions shown in Figure 10 are the same, and the specific dimensions are not marked in Figure 1;

The third embodiment selects size: R=302 (mm); D=304 (mm); r=32 (mm); H=20 (mm); L=139.087 (mm); s=35.527 (mm), substitute The head surface area S _total obtained by the formula (2) = 111360.1 (mm ² ), which is the same as the value of S _total in the first embodiment and the second embodiment;

It can be known from (301) that s1=s=35.527 (mm); L1=17.7635 (mm), which is brought into formula (3), and the surface area S _{thin of} the thinned area in the embodiment is obtained as:

The surface area S _{thick of} the thickening zone of the thickening head is calculated by formula (4):

S _thick = 111360.1-64727.45 = 46632.63 (mm ² );

(303) Based on the fact that the total volume of the thickening head under different thickness coefficients δ is equal to the total volume of the head before deformation under a uniform thickness t, according to S _total , S _thick , and S _thin obtained in step (02), determine The radial thickness t ₁ of the thinned area and the radial thickness t ₂ of the thickened area of the thickened head under different thickness coefficients δ;

Specifically, substituting the surface area S _{thick of} the thickened region and the surface area S _{thin of} the thinned region into (5),

V1＝S _thick *t ₂ +S _thin *t ₂ *δ＝46632.63*t ₂ +64727.45*t ₂ *δ;

Substituting the uniform thickness t of the disc-shaped head before deformation and the surface area S _total of the head into formula (6) to obtain:

V2＝S _total *t＝111360.1*1.85＝206016.1(mm ³ );

Substituting the obtained V2=206016.1(mm ³ )=V1 into the formula (5), it can be obtained: 46632.63*t ₂ +64727.45*t ₂ *δ=206016.1, that is, the thickness of the thinned area under different thickness coefficients δ The thickness t ₁ and the thickness t ₂ of the thickening zone are shown in Table 7;

Table 7: Thickness t ₁ of the thinned zone and thickness t ₂ of the thickened zone under different thickness coefficients δ

(304) Establish a thickened head simulation model; obtain the elastic modulus E, yield strength σ _y and Poisson's ratio μ of the thickened dished head; use the simulation model to draw the thickness coefficient δ-load coefficient k figure, wherein the load The coefficient k is the ratio of the ultimate load of the variable thickness head to the limit load of the equal thickness head; according to the diagram of the variable thickness coefficient δ-load coefficient k, the load coefficient k is selected to be greater than 1 and the value of the load coefficient k decreases with the increase of the variable thickness coefficient δ The value range of the corresponding thickening coefficient δ, and as a beneficial thickening interval; fitting the functional equation of the thickening coefficient δ-load coefficient k under the beneficial thickening interval;

In this step (304), the steps of establishing a thickened head simulation model and using the simulation model to determine the ultimate load of the thickened head are the same as those in the first embodiment and the second embodiment;

Use the simulation model in step (304) to draw the thickening coefficient δ-load coefficient k diagram as shown in Figure 11. Under this thickening scheme, when the thickening coefficient δ is 0.4 to 0.95, the buckling resistance of the thickened head It is obviously better than the ordinary uniform dished head, that is, the head before deformation. Then, when the thickness coefficient δ is 0.4-0.95, it is the effective thickening range of the scheme, and when the thickness coefficient δ is 0.5-0.95, it is the beneficial change of the scheme. thick interval.

The results of the load coefficient k less than 1 are discarded, and the function equation of the thickening coefficient δ-load coefficient k under the beneficial thickening interval is fitted;

It can be seen from Figure 11 that it is found that from δ=0.5 to δ=0.95, the thickness coefficient δ is in line with the load coefficient k, and the obtained fitting thickness coefficient-load coefficient equation is:

k=1.8-0.81267*δ;

(305) Utilize the function equation of the thickening coefficient δ-load coefficient k in step (304) to obtain the load coefficient k, and obtain the ultimate load of the head under the uniform thickness t before deformation, and determine the different deformations in the beneficial thickening interval The prediction model for the ultimate load of the thickened head under the thickness factor δ is:

Substitute the dimensional parameters and thickening coefficient δ used in this embodiment into the above formula and compare it with the numerical solution calculated by the simulation model, as shown in Figure 12, the formula for the ultimate load obtained by the thickened head ultimate load prediction model The solution is very close to the numerical solution obtained by the simulation model, which verifies the correctness of the prediction model for the ultimate load of the thickened head; The ultimate load prediction model can be used for the ultimate load of the thickened head under any thickening coefficient δ in the beneficial thickening interval, so that the calculation results can be reduced.

The thickened head design method, based on the total volume of the thickened head being equal to the total volume of the head before deformation, calculates the surface area of the thickened head, the surface area of the thinned area, and the surface area of the thickened area, and obtains The uniform thickness of the head before deformation, so as to determine the thickness of the thickening area and the thickness of the thinning area of the thickening head under the thickening coefficient. The thickening head obtained by using this design method can reduce the existing thickening head The stress concentration phenomenon caused by geometric curvature discontinuity can effectively improve the ultimate load of the thickening head; use the simulation model to obtain the ultimate load and load coefficient under multiple thickness coefficients, and draw the thickness coefficient-load coefficient diagram to determine The value range of the thickening coefficient is used as the beneficial thickening interval, and the functional equation of the thickening coefficient-load coefficient under the beneficial thickening interval is fitted; and based on the simulation results, that is, based on the functional equation of the thickening coefficient-load coefficient, a A thickened head limit load prediction model, which can calculate the ultimate load of the thickened head under any thickness coefficient δ in the beneficial thickening interval; by combining the formula solution obtained from the thickened head limit load prediction model with the simulation model Comparing the numerical solutions obtained, the results of the two are consistent, which verifies the correctness of the prediction model of the ultimate load of the thickened head; compared with the results of the ultimate load calculated by selecting several or more discrete point values in the simulation model, this The thickened head limit load prediction model can be used for the ultimate load of the thickened head under any thickening coefficient δ in the beneficial thickening interval, so that the calculation results can be reduced, and the calculation amount can be effectively reduced.

Claims (10)

1. A thickening head, having a central axis (01), the thickening head includes a ball head (1) bent downwards, a ring portion (2) connected to the end of the ball head and extending outward along the bending direction of the ball head ), and a cylinder (3) connected to the bottom end of the ring and extending vertically downwards, the ball head, the ring, and the cylinder are all arranged around the central axis; the middle position of the ball head has a top (4), There is a joint part (5) at the connection between the ball head and the ring part; it is characterized in that:

   The ball head includes a first thinned area (11), a first thickened area (12) connected to the end of the first thinned area and extending to the joint, and the ring includes a second thickened area connected to the joint (21), connected to the second thickening zone and extending to the second thinning zone (22) at the junction of the ring and the cylinder, the cylinder includes extending from the junction of the ring and the column to the bottom end of the column ( 7) A third thinned region (31) at the end; wherein,

   The radial thicknesses of the first thickening zone and the second thick zone are equal and are all set to t2, and the radial thicknesses of the first thinning zone, the second thinning zone (22), and the third thinning zone (31) are equal and Both are set as t1, and the thickening coefficient δ of the thickening head is set, t ₁ =t ₂ *δ.
2. The thickened head according to claim 1, characterized in that, in the section of the thickened head along its central axis, the arc length of the first thickened region is L1, and the arc length of the second thickened region is s1, the arc length of the outer annulus of the ring is s, where s1 is less than s, and L1 is less than s.
3. The thickening head according to claim 1, characterized in that the outer surfaces of the first thinned area, the first thickened area, the second thickened area, the second thinned area, and the third thinned area are smooth in sequence In series; the first thickening zone is smoothly connected with the inner surface of the second thickening zone; the second thinning zone is smoothly connected with the inner surface of the third thinning zone; the first thinning zone, the second thinning zone, the third The inner surface of the thinned region is radially concave relative to the second thickened region.
4. The thickened head according to claim 1, characterized in that the value range of the thickened coefficient δ is 0.2 to 1; when the thickened coefficient δ is equal to 1, the thickened head is a uniform thickness head.
5. The thickening head according to claim 1, characterized in that, the thickening head is a stainless steel structure, and the material properties of the thickening head include: modulus of elasticity E, yield strength σ _y and Poisson's ratio μ .
6. A design method applied to the thickening head described in any one of claims 1 to 5, characterized in that the design method comprises the following steps:

   (01), select an existing butterfly head as the head before deformation, determine the thickening range and thinning range of the thickening head relative to the thickening of the head before deformation: in the thickening head along its central axis In the cross-section in the direction, select the arc length L1 of the first thickening zone of the thickening head, the arc length s1 of the second thickening zone, and the arc length of the outer ring surface of the ring part is s, where s1 is less than s, and L1 less than s; set the radial thickness of the first thickening zone and the second thickening zone to be t2, and the radial thickness of the first thinning zone, the second thinning zone and the third thinning zone to be t1; calculate The thickening coefficient of the thickening head is δ, where t ₁ =t ₂ *δ;

   (02), select the distance D between the outer surfaces of the cylinder as the diameter of the thickening head, the radius R of the spherical surface of the ball, the height H of the cylinder, and the arc length of the spherical surface extending from the joint to the top L, the radius r of the ring; calculate the surface area S _total of the thickened head, the surface area of the thinned area S _thin of the thickened head, and the surface area of the thickened area S _ihick of the thickened head, respectively:

   

   

   S _thick = S _total - S _thin ;

   (03) Based on the fact that the total volume of the thickening head under different thickness coefficients δ is equal to the total volume of the head before deformation under a uniform thickness t, according to S _total , S _thick , and S _thin obtained in step (02), determine The radial thickness t ₁ of the thinned area and the radial thickness t ₂ of the thickened area of the thickened head under different thickness coefficients δ;

   (04) Obtain the material properties of the thickened head, including: elastic modulus E, yield strength σ _y and Poisson's ratio μ, and establish a simulation model of the thickened head; use the simulation model to draw a diagram of the thickness coefficient δ-load coefficient k , where the load coefficient k is the ratio of the ultimate load of the thickened head to the ultimate load of the equal-thickness head; according to the diagram of the variable thickness coefficient δ-load coefficient k, the load coefficient k is selected to be greater than 1 and the load coefficient k increases with the increase of the variable thickness coefficient δ The value range of the corresponding thickening coefficient δ when the value of the value is reduced, and as a beneficial thickening interval; fitting the functional equation of the thickening coefficient δ-load coefficient k under the beneficial thickening interval;

   (05) Use the function equation of the thickening coefficient δ-load coefficient k in step (04) to obtain the load coefficient k, and obtain the ultimate load of the head under the uniform thickness t before deformation, and determine the different deformation in the beneficial thickening interval The prediction model for the ultimate load of the thickened head under the thickness factor δ is:

   
7. The method for designing a thickened head according to claim 6, characterized in that, in step (01), the value range of the thickened coefficient δ is selected to be 0.2 to 1.
8. According to the design method of the thickened head according to claim 6, it is characterized in that, in step (03), the total volume V1 of the thickened head under different thickness coefficients δ is recorded, and the uniform volume of the head before deformation is recorded. The total volume V2 under the thickness t, V1=V2; and V1, V2 respectively satisfy the following formulas:

   V1＝S _thick *t ₂ +S _thin *t ₁ ＝S _thick *t ₂ +S _thin *t ₃ *δ;

   V2 = S _total *t.
9. According to the design method of thickened head according to claim 6, it is characterized in that, in step (04), according to the diagram of the thickness coefficient δ-load coefficient k, the corresponding thickness coefficient when the load coefficient k is greater than 1 is selected The value range of δ is used as the effective thickening interval.
10. According to the design method of thickened head according to claim 6, it is characterized in that, in step (04), the step of using the simulation model to draw the thickness coefficient δ-load coefficient k diagram comprises: using the simulation model to obtain a plurality of variable The ultimate load of the thickness coefficient δ, the ultimate load when obtaining the thickness coefficient δ=1, respectively calculate a plurality of load coefficients under the multiple thickness coefficients, and take the thickness coefficient as the horizontal axis and the load coefficient as the vertical In the Cartesian coordinate system of the axis, calibrate the position of the coordinate point formed by the load coefficients under multiple thickness coefficients, so as to draw the thickness coefficient δ-load coefficient k diagram.

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