A segment feedrate profile fitting method for parametric interpolation

2016 ◽  
Vol 232 (2) ◽  
pp. 267-280 ◽  
Author(s):  
Lei Lu ◽  
Lei Zhang ◽  
Shijun Ji ◽  
Dunlan Song ◽  
Ji Zhao
Keyword(s):  
Tool Path ◽  
Least Squares Method ◽  
Machining Accuracy ◽  
The Novel ◽  
Profile Fitting ◽  
Fitting Method ◽  
Calculation Process ◽  
Data Points ◽  
Simulation And Experiment ◽  
Parametric Interpolation

There are many researches in scheduling an optimal feedrate profile under various constraints by numerical calculation. A large number of discrete feedrate data points are obtained. They are inconvenient for the parametric interpolator. Therefore, these discrete feedrate data points need to be fitted by parameter curves. Different from the regular curve fitting, the inappropriate feedrate fitting method can generate larger acceleration and jerk that seriously affect the machining accuracy and stability, although the feedrate satisfies the error requirements. In order to generate a suitable feedrate profile, a segment feedrate profile fitting method using B-spline is proposed in this article. The discrete feedrate data points are segmented in the jerk discontinuous points. In each segment, the feedrate profile is fitted by the linear least squares method. These fitted feedrate profiles are combined to generate a unified feedrate profile. The unified fitted feedrate profile and the tool path trajectory are used in the controller to command the axis. In this article, the process of parametric interpolation is separated into the arc-length calculation process and the curve parameter calculation process. Using parallel computation, the two processes are calculated simultaneously in the controller, and the computational efficiency is improved. Both simulation and experiment are carried out to verify that the fitted feedrate profile satisfies the error requirements, and the novel interpolation can be applied to the controller appropriately.

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 Exponential Polynomial Fitting for Fibre Spectrum CCD Profiles

2010 ◽  
Vol 27 (3) ◽  
pp. 290-295 ◽  
Author(s):  
Zhangqin Zhu ◽  
Jia Zhu ◽  
Hanqin Qin ◽  
Chong Wang ◽  
Zhongfu Ye
Keyword(s):  
Least Squares ◽  
Spatial Orientation ◽  
Least Squares Method ◽  
Exponential Polynomial ◽  
Exponential Functions ◽  
Polynomial Fitting ◽  
Gaussian Functions ◽  
Profile Fitting ◽  
Fitting Method

AbstractA fibre spectrum profile fitting method based on the least-squares method is presented in this article. For each spectrum of one fibre in spatial orientation, two exponential functions are employed to approximate the profile. Experiments are performed with both simulated profiles and observed profiles to demonstrate the effectiveness of the algorithm. Specially, the proposed method has a better performance for profiles that are asymmetric or composed of multi-Gaussian functions.

A Surface Parameter-Based Method for Accurate and Efficient Tool Path Generation

2014 ◽  
Vol 8 (3) ◽  
pp. 428-436 ◽  
Author(s):  
Keigo Takasugi ◽  
◽  
Naoki Asakawa ◽  
Yoshitaka Morimoto ◽  
◽  
...  
Keyword(s):  
Tool Path ◽  
Simple Calculation ◽  
Machining Accuracy ◽  
Parametric Surface ◽  
Surface Parameter ◽  
Efficient Tool ◽  
Free Surfaces ◽  
Tool Paths ◽  
Calculation Process ◽  
The Cost

Along with the increasing need for multi-axis and multi-tasking machining tools for the machining of complex free surfaces, the importance of CAM applications related to the accuracy of the free surfaces has increased dramatically. The machining accuracy and surface integrity of a product depends not only on the performance of the machining tool itself but also on the tool path generated by CAM. At present, there is a trade off between numerical calculation errors and cost in CAM. There is no calculation method that satisfies both sides. Of particular importance is the fact that the cost increases exponentially with the rank of the free surface. Therefore, this paper proposes a new method of generating tool paths efficiently; it generates tool paths directly from 2-dimensional parametric space by using the parametric surface defined as a polynomial. We confirm that this method can reduce the cost and that the tool path can be generated by means of a simple calculation process, without considering singular points. Moreover, since commercial CAM kernels cannot accommodate to our method, we design and implement a new CAM kernel that can access the parametric surface directly in order to develop this method.

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.

Error correction technique for numerical control machine tools based on the simplex method

2021 ◽  
pp. 095440542110281
Author(s):  
Hongwei Liu ◽  
Rui Yang ◽  
Pingjiang Wang ◽  
Jihong Chen ◽  
Hua Xiang
Keyword(s):  
Machine Tool ◽  
Error Compensation ◽  
Simplex Method ◽  
Tool Path ◽  
Repeated Measurements ◽  
Numerical Control ◽  
Machining Accuracy ◽  
Correction Technique ◽  
Fluctuation Range ◽  
Nc Machine

The objective of this research is to develop a novel correction mechanism to reduce the fluctuation range of tools in numerical control (NC) machining. Error compensation is an effective method to improve the machining accuracy of a machine tool. If the difference between two adjacent compensation data is too large, the fluctuation range of the tool will increase, which will seriously affect the surface quality of the machined parts in mechanical machining. The methodology used in compensation data processing is a simplex method of linear programming. This method reduces the fluctuation range of the tool and optimizes the tool path. The important aspect of software error compensation is to modify the initial compensation data by using an iterative method, and then the corrected tool path data are converted into actual compensated NC codes by using a postprocessor, which is implemented on the compensation module to ensure a smooth running path of the tool. The generated, calibrated, and amended NC codes were immediately fed to the machine tool controller. This technique was verified by using repeated measurements. The results of the experiments demonstrate efficient compensation and significant improvement in the machining accuracy of the NC machine tool.

EXPRESS: Baseline Correction Based on a Search Algorithm from Artificial Intelligence

2020 ◽  
pp. 000370282097751
Author(s):  
Xin Wang ◽  
Xia Chen
Keyword(s):  
Artificial Intelligence ◽  
Objective Function ◽  
Least Squares ◽  
Least Squares Method ◽  
Search Algorithm ◽  
Absolute Error ◽  
Search Problem ◽  
Baseline Correction ◽  
Current Spectrum ◽  
Data Points

Many spectra have a polynomial-like baseline. Iterative polynomial fitting (IPF) is one of the most popular methods for baseline correction of these spectra. However, the baseline estimated by IPF may have substantially error when the spectrum contains significantly strong peaks or have strong peaks located at the endpoints. First, IPF uses temporary baseline estimated from the current spectrum to identify peak data points. If the current spectrum contains strong peaks, then the temporary baseline substantially deviates from the true baseline. Some good baseline data points of the spectrum might be mistakenly identified as peak data points and are artificially re-assigned with a low value. Second, if a strong peak is located at the endpoint of the spectrum, then the endpoint region of the estimated baseline might have significant error due to overfitting. This study proposes a search algorithm-based baseline correction method (SA) that aims to compress sample the raw spectrum to a dataset with small number of data points and then convert the peak removal process into solving a search problem in artificial intelligence (AI) to minimize an objective function by deleting peak data points. First, the raw spectrum is smoothened out by the moving average method to reduce noise and then divided into dozens of unequally spaced sections on the basis of Chebyshev nodes. Finally, the minimal points of each section are collected to form a dataset for peak removal through search algorithm. SA selects the mean absolute error (MAE) as the objective function because of its sensitivity to overfitting and rapid calculation. The baseline correction performance of SA is compared with those of three baseline correction methods: Lieber and Mahadevan–Jansen method, adaptive iteratively reweighted penalized least squares method, and improved asymmetric least squares method. Simulated and real FTIR and Raman spectra with polynomial-like baselines are employed in the experiments. Results show that for these spectra, the baseline estimated by SA has fewer error than those by the three other methods.

scholarly journals Towards Efficient Milling of Multi-Cavity Aeronautical Structural Parts Considering ACO-Based Optimal Tool Feed Position and Path

Micromachines ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 88
Author(s):  
Yupeng Xin ◽  
Yuanheng Li ◽  
Wenhui Li ◽  
Gangfeng Wang
Keyword(s):  
High Speed ◽  
Tool Path ◽  
Milling Process ◽  
Ant Colony ◽  
Machining Accuracy ◽  
Ant Colony Optimization Algorithm ◽  
Peripheral Milling ◽  
Structural Part ◽  
Milling Method ◽  
Structural Parts

Cavities are typical features in aeronautical structural parts and molds. For high-speed milling of multi-cavity parts, a reasonable processing sequence planning can significantly affect the machining accuracy and efficiency. This paper proposes an improved continuous peripheral milling method for multi-cavity based on ant colony optimization algorithm (ACO). Firstly, by analyzing the mathematical model of cavity corner milling process, the geometric center of the corner is selected as the initial tool feed position. Subsequently, the tool path is globally optimized through ant colony dissemination and pheromone perception for path solution of multi-cavity milling. With the advantages of ant colony parallel search and pheromone positive feedback, the searching efficiency of the global shortest processing path is effectively improved. Finally, the milling programming of an aeronautical structural part is taken as a sample to verify the effectiveness of the proposed methodology. Compared with zigzag milling and genetic algorithm (GA)-based peripheral milling modes in the computer aided manufacturing (CAM) software, the results show that the ACO-based methodology can shorten the milling time of a sample part by more than 13%.

Development of Gas Scintillation Proportional Counter

1999 ◽  
Vol 09 (03n04) ◽  
pp. 169-174
Author(s):  
N. Shigeoka ◽  
K. Mutaguchi ◽  
Y. Nakanishi ◽  
Y. Ito ◽  
T. Mukoyama ◽  
...  
Keyword(s):  
Proportional Counter ◽  
Pulse Height ◽  
Acceleration Region ◽  
X Ray ◽  
Gaussian Profile ◽  
Profile Fitting ◽  
Fitting Method

The properties of gas scintillation proportional counter are investigated for Mn K x-ray spectra. The pulse-height spectra are strongly affected by changing of the value of a potential V 2 in the acceleration region and analyzed by the Gaussian profile fitting method.

Aero-Engine Blade Deformation Control of Milling Process

2011 ◽  
Vol 308-310 ◽  
pp. 1198-1204
Author(s):  
Hui Xian Chen ◽  
Hao Li ◽  
Hai Tao Feng ◽  
Min Juan Du
Keyword(s):  
Finite Element ◽  
Finite Element Simulation ◽  
Error Compensation ◽  
Leaf Blade ◽  
Tool Path ◽  
Iterative Solution ◽  
Helical Milling ◽  
Machining Accuracy ◽  
Element Simulation ◽  
Compensation Plan

The leaf blade manufacture precision's influencing factors are numerous, and they have coupling relationship each other. So it is difficult to peel out a single factor on the influencing regularity of the blade's machining accuracy. By researching the engine blades of helical milling state under the existing fixture, the leaf blade deformable model based on the instantaneous milling strength was established. Meanwhile, the off-line multi-level error compensation plan was proposed based on the processing surface static error forecasts and compensation. In order to revise the primitive NC tool path code and eliminate the processing distortion inaccuracy, the elastic deformity on each knife position spot is solved on the basis of iterative solution, using the finite element simulation and milling strength model. By using ANSYS finite element simulation, it receives the real-time error compensation of the tool path. And then The experiment has proven the accuracy and the usability of the compensation plan.

scholarly journals Methods for Fitting the Limit State Function of the Residual Strength of Damaged Ships

2022 ◽  
Vol 10 (1) ◽  
pp. 102
Author(s):  
Zhiyao Zhu ◽  
Huilong Ren ◽  
Xiuhuan Wang ◽  
Nan Zhao ◽  
Chenfeng Li
Keyword(s):  
Least Squares ◽  
Residual Strength ◽  
Least Squares Method ◽  
Limit State ◽  
Nonlinear Least Squares ◽  
State Function ◽  
Limit State Function ◽  
Distribution Models ◽  
Sample Distribution ◽  
Fitting Method

The limit state function is important for the assessment of the longitudinal strength of damaged ships under combined bending moments in severe waves. As the limit state function cannot be obtained directly, the common approach is to calculate the results for the residual strength and approximate the limit state function by fitting, for which various methods have been proposed. In this study, four commonly used fitting methods are investigated: namely, the least-squares method, the moving least-squares method, the radial basis function neural network method, and the weighted piecewise fitting method. These fitting methods are adopted to fit the limit state functions of four typically sample distribution models as well as a damaged tanker and damaged bulk carrier. The residual strength of a damaged ship is obtained by an improved Smith method that accounts for the rotation of the neutral axis. Analysis of the results shows the accuracy of the linear least-squares method and nonlinear least-squares method, which are most commonly used by researchers, is relatively poor, while the weighted piecewise fitting method is the better choice for all investigated combined-bending conditions.

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