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**I. Introduction**

Square and rectangular tubes are used in a variety of applications, from structural components and building materials to home appliances and commercial shelving. Several methods are to make these tubes, including extrusion, hot or cold stretch & reduction and direct roll forming & welding. The most popular technique, though, is reshaping welded round tube in-line on a tube mill. This is particularly true for steel tubes. Tubes made from a variety of materials (cold rolled steel, stainless steel, aluminum, titanium, etc), and in a wide range of gages (different wall thicknesses), are reshaped in-line. However, controlling the forming parameters (corner radius, tolerance of squareness, etc) during the reshaping process presents some difficulties. This is due to the differences in physical properties among tubes made from dissimilar materials with various t/d ratios. The use of advanced tooling designs, which utilize numerical analysis to predict material deformation, can eliminate these problems and improve tooling performance to produce high quality square and rectangular tube products.

Properly designed tooling is essential to reshaping round tube into high quality square and rectangular tubular products. When the correct tooling is used, it ensures smooth material flow during the reshaping process and accurate geometry of the final product. In order to design this reshaping tooling, two parameters must be defined: (1) the diameter of the round mother tube required and (2) the amount of material deformation at each forming pass.

The first step in the tooling design process is calculating the diameter of the tube that will be reshaped. During the reshaping process, circumferential shrinkage and reduction in cross-sectional area occur and these factors must be taken into account. Theoretically, the circumference of the round mother tube is equal to the outside perimeter of the square or rectangular tube plus some amount of shrinkage that occurs during the reshaping process. Material shrinkage occurs mainly at the corners of the tube. The change in the shape of the corner depends on many factors including material gage, final tube size, the number of reshaping passes in the mill, the amount of work performed in each pass, material properties and even the surface finish of the tube. Analysis of the material deformation will help estimate the amount of shrinkage and the round tube size required; however, it is impossible to obtain an analytical solution due to the complexity of material deformation (material deformation involves bending, compression, nonlinear deformation and surface friction). A practical solution is to calculate the amount of shrinkage using a numerical simulation, such as a finite element analysis.

Finite element modeling has been used successfully in several metal forming operations, such as stamping and deep drawing, to obtain information about material flow. Modeling the tube reshaping process will provide similar information that will help determine the amount of material shrinkage in the round mother tube. Figure 1 shows a finite element model of a round tube that will be reshaped into a 3” square tube with a .188” gage. (Note: To simplify the analysis, only cross-sectional deformation is modeled and only a quarter of the model is shown due to the symmetry).

Figures 2 and 3 show a typical strain distribution of the tube at two different stages of the reshape process. The final corner radius of the reshaped tube can be generated using the results of this analysis. Figure 4 is a model showing the geometry of the final tube after reshape with the measured corner radii. Figures 2 and 3 indicate that the deformation is concentrated at the corners of the tube. These drawings also suggest that the shrinkage occurs mostly at the corner of the tube. As a result, the strain concentration at the corners increases as the tube size and gage increase.

By analyzing tubes of different sizes and gages, the effect on the corner radius is obtained. These results are shown in Figures 5 and 6 and indicate that the corner radius increases as tube size and gage increase. Based on this analysis, a moderate forming allowance of .200” (increase in length of the periphery of the tube) is suitable when reshaping round tube into a 2” square tube.

**2.3 Factors to Consider**

Many factors affect materialdeformation when reshaping round tube. These include tooling design, mill set-up and surface finish. Before finalizing the diameter of the round mother tube, consideration should be given to these factors. A common practice in tube reshaping is using the same set of tooling to reshape different gages of material. As analyzed in section 2.2, the corner radius increases as the material gage increases. To obtain the same corner radius, the diameter of the mother tube must be increased when the gage increases and vise versa. Different tooling designs and mill set-ups of the driven reshape passes produce a different axial force during the reshaping process. A pushing reshape set-up will produce a smaller corner than a pulling reshape set-up. To obtain the same corner radius from each set-up, decrease the mother tube diameter with the pushing reshape set-up. Finally, surface friction between the tooling and the tube varies with the material being used. A fine surface finish on the tube and tooling produces a low surface friction, allowing the material to flow easily. As a result, a smaller corner radius is produced than would be with a larger friction force, requiring a smaller diameter mother tube.

After determining the diameter of the round mother tube, calculate the amount of work to be done at each reshaping pass.

As a result of work hardening during forming, most of the reshaping work should be done in the first few passes. To progressively reduce the amount of work at each pass, the following formula has been developed to estimate the shape of the tube at each pass. Assuming that H is the height of the tube section after reshaping as shown in Figure 7, D is the diameter of the mother tube and N is the number of passes required to reshape the round tube, the height of the tube section at the pass can be expressed as:

For example, to reshape a 2.500” O.D. tube into a 2.000” square using 4 passes, where D = 2.500, H = 2.000 and N = 4, then K = 1.0574 anD

H1 = 2.3643

H2 = 2.2359

H3 = 2.1116

H4 = 2.000

The formula and calculations above are only estimates of the height of the tube section at each reshape pass. The results should be modified according to specific mill layout, material properties and gage thickness before being used. Most manufacturers use round tube forming mills to produce square and rectangular tubular products. These tube mills usually have only two types of roll stands in the sizing section (vertical driven passes and horizontal idle passes) where most of the reshaping is done. Theoretically, reshaping is only accomplished in one direction at each pass for axially oriented cross-sectional tube; therefore, the H should be only be calculated at the driven passes. For mills with double turkshead rolls, two turkshead stands can be regarded as a single pass when calculating the amount done at these rolls. The first set of rolls should be assigned more work than the second. In some cases, a convex contour on the turkshead rolls might be required to overform the tube to compensate for material springback at the final forming stage To reshape thin gage/high strength tube, a more aggressive reduction of the section height than that estimated by using the above formula is suggested due to material springback. To reshape thick gage/high strength tube, a less aggressive reduction is recommended due to difficulties in forming material into the corner. Also, excessive reduction can cause high pressure between the tooling and tube, resulting in surface marking.

Reshaping different cross-sectional tubes in line is a closed section forming process. During the forming process, the cross-sectional area of the tube changes. The length of the tube also changes. The change in length can be estimated by calculating the changes in the cross-sectional area. A common forming problem during the reshaping process is surface marking, especially when forming thin and thick gage tubes. When reshaping thin tubes, more springback exists in the material, increasing the pressure and friction between the tube and tooling. When reshaping thick gage tubes, the material has a strong resistance to flow into the corner, creating high pressure between the tube and tooling. The increases in pressure and friction in both cases results in surface marking on the tube. Mill set-up plays an important role in the tube reshaping process. It is easier to change the mill set-up to obtain the desired cross-sectional geometry than to change the tooling design or rework the tooling. By adjusting the mill set-up, different diameter round tubes can be formed to produce different corner radii in the final products. Also, changes in mill set-up can change the amount of work done at each pass. This is done to reduce surface marking. Tube and pipe roll forming is a material deformation process. Material deformation behavior should be considered when designing tooling and forming operations. Although tooling design is still considered an art, scientifically understanding the deformation process during the reshaping process will improve tooling design and tooling performance.

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