C 2 continuous time-dependent feedrate scheduling with configurable kinematic constraints

Abstract

We present a configurable trajectory planning strategy on planar paths for offline definition of time-dependent C 2 piecewise quintic feedrates. The more conservative formulation ensures chord tolerance, as well as prescribed bounds on velocity, acceleration and jerk Cartesian components. Since the less restrictive formulations of our strategy can usually still ensure all the desired bounds while simultaneously producing faster motions, the configurability feature is useful not only when reduced motion control is desired but also when full kinematic control has to be guaranteed. Our approach can be applied to any planar path with a piecewise sufficiently smooth parametric representation. When Pythagoreanhodograph spline curves are considered, the corresponding accurate and efficient CNC interpolator algorithms can be exploited.

Using Fuzzy Control for Feed Rate Scheduling of Computer Numerical Control Machine Tools

“…Compared with the method by Yeh and Hsu [10], the average tracking error is poorer than 0.004 mm; yet the processing time is better than 82 s. In experiment 2, the proposed system increases the cutting accuracy by 70% under the approximative same cutting time (46 and 45). Even though our method shows higher average tracking errors in comparison with [10] and [11], the machining time can be saved around 2.8 and 6.5 times, respectively. The butterfly shape experimental data illustrate that the maximum tracking error of 0.004 mm is better than that of the method by Giannelli et al [11], average tracking error is better than 0.002 mm, and processing time is half for the same maximum speed.…”

“…Even though our method shows higher average tracking errors in comparison with [10] and [11], the machining time can be saved around 2.8 and 6.5 times, respectively. The butterfly shape experimental data illustrate that the maximum tracking error of 0.004 mm is better than that of the method by Giannelli et al [11], average tracking error is better than 0.002 mm, and processing time is half for the same maximum speed. Under the same maximum speed as in the method by Yeh and Hsu [10], the maximum tracking error is better than 0.019 mm, average tracking error is better than 0.003 mm, and processing time is less than 11 s. Our method uses the same maximum speed as the method by Luan et al [9], and the maximum tracking error is better than 0.029 mm, average tracking error is better than 0.009 mm, and processing time is less than 6 s. In experiment 3, the average tracking error and machining time are all decreasing using the proposed method overall.…”

“…This study performs three experiments. At the same time, three methods proposed by Luan et al [9], Yeh and Hsu [10], and Giannelli et al [11] are also adopted to test and compare the results of the proposed method. The lower the tracking error the higher the accuracy and the less machining time the better the machining efficiency is.…”

“…Both simulation and experimental results for non-uniform rational B-spline (NURBS) examples were verified for the feasibility and precision of the proposed interpolation algorithm. Giannelli et al [11] proposed a configurable trajectory planning strategy which can be applied to any planar path with a piecewise sufficiently smooth parametric representation. The processing path-based dynamic feed rate scheduling does not need to install an extra sensor.…”

Using Fuzzy Control for Feedrate Scheduling of Computer Numerical Control Machine Tools

“…Fuzzy control was first proposed by L. A. Zadeh in 1964 [12], to develop a versatile control system and to avoid some of the difficulties associated with forcebased controllers, it has been widely used in various fields, such as signal processing, servo control, and image processing. The advantages of fuzzy controller are that it is suitable for nonlinear systems and that it is described by control laws made by experts in their field.…”