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In this article, a 3-dimensional Eulerian finite element method (FEM) model is introduced for simulation of end milling processes based on Abaqus/Explicit. Through the Coupled Eulerian Lagrangian (CEL) approach in model formulation, the chip formation process does not rely on the degradation of material or continuous remeshing algorithms to achieve chip separation. The process under investigation is the slot milling of Al6061-T6. A linear motion of the workpiece is adopted as a simplification of the trochoidal motion of the end mill. The workpiece is given a sinusoidal profile to achieve a varying uncut chip thickness in the cutting process. With a stationary tool and a confined region of mesh refinement, the computational cost of the model can be minimized. The model demonstrates good accuracy in cutting force predictions. The prediction error of the resultant cutting forces can be controlled within 12%. The proposed model also gives accurate predictions in terms of the morphology of chips. The excessive curling of chips in the early stages of chip formation can be predicted in the simulation process. The information obtained from the FEM model will provide more insights into the interactions between the cutting tool and the workpiece.

In this article, the dynamic modelling of machining process for high aspect ratio workpiece is presented considering the tool-workpiece compliance. The geometric surface of high aspect ratio workpiece is digitized and the dynamic interaction between cutting tool and workpiece is calculated in time domain. The transfer function from both cutting tool and workpiece is integrated with directional coefficients derived from forces and dynamic uncut chip thickness equations. The integrated time domain model considers three directional vibrations with consideration of workpiece and tooling vibration modes. Since workpiece movement continuously changes the dynamic uncut chip thickness in conjunction with tool movement, the workpiece surface nodes need to be continually updated for the prediction of the regenerative chatter. Especially the small diameter of workpiece may cause the dynamic shift in conjunction with cutting conditions. Traditional frequency domain models with simplified directional coefficients have limitations in the prediction of machining stability for high aspect ratio workpiece due to the nonlinear factors in directional coefficients. Finally, the predictions from the time domain model are compared with the experimental results.

This paper proposes a surface generation model based on a fast and comprehensive time domain solution which simulates regenerative vibrations as well as an interaction of cross edge and flank profiles with the undulation of machined surface. Depending on the profiles of the cutter geometry, the damping forces affect the stability of the milling processes which results in variations of the machined surface profile even under the same cutting conditions. By simulating dynamic cutter center affected by shearing and damping forces, runout, and feed motions, the time-dependent angular positions of the edge profiles can be precisely located, which are used to calculate the dynamic uncut chip thickness and the intersection area of the edge profiles against the surface undulation. As the cutting edges interacts with the machined surfaces, the positions of the edges are extracted and connected to form machined surface profiles. The simulated surface profiles are compared with the experimental ones by considering the damping effect depending on the cross edge and flank profiles.

This article introduces a time domain model of side and plunge milling stability by considering cutting edge radius as well as dynamic motion of cutter center. Dynamic uncut chip thickness generated by side, plunge and ultrasonic milling can be simulated by tracking the cutter center positions at the present and previous vibrations with phase difference. Finally, the dynamic uncut chip thickness models as well as the mechanistic cutting force coefficients considering cutting edge radius are integrated into the time domain model. Especially, cross edge radius varies due to tool wear which affects cutting force coefficients and dynamics as well. Finally, the machining stability and vibrations are estimated using an identified transfer function and predicted cutting forces through the time domain solution. Experimental tests are compared against predicted results for validation of the proposed model.