Micro-end-milling of single-crystal silicon

Ductile-regime machining of silicon using micro-end-mill is almost impossible because of the brittle properties of silicon, crystal orientation effects, edge radius of the cutter and the hardness of tool materials. Micro-end-milling can potentially be used to create desired three dimensional (3D) free form surface features using the ductile machining technology for single-crystal silicon. There is still a lack of fundamental understanding of micro-end-milling of single-crystal silicon using diamond-coated tool, specifically basic understanding of material removal mechanism, cutting forces and machined surface integrity in micro-scale machining of silicon. In this paper, further research to understand the chip formation mechanism was conducted. An analysis was performed to discover how the chips are removed during the milling process. Brittle and ductile cutting regimes corresponding to machined surfaces and chips are discussed. Experiments have shown that single-crystal silicon can be ductile machined using micro-end-milling process. Forces generated when micro-end-milling single-crystal silicon are used to determine the performance of the milling process. Experimental results show that the dependence of the cutting force on the uncut chip thickness can be well described by a polynomial function order n. As cutting regime becomes more brittle, the cutting force has more complex function.     

Feed rate scheduling model considering transverse rupture strength of a tool for 3D ball-end milling

This paper presents an analytical model of off-line feed rate scheduling to determine desired feed rates for 3D ball-end milling. Off-line feed rate scheduling is presented as the advanced technology to regulate cutting forces through change of feed per tooth, which directly affects variation of uncut chip thickness. In this paper, the uncut chip thickness is calculated by following the movement of the position of the cutter center, which is determined by runout and cutter deflection. Also, since the developed cutting force model uses the cutting-condition-independent coefficients, off-line feed rate scheduling can be effectively performed regardless of continuous change of cutting conditions. Transverse rupture strength of the tool is used to determine the reference cutting force at which resultant cutting forces are regulated through feed rate scheduling. Experiments validated that the presented feed rate scheduling model reduced machining time drastically and regulated cutting forces at the reference cutting force.     

Accurate 3-D cutting force prediction using cutting condition independent coefficients in end milling

The instantaneous uncut chip thickness and specific cutting forces have a significant effect on predictions of cutting force. This paper presents a systematic method for determining the coefficients in a three-dimensional mechanistic cutting force model—the cutting force coefficients (two specific cutting forces, chip flow angle) and runout parameters. Some existing models have taken the approach that the cutting force coefficients vary as a function of cutting conditions or cutter rotation angle. This paper, however, considers that the coefficients are affected only by the uncut chip thickness. The instantaneous uncut chip thickness is estimated by following the movement of the position of the center of a cutter. To consider the size effect, the present method derives the relationship between the re-scaled uncut chip thickness and the normal specific cutting force, K_n with respect to the cutter rotation angle, while the other two coefficients—frictional specific cutting force, K_f and chip flow angle, θ_c—remain constant. Subsequently, all the coefficients can be obtained, irrespective of cutting conditions. The proposed method was verified experimentally for a wide range of cutting conditions, and gave significantly better predictions of cutting forces.     

New procedures for calibration of instantaneous cutting force coefficients and cutter runout parameters in peripheral milling

In this paper, new procedures are proposed to calibrate the instantaneous cutting force coefficients and the cutter runout parameters for peripheral milling. By combining with optimization algorithm, i.e., the Nelder–Mead simplex method, detailed calibration schemes are derived for a mechanistic cutting force model in which the cutting force coefficients are described as the exponential functions of the instantaneous uncut chip thickness. Three different cutter runout models are considered in the calculation of instantaneous uncut chip thickness. Only one or two tests are required to perform the calibration. Experimental verifications are also conducted to validate the proposed procedures, and the results show that they are efficient and reliable. To see the effect of different runout models on milling process, comparisons among the predicted results under a wide range of cutting parameters are made to study the consistency and limitations of different models. It is found that the radial cutter runout model is a recommendable one for cutting force modelling.     

Phase width analysis of cutting forces considering bottom edge cutting and cutter runout calibration in flat end milling of titanium alloy

This paper is concerned with the combined cutting effects of both flank and bottom edges based on a systematic study of the cutting force in flat end milling of the titanium alloy. Besides the flank edge, the bottom edge of the cutter is also found to be an important factor influencing the cutting force distributions and can lead to uniform phase widths for non-zero cutting forces even under considerable cutter runout. One such phenomenon of uniform phase width induced by the bottom edge for the cutting force is deeply revealed. To do this, the models for characterizing the cutting force coefficients related to both edges are established based on the measured instantaneous cutting forces, and cutter runout is considered in the computation of process geometry parameters such as cutter/workpiece engagements and instantaneous uncut chip geometry parameters. Novel algorithms for identifying the cutter runout parameters and the bottom uncut chip width are also developed. Results definitely show that the flank cutting force coefficients can be treated as constants and that size effect obviously exists in the bottom cutting force coefficients that can be characterized by a power function of the bottom uncut chip width.The proposed model is validated through a comparative study with the existing model and experiments. From the outcomes of the current work, it is clearly seen that the prediction of cutting forces for titanium alloy can resort to the proposed model instead of traditional ones.     

Effect of tilt angle on cutting regime transition in glass micromilling

Recent development in mechanical micromachining technology has increased the realization of micromachining as a feasible manufacturing process of micro-scale components including glass-based devices. It has been found that glass can be machined in a ductile regime under certain controlled cutting configurations. However, favorable ductile regime machining instead of brittle regime machining in micromilling of brittle glass is still not fully understood as a function of cutting configuration. In this study, the effect of tilt angle along the feed direction on cutting regime transition has been studied in micromilling crown glass with a micro-ball end mill. Straight glass grooves were machined in water bath by varying the tool tilt angle and the feed rate, and the resulting surface was characterized using the scanning electron microscope and the profilometer to investigate the glass cutting regime transition. In characterizing the cutting regimes in glass micromilling, rubbing, ductile machining, and brittle machining regimes are hypothesized according to the undeformed chip thickness. It is found that a crack-free glass surface can be better machined in the ductile mode using a 45° tilt angle and feed rates up to 0.32 mm/min. During each milling pass, surface roughness was found to decrease from the entry zone to the groove bottom and then increase to the exit zone regardless of the cutting regime.     

Effect of cutter runout on process geometry and forces in peripheral milling of curved surfaces with variable curvature

This paper presents a novel method for cutting force modeling related to peripheral milling of curved surfaces including the effect of cutter runout, which often changes the rotation radii of cutting points. Emphasis is put on how to efficiently incorporate the continuously changing workpiece geometry along the tool path into the calculation procedure of tool position, feed direction, instantaneous uncut chip thickness (IUCT) and entry/exit angles, which are required in the calculation of cutting force. Mathematical models are derived in detail to calculate these process parameters in occurrence of cutter runout. On the basis of developed models, some key techniques related to the prediction of the instantaneous cutting forces in peripheral milling of curved surfaces are suggested together with a whole simulation procedure. Experiments are performed to verify the predicted cutting forces; meanwhile, the efficiency of the proposed method is highlighted by a comparative study of the existing method taken from the literature.     

A unified instantaneous cutting force model for flat end mills with variable geometries

A new and unified instantaneous cutting force model is developed to predict cutting forces for flat end mills with variable geometries. This model can routinely and efficiently determine the cutting properties such as shear stress, shear and normal friction angles (SSSNFAs) involved in the cutting force coefficients by means of only a few milling tests rather than existing abundant orthogonal turning tests. Novel algorithms are developed to characterize these properties using following steps: transformation of cutting forces measured in Cartesian coordinate system into a local system on the normal plane, establishment of explicit equations to bridge SSSNFAs and the transformed cutting forces, determination of SSSNFAs by solving the equations and fitting SSSNFAs as functions of process geometries. Results definitely show that shear stress can be treated as a constant whereas shear and normal friction angles should be characterized by Weibull functions of instantaneous uncut chip thickness. Experiments verify that the proposed unified model is effective to predict the cutting forces in flat end milling in spite of cutter geometries and cutting conditions.     

Molecular dynamics modelling of brittle–ductile cutting mode transition: Case study on silicon carbide

The mechanism of brittle–ductile cutting mode transition has received much attention over the past two decades. Due to the difficulties in directly observing the cutting zone during the brittle–ductile cutting mode transition by experimental techniques, many molecular dynamics (MD) studies have been conducted to investigate the atomicscale details of the phenomena, e.g. phase transformation, stress distribution and crack initiation, mostly under nanoscale undeformed chip thicknesses. A research gap is that direct MD modelling of the transition under practical undeformed chip thicknesses was not achieved in previous studies, due to the limitations in both computation capability and interaction potential. Important details of the transition under practical undeformed chip thicknesses thereby remain unclear, e.g. the location of crack formation and the stress distribution. In this study, parallel MD codes based on graphics processing units (GPU) are developed to enable large-scale MD simulations with multi-million atoms. In addition, an advanced interaction potential which reproduces brittle fracture much more accurately is adopted. As a result, the direct MD simulation of brittle–ductile cutting mode transition is realised for the first time under practical undeformed chip thicknesses. The MD-modelled critical undeformed chip thickness is verified by a plunge cutting experiment. The MD modelling shows that tensile stress exists around the cutting zone and increases with undeformed chip thickness, which finally induces brittle fractures. The location of crack formation and direction of propagation varies with undeformed chip thickness in the MD simulations, which agrees with the surface morphologies of the taper groove produced by the plunge cutting experiment. This study contributes significantly to the understanding of the details involved in the brittle–ductile cutting mode transition.     

Numerical simulation and prediction of cutting forces in five-axis milling processes with cutter run-out

Radial cutter runout is a common issue in milling processes and has a direct effect on milling stability due to variations of resulting chip load and forces. This paper presents a new method to effectively model and predict the instantaneous cutting forces in 5-axis milling processes with radial cutter runout based on tool motion analysis. First, the undeformed chip thickness model taking runout effect into account is established under continuous change of cutter axis orientation by means of the sweep traces of cutter edges. Second, the engaged cutting edge is determined and cutting coefficients are subsequently calibrated. Finally, the method of identifying runout parameters from the measured cutting forces is proposed, and mechanistic method is then applied to predict the cutting force. Since this method is completely based on the relative motion analysis of tool-part, it can reduce the prediction errors of cutting forces effectively and is suitable for generic rotation cutters. Several validation examples are given under different cutting conditions to prove its effectiveness and accuracy. The results reveal that the developed method can predict the cutter forces with a high accuracy and has the ability to be used in simulations and optimizations of five-axis machining.     

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.     

A More Realistic Cutting Force Model at Uncut Chip Thickness Close to Zero

The relevance of the results of many machining simulations depends on the quality of the cutting force model used. Most of the cutting force models raise problems for uncut chip thickness close to zero. It is mainly due to the management of strong discontinuity and the infinitive limit of the cutting stiffness when the uncut chip thickness goes to zero. Furthermore, the correlation of these models with the experimental results is not very good at low and high uncut chip thickness. To resolve these difficulties, a new model of cutting force is proposed. It gets the advantage to be a continuous law with a finished limit of cutting stiffness when the uncut chip thickness goes to zero. The validation of this model with experimental results in milling and drilling shows a good correlation for a large variation of uncut chip thickness.     

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.     

Systematic study on cutting force modelling methods for peripheral milling

This paper systematically studies the cutting force modelling methods in peripheral milling process in the presence of cutter runout. Emphasis is put on how to efficiently calibrate the cutting force coefficients and cutter runout. Mathematical derivations and implementation procedures are carried out based on the measured cutting force or its harmonics from Fourier transformation. Five methods are presented in detail. In the first three methods the cutting force coefficients are assumed to be constants whereas in the last two they are taken as functions of instantaneous uncut chip thickness. The first method and the fifth one are taken from literatures for comparison. The second, the third and the fourth methods are original contributions, which are carried out with optimization ideas. The second method proceeds using the first and Nkth harmonic forces as the source signal while the third and the fourth are derived based on the measured cutting forces and its first harmonics. The engagement of the cutter with the workpiece is considered in these three new calibration procedures without the requirement of a prior knowledge of the actual cutter runout. Comparisons among the calibrated results from different methods are made to study the limitations and consistency of the presented methods. Experiments are also conducted to show the prediction ability of all methods.     

Development of a virtual machining system, part 2: prediction and analysis of a machined surface error

In part 2 of this three-part paper, a newly developed method that predicts the three-dimensional machined surface errors generated during the peripheral end milling process is presented. From the cutting force prediction system of Part 1, since the uncut chip thickness is calculated by tracing the movement of the cutter, the positions at which the cutting edges pass over the workpiece surface can readily be obtained. In this part of the paper these positions are used to construct surface error maps. In addition, by using the estimated locations of the peak and valley values of the cutting force component normal to the machined surface, a quantitative analysis of the machined surface error is given and followed by theoretical explanations. A series of machining tests on aluminum workpieces were conducted to validate the effectiveness of the model. The predicted cutting forces and surface errors were found in good agreement with their measured counterparts.     

Simulation of cutting process in peripheral milling by predictive cutting force model based on minimum cutting energy

The cutting force and the chip flow direction in peripheral milling are predicted by a predictive force model based on the minimum cutting energy. The chip flow model in milling is made by piling up the orthogonal cuttings in the planes containing the cutting velocities and the chip flow velocities. The cutting edges are divided into discrete segments and the shear plane cutting models are made on the segments in the chip flow model. In the peripheral milling, the shear plane in the cutting model cannot be completely made when the cutting point is near the workpiece surface. When the shear plane is restricted by the workpiece surface, the cutting energy is estimated taking into account the restricted length of the shear plane. The chip flow angle is determined so as to minimize the cutting energy. Then, the cutting force is predicted in the determined chip flow model corresponding to the workpiece shape. The cutting processes in the traverse and the contour millings are simulated as practical operations and the predicted cutting forces verified in comparison with the measured ones. Because the presented model determines the chip flow angle based on the cutting energy, the change in the chip flow angle can be predicted with the cutting model.     

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.     

The prediction of cutting forces in the ball-end milling process—II. Cut geometry analysis and model verification

This paper presents a model for the prediction of cutting forces in the ball-end milling process. The steps used in developing the force model are based on the mechanistic principles of metal cutting. The cutting forces are calculated on the basis of the engaged cut geometry, the underformed chip thickness distribution along the cutting edges, and the empirical relationships that relate the cutting forces to the undeformed chip geometry. A simplified cutter runout model, which characterizes the effect of cutter axis offset and tilt on the undeformed chip geometry, has been formulated. A model building procedure based on experimentally measured average forces and the associated runout data is developed to identify the numerical values of the empirical model parameters for the particular workpiece/cutter combination.     

An in-depth analysis of the synchronization between the measured and predicted cutting forces for developing instantaneous milling force model

This paper proposes an analytical approach to synchronize the measured and predicted cutting forces for calibrating instantaneous cutting force coefficients that vary with the instantaneous uncut chip thickness in general end milling. Essential issues such as the synchronization criterion, phase determination of measured cutting forces, specification of calibration experiments and related cutting parameters are highlighted both theoretically and numerically to ensure the calibration accuracy. A closed-form criterion is established to select cutting parameters ensuring the single tooth engagement. Numerical cutting simulations and experimental test results are compared to validate the proposed approach.     

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.