ORIGINAL ARTICLE 3D coupled Eulerian-Lagrangian finite element analysis of end milling Yifan Gao 1,2 & Jeong Hoon Ko 1 & Heow Pueh Lee 2 Received: 9 January 2018 /Accepted: 4 June 2018 # Springer-Verlag London Ltd., part of Springer Nature 2018 Abstract In this article, a 3D coupled Eulerian-Lagrangian (CEL) finite element method (FEM) model is presented for simulation of end milling processes based on Abaqus/Explicit. In the proposed model, the chip formation process does not rely on the degradation of material or continuous remeshing algorithms to achieve chip separation. The processes under investigation are the slot and shoulder 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, which makes the proposed model compatible for parametric studies. The model demonstrates good accuracy in cutting force predictions. The prediction error of the resultant cutting forces can be controlled within 12% over various milling conditions. 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 which has been compared with the shape of the actual chips collected during machining. Keywords Coupled Eulerian-Lagrangian (CEL) . End milling . Chip morphology 1 Introduction Through the rapid development of high-performance comput- ing technologies, computational methods have been widely adopted to investigate the mechanics and dynamics of metal cutting processes. In metal cutting experiments, information that can be obtained through measurements is very limited, partially due to the fact that measurement of stresses is inher- ently difficult. Experimental evaluation of stresses in orthog- onal cutting has been conducted using composite tool [1] and photoelastic tool [2]. However, for 3D cutting such as a mill- ing process, no experimental method has been proposed for the assessment of stresses. As a powerful and versatile com- putational approach, the finite element method (FEM) has been helping researchers to understand metal cutting process- es beyond the limitations of experimental methods. For the finite element analysis of metal cutting processes, there are three commonly used approaches: Lagrangian, Arbitrary Lagrangian-Eulerian (ALE) and Coupled Eulerian Lagrangian (CEL). The traditional Lagrangian formulation has difficulties in simulating cutting processes with large de- formation. The element distortion caused by the high strain in chip formation process often leads to negative element volume and node penetrations. This approach requires a sacrificial layer and corresponding material failure criterion for chip for- mation since material separation is achieved through the deg- radation of elements. The degradation of elements in Lagrangian formulation leads to a decrease of total mass and stiffness in the workpiece material, which may introduce sig- nificant errors into the simulation process. Most of the existing 3D FEM simulations of milling [3–14] and turning [15–19] processes were conducted in traditional Lagrangian formula- tion. Some were able to make reasonable predictions of the cutting forces, but none were capable of predicting the Highlights 1. A new coupled Eulerian-Lagrangian FEM model is formulated for the accurate prediction of cutting forces as well as chip morphology in the end milling processes. 2. The proposed model does not require material damage model or con- tinuous remeshing for chip formation in the 3D domain. 3. The linear motion of the workpiece makes the model computationally efficient and suitable for parametric studies. * Jeong Hoon Ko jhko@simtech.a-star.edu.sg 1 Singapore Institute of Manufacturing Technology, 73 Nanyang Drive, Singapore 637662, Republic of Singapore 2 National University of Singapore, 9 Engineering Drive 1, Singapore 117575, Republic of Singapore The International Journal of Advanced Manufacturing Technology https://doi.org/10.1007/s00170-018-2284-3