A modelling of cutting for viscoplastic materials

A model is presented of stationary shearing produced during the chip formation in orthogonal cutting. The work material is supposed to be a thermal sensitive viscoplastic rigid material. The effects of material parameters, of heat conductivity and of inertia on the distribution of strain rate and of temperature in the primary shear zone are analysed. The cutting forces are calculated for a large range of cutting speeds including high speed machining. The results are obtained by developing a simple one-dimensional modelling of the primary shear zone. Experimental measurements are compared with the theoretical results.     

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.     

AN ANALYTICAL MODEL OF OBLIQUE CUTTING WITH APPLICATION TO END MILLING

A new analytical cutting force model is presented for oblique cutting. Orthogonal cutting theory based on unequal division shear zone is extended to oblique cutting using equivalent plane approach. The equivalent plane angle is defined to determine the orientation of the equivalent plane. The governing equations of chip flow through the primary shear zone are established by introducing a piecewise power law distribution assumption of shear strain rate. The flow stress is calculated from Johnson-cook material constitutive equation. The predictions were compared with test data from the available literature and showed good correlation. The proposed model of oblique cutting was applied to predict the cutting forces in end milling. The helical flutes are decomposed into a set of differential oblique cutting edges. To every engaged tooth element, the differential cutting forces are obtained from oblique cutting process. Experiments on machining AISI 1045 steel under different cutting conditions were conducted to validate the proposed model. It shows that the predicted cutting forces agree with the measurements both in trends and values.     

Thermoviscoplastic modelling of oblique cutting: forces and chip flow predictions

A modelling of oblique cutting for viscoplastic materials is presented. The thermomechanical properties and the inertia effects are accounted for to describe the material flow in the primary shear zone. At the tool–chip interface, a temperature-dependent friction law is introduced to take account of the extreme conditions of pressure, velocities and temperature encountered during machining. The chip flow angle is calculated by assuming that the friction force is collinear to the chip flow direction on the tool rake face. Due to the temperature dependence of the friction law at the tool–chip interface, the chip flow angle predicted by the model, is affected by the cutting speed, the undeformed chip thickness, the normal rake angle, the edge inclination angle and the thermomechanical behavior of the work material. This dependence and the trends predicted by the present approach are confirmed by experimental observations. Effects of cutting conditions on the cutting forces are also presented and compared to experiments.     

Predictive analytical modeling of cutting forces generated by high-speed machining of ductile and hard metals

This paper proposes an analytical cutting forces model based on an extension of the Oxley's machining theory (OMT) to high-speed machining of ductile and hard metals. In this model, the materials' behavior was modeled using the Marusich's constitutive equation (MCE). Furthermore, The OMT was modified to be able to capture the effects of the cutting tool edge radius and the burnishing phenomenon by implementing a variable rake angle equation and the Briks criterion, respectively. The predictive model was validated using experimental data obtained during the orthogonal machining of two aluminum alloys (AA6061-T6 and AA7075-T651) and induction-hardened AISI4340 steel (58-60 HRC). The results showed that the predicted and experimental cutting forces were in reasonable agreement for all tested materials. The strain rate constant in the primary shear zone (C₀) was found to be significantly sensitive to the cutting conditions and work material, and its effect on the predicted data was highlighted and discussed in depth. On one hand, it was found that AA6061-T6 is less sensitive to the strain rate compared to the AA7075-T651. On the other hand, all tested materials were found to be more sensitive to the strain rate at low cutting speeds and/or cutting feeds.     

基于改进温度模型的300M钢本构方程参数识别

为了提高通过切削实验获取材料本构方程参数的精度,提出了将基于移动热源理论的温度分布模型沿剪切面积分计算剪切区平均温度的方法,结合不等距剪切区模型求得等效应变和应变率,建立了材料Johnson-Cook(J-C)本构方程参数的求解模型。根据切削实验获取的切削力和切屑厚度数据并采用遗传算法求得了300M钢J-C本构方程参数。与AdvantEdge FEM软件自带的300M钢本构模型相比,用所求模型参数仿真得到的主切削力、进给力和切屑厚度的精度有显著提高,验证了所建本构方程参数求解模型的有效性。     

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.     

Investigation of the effect of cutting tool edge radius on material separation due to ductile fracture in machining

This paper investigates the interaction between cutting tool edge radius and material separation due to ductile fracture based on Atkins’ model of machining. Atkins’ machining model considers the energy needed for material separation in addition to energies required for shearing at the primary shear zone and friction at the secondary shear zone. However, the effect of cutting tool edge radius, which becomes significant at microcutting conditions, was omitted. In this study, the effect of cutting tool edge radius is included in the model and its influence on material separation is investigated. A modification to the solution methodology of Atkins’ machining model is proposed and it is shown that the shear yield stress and the fracture toughness of the work material can be calculated as a function of uncut chip thickness.     

The tribology of orthogonal finish machining — A review

A review of orthogonal finish machining is presented. The relations be- tween material flow conditions in the three distinct flow regions in metal cutting are examined: the deformation zone governs chip flow, the tool-chip contact zone is responsible for tool wear and the tool base rubbing zone controls workpiece integrity. In orthogonal machining the initial sharp tool cutting edge is of importance regarding the integrity of surface finish although tool edge forces have been the subject of more investigations. Material flow near the tool edge is considered with respect to the author's own model.     

SPH method applied to high speed cutting modelling

The purpose of this study is to introduce a new approach of high speed cutting numerical modelling. A Lagrangian smoothed particle hydrodynamics (SPH)-based model is carried out using the Ls-Dyna software. SPH is a meshless method, thus large material distortions that occur in the cutting problem are easily managed and SPH contact control permits a “natural” workpiece/chip separation. The developed approach is compared to machining dedicated code results and experimental data. The SPH cutting model has proved is ability to account for continuous to shear localized chip formation and also correctly estimates the cutting forces, as illustrated in some orthogonal cutting examples. Thus, comparable results to machining dedicated codes are obtained without introducing any adjusting numerical parameters (friction coefficient, fracture control parameter).     

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.     

材料强化因素对切削过程中尺寸效应的影响

针对航天航空常用材料TiAl6V4的正交切削过程开展了一系列的有限元模拟,进行了相应的切削实验用以验证模拟的可靠性。基于系统的数值仿真,考察了切削过程中主次剪切区的平均应变、应变率、温度随切削厚度的变化规律,集中研究了材料应变、应变率强化及热软化因素对切削过程中"尺寸效应"现象的影响。研究结果表明,材料应变和应变率强化因素对"尺寸效应"没有太大影响,而材料热软化作用是导致"尺寸效应"形成的重要因素。另外,随着切削厚度的减小,主剪切区温度降低以及刀具和切屑间单位接触长度非线性增加是造成"尺寸效应"的主要原因。     

Modeling of flow stress in orthogonal micro-cutting process based on strain gradient plasticity theory

The rapidly increasing demand for miniature components machining processes has drawn more attention to micro-machining research. Flow stress has always been a significant base for analyzing plastic deformation in machining processes. However, few studies have been conducted to predict accurately the material flow stress in the micro-cutting processes. In order to describe size effect in micro-cutting, this paper discusses the development of a circular primary deformation zone model, calculates the strain gradient in the primary zone, and presents a new flow stress model based on the theory of strain gradient plasticity. First, a series of orthogonal cutting experiments are performed and flow stress is calculated from the experiment data. Results from the proposed model have been successfully validated with experimentally determined results. It shows that the flow stress in micro-cutting is influenced greatly by the feed rate and the cutting edge radius.     

On modeling of cutting forces in micro-end milling operation

Micro-end milling is used for manufacturing of complex miniaturized components precisely in wide range of materials. It is important to predict cutting forces accurately as it plays vital role in controlling tool and workpiece deflections as well as tool wear and breakage. The present study attempts to incorporate process characteristics such as edge radius of cutting tool, effective rake and clearance angles, minimum chip thickness, and elastic recovery of work material collectively while predicting cutting forces using mechanistic model. To incorporate these process characteristics effectively, it is proposed to divide cutting zone into two regions: shearing- and ploughing-dominant regions. The methodology estimates cutting forces in each partitioned zone separately and then combines the same to obtain total cutting force at a given cutter rotation angle. The results of proposed model are validated by performing machining experiments over a wide range of cutting conditions. The paper also highlights the importance of incorporating elastic recovery of work material and effective rake and clearance angle while predicting cutting forces. It has been observed that the proposed methodology predicts the magnitude and profile of cutting forces accurately for micro-end milling operation.     

Slip-line solution for orthogonal cutting with a chip breaker and flank wear

A slip-line field model for orthogonal cutting with chip breaker and flank wear has been developed. For a worn tool, this slip-line field includes a primary deformation zone with finite thickness; two secondary shear zones, one along the rake face and the other along the flank face; a predeformation zone; a curled chip; and a flank force system. It is shown that the cutting geometry is completely determined by specifying the rake angle, tool-chip interface friction and the chip breaker constraint. The chip radius of curvature, chip thickness, and the stresses and velocities within the plastic region are readily computed. Grid deformation patterns, calculated with the velocity field determined, demonstrate that the predicted effects of changes in frictional conditions at the tool-chip interface and of the rake angle on chip formation are in accord with experimental observations. The calculated normal stress distribution at the tool-chip interface is in general agreement with previously reported experimental measurements. The model proposed predicts a linear relationship between flank wear and cutting force components. The results also show that non-zero strains occur at and below the machined surface when machining with a worn tool. Severity and depth of deformation below the machined surface increases with increasing flank wear. Forces acting on the chip breaker surface are found to be small and suggest that chip control for automated machining may be feasible with other means.     

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.     

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.     

NUMERICAL SIMULATION OF TITANIUM ALLOY DRY MACHINING WITH A STRAIN SOFTENING CONSTITUTIVE LAW

In this study, the commercial finite element software FORGE2005®, able to solve complex thermo-mechanical problems is used to model titanium alloy dry machining. One of the main machining characteristics of titanium alloys is to produce a special chip morphology named “saw-tooth chip” or serrated chip for a wide range of cutting speeds and feeds. The mechanism of saw-tooth chip formation is still not completely understood. Among the two theories about its formation, this study assumes that chip segmentation is only induced by adiabatic shear band formation and thus no material failure occurs in the primary shear zone. Based on the assumption of material strain softening, a new material law was developed. The aim of this study is to analyze the newly developed model's capacity to correctly simulate the machining process. The model validation is based on the comparison of experimental and simulated results, such as chip formation, global chip morphology, cutting forces and geometrical chip characteristics. A good correlation was found between the experimental and numerical results, especially for cutting speeds generating low tool wear.     

基于斜角切削理论的立铣切削力预测研究

为了预测立铣加工的切削力,把立铣刀的切削刃离散为一系列无限小的斜角切削单元。对于每个微元斜角切削单元,应用斜角切削理论来建立切屑通过时剪切区的应力、应变、应变率和温度的控制方程。采用数值方法根据控制方程计算出流动应力,并根据斜角切削和铣削之间的力变换关系,把流动应力转化为铣削力。最后,对45钢进行了多组不同切削参数的立铣实验,仿真和实验的对比结果验证了所提出模型的有效性。该方法同样可以用于其他加工方式（如车削和钻削）的建模。     

The investigation of mechanism of serrated chip formation under different cutting speeds

Chip type is determined by the coupled effects of workpiece material property, cutting speed, uncut chip thickness, feed rate, and tool edge geometry. The understanding of chip formation plays a critical role in studying surface integrity and optimization of machining process variables. Serrated chip, one of the major important chip type, is usually formed in hard cutting at high speed. In this study, a new analytical model has been proposed to better understand the formation of serrated chip, and the simulations have been acquired using ABAQUS/Explicit in machining AISI 1045 during different speeds (from 60 to 6000 m/min). The workpiece material property is modeled with the Johnson-Cook model, and the experiments have been conducted with AISI 1045 during speeds from 60 to 1200 m/min. It has been shown that flow stress is influenced simultaneously by the strain rate hardening and temperature softening. When the speed reaches very high, the temperature softening will fail, and the strain rate hardening will play a more important role. Also, it can be found that the hardening ratio increases when the cutting speed rises. The results of the simulations and experiments correlated well. The cutting force and thrust force both decrease as the cutting speed increases, and the difference between them will shrink when the machining speed reaches a high level.