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考虑铣刀螺旋角的影响,将刀齿的切削过程划分为连续,切入和切出3个过程,建立了高速铣削系统的动力学模型。运用半离散估计技术,将无限维特征值稳定性判定问题转化为有限维Floquet变换矩阵特征乘子稳定性判定问题,判定了系统的稳定性,获得了系统的稳定性极限图。结果显示,在考虑刀具螺旋角影响的情况下,铣削系统稳定性极限较传统情况有所增大,出现了类似“岛”的结构,其位置由轴向切削深度和螺旋齿距的关系决定,且由于切削刀齿切入、切出过程的影响,“岛”不是孤立的,而是有稳定性“桥”连接。理论结果通过铣削实验进行了验证。
Considering the influence of cutter helix angle, the cutter cutting process is divided into three steps: continuous, cut in and cut out. The dynamic model of high speed milling system is established. By using semi-discrete estimation technique, the problem of judging the stability of infinite dimensional eigenvalue is transformed into the problem of multiplicitor stability of the finite-dimensional Floquet transform matrix. The stability of the system is judged and the stability limit of the system is obtained. The results show that the stability of the milling system increases more than the traditional one, considering the influence of the helix angle of the cutter, and the similar “island” structure appears. The position of the milling system depends on the relation between the axial depth of cut and the helical pitch The decision, and because of the cutting edge of the cutter, the effect of the cut-out process, the “island” is not isolated but has a stability “bridge” connection. The theoretical results are verified by milling experiments.