Investigação sobre o método de cálculo da verificação da resistência do redutor
The reducer is an important steam and water piping component in power station boilers. The design calculation and strength checking methods of steel plate welded reducers in three standards of China, the United States, and Europe are comparatively analyzed, and the local stress distribution of redutores is analyzed by finite element calculation. The results show that for the wall thickness calculation of the reducer, the calculation methods of different standards are very similar. The difference in the calculation results is very small. Still, for the strength checking of the connection between the reducer and the straight pipe, the difference in the calculation results of different standards is large, and the calculation results of the ASME BPVC. Ⅷ-2017 Rules for Construction of Pressure Vessels show that the strength of the small end of the reducer with the straight pipe is very high, and the strength of the small end of the reducer with the straight pipe is very low. GB 150-2011 “Pressure Vessels,” the calculation results of different standards differ greatly, ASME BPVC. Ⅷ-2017 “Rules for Construction of Pressure Vessels” calculated that the thickness of reinforcement at the small end of the reducer and the connection with the straight pipe is the largest, and the calculation results of GB 150-2011 “Pressure Vessels” are slightly smaller than those of ASME BPVC. 2012 “Metallic industrial piping-Part 3: Design and Calculation” standard’s calculation results are significantly smaller. The finite element analysis shows a significant stress concentration at the small end of the receiver under either bending moment or internal pressure conditions, with the maximum stress being about 2.0 times the maximum stress at the small end.
0. Introdução
Reducers are acessórios para tubos that connect two different pipe diameters and are important components of industrial piping systems. Reducer is generally used for the connection between the import and export of equipment and pipeline and the branch pipe in the pipeline to reduce the pipe diameter, which can change the fluid flow rate, slow down the erosion of the fluid on the internal parts and reduce the consumption of pipeline materials. The reducers used in the steam sistema de tubagem of thermal power plants include tubo de aço molded reducers, steel plate welded reducers, and steel plate welded eccentric reducers. Steel pipe molding reducer is the use of tubo de aço sem costura through the abrasive hot-pressing molding; the reducer itself does not have a weld, and with the straight pipe welded to leave a straight section, so it has a high strength; steel plate welded reducer is through the steel plate is cut into a fan-shaped, the use of specific equipment rolled into, due to the reducer itself there is a weld, so the strength is relatively low. Reducer failure accidents often occur in industrial production, many of which are caused by welded reducer cone and receiver weld cracking. Finite element analysis also found that the welded part of the steel plate welded reducer and pipeline welding has an obvious stress concentration phenomenon. Therefore, in the design process of the steel plate welded reducer, the wall thickness at the connection with the pipeline must be strictly calibrated.
The design calculation of the reducer can be carried out according to the mathematical analysis method given in the corresponding pipeline design specification. The power industry standard DL/T 5054-2016 “Thermal power plant steam conceção de tubagens specification” gives the strength calculation and checking method of steel pipe molding reducer but not the steel plate welded reducer calculation method. The strength calculation and checking method of steel plate welded reducer is given in the EU standard EN 13480-3-2012 “Metallic industrial piping-Part 3: Design and Calculation”, Chinese national standard GB 150-2011 “Pressure Vessels”, American standard ASME BPVC. ASME BPVC. VIII-2017 “Rules for Construction of Pressure Vessels” are given, but the calculation methods are different.
This paper analyzes the influence of different internal pressure and pipe diameter parameters on the design of the reducer by comparing and calculating the welded reducer e welded eccentric reducer of three different standards in China, the United States, and Europe through finite element calculations, the detailed stress distribution state of the reducer under the action of the internal pressure and bending moment is analyzed, and the optimal reinforcement coefficient is obtained. The calculation results provide a reference for the selection and calculation of steel plate welded reducer.
1. Steel plate welded reducer strength calculation and checking methods
In the strength design of pipe components under pressure, the strength theory used is the maximum shear stress theory. The straight pipe wall thickness formula under internal pressure is derived from the thin film model and considers the effect of welded joints and temperature. The reduced diameter pipe formula is based on the straight pipe wall thickness formula; taking into account the cone angle of the tapered section obtained, the minimum wall thickness of the tapered section of the formula in different standards is shown in Table 1.
Table.1 Calculation of wall thickness of tapered section of reducer
Nota: S is the wall thickness, mm; p is the design pressure, Pa; D_{i} is the inner diameter of the pipe or reducer, mm; D_{o} is the outer diameter of the pipe or reducer, mm; [σ]^{t} is the permissible stress at the design temperature of the material, MPa; η is the permissible stress correction coefficient, dimensionless; θ is the half cone angle.
As seen from Table 1, the coefficient of pressure is below the denominator of the calculation formula of ASME BPVC. VIII-2017 “Rules for Construction of Pressure Vessels” is 1.2, while the coefficient of pressure below the denominator of GB 150-2011 “Pressure Vessels” and EN GB 150-2011 “Pressure Vessels” and EN 13480-3-2012 “Metallic industrial piping-Part 3: Design and Calculation” have a coefficient of 1. However, since the permissible pressure of welded steel reducers specified in the pipe regulations is lower, the effect of this deviation on the calculation results is not significant.
The connection between the reducer and the straight pipe has obvious stress concentration, so all three standards are calibrated for the straight pipe connection at the big and small ends, respectively. In GB 150-2011, the first, according to the design pressure, allowable stress, and welding coefficient to determine the need to strengthen the connection. When it is necessary to increase the thickness to be strengthened, it should be set between the reducer and the receiver to strengthen the section. The reducer strengthening section and the receiver strengthening section should have the same thickness, the thickness of the thickness of the receiver in the minimum wall thickness of the basis multiplied by the stress value-added coefficients, as shown in equation (5):
S=QS_{0 }(5)
Na fórmula:
- S_{0} is the minimum wall thickness of the receiver, mm;
- Q for the dimensionless stress value-added factor, by the design pressure, allowable stress, and welding coefficient of the determination size, in GB 150-2011 in the table to obtain.
ASME BPVC. VIII-2017 is by the method of the pressurized area that must be met; the pressurized area Ar that the reinforced section must meet is
A_{r}=[kQR/[σ]^{t}E_{1}](1-Δ/θ) tanθ (6)
Na fórmula:
- R is the radius of the receiver, mm; k, Q, E, and Δ are calculated correlation coefficients, which can be found in the specification.
The effective area A_{eL} of the big end is:
The effective area A_{eS} at the small end is:
In EN 13480-3-2012, it is first necessary to determine whether reinforcement is required through equation (9):
Na fórmula:
- β is the coefficient required for the calculation, obtained by checking the table in the specification.
2. Calculation results
Calculated pipe and reducer material for Q235, design nominal pressure PN16 (1.6MPa), design temperature of 200 ℃, reducer half cone angle of 15 °. Table 2 for the large end of the pipe reducer receiver at the thickness of the reinforcement of the calculation results, GB 150-2011 “Pressure Vessel” for the large end of the pipe reducer has no reinforcement requirements, EN 13480-3-2012 “Metallic industrial piping-Part 3: Design and Calculation”. The calculation result at the big end is less than the minimum wall thickness of the receiver, and no specific calculation can be made in the actual design. ASME BPVC. VIII-2017 “Rules for Construction of Pressure Vessels” has a reinforcement thickness of about 1.3-1.4 times the minimum wall thickness of the straight pipe, and the calculation result is most conservative. This is the most conservative calculation.
Table.2 Reinforcement thickness at the large end
Joint | Thickness of reinforcement at the large end | ||||
Outer diameter of large end connecting pipe | Minimum wall thickness of large end nozzle | Minimum wall thickness of cone section | GB 150—2011 | EN 13480-3-2012 | ASME BPVC.VIII—2017 |
2438 | 21 | 21.6 | No need for reinforcement | 10.1 (No reinforcement required) | 29 |
2235 | 19.2 | 19.7 | No need for reinforcement | 9.2 (No reinforcement required) | 26 |
2032 | 17.5 | 17.9 | No need for reinforcement | 8.4 (No reinforcement required) | 24 |
1829 | 15.7 | 16 | No need for reinforcement | 7.6 (No reinforcement required) | 22 |
1626 | 14 | 14.2 | No need for reinforcement | 6.7 (No reinforcement required) | 19 |
1422 | 12.2 | 12.3 | No need for reinforcement | 5.9 (No reinforcement required) | 17 |
Table 3 gives the calculation results of the thickness reinforcement at the receiver at the small end of the reducer. EN 13480-3-2012 “Metallic industrial piping-Part 3: Design and Calculation” calculations are the smallest, similar to the minimum wall thickness of the receiver, except for the outer diameter of 2235mm, the thickness of the reinforcement is less than the minimum wall thickness of the receiver. GB 150-2011 “Pressure Vessels” and ASME BPVC. VIII-2017 “Rules for Construction of Pressure Vessels” wall thickness reinforcement is significantly higher than the minimum wall thickness of the receiver. VIII-2017 “Rules for Construction of Pressure Vessels” the strengthened thickness is about 1.5-2.0 times the minimum wall thickness of the straight pipe. GB 150-2011 “Pressure Vessels” the strengthened thickness is about 1.4 times the minimum wall thickness of the straight pipe. The wall thickness reinforcement at the small-end receiver is greater than that at the large-end receiver, and the reinforcement calculation is in ASME BPVC. VIII-2017, Rules for Construction of Pressure Vessels, is still the most conservative.
Table 4 gives the large-end outer diameter of 1626mm, small-end outer diameter of 1219mm, material Q235, nominal pressure PN16 (1.6MPa), the design temperature of 200 ℃ reducers in different half-cone angle conditions of the complementary thickness calculation. From the calculation results, it can be seen that, for the small end of the pipe receiver, the three standards in the thickness of the reinforcement with the half-cone angle increase significantly. For the large end of the receiver, ASME BPVC. VIII-2017 reinforcement requirements are also increased with the increase in cone angle, GB 150-2011 and EN 13480-3-2012 on the large end of the receiver is no reinforcement requirements. Therefore, in the design process, the taper angle of the reducer should be minimized as much as possible when space allows.
Table.3 Thickness of small end reinforcement
Small end connecting pipe | Small end reinforcement thickness | |||
Nominal outside diameter | Minimum wall thickness | GB 150 | EN 13480 | ASME VIII |
2235 | 19.2 | 26.9 | 20 | 29 |
2032 | 17.5 | 24.5 | 18 | 29 |
1829 | 15.7 | 22 | 16 | 27 |
1626 | 14 | 19.6 | 13 | 25 |
1422 | 12.2 | 17.1 | 11 | 24 |
1219 | 10.5 | 14.7 | 9 | 22 |
Table.4 Effect of Cone Angle on Reinforcement Thickness
Angle/(°) | Small end reinforcement thickness/mm | Large end reinforcement thickness/mm | ||||
GB 150 | EN 13480 | ASME VIII | GB 150 | EN 13480 | ASME VIII | |
10 | 13.6 | 9 | 16 | No need for reinforcement | No need for reinforcement | 18 |
15 | 14.7 | 11 | 18 | No need for reinforcement | No need for reinforcement | 19 |
20 | 16.8 | 12 | 20 | No need for reinforcement | No need for reinforcement | 21 |
25 | 18.9 | 14 | 22 | No need for reinforcement | No need for reinforcement | 23 |
30 | 19.9 | 16 | 25 | No need for reinforcement | No need for reinforcement | 24 |
3. Finite element analysis
To obtain more details of the stress distribution of the reducer under the external force, finite element analysis calculations were carried out on the reducer and straight pipe receiver. The diameter of the small end of the model is 200mm, the diameter of the large end of the receiver is 300mm, the length of the receiver pipe is 800mm, and the half-cone angle of the reducer is 15°. The structured mesh is used, with 6 layers of mesh in the wall thickness direction, and the total number of meshes is 1.15 million, which is verified by the mesh correlation to meet the needs of stress analysis. The model was calculated only by the action of the bending moment, only by the action of the internal pressure, and at the same time by the action of the bending moment and internal pressure of the Von-Mises stress distribution. The bending moment is 5000N-m, and the internal pressure is 1.6MPa.
Fig.1 Von-Mises stress distribution of reducer under internal pressure/Pa
Fig.1 shows the distribution of Von-Mises stress under internal pressure only. As can be seen from the figure, the small end of the receiver and the middle of the reducer near the small end of the inner wall of the pipe for the stress value of the largest region, there is no stress concentration in the receiver, on the contrary, the small end of the receiver due to the role of the internal pressure outward push, the stress is less than the inner wall of the straight pipe. In straight pipe, in the case of internal pressure, the inner wall of the maximum value of stress, and with the increase in wall thickness, the stress at the inner wall gradually decreases with the increase in pipe diameter.
Figure 2 shows the distribution of Von-Mises stresses under the action of bending moment only. Under the action of bending moment, the stress concentration on the outside of the small end of the pipe reducer at the weld is more obvious, and the stress suffered is about 2.0 times the maximum stress of the small end of the straight pipe, as shown in Figure 2(a). In the big end of the receiver at the inner wall side, the stress is also slightly increased, but much lower than the small end of the receiver, such as in Figure 2 (b). The above position is also the position where the failure of the reducer often occurs in the production process.
Figure 3 shows the distribution of Von-Mises stresses under the combined effect of bending moment and internal pressure. Under the action of the bending moment, the small end of the reducer welded at the outside of the stress concentration is more obvious; the maximum stress is slightly smaller than only by the action of the bending moment, such as in Figure 3 (a), this is due to the internal pressure to offset the bending moment to make the straight tube bending tendency. In the big end of the receiver at the inner wall side, the stress is also slightly increased, but much lower than the small end of the receiver, as shown in Figure 3(b).
From the comparison of the finite element analysis results and the results calculated based on the code, the wall reinforcement value at the small end of each standard is larger than the corresponding large end wall reinforcement value because the stress concentration at the small end receiver is more obvious. In the case of a small cone angle, the big end of the connection, whether under internal pressure or bending moment, stress concentration is not obvious; therefore, in most conditions, it does not need to strengthen. From Table 3, calculation results can be seen, ASME BPVC. VIII-2017 calculated wall thickness reinforcement of the small end connection pipe wall thickness for the receiver minimum wall thickness of 1.5-2 times, GB 150-2011 calculated results for about 1.4 times, while EN 13480-3-2012 calculated wall thickness reinforcement thickness close to or even less than the minimum wall thickness of the receiver. In contrast ASME BPVC. VIII-2017 wall thickness reinforcement calculation results are closer to the finite element analysis.
Fig.2 Von-Mises stress distribution of reducer under bending moment/fPa
4. Conclusão
In this paper, three different standards in China, the United States, and Europe were used to compare and calculate the welded reducer. They welded the eccentric reducer and analyzed the influence of different parameters on the design of the reducer. Through the finite element method, the detailed stress distribution state of the reducer under the action of internal pressure and bending moment is analyzed, and the following conclusions are obtained:
- 1) The small end of the steel plate welded reducer and the connection of the receiver will produce obvious stress concentration under the action of bending moment. Attention must be paid to wall thickness strengthening in the design.
- 2) In case of space conditions, minimizing the reducer’s cone top angle can make the design safer and more reliable. The smaller the cone angle, the smaller the thickness of the wall thickness enhancement. But in principle, the reducer wall thickness shall not be less than the receiver wall thickness.
- 3) Through the Chinese, American, and European three codes for welded pipe reducer calculation and finite element analysis results in comparison, ASME BPVC. VIII-2017 boilers and pressure vessels are relatively conservative, while the calculation results of EN 13480-3-2012 are obviously small, ASME BPVC. VIII-2017 calculation of steel pipe welded pipe reducer wall thickness at the small end of the reinforcement of the results and the finite element analysis is closer. Finite element analysis is closer.
- 4) When the wall thickness of the straight pipe does not meet the requirement of wall thickness reinforcement, it is necessary to weld a section of straight pipe that meets the reinforcement thickness between the reducer and the straight pipe as reinforcement.
Figure.3 Stress distribution of reducer under bending moment and internal pressure Von-Mises/Pa
Author: Liu Lu