Abstract
Computer numerical control (CNC) machine tools have now become the primary production tool for all kinds of manufacturing industries. Manufacturers are under tremendous pressure to enhance product quality in terms of dimension accuracy while maintaining high productivity. To maintain product quality, the volumetric errors of machine tools should be calibrated or eliminated in advance to prevent the manufacture of defective parts. As modern products adopt more complex geometric shapes, it is becoming common for designers to employ free-form curves and surfaces. Non-uniform rational B-spline (NURBS) curves and surfaces are widely used in CAD/CAM systems. The NURBS formats have much more precise mold shape descriptions than conventional CAM approximations with tiny line segments. The data transfer burden is reduced due to the smaller NC data file with the NURBS format. The real cutting speed is increased and is stable for sufficient path length in the feedrate profile scheduler. All these benefits are important for high-speed cutting programming. The NURBS interpolator has recently become the standard module for the latest high-performance CNC controllers. Therefore, the designing and building of a CNC controller with NURBS interpolation and volumetric error compensation functions will be of great help to manufacturers. In this thesis, a fast real-time NURBS path interpolation method is proposed. The proposed method efficiently integrates the data processing of a NURBS path in a CNC controller, from pre-processing to real-time interpolation. In the calculation of the total length of the NURBS path, the numerical adaptive quadrature method adapts to the integrand, i.e. the first derivative of the length function, automatically, dividing the parameter interval into subintervals with fine or coarse spacing according to the varying condition of the integrand. This new method takes full advantage of the subdivision scheme. The key point is to generate inverse length functions (ILF) for each resulting subinterval. In the real-time NURBS path interpolation, the new setting path parameter can be calculated directly using the inverse length function without any time-consuming computation for NURBS parameter approximation. The proposed method is extremely fast, accurate and suitable for real-time implementation, and simulations and a practical cutting test have proved its effectiveness. Another important emphasis in this thesis is to present a new scheme for compensating the geometric errors of a CNC machine tool which is capable of NURBS interpolation. The proposed NURBS-based compensation method utilizes the same basis functions as the setting tool path to directly estimate the actual NURBS path. Due to the use of the same basis functions, the modification of control points is a fast and effective way to compensate the setting tool path. The knot insertion technique of NURBS is used to increase the flexibility and enhance the accuracy of compensation at the same time. This thesis proposes a fast method of on-line compensation of the total positioning errors of a setting NURBS tool path in advance without any additional real-time CPU loading. Both the simulation and experimental results show that the positioning deviations can be effectively enhanced using the fast geometric error compensation method. This proposed method can be also implemented in the post-processor of a CAM system for off-line compensation.