In the present work, the results of the generic definitions of flat end mills proposed by Tandon et al. [7,8] have been further developed, validated and applied to Finite Element Analysis. A mathematical model of the geometry of a flat end mill is formulated in terms of biparametric surface patches using the concept of surface modeling and computational geometry. The
End milling cutters are multi-point milling cutters with cutting edges both on the face end as well as on the periphery, and may be single or double end construction [12–14]. The teeth of the cutter may be straight (parallel with the axis of rotation) or at a helix angle. The cutter may be right-handed or left-handed. End mills combine the abilities of end cutting, peripheral cutting and face milling into one tool. End mills can be used on vertical and horizontal milling machines for a variety of facing, slotting, and profiling operations.
The geometry of a flat end mill projected on two-dimensional orthographic planes with its technical features is shown in Fig. 1a and the sectional view of its flute is shown in Fig. 1b. L1, L2 is the length of the fluted shank and length of the end mill respectively. DC , DS are the cutter diameter and shank diameter of the end mill.
model is generated keeping in mind that it is to be used for direct
analysis, prototyping, manufacturing and grinding of the cutters. The orientation of the surface patches is defined in a right hand coordinate frame of reference by three-dimensional angles, termed as rotational angles. The flutes of the flat end mill are modeled by sweeping the sectional profile of the cutter along the perpendicular direction. Mapping relations are developed between the proposed three-dimensional nomenclature and traditional two-dimensional (2D) projective geometry based nomenclatures. The output in the form of a graphical model of the flat end mill is shown in OpenGL for verification of the methodology. Besides, an interface is also developed to directly pull the detailed mathematical/parametric definition of the end mill in a commercial CAD package for further validation (in the form of a solid model). This exact solid model is analyzed for static and transient dynamic load conditions.
Section 2 of the manuscript describes the detailed surface modeling of a tooth of a flat end mill while the surface models of the body and blending surfaces are presented in Section 3. The schema for mapping the angles between the existing 2D standards and the proposed 3D nomenclature for an end mill is discussed in Section 4. Section 5 presents the algorithm to model a flat end mill. Section 6 shows the implementation of the algorithm in OpenGL and CATIA V5 environment for the validation of the methodology. Section 7 describes one of the downstream technological applications of the 3D model in terms of finite element based engineering analysis of the cutter. Finally, concluding remarks and the scope for future work are presented in the Section 8.
A e R 1R R
cutting edge angle, radial relief angle, radial clearance angle and radial rake angle respectively and are shown in Figs. 1a and 1b. The geometry of an end mill may consist of three classes, namely
• Geometry of fluted shank.
• End surface geometry.
• Shank geometry.
The geometry of a fluted shank consists of circumferential surface patches formed by sweeping a profile of a section of the fluted shank. The sweep operation is a combined rotational and parallel sweep, perpendicular to the axis of the cutter. The end geometry is dependent on the configuration of the flat end profile. A single tooth of a flat end mill may be modeled with the help of nine surface patches, labeled Σ1 to Σ9 as shown in Fig. 2a. They are Rake face (Σ1), Peripheral land (Σ2),. . . Rake face extension (Σ9). The shank geometry of the cutter may be a straight shank or tapered shank with surface patches labeled as Σ50 (axisymmetric surface of revolution) and Σ51 (flat end surface), as shown in Fig. 2b. 通用立铣刀的三维建模英文文献和中文翻译(2):http://www.chuibin.com/fanyi/lunwen_206285.html