An axle-bearing surface made of high carbon steel has worn beyond its useful life. When it was new, the diameter was 4.00 in. In order to restore it, the diameter was turned to 3.90 in to provide a uniform surface. Next the axle was built up so that it was oversized by the deposition of a surface weld bead, which was deposited in a spiral pattern using a single pass on a lathe. After the weld buildup, the axle was turned again to achieve the original diameter of 4.00 in. The weld metal deposited was a similar composition to the steel in the axle. The length of the bearing surface was 7.0 in. During the welding operation, the welding apparatus was attached to the tool holder, which was fed toward the head of the lathe as the axle rotated. The axle rotated at a speed of 4.0 rev/min. The weld bead height was 3/32 in above the original surface. In addition, the weld bead penetrated 1/16 in into the surface of the axle. The width of the weld bead was 0.25 in, thus the feed on the lathe was set to 0.25 in/ rev. Assuming the heat transfer factor was 0.80 and the melting factor was 0.65, determine
(a) the relative velocity between the work piece and the welding head,
(b) the rate of heat generated at the welding source, and
(c) how long it took to complete the welding portion of this operation.