Quintic Spline Interpolation With Minimal Feed Fluctuation  

Oleh:

Altintas, Yusuf ; Erkorkmaz, Kaan

Jenis: Article from Journal - ilmiah internasional
Dalam koleksi: Journal of Manufacturing Science and Engineering vol. 127 no. 2 (May 2005), page 339-349.
Topik: fluctuations; quintic spline; interpolation; feed fluctuation

Ketersediaan

Perpustakaan Pusat (Semanggi) Nomor Panggil: JJ93.7 Non-tandon: 1 (dapat dipinjam: 0) Tandon: tidak ada

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Isi artikel

This paper presents a parameterization and an interpolation method for quintic splines, which result in a smooth and consistent feed rate profile. The discrepancy between the spline parameter and the actual arc length leads to undesirable feed fluctuations and discontinuity, which elicit themselves as high frequency acceleration and jerk harmonics, causing unwanted structural vibrations and excessive tracking error. Two different approaches are presented that alleviate this problem. The first approach is based on modifying the spline tool path so that it is optimally parameterized with respect to its arc length, which allows it to be accurately interpolated in real - time with minimal complexity. The second approach is based on scheduling the spline parameter to accurately yield the desired arc displacement (hence feed rate), either by approximation of the relationship between the arc length and the spline parameter with a feed correction polynomial, or by solving the spline parameter iteratively in real - time at each interpolation step. This approach is particularly suited for predetermined spline tool paths, which are not arc - length parameterized and cannot be modified. The proposed methods have been compared to approximately arc-length C3 quintic spline parameterization (Wang, F.-C., Wright, P. K., Barsky, B. A., and Yang, D. C. H., 1999, "Approximately Arc - Length Parameterized C3 Quintic Interpolatory Splines," ASME J. Mech. Des, 121, No. 3., pp. 430 – 439) and first- and second-order Taylor series interpolation techniques (Huang, J.-T., and Yang, D. C. H., 1992, "Precision Command Generation for Computer Controlled Machines," Precision Machining : Technology and Machine Development and Improvement, ASME-PED 58, pp. 89 – 104; Lin, R.-S. 2000, "Real - Time Surface Interpolator for 3 - D Parametric Surface Machining on 3 - Axis Machine Tools," Intl. J. Mach. Tools Manuf., 40, No.10, pp. 1513 – 1526) in terms of feed rate consistency, computational efficiency, and experimental contouring accuracy.

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