Modelling and simulation of micro-milling cutting forces

The paper presents a new approach for predicting micro-milling cutting forces using the finite element method (FEM). The trajectory of the tool and the uncut chip thickness for different micro-milling parameters (cutting tool radius, feed rate, spindle angular velocity and number of flutes) are determined and used for predicting the cutting forces in micro-milling. The run-out effect is also taken into account. An orthogonal FE model is developed. A number of FE analyses (FEA) are performed at different uncut chip thicknesses (0–20 μm) and velocities (104.7–4723 mm/s) for AISI 4340 steel. Based on the FE results, the relationship between the cutting forces, uncut chip thickness and cutting velocity has been described by a non-linear equation proposed by the authors. The suggested equation describes the ploughing and shearing dominant cutting forces. The micro-milling cutting forces have been determined by using the predicted forces from the orthogonal cutting FE model and the calculated uncut chip thickness. Different feed rates and spindle angular velocities have been investigated and compared with experimentally obtained results. The predicted and the measured forces are in very good agreement.     

An analytical finite element technique for predicting thrust force and torque in drilling

An analytical finite element technique was developed for predicting the thrust force and torque in drilling with twist drills. The approach was based on representing the cutting forces along the cutting lips as a series of oblique sections. Similarly, cutting in the chisel region was treated as orthogonal cutting with different cutting speeds depending on the radial location. For each section, an Eulerian finite element model was used to simulate the cutting forces. The section forces were combined to determine the overall thrust force and drilling torque. Good agreement between the predicted and measured forces and torques was found in orthogonal and oblique cutting and in drilling tests. The drilling tests were performed on AISI 1020 for several drill diameters, spindle speeds, and feed rates. An extension of the technique for predicting drill temperatures has also been described.     

Modeling of turning process cutting forces for grooved tools

A mechanistic modeling approach to predicting cutting forces for grooved tools in turning has been developed. The model assumes the existence of an equivalent orthogonal cutting operation for any oblique operation. The effects of tool nose radius and chip flow have been incorporated by defining a set of equivalent groove parameters. Two calibration methods have been presented for the model. A variety of commercial grooved inserts were chosen to validate the model. The workpiece material used was AISI 1018 steel. The force predictions from the model were found in good agreement with the measured forces. The effects of cutting conditions and groove parameters on the cutting forces and their implication in designing grooved tools were also determined.     

Dynamic response analysis in end milling using pre-twisted beam finite elements

This paper develops an analytical model for estimating the dynamic responses in end milling, i.e. dynamic milling cutter deflections and cutting forces, by using the finite-element method along with an adequate end milling-cutting force model. The whole cutting system includes the spindle, the bearings and the cutter. The spindle is modelled structurally with the Timoshenko-beam element, the milling cutter with the pre-twisted Timoshenko-beam element due to its special geometry, and the bearings with lumped springs and dampers. Because the damping matrix in the resulting finite-element equation of motion for the whole cutting system is not one of proportional damping due to the presence of bearing damping, the state-vector approach and the convolution integral is used to find the solution of the equation of motion. To assure the accuracy of prediction of the dynamic response, the associated cutting force model should be sufficiently precise. Since the dynamic cutting force is proportional to the chip thickness, a quite accurate alogorithm for the calculation of the variation of the chip thickness due to geometry, run-out and spindle-tool viration is developed. A number of dynamic cutting forces and tool deflections obtained from the present model for various cutting conditions are compared with the experimental and analytical results available in the literature, good agreement being demonstrated for these comparisons. The present model is useful, therefore, for the prediction of end milling instability. Also, the tool deflections obtained using the pre-twisted beam element are found to be smaller than those obtained using the straight beam element without pre-twist angle. Hence neglecting the pre-twist angle in the structural model of the milling cutter may overestimate the tool deflections.     

Process modeling in machining. Part II: validation and applications of the determined flow stress data

The flow stress data, determined in Part I of the present study, is validated by using it as an input to the finite element method and analytical based computer programs to predict process variables in metal cutting. The predicted process variables in two-dimensional orthogonal turning and three-dimensional face milling operations, are compared with the published experimental data and the results of experiments conducted in the present work. The majority of the predictions have been found to be in reasonable agreement with the measured results. The comparisons have been discussed and, in the case of unsatisfactory agreement, the reasons for inaccurate predictions are reviewed. The flow stress data of AISI H13 tool steel (46 HRC), determined in Part I is used in this study to investigate the influence of edge preparation on forces in the cutting and feed directions, tool stresses and cutting temperatures. It has been concluded that the hone-radius edge with a hone radius of 0.1 mm provides the maximum resistance to chipping and the chamfered edge (20°×0.1 mm) has the minimum flank and crater wears for the conditions used in the present study.     

Prediction of micro-milling forces with finite element method

This paper presents the prediction of micro-milling forces using cutting force coefficients evaluated from the finite element (FE) simulations. First an FE model of orthogonal micro-cutting with a round cutting edge is developed for Brass 260. The simulated cutting forces are compared against the experimental results obtained from turning tests. The cutting force coefficients are identified from a series of FE simulations at a range of cutting edge radii and chip loads. The identified cutting force coefficients are used to simulate micro-milling forces considering the tool trajectory, run-out and the dynamometer dynamics. The same process is also simulated with a slip-line field based model. FE and slip-line field based simulation results are compared against the experimentally measured turning and micro-milling forces.     

Modelling the Effects of Flank Wear Land and Chip Formation on Residual Stresses

The selection of optimum machining parameters and tool geometry for difficult to cut materials used in aerospace applications is usually controlled by the quality and integrity of the surface produced, the burr formation and the part distortion. In this paper, a finite element model is developed to simulate the effects of tool flank wear and chip formation on residual stress when orthogonal cutting Ti-6AI-4V. A crack propagation module is also developed and incorporated into the finite element solver to accurately simulate the segmental chips produced during machining of titanium. The predicted results emphasize the importance of modelling the chip formation mechanism and tool wear correctly because of their effect on the cutting forces and temperature field. This subsequently influences the magnitude and distributions of the residual stress. Good correlation was obtained between measured and predicted residual stress distribution.     

Analysis on high-speed face-milling of 7075-T6 aluminum using carbide and diamond cutters

This research is concerned with the analytical and experimental study on the high-speed face milling of 7075-T6 aluminum alloys with a single insert fly-cutter. The results are analyzed in terms of cutting forces, chip morphology, and surface integrity of the workpiece machined with carbide and diamond inserts. It is shown that a high cutting speed leads to a high chip flow angle, very low thrust forces and a high shear angle, while producing a thinner chip. Chip morphology studies indicate that shear localization can occur at higher feeds even for 7075-T6, which is known to produce continuous chips. The resultant compressive residual stresses are shown for the variation of cutting parameters and cutting tool material. The analysis of the high-speed cutting process mechanics is presented, based on the calculation results using extended oblique machining theory and finite element simulation.     

FEA modeling and simulation of shear localized chip formation in metal cutting

The finite element analysis (FEA) has been applied to model and simulate the chip formation and the shear localization phenomena in the metal cutting process. The updated Lagrangian formulation of plane strain condition is used in this study. A strain-hardening thermal-softening material model is used to simulate shear localized chip formation. Chip formation, shear banding, cutting forces, effects of tool rake angle on both shear angle and cutting forces, maximum shear stress and plastic strain fields, and distribution of effective stress on tool rake face are predicted by the finite element model. The initiation and extension of shear banding due to material's shear instability are also simulated. FEA was also used to predict and compare materials behaviors and chip formations of different workpiece materials in metal cutting. The predictions of the finite element analysis agreed well with the experimental measurements.     

A new thermomechanical model of cutting applied to turning operations. Part I. Theory

In this paper, an analytical approach is used to model the thermomechanical process of chip formation in a turning operation. In order to study the effects of the cutting edge geometry, it is important to analyse its global and local effects such as the chip flow direction, the cutting forces and the temperature distribution at the rake face. To take into account the real cutting edge geometry, the engaged part in cutting of the rounded nose is decomposed into a set of cutting edge elements. Thus each elementary chip produced by a straight cutting edge element, is obtained from an oblique cutting process. The fact that the local chip flow is imposed by the global chip movement is accounted for by considering appropriate interactions between adjacent chip elements. Consequently, a modified version of the oblique cutting model of Moufki et al. [Int. J. Mech. Sci. 42 (2000) 1205; Int. J. Mach. Tools Manufact. 44 (9) (2004) 971] is developed and applied to each cutting edge element in order to obtain the cutting forces and the temperature distributions along the rake face. The material characteristics such as strain rate sensitivity, strain hardening and thermal softening, the thermomechanical coupling and the inertia effects are taken into account in the modelling. The model can be used to predict the cutting forces, the global chip flow direction, the surface contact between chip and tool and the temperature distribution at the rake face which affects strongly the tool wear. Part II of this work consists in a parametric study where the effects of cutting conditions, cutting edge geometry, and friction at the tool–chip interface are investigated. The tendencies predicted by the model are also compared qualitatively with the experimental trends founded in the literature.     

Predictive cutting force model in complex-shaped end milling based on minimum cutting energy

A force model is presented to predict the cutting forces and the chip flow directions in cuttings with complex-shaped end mills such as ball end mills and roughing end mills. Three-dimensional chip flow in milling is interpreted as a piling up of the orthogonal cuttings in the planes containing the cutting velocities and the chip flow velocities. Because the cutting thickness changes with the rotation angle of the edge in the milling process, the surface profile machined by the previous edge inclines with respect to the cutting direction. The chip flow model is made using the orthogonal cutting data with taking into account the inclination of the pre-machined surface. The chip flow direction is determined so as to minimize the cutting energy, which is the sum of the shear energy on the shear plane and the friction energy on the rake face. Then, the cutting force is predicted for the chip flow model at the minimum cutting energy. The predicted chip flow direction changes not only with the local edge inclination but also with the cutting energy consumed in the shear plane cutting model. The cutting processes with a ball end mill and a roughing end mill are simulated to verify the predicted cutting forces in comparison with the measured cutting forces.     

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.     

Thermomechanical modelling of oblique cutting and experimental validation

An analytical approach is used to model oblique cutting process. The material characteristics such as strain rate sensitivity, strain hardening and thermal softening are considered. The chip formation is supposed to occur mainly by shearing within a thin band called primary shear zone. The analysis is limited to stationary flow and the material flow within the primary shear zone is modelled by using a one-dimensional approach. Thermomechanical coupling and inertia effects are accounted for. The chip flow angle is determined by the assumption that the friction force on the tool face is collinear to the chip flow direction. At the chip–tool interface, the friction condition can be affected by the important heating induced by the large values of pressure and sliding velocity. In spite of the complexity of phenomena governing the friction law in machining, a reasonable assumption is to consider that the mean friction coefficient is primarily function of the average temperature at the tool–chip interface. Comparisons between model predictions and experimental results are performed for different values of cutting speed, undeformed chip thickness, normal cutting angle and inclination angle. A critical study is presented in order to show the influences of the input parameters of the model including the normal shear angle, the thickness of the primary shear zone and the pressure distribution at the tool–chip interface. The model permits to predict the cutting forces, the chip flow direction, the contact length between the chip and the tool and the temperature distribution at the tool–chip interface which has an important effect on tool wear.     

A new thermomechanical model of cutting applied to turning operations. Part II. Parametric study

In Part I of this work, Molinari and Moufki [Int. J. Mach. Tools Manufact., this issue], an analytical model of three-dimensional cutting is developed for turning processes. To analyse the influences of cutting edge geometry on the chip formation process, global effects such as the chip flow direction and the cutting forces, and local effects such as the temperature distribution and the surface contact at the rake face have been investigated. In order to accede to local parameters, the engaged part in cutting of the rounded nose is decomposed into a set of cutting edge elements. Thus each elementary chip, produced by a straight cutting edge element, is obtained from an oblique cutting process defined by the corresponding undeformed chip section and the local cutting angles. The present approach takes into account the fact that for each cutting edge element the local chip flow is imposed by the global chip movement. The material characteristics such as strain rate sensitivity, strain hardening and thermal softening, the thermomechanical coupling and the inertia effects are considered in the modelling. A detailed parametric study is provided in this paper in order to analyse the effects of cutting speed, depth of cut, feed, nose radius and cutting angles on cutting forces, global chip flow direction and temperature distribution at the rake face. The influence of friction at the tool–chip interface is also discussed.     

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.     

Prediction of machining chatter based on FEM simulation of chip formation under dynamic conditions

Machining chatter is an inherently nonlinear phenomenon that is affected by many parameters such as cutting conditions, tool geometry e.g., nose radius and clearance angle and frictional conditions at the tool/workpiece interface. Models for chatter prediction often ignore nonlinearities or introduce them through simple models for friction and geometry. In particular, the effect of chip–tool interaction on the occurrence of chatter is not investigated thoroughly. This paper presents a novel approach for prediction of chatter vibration and for investigation of the effects of various conditions on the onset of chatter. This approach uses finite element simulation to investigate the inter-relationship between the chatter vibration and the chip formation process. Simulation of chip formation is combined with dynamic analysis of machine tool to determine the interaction between the two phenomena. Mesh adaptation technique is used to move the tool inside the workpiece to form the chip, while a flexible tool is used to allow the tool to vibrate under variable loading conditions. By repeating the simulations under various widths of cut, it is shown that the onset of chatter can be detected, and the simulation is able to realistically predict various phenomena observed in actual machining process such as variation of shear angle and the increase of stability at lower speeds known as process damping. The stability map obtained from simulations is compared with experimental data attained through orthogonal cutting tests. Reasonable agreement observed between the two sets of results demonstrates the effectiveness of the simulation approach.     

Modelling of temperature and forces when orthogonally machining hardened steel

This paper initially considers heat generation in single-point metal cutting and the direct/indirect techniques employed to measure cutting temperatures. The development of analytical models of the cutting process is briefly reviewed, including more recent work involving finite element (FE) methods. Details are given of the different FE packages and formulation methods used by different researchers. Following on from this, an FE model is presented using FORGE 2® to simulate cutting forces and temperature distributions when orthogonal turning a hardened hot work die steel, AISI H13 (52HRC), with polycrystalline cubic boron nitride (PCBN) tooling. Experimental data from infrared chip surface temperature measurements and cutting force output are used to validate the model. Good correlation was obtained between experimental and modelled results for temperature; however, the FE analysis underestimated feed force results due to a lack of adequate workpiece property data and simplistic tool/chip friction assumptions.     

An investigation of cutting forces in machining with worn ball-end mill

Reliable tool wear monitoring technique is one of the important aspects for achieving an integrated and self-adjusting manufacturing system. In this study, an analytical model is proposed to estimate the cutting forces, the tool geometry, and the chip geometry in relation to the flank wear, when milling with a ball-end mill. Modeling is based on thermomechanical modelling of oblique cutting. The worn tool geometry is decomposed into a series of axial elementary cutting edges. At any active tooth element, the flank wear geometry is calculated and the chip formation is obtained from an oblique cutting process characterised by local undeformed chip section and local cutting angles. Coated carbide ball-end tool, and a titanium workpiece material have been considered in this paper. The results found by using developed models have shown good agreement with experimental results.     

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.     

Improved modelling of cutting force coefficients in peripheral milling

Titanium is one of the most widely used metals in the aircraft and turbine manufacturing industries. Accurate prediction of cutting forces is important in controlling the dimensional accuracy of thin walled aerospace components. In this paper, a general three-dimensional mechanistic model for peripheral milling processes is presented. The effects of chip thickness, rake angle and cutting geometry on chip flow, rake face friction and pressure, and cutting forces are analyzed. A set of closed form expressions with experimentally estimated cutting force factors are presented for the prediction of cutting forces. The model is verified experimentally in the peripheral milling of a titanium alloy. For a given set of cutting conditions and tool geometry, the model predicts the cutting forces accurately for the chip thickness and rake angle ranges tested.