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Traditional nomenclatures of specifying cutting tool geometries are two-dimensional (2D) in nature. The present work presents a paradigm to model the geometries of a variety of twist drills in terms of three-dimensional (3D) parameters. The work outlines the construction of a detailed computer-aided design (CAD) model for a fluted twist drill and establishes a new 3D definition for the geometry of drill in terms of biparametric surface patches. The flutes of the drill are modeled as helicoidal surfaces. For this, sectional geometry of tip-to-tip profile is developed and then swept. The geometric model of the shank is developed separately. The transitional surfaces are modeled as bicubic Bèzier surfaces. With this methodology, we propose a new 3D nomenclature for drill geometries in terms of 3D rotational angles. The relations necessary to map the proposed three-dimensional angles to two-dimensional conventional angles, known as forward mapping and their reverse relations (inverse mapping) are also developed. The new paradigm offers immense technological advantages in terms of numerous downstream applications. [ABSTRACT FROM AUTHOR]

In this paper we have established a new three-dimensional standard to specify single point cutting tool geometry. The paper models a single point cutting tool in terms of biparametric surface patches. Six new angles, called grinding angles, are proposed to define the orientation of these surface patches. Forward and inverse mappings among grinding angles (αi, βi,γi), conventional tool nomenclature (γy, γx, αy,αx, ..... ), and setting or swivel angles for grinding (θA, θB, θC) are established. The benefits of the new paradigm include ease of finite element based engineering analysis, simulation, and programming of the CNC tool cutter and grinder for tool sharpening. The proposed methodology is illustrated with a few numerical examples. [ABSTRACT FROM AUTHOR]