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.

Multi-Period Turning Interpolation Algorithm for High-Speed Machining of Continuous Line Segments With Limited Acceleration, Jerk and Chord Error

2012 ◽  
Author(s):  
Lixian Zhang ◽  
Xiao-shan Gao ◽  
Hongbo Li
Keyword(s):  
Real Time ◽  
High Speed ◽  
Control Method ◽  
Dynamic Performance ◽  
Interpolation Algorithm ◽  
Cnc Machine ◽  
Look Ahead ◽  
Geometric Precision ◽  
S Curve ◽  
Accumulated Error

In this paper, a multi-period turning interpolation algorithm, with real-time look-ahead scheme based on S-curve control method, is presented. In this interpolation algorithm, the geometric precision and the dynamic performance are both satisfied. The machining efficiency is improved by multi-period turning transition, and the precision is also improved by S-curve control method. The computational efficiency of this algorithm meets the need of real-time machining. In addition, there is no accumulated error. At last, this algorithm is verified the validation by the experiments on 3-axis CNC machine.

scholarly journals Study on Acc/Dec Algorithm Based on Piecewise Polynomial in CNC

2011 ◽  
Vol 2-3 ◽  
pp. 43-47 ◽  
Author(s):  
Guo Shun Ji ◽  
Zhi Ping Chen ◽  
Ju Yong Zhang ◽  
Wei Liu
Keyword(s):  
High Speed ◽  
Large Scale ◽  
Polynomial Function ◽  
Tracking Accuracy ◽  
Feedrate Planning ◽  
Smooth Motion ◽  
Planning Algorithm ◽  
S Curve ◽  
The Stability ◽  
Motion Profile

In order to improve the stability of feed movement in high speed CNC system, the feedrate planning algorithm based on piece-wise polynomial function was proposed. The flexible transition of feedrate was realized through maintaining linear continuous jerk. The principle of the proposed algorithm was introduced and the method to generate smooth motion profile based on the proposed algorithm was presented. The rapidity, stability and tracking accuracy of the feedrate planning algorithm to linearity, S curve and the proposed one were analyzed. The proposed algorithm is simple and it can be applied in acceleration/deceleration before interpolation in high speed feed movement to improve the stability of it. The proposed algorithm was applied in multi-contour high speed processing and the result indicated that it could improve the stability of large-scale parts motion.

An Interpolation Algorithm Based on S-Curve Feedrate Profile and Look-Ahead Function

2013 ◽  
Vol 300-301 ◽  
pp. 1389-1396 ◽  
Author(s):  
Ke Zheng Sun ◽  
Xue Feng Zhou ◽  
Gong Zhang ◽  
Xian Shuai Chen
Keyword(s):  
Machine Tools ◽  
High Speed ◽  
High Speed Machining ◽  
Interpolation Algorithm ◽  
Processing Efficiency ◽  
Look Ahead ◽  
Interpolation Accuracy ◽  
Acceleration And Deceleration ◽  
S Curve ◽  
Time Division

In this paper, a novel interpolation algorithm for high speed machining is presented, which integrates S-curve acceleration/deceleration method in look-ahead function. A time division based speed planning method is used to implement discrete S-curve acceleration/deceleration method. The implementation of the proposed algorithm is given out. The proposed algorithm improves the processing efficiency and avoids the shock of machine tools caused by frequent acceleration and deceleration. The experiment shows that the proposed algorithm satisfies the requirements of interpolation accuracy and machining efficiency in high speed machining.

Research on Feedrate Planning Model for Continuous Small Lines Contour with Look-Ahead

2012 ◽  
Vol 591-593 ◽  
pp. 414-418
Author(s):  
Qing Song Jiao ◽  
Shi Yong Wang
Keyword(s):  
High Speed ◽  
Machining Efficiency ◽  
Planning Model ◽  
Interpolation Function ◽  
Line Segments ◽  
Feedrate Planning ◽  
Look Ahead ◽  
Acceleration And Deceleration ◽  
Adjacent Segments

The traditional line or arc interpolation function treats small line segments separately and conducts feedrate planning within each of them. The rather small lengths of the segments result in low machining efficiency, and the frequent acceleration and deceleration also reduce the lifetime of the motor. To solve these problems, a look-ahead feedrate planning model for the continuous small lines contour (CSLC) is proposed in this paper to implement the high speed interpolating. The feedrate planning is elaborated from the aspects of the curvature characteristic of the contour, the turning feedrate, and the federate optimization between the adjacent segments. Simulations show that the proposed algorithm can efficiently improve the machining efficiency.

Look-Ahead NURBS-PH Interpolation for High Speed CNC Machining

2010 ◽  
Author(s):  
Behnam Moetakef Imani ◽  
Amirmohammad Ghandehariun
Keyword(s):  
High Speed ◽  
Cnc Machining ◽  
Corner Detection ◽  
Nurbs Curves ◽  
Look Ahead ◽  
Approximation Errors ◽  
Pythagorean Hodograph ◽  
Approximate Nature ◽  
Sharp Corners ◽  
Parametric Interpolation

Various methods for parametric interpolation of NURBS curves have been proposed in the past. However, the errors caused by the approximate nature of the NURBS interpolator were rarely taken into account. This paper proposes an integrated look-ahead algorithm for parametric interpolation along NURBS curves. The algorithm interpolates the sharp corners on the curve with the Pythagorean-hodograph (PH) interpolation. This will minimize the geometric and interpolator approximation errors simultaneously. The algorithm consists of four different modules: a sharp corner detection module, a PH construction module, a jerk-limited module, and a dynamics module. Simulations are performed to show correctness of the proposed algorithm. Experiments on an X-Y table confirm that the developed method improves tracking and contour accuracies significantly when compared to previously proposed adaptive-feedrate and curvature-feedrate algorithms.

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.

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.

Real-Time B-Spline Interpolator with Look-Ahead Scheme for High-Speed CNC Machine Tools

2010 ◽  
Vol 455 ◽  
pp. 599-605
Author(s):  
Yong Qiao Jin ◽  
Yu Han Wang ◽  
Jian Guo Yang
Keyword(s):  
Real Time ◽  
High Speed ◽  
Tool Path ◽  
Cnc Machine Tools ◽  
Interpolation Algorithm ◽  
Cnc Machine ◽  
Machining Time ◽  
B Spline ◽  
Optimal Speed ◽  
Look Ahead

NC tool paths of digital CAD models are currently generated as a set of discrete data points. The CNC interpolator must convert these points into continuous machine tool axis motions. In order to achieve high-speed and high-accuracy machining, the development of a real-time interpolation algorithm is really indispensable, which can deal with a large number of short blocks and still maintain smooth interpolation with an optimal speed. In this paper, a real-time local cubic B-spline interpolator with look-ahead scheme is proposed for consecutive micro-line blocks interpolation. First, the consecutive micro-line blocks that satisfy the bi-chord error constraints are fitted into a C1 continuous cubic B-spline curve. Second, machining dynamics and tool path contour constrains are taken into consideration. Third, local cubic B-spline interpolator with an optimal look-ahead scheme is proposed to generate the optimal speed profile. Simulation and experiment are performed in real-time environment to verify the effectiveness of the proposed method. Compared with the conventional interpolation algorithm, the proposed algorithm reduces the machining time by 70%.

Real-Time NURBS Interpolator with an Optimal Feed for High-Speed Machining

2009 ◽  
Vol 69-70 ◽  
pp. 461-465 ◽  
Author(s):  
Jing Chun Feng ◽  
Yu Han Wang ◽  
Ming Chen ◽  
Jin Sen Wang
Keyword(s):  
Real Time ◽  
High Speed ◽  
Interpolation Method ◽  
High Speed Machining ◽  
Chord Error ◽  
Look Ahead ◽  
Nurbs Interpolation ◽  
Optimal Feed ◽  
Error Constraint ◽  
Circular Interpolation

NURBS interpolation has many advantages over the traditional linear or circular interpolation in high-speed machining. The existing work in this regard focuses on adaptive feed interpolation considering the chord error constraints and tangent acceleration limits. However, regardless of the dynamic characteristics of individual axis, performance will inevitably suffer when the system is called upon to execute a complex trajectory beyond the range of its capabilities. The intent of the present work is to provide an optimal feed interpolation method respecting both the chord error constraint and the drive constraint of each axis. A look-ahead scheme is applied with a moving window to augment the calculation efficiency for real-time application. Simulations are performed to verify the resulting feedrate, acc/dec profiles and the real-time performance of the proposed interpolator.

Development of Advanced CNC Interpolation Algorithm With Consideration of Command and Dynamic Errors

2015 ◽  
Author(s):  
Meng-Shiun Tsai ◽  
Ying-Che Huang
Keyword(s):  
The Other ◽  
Contour Error ◽  
Interpolation Algorithm ◽  
Interpolation Scheme ◽  
Error Equation ◽  
The Past ◽  
Cnc Interpolation ◽  
Dynamic Errors ◽  
Simulation Results ◽  
The Given

In this paper, an integrated acceleration/deceleration with dynamics interpolation scheme is proposed to confine the maximum contour error at the junction of linear junction. The dynamic contour error equation is derived analytically and then it is utilized for the interpolation design. Based on the derived formulations which could predict the command and dynamic errors, the advanced interpolation design could adjust the connecting velocity of the two blocks to confine the overall contour errors under the given tolerance. Simulation results validate the proposed algorithm can achieve higher accurate trajectory as compared to the other interpolation algorithm proposed in the past.

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