List of Symbols
2.6 Numerical Modeling and Simulation of SPDT Process
35 was developed by using experimental data to predict the surface roughness. It was found that best surface roughness can be obtained on silicon was 31.6 nm at feed rate of 2.5 μm/rev, depth of cut of 1.5 μm and spindle speed of 1500 rpm.
Observations:
Surface roughness, an important product quality parameter affects several functional attributes of SPDT products viz. friction, wear, lubrication, light reflection/refraction, corrosion resistance. Theoretically, in case of the cutting process (turning or facing), the surface finish mainly depends on the tool nose radius and the feed rate. However, in reality, it depends upon the process parameters, tool geometry, workpiece and cutting tool interaction, workpiece and tool material properties, tool wear, cutting environment. As the surface roughness is measured after the completion of the machining operation, it is time-consuming and labor-intensive. Moreover, the SPDT process is slow as the volume of material removal is in micron or nanometric scale. Thus, carrying out extensive trials to optimize the process to obtain the desired surface finish is time-consuming. Literature reports that most of the works have been used either experimental or theoretical way to investigate the surface quality for SPDT process. There is hardly any attempt reported on modeling of surface roughness by using FEM simulations of SPDT process.
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nanometric machining. These include crystallographic orientation effects on plastic deformation, tool edge radius and minimum depth of cut effects on the chip formation mechanism, phase transition, effects of defect structure in the workpiece material, and diamond tool wear.
Figure 2.13 Dimensional comparisons of macro, FEM and MD simulations
Shimada and Ikawa (1992) presented MD simulations of nanometric chip removal process in micro-cutting of copper. In this study, the chip morphologies, cutting forces and specific energy were predicted and found in good agreement with experiments. Komanduri et al. (2000) studied the effects of crystal orientation, cutting direction and positive rake angle on nanometric cutting of single crystal aluminum. It was observed that the cutting forces vary cyclically with the orientation of the crystal and the direction of cutting. It was also noted that the cutting force decreases with the increase in the rake angle. Figure 2.14 shows the MD model used to simulate ultra-precision cutting of single crystal aluminum.
Figure 2.14 Schematic of the model used in the MD simulation of nanometric cutting of single crystal aluminum [Komanduri et al. (2000)]
90mm
15mm 2.5mm
2m
1m
300nm
Finite Element Method
Macro to nano scale Molecular dynamics
Nano to Angstrom scale Macro to micro scale
Macro cutting
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37 Further, Komanduri et al. (2001) carried out MD simulation on silicon using the Tersoff potential by varying the rake angle, width of cut, depth of cut and clearance angle and studied the nature of material removal and surface generation in ultra-precision machining and grinding. During the study, it was observed that four different material removal mechanisms exist viz. compression of the work material ahead of the tool; chip formation akin to an extrusion-like process; side flow; and subsurface deformation in the machined surface. Inamura et al. (1997) presented computer simulations of machining of silicon by using renormalized molecular dynamics (RMD) to investigate the crack initiation process.
The results showed that silicon can be machined in ductile mode under absolute vacuum medium; however it exhibits brittle-ductile transition depending on the scale of machining under normal atmosphere. Cai et al. (2007a) conducted physical experiments as well as MD simulations of nanometric machining of silicon wafer to study the mechanism of ductile chip formation. It was concluded that the plastic deformation occurred due to phase transformation rather than atomic dislocation. Similarly, Komanduri and Raff (2001), Oluwajobi (2012), Goel et al. (2015), Guo et al. (2016) and Abdulkadir et al. (2018) contributed significant knowledge by carrying out molecular dynamics (MD) based simulations and have laid a sound foundation for the study of nanometric cutting processes using MD simulation. Goel and his team reported extensive work on numerical simulations of nanometric machining of silicon and silicon carbide using MD simulation. Authors studied atomistic aspects of ductile response of SiC [Goel et al. (2011)], effect of temperature and crystal orientation on tool wear [Goel et al. (2012a, 2012b, 2013a)], brittle to ductile transition of SiC [Goel et al. (2013b)]
and effect of the microstructure on cutting behavior of silicon [Goel et al. (2016)]. Figure 2.15 shows the typical MD model developed by Goel et al. (2011) to simulate the SPDT process.
Figure 2.15 Schematic of MD simulation [Goel et al. (2011)]
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It was seen that the MD method successfully simulate the mechanism of nano cutting of brittle materials. However, the method has a limitation that it can be applied to a very small size of process continuum, i.e., several millions of atoms or even less. The time scales are in the order of picoseconds. As the results are available at atomistic scale, these are difficult to compare with the experimental data [Goel et al. (2017)] and apply in general, real-life process conditions of SPDT.
FEM is very widely used to model and simulate the machining processes from macro to nano level. It predicts the cutting forces, stresses, strains and temperatures. During FEM based modeling, the effects of large deformation; strain rate effect; tool-chip contacts and friction; local heating and temperature effect can easily be incorporated. In this method, various boundary and loading conditions such as thermal, structural, electrical, magnetic can be defined and complex physical interaction of tool and workpiece can be simulated.
Literature reports eminent studies on analysis of chip morphologies, cutting forces, temperature, stresses and strains and other output variables. Literature reports tremendous works on finite element based macro-micro cutting simulations of metals [Davim et al. (2008, 2009), Jagadesh & Samuel (2015, 2017)]. Yan et al. (2007) studied the effect of hydrostatic pressure and temperature in ductile machining of silicon using finite element simulation. It was demonstrated that the high pressure is the dominant reason for ductile machining of silicon rather than the high temperature. Subsequently, Yan et al. (2009a) simulated SPDT of silicon using FEM method and demonstrated that increase in the cutting edge radius causes decrease in the cut chip thickness and a corresponding increase in the thrust force. Lowering the cutting edge radius (below 200 nm) shifts the high temperature zone from the tool rake face to the tool flank face resulting in the transition of the wear pattern from crater to flank wear. Similarly, Patten et al. (2005, 2007, 2008) and Patten and Jacob (2008) simulated SPDT of single crystal 6H-SiC by employing a Drucker-Prager (pressure sensitive) yield criterion in a commercially available FEM package. Authors investigated the effect of rake angle and depth of cut on machining forces to study the ductile to brittle transition. It was found that the cutting forces agreed well with experimental results only under ductile-regime machining conditions. It is because the model did not include fracture criterion or brittle material removal mechanisms. Figure 2.16 depicts the FEM simulation model of SiC showing pressure developed at the cutting region.
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39 Figure 2.16 FEM simulation results of SPDT of SiC for 0º rake, 5º clearance [Patten and
Jacob (2008)]
Mir et al. (2017) carried out numerical simulation of surface defect machining (SDM) of silicon using Smooth particle hydrodynamics (SPH). Pressure sensitive Drucker-Prager yield criterion was employed to model the material behavior of silicon. It was found that SDM approach offers reduction in the cutting resistance of the material and thus reduces the requirement of cutting energy. Consequently, it reduces the diamond tool wear and improves the surface finish. Figure 2.17 depicts the SPH model employed to simulate SDM of silicon.
The von-Mises stress developed during SDM is slightly lower than that without incorporating SDM.
Figure 2.17 SPH simulations with or without SDM [Mir et al. (2017)]
Observations:
Analysis of machining forces and surface roughness is important in view of the analysis of process efficiency and product quality of ultra-precision machining process. Till date, significant experimental works have been reported on understanding of the cutting TH-2306_10610325
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mechanism and chip formation during machining of silicon and silicon carbide. However, as the machining scale enters from micro to nano regime, it is interesting to study the force, pressure, stress, and roughness during the cutting process. Numerical simulation regarded as a simple, efficient and computationally inexpensive method to study the complex nanometric cutting process of brittle materials. Significant numerical studies have been reported on molecular dynamics (MD) based simulations of SPDT. These were focused on the study of stress, chips formation, temperature, crystallographic effect, phase transformation during the ultra-precision cutting operation. However, experimental validation of these studies is difficult due to its very small, i.e., atomic level study domain. Few attempts have been reported on numerical simulations using finite element method. To the best knowledge; no literature has been reported on the study of the influence of material model during numerical simulation of SPDT process of brittle material. Selection of proper material model is essential in obtaining accurate results.