scholarly journals A parametric interpolation method based on prediction and iterative compensation

2019 ◽  
Vol 16 (1) ◽  
pp. 172988141982818 ◽  
Author(s):  
Hepeng Ni ◽  
Chengrui Zhang ◽  
Chao Chen ◽  
Tianliang Hu ◽  
Yanan Liu
Keyword(s):  
Tool Path ◽  
Interpolation Method ◽  
Second Order ◽  
Prediction Algorithm ◽  
Target Point ◽  
Original Curve ◽  
Current Period ◽  
Quintic Polynomial ◽  
Feedrate Fluctuation ◽  
Parametric Interpolation

Parametric interpolation for spline plays an increasingly important role in modern manufacturing. It is critical to develop a fast parametric interpolator with high accuracy. To improve the computational efficiency while guaranteeing low and controllable feedrate fluctuation, a novel parametric interpolation method based on prediction and iterative compensation is proposed in this article. First, the feedrate fluctuation and Taylor’s expansion are analyzed that there are two main reasons to reduce the calculation accuracy including the truncation errors caused by neglecting the high-order terms and discrepancy errors between the original curve and the actual tool path. Then, to reduce these errors, a novel parametric interpolation method is proposed with two main stages, namely, prediction and iterative compensation. In the first stage, a quintic polynomial prediction algorithm is designed based on the historical interpolation knowledge to estimate the target length used in the second-order Taylor’s expansion, which can improve the calculation accuracy and the convergence rate of iterative process. In the second stage, an iterative compensation algorithm based on the second-order Taylor’s expansion and feedrate fluctuation is designed to approach the target point. Therefore, the calculation accuracy is controllable and can satisfy the specified value through several iterations. When finishing the interpolation of current period, the historical knowledge is updated to prepare for the following interpolation. Finally, a series of simulations are conducted to evaluate the good performance in accuracy and efficiency of the proposed method.

A parametric interpolation method with minimal feedrate fluctuation by nonuniform rational basis spline

2016 ◽  
Vol 231 (18) ◽  
pp. 3301-3317 ◽  
Author(s):  
Lei Lu ◽  
Lei Zhang ◽  
Yan Gu ◽  
Ji Zhao
Keyword(s):  
Computational Efficiency ◽  
Interpolation Method ◽  
Optimization Method ◽  
Rational Basis ◽  
Computational Load ◽  
Fitting Method ◽  
Feedrate Fluctuation ◽  
Data Points ◽  
Parametric Interpolation ◽  
Line Fitting

Because the relation between the arc length s and curve parameter u cannot be represented by explicit function for most of the curves, it is difficult to consider the accuracy, robustness, and computational efficiency for most of the parametric interpolation, especially when the curves are complex or extremes. Therefore, an off-line fitting interpolation method by using nonuniform rational basis spline is presented in this paper. As nonuniform rational basis spline has many geometry implementation tools and numerous good properties as compared to the polynomial, the required fitting accuracy can be obtained more easily than with polynomial. After the de Boor method is applied, the computational load of nonuniform rational basis spline is decreased as compared to the Taylor approximation and the higher order polynomial fitting method. In order to obtain the proper s-u fitting nonuniform rational basis spline and reduce the computational load of the fitting process, the sampled s-u data points are divided according to the properties of nonuniform rational basis spline, and in each segment, the knot vectors, control points, and weights are calculated by the iterative-optimization method. Then the s-u nonuniform rational basis spline can be applied in real-time interpolation, and the accuracy, robustness, and computational efficiency are demonstrated by simulations and experiments.

scholarly journals Triple parametric tool path interpolation for five-axis machining with three-dimensional cutter compensation

2018 ◽  
Vol 10 (9) ◽  
pp. 168781401879822
Author(s):  
Chuanjun Li ◽  
Bin Zhang ◽  
XueLei Wang ◽  
Qiang Liu ◽  
Huan Liu
Keyword(s):  
Tool Path ◽  
Interpolation Method ◽  
Three Dimensional ◽  
Machining Accuracy ◽  
Great Success ◽  
Surface Machining ◽  
Smooth Motion ◽  
Simultaneous Interpolation ◽  
Five Axis ◽  
Parametric Interpolation

Parametric interpolation obtains a great success in three-axis surface machining with smooth motion, high accuracy, and high machining efficiency, but does not go well in five-axis surface machining due to lack of appropriate and efficient methods of tool path generation, interpolation, and three-dimensional cutter compensation. This article proposes a triple parametric tool path interpolation method for five-axis machining with three-dimensional cutter compensation, which proposes an appropriate triple parametric tool generation method for realizing the three-dimensional cutter compensation in five-axis parametric interpolation. A triple parametric interpolation algorithm is also proposed to realizing the simultaneous interpolation of the source data, which ensures the primitivity and maintains the accuracy. The proposed three-dimensional cutter compensation can compensate the errors caused by minor changes in cutter size, thus machining accuracy can be improved. Finally, illustrated example verifies the feasibility and applicability of the proposed methods.

Parametric interpolation method for probabilistic fatigue analysis of steel risers

2019 ◽  
Vol 90 ◽  
pp. 101838 ◽  
Author(s):  
J.S. Monsalve-Giraldo ◽  
P.M. Videiro ◽  
F.J. Mendes de Sousa ◽  
C.M.P.M. dos Santos ◽  
L.V.S. Sagrilo
Keyword(s):  
Interpolation Method ◽  
Fatigue Analysis ◽  
Parametric Interpolation

Five-Axis HSM Tool-Path Planning of Integral Impeller

2010 ◽  
Vol 426-427 ◽  
pp. 572-576
Author(s):  
Can Zhao ◽  
Y.Y. Guo ◽  
Guang Bin Bu
Keyword(s):  
High Speed ◽  
Control Algorithm ◽  
Tool Path ◽  
Control Method ◽  
Interpolation Method ◽  
Linear Interpolation ◽  
Normal Vector ◽  
Manufacture Process ◽  
Five Axis ◽  
Uniform Change

There are two key problems in the manufacture process of impeller with HSM(High Speed Machining). One is the collision between tool and blade, the other is gnawed-cutting arisen by non-uniform change of the cutter axis. The control algorithm of collision-free cutter-axis was described and applied in this paper. The cutter-axis vector was optimized by quaternary linear interpolation method to make normal vector of blade changing continuous, so. These methods were synthetically used in the manufacture experiment. And the qualified impeller was produced. It indicated that the tool vector control method was feasible.

Development of Real-Time Look-Ahead Methodology Based on Quintic PH Curve with G2 Continuity for High-Speed Machining

2013 ◽  
Vol 464 ◽  
pp. 258-264 ◽  
Author(s):  
Jing Shi ◽  
Qing Zhen Bi ◽  
Yu Han Wang ◽  
Gang Liu
Keyword(s):  
Real Time ◽  
High Speed ◽  
Tool Path ◽  
Approximation Error ◽  
Machining Process ◽  
Transition Curve ◽  
Look Ahead ◽  
Cad Cam ◽  
Feedrate Fluctuation ◽  
Ph Curve

Curving tool paths composed of straight lines, which are often represented as G01 blocks, are still the most widespread format form in the machining process chain of CAD/CAM/CNC. At the junctions between consecutive segments, the tangency and curvature discontinuities may lead to feedrate fluctuation and acceleration oscillation, which would deteriorate the machining efficiency and quality. In this paper, a real-time look-ahead interpolation methodology is proposed, which adopts a curvature-continuous PH curve as a transition to blend corner at the junction of adjacent lines in the tool path. The blending algorithm can guarantee the approximation error exactly, and the control points of the curve can be calculated analytically. On the other hand, the arc length and the curvature of the transition curve, which are important items in speed planning, also have analytical expressions. All the advantages are the guarantee of calculation efficiency during the interpolation. Except for a curvature-continuous tool path, our look-ahead algorithm adopts a speed planning window strategy to achieve a balance between the calculation capabilities and the real-time interpolation requirements. In this window, the corner transition algorithm and speed planning are implemented simultaneously and dynamically during the interpolation. By defining the width of this window, which is actually the number of linear segments contained in this window, can adjust the time consuming of speed planning. Simulation and experiments on our own developed CNC platform are conducted. The results demonstrate the feasibility and efficiency of the proposed algorithms.

Computer Simulation of Kinematic Surfaces

2015 ◽  
Vol 3 (4) ◽  
pp. 19-26 ◽  
Author(s):  
Усманова ◽  
E. Usmanova ◽  
Короткий ◽  
Viktor Korotkiy ◽  
Хмарова ◽  
...  
Keyword(s):  
Computer Simulation ◽  
Interpolation Method ◽  
Dimensional Space ◽  
Second Order ◽  
Surface Shape ◽  
Control Surface ◽  
Surface Model ◽  
Two Dimensional ◽  
Kinematic Method ◽  
Geometric Surface

A geometric surface model is formed taking into account given functional, structural, technological, economic, aesthetic requirements. These requirements are formulated in geometric terms and are expressed in terms of the surface parameters. The surface is modeled either Kinematics manner, or by way of a twodimensional interpolation. In accordance with in accordance with the kinematic method, the surface is formed as a continuous oneparameter many curves that form simulated in the surface. In accordance with the interpolation method, the surface consists of a set of elementary two-dimensional fragments. The article considered cinema optical method based on the use of curves of the second order of change-nests of the eccentricity as the main shaping element. To control the shape of the design surfaces are used for guide ruled surfaces (cilindroidy and conoid). Computer program is compiled, which determines the eccentricity of the forming curves of the second order depending on the boundary conditions. The program allows you to plot curve of the second order, given an arbitrary set of five coplanar points and tangents. When modeling the surface of the passing through a closed circuit, is used the mapping of this contour in four-dimensional space. Such mapping gives more possibilities for control surface shape. It is shown that the kinematics method computer simulation of the surface has technological advantages properties instead of interpolation method.

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.

Research on Kinematics Analysis and Trajectory Planning of Novel EOD Manipulator

2021 ◽  
Vol 11 (20) ◽  
pp. 9438
Author(s):  
Jianwei Zhao ◽  
Tao Han ◽  
Xiaofei Ma ◽  
Wen Ma ◽  
Chengxiang Liu ◽  
...  
Keyword(s):  
Trajectory Planning ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Random Number ◽  
Polynomial Interpolation ◽  
Interpolation Method ◽  
Joint Space ◽  
Work Requirements ◽  
Multiple Degrees Of Freedom ◽  
Quintic Polynomial

To address the problems of mismatch, poor flexibility and low accuracy of ordinary manipulators in the complex special deflagration work process, this paper proposes a new five-degree-of-freedom (5-DOF) folding deflagration manipulator. Firstly, the overall structure of the explosion-expulsion manipulator is introduced. The redundant degrees of freedom are formed by the parallel joint axes of the shoulder joint, elbow joint and wrist pitching joint, which increase the flexibility of the mechanism. Aiming at a complex system with multiple degrees of freedom and strong coupling of the manipulator, the virtual joint is introduced, the corresponding forward kinematics model is established by D–H method, and the inverse kinematics solution of the manipulator is derived by analytical method. In the MATLAB platform, the workspace of the manipulator is analyzed by Monte Carlo pseudo-random number method. The quintic polynomial interpolation method is used to simulate the deflagration task in joint space. Finally, the actual prototype experiment is carried out using the data obtained by simulation. The trajectory planning using the quintic polynomial interpolation method can ensure the smooth movement of the manipulator and high accuracy of operation. Furthermore, the trajectory is basically consistent with the simulation trajectory, which can realize the work requirements of putting the object into the explosion-proof tank. The new 5-DOF folding deflagration manipulator designed in this paper has stable motion and strong robustness, which can be used for deflagration during the COVID-19 epidemic.

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