基于PH曲线的数控拐角过渡方法

 为了减弱轨迹拐角处的向心加速度变化给加工带来的不利影响，使用五次PH曲线进行拐角过渡,在控制加工速度的同时对向心加速度进行控制。通过对拐角处连接情况的分析，确定了连接PH曲线中的参数计算方法。在拐角前后使用S加减速进行加工，以保证直线、圆弧轨迹加工中的平稳;在拐角连接区域内使用基于曲率的速度模型,通过对拐角前后S加减速和拐角速度的连接，使拐角前后的速度更加连续，得到平滑的速度曲线;通过拐角处的加速度和弓高误差的限制，计算平稳的加工速度。结果表明，使用五次PH曲线进行拐角过渡的误差小于7.4 μm，能够满足加工需要,同时，拐角处的向心加速度变化更加平稳。将拐角前后的S加减速和拐角区域内速度连接后，得到了平滑的速度曲线。

Corner Smoothing Using PH Curve for CNC System

To control the normal acceleration in a corner area for machining, a quintic Pythagorean-Hodograph (PH) curve is introduced for corner smoothing. The normal acceleration as well as the velocity of the trajectory is controlled. Parameters for constructing the PH curves are proposed according to the situation of the corner. S-shape velocity profile is used to ensure the speed in line and circle machining. The velocity based on the rate of curvature is presented to meet the shape of the corner. The jerk of the S-shape acceleration is modified at the start and the end of the corner for the connection of speed. The federate in the corner area is controlled by the constraint of acceleration and chord error. The results show that the replacement error of the PH curve in the corner is less than 7.4 μm，which is sufficient to satisfy the requirements for machining. Meanwhile the difference of the normal acceleration is suppressed. A smooth velocity profile is obtained by the connection of the S-shape for the trajectory and the curvature based on the corner.