Analytical prediction of cutting forces in orthogonal cutting using unequal division shear-zone model

This paper presents an analytical method based on the unequal division shear-zone model to study the machining predictive theory. The proposed model only requires workpiece material properties and cutting conditions to predict the cutting forces during the orthogonal cutting process. In the shear zone, the material constitutive relationship is described by Johnson?CCook model, and 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 the primary shear zone. The governing equations of chip flow through the primary shear zone are established by introducing a piecewise power law distribution assumption of the shear strain rate. The cutting forces are calculated for different machining conditions and flow stress data. Prediction results were compared with the orthogonal cutting test data from the available literature and found in reasonable agreement. In addition, an analysis of the deviation from experimental data for the proposed model is performed, the effects of cutting parameters and tool geometry were investigated.     

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.     

Experimental research on strain-hardening effect of 40CrMnMo in turning process based on the Oxley-Welsh theory

Based on the Oxley-Welsh theory, this paper focuses on the influence of strain-hardening behavior of oil country tubular goods (OCTG) 40CrMnMo (workpiece material) on a cutting model and the influence of cutting parameters on a stress distribution in the shear zone and the chip formation in turning processes by establishing a reasonable cutting experimental platform. Then a relationship model between the shear flow stress and the hydrostatic stress in the shear zone is built, and the size effect and strain-hardening effect of the shear zone in the turning process are explained reasonably, especially for the influence of them on the chip morphology. The research results show that the slope K of the relationship model is not caused by the Bridgman effect but results from a synergistic action of the size effect and the strain-hardening effect in the shear zone of the workpiece material. The workpiece 40CrMnMo in the shear zone can obtain a better resistance to the inhomogeneous plastic deformation under a certain cutting condition.     

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。     

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.     

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.     

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。     

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 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.     

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.     

Application of a comprehensive dynamic cutting force model to orthogonal wave-generating processes

The dynamics of a cutting process are very complex in nature. They involve not only the changes of plastic state in the intensive shear zone of the chip formation process but also the elastic behaviour of work material surrounding the plastic deformation zone, especially in the vicinity of the tool nose region. As an extension to the previous developments in formulating the shear angle oscillation in dynamic cutting (D. W. Wu, Development of dynamic shear angle model for wave-generating processes based on work-hardening slip-line field theory. Int. J. Mech. Sci. 29, 407–424, 1987; D. W. Wu, Governing equations of the shear angle oscillation in dynamic orthogonal cutting. Trans. ASME J. of Engng for Indust. 108, 280, 1986), a comprehensive dynamic cutting force model has been developed from the mechanics of the cutting process by taking into account the equilibrium of forces in the primary and secondary plastic deformation zones and the redistribution of the contact stress inside the workpiece in the vicinity of the tool nose region.The model has been tested through a computer simulation for orthogonal wave-generating processes. By reference to existing experimental evidence, the theoretical predictions show generally good agreement with the test results.     

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.     

An experimental study on influences of material brittleness on chip morphology

Though several material properties such as hardness, thermal conductivity, specific heat, strain hardening, and thermal softening ability have been studied in terms of influencing segmental or serrated chip formation process, rare study about material brittleness affecting the chip formation process has been carried out. In this paper, an orthogonal cutting experiment with four steels with different brittleness was carried out. The effect of workpiece material brittleness on segmental chip formation and consequent chip morphology was investigated. The experimental results show that the material brittleness heavily affects chip formation process and chip shape. A novel chip formation model was developed to explain the mechanism of material brittleness working on the chip formation process. The mechanism is that material brittleness lowers the value of failure strain and thus makes the maximum stress in flow stress curve occur earlier, which leads to the catastrophic shear instability in primary shear zone and consequent segmented chip.     

绝热剪切型锯齿形切屑第一变形区变形和温度的计算

根据对具有绝热剪切带的锯齿形切屑形成过程的分析，提出一种基于切屑显微测量的计算方法。利用该方法研究了两种回火硬度的30CrNi3MoV高强度钢在正交切削过程中形成的锯齿形切屑内第一变形区的变形和温度，并讨论了切削速度和回火硬度对它们的影响。     

基于修正滑移线场模型的倒棱刀具切削力预测

基于材料塑性滑移理论与刀具刃前材料流动状态分析,提出了一种考虑倒棱刀具负前角切削过程下的材料滞流区（死区）和预剪区的修正滑移线场模型,并给出了材料流动剪切应力和刃前切削几何参数的迭代求解方法,揭示了倒棱刃口几何形状与滑移线场几何参数之间的变化规律。将此模型应用于倒棱刀具切削过程,得到了适用于倒棱刀具正交切削力的预测方法。采用有限元仿真和切削试验相结合的方法对所提出的滑移线场模型和切削力预测方法分别进行了验证,模型预测结果与仿真结果和试验测量结果对比误差均在10%以内。研究结果为研究倒棱几何形状对工件材料流动特性和刀具切削性能的影响提供了参考。     

A New Slip-Line Field Modeling of Orthogonal Machining with a Rounded-Edge Worn Cutting Tool

In this study, a new slip-line field model and its associated hodograph for orthogonal cutting with a rounded-edge worn cutting tool are developed using Dewhurst and Collins's matrix technique. The new model considers the existence of dead metal zone in front of the rounded-edge worn cutting tool. The ploughing force and friction force occurred due to flank wear land, chip up-curl radius, chip thickness, primary shear zone thickness and length of bottom side of the dead metal zone are obtained by solving the model depending on the experimental resultant force data. The effects of flank wear rate, cutting edge radius, uncut chip thickness, cutting speed and rake angle on these outputs are specified.     

The mechanism of ductile chip formation in cutting of brittle materials

A theoretical analysis for the mechanism of ductile chip formation in the cutting of brittle materials is presented in this paper. The coexisting crack propagation and dislocation in the chip formation zone in the cutting of ductile materials are examined based on an analysis of the geometry and forces in the cutting region, both on Taylor’s dislocation hardening theory and the strain gradient plasticity theory. It was found that the ductile chip formation was a result of large compressive stress and shear stress in the chip formation zone, which shields the growth of pre-existing flaws by suppressing the stress intensity factor K _I . Additionally, ductile chip formation in the cutting of brittle materials can result from the enhancement of material yield strength in the chip formation zone. The large compressive stress can be generated in the chip formation zone with two conditions. The first condition is associated with a small, undeformed chip thickness, while the second is related to the undeformed chip thickness being smaller than the radius of the tool cutting edge. The analysis also shows that the thrust force F _t is much larger than the cutting force F _c . This indicates that large compressive stress is generated in the chip formation zone. This also confirms that the ductile chip formation is a result of large compressive stress in the chip formation zone, which shields the growth of pre-existing flaws in the material by suppressing the stress intensity factor K _I . The enhancement of material yield strength can be provided by dislocation hardening and strain gradient at the mesoscale, such that the workpiece material can undertake the large cutting stresses in the chip formation zone without fracture. Experiments for ductile cutting of tungsten carbide are conducted. The results show that ductile chip formation can be achieved as the undeformed chip thickness is small enough, as well as the undeformed chip thickness is smaller than the tool cutting edge radius.     

金属带材少无毛刺精密分切加工新工艺分析

在分析金属带材分切加工过程及其主要缺陷和分切毛刺去除技术的基础上,提出将上下成对圆盘刀设置为轴向负间隙、径向正间隙,在分切过程中,金属板材表面形成剪切缺口但不分开,随后增设压力分断辊使残留材料层延性断裂分离,亦即"塑性剪切压迫分离"。通过设置上下圆盘刀间隙,使刃口作用区材料处于压应力状态而塑性剪切变形形成切口,再经分断辊压力作用,产生二次变形分离,实现少无毛刺精密分切加工。     

Experimental investigation on cutting mechanisms in fixed diamond wire sawing of bone

Bone sawing has been widely used in performing bone surgery. However, thermal necrosis, loss of cutting precision and surface damage may occur in cutting process. The primary objective of this research is to improve cutting performance of bone by advantages of diamond wire sawing. Mechanism of material removal, cutting force, temperature and surface quality are analyzed based on experimental results. It is indicated that wire sawing provides small depth of cut, which is effective to obtain ductile material removal mode. Due to small material removal rate per abrasive, thermal energy is low and most of the heat can be taken away by the cyclic wire and bone chips. Consequently, cutting force and temperature in cutting zone are lower than that of traditional sawing. Due to the high efficiency of chip ejection, burrs and fracture are reduced and a significant improvement in surface quality is achieved. Based on cutting experiments with various values of cutting parameters, it is observed that better performance is achievable at higher wire speeds. These results provide a valuable basis for application of wire sawing and understanding of bone cutting mechanisms.