A tapered surface is turned on an automatic lathe (i. e. the workpiece has a conical shape). The workpiece is 550 mm long with minimum and maximum diameters of 120 mm and 200 mm at opposite ends. Computer controls on the lathe permit the surface speed to be maintained at a constant value of 150 m/min by adjusting the rotational speed as a function of workpiece diameter. Feed = 0.25 mm/rev, and depth of cut = 3.0 mm. The geometry of the piece has already been formed and this pass will be the final cut. Determine:

Using trig to calculate L and the equation (time cut, tc = L/fr) will give an erroneous result. Briefly discuss why this equation won’t work. - Note that fr is based on feed x RPM, the RPM will have to vary during the cut and feed rate will not be constant.