Mechanics and dynamics of general milling cutters. Part I: helical end mills

A variety of helical end mill geometry is used in the industry. Helical cyl indrical, helical ball, taper helical ball, bull nosed and special purpose end mills are widely used in aerospace, automotive and die machining indust ry. While the geometry of each cutter may be different, the mechanics and d ynamics of the milling process at each cutting edge point are common. This paper presents a generalized mathematical model of most helical end mills u sed in the industry. The end mill geometry is modeled by helical flutes wra pped around a parametric envelope. The coordinates of a cutting edge point along the parametric helical flute are mathematically expressed. The chip t hickness at each cutting point is evaluated by using the true kinematics of milling including the structural vibrations of both cutter and workpiece. By integrating the process along each cutting edge, which is in contact wit h the workpiece, the cutting forces, vibrations, dimensional surface finish and chatter stability lobes for an arbitrary end mill can be predicted. Th e predicted and measured cutting forces, surface roughness and stability lo bes for ball, helical tapered ball, and bull nosed end mills are provided t o illustrate the viability of the proposed generalized end mill analysis. ( C) 2001 Elsevier Science Ltd. All rights reserved.