径向浸入率通用型铣削稳定性谱元分析法

An Universal Immersion Spectral Element Method for Stability Analysis of Milling Process

铣削稳定性是影响铣削加工效率和精度的关键因素,谱方法和时间有限元法相结合的谱元法是一种快速高效的铣削稳定性分析方法,但小径向浸入率铣削的强不连续性会导致谱元收敛率降低。针对此问题,提出一种径向浸入率通用型铣削稳定性谱元分析方法,该方法将Legendre-Gauss-Lobatto节点高阶谱元与微分方程数值解法相结合提高状态向量离散映射矩阵计算效率,实现了大、小径向浸入率铣削稳定性叶瓣图的高效获取。仿真结果表明,径向浸入率为0.05的铣削工况下,所提方法相较经典谱元法在分析误差不超过1%的前提下,计算时间缩短60%以上,可见所提方法在同等分析精度下显著提高了铣削稳定性分析的效率和通用性,使无颤振切削参数在线优化成为可能。

Stability is a key factor affecting efficiency and precision of milling process.The spectral element method combining the spectral method and the temporal finite element method is an efficient method for milling process stability analysis.However,the strong discontinuity of low immersion milling leads to the decrease of the convergence rate of spectral elements.An universal immersion spectral element method is presented to deal with this problem.It combines the Legendre-Gauss-Lobatto high-order spectral elements with numerical method of integral equations to improve the computational efficiency of state vector discrete dynamic mapping matrix,so that stability lobes diagrams both of high and low immersion can be obtained efficiently.The simulation results show that the simulation time of the proposed method is more than 60%shorter than that of classic spectral element method with the analysis error less than 1%when the low immersion is 0.05.Therefore,universal immersion spectral element method has higher efficiency and universality than classic spectral element method with the same precision,which enables the online optimization of chatter-free milling parameters.