Micro-milling of fused silica based on instantaneous chip thickness

Abstract

The micro-milling process of brittle materials involves macro-scale tool and nano-scale cracks. This multi-scale coupling problem makes it difficult to accurately predict the milling morphology using conventional methods. In this paper, a novel method is proposed to predict the milled surface quality of brittle materials by the combined method of analytical model and finite element method (FEM) simulation. In the proposed method, the chip thickness model for inclined ball end mills was established. Thus, the multi-scale coupling milling process of fused silica was discretized into several nano-scale local cutting processes to accurately calculate the crack. The chip thickness, as the dominant factor to influence cracks of brittle materials, not only can be used to solve the multi-scale coupling problem, but can predict the crack distribution on the milling groves. In this paper, an instantaneous chip thickness model for inclined ball end mills was established. Then, the chip thickness and cutting force under different tool inclination angles were analyzed. Next, the chip thickness of serial characteristic positions were used as the cutting depth, and the nano-scale local simulations was carried out at several characteristic positions on the cross section of the milled grooves. At last, the milling experiments were carried out under different inclination angles and feed rates to verify the effectiveness of the proposed method. Besides, the collapse phenomenon on the upper surface and side surface was observed and discussed.

Introduction

Micro-fluidics chips, optical elements and Micro-TAS are widely used components made from fused silica which have micro structures with fine surface quality. In recent years, micro-milling has been widely applied to manufacturing these components due to its high machining efficiency, accurate removal amount and flexible machining ability. However, the milling of fused silica and other brittle materials still faces many challenges.

In the past decades, extensive research has been conducted on the machining of brittle materials. Moriwaki et al. (1992) realized the ductile cutting of soda-lime glass by applying ultrasonic vibration to a single crystal diamond tool. The grooving experiment indicated that the surface roughness could reach 30 nm by diamond turning. Ogura and Okazaki (2000) carried out turning experiment on BK7 glass and verified that damage-free surface could be obtained using 1 μm cutting depth in methanol and ethanol atmosphere. Shirakashi and Obikawa (2003) investigated the ductile regime machining of soda-lime glass and aluminum oxide ceramic. They concluded that ductile regime machining could also be realized if the chip thickness of brittle materials was small enough. The above research shows the possibility of glass processing in a ductile regime. In recent years, Fang et al. (2003) found that critical cutting depth (d_c) was the key parameter in silica machining process and its value was usually smaller than 1 μm. Abu Al-Rub (2007) analyzed the deformation of brittle materials in nanoindentation. They found that the material would be removed in ductile regime when the deformed regime was in the same magnitude with cutting edge. Ono and Matsumura (2008) investigated the micro-milling process of fused silica, and found that the tool inclined along feed direction could prominently improve the surface quality, but did not adequately explain the mechanism. Muhammad and Mustafizur (2012) established an analytical model to determine the critical feed in the milling process of brittle materials, which could be used to predict the transition from brittle regime to ductile regime. Ito et al. (2017) researched the micro milling of fused silica by selective laser-assisted, which further expanded the ductile regime and realized the ductile machining of fused silica. Niu et al. (2018) carried out experimental research on the dynamics of micro-milling. They quantitatively assessed the size effect, minimum chip thickness and their integral effect against the chip formation process. Xiao et al. (2015) researched the brittle-ductile transition of KDP crystal in micro milling process. The experimental results showed that the high spindle speed could effectively expand the ductile depth of the KDP material. In summary, although many researchers have conducted lots of research on the machining of brittle materials, they focused on the experimental method to verify its feasibility and explore its processing parameters. Yet, rare researched carried out on developing an effective model or method to predict and guide the milling process of brittle materials.

All of the above researches show that chip thickness is a key parameter in brittle material machining. If chip thickness is larger than critical thickness, materials will be removed in brittle regime with fracture appearance, if not, materials will be removed in ductile regime with continuous form. Therefore, chip thickness is an effective factor for predicting the milled surface quality of brittle materials. Bao (2000) developed a force model based on the chip thickness in micro-milling. The model could better predict micro-milling process compared with the simplified model for conventional milling. Li et al. (2001) developed a chip thickness model through calculated the intersection point of the path curve and the line passing through the current tool tip and tool axis. Zhu et al. (2001) established a force model that incorporated chip thickness, to predict the cutting force in the ball end milling process of free-form surfaces. Although these thickness models of micro-milling have been experimentally verified by Mamedov and Lazoglu (2016), they focused more on deriving the milling force of metal material through a simple chip thickness model which could not accurately characterize the real milling process. Therefore, it is urgently needed to develop a precise chip thickness model for inclined ball end mills in the micro-milling research of brittle materials.

Numerical simulation is an effective method to calculate crack propagation in brittle materials on micro-scale. Tanaka et al. (2007) investigated the requirements for defect-free machining based on deformation analysis of mono-crystalline silicon by molecular dynamics simulation, they found that crack growth can be avoided by the stable shearing under a compressive stress field. Yan et al. (2009) carried out FEM simulation research on submicron-scale cutting process of silicon used J-C model, investigated the effects of tool edge radius on cutting force, cutting stress, temperature and chip formation. Li (2013) simulated the single grain cutting of optical glass using JH-2 model. The simulation results of crack propagation were consistent with the nano-scratch results. Duan et al. (2013) carried out dynamic simulation on single grain cutting by FEM-SPH coupled algorithm, and obtained higher convergence of crack simulation. Mir et al. (2017) simulated the effect of rake angle in turning process of silicon used SPH method, they found that the material removal using positive rake angle tools was in the form of cracks rather than continuous chips. Zhang et al. (2019) carried out simulation on the diamond turning process using SPH and FEM method, they investigated the effect of tool rake angle in diamond turning of KDP crystal. Guo et al. (2020) researched the relationship between grinding depth and grinding force of K9 glass, the simulation results obtained by using SPH method were consistent with the experiments. The previous research shows the effectiveness of numerical simulation in the cutting process of brittle materials. However, as crack often occurs on the submicro scale, numerical simulation has poor performance in a global-scale milling process. In this paper, a combined method of analytical model and FEM simulation will be proposed to predict the surface quality of micro milled fused silica.