Analytical and graphical modelling of the cutting scheme when generating with a pinion cutter

Abstract

Abstract The teeth generation in the case of the cylindrical gears with involute profile is frequently realized with tools of pinion cutter type, on specialized slotting machine tools. In general, during gear teeth machining, several teeth of the tool are concomitantly in contact with the worked part, each one detaching a separate chip. The process is characterized by important unevenness of these chips cumulated area, depending on the relative position between the pinion cutter and the worked part. This transforms into cutting force and cutting torque unevenness and negatively influences both machine tool operating and tool life. The paper addresses the problem of smoothing the detached chips cumulated area at the consecutive strokes of the tool, along the rolling motion between it and the worked part, in order to obtain a main cutting torque as uniform as possible. In this purpose, the analytical modelling of the tool/worked part contact is realized at first, in the cases of generating both exterior and interior gears with involute straight teeth. Then, because the analytical solution is very laborious, a modelling algorithm is developed in one of the most performant graphical environments, which is CATIA. By implementing the graphical solution, the variation of detached chips cumulated area can be determined and the required variation law of the rolling feed, leading to process smoothing, can also be found. A numerical approached case study, concerning the teeth machining for an exterior gear is also presented.