Stability Analysis of Multi-Discrete Delay Milling with Helix Effects Using a General Order Full-Discretization Method Updated with a Generalized Integral Quadrature

Abstract

A tensor-based general order full-discretization method is enhanced with the capacity to handle multiple discrete delays and helix effects leading to a unique automated algorithm in the stability analysis of milling process chatter. The automated algorithm is then exploited in investigating the effects of interpolation order of chatter states and helix-induced terms on the convergence of milling stability lobes. The enhanced capacity to handle the distributed helix effects is based on a general order formulation of the Newton-Coates integral quadrature method. Application to benchmark milling models showed that high order methods are necessary for convergence of the low speed domain of stability lobes while all the numerically stable orders converge in the high speed domain where the ultra-high order methods are prone to numerical instability. Also, composite numerical integration of the helix-induced integrand beyond the usual zero-th order method leads to higher accuracy of stability lobes especially in the low speed domain.