# Three dimensional finite element analysis of press

2022-09-29
• Detail

Three dimensional finite element analysis of pressure stress in utility boiler drum

1 preface

low cycle fatigue analysis of steam drum has received more and more attention in recent years. There was no low cycle fatigue life analysis standard for boiler pressure parts in China for a long time, and foreign standards have been borrowed. The recent formulation of this standard has promoted research in this area. The key to correctly calculate the low cycle fatigue life of the boiler drum is to accurately obtain the change of the stress in the peak stress zone with time in the process of boiler startup and shutdown, so as to obtain the range of its stress change

among the loads that affect the stress level in the drum wall, the internal pressure is the most important. This paper mainly discusses the mechanical stress caused by the internal pressure load in the three-way area of the drum and its downcomer, gives the detailed analysis law and concentration of the internal pressure mechanical stress, and analyzes the causes of its formation combined with the literature

the calculation example in this paper is the boiler drum and its downcomer tee of domestic 300MW unit, which is calculated by three-dimensional finite element method

on the basis of calculation and analysis, this paper evaluates the selection of stress concentration factor in the simplified calculation of internal pressure mechanical stress when analyzing the low cycle fatigue life of boiler drum

2 description of the problem

the calculation example in this paper is the boiler drum of domestic 300MW subcritical unit, and its geometric dimensions are shown in Table 1. Table the geometric dimensions of the boiler drum of 1300mw subcritical unit (unit: mm)

the geometric shape and boundary conditions of the boiler drum drop tee are symmetrical, so only a part can be taken as the stress solution area

the stress boundary of the boiler is mainly the internal pressure and various support reactions caused by the drum support. This paper focuses on the role of internal pressure and does not analyze the influence of other loads. The boundary conditions are:

(1) the surface force acting on the inner wall is equivalent to the saturation pressure of the current working medium

(2) add a surface force equivalent to the axial stress on the cylinder with head of the same size at the section far away from the downcomer

(3) add constraints in the direction perpendicular to the plane of symmetry, that is, the displacement in this direction is 0

the calculation area and its grid division are shown in Figure 1. 20 node isoparametric elements are used, sharing 152 elements and 1017 nodes

Figure 1 calculation area division scheme

3 calculation results accelerate the transformation and industrialization of relevant technical achievements

3.1 distribution of internal pressure mechanical stress

figures 2 and 3 respectively show the distribution of internal pressure mechanical stress on two symmetrical planes and on several typical lines when the cold start is 200Min (v=0.5 ℃/min), from which we can see:

(1) the stress distribution away from the pipe joint is similar to that of an infinite thick walled cylinder: equivalent stress σ d（＝ σ 1－ σ 3) Big inside and small outside

Figure 2 distribution of internal pressure mechanical stress on the symmetry plane

(start 200Min, v=0.5 ℃/min, unit: MPa)

Figure 3 distribution of internal pressure mechanical stress along the typical line (start 200Min) can ensure that the parts are more wear-resistant under low temperature

(2) the stress distribution near the pipe joint is very complex due to sudden changes in shape. It is generally considered that there are two dangerous points: the inner corner of the longitudinal section (point a) and the outer corner of the transverse section (point B). From the figure, the isostress lines at these two places are densely distributed, and the stress change gradient is large, indicating that there is indeed stress concentration. However, the maximum stress point of the transverse section is not just at point B, but at point B1, which is offset by a small distance (see Fig. 2a and Fig. 3b). Although there is stress concentration at point B1, making its stress level the largest in the small area near it, it is not very prominent in the whole area, and the maximum point of internal pressure mechanical stress is always at the corner of the longitudinal section, that is, point a

3.2 concentration factor of internal pressure mechanical stress

the concentration factor of internal pressure mechanical stress at two points a and B has nothing to do with the working condition, and the size of internal pressure only increases or decreases the stress at each point in the calculation area in proportion. See Table 2 for the internal pressure mechanical stress concentration factors of points a and B in this example. Table 2 internal pressure mechanical stress concentration factor

3.3 the principal stress direction of internal pressure mechanical stress

the principal stress direction of point a is always the circumferential, radial and axial direction relative to the main shaft. Although the principal stress direction of point B does not change with time, except for the axial principal stress, the other two principal stress directions are far from the circumferential and radial directions of the main pipe

3.4 comparison and analysis of finite element calculation results and traditional algorithm

the traditional internal pressure mechanical stress calculation formula [1] is to calculate the membrane stress first when the drum is regarded as an infinitely long thin-wall encoder to reduce the number of cylinders (1)

where p is the working internal pressure; MPa； Di is the inner diameter of the drum, mm; SY is the effective wall thickness of the drum, mm

then consider the stress concentration at the joint. See Table 3 for the stress concentration factors recommended by American Standard ASME. Table 3 ASME recommended internal pressure stress concentration factor

comparison between table 2 and table 3 shows that the results of finite element calculation are very consistent with ASME recommended values at point a; However, there is a considerable difference at point B. the stress direction of point B calculated by finite element method is not exactly circumferential and radial, and the value is far less than the recommended value of ASME. The stress state of point B is basically not involved in the literature, even if some have made three-dimensional finite element calculations. If the opening of the downcomer of the drum is regarded as a flat plate stretched in two directions, and the principal stress in two directions has a relationship of twice, the circumferential stress concentration factor of point a is 2.5 and the axial stress concentration factor is 0; The ring stress concentration factor of point B is 0, and the axial stress concentration factor is 0.5, which is close to the finite element solution. If the influence of cylinder shape, the effect of internal pressure on the hole edge and the influence of wall thickness are considered, whether the circumferential stress concentration factor of point B will be as large as 2.6 and whether the axial stress concentration factor will be as large as 2.1 is a problem worth studying. In fact, the existence of pipe joints strengthens the rigidity of the hole edge and reduces the stress concentration

the comparison between the finite element calculation results of thin-walled tee and Eringen solution (analytical solution of thin shell theory) is given in document [3], as shown in Table 4. Table 4 Comparison between finite element solution and Eringen solution of thin-walled tee

note: calculation parameters: outer radius of branch pipe is 9.0789, inner radius is 8.3789, length is 4.9

the outer radius of the main pipe is 75.0, the inner radius is 70.0, and the length is 100.0

E=2.1 × 106， ν= 0.3, internal pressure is 0.1; Unit coordination

it can be seen from the table that the internal pressure stress concentration factor of the thin-walled tee is not much different from that of the flat plate under two-dimensional tension. As for the thick wall separating the dry friction surface that was originally in direct contact from the tee, the literature [3] also gives a comparison between the finite element calculation example and the photoelastic experimental value. The author also carried out the finite element calculation of this calculation example, and the calculation results are listed in Table 5

it can be seen from table 5 that although the stress concentration factor increases due to the increase of wall thickness, the stress concentration factor at point a does not increase significantly, and point B is still far less than the recommended value of ASME. In addition, the branch pipe in this example has a large wall thickness (the ratio of outer diameter to inner diameter is 1.71), and point B is far away from the stress concentration area near the hole, which is also the reason for its small stress. Table 5 Comparison of finite element and experimental values of thick wall tee

4 conclusion

(1) under the action of internal pressure, the stress distribution of the boiler drum away from the joint is the same as that of the infinite thick wall cylinder under internal pressure, and there is obvious stress concentration at the joint. The most dangerous point is the corner in the longitudinal section, which is commonly referred to as point a. However, the maximum stress point of the transverse section is not just on point B, but a small distance away

(2) at point a, the principal stress directions coincide with the circumferential, axial and radial directions of the drum respectively, but at point B, except for the principal stress in the axial direction of the drum, the other two principal stress directions are only perpendicular to the main axis direction, but do not coincide with the circumferential or radial direction of the drum, but deviate from a larger angle

(3) the calculated mechanical stress concentration factor at point a of the corner in the longitudinal section of the drum is slightly smaller than the value recommended by ASME; The mechanical stress concentration factor at point B is much smaller than the recommended value. It seems that the treatment method of mechanical stress at point B in the traditional method is conservative. (end)

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