Generalized modeling of mechanics and dynamics of milling cutters

This paper presents a generalized mathematical model of most helical end mills and inserted cutters used in industry. The end mill geometry is modeled by wrapping the helical flutes around a parametric envelope of a cutter body. The edge geometry for inserted cutter is defined in the local coordinate system of each insert, and placed and oriented on the cutter body using cutter's global coordinate system. The coordinates of a cutting edge are mathematically expressed for both cases. The chip thickness 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 or tooth, which are in contact with the workpiece, the cutting forces, vibrations, dimensional surface finish, and chatter stability lobes for arbitrary end mills and inserted cutters are predicted. The predicted and measured cutting forces, surface roughness and stability lobes for helical tapered ball, bull nosed end mills and inserted cutters are provided to illustrate the viability of the proposed generalized end mill analysis. The algorithms are integrated to an advanced cutting process simulation program which is used for process planning of milling operations to avoid chatter vibrations, torque and power limit constraints, and dimensional form errors.