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.

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.

The Research of NURBS Curve Interpolation Algorithm Based on Parabolic and the First-Order Taylor Expansion Interpolation Algorithm

2014 ◽  
Vol 1003 ◽  
pp. 260-263
Author(s):  
Zhi Qiang Zhang ◽  
Wen Jin Wang ◽  
Jing Zhang ◽  
Jian Zhao ◽  
Li Ying Sun ◽  
...  
Keyword(s):  
Surface Quality ◽  
Taylor Expansion ◽  
Interpolation Error ◽  
Interpolation Algorithm ◽  
Nurbs Curve ◽  
First Order ◽  
Parabolic Interpolation ◽  
Curve Interpolation ◽  
Part Surface ◽  
Current Point

The NURBS curve interpolation algorithm based on parabolic interpolation error and the first-order Taylor expansion interpolation algorithm is proposed to improve part surface quality and chord error of NURBS curve interpolation algorithm. The part surface quality is improved effectively by the parabolic interpolation algorithm in the conduction that the previous point, the current point and the next point which was computed by the first order Taylor expansion interpolation algorithm were known. The effectiveness of this algorithm is proved by the NURBS curve interpolation simulation.

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.

An accurate NURBS curve interpolation algorithm with short spline interpolation capacity

2012 ◽  
Vol 63 (9-12) ◽  
pp. 1257-1270 ◽  
Author(s):  
Haitao Dong ◽  
Bing Chen ◽  
Youping Chen ◽  
Jingming Xie ◽  
Zude Zhou
Keyword(s):  
Spline Interpolation ◽  
Interpolation Algorithm ◽  
Nurbs Curve ◽  
Curve Interpolation

scholarly journals A Novel Approach for NURBS Interpolation with Minimal Feed Rate Fluctuation Based on Improved Adams-Moulton Method

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Junquan Peng ◽  
Xinhua Liu ◽  
Lei Si ◽  
Jingjing Liu
Keyword(s):  
Feed Rate ◽  
Step Length ◽  
Nurbs Curve ◽  
Novel Approach ◽  
Rate Fluctuation ◽  
Curve Interpolation ◽  
Nurbs Interpolation

In order to reduce the feed rate fluctuation of interpolation, a novel approach for NURBS interpolation with minimal feed rate fluctuation based on improved Adams-Moulton (IAM) method is proposed. At first, the representation and calculation of NURBS curve interpolation are described. Then, the constraints of feeding step length are firstly given out to calculate the minimal hoping feeding step length and the detailed IAM method of NURBS curve interpolation is presented. Finally, simulations and experiments are carried out to verify the feasibility and applicability of proposed IAM method.

scholarly journals The Real-Time Look-Ahead NURBS Curve Interpolation Algorithm

2011 ◽  
Vol 2-3 ◽  
pp. 523-526
Author(s):  
Geng Zhu Wang
Keyword(s):  
Real Time ◽  
Transition Curve ◽  
Interpolation Algorithm ◽  
Nurbs Curve ◽  
The Real ◽  
Look Ahead ◽  
Time Period ◽  
Curve Interpolation ◽  
Acceleration And Deceleration ◽  
Deceleration Time

To ensure a given chord error, through the division of the cusp, the NURBS (Non-Uniform Rational B-Splins) curve is divided into several sections and the speed of the various sections is planned accordingly. The acceleration and deceleration time period is recalculated, which results in a smooth speed transition curve.

Sign in / Sign up

Export Citation Format

Share Document