Determination of the expansion ratio for the heat exchange tubes and tube sheets in shell-and-tube heat exchangers

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This post was last edited by Yixin Electromechanical on 2020-4-27 at 13:38. Liu Min (Dalian Refrigerator Co., Ltd., Dalian, Liaoning 116033). Abstract: A detailed discussion is provided on the control of the expansion ratio, and the various methods for calculating this ratio are compared, thereby determining the appropriate control ranges for the expansion ratio of different materials. Additionally, the factors that affect the quality of expansion joining are summarized. Keywords: tube expansion ratio; forced expansion; press-fit expansion; inner diameter control method. Articles 104 and 105 of the \"Regulations on Safety Technical Inspection of Pressure Vessels\" issued by the **Quality and Technical Supervision Bureau provide principle-based guidelines regarding the methods of expanding heat exchange tubes to the tube sheet as well as the basic requirements for such expansion, but no specific provisions are given regarding the tube expansion ratio; currently, there are also no **standards to follow in this regard. And expansion joining is one of the important processes in the manufacturing of shell-and-tube heat exchangers; therefore, to ensure the quality of expansion joining, it is particularly important to determine the appropriate expansion joining method and the suitable expansion ratio. 1　Expansion joining method: The expansion joining methods for heat exchange tubes and tube sheets include mechanical expansion joining and flexible expansion joining (also known as uniform expansion joining). The mechanical expansion joining method is a type of non-uniform expansion joining; lubrication with oil is generally required during this process (as oil contamination can prevent optimal welding quality and compromise the surface quality of the joined area). Moreover, the mechanical balls used in the rolling process cause the pipe diameter to increase, generating significant cold-working stress. Therefore, mechanical expansion joining is not suitable for applications where stress corrosion is a concern. However, due to its simplicity of operation, many manufacturers still widely use it for expansion joining of medium and thin tube sheets to this day. This article will focus on introducing the expansion ratios of heat exchange tubes made of different materials using the mechanical expansion method. 2 Determination of the expansion ratio 2.1 Expansion ratio To ensure the quality of the expansion process, it is necessary to determine an appropriate expansion ratio. This ratio is usually expressed as a percentage of the degree of expansion relative to the original diameter of the tube sheet hole, the inner diameter of the heat exchange tube, or the wall thickness of the heat exchange tube. The degree of expansion can be calculated using equation (1): H = d12 – d11 – b (1) Where H represents the degree of expansion of the heat exchange tube, in mm; d11 and d12 represent the inner diameters of the heat exchange tube before and after expansion, in mm; b represents the bilateral gap between the heat exchange tube and the tube sheet hole before expansion, in mm. The expansion ratio is thus expressed as a percentage of the degree of expansion relative to the inner diameter of the heat exchange tube, the diameter of the tube sheet hole, or the wall thickness of the heat exchange tube. 2.2 Expansion ratio of common materials Table 1 provides reference values for the expansion ratio of common materials; the inner diameter range of the heat exchange tubes after expansion can be calculated using equation (1). 　　When determining the tube expansion ratio, in addition to considering the expansion method (there is a significant difference in the degree of tightening between force expansion and suction expansion), factors such as the tolerance range of the tube sheet holes, as well as the tolerances for the outer diameter and wall thickness of the heat exchange tubes, also need to be taken into account. 2 3　Methods for calculating the tube expansion ratio There are various ways to calculate the tube expansion ratio; the following are some of the common formulas used both domestically and internationally. In the formula:
K———Japan: percentage reduction in tube wall thickness, %; Former Soviet Union: relative percentage of the diameter of the tube sheet hole, %
D———Diameter of the tube sheet hole, mm
σ———Thickness of the heat exchange tube wall before expansion, mm
b———Double-sided clearance between the heat exchange tube and the tube sheet hole before expansion, mm; b = D – dw
dw———Outer diameter of the heat exchange tube before expansion, mm
h———Relative percentage of the tube’s inner diameter, %
h0———Relative percentage of the increase in the tube’s inner diameter compared to the diameter of the tube sheet hole, %
hd———Relative percentage of the increase in the tube’s inner diameter compared to its own original inner diameter, %
hs———Relative percentage of the increase in the tube’s inner diameter compared to its wall thickness, %

2.4 Determination of the expansion rate using the inner diameter control method
Regardless of the calculation method used, the fundamental aspect in determining the expansion rate is the control of the amount of thinning of the heat exchange tube wall. Below, the inner diameter control method is used to verify the determination of the expansion rates for forced expansion and seamless expansion. Equation (8) is the formula for calculating the expansion ratio using the inner diameter control method: Where Hn represents the expansion ratio, in %; d1 is the actual inner diameter of the heat exchange tube after expansion, in mm; t is the actual wall thickness of the heat exchange tube before expansion, in mm; and d is the actual diameter of the tube sheet holes before expansion, in mm. 2.4.1 Expansion ratio for strength expansion. Example 1: The material of the heat exchange tube is T2, with an outer diameter of 1905 mm and a wall thickness of 1.3 mm. The material of the tube sheet is Q235-B, with a thickness of 42 mm. The diameter of the tube sheet holes is 1925 mm, and these holes are arranged in an equilateral triangle pattern, with two sealing grooves provided. The connection between the heat exchange tube and the tube sheet shall be a strength expansion joint. Based on the known conditions, the actual measured values for the diameter of the heat exchange tubes and the holes in the tube sheet are as follows: (For the heat exchange tubes, 5 to 10 tubes were sampled; for the holes in the tube sheet, 5 to 10 holes taken from different locations were sampled.) (1) Heat exchange tubes: Outer diameter: Φ19.05–Φ19.03 mm, average value Φ19.04 mm; Wall thickness: 1.35–1.25 mm, average value 1.3 mm; Inner diameter: Φ16.55–Φ16.35 mm, average value Φ16.45 mm. (2) Tube sheet hole diameter: Φ19.35～Φ19.25 mm, average value Φ19.3 mm. The expanded inner diameter value of the heat exchange tube is initially determined using equation (1) and Table 1. Referring to Table 1, the tube expansion ratio H for copper or copper alloys and steel tube sheets is 5%–8%; the average value is taken as H = 6.5%, which is rounded to H = 7%. This value is then substituted into Equation (1) to determine the diameter of the heat exchange tube after expansion. H = d12 – d11 – b, where b = D – dw = 193 – 1904 = 0.26 mm. Therefore, d12 = H + d11 + b = 16.78 mm. Based on this, a three-ball expansion tube expander with an inner diameter of Φ16.78 mm is selected; its minimum outer diameter is 15.6 mm, its maximum diameter is 17.8 mm, and the length of the balls is 38 mm. The trial inflation showed very good results. The actual measured dimensions of the heat exchange tubes after expansion are as follows: (1) Outer diameter: Φ19.25～Φ19.30 mm, with an average value of Φ19.28 mm; (2) Wall thickness: 1.2～1.22 mm, with an average value of 1.21 mm; using the Japanese formula, the wall thinning rate is 58%; (3) Inner diameter: Φ16.87～Φ16.85 mm, with an average value of Φ16.86 mm, showing an expansion of 0.41 mm compared to the original diameter of Φ16.45 mm before expansion. The average value obtained from measuring the expansion of the heat exchange tubes is substituted into equation (9) to determine the tube expansion ratio. Example 2: It is known that the material of the heat exchange tubes is 20 steel, with an outer diameter of Φ38 mm and a wall thickness of 3 mm. The material of the tube sheet is 16MnR, with a thickness of 48 mm. The diameter of the holes in the tube sheet is Φ38.5 mm, and these holes are arranged in an equilateral triangle pattern. Two sealing grooves are provided, and it is required that the connection between the heat exchange tubes and the holes in the tube sheet be achieved through strong expansion fitting. Based on the known conditions, random inspections were conducted at various positions on the heat exchange tubes and tube sheet holes at a rate of 3% to 5%, and the actual measurement results are as follows: (1) Heat exchange tubes: outer diameter: Φ38.2～Φ37.8 mm, average value Φ38 mm; wall thickness: 31～33 mm, average value 32 mm; inner diameter: Φ31.4～Φ31.8 mm, average value Φ31.6 mm. (2) Tube sheet hole diameter: Φ38.65～Φ38.4 mm, average value Φ38.53 mm. Referring to Table 1, the expansion ratio H is set at 10%. Substituting this value into Equation (1) yields the diameter of the heat exchange tube after expansion: H = d12 – d11 – b. Here, b = D – dw = 3853 – 38 = 0.53 mm. Therefore, d12 = H + d11 + b = 32.23 mm. Actual measurements of the inner diameter of the heat exchange tube after expansion showed values ranging from Φ32.82 to Φ32.84 mm, with an average value of Φ32.83 mm. The average value measured after expanding the heat exchange tubes is substituted into equation (8) to determine their expansion rate. Using the example above, expansion tests and calculations were conducted on heat exchange tubes made of 1Cr18Ni9Ti with a diameter of Φ57×3 and HAL77-2 (navy copper) with a diameter of Φ19×2; the expansion rates determined were 0.87% and 1.56%, respectively. 2.4.2 Comparison with domestic and international expansion ratios: Through trial expansion, in order to establish the correct expansion process, several expansion ratios determined using the inner diameter control method are compared with those used in Japan, the former Soviet Union, and other industries in China. 　　 (1) Calculation of the tube expansion rate in Japan: Table 2 shows the common tube expansion rates in Japan, while Table 3 presents the tube expansion rates calculated using the Japanese formula (Equation (2)). (2) Calculation of the tube expansion rate in the former Soviet Union: Table 4 shows the tube expansion rate for the former Soviet Union, while Table 5 presents the tube expansion rate calculated using the formula from the former Soviet Union (Equation (3)). (3) The formulas for calculating the expansion rate in other domestic industries are identical to formulas (1) and (7), (3) and (5), and (4) and (6); in other words, the calculation and simulation of the expansion rate in these other domestic industries also rely on those used in Japan and the former Soviet Union. Here, the relative percentage of the tube inner diameter used in China’s boiler industry is employed to verify the process parameters for the tube expansion rate obtained through the inner diameter control method. The expansion ratio h in the boiler industry is 0.8% to 1.2%. Table 6 shows the expansion rate calculated using the common formula in China’s boiler industry (Formula 4). 2.4.3 Expansion rate during expansion fitting: For expansion fitting, the only requirement is that the heat exchange tubes be bonded to the holes in the tube sheet through expansion. Currently, there are no specific requirements regarding the degree of expansion both domestically and internationally. Based on years of experience in expanding carbon steel and stainless steel heat exchange tubes, an expansion rate of 0.1% to 0.3% is generally sufficient. 3 Factors affecting the quality of expansion jointing: (1) The hardness of the tube sheet material should be higher than that of the heat exchange tubes. When the hardness of the heat exchange tubes is greater than that of the tube sheet, annealing treatment is necessary. Generally, the annealing length at the tube ends should be no less than 100 mm, and it should also be at least 15–30 mm greater than the thickness of the tube sheet. (2) The gap between the tube sheet holes and the outer diameter of the heat exchange tubes must be strictly controlled. (3) In terms of structural configuration, the expansion joining methods are divided into three types: strength expansion joining with sealing welding, strength welding combined with surface expansion, and strength expansion joining with strength welding. For these three methods, attention should be paid to the sequence of expansion. Generally, when full expansion is required, the process of expanding first and then welding should be used; whereas if expansion is not to be carried out 15 mm from the tube end, the process of welding first and then expanding should be adopted. 4 Conclusions: (1) When the material of the heat exchange tubes is copper, copper alloy, or stainless steel, the tube expansion rate is generally kept within the range of 0.5% to 1.2%; (2) When the material is 10 steel or 20 steel, the tube expansion rate is generally kept within the range of 0.7% to 2.1%; (3) When the material is brass (Naval Copper HAL77-2), the tube expansion rate is generally kept within the range of 1% to 1.8%. Once the aforementioned expansion ratio is determined, it is not necessary to conduct expansion tests on similar products every time; simply follow the established expansion process.