Abstract
Driven by the ever increasing need for the high-speed high-accuracy machining of freeform surfaces, the interpolators for parametric curves become highly desirable, as they can eliminate the feedrate and acceleration fluctuation due to the discontinuity in the first derivatives along the linear tool path. The interpolation for parametric curves is essentially an optimization problem, and it is extremely difficult to get the time-optimal solution. This paper presents a novel real-time interpolator for parametric curves (RTIPC), which provides a near time-optimal solution. It limits the machine dynamics (axial velocities, axial accelerations and jerk) and contour error through feedrate lookahead and acceleration lookahead operations, meanwhile, the feedrate is maintained as high as possible with minimum fluctuation. The lookahead length is dynamically adjusted to minimize the computation load. And the numerical integration error is considered during the lookahead calculation. Two typical parametric curves are selected for both numerical simulation and experimental validation, a cubic phase plate freeform surface is also machined. The numerical simulation is performed using the software (open access information is in the Acknowledgment section) that implements the proposed RTIPC, the results demonstrate the effectiveness of the RTIPC. The real-time performance of the RTIPC is tested on the in-house developed controller, which shows satisfactory efficiency. Finally, machining trials are carried out in comparison with the industrial standard linear interpolator and the state-of-the-art Position-Velocity-Time (PVT) interpolator, the results show the significant advantages of the RTIPC in coding, productivity and motion smoothness.
Highlights
Parametric curves are represented in parametric form, each coordinate of the curve is given by an explicit function of an independent parameter, in a form of CðuÞ 1⁄4 ðxðuÞ; yðuÞÞ u 2 1⁄2a; b
Parametric curves have seen their wide applications in computer-aided design (CAD) of products like optics, molds/dies, biomedical implants, etc., where freeform surfaces are of great importance [2]
This approach results in the following undesirable problems: (1) To achieve higher contour accuracy, more segments are needed to approximate the original surface, which pose huge burden for data transfer and memory of the computer numerical control (CNC) system; (2) Increased feedrate and acceleration fluctuation, which is due to the discontinuity in the first derivatives along the tool path, reduces the average feedrate and causes vibration, i.e. lower productivity and poorer surface finish [3]
Summary
Parametric curves are represented in parametric form, each coordinate of the curve is given by an explicit function of an independent parameter, in a form of CðuÞ 1⁄4 ðxðuÞ; yðuÞÞ u 2 1⁄2a; b. Jin and co-workers [24] realized their lookahead method by calculating the length of deceleration repeatedly at each interpolation period This kind of lookahead technique can determine deceleration position rapidly and tend to achieve near time-optimal feedrate profile. The interpolator will fully take into consideration of constraints from machine dynamics (axial velocities, axial accelerations and jerk) and contour error while maintaining the feedrate as high as possible. The dynamic lookahead length technique, the numerical integration error consideration, the multi-cases design for feedrate lookahead and intelligent activation of the acceleration lookahead are introduced for the first time, which greatly enhance the interpolation efficiency and accuracy. The rest of the paper is organized as follows: the detailed description of the proposed interpolator is given in Section 2; the numerical simulation is performed in Section 3; the real-time performance test, machining trials and discussions are presented in Section 4; Section 5 concludes the paper
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