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.
Highlights
The flutes of technically used milling tools have helix shapes which help to minimize impacts with the workpiece at face value, mitigates chatter and improves machined surface quality.Helix shape plays positive roles in chip evacuation by inducing axial chip motions
It is noteworthy that in a part of the high speed lobes, pc = 1 resulted in the highest convergence, highlighting that the most accurate stability lobe is multi-order in the sense that it should be built from different sub-ranges computed from different combinations of interpolation orders that are most accurate for the sub-ranges
An algorithm based on the arbitrary order full-discretization method and arbitrary order Newton-Coates integral quadrature is developed and implemented for fully automated identification of the stability lobes of multiple delay milling processes with helix effects
Summary
The flutes of technically used milling tools have helix shapes which help to minimize impacts with the workpiece at face value, mitigates chatter and improves machined surface quality. In [11], an adaptation of the first order semi-discretization method was used to identify the stability lobes of non-uniform pitch helix tools, and comparison to the method of [1,7] showed some predictive improvement. The approach in [17] was an adaptation of the first order semi-discretization for non-uniform pitch helix tools which showed a noticeable region of improved prediction relative to the method in [1]. In [21], the combined effect of inter-flute non-uniformities of both pitch and helix angles was investigated with an updated first order semi-discretization method Their results agreed closely with the method of the work [2].
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