Smooth time-optimal tool trajectory generation for CNC manufacturing systems

Zhang, Qiang; Li, Shurong; Jun, Guo

doi:10.1016/j.jmsy.2012.06.001

Cited by 36 publications

(13 citation statements)

References 18 publications

(27 reference statements)

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“…Content may change prior to final publication. The feedrate of the star path is scheduled with three different ways: constant based feed, radau-pesudo-spectral (RPM) based feed, and control vector parameterized (CVP) based feed [13]. The constant feed (dashed line) is composed of seven stages, i.e.…”

Section: Example Iii: a Star Pathmentioning

confidence: 99%

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Smooth Trajectory Generation for Predefined Path With Pseudo Spectral Method

2020

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In view of smooth trajectory generation for a 3-axis machine tool, many methods have been presented. Among them, the optimal control based method is increasingly concerned, because it is considered to be able to make full use of kinematic abilities of machine tools. Under the unified framework of optimal control, the feedrate can be adjusted flexibly by adding or removing axial constraints and tangential constraints. But the problem of smooth trajectory generation (PSTG) based on optimal control for a machine tool is not easily to be solved. In this paper, to efficiently solve the PSTG, it is divided into two sub-problems: the problem of minimum time trajectory planning (PMTTP) and the pseudo problem of smooth trajectory generation (PPSTG). Since both sub-problems are convex, the existence of unique solutions can be guaranteed. Then, the PMTTP and the PPSTG are transformed into nonlinear programming (NLP) problems with radau-pseudo-spectral (RPM) method successively. Due to convexity, the two NLP problems can be efficiently solved with mature optimization methods. In addition, the RPM method allows two sub-problems to have different Legendre-Gauss-Radau (LGR) points, thereby further saving computational costs. Finally, three different predefined paths are employed to test the proposed method, and simulation results show the effectiveness of proposed method.

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Section: Example Iii: a Star Pathmentioning

confidence: 99%

“…The scheme can obtain near time-optimal feedrate by transforming jerk constraints into limits for the curvature of the phase-space velocity. In fact, time optimal control problems can also be solved with numerical methods, such as control vector parameterization (CVP) method [13].…”

Section: Introductionmentioning

confidence: 99%

Smooth Trajectory Generation for Predefined Path With Pseudo Spectral Method

2020

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“…These constraints express that the position, velocity and acceleration at the end of the trajectory associated with segment j have to be equal to the corresponding values at the beginning of the trajectory traversing segment j + 1. Assembling all elements from Section II-A, adapting them to account for multiple segments and adding (7), leads to the final OCP:…”

Section: B Trajectory Generation For Multiple Segmentsmentioning

confidence: 99%

“…However, a discontinuity in the axis acceleration can lead to vibrations in the machine tool [6]. To avoid vibrations, the authors of [7] formulate a jerkconstrained nonlinear optimization problem. The downside of these methods is that they require following the contour exactly.…”

Section: Introductionmentioning

confidence: 99%

Spline-Based Trajectory Generation for CNC Machines

Mercy

Jacquod

Herzog

et al. 2019

IEEE Trans. Ind. Electron.

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Manufacturing of workpieces with CNC machines requires computing machine tool trajectories that fast and accurately track the desired workpiece contour. This paper presents a novel B-spline trajectory generation method for machine tools. The method solves an optimal control problem to minimize the motion time of the tool, while taking into account the velocity, acceleration and jerk limits of the tool axes. Furthermore, it directly includes the allowed workpiece tolerance, by constraining the trajectory to lie inside a tube around the nominal geometry contour. This allows exploring the trade-off between accuracy and productivity, while computing near-optimal trajectories. The presented method creates fluent connections between segments that build up the contour by simultaneously optimizing trajectories for multiple segments. On the other hand, limiting the amount of simultaneously optimized segments and using an efficient problem formulation keeps the computation time acceptable. The trajectory generation method is validated in simulation by comparison with industrial benchmarks, showing a reduction in machining time of more than 10%. The comparison to a state-of-the-art corner smoothing approach shows that the presented method obtains similar or slightly faster trajectories, at a computation time that is up to 45 times lower. In addition, the method is validated experimentally on a 3-axis micro-milling machine. To easily generate trajectories for different workpieces and machines, the method is included in a user-friendly open-source software toolbox.

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“…results. These issues are also the topics of interest in other engineering applications, e.g., trajectory planning in robotics [60,61] and machining processes [62,63]. The importance of parameterization in IGA is studied in different researches.…”

Section: Introductionmentioning

confidence: 99%

Effects of parameterization and knot placement techniques on primal and mixed isogeometric collocation formulations of spatial shear-deformable beams with varying curvature and torsion

Marino

Hosseini

Hashemian

et al. 2020

Computers & Mathematics with Applications

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We present a displacement-based and a mixed isogeometric collocation (IGA-C) formulation for free-form, three-dimensional, shear-deformable beams with high and rapidly-varying curvature and torsion. When such complex shapes are concerned, the approach used to build the IGA geometric model becomes relevant. Although IGA-C has been so far successfully applied to a wide range of problems, the effects that different parameterization and knot placement techniques may have on the accuracy of collocation-based formulations is still an unexplored field. To fill this gap, primal and mixed formulations are used combining two parameterization methods (chord-length and equally spaced) with two knot placement techniques (uniformly spaced and De Boor). With respect to the space-varying Frenet local frame, we derive the strong form of the governing equations in a compact form through the definition of two matrix operators conveniently used to perform first and second order derivatives of the vector fields involved in the formulations. This approach is very efficient and easy to implement within a collocation-based scheme. Several challenging numerical experiments allow to test the different considered parameterizations and knot placement techniques, revealing in particular that with the primal formulation an equally spaced parameterization is definitively the most recommended choice and it should always be used with an approximation degree of, at least, p = 6, although some caution must be adopted when very high

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Smooth time-optimal tool trajectory generation for CNC manufacturing systems

Cited by 36 publications

References 18 publications

Smooth Trajectory Generation for Predefined Path With Pseudo Spectral Method

Smooth Trajectory Generation for Predefined Path With Pseudo Spectral Method

Spline-Based Trajectory Generation for CNC Machines

Effects of parameterization and knot placement techniques on primal and mixed isogeometric collocation formulations of spatial shear-deformable beams with varying curvature and torsion

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