Discussion on Calculation of Flange Stiffness

When calculating the flange stiffness index according to Pressure Vessels (GB 150.1-150.4-2011), under the same design conditions, the stiffness of flanges made of high-strength materials may be unqualified, while that of flanges made of high-strength materials may be qualified. Taking an equipment flange as an example, the causes of the problems are analyzed and discussed. It is believed that the difference in the value of flange design torque M₀ in the process of standard conversion at home and abroad is the cause. It is recommended to follow ASME BPVC in flange stiffness calculation Ⅷ – 1 The flange design torque M₀ is selected according to Rules for Construction of Pressure Vessels to avoid problems related to stiffness index and strength.

Pressure Vessels (GB 150.1-150.4-2011) and ASME BPVC Ⅷ – 1-2004 Rules for Construction of Pressure Vessels [2] adopts the Waters method for flange design of pressure vessels, and the calculation of flange stiffness index is ASME BPVC Ⅷ – 1-2004, GB 150.1-150.4-2011 also supplements the same stiffness verification requirements. According to literature [3], the essence of flange stiffness index calculation is to ensure the sealing performance of flange by controlling the angle of flange. However, in design practice, it is found that under the same design conditions, the stiffness of flanges made of high-strength materials may not be qualified, while that of flanges made of high-strength metal materials may be qualified. According to the principle of flange stiffness, the stiffness calculation of flange should be related to the elastic modulus of flange material, rather than the strength of flange. The reason for the above problems in the design may be the deviation in the process of converting ASME standards into domestic standards.
Taking an equipment flange as an example, the author analyzes and discusses the above problems in the calculation of flange stiffness index.

1. Example of flange stiffness calculation

The flange of an equipment is a PN1.6MPa, DN1300mm standard long neck equipment flange, with a design pressure of 0.97MPa, a design temperature of 100 ℃, a cylinder material of Q345R, a corrosion allowance of 1.5mm, and a welding joint coefficient of 1.0. Flange materials are #20 forged, 16Mn forged and 12Cr2Mo1V forged respectively.

The inner diameter of the flange D=1300mm, the outer diameter of the flange D₀=1460mm, the diameter of the bolt center circle D_b=1415mm, the height of the flange neck h=40mm, the thickness of the big end of the flange neck 26mm, and the effective thickness of the big end of the flange neck δ₁=24.5mm, the thickness of small end of flange neck is 16mm, and the effective thickness of small end of flange neck δ₀=14.5mm, effective thickness of flange δ_f=74mm. The flange sealing surface is concave.
The outer diameter D of the contact between the gasket and the sealing surface is 1353mm, and the inner diameter D of the contact between the gasket and the sealing surface is 1315mm. There are 44 bolts in total, the bolt material is 35CrMoA, and the diameter is 24mm. The gasket is metal clad gasket (stainless steel with graphite inside), with gasket coefficient m=3.75 and gasket specific pressure y=62.1MPa.

2. Calculation formula of flange stiffness index and existing problems

The check condition of flange stiffness is the stiffness index J ≤ 1, and the calculation formula of J is [1]:

Formula (1) – In Formula (2), M₀ is the flange design torque, N·mm; VI is the integral flange coefficient, λ Is the coefficient; E is the elastic modulus of flange material, MPa; K_I is the stiffness coefficient, taking K_I=0.3; D_i is the inner diameter of flange after deducting corrosion allowance, mm.
There are three cases in flange stiffness calculation: (1) flange material is 20 forged, and the stiffness index J=0.971<1 calculated according to formula (1), the stiffness is qualified. (2) The flange material is 16Mn forged, the stiffness index J=1.055>1 calculated according to formula (1), and the stiffness is unacceptable. (3) The flange material is 12Cr2Mo1V forged, and the stiffness index J=1.009>1 calculated according to formula (1), so the stiffness is unacceptable.
In the three cases, except for different flange materials, the design pressure, design temperature, cylinder material, flange structure size, bolt size, bolt number, bolt material, gasket size and gasket material are all identical. Under the same design conditions, there is a problem that the stiffness of flanges made of low strength materials is qualified, but the stiffness of flanges made of high strength materials is not.

According to the analysis formula (1), the parameters that affect the stiffness index are M₀、V_I、λ、E、 δ₀、K_I、h₀. Among them:

• (1) The stiffness coefficient K_I is a constant, independent of the material, and does not affect the change of flange stiffness index in the three cases of flange stiffness index calculation.
• (2) H₀ is only related to flange geometry dimension D_i、δ₀ related, independent of material, 3 cases δ₀=14.5mm, D_i=1303mm, so h₀=137.45mm, which is a fixed value, does not affect the change of flange stiffness index.
• (3) It can be seen from Figure 7-4 in Pressure Vessels Part 3: Design (GB 150.3-2011) [4]that VI is based on h/h₀ and δ₁/ δ₀ is a function of variable. In this example, h=40mm, h₀=137.45mm δ₁=24.5mm、 δ₀=14.5mm, both are fixed values, then h/h₀ and δ₁/ δ₀ is also a fixed value. After calculation, V_I=0.34214, which is also a fixed value in three cases, does not affect the change of flange stiffness index.
• (4) Coefficient in this example λ= 1.04, analysis and actual calculation show that, λ value is only related to the geometric dimension of the flange, and is not affected by the change of material and the change of flange stiffness index.
• (5) The elastic modulus E is a variable related to the material, but the flange materials 20 forged and 16Mn forged belong to carbon steel and carbon manganese steel, both of which have the same elastic modulus but different stiffness calculation results. Therefore, the elastic modulus is not the reason that affects the change of flange stiffness index.

According to the above analysis, the only parameter affecting the stiffness index is the design moment M₀. From GB 150.1-150.4-2011, M₀ is M_a[σ]_f^t/[σ]_f and M_p (M_p is the flange operating torque), the three calculation cases of the flange in this example are all controlled by the flange pretightening torque, namely M_a[σ]_f^t/[σ]_f is large, so there are:

Formula (3) – Formula (4), M_a is the flange pre tightening torque, N·mm; [σ]_f^t is the allowable stress of flange material at design temperature[σ]_f is the allowable stress of flange material at room temperature[σ]_b is the allowable stress of bolt material, MPa; Am is the total sectional area of the required bolt, A_b is the total sectional area of the actually used bolt, mm²; L_G is flange preload arm, mm.
A_m, A_b[σ]_b It is only related to bolt size, bolt quantity and bolt material, but not to flange material. L_G is a parameter related to flange geometric structure and size, and is also independent of flange material, so the size of Ma is independent of flange material. And[σ]ft、[σ]F is obviously related to flange material, 20 forged[σ]_f^t=140MPa、[σ]_f=152.0MPa，[σ]_f^t/[σ]_f=0.92; 16Mn forged[σ]_f^t=178MPa、[σ]_f=178MPa，[σ]_f^t/[σ]_f=1. Therefore, the ratio of 20 forging to 16Mn forging stiffness index should be 0.92. The stiffness index of 20 forged flange J=0.971,16Mn forged flange J=1.055 calculated according to formula (1), and the ratio of the two stiffness indexes is 0.971/1.055=0.92. It can be seen that when the pre tightening torque M_a is the control torque, the allowable stress ratio of flange material will affect the flange stiffness index value, and the higher the material strength is, to be exact, the higher the allowable stress ratio of flange material is, the greater the flange stiffness index value will be, and the stiffness will be unqualified.

3. Difference analysis of flange design torque M₀ values in domestic and foreign standards [5,6,7,8,9,10,11,12,13,14,15]

Unlike the value of flange design moment M₀ in GB 150.1-150.4-2011, ASME BPVC.Ⅷ-1[2,16,17] stipulates that the flange design moment M₀ is calculated by taking the flange preload moment M_a and flange operating moment M_p, respectively, instead of taking the larger of M_a[σ]_f^t/[σ]_f and M_p.

The author believes that ASME BPVC The M₀ value taking method in Ⅷ – 1 is correct for stiffness index calculation. GB 150.1-150.4-2011 and ASME BPVC The design method of vessel flange in Ⅷ – 1 adopts Waters method, and the calculation of flange stiffness index in GB 150.1-150.4-2011 is derived from ASMEBPVC Ⅷ – 1-2004, so the calculation principle and method of flange strength and stiffness in the two standards are essentially the same, and the difference in value is due to the different treatment methods of calculation methods.

3.1 ASME BPVC.Ⅷ-1

ASME BPVC.Ⅷ-1 differs from GB 150.1 to 150.4-2011 in its treatment of strength calculation methods. the treatment of flange calculations in ASME BPVC.Ⅷ-1 is to calculate the flange operating moment M_p and flange preload moment M_a separately, and the resulting stresses are also calculated separately. The stress σ_f^t under the flange operating moment is calculated with the flange operating moment M_p and controlled with the allowable stress [σ]_f^t at the design temperature of the flange material; the stress σ_f under the flange preload moment is calculated with the flange preload moment Ma and controlled with the allowable stress [σ]_f at room temperature of the flange material, i.e., respectively.

There is no need to introduce in this calculation [σ]_f^t/[σ]_f. There is no need to compare sizes. The calculation formula of flange stiffness index J is the same as that of formula (1), but the flange design torque M₀ is calculated by taking M_a and M_p respectively, and the flange stiffness index J obtained is qualified if it is less than or equal to 1. ASME BPVC. The M0 value taking method in Ⅷ – 1 is simple and clear, and it is correct for both flange strength calculation and stiffness index calculation.

3.2 GB 150.1-150.4—2011

The flange strength calculation method in GB 150.1-150.4-2011 is derived from GB 150-1998 “Steel Pressure Vessels” [18], using the same formula as ASME BPVC.Ⅷ-1 to calculate the flange operating moment M_p and flange preload moment M_a respectively after conversion process, and unified with the allowable material stress [σ]_f^t at design temperature is controlled.
The stress σft calculated under the flange operating moment Mp is still controlled by the allowable stress [σ]_f^t at the design temperature of the flange material, i.e., σ_f^t≤[σ]_f^t. The stress control formula for the preload moment M_a should originally be equation (6), but in order to unify the control by [σ]_f^t, both sides of equation (6) are converted by multiplying by [σ]_f^t/[σ]_f to obtain σ_f[σ]_f^t/[σ]_f≤[σ]_f[σ]_f^t/[σ]_f, which is simplified to obtain:

The above conversion is an equivalent conversion, and if equation (6) holds, equation (7) must hold, and vice versa. The [σ]_f^t/[σ]_f can be regarded as the stress conversion factor, whose function is to convert the stress at room temperature of the flange material to the stress at design temperature. After the above conversion, the stress σ_f generated by M_a under the preload torque and the stress σft generated by M_p under the operating torque can be unified and controlled by [σ]_f^t by taking the larger value of σ_f[σ]_f^t/[σ]_f and σft with [σ]_f^t. Since the stress of the flange is proportional to the moment it is subjected to, the conversion of the stress can be replaced by the conversion of the moment, i.e., the moment when the stress is σf is M_a, the moment when the stress is σ_f[σ]_f^t/[σ]_f is M_a[σ]_f^t/[σ]_f, and the moment when the stress is σ_f^t is M_p. Comparing the magnitude of σ_f[σ]_f^t/[σ]_f with that of σ_f^t is converted to comparing M_a[σ]_f^t/[σ]_f and M_p by simply taking the larger of these values for calculation, which leads to the conclusion that M0 is to be calculated by taking the larger of M_a[σ]_f^t/[σ]_f and M_p.

3.3 Variance analysis

The essence of the GB 150.1-150.4-2011 calculation method is the same as the flange strength calculation method in ASME BPVC.Ⅷ-1, but reduces the calculation volume for separate calculations, making the flange strength calculation more simplified. Therefore, it can be considered that the flange design moment M₀ selected the larger value of M_a[σ]_f^t/[σ]_f and M_p, is for the flange strength calculation, there is no problem in performing strength calculations. However, GB 150.1-150.4-2011 completely follows the flange strength calculation method in GB 150-1998, while directly quoting the flange stiffness index calculation formula in ASME BPVC.Ⅷ-1-2004, but ignores the GB 150 Ⅷ-1-2004, but ignored the difference between the flange design moment M₀ in GB 150-1998 and the flange design moment M₀ in ASME BPVC.Ⅷ-1, which caused the unreasonable phenomenon related to strength in the flange stiffness calculation.
Therefore, I suggest that in the calculation of flange stiffness index, M₀ should be taken as M_a and M_p respectively according to the value method in ASME BPVC.Ⅷ-1. In this way, there will be no problem that the flange stiffness index is related to the ratio of the allowable stress of the flange material, and the stiffness index is only related to the elastic modulus of the flange material.

4. Conclusion

Under the same design conditions in flange stiffness calculation, the problem that the stiffness of high-strength material flanges may not be qualified and that of low-intensity material flanges may be qualified is analyzed and discussed, and the causes of the problem are pointed out for discussion by the peers.

Author: Ding Jinxiang

Source:  China Flange Forgings Manufacturer: www.epowermetals.com

(Yaang Pipe Industry is a leading manufacturer and supplier of nickel alloy and stainless steel products, including Super Duplex Stainless Steel Flanges, Stainless Steel Flanges, Stainless Steel Pipe Fittings, Stainless Steel Pipe. Yaang products are widely used in Shipbuilding, Nuclear power, Marine engineering, Petroleum, Chemical, Mining, Sewage treatment, Natural gas and Pressure vessels and other industries.)

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