Adaptive interpolation scheme for NURBS curves with the integration of machining dynamics |
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Authors: | Xianbing Liu Fahad Ahmad Kazuo Yamazaki Masahiko Mori |
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Affiliation: | aIMS-Mechatronics Laboratory, Department of Mechanical and Aeronautical Engineering, University of California, One Shields Avenue, Davis, CA 95616 5294, USA;bMori Seiki Co. LTD., 2-35-16, Meieki, Nakamura, Nagoya, Aichi 450-0002 Japan |
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Abstract: | This paper develops a comprehensive interpolation scheme for non-uniform rational B-spline (NURBS) curves, which does not only simultaneously meet the requirements of both constant feedrate and chord accuracy, but also real-time integrates machining dynamics in the interpolation stage. Although the existing work in this regard has realized the importance to simultaneously consider chord error and machining dynamics, none has really incorporated these in one complete interpolation scheme. In this paper, machining dynamics is considered for three aspects: sharp corners or feedrate sensitive corners on the curves, components with high frequencies or frequencies matching machine natural ones and high jerks. A look-ahead module was developed for detecting and adaptively adjusting the feedrate at the sharp corners. By Fast Fourier Transform (FFT) analysis with a moving window in the interpolation stage identified were some special frequency components such as those containing high frequencies or with frequencies matching machine natural ones. Then, the notch filtering or time spacing method was used to eliminate these components. To more completely reduce feedrate and acceleration fluctuations, the jerk-limited algorithm was also developed. Finally, the interpolated feedrate was further smoothened with B-spline fitting method and the NURBS curves were re-interpolated with the smoothened feedrate. During the interpolation, the chord error was repeatedly checked and confined in the prescribed tolerance. Two NURBS curves were used as examples to test the feasibility of the developed interpolation scheme. |
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Keywords: | NURBS curves Constant feedrate Chord error tolerance Machining dynamics |
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