International Journal of Machine Tools & Manufacture 48 (2008) 1–14 Modelling and analysis of micro scale milling considering size effect, micro cutter edge radius and minimum chip thickness Xinmin Lai a, , Hongtao Li a , Chengfeng Li a , Zhongqin Lin a , Jun Ni b a State Key laboratory of Vibration, Shock and Noise, Shanghai Jiaotong University, Shanghai 200030, China b Shien-Ming Wu Manufacturing Research Center, University of Michigan, MI 48109, USA Received 7 April 2007; received in revised form 2 August 2007; accepted 8 August 2007 Available online 22 August 2007 Abstract This paper presents mechanisms studies of micro scale milling operation focusing on its characteristics, size effect, micro cutter edge radius and minimum chip thickness. Firstly, a modified Johnson–Cook constitutive equation is formulated to model the material strengthening behaviours at micron level using strain gradient plasticity. A finite element model for micro scale orthogonal machining process is developed considering the material strengthening behaviours, micro cutter edge radius and fracture behaviour of the work material. Then, an analytical micro scale milling force model is developed based on the FE simulations using the cutting principles and the slip-line theory. Extensive experiments of OFHC copper micro scale milling using 0.1 mm diameter micro tool were performed with miniaturized machine tool, and good agreements were achieved between the predicted and the experimental results. Finally, chip formation and size effect of micro scale milling are investigated using the proposed model, and the effects of material strengthening behaviours and minimum chip thickness are discussed as well. Some research findings can be drawn: (1) from the chip formation studies, minimum chip thickness is proposed to be 0.25 times of cutter edge radius for OFHC copper when rake angle is 101 and the cutting edge radius is 2 mm; (2) material strengthening behaviours are found to be the main cause of the size effect of micro scale machining, and the proposed constitutive equation can be used to explain it accurately. (3) That the specific shear energy increases greatly when the uncut chip thickness is smaller than minimum chip thickness is due to the ploughing phenomenon and the accumulation of the actual chip thickness. r 2007 Elsevier Ltd. All rights reserved. Keywords: Micro scale milling process; Size effect; Minimum chip thickness; Cutter edge radius; Strain gradient 1. Introduction Recent years, the production of miniaturized compo- nents with complex small features is gaining increasing importance due to the trend of miniaturization which is determining the development of products for various industries, such as biomedical instruments, electronic products, defence industry and so on. Most of these components fall into the scales from 10 mm to 1 mm known as micro/meso scale in mechanical engineering. Considered as one of the most effective techniques, micro scale milling process can be used to fabricate these components with complex micro features over a wide range of material types. However, further advances in both the efficiency and the quality are limited by the incomplete understanding of its basic mechanisms. To satisfy the increasing need of miniaturized manufacturing, the mechanisms studies are becoming more and more important. Micro scale milling is not simply downsized from the conventional operation but has its own characteristics, such as size effect, cutter edge radius and minimum chip thickness. Shaw [1] studied the effect of round edges on the chip formation in micro scale machining and stated that the plastic deformations would be prevented when the cutter edge radius is relatively larger than the uncut chip thickness. Kim [2] investigated the effect of static tool deflection on the micro milling and proposed a static chip model based on the attainable micro scale machining force data. Ni [3] investigated the chip formation using molecule ARTICLE IN PRESS www.elsevier.com/locate/ijmactool 0890-6955/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmachtools.2007.08.011 Corresponding author. E-mail address: xmlai@sjtu.edu.cn (X. Lai).