Slip-line field modeling of orthogonal machining pressure sensitive materials

The slip-line field methods are widely used in solving cutting problem; however, most of which were focused on the pressure-independent materials. In this work, a new slip-line field model for orthogonal cutting of pressure sensitive materials is developed. Analytical characterization for orthogonal cutting process is obtained, which can give the explicit expressions for the shear angle, cutting force, and chip thickness in terms of the tool geometry, the friction coefficients on the tool flat, and the internal friction angle of the materials. To investigate the effect of the material and cutting parameters on cutting process, the finite element simulation is performed as well. The comparisons between the shear angle and cutting force predicted by the theoretical model with those obtained from finite element model simulation are made. The good agreement of the predicted results with the numerical results clearly reveals that the proposed slip-line field model can satisfactorily characterize the orthogonal cutting behavior of the pressure sensitive materials. Further analysis has demonstrated that the pressure sensitivity of materials has a significant influence on cutting process.     

基于三维多相有限元的CFRP细观切削机理研究

为深入揭示碳纤维增强树脂基复合材料(Carbon fiber reinforced plastic/polymer,CFRP)切削机理,针对目前宏观单相有限元方法无法直观体现纤维和基体的失效形式、切屑类型等问题,借助数值仿真方法建立了CFRP直角切削的三维多相有限元模型。测量刀具刀尖形貌,根据刀具和CFRP设计数据提取CFRP纤维、基体细观几何信息,建立直角切削细观几何模型;基于定义材料本构用户子程序(User subroutine to define material behavior,VUMAT)分别定义纤维和基体的材料本构(弹塑性、失效准则、损伤演化方式),对不同纤维方向角的三维多相CFRP直角切削模型进行仿真分析;设计直角切削试验对仿真结果进行对比验证。仿真结果直观地展示了基体和纤维的失效形式、切屑形成过程、不同情况下切削亚表面损伤深度,通过各种情况下切削力数据的分析,揭示了切削力随纤维方向角的变化规律,并通过试验验证了该有限元建模仿真方法的有效性。     

Research on chip formation parameters of aluminum alloy 6061-T6 based on high-speed orthogonal cutting model

Chip formation, an important aspect of the high-speed cutting (HSC) mechanism, is generally accepted as the result of shear deformation in the shear zone and tool-chip friction. In order to accurately study chip formation process in HSC, a theoretical model for the high-speed orthogonal cutting of aluminum alloy 6061-T6 was built, which can be used to calculate the important parameters of chip formation, such as shear angle, friction angle, length of shear plane, tool-chip contact length, and width of the first shear zone. A series of orthogonal cutting experiments, with the YG6 carbide tool and on a wide range of cutting speed (100–1,900 m/min) and feed (0.06–0.15 mm/r), were performed in order to obtain the parameters required in the model, including the cutting forces, the chip thickness, and the shear slip distance. Seven kinds of chip formation parameters were obtained with different cutting parameters in the experiment, and the built theoretical model can well explain the formation process and the morphology characteristics of these chips, which proves that the combined method of theoretical model and orthogonal cutting experiment is an effective and easy approach to obtain the parameters of chip formation in HSC, avoiding the cutting speed limitation and the safety risk in quick-stop test. Within the range of parameters set in the experiments, the chip mainly appears to be continuous chip, curling chip, or discontinuous chip. And the chip thickness, friction angle, length of shear plane, and width of the first shear zone decrease with the increase of the cutting speed; meanwhile, the shear slide distance and shear angle increase.     

精密切削过程三维有限元分析

采用有限元方法模拟三维精密切削过程,包括三维正交切削和三维斜角切削。切屑和刀具的摩擦应力采用修正库仑摩擦方程来计算,工件的流动应力是应力、应变、应变率和温度的函数,采用局部网格重划分技术。通过三维切削模拟可以获得在不同刃倾角精密切削过程的条件下切屑形状、切削力和切削温度场的分布情况。仿真结果表明:刃倾角对主切削力和切深抗力影响不大,但对切屑形状、进给抗力和切削温度场分布影响较大。     

The Merchant's model of orthogonal cutting revisited: A new insight into the modeling of chip formation

The Merchant's model, as the most famous approach of orthogonal cutting, is widely used in introductive courses on machining. However, the shear angle predicted by the Merchant's model from the criterion of minimization of the cutting energy, does not generally agree with experimental data and numerical simulations. The aim of this paper is to elucidate the theoretical reason for which the Merchant's model fails to predict the correct orientation of the primary shear zone. It is shown that the principle of minimum of the cutting energy must be supplemented by a stability criterion of the chip morphology. A modified Merchant's formula is then obtained for the value of the shear angle.     

Hybrid analytical–numerical solution for the shear angle in orthogonal metal cutting — Part I: theoretical foundation

In metal cutting, the shear angle is considered as a fundamental parameter that defines the plastic deformation and the geometry of the process. The present paper presents a further development of the energy method for prediction of the shear angle in case of orthogonal metal cutting. Parallel-sided shear zone model is utilized to describe the geometry of chip formation. The material velocity in the primary shear zone is allowed to change gradually from the bulk material velocity to the chip velocity. The interaction between chip and tool in the secondary shear zone is modeled as sticking to sliding transition. The work material is characterized by an empirical equation, which allows for the influence of temperature, strain, and strain rate as well as their histories. To take into consideration the influence of the temperature on the work material properties, a finite element model (FEM) of heat transfer is employed. The FEM is developed as an adaptive model to reflect the change in the domain geometry. As the work material properties strongly depend on the temperature, an overall iterative calculation procedure including FEM is essential. In Part I, the theoretical basis of the model is described. In Part II the predicted values of the shear angle are compared with data from machining 0.18% C carbon steel over a range of cutting conditions and tool geometry.     

A MODEL-BASED ANALYSIS OF ORTHOGONAL CUTTING FOR SINGLE-CRYSTAL FCC METALS INCLUDING CRYSTALLOGRAPHIC ANISOTROPY

The anisotropy of workpiece crystals becomes prominent as the uncut chip thickness approaches to the grain size of the workpiece material. As such, in mechanical micromachining, precision machining, and diamond turning operations, the cutting forces exhibit significant variations with crystallographic orientations. In this work, a crystal-plasticity based model is used to analyze the effects of cutting geometry, friction and crystallographic anisotropy when machining face-centered cubic (fcc) single-crystals using ideally sharp cutting edges. The model adapts and combines Bishop and Hill's crystal plasticity theory with Merchant's machining force model. The total power, including the shearing and friction powers, is minimized over allowable shear angles to determine the shear angle solution and associated specific energies. The model is validated using data from the literature for both aluminum and copper single crystals; a good match is observed between the model predictions and experimental data, indicating the model's capability to capture crystallographic anisotropy and symmetry. The validated model is used to analyze the effects of rake angle, friction, and crystallographic orientation on specific energies and shear angles. Subsequently, a further simplification to the model is proposed through the use of Merchant's shear-angle formula.     

Finite element analysis of the rake angle effects in orthogonal metal cutting

The plane-strain finite element method is developed and applied to model the orthogonal metal cutting of annealed low carbon steel with continuous chip formation. Four sets of simulation results for cutting with −2°, 0°, 5°, and 15° rake angle are summarized and compared to analyze the effects of rake angle in the cutting processes. The initial and deformed finite element meshes, as the cutting reaches steady-state condition, are first presented. Simulation results of the cutting forces and residual stresses, along with the X-ray diffraction measurements of the residual stresses generated using a worn cutting tool with 5° rake angle, are used to identify the influences of the rake angle and tool sharpness. Elements are selected to represent three sections along the shear and contact zones and under the cut surface. The normal and shear stresses, distributions of parameters along these three sections, and contours of temperature, plastic strain, and effective stress are then presented. Limitations of the finite element method for metal cutting simulation are discussed.     

Effects of texture gradients and strain paths on localization phenomena in polycrystals

Applications of crystal plasticity theory to the numerical modelling of large strain plasticity phenomena are considered. In particular, instabilities and localized deformation phenomena for FCC polycrystals subjected to various deformation modes are investigated. In-house finite element analyses based on a rate-dependent crystal plasticity model have been developed to simulate the large strain behaviour for sheet specimens subjected to plane strain, plane stress, and simple shear deformation modes. In the formulation, the plastic deformation of an individual crystal is assumed to be due to crystallographic slip. In the simulations, polycrystalline aggregates are modelled at various scales. This formulation accounts for initial textures, as well as texture evolution during large plastic deformations. The numerical analyses incorporate parallel computing features. The results of simulations for the above-mentioned deformation modes are discussed, and the formation of localized deformation in the form of shear bands is investigated.     

Orthogonal cutting of fiber-reinforced composites: A finite element analysis

Orthogonal cutting of unidirectional fiber-reinforced polymer composites was analyzed using the finite element method. A dual fracture process was used to simulate chip formation incorporating both the maximum stress and Tsai—Hill failure criteria. All aspects of the cutting tool geometry are considered in the model including the tool rake and clearance angles, nose radius and wear land, as well as friction between the tool and work material. Predictions for the cutting forces from numerical simulations are verified with experimental measurements for orthogonal trimming of unidirectional graphite/epoxy. The principal cutting force predictions agree very well with those obtained from experiments. The influence of fiber orientation and tool geometry on the fracture stress are highlighted and their effects on the material removal process in orthogonal trimming of reinforced polymers are discussed.     

Hybrid analytical–numerical solution for the shear angle in orthogonal metal cutting — Part II: experimental verification

The hybrid analytical–finite element model described in Part I is applied to predict the shear angle for a range of cutting velocity, uncut chip thickness, and two tool orthogonal rake angles. Experimental results and an empirical equation are also presented for the influence of the cutting conditions and cutting tool geometry on the chip–tool contact length. It is shown that there is a linear dependence between the chip–tool contact length/uncut chip thickness ratio and chip thickness/uncut chip thickness ratio over the range of cutting conditions assumed. The increase of the shear angle with the tool orthogonal rake is mostly due to the reduction of the specific shear energy in the primary shear zone and the specific friction energy in the secondary shear zone accompanied by a reduction of the chip–tool contact zone. The uncut chip thickness and cutting velocity influence the shear angle through their effect on the interface temperature and hence on the material flow stress in the secondary shear zone. The change in both parameters does not change significantly the specific shear energy in the primary shear zone. The model results are compared with the experimental results for a work material 0.18% C steel. The agreement between the predicted and experimental results is seen to be exceptionally good.     

OPTIMIZATION OF THE CUTTING EDGE GEOMETRY OF COATED CARBIDE TOOLS IN DRY TURNING OF STEELS USING A FINITE ELEMENT ANALYSIS

This paper investigates the effects of edge radius of a round-edge coated carbide tool on chip formation, cutting forces, and tool stresses in orthogonal cutting of an alloy steel 42CrMo₄ (AISI 4142H). A comprehensive experimental study by end turning of thin-walled tubes is conducted, using advanced coated tools with well-defined cutting edge radii ranging from 5 to 68 microns. In parallel, 2-D finite element cutting simulations based on Lagrangian thermo-viscoplastic formulation are used to predict the cutting temperatures and tool-stress distributions within the tool coating and substrate. The results obtained from this study provide a fundamental understanding of the cutting mechanics for the coated carbide tool used, and can assist in the optimization of tool edge design for more complex geometries, such as chamfered edge. Specifically, the results obtained from the experiments and simulations of this study demonstrated that finite element analysis can significantly help in optimizing the design of coated cutting tools through the prediction of tool stresses and temperatures, especially within the coating layer.     

Adiabatic shear in chip formation with negative rake angle

The mechanics of chip formation in grinding is investigated based on thermo-elastic-plastic finite element simulations of orthogonal cutting with a large negative rake abrasive-grits. The modeling is coupled with temperature and strain-rate-dependent flow stress characteristics of a work material SK-5 (0.93%C carbon steel). The shape of chip calculated is affected by the cutting speed and the undeformed chip thickness. In high-speed cutting, serrated chip formation caused by adiabatic shear, which is usually observed experimentally under the cutting conditions of grinding region, is obtained analytically without any consideration of crack propagation. Temperature and flow stress calculated in the primary shear zone vary periodically according to the segmentation of serrated chip. Then changes in temperature, flow stress, strain rate and strain at a material point fixed to and moving with chip is monitored in order to investigate the chip formation process. This clarifies the cutting mechanisms of different types of chip formation with negative rake.     

An explicit finite element model to study the influence of rake angle and friction during orthogonal metal cutting

A fundamental understanding of the tribology aspects of machining processes is essential for increasing the dimensional accuracy and surface integrity of finished products. To this end, the present investigation simulates an orthogonal metal cutting using an explicit finite element code, LS-DYNA. In the simulations, a rigid cutting tool of variable rake angle was moved at different velocities against an aluminum workpiece. A damage material model was utilized for the workpiece to capture the chip separation behavior and the simultaneous breakage of the chip into multiple fragments. The friction factor at the cutting tool–workpiece interface was varied through a contact model to predict cutting forces and dynamic chip formation. Overall, the results showed that the explicit finite element is a powerful tool for simulating metal cutting and discontinuous chip formation. The separation of the chip from the workpiece was accurately predicted. Numerical results found that rake angle and friction factor have a significantly influence on the discontinuous chip formation process, chip morphology, chip size, and cutting forces when compared to the cutting velocity during metal cutting. The model was validated against the experimental and numerical results obtained in the literature, and a good agreement with the current numerical results was found.     

FEM mesh-dependence in cutting process simulations

The process simulations based on FEM techniques have been investigated for many years, some fundamental problems are still unsolved, e.g. the element size effect on the computational results. In present contribution, orthogonal cutting simulations of AISI4340 steel are considered. The major concerns are accuracy of computational results, influence of element size and effects of damage model in accommodating modeling of failure phenomenon for cutting process simulations. Numerical simulations are verified with the measured values of cutting force by considering certain case of influencing cutting parameters combination taken from literature. Element size is treated to be the most influencing constituent in the cutting process simulations. The chip morphology is related to the adiabatic assumption considered in the process simulation, the feed value and the element size. The simulation results are presented by neglecting temperature effects to show the influence of failure criterion based on plastic displacement of the numerical results. Though the chip morphology and shear band formation are most sensitive to the element size, the cutting force of process simulations is hardly influenced. The formation of saw-tooth chip in the present simulations is the result of adiabatic shear band at the tool tip and propagating towards the chip’s outer surface. The present work confirms that the effect of element size on computational results is reduced significantly if the failure criterion in the process simulation is controlled by a characteristic element length considered from the progressive damage model.     

An experimental investigation of oblique cutting mechanics

In this study, an experimental investigation of oblique cutting process is presented for titanium alloy Ti-6Al-4V, AISI 4340, and Al 7075. Important process parameters such as shear angle, friction angle, shear stress, and chip flow angle are analyzed. Transformation of the data from the orthogonal cutting test results to oblique cutting process is applied, and the results are compared with actual oblique cutting tests. Effects of hone radius on cutting forces and flank contact length are also investigated. It is observed that the shear angle, friction angle, and shear stress in oblique cutting have the same trend with the ones obtained from the orthogonal cutting tests. The transformed oblique force coefficients from orthogonal tests have about 10% discrepancy in the feed and tangential directions. For the chip flow angle, the predictions based on kinematic and force balance results yield better results than Stabler's chip flow law. Finally, it is shown that the method of oblique transformation applied on the orthogonal cutting data yields more accurate results using the predicted chip flow angles compared to the ones obtained by the Stabler's rule.     

基于ABAQUS的高速切削切屑形成过程的有限元模拟

基于有限元分析软件ABAQUS的Johnson-Cook材料模型以及断裂准则模拟高速切削淬硬钢锯齿状切屑形态,并讨论刀具前角和锯齿状切屑形态对切削力的影响.研究表明仿真结果和试验结果是一致的,文中介绍的有限元模拟方法可以准确地模拟并预测高速切削淬硬钢时的切屑形成过程.     

切削工艺参数对切屑形状的影响及其有限元分析

以刚塑性有限元理论为基础,采用有限元仿真技术,对金属正交切削过程中切屑成形进行了模拟仿真,得到了不同的刀具前角和摩擦条件对切屑形状的影响规律。对二维切削过程进行加工实验,结果表明切削模拟结果与实际加工情况比较吻合,可以为实际加工提供参数选择的依据。     

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.     

金属正交切削加工过程的有限元分析

运用大型通用有限元程序对金属正交切削加工过程进行非线性弹塑性有限元模拟分析，得到不同刀具前角在加工过程中对切屑形状、应力分布、应变分布、残余应力及残余变形的影响，得出刀具前角值与剪切角的关系。计算验证了一些实验结果，结论可供工程应用参考。