Features of a real-time s-shaped acceleration/deceleration curve constructing with piecewise linear interpolation of complex-shaped surfaces

2021 ◽  
Vol 9 (3) ◽  
pp. 186-195
Author(s):  
Alexander Zelensky ◽  
Tagir Abdullin ◽  
Andrei Alepko
Keyword(s):  
Real Time ◽  
Feed Rate ◽  
High Speed ◽  
Spline Interpolation ◽  
Piecewise Linear ◽  
Time Frame ◽  
Numerical Control ◽  
Segment Length ◽  
Rounding Errors ◽  
Piecewise Linear Interpolation

In this paper we considered the problem of an s-shaped acceleration/deceleration curve constructing in real time with linear-spline interpolation, taking into account given constraints on the contour acceleration, jerk, and feed rate. The input data for the s-curve were defined in the lookahead algorithm and the geometric smoothing module. The choice of a particular acceleration/deceleration strategy depends on the segment length, the allowable feed rates at the segment junction, and the given kinematic constraints. Each trajectory segment can have a maximum of seven time intervals and their rounding will produce inaccuracies when forming the velocity profile. Therefore, to compensate for rounding errors, the method of half division was applied, which made it possible to remove gaps in the velocity contour. The experimental data obtained indicate the correctness of the chosen approach for its implementation as part of the CNC for high-speed machining of surfaces with complex shapes. Key words Feed-rate planning algorithm, s-shaped acceleration/deceleration, trajectory smoothing, numerical control system, real-time, frame preview algorithm. Acknowledgements The research was carried out with financial support of Ministry of Science and Higher Education of Russian Federation in the frame of state assignment (project no.FSFS-2020-0031).

Quintic Spline Interpolation With Minimal Feed Fluctuation

2005 ◽  
Vol 127 (2) ◽  
pp. 339-349 ◽  
Author(s):  
Kaan Erkorkmaz ◽  
Yusuf Altintas
Keyword(s):  
Real Time ◽  
Feed Rate ◽  
Tool Path ◽  
Interpolation Method ◽  
Spline Interpolation ◽  
Tracking Error ◽  
Arc Length ◽  
Quintic Spline ◽  
Rate Profile ◽  
Spline Parameter

This paper presents a parameterization and an interpolation method for quintic splines, which result in a smooth and consistent feed rate profile. The discrepancy between the spline parameter and the actual arc length leads to undesirable feed fluctuations and discontinuity, which elicit themselves as high frequency acceleration and jerk harmonics, causing unwanted structural vibrations and excessive tracking error. Two different approaches are presented that alleviate this problem. The first approach is based on modifying the spline tool path so that it is optimally parameterized with respect to its arc length, which allows it to be accurately interpolated in real-time with minimal complexity. The second approach is based on scheduling the spline parameter to accurately yield the desired arc displacement (hence feed rate), either by approximation of the relationship between the arc length and the spline parameter with a feed correction polynomial, or by solving the spline parameter iteratively in real-time at each interpolation step. This approach is particularly suited for predetermined spline tool paths, which are not arc-length parameterized and cannot be modified. The proposed methods have been compared to approximately arc-length C3 quintic spline parameterization (Wang, F.-C., Wright, P. K., Barsky, B. A., and Yang, D. C. H., 1999, “Approximately Arc-Length Parameterized C3 Quintic Interpolatory Splines,” ASME J. Mech. Des, 121, No. 3., pp. 430–439) and first- and second-order Taylor series interpolation techniques (Huang, J.-T., and Yang, D. C. H., 1992, “Precision Command Generation for Computer Controlled Machines,” Precision Machining: Technology and Machine Development and Improvement, ASME-PED 58, pp. 89–104; Lin, R.-S. 2000, “Real-Time Surface Interpolator for 3-D Parametric Surface Machining on 3-Axis Machine Tools,” Intl. J. Mach. Tools Manuf., 40, No.10, pp. 1513–1526) in terms of feed rate consistency, computational efficiency, and experimental contouring accuracy.

Development of a Smart Computer Numerical Control System

2013 ◽  
Author(s):  
Zhiqian Sang ◽  
Xun Xu
Keyword(s):  
Real Time ◽  
High Speed ◽  
Computer Numerical Control ◽  
Numerical Control ◽  
Machining Process ◽  
Cnc Machine ◽  
Field Bus ◽  
Nc System ◽  
Tool Paths ◽  
Cnc Controller

Traditional Computer Numerical Control (CNC) machines use ISO6983 (G/M code) for part programming. G/M code has a number of drawbacks and one of them is lack of interoperability. The Standard for the Exchange of Product for NC (STEP-NC) as a potential replacement for G/M code aims to provide a unified and interoperable data model for CNC. In a modern CNC machine tool, more and more motors, actuators and sensors are implemented and connected to the NC system, which leads to large quantity of data being transmitted. The real-time Ethernet field-bus is faster and more deterministic and can fulfill the requirement of data transmission in the high-speed and high-precision machining scenarios. It can provide more determinism on communication, openness, interoperability and reliability than a traditional field-bus. With a traditional CNC system using G/M code, when the machining is interrupted by incidents, restarting the machining process is time-consuming and highly experience-dependent. The proposed CNC controller can generate just-in-time tool paths for feature-based machining from a STEP-NC file. When machining stoppage occurs, the system can recover from stoppage incidents with minimum human intervention. This is done by generating new tool paths for the remaining machining process with or without the availability of the original cutting tool. The system uses a real-time Ethernet field-bus as the connection between the controller and the motors.

G2-stetiges Klothoidenüberschleifen*/G2-continuous clothoid smoothing – Results of a real-time smoothing process on the basis of piecewise defined clothoids

2019 ◽  
Vol 109 (06) ◽  
pp. 491-495
Author(s):  
T. König ◽  
A. Atmosudiro ◽  
A. Verl ◽  
A. Lechler
Keyword(s):  
Real Time ◽  
Feed Rate ◽  
Numerical Control ◽  
Continuous Transition ◽  
Machine Load ◽  
Smoothing Process

Das Klothoidenüberschleifverfahren ermöglicht einen G2-stetigen Übergang zwischen NC (Numerical Control)-Sätzen bei linearem Krümmungsprofil. Zudem ist dieses Profil über die Verteilung der Klothoiden- und Kreissegmente steuerbar und bietet die Möglichkeit beispielsweise hinsichtlich der Vorschubgeschwindigkeit optimiert zu werden. Allgemein entstehen glattere Dynamikprofile, welche die Maschinenbelastung reduzieren oder höhere Bearbeitungsgeschwindigkeiten zulassen.   The clothoid smoothing process enables a G2-continuous transition between NC blocks with a linear curvature profile. In addition, this profile can be controlled via configuration of the clothoid and circle segments and offers the possibility to be optimized, for example, with regard to the feed rate. In general, smoother dynamic profiles are created, which reduce the machine load or allow for higher machining velocities.

scholarly journals Study on the Algorithm for Real-Time Interpolation of NURBS Curve

2011 ◽  
Vol 1 ◽  
pp. 262-267
Author(s):  
Ji Zhuang Hui ◽  
Yan Ma ◽  
Ze Feng Liu
Keyword(s):  
Real Time ◽  
High Speed ◽  
Numerical Control ◽  
Contour Error ◽  
Processing Quality ◽  
Numerical Control Machining ◽  
Nurbs Curve ◽  
B Spline ◽  
Speed Optimization ◽  
Feeding Speed

In order to meet the needs of high speed and high precision computerized numerical control machining, a calculation based on the control of contour error and feeding acceleration for the real-time interpolation of Non-uniform rational B-spline (NURBS) curves was presented in this paper. On the premise of meeting the error requirement, machine can process parts with the highest feeding speed to achieve interpolation precision and interpolation speed optimization, and improve processing quality and efficiency.

Acceleration smoothing algorithm for global motion in high-speed machining

2018 ◽  
Vol 233 (8) ◽  
pp. 1844-1858 ◽  
Author(s):  
Jinfeng Du ◽  
Liqiang Zhang ◽  
Tian Gao
Keyword(s):  
Control System ◽  
Spline Interpolation ◽  
Computer Numerical Control ◽  
Numerical Control ◽  
Segment Length ◽  
Linear Segment ◽  
Interpolation Algorithm ◽  
Numerical Control System ◽  
Spline Curve ◽  
Computer Numerical Control System

When machining a series of short linear segments, the computer numerical control system interpolates the machining path with the pre-specified spline curve to obtain continuous feed motion. However, to obtain adequate smooth tool-paths to smooth the feed velocity and acceleration, the computer-aided manufacturing system needs to use a higher order spline curve, which will be limited by some technical bottlenecks. In this article, a new real-time interpolation algorithm is proposed from the perspective of kinematics to achieve uninterrupted feed motion throughout the global tool-path. At the same time, the acceleration profile achieves G2 continuous to avoid unnecessary feed frustration and inertial impact, reaching the balance between time-optimal and motion performance. First, the jounce-limited acceleration curve is blended at the corner of the machining path, and the optimal cornering transition velocity is obtained by adding the velocity, acceleration and contour error constraints to the corner transition motion. Then, according to the linear segments with different lengths between the corners, combined with the feed motion around the corner, a look-ahead interpolation algorithm is proposed to calculate the maximum feed rate with the constraint of the linear segment length and kinematic boundary conditions. At last, for the linear segments whose corner contours overlap with each other after interpolation, the smooth transition between the two corners can be realized by mixing the feed motion of the next corner. Compared with non-uniform rational B-spline interpolation algorithm, the proposed algorithm reduces the total machining time by 14% and the computer numerical control system improves the computational efficiency by 11%. It proves that the proposed algorithm has better application value in the manufacturing of complex parts.

Design and Implementation of an Interpolation Processor for CNC Machining

2013 ◽  
Vol 819 ◽  
pp. 322-327
Author(s):  
Jing Chuan Dong ◽  
Tai Yong Wang ◽  
Bo Li ◽  
Xian Wang ◽  
Zhe Liu
Keyword(s):  
Real Time ◽  
High Speed ◽  
High Performance ◽  
Low Cost ◽  
Parallel Architecture ◽  
Cnc Machining ◽  
Numerical Control ◽  
Experimental Result ◽  
Interpolation Algorithm ◽  
Asynchronous Instruction

As the demand for high speed and high precision machining increases, the fast and accurate real-time interpolation is necessary in modern computerized numerical control (CNC) systems. However, the complexity of the interpolation algorithm is an obstacle for the embedded processor to achieve high performance control. In this paper, a novel interpolation processor is designed to accelerate the real-time interpolation algorithm. The processor features an advanced parallel architecture, including a 3-stage instruction pipeline, very long instruction word (VLIW) support, and asynchronous instruction execution mechanism. The architecture is aimed for accelerating the computing-intensive tasks in CNC systems. A prototype platform was built using a low-cost field programmable gate array (FPGA) chip to implementation the processor. Experimental result has verified the design and showed the good computing performance of the proposed architecture.

scholarly journals MATHEMATICAL MODEL OF SPEED DATA TRANSMISSION FROM SEGMENT LENGTH OF SPECIALIZED G3-PLC DIGITAL NETWORK

2019 ◽  
pp. 120-127
Author(s):  
S. M. Babchuk ◽  
B. S. Nezamay
Keyword(s):  
Mathematical Model ◽  
Real Time ◽  
Data Transmission ◽  
High Speed ◽  
High Reliability ◽  
Electricity Consumption ◽  
Segment Length ◽  
Long Distance ◽  
Digital Network ◽  
Automation Systems

Power Line Communication (PLC) systems are actively evolving and becoming more and more widespread worldwide. They are used in the automation of technological processes, the organization of video surveillance systems and to control the "smart" home. The G3-PLC provides high-speed and high-reliability long-distance communication over the existing power grid. Due to the fact that G3-PLC provides the ability to transmit data including through transformers, infrastructure costs are reduced. In addition, the G3-PLC network can support IPv6, which will allow the G3-PLC to easily integrate into common IPv6-based communication lines in the future. G3-PLC-based bilateral communications networks can provide grid operators with intelligent monitoring and control capabilities. Operators will be able to monitor electricity consumption across the network in real time, apply variable tariff schedules and set limits on electricity consumption. In turn, consumers will be able to control electricity consumption in real time. By using variable tariffs, users can reduce their electricity consumption during peak use. The G3-PLC dedicated digital network can be used in process automation systems where traditional or traditional data transmission is difficult or impossible. As a result of the research, a polynomial mathematical model was found that best reflects the change in data rate depending on the length of the G3-PLC network segment. It is also found that for the simplified calculation, a linear model determined during the studies can be used. The established mathematical models of data transmission rate dependence on the segment length of the G3-PLC dedicated digital network will contribute to better design of G3-PLC-based networks.

scholarly journals MODELING OF ASYMPTOTICALLY OPTIMAL PIECEWISE LINEAR INTERPOLATION OF PLANE PARAMETRIC CURVES

2021 ◽  
pp. 57-68
Author(s):  
О. V. Frolov ◽  
M. U. Losev
Keyword(s):  
Spline Interpolation ◽  
Piecewise Linear ◽  
Linear Interpolation ◽  
Integral Function ◽  
Computer Algorithms ◽  
Parametric Curves ◽  
Asymptotically Optimal ◽  
Piecewise Linear Interpolation ◽  
Curve Approximation ◽  
Distribution Parameters

Context. Piecewise linear approximation of curves has a large number of applications in computer algorithms, as the reconstruction of objects of complex shapes on monitors, CNC machines and 3D printers. In many cases, it is required to have the smallest number of segments for a given accuracy. Objective. The objective of this paper is to improve the method of asymptotically optimal piecewise linear interpolation of plane parametric curves. This improvement is based to research influence of the method parameters and algorithms to distributions of approximation errors. Method. An asymptotically optimal method of curves interpolation is satisfied to the condition of minimum number of approximation units. Algorithms for obtaining the values of the sequence of approximation nodes are suggested. This algorithm is based on numerical integration of the nodes regulator function with linear and spline interpolation of its values. The method of estimating the results of the curve approximation based on statistical processing of line segments sequence of relative errors is substantiated. Modeling of real curves approximation is carried out and influence of the sampling degree of integral function – the nodes regulator on distribution parameters of errors is studied. The influence is depending on a method of integral function interpolation. Results. Research allows to define necessary the number of discretization nodes of the integral function in practical applications. There have been established that with enough sampling points the variance of the error’s distribution stabilizes and further increasing this number does not significantly increase the accuracy of the curve approximation. In the case of spline interpolation of the integral function, the values of the distribution parameters stabilized much faster, which allows to reduce the number of initial sampling nodes by 5–6 times having similar accuracy. Conclusions. Modelling of convex planar parametric curves reconstruction by an asymptotically optimal linear interpolation algorithm showed acceptable results without exceeding the maximum errors limit in cases of a sufficient discretization of the integral function. The prospect of further research is to reduce the computational complexity when calculating the values of the integral distribution function by numerical methods, and to use discrete analogues of derivatives in the expression of this function.

Sign in / Sign up

Export Citation Format

Share Document