Stability prediction for milling process with multiple delays using an improved semi‐discretization method

Abstract

Communicated by I. StratisMilling chatter leads to a poor surface finish, premature tool wear, and potential damage to the machine or tool. Thus, it is desirable to predict and avoid the onset of this instability. Considering that the stability of milling with variable pitch cutter or tool runout case is characterized by multiple delays, in this paper, an improved semi-discretization method is proposed to predict the stability lobes for milling processes with multiple delays. Taking the variable pitch milling, for example, a comparison with prior methods is conducted to verify the accuracy and efficiency of the proposed approach for the stability prediction both in low and high radial immersion ratios. In addition, the rate of convergence of the proposed method is also evaluated. The results show that the proposed method has high computational efficiency.

Stability Analysis of Milling Process with Variable Spindle Speed and Pitch Angle considering Helix Angle and Process Phase Difference

“…Obviously, each region corresponds to different calculation methods of the upper and lower limits of integration in equation (2). Here, function G(ϕ j ) is introduced instead of the original g(ϕ j ), and the unified calculation models for the upper and lower limits of integration; that is, ϕ ej (t) � min(ϕ j (t, 0), ϕ e ) and ϕ sj (t) � max(ϕ j (t, a p ), ϕ s ) are utilized (for more details, see [17,18]). en, equation (2) can be transformed into…”

“…In this case, the modulation in chip thickness caused by a nonuniform pitch can reduce the vibration under disturbance. Aiming at predicting the stability of milling process with VPC, frequency-domain model [12,13], the Cluster Treatment of Characteristic Roots [14], unified SDM [15], improved FDM [16,17], and improved SDM [18] have been proposed successively. Furthermore, Sims et al [19], Sims [20], Dombovari and Stepan [21], and Jin et al [22,23] proposed efficient methods to predict the stability for VPC and variable helix cutter, while Yusoff and Sims [24] optimized the geometry of variable helix tool to suppress regenerative chatter.…”

Dynamic milling stability prediction of thin-walled components based on VPC and VSS combined method

“…Using the finite element analysis method [25] and the multiple delays semi-discretization method presented in Ref. [26][27][28][29][30], the milling stability of cutter-workpiece system by VPC and VSS can be obtained. The new SLD was obtained as the computational flow of SLD shown in Fig.…”

A Method for Stability Analysis of Periodic Delay Differential Equations with Multiple Time-Periodic Delays

“…Bayly et al [19] carried out a temporal finite element analysis for solving the DDEs, which are written in 2 Mathematical Problems in Engineering the form of a state space model and discretizing the time interval of interest into a finite number of temporal elements. Based on the direct integration scheme, Ding et al [20], Liu et al [21], and Jin et al [22] used a full-discretization method to gain stability chart efficiently. Recently, Khasawneh and Mann [23] and Lehotzky et al [24] presented a numerical algorithm called spectral element method.…”