NURBS Interpolation Algorithm Based on Feedrate Sensitive Points Identification

2011 ◽  
Vol 383-390 ◽  
pp. 2567-2572
Author(s):  
Feng Lin
Keyword(s):  
Industrial Application ◽  
Reference Value ◽  
Interpolation Algorithm ◽  
Cnc System ◽  
Nurbs Curve ◽  
Chord Error ◽  
B Spline ◽  
Cad Cam ◽  
Nurbs Interpolation ◽  
Simulation Results

The Non-uniform rational B-spline (NURBS) is widely used in CAD/CAM/CNC. The NURBS interpolation is crucial for an advanced CNC system compatible with NURBS. Classic NURBS interpolation algorithms always do not well consider both the contour precision and feedrate smoothness. This paper proposes a NURBS interpolation algorithm based on the feedrate sensitive points identification. The feedrate sensitive points is found out according to the chord error which is relative to the feedrate passing this point. Furthermore, the feedrate profile is adaptively planned between two adjacent sensitive points according to the distance between them. The feedrate profile of the whole NURBS can be connected with these feedrate sections. A cubic NURBS curve is adopted to evaluate the interpolation algorithm. Simulation results show that the proposed interpolation algorithm is available with reference value for industrial application.

A Multi-Objective Coordinated Control Oriented New Algorithm for NURBS Curve Interpolation

2011 ◽  
Vol 305 ◽  
pp. 80-87
Author(s):  
Zi Hua Hu ◽  
You Ren Zhan ◽  
Man Ke Gao
Keyword(s):  
Machine Tools ◽  
Coordinated Control ◽  
Experimental Simulation ◽  
Interpolation Algorithm ◽  
Nurbs Curve ◽  
Chord Error ◽  
Multi Objective ◽  
Machining Quality ◽  
Curve Interpolation ◽  
Nurbs Interpolation

The coordinated control of machining quality and efficiency is the ultimate goal for the next generation NURBS curve interpolation algorithm. Recently, the existing researches on NURBS curve interpolation algorithm mainly focus on chord error, feedrate, machine tools acceleration/deceleration capability, but the reasonable matching between multi-objective’s parameter and error redundancy coordinated control has not been considered yet. Therefore, a new NURBS interpolation algorithm is proposed with multi-objective coordinated control in this paper, which does not only consider chord error, error redundancy, acceleration/deceleration capability of machine tools, real-time ability simultaneously, but also satisfy the reasonable matching between multi-objective’s parameter and error redundancy coordinated control. The results of experimental simulation indicate that the obtained new NURBS interpolation algorithm is reliable, and the coordinated control ability of machining quality and efficiency is improved obviously.

A Tool-Path Interpolation Algorithm Based on Unfolding-Bending Parametric Curves

2009 ◽  
Vol 407-408 ◽  
pp. 220-224
Author(s):  
Li Cheng Fan ◽  
Li Ning Sun ◽  
Zhi Jiang Du
Keyword(s):  
Tool Path ◽  
Discrete Data ◽  
Sculptured Surface ◽  
Interpolation Algorithm ◽  
Parametric Curves ◽  
Chord Error ◽  
B Spline ◽  
Spline Curves ◽  
Cutting Vibration ◽  
Simulation Results

To grind sculptured surface by swing motion, it’s needed to interpolate the discrete data nodes on the arc-driving surface. To ensure that all the sample points locate on the arc surface, a novel unfolding parameter curve is proposed. Firstly, all the discrete data are stretched onto a plane, inside which the cubic B-spline curves are interpolated. After that, some points are sampled from the spline curves and bended to the arc-driving surface according to the swing radius. To eliminate cutting vibration and chord error exceeds limitation; radial speed is tuned by controlling the chord error. The simulation results are given to prove the proposed algorithm.

scholarly journals A METHOD OF REAL-TIME NURBS INTERPOLATION WITH CONFINED CHORD ERROR FOR CNC SYSTEMS

2017 ◽  
Vol 55 (5) ◽  
pp. 650
Author(s):  
Quang Huu Nguyen ◽  
Long Tien Banh
Keyword(s):  
Real Time ◽  
Efficient Method ◽  
Sampling Period ◽  
Critical Value ◽  
Free Form ◽  
Radius Of Curvature ◽  
Interpolation Algorithm ◽  
Chord Error ◽  
Nurbs Interpolation ◽  
Cnc Interpolation

This paper presents a method of real-time CNC interpolation for free-form NURBS curves. The interpolation algorithm is based on second order Taylor’s expansion with the principle part being a formula for updating the parametric value u after each sampling period. With the updated value of u, a new interpolated point is calculated based on the DeBoor’s algorithm. In this paper, an efficient method of limiting chord error introduced by the interpolation algorithm is also presented with the basic idea of reducing machining feedrate at positions with a radius of curvature smaller than a critical value.

Cam Grinding Interpolation Research Based on Cubic Non-Uniform Rational B-Splines

2012 ◽  
Vol 443-444 ◽  
pp. 843-849
Author(s):  
Bao Ying Peng ◽  
Qiu Shi Han
Keyword(s):  
Aviation Industry ◽  
Processing Quality ◽  
Nurbs Curve ◽  
Quality Requirements ◽  
B Spline ◽  
B Splines ◽  
Advantages And Disadvantages ◽  
Curve Interpolation ◽  
Nurbs Interpolation ◽  
Fitting Error

With the development of auto industry and aviation industry,the cam quality requirements higher and higher. The NURBS curve has excellent natures that can smooth the cam grinding path and improve its processing quality. Combined with existing CAD software and CNC systems, respectively, from reverse and forward two aspects of NURBS curve to illustrate the non-uniform B-spline principle and given the relevant formulas. Choosing X-C coordinates points of the cam grinding as the research object, adopt reverse and forward NURBS curve interpolation to fit the cam grinding path. Analysed the fitting error caused by line segment fit NURBS curve and cam lift error caused by NURBS interpolation. Summarized the advantages and disadvantages of two ways Nurbs interpolation discussed the method to improve NURBS interpolation for cam grinding.

NURBS Curve Interpolation Algorithm Based on Motion Axis Control

2013 ◽  
Vol 378 ◽  
pp. 584-588
Author(s):  
Liang Bao Tang ◽  
Shuai Shuai Li ◽  
Yan Qing Liu
Keyword(s):  
Servo System ◽  
System Capacity ◽  
Interpolation Point ◽  
Interpolation Algorithm ◽  
Cnc System ◽  
Nurbs Curve ◽  
Check Calculation ◽  
Curve Interpolation ◽  
Calculation Process ◽  
Motion Characteristics

This paper based on the interpolation point check calculation process, which uses the movement aixs of the CNC system on the velocity and acceleration components checking , instead of the traditional motion characteristics of the checking calculation. In this way, we can avoid complex NURBS curve derivative computation and simplify the process of the interpolation point calibration. Therefore, it also can ensure the precision of curve machining based on curve, at the same time, the interpolation speed and acceleration control strictly in the scope of the corresponding axis servo system capacity. Whats more, we can ensure that processing does not appear too large shock and vibration at any time.

Real-Time Coplanar NURBS Curves Fitting in Motion Controller

2013 ◽  
Vol 740 ◽  
pp. 105-111
Author(s):  
Chin Sheng Chen ◽  
Chih Wei Chu ◽  
Yen Shin Lai
Keyword(s):  
Real Time ◽  
Curve Fitting ◽  
Experimental Results ◽  
Motion Controller ◽  
Nurbs Curve ◽  
B Spline ◽  
The Real ◽  
Nurbs Curves ◽  
Cad Cam ◽  
Fitting In

This paper proposes a real-time coplanar Non-Uniform Rational B-Spline (NURBS) curves fitting in CAD/CAM system to improve the fitting quality and reduce the calculation effort. The real-time NURBS curve fitting process consists of (1) the reading discrete points, (2) curve segmentation and data reshaping, (3) curve fitting, and (4) local and global modulation. According to the simulation and experimental results, the proposed approach certainly raises the fitting quality and the efficiency of calculation.

The Confined Chord Error Algorithmfor Machining Complex Parametric Curve

2010 ◽  
Vol 458 ◽  
pp. 55-62
Author(s):  
Yong Jiang Hao ◽  
Zhi Qiang Zhang ◽  
Tai Yong Wang ◽  
Q.J. Liu ◽  
Zhi Feng Qiao
Keyword(s):  
Nc Machining ◽  
Order Derivative ◽  
Precision Machining ◽  
Interpolation Algorithm ◽  
Arc Length ◽  
Parametric Curve ◽  
Nurbs Curve ◽  
Chord Error ◽  
First Order

The part’s precision-machined quality of NC machining is influenced by the chord error greatly during precision machining. The confined chord error Algorithm for Machining Complex Parametric Curve is proposed for the complexity of the chord error. The information of the arc length error is utilized to control the chord error of the interpolated point indirectly. The arc length error of interpolated point is computed by Simpson expressions, the information of coordinate and the first order derivative of interpolated point is computed by the interpolation algorithm, so the computed difficulty is not increased greatly. The computed error of the algorithm is discussed and the simulation example of NURBS curve proves that the destined precision of the chord error can be satisfied by this algorithm.

scholarly journals The Research of the NURBS Curve Interpolation Algorithm

2011 ◽  
Vol 2-3 ◽  
pp. 614-618
Author(s):  
Wen Jie Zhang
Keyword(s):  
Adaptive Control ◽  
Real Time ◽  
Feed Rate ◽  
Interpolation Algorithm ◽  
Nurbs Curve ◽  
B Spline ◽  
The Real ◽  
Spline Curves ◽  
Curve Interpolation ◽  
Rate Adaptive

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.

scholarly journals An Intelligent Evaluation Method to Analyze the Competitiveness of Airlines

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Jun Zhao ◽  
Xumei Chen
Keyword(s):  
Neural Network ◽  
Prior Knowledge ◽  
Evaluation Method ◽  
Standard Sample ◽  
Reference Value ◽  
The Self ◽  
Index Data ◽  
Som Neural Network ◽  
Simulation Results ◽  
Self Organizing

An intelligent evaluation method is presented to analyze the competitiveness of airlines. From the perspective of safety, service, and normality, we establish the competitiveness indexes of traffic rights and the standard sample base. The self-organizing mapping (SOM) neural network is utilized to self-organize and self-learn the samples in the state of no supervision and prior knowledge. The training steps of high convergence speed and high clustering accuracy are determined based on the multistep setting. The typical airlines index data are utilized to verify the effect of the self-organizing mapping neural network on the airline competitiveness analysis. The simulation results show that the self-organizing mapping neural network can accurately and effectively classify and evaluate the competitiveness of airlines, and the results have important reference value for the allocation of traffic rights resources.

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