基于精细积分全离散法的变齿距铣削稳定性研究

Stability Prediction of Milling With Variable Pitch Cutter Using Precise Integration-Based Full-Discretization Method

变齿距铣刀铣削作为一种有效的颤振抑制方法,受到了国内外学术界和工业界的广泛关注。针对变齿距引发的系统多时滞问题,提出了一种适用于变齿距铣削稳定性高效预测的精细积分全离散法。基于再生颤振原理,构建了考虑螺旋角的变齿距铣削动力学时滞微分方程。对时滞微分方程中的状态项与时滞项进行线性插值,构建状态传递矩阵,然后基于Floquet理论,获得系统的稳定性叶瓣图。在稳定性预测过程中,运用精细积分算法,避免了求解矩阵指数时的求逆运算,有效提升了计算效率。改进半离散法的对比及时域仿真试验表明,该方法具有更高的预测精度和计算效率。

The effectiveness of variable pitch cutter in suppressing chatter vibrations during milling has received extensive attention.An efficient precise integration-based full-discretization method is proposed for predicting stability of milling process with multiple delays that arise from variable pitch angle.The dynamic model of milling process considering helix angle is constructed and the state term and time delay term are approximated by linear interpolation method.Then,the stability lobe diagrams are obtained based on Floquet theory.In the process of stability prediction,the precise integration algorithm is used to avoid the inverse operation when solving the exponential matrix,which effectively improves the calculation efficiency.Finally,it shows that the proposed method is more efficient and accurate to predict the stability compared with the updated semi-discretization method.