ORIGINAL ARTICLE A study on helical surface generated by the primary peripheral surfaces of ring tool S. Berbinschi & V. Teodor & N. Oancea Received: 1 June 2011 /Accepted: 3 October 2011 /Published online: 22 October 2011 # Springer-Verlag London Limited 2011 Abstract Often in the engineering practice, cutting tools bounded by primary peripheral surfaces of revolution are used because of their effectiveness. Among these, ring and tangential tools can be used for the generation of constant pitch cylindrical helical surfaces. In this paper, we present an algorithm for the profiling of these types of tools. The algorithm is based on the topological representation of the tool’ s primary peripheral surface. The main goal is to devise a methodology for the profiling of tools whose surfaces are reciprocally enveloping with cylindrical helical surfaces. We present a numerical example for the numerical determination of the axial section form for this type of tools. The application method for this algorithm was developed in the CATIA graphical design environment within which the procedure is developed as a vertical application. In addition, we present a solution for the shape correction of the tool’ s axial cross- section by considering the existence of singular points on the 1 Introduction The ring and tangential tools are tools bounded by a revolution primary peripheral surface. The ring tools are tools designated for the generation of the cylindrical helical surfaces with constant pitch (threads) on specialized machine tools or using specialized technological equip- ments for longitudinal turning machines. The ring tool is frequently made as an enwrapping milling tool. The advantage of this technological solution is the increased productivity of this process. Although the tools of this type generate in the cutting motion a revolving surface, the issue of profiling the primary peripheral surface of this surfaces reciprocally enveloping with cylindrical helical surfaces with constant pitch, is a problem different from the profiling of the side mill [1–4]. The profiling method of this type of tool uses the fundamental theorems of the surfaces generation [1, 5] or the complementary methods as “the minimum distance method” [1], “the in-plane generating trajectories method” [6]. Also, the development of the graphical design environ- ment allows solving these problems using 3D design environment [7–10] or using solid modeling [11, 12]. 2 Ring tool’s profiling algorithm The basic idea behind the proposed algorithm is that a helical movement, with ~ V axis and p helical parameter, can be decomposed in two rotations conjugated with this relative motion as shown in Fig. 1. The three movements, as shown in Fig. 1, are: I is the translation movement correlated with the rotation movement II, in order to produce a helical motion with the same helical parameter p as of the surface to be generated. In most cases, this motion is executed by the workpiece; S. Berbinschi : V. Teodor (*) : N. Oancea Manufacturing Science and Engineering Department, “Dunărea de Jos” University of Galaţi, Galaţi, Romania e-mail: virgil.teodor@ugal.ro Int J Adv Manuf Technol (2012) 61:15–24 DOI 10.1007/s00170-011-3687-6 profile of the helical surface to be generated where multiple normals to the surface exist. Keywords Ring tool . Helical surfaces generation . Topological representation