Wu Yi, Deng Bin, Zhao Qinghua, Ye Tuo, Liu Anmin, Jiang Wenbo
School of Intelligent Manufacturing and Mechanical Engineering, Hunan Institute of Technology, Hengyang 421002, China.
Hunan Meibeida Technology Co., Ltd., Leiyang 421800, China.
Micromachines (Basel). 2025 Aug 29;16(9):997. doi: 10.3390/mi16090997.
Regenerative chatter is an unfavorable phenomenon that severely affects machining efficiency and surface finish in milling operations. The prediction of chatter stability is an important way to obtain the stable cutting zone. Based on implicit multistep schemes, this paper presents the third-order and fourth-order implicit exponentially fitted methods (3rd IEM and 4th IEM) for milling stability prediction. To begin with, the delay differential equations (DDEs) with time-periodic coefficients are employed to describe the milling dynamics models, and the principal period of the coefficient matrix is firstly decomposed into two different subintervals according to the cutting state. Subsequently, the fourth-step and fifth-step implicit exponential fitting schemes are applied to more accurately estimate the state term. Two benchmark milling models are utilized to illustrate the effectiveness and advantages of the high-order implicit exponentially fitted methods by making comparisons with the three typical existing methods. Under different radial immersion conditions, the numerical results demonstrate that the 3rd IEM and the 4th IEM exhibit both faster convergence rates and higher prediction accuracy than the other three existing prediction methods, without much loss of computational efficiency. Finally, in order to verify the feasibility of the 3rd IEM and the 4th IEM, a series of experimental verifications are conducted using a computer numerical control machining center. It is clearly visible that the stability boundaries predicted by the 3rd IEM and the 4th IEM are mostly consistent with the cutting test results, which indicates that the proposed high-order exponentially fitted methods achieve significantly better prediction performance for actual milling processes.
再生颤振是一种不利现象，严重影响铣削加工的效率和表面光洁度。颤振稳定性预测是获得稳定切削区域的重要途径。基于隐式多步法，本文提出了用于铣削稳定性预测的三阶和四阶隐式指数拟合方法（3rd IEM和4th IEM）。首先，采用具有时间周期系数的延迟微分方程（DDEs）来描述铣削动力学模型，并根据切削状态将系数矩阵的主周期首先分解为两个不同的子区间。随后，应用第四步和第五步隐式指数拟合方案来更准确地估计状态项。通过与三种典型的现有方法进行比较，利用两个基准铣削模型来说明高阶隐式指数拟合方法的有效性和优势。在不同的径向切入条件下，数值结果表明，与其他三种现有预测方法相比，3rd IEM和4th IEM具有更快的收敛速度和更高的预测精度，且计算效率损失不大。最后，为了验证3rd IEM和4th IEM的可行性，使用计算机数控加工中心进行了一系列实验验证。可以清楚地看到，3rd IEM和4th IEM预测的稳定性边界大多与切削试验结果一致，这表明所提出的高阶指数拟合方法在实际铣削过程中具有显著更好的预测性能。
