Simulation of machining errors of Bspline and Cspline

Msaddek, El Bechir; Bouaziz, Zoubeir; Baili, Maher; Dessein, Gilles; Akrout, Mohsen

doi:10.1007/s00170-016-9276-y

Cited by 7 publications

(6 citation statements)

References 7 publications

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“…The CAD and CAM systems spline bases are usually unknown for the user. In other works, such as [29], the interpolation algorithm had to be experimentally extracted to simulate the interpolation errors. In this work, the interpolation errors were calculated graphically in the CAM program.…”

Section: Analysis Of the Curve Fitting Errorsmentioning

confidence: 99%

Trajectory Definition with High Relative Accuracy (HRA) by Parametric Representation of Curves in Nano-Positioning Systems

et al. 2019

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Nanotechnology applications demand high accuracy positioning systems. Therefore, in order to achieve sub-micrometer accuracy, positioning uncertainty contributions must be minimized by implementing precision positioning control strategies. The positioning control system accuracy must be analyzed and optimized, especially when the system is required to follow a predefined trajectory. In this line of research, this work studies the contribution of the trajectory definition errors to the final positioning uncertainty of a large-range 2D nanopositioning stage. The curve trajectory is defined by curve fitting using two methods: traditional CAD/CAM systems and novel algorithms for accurate curve fitting. This novel method has an interest in computer-aided geometric design and approximation theory, and allows high relative accuracy (HRA) in the computation of the representations of parametric curves while minimizing the numerical errors. It is verified that the HRA method offers better positioning accuracy than commonly used CAD/CAM methods when defining a trajectory by curve fitting: When fitting a curve by interpolation with the HRA method, fewer data points are required to achieve the precision requirements. Similarly, when fitting a curve by a least-squares approximation, for the same set of given data points, the HRA method is capable of obtaining an accurate approximation curve with fewer control points.

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Section: Analysis Of the Curve Fitting Errorsmentioning

confidence: 99%

Trajectory Definition with High Relative Accuracy (HRA) by Parametric Representation of Curves in Nano-Positioning Systems

et al. 2019

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“…After the simulation of machining errors of the interpolations, Bspline and Cspline [2], our choice was oriented towards the method of the node insertion, in order to compensate the machining errors. It consists of adding nodes in the toolpath as a means to respect the proposed tolerance.…”

Section: Principlementioning

confidence: 99%

“…Among these interpolations object of the study, we find the polynomial or spline functions (NURBS, Bspline). Our previous research [1,2] has shown the influence of the interpolation type, such as the functions: Bspline and Cspline, on the machining errors in HSM of a free form (Fig. 1).…”

Section: Introductionmentioning

confidence: 99%

Compensation of machining errors of Bspline and Cspline

Msaddek

Baili

Bouaziz

et al. 2018

Int J Adv Manuf Technol

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The evolution of the interpolation methods towards a very high technicality requires a good choice of used type in the operation of high-speed milling (HSM). The "Bspline" and "Cspline" interpolations present good solutions to guarantee the tool's continuous movement during machining. However, in a previous article, we have shown by a simulation tool that they generate significant dimensional errors that decrease the precision of the machined part. In this article, a method of compensating for these errors based on the insertion of the nodes, while respecting the predefined tolerance, has been developed. To do this, we have modeled and simulated machining errors before and after compensation for each type of interpolation. To validate our results, we have machined a test piece with the compensated and uncompensated Bspline and Cspline interpolations on the Huron KX10 machine and we have measured the corresponding machining errors. The results have shown that the method of compensation by the insertion of the nodes causes a significant reduction of the machining errors.

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“…Based on the nonuniform rational B-spline, an adaptive mathematical expression model was established to describe the spatial errors of machine tools. El Bechir et al [10] suggested a simulation methodology for errors caused by the interpolations B-spline and C-spline in high-speed machining of warped shapes and developed analytical models expressing the basic paths of the interpolations. In 2017, Chen et al [11] attempted to establish an error model of 12 terms of polynomial in total for the triaxial linkage of machine tools based on the error measurement data of the whole working space of machine tools and preliminarily discussed the error prediction method for the points at different spatial locations of machine tools.…”

Section: Introductionmentioning

confidence: 99%

Modeling and Prediction Method for CNC Machine Tools’ Errors Based on Spatial Feature Points

Chen

Zhang

Xiang

et al. 2020

Advances in Materials Science and Engineering

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In order to improve the precision of CNC machine tools effectively, a method for modeling and predicting their spatial errors based on spatial feature points was proposed. Taking three-axis vertical CNC machine tools as the research object, we think that the whole space formed by machine tools’ working can be seen as the combination of a number of cubes, whose vertices are considered to be feature points, and others in the cubes are called nonfeature points. So, each nonfeature point’s errors can be predicted by the cube’s eight vertices’ errors. Based on the above ideas, an approach including the installing instrument for measuring any spatial feature point’s errors was put forward. In this way, all data of the feature points’ errors could be obtained. Moreover, according to these error data, the prediction model of nonfeature points’ errors was established by using the internal division ratio method. The method has the advantages of small interpolation operation, easy integration in the numerical control system, and high compensation precision. Finally, an example was used to prove its effectiveness and feasibility.

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Simulation of machining errors of Bspline and Cspline

Cited by 7 publications

References 7 publications

Trajectory Definition with High Relative Accuracy (HRA) by Parametric Representation of Curves in Nano-Positioning Systems

Trajectory Definition with High Relative Accuracy (HRA) by Parametric Representation of Curves in Nano-Positioning Systems

Compensation of machining errors of Bspline and Cspline

Modeling and Prediction Method for CNC Machine Tools’ Errors Based on Spatial Feature Points

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