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中文摘要：
应用3D刀补功能进行五轴端铣加工时，如果某一点处的刀具半径补偿矢量出现奇异解，会导致直线轴控制点在该位置附近发生运动突变。为了准确检测出发生运动突变的位置，从而为进一步解决该类型突变问题提供前提条件，以平底刀为研究对象，在建立切触点与直线轴控制点空间映射关系的基础上，分析了3D刀补中加工奇异点产生的原因；针对奇异点、奇异点相邻点以及奇异区域边界三处会发生运动突变的位置，给出了基于计算刀轴法矢量夹角与观察刀轴姿态主导角符号的检测算法。仿真实验证明了该算法的正确性与有效性。
英文摘要：
In the process of five-axis end milling with a flat-bottomed tool, if the 3D cutter compensation function was adopted, the motion of linear axis control point would be unsteady because there would be singular solution during solving the radius compensation vector. To provide the precondition for solving such problem, it was needed to detect positions where motion mutation will happen. The reason that the singular point generated during 3D cutter compensation was analyzed based on building the relationship between coordinates of the cutter contact point and the linear axis control point. For the singular point, the adjacent points of the singular point and the boundary of the singular area, which were three positions where motion mutation would happen,a detected algorithm was advanced, which was based on calculating the angle between the tool axis vector and the normal vector and observing the symbol of the dominant angle of the tool axis posture. A simulation experiment was performed to verify the correctness and the effectiveness of this algorithm.
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