Material removal is one of the most used processes in manufacturing. Initially, the computer numerically controlled (CNC) machine tools were only used for cuts along trajectories with simple geometries. Presently, the complexity of the surfaces in moulds and dies, turbine blades or car bodies manufactured in today’s aerospace or automobile industries demands for much more sophisticated algorithms in tool path generation. Five-axis CNC machines is believed to be the best tools in sculptured surface machining. The research studies performed in the last decade outlined the significant advantages of five-axis milling over traditional three-axis milling. However, the five-axis machining features are still far to be completely understood. The two additional rotational axes of these machines provide them both with an increased flexibility and an increased gouging risk with the fixtures or part. Also, the complex tool trajectory introduces additional errors due to machine tool configuration and local surface geometry, investigation of which constitutes the main object of the present study.

As a first step to accomplish this goal, a generic and unified kinematic model is developed in this study as a viable alternative to the particular solutions that are only applicable to individual machine configurations. This versatile model is then used to verify the feasibility of the two rotational joints within the kinematic chain of three main types of five-axis machine tools. The corresponding kinematic analyses have confirmed the advantages of the popular machine design that employs the intersecting rotational axes and the common industrial practice during setup that minimizes the characteristic rotating arm length of the cutting tool and/or workpiece.

The core of the present study is constituted by the new and accurate method to determine the errors introduced by the Computer-Aided Manufacturing (CAM) software as opposed to the conventional chordal deviation method. This method allows establishing the exact linearly interpolated tool positions between two cutter-contact points on a given tool path, based on the inverse kinematics analysis of the machine tool. A generic procedure has been developed to ensure wide applicability of the proposed method. Analytical derivation of the geometry-based errors provides insights regarding the origin of these errors and their affecting parameters. Besides the local surface geometry, the configuration of the kinematic chain of the CNC machine has been found to be the primary factor controlling the resulting value and type of the geometry-based errors. Implementations with a typical complex free-form surface demonstrated that the conventional chordal deviation method is not reliable and could significantly underestimate the geometry-based errors. While the method to evaluate the geometry-based errors was initially developed for an interpolator to perform linear interpolations only, it has been also found out that the method is equally applicable for the latest generations of numerical controllers capable of spline interpolation.

Finally, a technique to optimize the tool path discretization process is proposed in this study. The use of the chordal deviations in evaluation of the forward step in five-axis machining has been replaced by the more accurate geometry-based errors. The results obtained for a sample Bezier patch revealed a reduction of about 30% in data to be processed when compared with the conventional method.