Prediction and experimental validation of micro-milling cutting forces of AISI H13 steel at hardness between 35 and 60 HRC

This paper presents prediction and validation of micro-milling cutting forces of AISI H13 steel at hardnesses between 35 and 60 HRC. The cutting forces are predicted based on an approach considering the full kinematics of the cutting tool including the run-out effect, effects of the cutting velocity and tool geometry, ploughing and chip formation phenomena and the hardness of the AISI H13 steel. A plane strain dynamic thermo-mechanical finite element (FE) model of orthogonal cutting is used to predict the cutting forces where the geometry of the cutting tool edge is modelled based on scanning electron microscope measurements. A constitutive elastic–plastic isotropic material model describing the relationship between stresses, strains, strain rates and hardnesses is modelled and implemented into ABAQUS/Explicit FE code by the user-defined subroutine VUMAT. Finite element analyses (FEA) are employed to obtain the relationship between cutting forces, uncut chip thickness, cutting velocity and material hardness. Numerous FEA are performed at different uncut chip thicknesses (0–20?μm), cutting velocities (104.7–4,723?mm/s) and hardnesses (35–60 HRC) using the FE model of orthogonal cutting. The full kinematics of the cutting tool including the run-out effect and the FE-predicted cutting forces are incorporated to predict the micro-milling cutting forces. The predicted micro-milling cutting forces have been experimentally validated at hardness of 43.2 HRC at different feed rates and spindle speeds. The result showed that the cutting forces and cutting temperatures increase by increasing the hardness of the AISI H13 while the stability limits of the process decrease by increasing the hardness.     

Finite element simulation of high-speed machining of titanium alloy (Ti�C6Al�C4V) based on ductile failure model

A Johnson?CCook material model with an energy-based ductile failure criterion is developed in titanium alloy (Ti?C6Al?C4V) high-speed machining finite element analysis (FEA). Furthermore, a simulation procedure is proposed to simulate different high-speed cutting processes with the same failure parameter (i.e., density of failure energy). With this finite element (FE) model, a series of FEAs for titanium alloy in extremely high-speed machining (HSM) is carried out to compare with experimental results, including chip morphology and cutting force. In addition, the chip morphology and cutting force variation trends under different cutting conditions are also analyzed. Using this FE model, the ductile failure parameter is modified for one time, afterword, the same failure parameter is applied to other conditions with a key modification. The predicted chip morphologies and cutting forces show good agreement with experimental results, proving that this ductile failure criterion is appropriate for titanium alloy in extremely HSM. Moreover, a series of relatively low cutting speed experiments (within the range of HSM) were carried out to further validate the FE model. The predicted chip morphology and cutting forces agree well with the experimental results. Moreover, the plastic flow trend along an adiabatic shear band is also analyzed.     

Chatter and dynamic cutting force prediction in high-speed ball end milling

Machine tool chatter is a serious problem which deteriorates surface quality of machined parts and increases tool wear, noise, and even causes tool failure. In the present paper, machine tool chatter has been studied and a stability lobe diagram (SLD) has been developed for a two degrees of freedom system to identify stable and unstable zones using zeroth order approximation method. A dynamic cutting force model has been modeled in tangential and radial directions using regenerative uncut chip thickness. Uncut chip thickness has been modeled using trochoidal path traced by the cutting edge of the tool. Dynamic cutting force coefficients have been determined based on the average force method. Several experiments have been performed at different feed rates and axial depths of cut to determine the dynamic cutting force coefficients and have been used for predicting SLD. Several other experiments have been performed to validate the feasibility and effectiveness of the developed SLD. It is found that the proposed method is quite efficient in predicting the SLD. The cutting forces in stable and unstable cutting zone are in well agreement with the experimental cutting forces.     

Dynamic cutting force modeling and experimental study of industrial robotic boring

In this paper, a new approach based on industrial robotic boring is proposed to solve problems associated with intersection holes during aircraft assembly. A model is established to predict the dynamic cutting force of a robotic machining system. The robot stiffness coupling, chip deformation, and plowing interference affecting the cutting force are considered using the principles of cutting mechanics and the Oxley orthogonal cutting model. By solving a numerical solution of motion differential equation, the cutting force components in the radial, tangential, and feed directions are obtained by the model. In addition, an advanced curve intersection method is developed to identify the instantaneous uncut chip area and cutting edge contact length. Verification tests were performed on an ABB-IRB6600-175/2.55 robot for titanium alloy TC4 to determine the accuracy of the predictions. The results show that the simulated and measured cutting forces were in good agreement under different cutting conditions. By analyzing simulated and experimental results, we show that the model can be applied to predict the occurrence of vibration and has application value in terms of suppressing vibration during robotic boring.     

Thermomechanical modeling of oblique turning in relation to tool-nose radius

This article aims at predicting machining performances for oblique turning in relation to tool-nose radius. A new geometric analysis for the uncut chip area is proposed as function of depth of cut, feed rate, tool-nose radius, and edge direction angle. Cutting edge is discretized into increments and average uncut chip thickness, elementary direction angle and elementary depth of cut are determined for each one. A new thermomechanical model is developed for each increment which is supposed to be an oblique machining with single cutting edge. The predicted cutting force components are in good agreement with experimental data over a wide range of cutting conditions. In particular, the effect of tool-nose radius and cutting parameters on chip geometry, cutting temperature, and cutting force components are studied. It is underlined that tool-nose radius promotes the increase in radial force, however, its influence on the other parameters is negligible.     

Development and experimental validation of a mechanistic model of cutting forces in micro- ball end milling of full slots

In the present work, a mechanistic model of cutting forces is developed with a novel approach to arrive at the cutting edge geometry as well as the cutting mechanics. The geometry of cutting elements derived and verified using a virtual tool generated in CAD environment is considered. The cutting and edge force coefficients at every discrete point on the cutting edge of micro-ball end mill are established in a novel way from the basic metal cutting principles and fundamental properties of materials, considering edge radius and material strengthening effects. Further, measured edge radius is used in the model. Full slot micro-ball end milling experiments are conducted on a high-precision high-speed machining center using a 0.4 mm diameter tungsten carbide tool and cutting forces are measured using a high-sensitive piezo-electric dynamometer. It is established that the predicted as well as experimental cutting forces are higher at very low uncut chip thickness in comparison with the cutting edge radius in micro-ball end milling also. Amplitudes of cutting forces and instantaneous values with incremental rotation of the tool are compared with predicted values over two revolutions for validation of proposed model.     

An Improved Method for the Determination of 3D Cutting Force Coefficients and Runout Parameters in End Milling

A simple improved method is suggested for determining constant cutting force coefficients, irrespective of the cutting condition and cutter rotation angle. This can be achieved through the combination of experimentally deternimed cutting forces with those from simulation, performed by a mechanistic cutting force model and a geometric uncut chip thickness model. Additionally, this study presents an approach that estimates runout-related parameters, and the runout offset and its location angle, using only one measurement of cutting force. This method of estimating 3D end milling force coefficients was experimentally verified for a wide range of cutting conditions, and gave significantly better predictions of cutting forces than any other methods. The estimated value of the runout offset also agreed well with the measured value.     

径向跳动对球面铣刀切削力的影响研究

研究了径向跳动对刀齿的实际切削半径、切屑形状以及切屑厚度的影响机理。研究了各刀齿沿刀刃螺旋线的切削微元实际切削半径的数学表示和变化规律,实际切削半径的变化改变了刀齿的切削路径,使各刀齿上切屑形状分布不均匀。建立了三维切削下切屑厚度的数学表示,提出了递延累加切屑厚度计算算法。实验验证表明,计算的切削力与测量结果能很好地吻合,瞬时切削力、切削力峰值、平均切削力的预测精度达到85%以上。     

An exploration of friction models for the chip–tool interface using an Arbitrary Lagrangian–Eulerian finite element model

A better understanding of friction modeling is required in order to produce more realistic finite element models of machining processes to support the goals of longer tool life and better surface quality. In this work an attempt has been made to explore and evaluate various friction models used in numerical metal cutting simulations. A finite element model, based on the ALE approach, was developed for orthogonal machining and used to study the conditions prevailing at the chip–tool interface for hardened steel. The ALE approach does not require any chip separation criteria and enables an approximate initial chip shape to smoothly evolve into a reasonable chip shape, while maintaining excellent mesh properties. The results, for a wide range of feed values, were obtained using different friction models and are compared to previously published experimental findings. A reasonable agreement was obtained between the measured and predicted forces with some discrepancy between the cutting and feed force depending on the friction model: if agreement with the cutting forces was good, then the feed force was underestimated; if the feed force agreed well, then the cutting force was overestimated. In all cases the chip thickness was well estimated but the chip–tool contact length was underestimated.     

A new method for cutting force prediction in peripheral milling of complex curved surface

The instantaneous uncut chip thickness and entry/exit angle of tool/workpiece engagement vary with tool path, workpiece geometry and cutting parameters in peripheral milling of complex curved surface, leading to the strong time-varying characteristic for instantaneous cutting forces. A new method for cutting force prediction in peripheral milling of complex curved surface is proposed in this paper. Considering the tool path, cutter runout, tool type(constant/nonconstant pitch cutter) and tool actual motion, a representation model of instantaneous uncut chip thickness and entry/exit angle of tool/ workpiece engagement is established firstly, which can reach better accuracy than the traditional models. Then, an approach for identifying of cutter runout parameters and calibrating of specific cutting force coefficients is presented. Finally, peripheral milling experiments are carried out with two types of tool, and the results indicate that the predicted cutting forces are highly consistent with the experimental values in the aspect of variation tendency and amplitude.     

Prediction of mechanistic cutting force coefficients using ALE formulation

This paper demonstrated the use of an efficient and accurate numerical tool (i.e., FEA) in simulating the cutting process and determining both the average and instantaneous cutting force coefficients. The main advantage of this approach compared to other available methods is that it eliminates the need for experimental calibrations. In this approach, an Arbitrary Lagrangian Formulation was employed in the finite element method simulations. This formulation has been gaining more recognition in structural analysis for its combined advantages of both Lagrangian and Eulerian formulations in a single model. Based on the work of Kline et al. (ASME J Eng Ind 104:272–278, 10), the tool is discretised along the axis into segments and the cutting forces acting on the cutting edge segment are presented in terms of cutting force coefficients. Cutting force coefficients are obtained using the least squares method and cutting force predictions using evaluated coefficients are shown to match experimental results with satisfactory accuracy.     

ANALYTICAL MODELING OF MICRO END-MILLING FORCES WITH EDGE RADIUS AND MATERIAL STRENGTHENING EFFECTS

The study aims at developing a predictive analytical force model for the micro end-milling operation taking into account the material strengthening as well as the edge radius effects that come into play at the micro level. The mechanistic models for macro end-milling process have been extensively reported in literature and such models predominantly use milling force coefficients which are empirically determined from end-milling experiments. The proposed model for micro end-milling is based on determination of milling force coefficients from fundamental oblique cutting approach. The edge radius effect has been accounted by analyzing the rubbing action similar to the rolling of a cylinder over work surface. Johnson-Cook material model has been modified based on the strain gradient plasticity theory incorporating the increase in material strength with decreasing uncut chip thickness. From the micro orthogonal cutting experiments, a good agreement between the experimental and predicted shear strength values is observed. The force model is validated against measured forces in end-milling experiments carried out on the KERN Evo 5 axis micro machining center. The feed and lateral forces are predicted within 10% deviation on an average.     

INFLUENCE OF FRICTION AND PROCESS PARAMETERS ON THE SPECIFIC CUTTING FORCE AND SURFACE CHARACTERISTICS IN MICRO CUTTING

For the production of small quantities of micro devices, machining is a low cost alternative to lithographic processing techniques. However, machining shows process specific size-effects upon miniaturization to the micrometer regime. Hence, the orthogonal turning process is chosen to study the influence of process parameters like uncut chip thickness h, cutting velocity v_c and cutting edge radius r_β on the cutting force and the surface plastification by two-dimensional, thermo-mechanically coupled finite element simulations. A rate-dependent plasticity law is used for investigation of a normalized medium carbon steel (AISI 1045). Furthermore, the characteristics of the influences of the different parameters are analyzed mathematically by similarity mechanics. In particular, the frictional effects on the cutting process are studied in detail using a friction coefficient μ based on experimental results, and the influences of the process parameters on the cutting force and the plastic deformation of the surface layer are determined numerically. These results are compared with experimental measurements. The specific cutting forces are analyzed and discussed in detail. Size-effects observed experimentally are also found by numerical simulations.     

Development of a capacity analysis and planning simulation model for semiconductor fabrication

Micro-machining has gained increased application to produce miniaturized parts in various industries. However, the uncut chip thickness in micro-machining is comparable to cutting edge radius. The relationship between the cutting edge radius and uncut chip thickness has been a subject matter of increasing interest. The acoustic emission (AE) signal can reflect the stress wave caused by the sudden release of the energy of the deformed materials. To improve the precision of machining system, determination of the minimum uncut chip thickness was investigated in this paper. The AE signal generated during micro-cutting experiments was used to analyze the chip formation in micro-end milling of Inconel 718. The finite element method (FEM) simulation was used to analyze the results of the experiments. The results showed that the cutting tool geometry and material properties affected the minimum uncut chip thickness. The estimation of the minimum uncut chip thickness based on AE signals can produce quite satisfactory results. The research on the minimum uncut chip thickness can provide theoretical basis for analysis of surface quality and optimal choice of cutting parameters.     

An improved cutting force model for micro milling considering machining dynamics

Micro milling, as a versatile micro machining process, is kinematically similar to conventional milling; however, it is significantly different from conventional milling with respect to chip formation mechanisms and uncut chip thickness modelling, due to the comparable size of the edge radius to the chip thickness, and the small per-tooth feeding. Considering tool runout and dynamic displacement between the tool and the workpiece, the contour of the workpiece left by previous tool paths is typically in a wavy form, and the wavy surface provides a feedback mechanism to cutting force generation because the instantaneous uncut chip thickness changes with both the vibration during the current tool path and the surface left by the previous tool paths. In this study, a more accurate uncut chip thickness model was established including the precise trochoidal trajectory of the cutting edge, tool runout and dynamic modulation caused by the machine tool system vibration. The dynamic regenerative effect is taken into account by considering the influence of all the previous cutting trajectories using numerical iteration; thus, the multiple time delays (MTD) are considered in this model. It is found that transient separation of the tool-workpiece occurring at a low feed per tooth, caused by MTD and the existing cutting force models, is no longer applicable when transient tool-workpiece separation occurs. Based on the proposed uncut chip thickness model, an improved cutting force model of micro milling is developed by full consideration of the ploughing effect and elastic recovery of the workpiece material. The proposed cutting force model is verified by micro end milling experiments, and the results show that the proposed model is capable of producing more accurate cutting force prediction than other existing models, particularly at small feed per tooth.     

A study on the cutting force and chip shrinkage coefficient in high-speed milling of A6061 aluminum alloy

In this paper, finite element (FE) simulation for high-speed milling of aluminum alloy was performed using a ductile fracture model with Mohr–Coulomb criterion proposed by Bai and Wierzbicki (BW). To verify the model, predicted cutting forces were compared to experimental results in the same cutting conditions. Then, further simulations were performed to estimate the cutting forces and chip shrinkage coefficients subjected to different cutting parameters such as cutting speeds, cutting depths, and clearance angles of a cutting tool. The obtained results were also used to determine optimal cutting parameters using the Taguchi method. The analysis of variance (ANOVA) was employed to investigate the influence percentage of each cutting parameter on cutting force and chip shrinkage coefficient. The simulation results showed that inclusion of strain rate in numerical model significantly improved the accuracy of estimated cutting force in comparison to experiment. The optimum values obtained for high-milling process were cutting speed 1000 m/min, cutting depth 1 mm, clearance angle 15°, and rake angle 4°.     

硬质合金刀具高速切削Ti6Al4V合金时扩散磨损的数值模拟

应用通用商业有限元软件Deform-2D,对航空用钛合金Ti6Al4V进行了不同冷却润滑条件下的正交切削有限元模拟。在参考已有刀具扩散磨损率模型的基础上,利用有限元模拟出的刀具/工件接触区的切削温度与相对滑动速度等基本变量,对高速切削钛合金Ti6Al4V时的WC-Co类硬质合金刀具前刀面的扩散磨损率进行了预测,进而分析了切削介质的冷却与润滑作用对刀具扩散磨损率的影响。研究结果表明:切削介质的润滑作用对刀具前刀面的扩散磨损率具有较大影响,而切削介质的冷却作用则对刀具前刀面扩散磨损率无显著影响。     

Cutting force prediction for ball nose milling of inclined surface

Ball nose milling of complex surfaces is common in the die/mould and aerospace industries. A significant influential factor in complex surface machining by ball nose milling for part accuracy and tool life is the cutting force. There has been little research on cutting force model for ball nose milling on inclined planes. Using such a model ,and by considering the inclination of the tangential plane at the point of contact of the ball nose model, it is possible to predict the cutting force at the particular cutting contact point of the ball nose cutter on a sculptured surface. Hence, this paper presents a cutting force model for ball nose milling on inclined planes for given cutting conditions assuming a fresh or sharp cutter. The development of the cutting force model involves the determination of two associated coefficients: cutting and edge coefficients for a given tool and workpiece combination. A method is proposed for the determination of the coefficients using the inclined plane milling data. The geometry for chip thickness is considered based on inclined surface machining with overlapping of previous pass. The average and maximum cutting forces are considered. These two forces have been observed to be more dominating force-based parameters or features with high correlation with tool wear. The developed cutting force model is verified for various cutting conditions.     

AN EXPERIMENTAL STUDY OF ORTHOGONAL MACHINING OF GLASS

An experimental study of machining glass with a geometrically defined cutting tool is presented. Orthogonal cutting conditions are employed to permit a focus on the fundamental modes of chip and surface formation. Analysis of the machined surfaces under an optical microscope identifies four regimes that are distinctly different with respect to either chip formation or surface formation. For a very small target uncut chip thickness, one on the order of the cutting edge radius, pure rubbing of the edge with no chip formation is observed. Edge rubbing imparts light scuffmarks on the machined surface giving it a frosted appearance. At a larger uncut chip thickness, ductile-mode chip formation occurs ahead of the cutting edge and a scuffed surface remains after the subsequent rubbing of the edge across the freshly machined surface. A further increase in uncut chip thickness maintains a ductile-mode of chip formation, but surface damage initiates in the form of surface cracks that grow down into the machined surface and ahead of the tool. The transition to this machining mode is highly dependent on rake angle. Increasing the uncut chip thickness further causes brittle spalling of chips leaving half-clamshell shaped divots on the surface. This experimental identification of the machining modes and their dependence on uncut chip thickness and rake angle supports the use of geometrically defined cutting tools to machine glass in a rough-semi-finish-finish machining strategy as is traditionally employed for machining metals.