Algorithms for modelling the load of teeth from pinion cutter tool used at worms machining

The turning of worms with tools of pinion cutter type means to generate helical surfaces by rolling. In this case, the process of detaching the chip by tool successive teeth is characterized by uneven variation of chip total area, calculated as sum of the areas corresponding to the chips simultaneously detached by all tool teeth in contact at a time with the machined part. As consequence, the cutting forces that load the tool cutting edges are also uneven which negatively impacts the machining process: uneven wear of tool teeth and uneven elastic deformation of technological system with bad effects onto the precision of generated worm flanks. This paper proposes the analytical modelling for both area and shape of the chips detached, during the machining process, by the successive teeth of the pinion cutter that generates a cylindrical worm. The tool tooth involute flanks and the arc from tooth head are modelled, thus delimiting the region formed by the successive active teeth of the tool. The model of the chip detached during the rolling between tool and part centrodes is determined and, on this base, the area of the chip detached for an increment of tool rotation is found. Starting from proposed model, a graphical application in CATIA environment was developed in order to calculate the cumulated area of chips simultaneously detached by tool teeth, which is further needed in order to reduce the cutting force unevenness.