Abstract Chatter frequently occurs during cutting operations, which seriously restricts the machining productivity and workpiece accuracy. Consequently, accurate and efficient stability prediction is of great significance to determine stable machining parameters. A cubic Hermite–Newton approximation method which can determine the chatter stability boundaries more efficiently is presented in this paper. The milling dynamic system can be expressed as time-periodic delay differential equations (DDEs) with consideration of the regeneration effect. A typical benchmark example is provided to assess the convergence feature and stability lobes of the cubic Hermite–Newton approximation method and several existing methods. The results indicate that the cubic Hermite–Newton approximation method can achieve satisfactory results. For the sake of developing the cubic Hermite–Newton approximation method with higher convergence rate and computational efficiency, the tooth-passing period is further separated into two distinct phases according to whether the value of coefficient matrix equals to zero. Meanwhile, the linear interpolation polynomial is used to predict milling stability, and then piecewise polynomial interpolation was utilized in two adjacent time intervals to correct this prediction. By adopting the two benchmark examples, the effectiveness of the two new methods can be analyzed using existing methods. The results demonstrate that the two new methods have superior accuracy and efficiency.

中文翻译：

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基于分段多项式插值的铣削稳定性预测新预测校正方法

摘要 切削加工过程中经常发生颤振，严重制约了加工生产率和工件精度。因此，准确高效的稳定性预测对于确定稳定的加工参数具有重要意义。本文提出了一种可以更有效地确定颤振稳定性边界的三次 Hermite-Newton 近似方法。考虑到再生效应，铣削动力系统可以表示为时间周期延迟微分方程（DDE）。提供了一个典型的基准示例来评估三次 Hermite-Newton 近似方法和几种现有方法的收敛特征和稳定性波瓣。结果表明，三次 Hermite-Newton 近似方法可以获得满意的结果。为了开发具有更高收敛速度和计算效率的三次 Hermite-Newton 近似方法，根据系数矩阵的值是否为零，将过齿周期进一步分为两个不同的阶段。同时，利用线性插补多项式来预测铣削稳定性，然后在相邻的两个时间间隔内利用分段多项式插值来修正这一预测。通过采用两个基准示例，可以使用现有方法分析两种新方法的有效性。结果表明，这两种新方法具有优越的准确性和效率。根据系数矩阵的值是否为零，将过齿周期进一步分为两个不同的阶段。同时，利用线性插补多项式来预测铣削稳定性，然后在相邻的两个时间间隔内利用分段多项式插值来修正这一预测。通过采用两个基准示例，可以使用现有方法分析两种新方法的有效性。结果表明，这两种新方法具有优越的准确性和效率。根据系数矩阵的值是否为零，将过齿周期进一步分为两个不同的阶段。同时，利用线性插补多项式来预测铣削稳定性，然后在相邻的两个时间间隔内利用分段多项式插值来修正这一预测。通过采用两个基准示例，可以使用现有方法分析两种新方法的有效性。结果表明，这两种新方法具有优越的准确性和效率。可以使用现有方法分析这两种新方法的有效性。结果表明，这两种新方法具有优越的准确性和效率。可以使用现有方法分析这两种新方法的有效性。结果表明，这两种新方法具有优越的准确性和效率。