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.

The Confined Chord Error Algorithm for High Precision Machining Parametric Surface

2011 ◽  
Vol 201-203 ◽  
pp. 2334-2337 ◽  
Author(s):  
Zhi Qiang Zhang ◽  
Wen Jin Wang ◽  
Zhao Jian ◽  
Tai Yong Wang
Keyword(s):  
Surface Quality ◽  
High Precision ◽  
Order Derivative ◽  
Precision Machining ◽  
Interpolation Algorithm ◽  
Arc Length ◽  
Parametric Surface ◽  
Chord Error ◽  
First Order

The part’s surface quality of NC machining is influenced by the chord error greatly. The confined chord error algorithm for machining complex parametric surface is proposed for controlling the chord error. 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 trapezia expressions, the coordinate and the first order derivative of interpolated point is computed by the interpolation algorithm. The computed error of confined chord error algorithm is discussed and the simulation indicate that the destined precision of the chord error can be satisfied by this algorithm.

NURBS Curve Fitting Based on Arc Centripetal Parameterization for Tool Path Generation

2013 ◽  
Vol 274 ◽  
pp. 121-123 ◽  
Author(s):  
Cun Guang Yu
Keyword(s):  
Curve Fitting ◽  
Tool Path ◽  
Nc Machining ◽  
Tool Path Generation ◽  
Sculptured Surface ◽  
Arc Length ◽  
Tool Path Planning ◽  
Nurbs Curve ◽  
Location Data ◽  
Cutter Location Data

NURBS curve fitting is used for tool path planning for sculptured surface NC machining. The cutter location data is parameterized by equal chord arc length parameterization, and Centripetal Parameterization is improved. It is not only more approach to curves nature equation in theory, but also closer to the interpolated curves in actual fitting. It is directly to reflect the curvature of curves of cutter location in NC machining.

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.

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.

A Parametric Interpolator with Smooth Kinematic Profiles for High Speed Machining

2006 ◽  
Vol 315-316 ◽  
pp. 169-173 ◽  
Author(s):  
You Peng You ◽  
Jun He
Keyword(s):  
High Speed ◽  
Contour Error ◽  
Interpolation Algorithm ◽  
Tracking Accuracy ◽  
Parametric Curve ◽  
Chord Error ◽  
Feedrate Planning ◽  
Profile Matching ◽  
Look Ahead ◽  
Parametric Interpolation

Smooth kinematic profiles are very important for high speed curve machining. During parametric interpolation, simple adaptive feedrate with confined contour error may cause acceleration and jerk to fluctuate acutely. To avoid the undesirable influence, an interpolation algorithm for parametric curves with smooth kinematic profiles is presented. The interpolator consists of three parts, look-ahead module, feedrate planning module and interpolation module. In look-ahead module, a pre-interpolator is designed to produce the required feedrate profile considering chord error. By feedrate planning, a smooth feedrate profile with confined acceleration and jerk is schemed based on bell-shape ACC/DEC profile by feedrate profile matching and feedrate profile synthesis. Then the parametric curve can be interpolated with the planned feedrate in interpolation module. Simulation results have been also provided to illustrate that the proposed interpolator can generate smooth kinematic profiles required for the high tracking accuracy at high speed with confined chord error, acceleration and jerk, and can be used for high speed and precision curve machining.

A Parametric Curve Interpolation Algorithm for High Speed Machining

2010 ◽  
Vol 458 ◽  
pp. 35-41
Author(s):  
Q.J. Liu ◽  
J.H. Yue ◽  
Y.F. Wang ◽  
J.C. Dong ◽  
Tai Yong Wang
Keyword(s):  
Machine Tools ◽  
High Speed ◽  
Error Control ◽  
High Surface ◽  
High Speed Machining ◽  
Interpolation Algorithm ◽  
Parametric Curve ◽  
First Order ◽  
Adaptive Error Control ◽  
Curve Interpolation

This paper proposed a new and effective parametric curve interpolation algorithm with error compensation capability for high speed machining. The proposed algorithm is developed from the first-order Taylor expansion interpolation algorithm and the speed-controlled interpolation algorithm. It is also incorporated the geometry features of the machined curves, the dynamic characteristics of machine tools and the adaptive error control. The proposed algorithm achieves high surface accuracy and avoids feedrate fluctuations. Simulation results have demonstrated the effectiveness and satisfactory performance of the proposed algorithm.

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.

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