基于斜角切削的曲线端铣切削力建模

切削力预测是制定与优化加工工艺的重要环节。针对曲线端铣加工过程,提出一种基于斜角切削的切削力建模方法。将刀具沿轴向微分,以曲线微分几何计算微元刃上的工作基面。在微元刃的工作法平面参考系中,应用最小能量原理,构建微元刃中力矢量、速度矢量、流屑角、法向摩擦角、法向剪切角及剪应力等切削参数之间的约束。以单齿直线铣削试验对切削参数进行标定,其中法向摩擦角、法向剪切角及剪应力等可表示为瞬时未变形切屑厚度的函数。选取高强度钢PCrNi3MoVA试件,分别进行圆弧和Bézier曲线端铣加工试验。试验结果表明,曲线端铣时切削力的变化与瞬时进给方向和曲线曲率相关。切削力预测值的幅值大小和变化趋势与试验值一致,验证了该切削力建模方法的有效性。     

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.     

KDP晶体超精密切削各向异性的理论研究

KDP晶体作为优质的非线性光学材料被广泛应用于“惯性约束核聚变”固体激光器中,且被赋予相当严格的制造精度。本文利用剪切变形比能最大及单晶材料不同晶面晶向剪切弹性模量不同的原理,结合超精密切削模型,从理论上计算出不同晶面、不同晶向及不同刀具前角超精密切削条件下的剪切角,得到其在不同切削条件下的变化规律,并由此解释了切削加工中由KDP晶体各向异性所导致的工件表面粗糙度的各向异性。     

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.     

High-speed milling of CFRP composites: a progressive damage model of cutting force

Three-dimensional Hashin failure criterion and material stiffness degradation model were compiled by VUMAT subroutine. The Abaqus/Explicit solver was performed to establish progressive damage model of cutting force for CFRP high-speed milling, and high-speed milling experiments with different cutting parameters were carried out. Further, the impact mechanism of fiber cutting angle and cutting parameters on cutting force, stress, and material failure during milling was explored, and the material removal mechanism in high-speed milling of CFRP was revealed. The results show that the error between the experimental and simulated of cutting forces is less than 5%, which indicates that the progressive damage model is feasible. The fiber cutting angle has significant influence on cutting force and stress in cutting process, and the cutting direction has a significant influence on cutting force. In addition, cutting parameters play a critical role in cutting force, and the feed per tooth is the most significant factor affecting the cutting force. Simultaneously, the progressive damage model predicts that the shear failure of materials mainly concentrates in the cutting area and extends along the feed direction. Finally, the material removal mechanism of CFRP in high-speed milling was revealed combining cutting force experiment.     

Fundamental modeling for oblique cutting by thermo-elastic-plastic FEM

In this paper, the finite deformation theory and updated Lagrangian formulation were used to describe the oblique cutting process. Either the tool geometrical location condition or the strain energy density constant was combined with the twin node processing method to act as the chip separation criterion. An equation of three-dimensional tool face geometrical limitation was first established to inspect and correct the relation between the chip node and the tool face. And, a three-dimensional finite-difference heat transfer equation was derived. Based on this approach, tool advancement was achieved in displacement increment step by step from the initial tool contact with the workpiece till the formation of steady cutting force. In this case, a large deformation thermo-elastic–plastic finite element model for oblique cutting was established. The mild steel was used as the workpiece, the tool was P20 and the cutting speed was 274.8 mm/s in this article. The chip deformation process and temperature effect on the strain energy density, chip flow angle, cutting force and specific cutting energy were studied first. Finally, the integrity on machined workpiece surface was explored from the variation of residual stresses and temperature distribution on it after cutting. During the chip deformation process, the chip flow angle obtained by this simulation result was approximately equal to the tool inclination angle, which confirmed with the geometrical requirement of Stabler’s criterion. Besides, the simulated specific cutting energy was compared with the experimental specific cutting energy value, the result of which was within acceptable range. It is obvious from the above findings that the model presented in this paper is consistent with the geometrical and mechanical requirements, which verifies the proposed model is acceptable.     

A NEW MECHANISTIC MODEL FOR PREDICTING WORN TOOL CUTTING FORCES

An enhanced model for predicting worn tool cutting forces in metal cutting without the need for any worn tool calibration tests is presented in this paper. The new model utilizes a previously developed slip-line field approach in conjunction with a mechanistic force model to predict the shear flow stress and shear angle for a range of cutting conditions with only a minimal number of sharp tool calibration tests. The shear flow stress and shear angle values are then used as inputs into a worn tool force model to predict the cutting forces due to tool flank wear. Predictions of worn tool cutting forces from the new model have been compared to experimental data from both a steel and a ductile iron workpiece. Ductile iron tests are significant because previous shear flow stress and shear angle models require chip measurements which cannot be made with the chips produced by iron workpieces. Model predictions are also compared to literature data obtained using an aluminum workpiece. An excellent comparison between the model predictions and the experimental data is found for all of the materials considered.     

PDC钻头切削断面对破岩效率的影响

基于弹塑性力学和岩石力学,以Drucker-Prager 准则作为岩石的本构关系,采用剪切失效准则,在验证岩石模型及PDC齿破岩建模方法可行性的基础上,建立了PDC齿切削3种典型断面岩石的三维有限元模型,并针对井底不同围压,研究了切削断面的面积、切削齿的后倾角及侧转角对破岩效率的影响。结果表明：不论何种围压,减小切削断面的面积有利于岩石的破碎,且应多采用宽切削断面进行PDC钻头径向布齿;切削齿后倾角对岩石破碎效率影响大于切削齿的侧转角对岩石破碎效率影响,切削齿最优破岩后倾角在低围压下为5°,在高围压下为20°。     

Upper Bound Analysis of Turning Using Sharp Corner Tools

A generalized upper bound model of turning operations using flat-faced sharp corner tools with both the side and end cutting edges engaged in cutting is described. The projection of the uncut chip area on the rake face plane is divided into a few regions separated by lines parallel to the chip flow direction at transition points. The area of each of these regions is transformed to the area of the corresponding regions of the shear surface using the ratio of the shear speed to the chip speed. Summing up the area of these regions, the total shear surface area is obtained. The tool-chip contact length at vertices is obtained from the length along the shear surface using the similarity between orthogonal and oblique cutting in the “equivalent” plane (the plane formed by the cutting velocity and chip velocity). Knowing the tool-chip contact length, the friction area is calculated. The chip flow angle and chip speed are obtained by minimizing the cutting power with respect to both these variables. Comparison of the chip flow angle predicted by the current model with the chip flow angle measured by direct high speed photography of the chip motion over the tool rake face shows good correlation between the two for various tool geometries and cutting conditions. The shape of the shear surface and the chip cross section predicted by the model are also presented.     

高速切削过程绝热剪切局部化断裂预测

基于高速切削过程绝热剪切饱和极限理论,结合锯齿形切屑绝热剪切带的变形和受力条件,以及材料的动态塑性本构关系,建立以切削速度、切削厚度和刀具前角为预测变量的高速切削过程绝热剪切局部化断裂的预测模型,并以淬硬45钢和FV520(B)不锈钢为例,预测其发生绝热剪切局部化断裂的临界切削条件。通过高速切削试验和金相试验,讨论了切削条件对绝热剪切局部化断裂过程的影响规律和敏感程度,验证了绝热剪切局部化断裂的预测结果。结果表明:较大切削厚度和较小刀具前角会降低绝热剪切局部化断裂的临界切削速度,建立的绝热剪切局部化断裂预测模型能有效预测切屑发生绝热剪切局部化断裂的临界切削条件。     

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.     

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.     

Crystal anisotropy-dependent shear angle variation in orthogonal cutting of single crystalline copper

Shear deformation that dominates elementary chip formation in metal cutting greatly relies on crystal anisotropy. In the present work we investigate the influence of crystallographic orientation on shear angle in ultra-precision orthogonal diamond cutting of single crystalline copper by joint crystal plasticity finite element simulations and in-situ experiments integrated in scanning electron microscope. In particular, the experimental cutting conditions including a straight cutting edge are the same with that used in the 2D finite element simulations. Both simulations and experiments demonstrate a well agreement in chip profile and shear angle, as well as their dependence on crystallography. A series of finite element simulations of orthogonal cutting along different cutting directions for a specific crystallographic orientation are further performed, and predicated values of shear angle are used to calibrate an extended analytical model of shear angle based on the Ernst–Merchant relationship.     

用切削速度模型求解剪切角的新方法

通过对切削区速度场的分析，建立了切削过程的速度模型。根据此模型，导出了二元切削时求解剪切角φ的简化公式。此公式的计算结果比现有的其他公式更接近实际情况。由此得出结论：在切削过程中，剪切角φ的大小不仅取决于刀具前角γｏ，而且和被切材料在剪切前后的速度之比｜ｖ｜／｜ｖｃ｜有较大关系。     

Effect of material anisotropy on shear angle prediction in metal cutting—a mesoplasticity approach

Material anisotropy plays an important role in the formation of shear angle in metal cutting. Crystallographic textures contribute to an important source of material anisotropy. A simplified mesoplasticity model is proposed in this paper to predict the effect of crystallographic orientations on the shear angle formation in machining a polycrystalline work material. The most likely shear angle is the one at which the Taylor factor is minimum. A good agreement is found between the predicted shear angle in machining a polycrystalline OFHC copper and the experimental data reported in the published literature. The assumptions made in the model approximate well the cutting conditions commonly encountered in single point diamond turning process.     

考虑后刀面磨损条件下的正交切削模型分析

在试验研究基础上进行了有后刀面磨损的正交切削模型分析。经过正交切削试验及理论分析,发现后刀面磨损无论是定性上还是定量上都不影响刀具基本切削或剪切过程,即不改变剪切角和摩擦角,但是在磨损区的摩擦力及整个切削力都会增加。充分利用剪切区分析理论,确定了剪切区的切削力、后刀面磨擦力和后刀面磨损量的对应关系,从而建立了在后刀面磨损情况下的切削力模型。     

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.     

基于斜角切削理论的钛合金螺旋铣孔切削力建模

通过分析螺旋铣孔的加工原理和计算加工过程中的运动向量,结合侧刃和底刃对切削力的影响,建立了螺旋铣孔过程的切削力解析模型。提出了基于斜角切削的切削力系数辨识方法,并根据斜角切削过程几何关系推导出摩擦角、剪切角、剪切应力的约束方程。开展切削力系数辨识试验和钛合金螺旋铣孔试验对仿真值进行验证,结果表明,切削力的仿真值与试验值误差较小,平均误差为9.55%,从而验证了斜角切削系数辨识方法的有效性和切削力模型的正确性。     

ROLE OF MICROSTRUCTURAL SOFTENING EVENTS IN METAL CUTTING

Oxley's model for predicting equilibrium shear angle turns out to be the most comprehensive approach that incorporates both the mechanics of metal cutting and dynamic behavior of metal during metal cutting. Oxley's prediction of equilibrium shear angle for flow chip morphology is validated in metal cutting at low cutting speeds. However, the domain of flow chip is limited by major microstructural softening events that occur at high cutting speeds particularly if the matrix is hardened by heat treatment or there is a large volume fraction of second phase particles. Dynamic recrystallisation and phase transformation are identified as major microstructural softening events occurring in the hardened matrix that cause shear localisation. Incompatibility of deformation between the matrix and second phase particles causes shear localisation due to geometric softening.

Quantitative modeling to predict the critical speed for the onset of shear localised chip morphology requires quantitative database on the dynamic flow stress behavior of materials that duly incorporates the microstructural softening events, which is the critical path. Quantitative analysis of phenomenological database in model alloys has shown that shear localisation can be suppressed by engineering glassy oxide inclusions that lubricate in-situ the tool-chip interface. This concept underlies the development of self-lubricating steel designed to suppress chemical wear in high speed machining.