VOL. 12, NO. 19, OCTOBER 2017 ISSN 1819-6608 ARPN Journal of Engineering and Applied Sciences ©2006-2017 Asian Research Publishing Network (ARPN). All rights reserved. www.arpnjournals.com 5642 MATHEMATICAL MODEL FOR CALCULATING SCALLOP HEIGHT OF TOROIDAL CUTTER IN FIVE-AXIS MILLING Hendriko Hendriko Politeknik Caltex Riau, Pekanbaru, Riau Indonesia E-Mail: hendriko@pcr.ac.id ABSTRACT The scallop height is the most substantial variable in determining the quality of machined surface. Many analytical approacheswere proposed to calculated the scallop height infive-axis milling.Most of them addressed the issue of scallop height for toroidal cutter by approximating the inclined cutting tool using two common primitive geometries, either circle or ellipse.This paper presents an analytical method to calculate the scallop height of toroidal cutter produced by predefined tool path in five-axis milling. The present study was aimed to improve the drawback of the existing method in representing the swept curve of inclined toroidal cutter. In this study, the swept curve was calculated analytically by adopting the method to calculate the grazing point in swept envelope development. The coordinate of intersection point was calculated by using the combination of swept curve algorithm and coordinate mapping equations. The proposed method was successfully used to generate scallop height data for two machining processes with different step over. Keywords: scallop height, toroidal cutter, grazing toroidal approximation, five-axis milling. 1. INTRODUCTION Many products, such as mould and dies, are designed with free-form surfaces. Currently, those part surfaces are often produced by five-axis milling. Theoretically, five-axis milling offers better efficiency than three-axis milling in producing complex part surface. In five-axis milling, the tool orientation relative to the workpiece can be controlled by two additional degrees of freedom. However, the additional degrees of freedom created complexity as well as flexibility compared to three-axis milling. Machining free-form part is normally involving a huge number of tool movements. Consequently, it is both a long and costly process. Considering the time needed for finishing and polishing which could consume as much as 75% of the total machining time [1], therefore, selecting and controlling the cutting conditions and the strategies employed to increase product quality become very important. In general, there are three parameters that are commonly used to control the accuracy of the machined surface: 1) machining tolerance, 2) scallop height, and 3) surface roughness. In multi-axis milling, scallop height becomes the most substantial component in determining the quality of mahined surface. It is influenced by four factors, 1) cutting tool geometry, 2) tool orientation, 3) part surface geometry, and 4) the distance between adjacent tool path (step over). In order to achieve the expected surface quality, the scallop must be well controlled. However, due to the complexity of the part surface and tool orientation, scallop height is difficult to calculate and it cannot be represented easily. In developing tool path for free-form surfaces, the method to determine the scallop height accurately is still a major challenge. Many studies developed the method to calculate the scallop height during sculptured surface machining. Most of the proposed method calculated the scallop height usinganalytical approaches. Analytical approachwas used to calculate the cut geometry and scallop height in five axis milling because it was much faster and more accurate when compared to the discrete approaches [2-4]. Several researchers [5-8] have performed the study on the effectiveness of inclined flat end mills in the machining of curved surfaces. The results show that flat-end mill produces smaller scallops as compared to ball-end mill. Other studies [9-13] proposed method for calculating the scallop height for ball-end mill to achieve optimal tool path. Ozturk et al. [14] investigated the effect of tool orientation to the scallop height in five-axis milling. Meanwhile [8, 13,15] addressed the issue of scallop height for toroidal cutter by simply assumed that the curvature was constant and cutter geometry was approximated by two common primitive geometry, either circle or ellipse. Senatore et al. [10] represented the tool swept envelope by calculating the effective radius of toroidal cutter due to the inclination angle. Then the scallop height with respect to radius of part surface was calculated and finally the optimal step over can be determined. Others studies [5-12, 15, 16] defined the inclined flat and ball end mills as an ellipse. Mathematically, the shape of swept curves (SV) of inclined flat and ball end mill, which are projected into 2D, can be precisely determined by parametric equation of ellipse curve. However, this approach is not applicable to toroidal cutter. Toroidal cutter is decomposed into cylindrical surface and toroidal surface, consequently, determining the swept curve when the inclination angle existsbecomes much more complicated. This statement will be prooved in the section of Implementation and Discussion. This paper presents an analytical method to calculate the scallop height of toroidal cutter produced by predefined tool path in five-axis milling. The present study was addressed to improve the drawback of the existing method in representing the swept curve of inclined toroidal cutter. In this study, the swept curve was calculated analytically by adopting the method to calculate the grazing point in swept envelope development. The coordinate of intersection point was calculated by using