Mathematical modeling for the design of a generic custom-engineered form mill

Abstract

This paper presents a mathematical model for the geometric design of a custom-engineered form milling (CEFM) cutter and develops an accurate 3D surface-based generic definition of the form mill. The proposed geometric definition of the CEFM cutter is developed in terms of biparametric surface patches using newly defined 3D rotational angles rather than the conventional 2D angles. The non-uniform rational B-spline curve fairing and sweep surface approaches are used to design the cutting edge and flank surface, respectively, of the cutter. To validate the methodology, an interface is developed that converts the proposed 3D parametric definition of the cutter into an intermediate neutral CAD format and then renders the cutter model in any CAD modeling environment. The accuracy of the mathematical model is verified by evaluating the deviation plot between the surfaces of the proposed cutter model and the surfaces developed using digitized data of an existing actual CEFM cutter. The satisfactory comparison verifies the shape design methodology for custom cutters presented in this paper. The method described here offers a simple and intuitive way of generating shape design of custom cutters for possible use in machining process simulations, finite element analysis, and other applications.