在数控加工中, 速度规划是优化加工时间的核心问题. 文章针对圆弧-线段型路径, 提出最优速度规划算法. 文章通过建立加工时间最短的速度规划模型, 基于``Bang-Bang"控制, 对圆弧进行最优速度规划. 通过圆弧相邻线段的速度可达性检验修调速度, 提出圆弧样条的最优速度规划算法. 与高速小线段拐角过渡插补算法相比, 实验结果表明文章的算法更加高效.

In computer numerical control (CNC) machining, time minimization achieved by optimal velocity planning is a critical topic. In this paper, we propose an optimal velocity planning algorithm for arc-line toolpaths. Velocity planning for arcs is used instead of the traditional micro-line interpolation method. We first present the optimal velocity planning algorithm for arcs. Under the constraints of machining ability, such as the maximal acceleration at each axis, we build up the optimal model to minimize the machining time. Based on ``Bang-Bang" control, the optimal solution could be obtained by solving the corresponding ordinary differential equations. Thus, we get the initial velocity curve for each arc. The final velocity curve depends on the acceleration, the $\mathrm{V}\mathrm{L}\mathrm{C}$ and the critical points. For an arc-line toolpath, we transfer it into an arc spline whose $G^1$ continuity could take advantage of the maximal machining ability. We revise each arc's velocity curve by the accessibility test at each line. Then we give the optimal velocity planning algorithm for arc-line toolpaths. Compared with the existed turning transition algorithm, our method provides faster velocity.