A general order full-discretization algorithm for chatter avoidance in milling

Based on the full-discretization method, this work presents a generalized monodromy matrix as an exact function of the order of polynomial approximation of the milling state for chatter avoidance algorithm. In other words, the computational process is made smarter since the usual derivation of the monodromy matrices on order-by-order basis – a huge analytical involvement that rapidly gets heavier with a rise in the order of approximation – is bypassed. This is the highest possible level of generalization that seems to be the first of its kind among the time-domain methods as the known generalizations are limited to the interpolating/approximating polynomial of the milling state. It then became convenient in this work to study the stability of milling process up to the tenth order. More reliable methods of the rate of convergence analysis were suggested and utilized in consolidating the known result that the best accuracy of the full-discretization method lies with the third and fourth order. It is seen from numerical convergence analyses that, although accuracy most often decreases with rising order beyond the third-order methods, the trend did not persist with a continued rise in order.