Parametric multi-axis tool path planning for CNC machining: the case of spur gears.

Four and five axis machining strategies are difficult to standardise in the general case. General purpose CAM systems are an important tool allowing the experienced machinist to experiment with machining strategies and assess quality of the resulting tool paths. However, in the case of machine elements, such as gears, shape definition by parametric equations is most inviting for development of fit-for-purpose machining strategies and corresponding parametric tool paths without the use of CAM software. Such an approach is materialised in this paper for spur gears, drawing on discretisation of involute and trochoidal curves constituting the tooth profile, so as to satisfy scallop height constraints. The roughing stage is performed with a flat end mill, implementing slot milling along a meander type tool path. The finishing stage is performed with a bull-nose end mill, implementing peripheral milling circumferentially around the full gear profile. The algorithms were tested on a three-axis machining centre equipped with an additional 4th rotary axis to manufacture a plastic spur gear.