Rolled Transition Cone Comes Up Short
A shop is rolling a truncated-cone transition from 8 mm mild steel plate. The finished piece must fit between two existing flanges: inside diameter 1200 mm at the large end, 600 mm at the small end, and a vertical height of 900 mm. The joint is a single longitudinal butt weld with a 2 mm root gap and no overlap. The layout was developed by a second-year apprentice using the inside diameters and a 900 mm vertical height. After rolling and tacking, the large-end circumference measures about 40 mm smaller than the mating flange spigot, and the cone does not pull round. The apprentice wants to split the seam, hammer the edges, and add a 40 mm filler strip. The shop has a plate roller, a plasma table, and a qualified welder, but no hydraulic press. The lead hand asks you to check the pattern before any cutting or welding continues.
1. Calculate the mean diameters, true slant height, development radii, and included angle for the pattern. State what happens if inside diameters are used directly.
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Use mean diameters because the neutral axis of the rolled plate is approximately one thickness outside the inside surface: D_large = 1200 + 8 = 1208 mm; D_small = 600 + 8 = 608 mm. The radial difference is (1208 - 608) / 2 = 300 mm. True slant height L = sqrt(900^2 + 300^2) = 948.7 mm. Development radius at the large end R = L x D_large / (D_large - D_small) = 948.7 x 1208 / 600 = 1909 mm. Small radius r = R - L = 960 mm. Included angle = 180 x D_large / R = 180 x 1208 / 1909 = 113.9 degrees. The large-end arc length should be pi x 1208 = 3795 mm. If the inside diameter is used, the arc is pi x 1200 = 3770 mm, about 25 mm short. That is one plate thickness times pi, so the finished mean circumference will be undersize before weld shrinkage and gap effects are considered.
2. The finished large-end circumference is about 40 mm short. Is that fully explained by the inside-diameter error? What else could cause it, and should the filler strip be used?
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No. The inside-diameter error explains only about 25 mm of the 40 mm shortfall. The remaining 15 mm is likely a combination of the 2 mm root gap not being added to the developed arc, weld shrinkage after tacking, measuring the flange spigot instead of the true mating circumference, or marking the pattern as a chord rather than an arc. A filler strip is not an acceptable correction here. It adds a second longitudinal seam, creates an abrupt thickness and hardness change, increases ovality, and makes the cone harder to fit and weld. For a cone that must mate with an existing flange, the correct action is to redevelop the pattern on mean diameters, include the root gap, and cut a new plate or trim and re-roll if there is enough material. Hammering the edges will only disguise the error and induce residual stress.
3. Describe the correct layout and fit-up checks before rolling and tacking.
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Lay out the pattern on the mean diameters, not the inside or outside diameters. Calculate the large and small arc lengths and add the root gap to the developed length so the finished circumference includes the joint opening. Mark the longitudinal seam centerline, quarter points, rolling direction, and a reference line for flange alignment. After rolling, check the large-end and small-end circumferences at the mean diameter, not at the inside edge. Check ovality with a trammel or template, check the slant length at several points, and verify that the flange faces can be brought parallel without force. Tack with strongbacks and confirm a uniform root gap before welding. If the circumference is outside tolerance, adjust the pattern or trim the seam rather than using filler plates or localized hammering.