Int J Adv Manuf Technol (2003) 21:627–636 Ownership and Copyright  2003 Springer-Verlag London Limited Accurate Machining of Freeform Surfaces by Restraining Cutter Contouring Errors A. Jaganathan and Y. J. Lin Department of Mechanical Engineering, The University of Akron, Akron, OH 44325-3903, USA Machined parts having sculptured surfaces pose challenges in the field of CAD/CAM. Sculptured surfaces are essential in the manufacture of components with curved geometry, which are demanded mostly in the aerospace and die and mould indus- tries. This paper presents an adaptive cutter path restraining method for freeform surface machining and its implementation in milling. The ultimate goal is to achieve high contouring accuracy for sculptured parts machining which is a principal index for the performance evaluation of CNC machines. The proposed method is robust in achieving the desired surface cutting with the capability of satisfying pre-specified tolerance requirements using certain adaptive laws. The given tolerance is measured as the angular deviation by which the generated cutter path differs from the desired path. Since the feedrate is considered to be the most significant cutting parameter, only feedrate variations from 5 mm s -1 to 30 mm s -1 are applied in this system. The tool paths generated with and without the adaptive mechanism are compared. The proposed methodology has been tested on a CNC milling system with an open- architecture controller. The experimental results demonstrate that the proposed tolerance feedback mechanism is very effec- tive for producing parts with sculptured surfaces. Keywords: Adaptive method; Contouring error control; Free- form parts; Sculptured surface milling 1. Introduction CNC machine tools play an important role in modern automatic manufacturing systems. With the increasing demands for better machining precision, methods for improving the performance of the CNC systems in contour machining are continuously being sought. One of the important techniques in manufacturing is to produce a part with freeform or parametric surfaces that Correspondence and offprint requests to: Dr Y. J. Lin, Department of Mechanical Engineering, The University of Akron, Akron, OH 44325-3903, USA. E-mail: yl@uakron.edu Received 5 January 2002 Accepted 12 April 2002 are widely used in modern CAD/CAM systems. The develop- ment of NC machines, computer-aided geometric design (CAGD), etc., enable sculptured surfaces to be widely used in many areas, such as the design and manufacture of airplanes, ship hulls, and complicated parts. To cut the parametric sur- faces, three-axis CNC milling machines using ball-end cutters are frequently used. However, a ball-end cutter is not a standard or highly productive cutter. In order to manufacture sculptured surfaces with an end- milling cutter, two tasks must be undertaken. One is to set up a formula to generate the tool-centre path, the other is to generate the required tool paths for the one sculptured surface to obtain the required surface finish and accuracy. In this work, an adaptive tool-path generation algorithm is proposed for CNC which is economical for mass, batch, and, in many cases, single-item production. In this work, an adaptive tool-path generation algorithm is proposed for machining the sculptured surface of a part using a CNC machine. This algorithm has an adaptive capability so that it can direct the tool paths generated on the part in such a way that the error between the generated path and the desired path based on a CAD model will always fall within an allowable machining tolerance based on the precision requirements. The generation of an NC “Part programs” to machine com- plex geometries, such as freeform surfaces, is a basic problem in computer-aided manufacturing. Several constraints of a purely geometrical/kinematical nature determine the accuracy and efficiency of this solution: 1. The surface cannot, in general, be described as the envelope of successive positions of simple (cylindrical, spherical or toroidal) tools that execute finite trajectories – the need for a finite “step over” between successive contact loci produces ridges or scallops on the machined surface. 2. Tool-centre paths, corresponding to desired geometrical properties of the surface contact loci – e.g. equidistant spacing on the surface or with respect to a coordinate axis – do, not ordinarily have exact (rational) representations compatible with contemporary systems. 3. Commercial CNC machines are currently restricted by the machine specific software to simple (linear/circular) motions – the necessity of using large numbers of such