A full-discretization method for prediction of milling stability

Reducing computational requirement of stability analysis of milling by partial averaging

“…Only slight deviation is seen to be caused by PA at low spindle speed. The more striking thing to note is that results of FTRMPA and PTRMPA are almost identical with the result of Full-discretization by Ding et al [1]. This suggests that PA is strongly applicable to the Full-discretization as verified in the next section.…”

“…The latter is demonstrated to be more accurate and more time conserving in stability analysis of milling process (both one and two degree of freedom systems were considered) and delayed damped Mathieu equation. With all other things being equal the results of stability analysis of fully-immersed milling process using FTRMPA and PTRMPA are seen to be identical with those of full-discretization by Ding et al [1] further validating the presented reformulation. PA is applied on the Second Order Least Squares Approximated Full-discretization method of [18] to illustrate its usefulness for reducing the cumbersome analysis and CT of the full-discretization method when analysis gets more complicated by higher order interpolation/ approximation theory.…”

“…The semi-discretization method basically involves discretization of the delayed term while leaving the undelayed terms undiscretized and approximating the periodic coefficient matrices as piecewise constant functions. Ding et al [1] subsequently extended the discretization scheme to the periodic coefficient matrices and the associated state terms to develop the so-called full-discretization method. The full-discretization method turned out to be slightly less accurate than semi-discretization method of same order [9,10] but it is as incisive in revealing various stability features of milling.…”

“…An ingenious application of the Hermite interpolation theory by Liu et al [12] has led to a full-discretization method with further improvements in accuracy and CT. Least squares approximated first and second order full-discretization methods have been introduced in [18] to save considerable amount of CT of the original full-discretization methods in the works [1,10]. The basic interest in this work is to introduce a simplification called Partial Averaging (PA) that further reduces computational cost from the perspectives of amount of analysis involved and CT without loss of accuracy.…”

Operational stability prediction in milling based on impact tests

“…Some of them apply the measured frequency response functions (FRFs) directly, such as the zero-order approximation (ZOA) [3], the multi-frequency solution (MFS) [4] or the extended multi-frequency solution (EMFS) [5]. Other techniques, such as the semidiscretization method [6], the full-discretization method [7], the integration method [8] and their extension by the implicit subspace iteration method [9], the Chebyshev collocation method [10,11], the spectral element method [12] and the temporal finite element analysis [13,14], require fitted modal parameters as input.…”