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Five-axis Tri-NURBS spline interpolation method considering compensation and correction of the nonlinear error of cutter contacting paths

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Abstract

In order to improve the accuracy of position and direction of the tool axis vector and the controlling accuracy of cutter contacting (CC) paths between the cutter and workpiece in the traditional five-axis NURBS interpolation method, a five-axis Tri-NURBS spline interpolation method is proposed in this paper. Firstly, the spline interpolation instruction format is proposed, which includes three spline curves, the CC point spline, the tool center point spline, and the tool axis point spline. The next interpolation parameter is calculated based on the tool center point spline combined with the conventional parametric interpolation method. Different from the traditional spline interpolation using the same interpolation parameter for all spline curves, the idea of equal ratio configuration of parameters is proposed in this paper to obtain the next interpolation parameter of each spline curve. The next interpolation tool center point, tool axis point, and CC point on the above three spline curves can be obtained by using different interpolation parameters, so as to improve the accuracy of position and direction of the tool axis vector. Secondly, the producing mechanism of the nonlinear error of CC paths of the traditional spline interpolation is analyzed and the mathematical calculation model of the nonlinear error is established. And then, the compensation and correction method of nonlinear error is also proposed to improve the controlling accuracy of CC paths. In this method, the next CC point on the cutter can be first obtained according to the next interpolation tool center point, tool axis point, and CC point on the three spline curves. And then, the error compensation vector is determined with the two next CC points. To correct the nonlinear error between the next CC point on the cutter and the CC point spline curve, the cutter is translated so that the two next CC points can coincide. In the end, the new tool center point and tool axis point after translation can be calculated to obtain the motion control coordinates of each axis of the machine tool. The MATLAB and VERICUT software are used as a simulation of the real machining data. The results show that the proposed method can effectively reduce the nonlinear error of CC paths. It has high practical value for five-axis machining in effectively controlling the accuracy of CC paths and improving the machining accuracy of complex surfaces.

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Availability of data and material

The datasets used or analyzed during the current study are available from the corresponding author on reasonable request.

Code availability

The codes used or analyzed during the current study are available from the corresponding author on reasonable request.

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Funding

This research was supported by Guangxi Natural Science Foundation under Grant No.2021GXNSFAA220019 and Professor Kaihong Zhou received a grant from the National Natural Science Foundation of China (Award Number: 52075110).

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Authors and Affiliations

  1. College of Mechanical and Control Engineering, Guilin University of Technology, Guilin, 541004, China

    Liangji Chen

  2. School of Mechanical Engineering, Tiangong University, Tian**, 300387, China

    Liangji Chen, Zisen Wei & Longfei Ma

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  1. Liangji Chen
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  2. Zisen Wei
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  3. Longfei Ma
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Contributions

The overarching research goals were developed by Liangji Chen, Zisen Wei, and Longfei Ma. Liangji Chen, Zisen Wei, and Longfei Ma established the models and calculated the predicted consequence. Liangji Chen and Zisen Wei analyzed the calculated results. The initial draft of the manuscript was written by Liangji Chen, Zisen Wei, and Longfei Ma.

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Correspondence to Zisen Wei.

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On behalf of my coauthors, I submit our manuscript entitled “Five-axis Tri-NURBS spline interpolation method considering compensation and correction of the nonlinear error of cutter contacting paths” to “The International Journal of Advanced Manufacturing Technology” for publishing.

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Chen, L., Wei, Z. & Ma, L. Five-axis Tri-NURBS spline interpolation method considering compensation and correction of the nonlinear error of cutter contacting paths. Int J Adv Manuf Technol 119, 2043–2057 (2022). https://doi.org/10.1007/s00170-021-08208-7

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