Toolpath Interpolation and Smoothing for Computer Numerical Control Machining of Freeform Surfaces: A Review

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Driven by the ever increasing demand in function integration, more and more next generation high value-added products, such as head-up displays, solar concentrators and intra-ocular-lens, etc., are designed to possess freeform (i.e., non-rotational symmetric) surfaces. The toolpath, composed of high density of short linear and circular segments, is generally used in computer numerical control (CNC) systems to machine those products. However, the discontinuity between toolpath segments leads to high-frequency fluctuation of feedrate and acceleration, which will decrease the machining efficiency and product surface finish. Driven by the ever-increasing need for high-speed high-precision machining of those products, many novel toolpath interpolation and smoothing approaches have been proposed in both academia and industry, aiming to alleviate the issues caused by the conventional toolpath representation and interpolation methods.


In September, IJAC published a review by Prof. Luo Xichun from University of Strathclyde. This paper has provided a review of the toolpath interpolation and smoothing methods for CNC machining of freeform surfaces.


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Toolpath Interpolation and Smoothing for Computer Numerical Control Machining of Freeform Surfaces: A Review

Wen-Bin Zhong, Xi-Chun Luo, Wen-Long Chang, Yu-Kui Cai, Fei Ding, Hai-Tao Liu, Ya-Zhou Sun

SpringerLink (Open Access)


The following conclusions can be drawn:


1)The conventional toolpath comprised of linear and circular segments has become the bottleneck for highspeed high-precision machining of freeform surfaces, because the high density short segments results in high frequency fluctuation of feedrate and acceleration, which will decrease the productivity and product surface finish.

2) The parametric curve is the desirable toolpath representation method for freeform surface machining. It can preserve the surface information with high continuity and avoid the drawbacks of linear and circular segments. However, the parametric toolpath has not been included in the standard. Some CNC manufacturers support proprietary parametric toolpaths.

3) It is extremely difficult to achieve the time-optimal solution for the interpolation of parametric curves subject to constraints of machine dynamics and accuracy. The arc length parametrization can achieve higher interpolation accuracy than the Taylor′s expansion method, but the high computational cost makes it ideal for the offline postprocessor of CAM.

4) The lookahead technique has been an effective way for the feedrate scheduling for the parametric interpolator. The lookahead process allows the flexibility of adding various constraints to the interpolator.

5) PVT interpolation is actually a cubic Hermite spline interpolation, which allows users to specify the polynomial toolpath for freeform surface machining. However, the acceleration is not continuous at the boundaries, and it is error-prone.

6) The CNC built-in toolpath smoothing algorithm can mitigate the problems of linear and circular segments, without changing current practice of CNC machining.

7) The local curve corner rounding method provides an analytical solution to the corner rounding problem, but it has severe limitation when smoothing high density short segments, which are very common in the finish machining of freeform surfaces. The limitation is found in a) The adjacent corner transition path may overlap with each other and make the subsequent interpolation impossible;

b) Alternatively, the length of the transition path is constrained which leads to high curvature and the feedrate must slow down to avoid saturating drives.

8) The global curve approximation method can avoid the limitations of local curve corner rounding method. However, it suffers from the difficulty of controlling the Hausdorff distance between the original toolpath and the approximation curve.

9) The velocity blending method can achieve higher efficiency than the curve based smoothing methods, because it schedules the velocity profile of each axis directly at the corner without planning a transition curve.

Based on the assessment of current literatures, some possible future work for the freeform surface machining are offered:

1) Little work can be found that deals with the process dynamics in the CNC interpolator for freeform surface machining, while more and more difficult-to-cut materials are being used for the 3D product.

2) More work is needed to improve the interpolator so that it can suppress the chatter and severe tool wear with embedded sensors.

3) Interpolators that can automatically correct freeform surface machining errors with on-machine metrology are highly desirable in some demanding applications.

4) The hybrid machining, which simultaneously applies more than one machining processes on the workpiece, has been an emerging solution for high-efficiency and cost-effective machining of freeform surfaces. There is a gap in the CNC interpolation and toolpath representation methods to accommodate more than one processes.



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Current Issue

2020 Vol.17 No.2

Table of Contents

ISSN 1476-8186

E-ISSN 1751-8520

CN 11-5350/TP

Tieniu TAN, Chinese Academy of Sciences Guoping LIU, University of South Wales Huosheng HU, University of Essex
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