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.     

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.     

Analysis of orthogonal finish machining using tungsten carbide and diamond tools of different heat transfer coefficients

An orthogonal cutting model for finish machining, using diamond and tungsten carbide tools which have different coeffficients of thermal conductivity, was simulated and analyzed. It was assumed that the tool had a minute amount of tool flank wear. The distribution of strain rate and stress within the machined workpiece and the determination of the cutting force were obtained after simulation. The generation and distribution of temperature and stress within the chip through cutting of the workpiece were also acquired. In addition, the temperature of the tool, the workpiece and the chip during finish machining by the two different tools, that show the effects of the different friction coefficients of the diamond tool and the tungsten carbide tool on cutting, were compared. Finally, the cutting forces predicted by the model for orthogonal finish machining were compared with those obtained by experiment, and it appears that the present orthogonal finish machining model is reasonable.     

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.     

网格属性对航空薄壁圆筒车削仿真过程的影响

为了探索单元类型以及网格划分方式对航空薄壁圆筒车削仿真过程的影响,利用Abaqus软件和AdvantEdge软件对薄三维模型以及薄壁圆筒模型的车削过程进行了对比分析,同时以主切削力和切屑形态为指标对切削仿真质量进行了评价。结果表明:在保证薄三维切削仿真精度的前提下,六面体网格可以极大地节省计算时间,更好地反映切削过程中的切屑形态和已加工表面质量等物理量的变化;航空薄壁圆筒车削仿真中采用扫略网格画法可以在一定程度上提高计算效率和工件表面质量。      

Theoretical modelling and simulation of cutting forces in face milling with cutter runout

A new approach to theoretical modelling and simulation of cutting forces in face milling is presented. Based on a predictive machining theory, the action of a milling cutter is modeled as the simultaneous actions of a number of single-point cutting tools. The milling forces are predicted from the workpiece material properties, cutter parameters, tooth geometry, cutting conditions and types of milling. The properties of the workpiece material are considered as functions of strain, strain-rate and temperature in the cutting region. It takes into account the effect of the intermittent contact between each milling tooth and the workpiece on the temperature in the cutting region. It also takes into account the effect of cutter runout on the undeformed chip thickness. Milling experiments have been conducted to verify the proposed model. Good agreements between the experimental and simulated results are presented.     

基于正交切削模型的铣削加工残余应力预测方法

提出了一种基于正交切削模型的铣削加工残余应力预测方法.针对直齿圆柱铣刀建立了铣削加工的平面应变有限元模型,并通过分段曲线限定不同温度下应力与应变间的关系,详细表明材料的加工硬化规律.有限元模型采用相关的实验数据进行了验证.在铣削用量确定的前提下,通过对航空铝合金70507451进行加工模拟,研究了直齿圆柱铣刀前角对已加工表面残余应力的影响.     

Effect of direction of parameterization on cutting forces and surface error in machining curved geometries

The present paper investigates the effect of two variables, namely direction of parameterization and cutter diameter on process geometry, cutting forces, and surface error in peripheral milling of curved geometries. In machining of curved geometries where the curvature varies continuously along tool path, the process geometry variables, namely feed per tooth, engagement angle, and maximum undeformed chip thickness too vary along tool path. These variations will be different when a given geometry is machined from different parametric directions and with different cutter diameters. This difference in process geometry variations result in changed cutting forces and surface error along machined path. This aspect has been studied for variable curvature geometries by machining from both parametric directions and using cutters of different diameter. The computer simulation studies carried out show considerable amount of shift in the location of peak cutting forces with the change in cutting direction and cutter diameter, particularly in concave regions of workpiece geometry. A new parameter γ that relates the instantaneous curvature of workpiece with cutter radius is defined. The larger value of γ is an indicator of greater shift in the location of peak forces from the point of maximum curvature on the workpiece. The simulation results are validated by carrying out machining experiments with curved workpiece geometry and are found to be in good agreement.     

Mechanics of high speed cutting with curvilinear edge tools

High speed cutting is advantageous due to the reduced forces and power, increased energy savings, and overall improved productivity for discrete-part metal manufacturing. However, tool edge geometry and combined cutting conditions highly affects the performance of high speed cutting. In this study, mechanics of cutting with curvilinear (round and oval-like) edge preparation tools in the presence of dead metal zone has been presented to investigate the effects of edge geometry and cutting conditions on the friction and resultant tool temperatures. An analytical slip-line field model is utilized to study the cutting mechanics and friction at the tool-chip and tool–workpiece interfaces in the presence of the dead metal zone in machining with negative rake curvilinear PCBN tools. Inserts with six different edge designs, including a chamfered edge, are tested with a set of orthogonal cutting experiments on AISI 4340 steel. Friction conditions in each different edge design are identified by utilizing the forces and chip geometries measured. Finite-element simulations are conducted using the friction conditions identified and process predictions are compared with experiments. Analyses of temperature, strain, and stress fields are utilized in understanding the mechanics of machining with curvilinear tools.     

Characteristics of high speed micro-cutting of tungsten carbide

In this study, experiments are carried out to evaluate the characteristics of high speed cutting of tungsten carbide material using a Makino V55 high speed machine tool with cubic boron nitride (CBN) tool inserts. The cutting forces were measured using a three-component dynamometer, the surface roughness of the machined workpiece was measured using a Mitutoyo SURFTEST 301, and the machined workpiece surfaces and the chip formation were examined using a scanning electron microscope (SEM). Experimental results indicate that the radial force F_x is much larger than the tangential force F_z and the axial force F_y. Two types of surfaces of the machined workpiece are achieved: ductile cutting surface and fracture surface. Continuous chips and discontinuous chips are formed under different cutting conditions. Depth of cut and feed rate almost have no significant effect on the surface roughness of the machined workpiece. The SEM observations on the machined workpiece surfaces and chip formation indicate that the ductile mode cutting is mainly determined by the undeformed chip thickness when the tool cutting edge radius is fixed. Ductile cutting can be achieved when the undeformed chip thickness is less than a critical value.     

In situ strain measurement in the chip formation zone during orthogonal cutting

The strain and stress state in the chip formation zone determines the chip formation. However, it is difficult to obtain experimental data about the strain/stress fields during machining. For this reason, present chip formation models highly simplify the chip formation process. In order to extend the knowledge regarding the chip formation mechanisms, an experimental method for the in situ measurement of the elastic deformations within the chip formation zone during the cutting process has been developed. Using these deformations, the stress state can subsequently be calculated. The method is based on X-ray diffraction using high-energy synchrotron X-radiation during machining the workpiece in an orthogonal cutting process under quasistatic experimental conditions. The diffraction patterns are captured with a 2D detector. A comparison of the experimentally determined stresses at different measuring positions within the chip formation zone with results from a FEM cutting simulation shows a good qualitative and partially also quantitative consistency. Possibilities for the further performance increase of the method are identified so that the method can be used for the verification and extension of existing chip formation models in future.     

A chip formation based analytic force model for oblique cutting

An oblique cutting force model has been developed using an analytic orthogonal force model. The force model uses a thermo-visco-plastic material constitutive law to represent the shear stress during deformation of the material. The strains and strain rates used for defining the shear stress were obtained from chip formation and morphology derived from orthogonal cutting tests and has been extended to oblique cutting. A time domain simulation using the in-cut chip geometry to define the chip load area has been developed. The oblique force model was used to predict the cutting forces during ball milling of hardened AISI D2 tool steel. The predicted forces were verified experimentally and showed good correlation.     

条形槽微织构对PCBN刀具切削性能的影响

微织构作为刀具结构设计的新方法，对刀具的性能产生一定的影响。在刀具前刀面设计制备条槽型微织构，结合有限元仿真技术，从理论上分析条形槽微织构对切削力和已加工表面质量的影响，再设计切削试验，对有限元仿真结果进行实际验证。结果表明:有限元仿真和切削试验结果基本一致；与无织构刀具相比，条形槽微织构能够减小切削力且对主切削力的影响最显著，对进给力的影响较弱；条形槽微织构使工件表面应力、塑性应变和粗糙度均小于无织构刀具的，提高了工件已加工表面质量，其表面粗糙度仅为1.54 μm。      

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.     

Numerical and experimental study of dry cutting for an aeronautic aluminium alloy (A2024-T351)

In the present contribution, numerical and experimental methodologies concerning orthogonal cutting are proposed in order to study the dry cutting of an aeronautic aluminium alloy (A2024-T351). The global aim concerns the comprehension of physical phenomena accompanying chip formation according to cutting velocity variation.For the numerical model, material behaviour and its failure criterion are based on the Johnson–Cook law. The model proposes a coupling between material damage evolution and its fracture energy. A high-speed camera was used to capture the chip formation sequences. The numerical results show that the chip–workpiece contact and the tool advancement induce bending loads on the chip. Consequently, a fragmentation phenomenon takes place above the rake face when the chip begins to curl up. The computed results corroborate with experimental ones. The numerical results predict the residual stress distribution and show high values, along the cutting direction, on the machined workpiece surface.     

Identification of the specific cutting force for geometrically defined cutting edges and varying cutting conditions

Cutting force modeling is a major discipline in the research of cutting processes. The exact prediction of cutting forces is crucial for process characterization and optimization. Semi-empirical and mechanistic force models have been established, but the identification of the specific cutting force for a pair of tool and workpiece material is still challenging. Existing approaches are depending on geometrical idealizations and on an extensive calibration process, which make practical and industrial application difficult. For nonstandard tools and five axis kinematics there does not exist a reasonable solution for the identification problem.In this paper a co-operative force model for the identification of the specific cutting forces and prediction of integral forces is presented. The model is coupled bidirectionally with a multi-dexel based material removal model that provides geometrical contact zone information. The nonlinear specific forces are modeled as polynomials of uncut chip thickness. The presented force model is not subjected to principal restrictions on tool shape or kinematics, the specific force and phase shift are identified with help of least square minimization. The benefit of this technique is that no special calibration experiments are needed anymore, which qualifies the method to determine the specific forces simultaneously during the machining process. In this paper, experiments with different cutting conditions are analyzed and systematically rated. Finally, the method is validated by experiments using different cutting conditions.     

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.     

An improved cutting force and surface topography prediction model in end milling

During the milling operation, the cutting forces will induce vibration on the cutting tool, the workpiece, and the fixtures, which will affect the surface integrity of the final part and consequently the product's quality. In this paper, a generic and improved model is introduced to simultaneously predict the conventional cutting forces along with 3D surface topography during side milling operation. The model incorporates the effects of tool runout, tool deflection, system dynamics, flank face wear, and the tool tilting on the surface roughness. An improved technique to calculate the instantaneous chip thickness is also presented. The model predictions on cutting forces and surface roughness and topography agreed well with experimental results.     

Influence of scaled undeformed sections of cut on strain rate,cutting force and temperature

In machining processes, a decreasing undeformed chip thickness leads to an increase in the specific machining forces. This effect is commonly known as the scaling effect in chip formation. In the literature, several reasons for this effect are discussed. One approach focuses on the increase in the strain rate due to a decrease in the undeformed chip thickness. The increase in the strain rate leads to a hardening effect of the machined material which results in higher specific cutting forces. However, it has not been definitely proven that this is the cause of the scaling effect in chip formation. This paper describes an approach for examining the influence of the strain rate on the scaling effect. Firstly, FE-simulations have been carried out to gain knowledge about the strain rates in the center of the shear zone. By means of these simulations, cutting speeds which lead to constant strain rates in the center of the shear zone have been determined for a broad range of chip thickness. In a second step, experimental investigations have been carried out using the simulated cutting speeds and chip thicknesses. The chip formation processes and the machining forces have been analyzed with constant strain rates and different chip thicknesses as well as with a constant cutting speed. The main result of these investigations is that the strain rate has only a minor influence on the specific cutting forces. It is shown that the temperature in the shear zone decreases with a decrease in the chip thickness. This leads to lower thermal softening of the material and thus to higher specific cutting forces.     

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.