A novel Chebyshev-Gauss pseudospectral method for accurate milling stability prediction

摘要

As a major limitation on the process efficiency of the manufacturing industry, milling chatter can be effectively alleviated by the optimal parameter from the stability lobe diagrams. Numerical algorithms based on the equidistant discretization points are usually applied to solve delay differential equations that occurred in the milling dynamics. However, for the presence of the Runge phenomenon, the computational accuracy does not continuously improve with the increase of the approximation order. This paper proposes a novel Chebyshev-Gauss pseudospectral method and implements it in the angle domain for fast and accurate milling stability prediction. The highlights of the proposed method are that the state term in the forced vibration interval of the milling model is approximated with the barycentric Lagrange interpolation with nonuniform Chebyshev-Gauss points, the corresponding derivative term is calculated by an improved Chebyshev-Gauss differential matrix, and then the weighted residual technique with the Clenshaw-Curtis quadrature rule is applied for the first time to minimize the error function. By taking advantage of the above obtained algebraic equations and analytical solution of the free vibration interval, the Floquet transition matrix is constructed, and its critical eigenvalue is utilized for determining the milling stability. Finally, two benchmark milling examples demonstrate that the proposed method achieves the most stable and fastest spectral convergence rate, and brings a great improvement on the computational efficiency and accuracy, compared with the representative methods. Meanwhile, experimental verification in the low-speed and high-speed domains further indicates the applicability of the proposed method.