An Improved Time Domain Simulation for Dynamic Milling at Small Radial Immersions

Abstract

This paper presents an improved milling time domain model to simulate vibratory cutting conditions at very small radial widths of cut. The improved kinematics model allows simulation of very small radial immersions. The model can predict forces, surface finish, and chatter stability, accurately accounting for non-linear effects that are difficult to model analytically. The discretized cutter and workpiece kinematics and dynamic models are used to represent the exact trochoidal motion of the cutter, and to investigate the effects of forced vibrations and changing radial immersion due to deflection and vibrations on chatter stability. Three dimensional surface finish profiles are predicted and are compared to measured results. Stability lobes generated from the time domain simulation are also shown for various cases.

Analytical prediction of chatter stability for variable pitch and variable helix milling tools

“…This simulation used the model described in reference [34], which is a kinematic model of the milling process based upon reference [35] Figure 10. In this case, the semi-discretisation characteristic multipliers indicate a cyclic-fold bifurcation between 4mm and 5mm.…”

The influence of feed rate on process damping in milling: modelling and experiments

“…Their method incorporated the time domain milling model developed by Sutherland [25], which calculates the location of the tool centre at each simulation time step. The chip thickness calculation simplifies the geometry of the cutting kinematics, and so the approach is less accurate than that adopted by Campomanes and Altintas [17]. Although Ranganath's work used a numerical integration routine, no convergence study was mentioned, and in the corresponding thesis [26] the problems of simulating very flexible structures were resolved by including additional damping terms in the model.…”

“…Montgomery and Altintas [16] attempted to include process-damping forces in a model of milling. It seems that this model did not fully consider the surface waviness on the process damping forces, and more recent work by Campomanes and Altintas [17] has focused on developing advanced models of higher speed milling.…”

“…implement a workpiece/tool flank interference model based upon the surface discretization methodology proposed by Campomanes and Altintas [17] and implemented by Sims [29]; . following a convergence study, utilize the model at an appropriately small numerical time step to ensure stable and steady-state predictions of cutting forces and displacements; .…”

Finite Element Analysis of Machining Thin-Wall Parts: Error Prediction and Stability Analysis

“…The stability analysis of the milling system can be performed only by applying approximated numerical methods since there is no closed solution to time-delay differential equation of milling dynamics. Alternatively it can be carried out by means of time-domain simulations [21], in the frequency domain [22] or by applying methods based on delay differential equation theory, such as the semi-discretization method [23] and the time finite element approach (TFEA) [24]. Budak and Tekeli [25] proposed a method to determine the optimal combination of depths of cut, so that chatter free material removal rate is maximized, with application on a pocketing example and significant reduction in the machining time is obtained.…”