A New Uncut Chip Thickness Model for Tilted Helical End Mills through Direct Correspondence with Local Oblique Cutting Geometry

Machining optimization algorithms in end-milling with helical cutters require an efficient and accurate model of the uncut chip thickness (UCT) at every location along the cutting flutes. Past work has either ignored the effects of tool tilt and orientation or treated them with simple assumptions about their coupling with tool shape. The current paper treats the problem with considerably greater generality using an arc-length parameterization of the axis-symmetric tool profile. Each discrete tool move was considered a 3-axis motion. Ignoring tool run-out, UCT was calculated in the direction of direct correspondence to local oblique cutting geometry, i.e., perpendicular to the local cutting edge and cutting velocity. The flute curves were intersected with the engagement contour corresponding to the instantaneous tool-work contact and the UCT inspected within. For a candidate taper ball end mill, the UCT results of the new model were compared with the standard Martellotti model. The new model agrees closely with the Martellotti model in the flank region and predicts a more realistic variation in the ball region.