Computer-Aided Design 41 (2009) 106–114 Contents lists available at ScienceDirect Computer-Aided Design journal homepage: www.elsevier.com/locate/cad Three dimensional modeling and finite element simulation of a generic end mill Puneet Tandon ∗ , Md. Rajik Khan PDPM Indian Institute of Information Technology, Design & Manufacturing Jabalpur, 482011, India article info Article history: Received 16 September 2008 Accepted 9 January 2009 Keywords: Surface modeling Surface patches Mapping End mill Finite element analysis abstract The geometry of cutting flutes and the surfaces of end mills is one of the crucial parameters affecting the quality of the machining in the case of end milling. These are usually represented by two-dimensional models. This paper describes in detail the methodology to model the geometry of a flat end mill in terms of three-dimensional parameters. The geometric definition of the end mill is developed in terms of surface patches; flutes as helicoidal surfaces, the shank as a surface of revolution and the blending surfaces as bicubic Bezier and biparametric sweep surfaces. The proposed model defines the end mill in terms of three-dimensional rotational angles rather than the conventional two dimensional angles. To validate the methodology, the flat end milling cutter is directly rendered in OpenGL environment in terms of three-dimensional parameters. Further, an interface is developed that directly pulls the proposed three-dimensional model defined with the help of parametric equations into a commercial CAD modeling environment. This facilitates a wide range of downstream technological applications. The modeled tool is used for finite element simulations to study the cutting flutes under static and transient dynamic load conditions. The results of stress distribution (von mises stress), translational displacement and deformation are presented for static and transient dynamic analysis for the end mill cutter flute and its body. The method described in this paper offers a simple and intuitive way of generating high-quality end mill models for use in machining process simulations. It can be easily extended to generate other tools without relying on analytical or numerical formulations. © 2009 Elsevier Ltd. All rights reserved. 1. Introduction Modeling and simulation of machining processes is a critical step in the realization of high quality machined parts. To precisely simulate the machining operations, accurate models of cutting tools used in the machining processes are required. In metal cutting industry, an end mill cutter plays an important role for obtaining the desired shape and size of a component. A variety of helical end mill cutters are used in the industry. Helical cylindrical, helical ball, taper helical ball, bull-nosed and special purpose end mills are widely used in aerospace, automotive and die machining industries. The analysis of the geometry of the tool surfaces and cutting flutes along with the cutting forces acting on the end mill plays an important part in the design of the end mill and the quality of the manufacturing process. Traditionally, the geometry of cutting tools has been defined using the principles of projective geometry. The advancements in the domain of Computer Aided Design (CAD) allow a designer to specify the cutting tool surfaces in terms of biparametric surface patches [1,2]. Using such an approach, one may develop the comprehensive three-dimensional ∗ Corresponding author. Tel.: +91 761 2632924; fax: +91 761 2632524. E-mail addresses: ptandon@iiitdm.in (P. Tandon), mdrajik@iiitdm.in (Md. Rajik Khan). (3D) surface based definitions of the cutting tools. The surface model of a cutting tool can be converted into a solid model and may further be used for the Finite Element based engineering analysis, stress analysis and simulation of the cutting process; besides the precise grinding / sharpening of cutting tool surfaces. A wide range of cutters used in practice are fluted in geometry. Among fluted cutters considerable work has been done in the area of geometric modeling of slab mill, helical end mill, and twist drills for their design, analysis and grinding. However, surface-based parametric modeling and developing the interface between modeling and analysis for fluted cutters has not received much attention. End mills are cylindrical cutters with teeth on the circumferential surface and one of the ends for chip removal [3–5]. Whatever work is done on modeling end mills, is not in the direction of development of unified representation schemes that can provide direct 3D models for downstream technological applications. Tandon et al. have proposed unified modeling schemes for single-point cutting tools [6], end mills [7], slab mills, and fluted cutters [8]. The work in the direction of development of geometry design of a form milling cutter for precisely obtaining the complex freeform surfaces is done by Wang et al. [9]. Recently, Vijayaraghavan and Dornfield [10] have shown finite element simulation and modeling of a two-flute conical twist drill. S. P. Radzevich has worked for the surface generation in the design of plunge shaving cutters for the finishing of precision involute gears [11]. 0010-4485/$ – see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.cad.2009.01.005