A NURBS interpolator with constant speed at feedrate-sensitive regions under drive and contour-error constraints

Zhang, Jia; Song, De-Ning; Ma, Jian-wei; Hu, Guo-qing; Sui, Weiwei

doi:10.1016/j.ijmachtools.2016.12.007

Cited by 110 publications

(56 citation statements)

References 35 publications

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“…At the end of each feedrate scheduling cycle, the look-ahead window slides forward to another by a third of its length L smax . W 2 i and W 3 i become W 1 i + 1 and W 2 i + 1 of the next window W i + 1 , and newly buffered reference points comprise the third part of W i + 1 . This tri-step forward lookahead strategy guarantees that the critical points with feedrate violation are always located in the third part of the look-ahead window because the length of a nonschedulable block is always shorter than L smax .…”

Section: Windowed Look-ahead Feedrate Scheduling Methodsmentioning

confidence: 99%

“…By comparison, the feedrate scheduling is accomplished in the off-line stage in some prior works. 3,15 Since the feedrate profile generation is displacementcontrolled, and the NURBS interpolation uses chord length to approximate the curve length by its very nature, the terminal error always exists at the end of an NURBS block when interpolating the NURBS curve with the scheduled feedrate profile. In this article, a compensation feedrate profile scheduling method is proposed to eliminate the terminal error, which also considers the rounding error at the transition point between a constant speed stage and a variable speed stage.…”

Section: Introductionmentioning

confidence: 99%

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Sliding look-ahead window-based real-time feedrate planning for non-uniform rational B-splines curves

Liu

Qin

et al. 2018

Advances in Mechanical Engineering

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This article presents an online three-axis non-uniform rational B-splines preprocessing and feedrate scheduling method with chord error, axial velocity, acceleration, and jerk limitations. A preprocessing method is proposed to accurately locate the critical points by reducing pre-interpolation feedrate in feedrate limit violation regions. In the preprocessing stage, the non-uniform rational B-splines curve is subdivided into segments by the critical points and the corresponding feedrate constraints are obtained. A sliding look-ahead window-based feedrate scheduling method is proposed to generate smooth feedrate profile for the buffered non-uniform rational B-splines segments. The feedrate profile corresponding to each non-uniform rational B-splines block is constructed according to the block length and the given limits of acceleration and jerk. The feedrate modification method for non-schedulable short blocks is also described which aimed at avoiding feedrate discontinuity at the junction of two non-uniform rational B-splines blocks. With the proposed method, a successful feedrate profile could be generated with sufficient look-ahead trajectory length in the buffer, which enables that the preprocessing and feedrate planning to be performed progressively online. Simulation and experimental tests with different non-uniform rational B-splines curves are carried out to validate the feasibility and advantages of the proposed method. The results show that the proposed method is capable of making a balance between the machining efficiency, machining precision, and computational complexity.

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Section: Windowed Look-ahead Feedrate Scheduling Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Sliding look-ahead window-based real-time feedrate planning for non-uniform rational B-splines curves

Liu

Qin

et al. 2018

Advances in Mechanical Engineering

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“…The toolpath is planned in commercial CAM software, the cutting force can be predicted from the tool engagement geometry and the local feedrate limit is imposed to confine the resultant cutting force according to the cutting force model. Guo et al [56] added the axis tracking error to the constraints. They established the relationship between the tracking error and the input signal of the high-order servo system.…”

Section: Feedrate Schedulingmentioning

confidence: 99%

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

Zhong

Luo

Chang

et al. 2019

Int. J. Autom. Comput.

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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. This paper provides a comprehensive review of the state-of-the-art toolpath interpolation and smoothing approaches with systematic classifications. The advantages and disadvantages of these approaches are discussed. Possible future research directions are also offered.

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“…The feedrate-sensitive point method searches dangerous corners with considered constraints, and connects the allowable speed values at these corners smoothly. For example, Yong and Narayanaswami 7 scheduled the feedrate-sensitive corners under limited chord-error, and connected the sensitive corners with acceleration constriants; Fan et al 8 determined the permissible velocities of critical points with acceleration and jerk constraints, and connected them with a proposed jounce confined feedrate profile; Jia et al 9 scheduled feedrate-sensitive regions under confined chord error, acceleration, jerk, and contour error, and connected these regions with the jerk-limited S-shape feedrate profile. This kind of method is mainly applicable to three-axis machine tools.…”

Section: Introductionmentioning

confidence: 99%

Look-ahead-window-based interval adaptive feedrate scheduling for long five-axis spline toolpaths under axial drive constraints

Song

Zhong

2020

Proceedings of the Institution of Mechanical Engineers, Part B:

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Scheduling of the five-axis spline toolpath feedrate is of great significance for high-quality and high-efficiency machining using five-axis machine tools. Due to the fact that there exists nonlinear relationship between the Cartesian space of the cutting tool and the joint space of the five feed axes, it is a challenging task to schedule the five-axis feedrate under axial drive constraints. Most existing methods are researched for routine short spline toolpaths, however, the five-axis feedrate scheduling method expressed for long spline toolpaths is limited. This article proposes an interval adaptive feedrate scheduling method based on a dynamic moving look-ahead window, so as to generate smooth feedrate for long five-axis toolpath in a piecewise manner without using the integral toolpath geometry. First, the length of the look-ahead window which equals to that of the toolpath interval is determined in case of abrupt braking at the end of the toolpath. Then, the interval permissible tangential feed parameters in terms of the velocity, acceleration, and jerk are determined according to the axial drive constraints at each toolpath interval. At the same time, the end velocity of the current interval is obtained through looking ahead the next interval. Using the start and end velocities and the permissible feed parameters of each interval, the five-axis motion feedrate is scheduled via an interval adaptive manner. Thus, the feedrate scheduling task for long five-axis toolpath is partitioned into a series of extremely short toolpaths, which realizes the efficient scheduling of long spline toolpath feedrate. Experimental results on two representative five-axis spline toolpaths demonstrate the feasibility of the proposed approach, especially for long toolpaths.

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A NURBS interpolator with constant speed at feedrate-sensitive regions under drive and contour-error constraints

Cited by 110 publications

References 35 publications

Sliding look-ahead window-based real-time feedrate planning for non-uniform rational B-splines curves

Sliding look-ahead window-based real-time feedrate planning for non-uniform rational B-splines curves

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

Look-ahead-window-based interval adaptive feedrate scheduling for long five-axis spline toolpaths under axial drive constraints

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