Modelling and analysis of micro scale milling considering size effect, micro cutter edge radius and minimum chip thickness

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 10° and the cutting edge radius is 2 μm; (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.

Introduction

Recent years, the production of miniaturized components 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 μm 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 dynamic (MD) simulations and presented an approach to calculate the minimum chip thickness by identifying a local maximum in the radial thrust forces in the micro milling. Vogler [4] determined the minimum chip thickness for steel using finite element (FE) simulations with regard of the microstructure properties of work material. According to their research, the critical chip thickness is 0.2 and 0.3 times of the edge radius for pearlite and ferrite, respectively. In addition, several analytical cutting force models ([5], [22], [23], [26]) had been developed to investigate the micro scale machining process. Chae [6] surveyed the state of art of micro scale machining and reported that current researches had made valuable attempts in this field though most of them were carried out by means of nano-level and macro-level approaches. From the discussions above, it is obviously that the processing system for micro scale milling is far from established. Its characteristics need to be studied and the related mechanisms need to be revealed through experiments and theoretical modelling.

One of the most significant characteristics of the micro scale milling operation is the size effect. Some efforts have been carried out to explain it. Lucca [7] investigated the size effect of cutting energy of micro scale machining process through the experiments; they found nonlinear increase in specific cutting energy or cutting forces as the uncut chip thickness was decreased. Kopalinsky and Oxley [8] studied the size effect with sharp tools by turning tests. They concluded that the cause was the decrease in the tool chip interface temperature. Nakayama and Tamura [9] analyzed the size effect through experiments performed at a very low cutting speed to minimize the temperature and strain rate effects. They attributed this effect to plastic flow in the workpiece subsurface. The experiments of the literature (Oxley, [8]; Nakayama, [9]) implied that there should be other underlying mechanisms for the size effect besides cutter edge radius, temperatures and strain rate. On the other hand, a similar size effect in micro indentation tests was found in the mechanics studies, which was shown as remarkable material strengthening behaviours at the micron level.

Fleck [10] found that the torsion strengthened three times when the diameter of the sample was decreased from 170 to 12 μm. Stolken and Evans [11] found the similar trend in bending material tests. The bending strength increased significantly when the thickness of thin beam was decreased from 100 to 12.5 μm. This size effect in material properties has turned to be the focus of mechanics research recent years. Strain gradient (SG) plasticity is the most effective method to interpret this phenomenon. Fleck [12] developed SG theory by introducing the material inner variable. Then, Nix and Gao [13] improved it by describing the concept of inner variable and mechanism-based strain gradient (MSG) theory was developed. From this point, it is supposed that there might be some similarities between the two size effect phenomena. The size effect of material behaviours may be the cause of size effect in micro scale machining. Melkote [14] attempted to analyze the size effect using SG plasticity based on analytical solutions. The results showed that it is capable of explaining the size effect. However, this model could not consider many other characteristics of micro scale machining process, such as large strain, high strain rate, cutter edge radius, minimum chip thickness and so on. Therefore, further studies are needed and more precise FE models should be developed.

The goal of this research is to provide deeper understanding of micro scale milling process. Firstly, a modified Johnson–Cook (JC) constitutive equation is formulated using SG plasticity. A FE model for micro scale orthogonal machining process is developed considering material strengthening behaviours, tool geometry and fracture behaviour. Then, a milling force model is developed based on the FE simulations using the cutting principles and slip-line theory. Finally, chip formation and size effect of micro scale milling are investigated by applying the model, and the effects of the main characteristics of micro scale process, size effect of material behaviours, micro mill cutter radius and minimum chip thickness are discussed as well. The results demonstrate that the proposed approach for micro scale milling is capable of the analysis of micro scale milling process and provides the academic foundation for further process design and optimization studies.