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Spline-Based Trajectory Generation for CNC Machines

机译：用于数控机床的条形图曲轨迹生成

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摘要

Manufacturing of workpieces with computerized numerical control 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 three-axis micromilling machine. To easily generate trajectories for different workpieces and machines, the method is included in a user-friendly open-source software toolbox.
机译：具有计算机式数控机器的工件制造需要计算机床轨迹，快速准确地跟踪所需的工件轮廓。本文提出了一种用于机床的新型B样条轨迹生成方法。该方法解决了最佳控制问题，以最小化工具的运动时间，同时考虑到刀具轴的速度，加速度和混凝剂限制。此外，通过约束轨迹在围绕标称几何轮廓围绕管子内部的轨迹直接包括允许的工件容差。这允许在准确性和生产力之间探索权衡，同时计算近最佳轨迹。呈现的方法通过同时优化多个段的轨迹，在构建轮廓之间建立轮廓之间的流畅连接。另一方面，限制同时优化的段的量和使用有效的问题配方保持计算时间可接受。通过与工业基准进行比较，在仿真中验证了轨迹生成方法，显示了超过10％的加工时间减少。与最先进的角落平滑方法的比较表明，所呈现的方法在计算时间下获得相似或稍微更快的轨迹，该计算时间可达45倍。此外，该方法通过实验在三轴微磨机上进行验证。为了轻松生成不同工件和机器的轨迹，该方法包括在用户友好的开源软件工具箱中。

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