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

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.     

Influence of asymmetric cutting edge roundings on surface topography

For finishing operations in machining, hardened steel hard turning can compete with grinding operations by means of accuracy and productivity. In the past research focussed on the effect of process parameters and tool macro geometry on the resulting surface roughness. Recent investigations show, that the cutting edge micro geometry is an important factor to influence surface quality. The knowledge generated by new methods displays the importance of asymmetric cutting edge roundings on cutting forces, chip formation and tool life. It is known, that chip formation also affects the resulting surface quality. Therefore, this paper investigates the effect of asymmetric cutting edge roundings on the resulting surface roughness in hard turning of roller bearing inner rings. Cutting tests with differently shaped cutting edges and two different feed values are conducted. The resulting surface roughness is measured. The consequent surface quality is explained by geometric coherences between uncut chip thickness and stresses along the cutting edge and the effect of material side flow. It is found, that the cutting edge geometry and the resulting stress distribution around the cutting edge affects the generated surface quality.     

Role of phase transformation in chip segmentation during high speed machining of dual phase titanium alloys

Chip segmentation during machining of titanium alloys is primarily due to adiabatic shear localization associated with thermally driven α–β phase transformation at extremely high speeds. Current constitutive material models used in simulating the machining process ignore the role of phase transformation in shear localization and its influence on the material associated dynamic response. This research presents a new phase approach to chip segmentation that includes a recently developed constitutive material model based on the self-consistent method (SCM) that accounts for material composition, as well as α–β phase transformation, during machining. This SCM-based model is implemented in the finite element framework to validate and predict the effects of starting material property, cutting speeds, uncut chip thicknesses, rake angles, tool radius, and friction coefficients on the strains, temperatures and β volume fractions in chip segmentation. It confirms that cutting speed and uncut chip thickness have great impact, rake angle has less effect, tool radius and friction coefficient have the least effects on chip segmentation. However, tool geometry as well as machining parameters have great influence on the machined surface in terms of temperature magnitude, affected depth and the associated α–β phase transformation.     

Experimental and numerical modelling of the residual stresses induced in orthogonal cutting of AISI 316L steel

Residual stresses in the machined surface layers are affected by the cutting tool, work material, cutting regime parameters (cutting speed, feed and depth of cut) and contact conditions at the tool/chip and tool/workpiece interfaces. In this paper, the effects of tool geometry, tool coating and cutting regime parameters on residual stress distribution in the machined surface and subsurface of AISI 316L steel are experimentally and numerically investigated. In the former case, the X-ray diffraction technique is applied, while in the latter an elastic–viscoplastic FEM formulation is implemented. The results show that residual stresses increase with most of the cutting parameters, including cutting speed, uncut chip thickness and tool cutting edge radius. However, from the range of cutting parameters investigated, uncut chip thickness seems to be the parameter that has the strongest influence on residual stresses. The results also show that sequential cuts tend to increase superficial residual stresses.     

The effect of vibration cutting on minimum cutting thickness

In the ultra-precision diamond cutting process, the rake angle of the tool becomes negative because the edge radius of a tool is considerably larger compared to the sub-micrometer depth of the cut. The effects of plowing due to the large negative rake angle result in an unstable cutting process without continuous chip. For this reason, it is important to determine minimum cutting thickness in order to enable greater machining accuracy to be obtained by fine and stable machining. It was previously reported that the critical depth of cut with a continuous chip was determined by the tool sharpness and the friction coefficient between a workpiece and a tool [S.M. Son, et al., Effects of the friction coefficient on the minimum cutting thickness in micro cutting, International Journal of Machine Tools and Manufacture 45 (2005) 529–535]. For the same edge radius of a tool, the higher the friction coefficient of the tool–workpiece, the thinner the minimum cutting thickness becomes. Therefore, it is believed that increasing the friction coefficient by a physical method would be effective to achieve thinner stable cutting. In this study, the possibility of reducing the minimum cutting thickness was investigated through changing the friction coefficient of a tool–workpiece. The vibration cutting method is applied to increase the friction coefficient. Experimental results show that the cutting technology is efficient for increasing the friction coefficient and decreasing the minimum cutting thickness. The minimum cutting thickness was reduced by about 0.02–0.04 μm depending on materials and vibration conditions.     

Modelling the cutting edge radius size effect for force prediction in micro milling

This paper presents a theoretical model for cutting force prediction in micro milling, taking into account the cutting edge radius size effect, the tool run out and the deviation of the chip flow angle from the inclination angle. A parameterization according to the uncut chip thickness to cutting edge radius ratio is used for the parameters involved in the force calculation. The model was verified by means of cutting force measurements in micro milling. The results show good agreement between predicted and measured forces. It is also demonstrated that the use of the Stabler's rule is a reasonable approximation and that micro end mill run out is effectively compensated by the deflections induced by the cutting forces.     

A finite element modeling approach to predicting white layer formation in nickel superalloys

This paper presents a finite element (FE)-based model to predict critical parameters for the formation of white layer and bent grains in finish-machining of a nickel superalloy. A “piece-wise” Johnson-Cook model was constructed for describing the material flow behavior. Chips predicted and collected during orthogonal turning tests show clear shear banding even under low-speed. The machined surfaces contain a distorted layer with elongated grains. The ratio of edge radius to uncut chip thickness is found to be the most dominant factor in determining the amount of plastic strain in the machined surfaces, which is believed to be the cause for white layer and bent grains in low-speed machining of nickel alloys.     

Modelling the effects of tool-edge radius on residual stresses when orthogonal cutting AISI 316L

Tool-edge geometry has significant effects on the cutting process, as it affects cutting forces, stresses, temperatures, deformation zone, and surface integrity. An Arbitrary-Lagrangian–Eulerian (A.L.E.) finite element model is presented here to simulate the effects of cutting-edge radius on residual stresses (R.S.) when orthogonal dry cutting austenitic stainless steel AISI 316L with continuous chip formation. Four radii were simulated starting with a sharp edge, with a finite radius, and up to a value equal to the uncut chip thickness. Residual stress profiles started with surface tensile stresses then turned to be compressive at about 140 μm from the surface; the same trend was found experimentally. Larger edge radius induced higher R.S. in both the tensile and compressive regions, while it had almost no effect on the thickness of tensile layer and pushed the maximum compressive stresses deeper into the workpiece. A stagnation zone was clearly observed when using non-sharp tools and its size increased with edge radius. The distance between the stagnation-zone tip and the machined surface increased with edge radius, which explained the increase in material plastic deformation, and compressive R.S. when using larger edge radius. Workpiece temperatures increased with edge radius; this is attributed to the increase in friction heat generation as the contact area between the tool edge and workpiece increases. Consequently, higher tensile R.S. were induced in the near-surface layer. The low thermal conductivity of AISI 316L restricted the effect of friction heat to the near-surface layer; therefore, the thickness of tensile layer was not affected.     

Characterization of the transition from ploughing to cutting in micro machining and evaluation of the minimum thickness of cut

When the machining process is miniaturized two process mechanisms, ploughing and chip formation, are essential and a critical cutting thickness needs to be exceeded so that not only ploughing will occur but chips will also be formed. The ploughing effect thereby influences the chip formation process, workpiece surface roughness, burr formation and residual stress state after processing and is therefore of great interest. In order to optimize the machining process a better understanding of the minimum thickness of cut is crucial.The changes in surface topography along the cutting track occurring during machining with a constant feed rate of the cutting tool were analyzed. The influence of the built-up edge phenomena on the micro machining process was investigated for normalized AISI 1045 using confocal white light microscopy and scanning electron microscopy. Furthermore the sin²ψ-method was applied in order to study the residual stress state in the workpiece surface induced by the machining process. Both surface layer properties investigated, surface roughness and residual stresses, show a characteristic transition indicating a change in the dominating process mechanisms. Based on these results a model is developed to determine the minimum thickness of cut. The minimum thickness of cut is found to significantly decrease with higher cutting velocities and to moderately increase with higher cutting edge radii. In addition a propagation of error for the values obtained with the model was performed, proving the quality of the model developed.     

Crack initiation in relation to the tool edge radius and cutting conditions in nanoscale cutting of silicon

In cutting of brittle materials, experimentally it was observed that there is a ductile–brittle transition when the undeformed chip thickness is increased from smaller to larger than the tool cutting edge radius of the zero rake angle. However, how the crack is initiated in the ductile–brittle mode transition as the undeformed chip thickness is increased from smaller to larger than the tool cutting edge radius has not been fully understood. In this study, the crack initiation in the ductile–brittle mode transition as the undeformed chip thickness is increased from smaller to larger than the tool cutting edge radius has been simulated using the Molecular Dynamics (MD) method on nanoscale cutting of monocrystalline silicon with a non-zero edge radius tool, from which, for the first time, a peak deformation zone in the chip formation zone has been found in the transition from ductile mode to brittle mode cutting. The results show that as the undeformed chip thickness is larger than the cutting edge radius, in the chip formation zone there is a peak deformation depth in association with the connecting point of tool edge arc and the rake face, and there is a crack initiation zone in the undeformed workpiece next to the peak deformation zone, in which the material is tensile stressed and the tensile stress is perpendicular to the direction from the connecting point to the peak. As the undeformed chip thickness is smaller than the cutting edge radius, there is no deformation peak in the chip formation zone, and thus there is no crack initiation zone formed in the undeformed workpiece. This finding explains well the ductile–brittle transition as the undeformed chip thickness increases from smaller to larger than the tool cutting edge radius.     

Thermal and mechanical modeling analysis of laser-assisted micro-milling of difficult-to-machine alloys

This study is focused on numerical modeling analysis of laser-assisted micro-milling (LAMM) of difficult-to-machine alloys, such as Ti6Al4V, Inconel 718, and stainless steel AISI 422. Multiple LAMM tests are performed on these materials in side cutting of bulk and fin workpiece configurations with 100-300 μm diameter micro endmills. A 3D transient finite volume prismatic thermal model is used to quantitatively analyse the material temperature increase in the machined chamfer due to laser-assist during the LAMM process. Novel 2D finite element (FE) models are developed in ABAQUS to simulate the continuous chip formation with varying chip thickness with the strain gradient constitutive material models developed for the size effect in micro-milling. The steady-state workpiece and tool cutting temperatures after multiple milling cycles are analysed with a heat transfer model based on the chip formation analysis and the prismatic thermal model predictions. An empirical tool wear model is implemented in the finite element analysis to predict tool wear in the LAMM side cutting process. The FE model results are discussed in chip formation, flow stresses, temperatures and velocity fields to great details, which relate to the surface integrity analysis and built-up edge (BUE) formation in micro-milling.     

An analysis of the surface generation mechanics of the elliptical vibration texturing process

The elliptical vibration texturing process is a vibration assisted machining method for the fast generation of micro structured surfaces. It adds a higher order motion component to the cutting tool that leads to periodic changes in the cutting depth during the machining process. This results in the creation of micro-dimples on the machined surface, whose shape is a function of the tool geometry and trajectory. This paper studies the surface generation mechanics of the elliptical vibration texturing process through experimentation and modeling. A surface generation algorithm is presented for this newly developed process. The model fully describes the motion and the 3D geometry of the cutting tool including its rake face, flank face, and the cutting edge, since all these tool features influence the topography of the generated surface. Since the process takes place in the micro/meso-scale cutting regime, the model includes the minimum chip thickness and elastic recovery effects. The experimental results are shown to validate the simulation model. The simulation model is used to characterize the influences of the process parameters on the texture patterns. The effects of the tool geometry on the process, including the cutting edge radius, are also analyzed.     

Process geometry modeling with cutter runout for milling of curved surfaces

Prediction of cutting forces and machined surface error in peripheral milling of curved geometries is non-trivial due to varying workpiece curvature along tool path. The complexity in this case, arises due to continuously changing process geometry as workpiece curvature varies along tool path. In the presence of cutter runout, the situation is further complicated owing to changing radii of cutting points. The present work attempts to model process geometry in machining of curved geometries and in the presence of cutter runout. A mathematical model computing process geometry parameters which include cutter/workpiece engagements and instantaneous uncut chip thickness in the presence of cutter runout is presented. The developed model is more realistic as it accounts for interaction of cutting tooth trajectory with that of preceding teeth trajectories in computing process geometry. Computer simulation studies carried for this purpose has shown that it is essential to account for teeth trajectory interactions for accurate prediction of process geometry parameters. This aspect is further confirmed with machining experiments, which were conducted to validate this aspect. From the outcomes of present work, it is clearly seen that the computation of process geometry during machining of curved geometries and in presence of cutter runout is not straightforward and requires a systematic approach as presented in this paper.     

Analytical modeling of turn-milling process geometry,kinematics and mechanics

This paper presents an analytical approach for modeling of turn-milling which is a promising cutting process combining two conventional machining operations; turning and milling. This relatively new technology could be an alternative to turning for improved productivity in many applications but especially in cases involving hard-to-machine material or large work diameter. Intermittent nature of the process reduces forces on the workpiece, cutting temperatures and thus tool wear, and helps breaking of chips. The objective of this study is to develop a process model for turn-milling operations. In this article, for the first time, uncut chip geometry and tool–work engagement limits are defined for orthogonal, tangential and co-axial turn-milling operations. A novel analytical turn-milling force model is also developed and verified by experiments. Furthermore, matters related to machined part quality in turn-milling such as cusp height, circularity and circumferential surface roughness are defined and analytical expressions are derived. Proposed models show a good agreement with the experimental data where the error in force calculations is less than 10% for different cutting parameters and less than 3% in machined part quality analysis.     

A model to calibrate and predict forces in machining with honed cutting tools or inserts

This paper describes a mechanistic approach towards modeling the effects on machining forces of the edge hone commonly ground on machining tools and tool inserts. This approach proposes that the ratio of the shearing to ploughing forces would remain identical for tools with different honed radii, machining under identical conditions of chip thickness to edge hone radius ratios and cutting velocity. This concept allows a very simple and new calibration technique toward separating out the effects of tool and machining parameters that influence the force coefficients in machining without a need for any additional parameters. The model has been presently developed for orthogonal cutting and its validation using a tube turning process on gray cast iron with straight edged inserts has shown very promising results. Continued research is being performed to evaluate the applicability of the model for more complex machining operations.     

Effects of the friction coefficient on the minimum cutting thickness in micro cutting

In the ultra precision diamond cutting process, the rake angle of the tool is likely to become negative because the edge radius of tool is considerably large compared to the sub-micrometer depth of cut. The round edge of the tool might sometimes cause plowing results in a poor surface, or burnishing which results in a shiny surface depending on the depth of cut. This study deals with the relationship between the friction of a tool-workpiece and the minimum cutting thickness in micro cutting. Proposed is an ultra precision cutting model in which the tool edge radius and the friction coefficient are the principal factors determining the minimum cutting thickness with a continuous chip. According to the model, a smaller edge radius and a higher friction coefficient make the cutting depth thinner. The experimental results verify the proposed model and provide various supporting evidence.     

Precise prediction of forces in milling circular corners

Pocket corner is the most typical characters of aerospace structure components. To achieve high-quality product and stable machining operation, manufacturer constantly seek to control the cutting forces in pocket corner milling process. This paper presents the cutting force in corner milling considering the precision instantaneous achievements of tool engagement angle and undeformed chip thickness. To achieve the actual milling tool engagement angle in corner milling process, the details of tool–corner engagement relationship are analyzed considering the elements of tool trajectory, tool radius, and corner radius. The actual undeformed chip thicknesses in up and down milling operations are approached on account of the trochoid paths of adjacent teeth by a presented iteration algorithm. Error analysis shows that the presented models of tool engagement angle and undeformed chip thickness have higher precision comparing with the traditional models. Combined with the cutting force coefficients fitted by a series of slot milling tests, the predicted cutting force in milling titanium pocket with different corner structure and milling parameters are achieved, and the prediction accuracy of the model was validated experimentally and the obtained predict and the experiment results were found in good agreement.     

Process simulation using finite element method — prediction of cutting forces, tool stresses and temperatures in high-speed flat end milling

End milling of die/mold steels is a highly demanding operation because of the temperatures and stresses generated on the cutting tool due to high workpiece hardness. Modeling and simulation of cutting processes have the potential for improving cutting tool designs and selecting optimum conditions, especially in advanced applications such as high-speed milling. The main objective of this study was to develop a methodology for simulating the cutting process in flat end milling operation and predicting chip flow, cutting forces, tool stresses and temperatures using finite element analysis (FEA). As an application, machining of P-20 mold steel at 30 HRC hardness using uncoated carbide tooling was investigated. Using the commercially available software DEFORM-2D™, previously developed flow stress data of the workpiece material and friction at the chip–tool contact at high deformation rates and temperatures were used. A modular representation of undeformed chip geometry was used by utilizing plane strain and axisymmetric workpiece deformation models in order to predict chip formation at the primary and secondary cutting edges of the flat end milling insert. Dry machining experiments for slot milling were conducted using single insert flat end mills with a straight cutting edge (i.e. null helix angle). Comparisons of predicted cutting forces with the measured forces showed reasonable agreement and indicate that the tool stresses and temperatures are also predicted with acceptable accuracy. The highest tool temperatures were predicted at the primary cutting edge of the flat end mill insert regardless of cutting conditions. These temperatures increase wear development at the primary cutting edge. However, the highest tool stresses were predicted at the secondary (around corner radius) cutting edge.     

Partitioning of primary shear zone heat in face milling

The outcome of this paper allows calculating the fraction of heat generated in the primary shear zone that is transferred to the workpiece in face milling. The proposed approach is based on a sequentially coupled analysis of the heat partitioning in the cutting edge normal plane and in the reference plane. The latter, for the first time, allows to systematically take into account the removal of heated workpiece material by subsequent cutting tool engagements. The generated heat is related to the uncut chip thickness. Utilizing Weiner's approach, the heat flux density distribution is determined which serves as input for a three-dimensional thermal finite element simulation that is validated experimentally by temperature measurements.     

Study of the mechanism of nanoscale ductile mode cutting of silicon using molecular dynamics simulation

In cutting of brittle materials, it was observed that there is a brittle-ductile transition when two conditions are satisfied. One is that the undeformed chip thickness is smaller than the tool edge radius; the other is that the tool cutting edge radius should be small enough—on a nanoscale. However, the mechanism has not been clearly understood. In this study, the Molecular Dynamics method is employed to model and simulate the nanoscale ductile mode cutting of monocrystalline silicon wafer. From the simulated results, it is found that when the ductile cutting mode is achieved in the cutting process, the thrust force acting on the cutting tool is larger than the cutting force. As the undeformed chip thickness increases, the compressive stress in the cutting zone decreases, giving way to crack propagation in the chip formation zone. As the tool cutting edge radius increases, the shear stress in the workpiece material around the cutting edge decreases down to a lower level, at which the shear stress is insufficient to sustain dislocation emission in the chip formation zone, and crack propagation becomes dominating. Consequently, the chip formation mode changes from ductile to brittle.