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

Abstract

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 fulldiscretization 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.

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

“…The helix-induced integrand h j (t, z) is then interpolated with general order polynomial tensors according to Equations ( 23) to (25). The integration is implemented to give the general order Newton-Coates integral quadrature method…”

“…It is proposed to generalize and automatize the four steps for chatter stability analysis of non-uniform pitch tools subjected to helix effects in order to avoid case by case manual analysis/re-analysis, and to allow easy investigation of the effect of interpolation orders of the states and helix-induced integrand on stability lobes accuracy. The methods in [23,24] provided the framework for the first least squares based attempt in [25] on partial generalization of monodromy matrix of the full-discretization methods for arbitrary order approximation of the current state (linear approximation was maintained on the delayed state thus the reference to the method as partial generalization). A complete generalization for the single delay milling model without helix effects was attained in [26] using polynomial tensor representation of cutting states.…”

Intelligent manufacturing/production systems: Modeling, algorithms, and optimization

“…The proposed approach demonstrates the strength of applying machine learning to standardized processes, such as quality control. Ozoegwu 9 addresses the problem of chatter in process of milling. The research provides a novel method for reducing this through better approximation of the process itself and thus better ability to control the process.…”