A Feedrate Planning Method for the NURBS Curve in CNC Machining Based on the Critical Constraint Curve

Guo, Peng; Wu, Yicheng; Yang, Guang; Shen, Zhebin; Zhang, Haorong; Zhang, Peng; Lou, Fei; Li, Hengbo

doi:10.3390/app11114959

Cited by 9 publications

(5 citation statements)

References 32 publications

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“…Then, the first-level parameter compensation is performed. In this process, the adaptive velocity of the next interpolation point is calculated using the adaptive velocity approach described in Equation ( 5) and is restrained under the command feedrate constraint according to Equation (6). The estimated parameters u pre,i+1 of the next interpolation point are obtained by using the FAM or SAM described in Equations ( 7) and (8).…”

Section: Feedrate Fluctuation Elimination Strategymentioning

confidence: 99%

“…Li et al [5] employed the Sigmoid function for feedrate planning, considering both geometric and kinematic errors. Guo et al [6] presented a federate scheduling method to overcome the NURBS curvature changing along the trajectory. Hu et al [7] presented a brand-new feedrate scheduling approach based on an S-shape feedrate profile to improve interpolation accuracy.…”

Section: Introductionmentioning

confidence: 99%

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NURBS Interpolator with Minimum Feedrate Fluctuation Based on Two-Level Parameter Compensation

Nie

Zhu

2023

Sensors

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Feedrate plays a crucial role in determining the machining quality, tool life, and machining time. Thus, this research aimed to improve the accuracy of NURBS interpolator systems by minimizing feedrate fluctuations during CNC machining. Previous studies have proposed various methods to minimize these fluctuations. However, these methods often require complex calculations and are not suitable for real-time and high-precision machining applications. Given the sensitivity of the curvature-sensitive region to feedrate variations, this paper proposed a two-level parameter compensation method to eliminate the feedrate fluctuation. First, in order to address federate fluctuations in non-curvature sensitive areas with low computational costs, we employed the first-level parameter compensation (FLPC) using the Taylor series expansion method. This compensation allows us to achieve a chord trajectory for the new interpolation point that matches the original arc trajectory. Second, even in curvature-sensitive areas, feedrate fluctuations can still occur because of truncation errors in the first-level parameter compensation. To address this, we employed the Secant-based method for second-level parameter compensation (SLPC), which does not require derivative calculations and can regulate feedrate fluctuation within the fluctuation tolerance. Finally, we applied the proposed method to the simulation of butterfly-shaped NURBS curves. These simulations demonstrated that our method achieved maximum feedrate fluctuation rates below 0.01% with an average computational time of 360 us, which is sufficient for high-precision and real-time machining. Additionally, our method outperformed four other feedrate fluctuation elimination methods, highlighting its feasibility and effectiveness.

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Section: Feedrate Fluctuation Elimination Strategymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

NURBS Interpolator with Minimum Feedrate Fluctuation Based on Two-Level Parameter Compensation

Nie

Zhu

2023

Sensors

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“…Therefore, the path is smoothed by using a cubic non-uniform rational B-spline (NURBS) curve with C 2 continuity in this paper. The k-th order NURBS curve is defined as follows [34]. (7) Where: w i (0 ≤ i ≤ n;w 0 , w 1 > 0;w i ≥ 0) is the weight factor, and the adjacent k weight factors cannot be 0 simultaneously; d i (0 ≤ i ≤ n) is the control vertex; node vector U = [u 0 , u 1 , .…”

Section: Nurbs Curve Fittingmentioning

confidence: 99%

Collision-free trajectory planning for multi-robot simultaneous motion in preforms weaving

Meng

et al. 2022

Robotica

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In this paper, an automatic obstacle avoidance trajectory planning strategy is proposed for the simultaneous motion of multi-robots, which perform anthropomorphic skill operations in a large curved preformed three-dimensional (3D) weaving environment with multiple obstacles and limited space, to eliminate tedious manual calibration work of robot path in engineering. Firstly, an Adaptive Goal-guided Rapidly-exploring Random Trees (AGG-RRT) algorithm is proposed, combined with the robot obstacle avoidance strategy, to search the discrete position of the collision-free path of the end-effector gradually from the starting point to the ending point. Then the optimization of the path is completed by bidirectional pruning of redundant nodes and cubic non-uniform rational B-spline (NURBS) curve fitting. And finally, the robot trajectory is interpolated based on S-shaped acceleration/deceleration planning to ensure smooth robot joint motion. The simulation results demonstrate the superiority of the AGG-RRT algorithm over the basic RRT algorithm and related improved algorithms in terms of search time and success rate. The simulated experiments also achieve the smooth trajectory planning of multiple robotic arms with the synchronous obstacle avoidance motion, which shows that the AGG-RRT algorithm is successfully applied and the collision-free trajectory planning strategy is effective.

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“…Also, the feedrate scheduling process of the NURBS is critical for CNC machines. Because feedrate scheduling is directly related to the high speed and high precision control of CNC machines, researchers have introduced new feedrate scheduling methods for NURBS [12,13,[17][18][19][20]. Zhang et al [19] proposed an optimal nonlinear feedrate scheduling algorithm that can determine the interpolating compensation distance for each interpolating segment and obtain the interpolation points using a second-order Taylor series expansion with a minimal interpolating error.…”

Section: Introductionmentioning

confidence: 99%

Fast and High Precision Control Approach: Polyline Analysis and Optimal NURBS Interpolation for CNC Machine Tools

Kelekçi,

Kizir

2024

Preprint

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In CNC operations, smooth motions generated using a parametric curve such as NURBS, Bezier curve, and B-spline are crucial for surface quality and machine control. A parametric curve is formed by microlines in CAD/CAM software; however, instead of microlines, polylines are used to define a parametric curve to prevent an increase in NC-file size. It is also possible to see situations where smooth motion is not required due to production requirements. In these cases, point-to-point motion is necessary instead of smooth motion. In this study, a polyline analysis algorithm is proposed to classify the normal line and polyline within the NC-file. A global tool path smoothing method is also applied, where the data points in a polyline group are converted into NURBS because CAD/CAM software commonly uses NURBS as a parametric curve for precision control of CNC machines. In addition, this study presents an optimal feedrate scheduling algorithm for the NURBS curve that generates an optimal feedrate profile for each segment by considering critical parameters such as segment length, initial and final velocity of each segment, maximum jerk, acceleration, and velocity. As the proposed algorithm is compatible with existing feedrate scheduling methods in which different feedrate values at the transition point of the NURBS segments are determined, this study provides an important contribution to the literature. The proposed methods in this study are verified by operating a spherical surface using industrial NC-files on a 3-axis CNC-Milling machine. The proposed methods demonstrate effective performance in experiments that require precision production operations.

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A Feedrate Planning Method for the NURBS Curve in CNC Machining Based on the Critical Constraint Curve

Cited by 9 publications

References 32 publications

NURBS Interpolator with Minimum Feedrate Fluctuation Based on Two-Level Parameter Compensation

NURBS Interpolator with Minimum Feedrate Fluctuation Based on Two-Level Parameter Compensation

Collision-free trajectory planning for multi-robot simultaneous motion in preforms weaving

Fast and High Precision Control Approach: Polyline Analysis and Optimal NURBS Interpolation for CNC Machine Tools

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