基于接触区域的球头铣刀颤振稳定域预报方法研究

Research on Prediction Method of Stability Lobe Diagram for Ball-end Mill Based on Engagement

运用半解析法精准搭建出球头铣刀与工件接触区域边界的投影方程,对铣削系统时滞动力学方程进行全离散时域数值求解,在单齿周期内球头铣刀视为圆弧切削的基础上,通过接触区域投影和切削刃投影不同时刻的关系,确定出数值求解方程中所需要的瞬时参与切削刀刃的实际切削部位,利用Floquet定理获得了不同转速下的临界切削深度,构建出了高精度的球头铣刀颤振稳定域叶瓣图,并在三轴数控机床上进行了试验验证,试验结果与预测结果相符合,表明了该方法的正确性。同时,与传统方法相比,这里所提供的方法拥有较高的预测精度,最后分析了不同参数对颤振稳定域的影响规律,为叶瓣图指导实际加工奠定了基础。

The equations for the boundaries of ball-end mill-workpiece engagement(BWE)are precisely established by a semi-analytical method at first.The differential dynamic equation derived from the ideal 2-Dof milling system is solved by the complete discrete method.Based on the cutter within a tooth passing period considered as arc path cutting,the instantaneous cutting positions required in the numerical solution are identified by the relationship of cutter edge and BWE.The stability lobe diagram is constructed by Floquet theory,which is subsequently verified on a three-axis NC machine tool.The experimental results are in good agreement with the predicted results,indicating the validity of this method.In contrast to traditional method,the proposed method shows higher prediction precision.The influence laws of different parameters on stability are analyzed at last,which can give a help for the actual machining.