An Improvement and Simulation of NURBS Curve Algorithm

2013 ◽  
Vol 655-657 ◽  
pp. 1191-1194 ◽  
Author(s):  
Guo Qing Qiu ◽  
Le Fei Tu ◽  
Tian Yue Jiang ◽  
Han Qing Feng
Keyword(s):  
Feed Rate ◽  
Adaptive Algorithm ◽  
High Speed ◽  
Nurbs Curve ◽  
Curve Interpolation ◽  
Variable Step ◽  
Speed Fluctuation ◽  
Acceleration And Deceleration ◽  
Simulation Results ◽  
Circular Interpolation

Although the chord height error might be ensured, the adaptive algorithm of the NURBS curve circular interpolation feed rate is still likely to result in the speed fluctuation which is not in accordance with given acceleration or deceleration rules. On the foundation of the analytic principle of the NURBS curve circular interpolation, a kind of interpolating algorithm based on the NURBS curve continuous small segments of S-shaped acceleration and deceleration is presented. And considering the chord height error, the variable step and feed rate can be effectively combined to make a better estimation. The simulation results on real examples show that the method not only simplifies the complicated calculation of curve interpolation process, simultaneously improves the speed of Motion Smoothing Implementation for NURBS curve interpolation, but also ensures the interpolation precision. The algorithm can be commonly applied in real manufacturing for high-speed and high-precision curve process.

Research on a Algorithm of Adaptive Interpolation for NURBS Curve

2014 ◽  
Vol 687-691 ◽  
pp. 1600-1603 ◽  
Author(s):  
Wan Jun Zhang ◽  
Feng Zhang ◽  
Guo Hua Zhang
Keyword(s):  
Feed Rate ◽  
Interpolation Process ◽  
A Algorithm ◽  
Nurbs Curve ◽  
Adaptive Interpolation ◽  
Curve Interpolation ◽  
Simulation Results

The article briefly deals with a algorithm of adaptive interpolation for NURBS curve which NURBS curve reache any point, while, the feed rate can keep costant as during the whole interpolation process. The interpolation of NURBS curve should be finished. The simulation results show that the algorithm is correct; it is consistent with a NURBS curve interpolation requirements.

A Variable Step Size LMS Adaptive Filtering Algorithm and Simulations Based on Computational Verb Theory

2013 ◽  
Vol 756-759 ◽  
pp. 3972-3976 ◽  
Author(s):  
Li Hui Sun ◽  
Bao Yu Zheng
Keyword(s):  
Adaptive Filtering ◽  
Adaptive Algorithm ◽  
Linear Functional ◽  
Functional Relationship ◽  
Lms Algorithm ◽  
Variable Step Size ◽  
Step Size ◽  
Filtering Algorithm ◽  
Variable Step ◽  
Simulation Results

Based on traditional LMS algorithm, variable step LMS algorithm and the analysis for improved algorithm, a new variable step adaptive algorithm based on computational verb theory is put forward. A kind of sectorial linear functional relationship is established between step parameters and the error. The simulation results show that the algorithm has the advantage of slow change which is closely to zero. And overcome the defects of some variable step size LMS algorithm in adaptive steady state value is too large.

Interpolation Algorithm on Numerical Control Technology

2011 ◽  
Vol 467-469 ◽  
pp. 247-251
Author(s):  
Zhen Yu Zhao ◽  
Ming Jun Liu ◽  
Yong Shan Xiao ◽  
Bai Liu
Keyword(s):  
High Speed ◽  
High Efficiency ◽  
Linear Interpolation ◽  
Numerical Control ◽  
Machining Accuracy ◽  
B Spline ◽  
Curve Interpolation ◽  
Nurbs Interpolation ◽  
High Flexibility ◽  
Circular Interpolation

High speed machining (HSM) features in high efficiency, high precision, high flexibility and high quality. The key techniques on HSM such as linear interpolation, circular interpolation, cubic B-spline curve interpolation, non-uniform rational B-spline (NURBS) curve interpolation and their respective characteristics are paid more attention and expatiated. Circle arcs are approximated by using intersecting polygons instead of general inscribed polygons. NURBS interpolation algorithms can reduce feedrate fluctuation and improve machining accuracy.

Generation of NC Program for Realizing High Speed Feed Rate of Cutting Tool

2012 ◽  
Vol 523-524 ◽  
pp. 398-403
Author(s):  
Shintaro Sakurai ◽  
Hideki Aoyama ◽  
Noriaki Sano
Keyword(s):  
Feed Rate ◽  
High Speed ◽  
Cutting Tools ◽  
Sampling Time ◽  
Machined Surface ◽  
Nc Program ◽  
Circular Arcs ◽  
Offset Curves ◽  
Acceleration And Deceleration

As the feed rate of cutting tools is influenced by the quality of NC programs, this causes two problems when cutting freeform surfaces using NC machine tools, one is the feed rate does not reach the specified value, and the other is the quality of the machined surface decreases due to the large acceleration and deceleration of the control axes. One reason for these problems is that the method to generate cutter location data does not take into consideration the sampling time of the NC controller. To improve these problems, the approximation of offset curves with a series of circular arcs has generally been proposed. But conventionally, circular arc interpolation algorithms are complicated and not rational. So, in this study, we proposed two simple NC program generation methods. (1) Approximate the offset form with circular arcs based on the location of the center of curvature. (2) Make the distance between the cutter location points of the NC data an integral multiple of the “feed rate command F × sampling time T”. We also confirm the effectiveness of the proposed methods by simulations and experiments.

Design of Numeric Control Interpolation Compensation Algorithm Based on DSP

2012 ◽  
Vol 433-440 ◽  
pp. 5686-5691
Author(s):  
Xin Na Wang ◽  
Xi Yan Bi ◽  
Ping Chuan Zhang
Keyword(s):  
Control Systems ◽  
Real Time ◽  
High Speed ◽  
Logic Circuits ◽  
Pulse Number ◽  
Precision Motion Control ◽  
Digital Control Systems ◽  
Acceleration And Deceleration ◽  
Precision Motion ◽  
Circular Interpolation

Using the TMS320C31 floating-point family DSP devices from the U.S. TI Company to have built the slave system for numeric control lathes. It makes full use of the advantages of TMS320C31 DSP, such as high-speed, high precision motion control in real time, to implement the linear and circular interpolation algorithms, sports section of acceleration and deceleration control content. Experiments show that: not only ensured the precision of digital control systems, and improved the interpolation of real time; solved the uniform allocation while any given pulse number in interpolation cycle; overcame the poor flexibility of original digital logic circuits of interpolation. Multi-axis control can be achieved to improve overall system performance. It’s with high practical value.

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.

Research on CNC Key Technology for High Speed Milling

2011 ◽  
Vol 467-469 ◽  
pp. 252-256
Author(s):  
Zhen Yu Zhao ◽  
Dong Ying Liang ◽  
Yong Shan Xiao ◽  
Bai Liu
Keyword(s):  
High Speed ◽  
Tool Path ◽  
High Efficiency ◽  
Linear Interpolation ◽  
Machining Performance ◽  
B Spline ◽  
Curve Interpolation ◽  
High Flexibility ◽  
Circular Interpolation ◽  
Cutting Mechanisms

At present, high speed machining (HSM) features in high efficiency, high precision, high flexibility and high quality. HSM technology involves many factors, including cutting mechanisms, machining performance, tool path and other aspects. The key techniques on HSM such as linear interpolation, circular interpolation, cubic B-spline curve interpolation, non-uniform rational B-spline (NURBS) curve interpolation and their respective characteristics are paid more attention and expatiated.

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.

Chord Error Closed-Loop Controlled NURBS Interpolator and Trajectory Planning

2009 ◽  
Vol 16-19 ◽  
pp. 925-929
Author(s):  
Yu Liu ◽  
Jie Liu
Keyword(s):  
Trajectory Planning ◽  
High Speed ◽  
Closed Loop ◽  
Time Characteristic ◽  
Maximal Velocity ◽  
Nurbs Curve ◽  
Chord Error ◽  
Curve Interpolation ◽  
Planning Algorithm ◽  
Braking Distance

Focusing on the problem of NURBS curve interpolation in high speed manufacture, a new trajectory planning algorithm, which is suitable for chord error closed loop controlled interpolator is proposed. This tragjectory can determine accelerating, decelerating or maintenance last velocity in the next period via judging the braking distance. By the way of testing different calculating time under different CPU core, the real-time characteristic is validated. The simulation shows that chord error closed loop interpolator can automatically adjust the velocity to satisfying the precision demand, through calculating the curvature. In addition, it can assure that the maximal velocity and the acceleration were equal to the referenced parameters and machine runs with the dynamic characteristic of operator set completely.

scholarly journals Simulation of NURBS Curve Interpolation Algorithm and Five S-Phased Acceleration and Deceleration Control Algorithm

2011 ◽  
Vol 2-3 ◽  
pp. 619-623
Author(s):  
Geng Zhu Wang
Keyword(s):  
Computer Simulation ◽  
Control Algorithm ◽  
Control Method ◽  
Simulation Method ◽  
Interpolation Algorithm ◽  
Nurbs Curve ◽  
Computer Simulation Method ◽  
Curve Interpolation ◽  
Acceleration And Deceleration

The computer simulation method is used to test the correctness of the NURBS curve interpolation algorithm, through the comparison of the five S-phased curve acceleration and deceleration control method and the line acceleration and deceleration control method, to validate the superiority of the five S-phased curve acceleration and deceleration control method.

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