A realtime curvature-smooth interpolation scheme and motion planning for CNC machining of short line segments

Fan, Wei; Lee, Chen-Han; Chen, Jihong

doi:10.1016/j.ijmachtools.2015.04.009

Cited by 122 publications

(40 citation statements)

References 49 publications

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“…Interpolating splines in the context of real-time/online applications were also researched in [7,15,19], and [29]. Online trajectory generation methods in robotic systems are described in [23].…”

Section: Related Workmentioning

confidence: 99%

Real-time interpolation of streaming data

Debski

2020

csci

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One of the key elements of real-time $C^1$-continuous cubic spline interpolation of streaming data is an estimator of the first derivative of the interpolated function that is more accurate than the ones based on finite difference schemas.Two such greedy look-ahead heuristic estimators (denoted as MinBE and MinAJ2) based on Calculus of Variations are formally defined (in closed form) together with the corresponding cubic splines they generate, and then comparatively evaluated in a series of numerical experiments involving different types of performance measures. The results presented show that the cubic Hermite splines generated by heuristic MinAJ2 significantly outperformed these based on finite difference schemas in terms of all tested performance measures (including convergence).The proposed approach is quite general. It can be directly applied to streams of univariate functional data like time-series. Multidimensional curves defined parametrically, after splitting, can be handled as well. The streaming character of the algorithm means that it can also be useful in processing data sets that are too large to fit in memory (e.g., edge computing devices, embedded time-series databases).

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Section: Related Workmentioning

confidence: 99%

Real-time interpolation of streaming data

Debski

2020

csci

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“…Zhao et al [14] adopted a curvature-continuous cubic B-spline to blend the linear segments. Fan et al [15] proposed a real-time local smoothing method, which generates G 3 interpolative tool path with quartic Bézier curves. Duan and Okwudire [16] used an optimal control method to generate the best free-form curve that minimizes machining time under the constraints of path tolerance and kinematics.…”

Section: Introductionmentioning

confidence: 99%

An Analytical Decoupled Corner Smoothing Method for Five-Axis Linear Tool Paths

Zhao

Wan

et al. 2019

IEEE Access

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Nowadays, the tool path in five-axis machining is usually described with linear segments. Tangential and curvature discontinuities of the linear tool path lead to poor machining efficiency and quality. Due to the complexities in constraining approximation errors and synchronization of tool tip position and tool orientation, it still remains a challenge to smooth five-axis linear tool path in real-time. To solve this problem, this paper developed an analytical decoupled corner smoothing method by inserting an asymmetric cubic B-spline and a pair of symmetric quartic spherical Bézier curves for tool tip position and tool orientation, respectively. The maximal approximation errors for tool tip position and tool orientation are fully constrained in the blending procedures. Tool tip position and tool orientation are synchronized by adjusting the blending lengths and angles, which guarantees the C 2 continuity of the tool path. The blending and synchronous scheme are analytical. Therefore, the proposed method can be employed in real-time. To verify the proposed method, simulations and experiments on a five-axis machine tool are conducted, the results demonstrate the feasibility and efficiency of the proposed method.

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“…& The real-time machining: The user defines the model of the smoothing. Mono and double parametric curves of degrees 3, 4, and 5 and those of type Bezier, b-spline, and Nurbs have been proposed as transition blocks inserted at the level of the discontinuities to ensure the continuity in tangency and curvature of the tool trajectory [3][4][5][6][7][8][9][10][11][12][13]. However, this machining mode is still limited at the level of research units.…”

Section: Introductionmentioning

confidence: 99%

Analytical modeling of the CNC machine axis motion in high-speed milling with local smoothing

Essid

Baili

Hbaieb

et al. 2019

Int J Adv Manuf Technol

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In high-speed milling (HSM) of free-form surfaces, the tool path is mainly characterized by a set of short discontinuous segments in tangency. These discontinuities bring an intense kinematic parameter fluctuation of the computer numerical control (CNC) machine axes. The smoothing of the programmed tool path and the optimal choice of the manufacturing process parameters ensure a high productivity with the required quality of the machined surfaces. Precise estimation of the machining time allows an accurate evaluation of the machined product cost. Thereby, this is achieved by studying the effect of the tool path smoothing and the CNC controller parameters on the axis kinematics and the following errors. This paper focuses on the geometrical modeling of the local smoothing block adopted by Sinumerik CNC. Further, a kinematic model is proposed to simulate the axis motion in linear interpolation mode with local smoothing. The identification of the interpolator reduction effect on the programmed tolerance leads to the identification of the smoothing model adopted by the CNC unit. Then, the axis kinematic behavior is modeled while taking into account the drive parameter axes defined by the manufacturer of the CNC unit. The experimental results showed a smooth variation of the axis feed rate along the smoothing blocks and a good correlation with the proposed models.

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A realtime curvature-smooth interpolation scheme and motion planning for CNC machining of short line segments

Cited by 122 publications

References 49 publications

Real-time interpolation of streaming data

Real-time interpolation of streaming data

An Analytical Decoupled Corner Smoothing Method for Five-Axis Linear Tool Paths

Analytical modeling of the CNC machine axis motion in high-speed milling with local smoothing

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