Tool orientations’ generation and nonlinear error control based on complex surface meshing

Int J Adv Manuf Technol

2021

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.

Section: Approximation Of the Nonlinear Error Of CC Pointmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Chen

Int J Adv Manuf Technol

2021

“…After that, the relatively small distance and its corresponding parameter can be obtained by using Eq. (12). With the parameter as the central parameter, the search interval is narrowed and then divided again at equal spacing until the difference between the smaller distances obtained before and after is less than the preset solution error.…”

Section: Compensation and Repair Of Nonlinearerror For CC Pointmentioning

confidence: 99%

“…Aiming to ensure the continuity of the interpolation path, Hong et al [12] proposed an interpolation method that can reduce the rotation error angle by analyzing the nonlinear error between cutter positions during machining. Xu et al [13] proposed a fairing method for five-axis machining cutter path, which ensures the smooth transition between cutter orientations so as to reduce nonlinear errors.…”

Section: Introductionmentioning

confidence: 99%

Five-axis Tri-NURBS Spline Interpolation Method Considering Nonlinear Error Compensation and Correction of CC Paths

Chen

2021

Preprint

In order to improve the accuracy of tool axis vector position and direction in traditional five-axis NURBS interpolation methods and the controlling accuracy of cutter contacting(CC) paths between cutter and work-piece, a five-axis Tri-NURBS spline interpolation method is presented in this article. Firstly, the spline interpolation instruction format is proposed, which includes three spline curves, such as CC point spline, tool center point spline and tool axis point spline. The next interpolation parameter is calculated based on the tool center point spline combined with the conventional parametric interpolation idea. 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 tool axis vector position and direction. Secondly, the producing mechanism of CC paths’ nonlinear error of the traditional spline interpolation is analyzed and the mathematical calculation model of the nonlinear error is established. And then, the nonlinear error compensation and correction method is also put forward to improve the controlling accuracy of CC paths. In this method, the next CC point on the cutter can be firstly 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 be coincided. 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 machine tool. The MATLAB software is used as simulation of the real machining data. The results show that the proposed method can effectively reduce the CC paths’ nonlinear error. It has high practical value for five-axis machining in effectively controlling the accuracy of CC paths and im-proving the machining accuracy of complex surfaces.

“…Fan et al [33,34] proposed an optimization algorithm for cutter axis vector plane interpolation. Hong et al [35] put forward a tool direction generation method based on surface triangular mesh. Although these methods can effectively prevent overcutting and improve the surface quality of parts when the tool rotation angle changes remarkably, they ineffectively compensate for nonlinear errors when adjacent tool axis vectors are in linear ratio or the tool feed direction is on the vertical plane.…”

Section: Introductionmentioning

confidence: 99%

Regionalized compensation method for nonlinear error control

Int J Adv Manuf Technol

Tang²,

Wang³

et al. 2022

Although the five-axis machine tool presents excellent advantages of high-speed,efficiency, and -precision machining of complex curved surface parts (impeller and blade), its actual motion demonstrates nonlinear principle error due to the participation of the rotating axis. Traditional methods, such as linear interpolation, Rotation Tool Centre Point(RTCP), and tool point optimization, can effectively control nonlinear errors despite their limitations. A regional compensation optimization method is proposed in this study to solve nonlinear error problems effectively in five-axis machining of complex curved surface parts. First, feature points of the complex free-form surface are identified, and regions are divided to distinguish the compensation optimization algorithm of each interval. Second, JAVA language is applied to develop a special postprocessor with nonlinear error partition compensation module. Finally, the BV100 machine tool is used as the experimental platform, and a turbine blade is utilized as the specimen for simulation and cutting experiments. Results showed that the surface quality and contour accuracy of machined parts improved when the nonlinear error regional compensation optimization algorithm is used.