Real-time NURBS command generators for CNC servo controllers

Cheng, Ming; Tsai, Mi-Ching; Kuo, Jui Chao

doi:10.1016/s0890-6955(02)00015-9

Cited by 205 publications

(96 citation statements)

References 13 publications

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“…(2) In terms of manufacturing process, the division of the curve into short straight lines affects the part contour curve first order derivative continuity and the surface smooth. (3) In terms of processing efficiency, the usage of a large number of tiny lines to approximate the contour curve of the part will cause the difficulty of the processing speed to reach the program feed rate.…”

Section: The Significance Of Nurbs Curve Interpolation In High-speed mentioning

confidence: 99%

The Research of the NURBS Curve Interpolation Algorithm

Zhang

2011

AEF

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Abstract:In this article, the definition, the nature and the parameter of the NURBS (Non-Uniform Rational B-spline) curves are defined, the more thorough analysis and research of the real-time NURBS curve interpolation algorithm and the feed rate adaptive control are carried out. The significance of NURBS curve interpolation in high-speed high-precision CNC machiningIn the current CAD/CAM system, the complex shape parts such as molds, aircraft wings, and wheels are commonly expressed with the parametric equation. Because the conventional CNC machine tools only provide the linear and circular interpolation, CAD/CAM systems have to divide the parameter curve into a large number of tiny segments. The treatment has the following drawbacks(1) There is always a conflict between the accuracy and data generation, the higher the precision the larger the data generate, and reducing the amount of data will decrease the manufacturing accuracy.(2) In terms of manufacturing process, the division of the curve into short straight lines affects the part contour curve first order derivative continuity and the surface smooth. (3) In terms of processing efficiency, the usage of a large number of tiny lines to approximate the contour curve of the part will cause the difficulty of the processing speed to reach the program feed rate.NURBS curve interpolation can directly transfer the curve to CNC system, there is no need to break down the curve into tiny segments. It has the following advantages [3] .(1) Unified mathematic model The method can not only express the freedom of curves and surfaces, but also can accurately represent conical surface curves and surfaces, which provide an unified mathematic model for CAD/CAM system. (2) Flexible shape control By modifying the control vertex, weighted factor or node value, to modify and control the shape of the curve or surface, which provide sufficient flexibility for a variety of shapes design. (3) Powerful modeling capability The method has a series of powerful geometric shaping technologies (including node insertion, subdivision, etc.), which can be used for all aspects of the design, analysis and processing. Curve express for NURBSConcept of the NURBS curve. The parameter equation of the 3-dimensin curve is ( ) ( ) (

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Section: The Significance Of Nurbs Curve Interpolation In High-speed mentioning

confidence: 99%

The Research of the NURBS Curve Interpolation Algorithm

Zhang

2011

AEF

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“…However, the above tool path generated by CAM system cannot be directly input into 5-axis CNC machine to execute accurate cutting because of local gouging between cutter and workpiece. Tikhon [2]and Cheng [3,4]had presented a surface machining method for ball-end cutting tool, respectively. However, these ball-end cutting methods had disadvantages such as lower manufacturing efficiency and so on.…”

Section: Introductionmentioning

confidence: 99%

Tool Path Generation Method of Complex Surface 5-axis Machining

Li¹,

Chen²

2016

Proceedings of the 2016 International Conference on Electrical, Mechanical and Industrial Engineering

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Abstract-To enhance 5-axis CNC machining precision of complex surfaces with a ball-end cutter, the generation method of cutter contacting (CC) paths is presented in this paper. By means of curvature circle, the feeding length was calculated within allowable error. The step-over in the perpendicular direction of feeding one, was figured out according to the permissible remnant cusps. With the local curvature and the machining error, the step-size was calculated to get the parameter of the next cutter-contacting point. The corresponding spline path of tool center points including knot vector and controlling points was obtained from the cutter contacting points.

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“…In order to tackle the above problems and to handle these NURBS calculations efficiently, Yau and Kuo (2001), Farouki and Tsai (2001), Yeh (2000) have proposed different methods for reducing the computational work and shortening the calculation time, respectively. Cheng, Tsai, and Kuo (2002) proved that Taylor second-order approximation is a better choice to achieve real-time interpolation without sacrificing too much geometric accuracy. All these methods are all based on reducing fitting time and made real-time implementation of the curve fitting for large number of CSBs become feasible.…”

Section: Introductionmentioning

confidence: 99%

“…Many scholars have proposed methods for feedrate improvements: for example, Yen and Hsu (2002) proposed feedrate improvement by judging the relationship between feedrate and chord error. However, the study ignored the limitations of acceleration and jerk, and may cause significant deceleration; Cheng, Tsai, and Kuo (2002) took various error factors into consideration and fitted a large number of G01 code into NURBS curves in an efficient way. However, the interpolation process was based on a constant feedrate interpolation method.…”

Section: Introductionmentioning

confidence: 99%

NURBS curve interpolation algorithm based on tool radius compensation method

Zhou

Zhao

et al. 2015

International Journal of Production Research

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This paper focuses on developing an algorithm that can generate toolpaths in NURBS form for smooth, high speed and accurate machining. The initial toolpaths are obtained by tool radius compensation method which is based on the workpiece boundary offsetting. According to different lengths and the continuous short block (CSB) criterion, these offset linear segments can be regarded as CSBs or long straight segments. Junctions are located where the curvature value is greater than the preset curvature threshold value or where it changes abruptly, or at the two end points of any long straight segment. During machining, the NURBS fitting module first looks ahead several CSBs and converts them into parametric curves in real time. During the conversion, continuities of the position, slope or even curvature at the transition of the parametric curves and unfitted line segments can be guaranteed. Then the acceleration/deceleration feedrate-planning scheme is proposed to determine the transition feedrate at the junction between the fitted curves and unfitted long straight segments, and the corner feedrate within the fitted curve. Simulations and experiments show that the proposed algorithm can significantly improve machining accuracy and reduce cutting time to satisfy today's high-speed and high-accurate machining requirements.

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Real-time NURBS command generators for CNC servo controllers

Cited by 205 publications

References 13 publications

The Research of the NURBS Curve Interpolation Algorithm

The Research of the NURBS Curve Interpolation Algorithm

Tool Path Generation Method of Complex Surface 5-axis Machining

NURBS curve interpolation algorithm based on tool radius compensation method

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