Dual NURBS Path Smoothing for 5-Axis Linear Path of Flank Milling

Li, Dongdong; Zhang, Weimin; Zhou, Wei; Shang, Tengfei; Fleischer, Jürgen

doi:10.1007/s12541-018-0209-6

Cited by 25 publications

(6 citation statements)

References 23 publications

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“…It can be seen that despite a slight improvement of feed time (3.595 s), the acceleration of X-axis and velocity of C-axis exceed the corresponding constraints. The axial velocities and accelerations using the parameter synchronization [23] are demonstrated in Figure 17. The accelerations of all axes are far greater than the allowable values at certain locations.…”

Section: Simulation and Experiments Validationsmentioning

confidence: 99%

“…The local corner-smoothing method applied to five-axis linear-segment toolpath can guarantee high-order continuity while respect error tolerance and synchronization of the tool-tip position and tool orientation is achieved by adjusting the joint points of the linear and curvilinear segments [19][20][21]. The global curve-fitting method applied to five-axis linear-segment toolpath can ensure toolpath smoothness, but the fitting error is hard to control and evaluate [22,23]. Moreover, the global curve-fitting method usually synchronizes two trajectories by sharing the same curve parameter (parameter synchronization).…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, the global curve-fitting method usually synchronizes two trajectories by sharing the same curve parameter (parameter synchronization). The parameter synchronization method [22,23] plans the tool-tip trajectory according to translational motion constraints and then makes the tool orientation follow the tool-tip in the curve parameter space. However, if the tool orientation is merely parameter synchronized with tool-tip position, the rotary motion may be discontinuous at certain locations.…”

Section: Introductionmentioning

confidence: 99%

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Double B-Spline Curve-Fitting and Synchronization-Integrated Feedrate Scheduling Method for Five-Axis Linear-Segment Toolpath

et al. 2020

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The discontinuities of a five-axis linear-segment toolpath result in fluctuation in the feedrate, acceleration and jerk commands that lead to machine tool vibration and poor surface finish. For path smoothing, with the global curve-fitting method it is difficult to control fitting error and the local corner-smoothing method has large curvature extreme. For path synchronization, the parameter synchronization method cannot ensure smooth rotary motion. Aiming at these problems, this paper proposes a double B-spline curve-fitting and synchronization-integrated feedrate scheduling method. Two C2-continuous and error-bounded B-spline curves are produced to fit tool-tip position and tool orientation, respectively. The fitting error is controlled by locally refining the curve segments that exceed the fitting tolerance. The tool-tip position trajectory is firstly planned to address axial kinematic constraints in the feedrate scheduling process. Then the feedrate is deformed for the tool orientation to guarantee smooth rotary motion as well as to share the same motion time with the tool-tip position segment by segment. The feasibility and effectiveness of the proposed method have been validated by simulations and experiments on the S-shape test piece. Simulations show that the proposed curve-fitting method can generate smooth toolpath and constrain fitting error. The proposed feedrate scheduling method can guarantee smooth rotary motion and keep axial motions under kinematic limits, compared with the method that does not consider axial kinematic constraints and the parameter synchronization method. Experimental results verify that the proposed curve-fitting method can generate smooth tool path under fitting tolerance, and the proposed feedrate scheduling method can produce smooth and restricted axial motions.

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Section: Simulation and Experiments Validationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Double B-Spline Curve-Fitting and Synchronization-Integrated Feedrate Scheduling Method for Five-Axis Linear-Segment Toolpath

et al. 2020

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“…Their machining experiment showed that the contouring accuracy of the machined workpiece could reach 10 -6 mm level. Li et al [23] used the least-squares approach to obtain the double NURBS curve to meet the fitting accuracy. Then the secondorder Taylor expansion method was used to obtain the interpolation points of the tool tip curve.…”

Section: Introductionmentioning

confidence: 99%

Smooth toolpath interpolation for a 5-axis hybrid machine tool

Fang

Bao

et al. 2022

Robotica

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Due to the merits of high rigidity and good dynamics, hybrid machine tools have been gradually applied to efficient machining of thin-walled workpiece with complex geometries. However, the discontinuity of tangential component of toolpath in hybrid machine tools may cause velocity fluctuations, leading to poor surface quality of workpiece. In this paper, a novel 5-axis hybrid machine tool is taken as an example to demonstrate a smooth toolpath interpolation method. First, an adaptive acceleration and deceleration control algorithm is presented to realize the smooth transition between two constrained velocity points. Second, a spline curve-based interpolation algorithm is proposed to realize the smoothness of the trajectory. Meanwhile, a parameter synchronization method is proposed to ensure the synchronization of the interpolated tool-axis vector and the interpolated tool tip. Thirdly, an inverse kinematic analysis is conducted based on an inverse position solution model and a velocity mapping model. Finally, a set of machining tests on S-shape workpiece in line with the ISO standard is carried out to verify the effectiveness of the proposed smooth toolpath interpolation method.

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“…All of the above methods can effectively reduce the nonlinear error of the tool center point path in the five-axis machining, but these are limited in precisely controlling the accuracy of the CC path. To address these problems, this paper proposes a five-axis Tri-NURBS interpolation method based on the spline interpolation synchronization method in the literature [18][19][20], which takes into account the nonlinear error control of the CC path and realizes the interpolation control of the tool center point spline path, tool axis point spline path, and CC point spline path, and obtain the current interpolation tool center point, the current interpolation tool axis point and the current interpolation CC point. When these three points are obtained, the real CC points can be obtained according to their geometric relationships.…”

Section: Introductionmentioning

confidence: 99%

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

Chen

Wei

2021

Int J Adv Manuf Technol

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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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Dual NURBS Path Smoothing for 5-Axis Linear Path of Flank Milling

Cited by 25 publications

References 23 publications

Double B-Spline Curve-Fitting and Synchronization-Integrated Feedrate Scheduling Method for Five-Axis Linear-Segment Toolpath

Double B-Spline Curve-Fitting and Synchronization-Integrated Feedrate Scheduling Method for Five-Axis Linear-Segment Toolpath

Smooth toolpath interpolation for a 5-axis hybrid machine tool

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

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