Research On Real-time Algorithms Of NURBS Tool-paths Interpolation

NURBS method is widely used in CAD/CAM for its good curve and surface description properties, which is also specified by STEP standard as the unique mathematical tool for describing the geometry form of industrial production. In the field of CNC machining, the technology of NURBS tool path interpolation may be used both to extend the function of traditional CNC system and to offer key technology support for developing STEP-NC system. This dissertation mainly research on the technique of NURBS tool-paths real-time interpolation for new generation of CNC systems. The main contributions include the following aspects.(1) A new fast algorithm to calculate NURBS curve value and derivation is researched. NURBS tool path interpolation requires computing its value and multi-order derivation at the same time. The de Boor algorithm becomes inefficient in this case. A high efficiency algorithm to calculate B-spline function is investigated by defining vector-extended operation. Based on it, a fast algorithm can be achieved for getting NURBS curve value and derivation. The application and analysis show that the given algorithm can improve the calculating efficiency and accuracy in real-time task of NURBS curve interpolation.(2) An exact feedrate-controlled method of NURBS tool-paths interpolation is researched. Through analyzing the theory of curved-path interpolating feedrate fluctuation, it's pointed out that interpolation points should be calculated under the condition of the step chord length, not the arc. Then, a precise feedrate-controlled method of NURBS tool-paths interpolation is proposed. Adopted the proposed method, the interpolation feedrate fluctuation can be approved distinctly without more calculation time spending.(3) A velocity limited method of NURBS tool-paths interpolation is proposed for high speed CNC. The limit feedrate of curved path interpolation is bounded by both dynamic properties of the CNC machine tool and the geometrical properties of the path. Through establishing the hybrid electromechanical model of every machine federate axis in Cartesian coordinate, the velocity limited analytical curve (VLC) is expressed under the constraints of system dynamic conditions. When the estimation of max chord error meets the interpolation accuracy requirement, the chord error conditions can be neglected. The conclusion is helpful to simplify the feedrate planning restriction conditions, and provides a theory for feedrate planning of NURBS tool-paths interpolation.(4) A time-optimized federate planning method of NURBS tool-paths interpolation is investigated in Cartesian coordinate. The method, built upon the optimization control theory, can achieve the minimum machining time under constraint of system dynamics along the NURBS tool path, which is distinguished form the other federate planning methods. In real-time interpolating task, the given method can proved time-optimized federate curve which is built on the global information of the NURBS tool path and has the same parameter definition domain with the curved path.(5) A new structure of real-time NURBS interpolator is presented with feedrate guide curves. With the proposed structure, the real-time federate of NURBS tool path interpolation is given by high-order smooth guided curves. Based on it, software and hardware of CNC system are designed and realized. Experiment results show that feedrate guided curves commendably inherit the results of time-optimized feedrate planning, and the real-time NURBS interpolator with feedrate guide curves can accomplish the real-time tasks in the time of 200μs for high speed CNC.Through the research, five key problems of NURBS tool-paths interpolation are figured out reasonably, which are fast calculating, feedrate fluctuation controlling, feedrate-optimized planning, real-time NURBS interpolator realizing, and so on. The experimental results indicate that the proposed methods are effective and can be used as an integrated solution for further NURBS tool-paths real-time interpolation.