Analytical and experimental investigation of rake contact and friction behavior in metal cutting

In this study, the friction behavior in metal cutting operations is analyzed using a thermomechanical cutting process model that represents the contact on the rake face by sticking and sliding regions. The relationship between the sliding and the overall, i.e. apparent, friction coefficients are analyzed quantitatively, and verified experimentally. The sliding friction coefficient is identified for different workpiece–tool couples using cutting and non-cutting tests. In addition, the effect of the total, sticking and sliding contact lengths on the cutting mechanics is investigated. The effects of cutting conditions on the friction coefficients and contact lengths are analyzed. It is shown that the total contact length on the rake face is 3–5 times the feed rate. It is observed that the length of the sliding contact strongly depends on the cutting speed. For high cutting speeds the contact is mainly sliding whereas the sticking zone can be up to 30% of the total contact at low speeds. From the model predictions and measurements it can be concluded that the sticking contact length is less than 15% for most practical operations. Furthermore, it is also demonstrated that the true representation of the friction behavior in metal cutting operations should involve both sticking and sliding regions on the rake face for accurate predictions. Although the main findings of this study have been observed before, the main contribution of the current work is the quantitative analysis using an analytical model. Therefore, the results presented in this study can help to understand and model the friction in metal cutting.     

Mechanics of boring processes—Part II—multi-insert boring heads

Mechanics of boring operations are presented in the paper. The distribution of chip thickness along the cutting edge is modeled as a function of tool inclination angle, nose radius, depth of cut and feed rate. The cutting mechanics of the process is modeled using both mechanistic and orthogonal to oblique cutting transformation approaches. The forces are separated into tangential and friction directions. The friction force is further projected into the radial and feed directions. The cutting forces are correlated to chip area using mechanistic cutting force coefficients which are expressed as a function of chip-tool edge contact length, chip area and cutting speed. For tools which have uniform rake face, the cutting coefficients are predicted using shear stress, shear angle and friction coefficient of the material. Both approaches are experimentally verified and the cutting forces in three Cartesian directions are predicted satisfactorily. The mechanics model presented in this paper is used in predicting the cutting forces generated by inserted boring heads with runouts and presented in Part II of the article [1].     

Mechanics of boring processes—Part I

Mechanics of boring operations are presented in the paper. The distribution of chip thickness along the cutting edge is modeled as a function of tool inclination angle, nose radius, depth of cut and feed rate. The cutting mechanics of the process is modeled using both mechanistic and orthogonal to oblique cutting transformation approaches. The forces are separated into tangential and friction directions. The friction force is further projected into the radial and feed directions. The cutting forces are correlated to chip area using mechanistic cutting force coefficients which are expressed as a function of chip-tool edge contact length, chip area and cutting speed. For tools which have uniform rake face, the cutting coefficients are predicted using shear stress, shear angle and friction coefficient of the material. Both approaches are experimentally verified and the cutting forces in three Cartesian directions are predicted satisfactorily. The mechanics model presented in this paper is used in predicting the cutting forces generated by inserted boring heads with runouts and presented in Part II of the article [1].     

Slip-line field model of micro-cutting process with round tool edge effect

This paper presents a slip-line field model which considers the stress variation in the material deformation region due to the tool edge radius effect. The Johnson-Cook constitutive model is applied to obtain the shear flow stress and hydrostatic pressure as functions of strain, strain-rate, and temperature in the primary shear zone. The friction parameters between the rake face and chip are identified from cutting tests. The sticking and sliding contact zones between the tool and chip are considered in the secondary shear zone. The total cutting forces are evaluated by integrating the forces along the entire chip-rake face contact zone and the ploughing force caused by the round edge. The proposed model is experimentally verified by a series of cutting force measurements conducted during micro-turning tests. Micro-cutting process is analyzed from a series of slip-line field simulations.     

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.     

Prediction of tool and chip temperature in continuous and interrupted machining

In this paper, a numerical model based on the finite difference method is presented to predict tool and chip temperature fields in continuous machining and time varying milling processes. Continuous or steady state machining operations like orthogonal cutting are studied by modeling the heat transfer between the tool and chip at the tool—rake face contact zone. The shear energy created in the primary zone, the friction energy produced at the rake face—chip contact zone and the heat balance between the moving chip and stationary tool are considered. The temperature distribution is solved using the finite difference method. Later, the model is extended to milling where the cutting is interrupted and the chip thickness varies with time. The time varying chip is digitized into small elements with differential cutter rotation angles which are defined by the product of spindle speed and discrete time intervals. The temperature field in each differential element is modeled as a first-order dynamic system, whose time constant is identified based on the thermal properties of the tool and work material, and the initial temperature at the previous chip segment. The transient temperature variation is evaluated by recursively solving the first order heat transfer problem at successive chip elements. The proposed model combines the steady-state temperature prediction in continuous machining with transient temperature evaluation in interrupted cutting operations where the chip and the process change in a discontinuous manner. The mathematical models and simulation results are in satisfactory agreement with experimental temperature measurements reported in the literature.     

基于有限元的前刀面应力分布研究

利用有限元方法研究切削加工过程中刀具与切屑的接触区域内前刀面应力分布，发现接触区域的摩擦系数和最大切应力值的选取与接触表面信息有关。结果表明:从刀尖到刀屑分离点处，前刀面应力呈快速下降—缓慢降低—明显下降的过程；切削厚度对应力分布有较大影响，当切削厚度为0.13 mm时应力曲线不再出现缓慢降低的过程；切削速度对应力分布、接触长度和切屑厚度的影响较小。      

Prediction of ball-end milling forces from orthogonal cutting data

The mechanics of cutting with helical ball-end mills are presented. The fundamental cutting parameters, the yield shear stress, average friction coefficient on the rake face and shear angle are measured from a set of orthogonal cutting tests at various cutting speeds and feeds. The cutting forces are separated into edge or ploughing forces and shearing forces. The helical flutes are divided into small differential oblique cutting edge segments. The orthogonal cutting parameters are carried to oblique milling edge geometry using the classical oblique transformation method, where the chip flow angle is assumed to be equal to the local helix angle. The cutting force distribution on the helical ball-end mill flutes is accurately predicted by the proposed method, and the model is validated experimentally and statistically by conducting more than 60 ball-end milling experiments.     

Effects of micro-milling conditions on the cutting forces and process stability

Determining stable cutting conditions for corresponding cutting tools with specific geometries is essential for achieving precision micro-milling with high surface quality. Therefore, this paper investigates the influence of the tool rake angle, tool wear and workpiece preheating on the cutting forces and process stability. An advanced micro-milling cutting force model considering the tool wear is proposed. The micro-milling cutting forces are predicted and compared with experimentally obtained results for two cutting conditions and four edge radii measured at different stages of the tool wear. It is found that the cutting forces increase by increasing the edge radius. It is also observed that the cutting forces are higher at a rake angle of 0° compared with a rake angle of 8°. The increase of the cutting forces is mainly associated with the change of the friction conditions between the tool and workpiece contact. Stability lobes are obtained for different edge radii, rake angles of 0° and 8°, initial workpiece temperature and different measured static run-outs. The predicted stability lobes are compared with the micro-milling force signals transformed into the frequency domain. It is observed that the predicted stability limits result in good correlation with the experimentally obtained chatter free conditions. Also, the stability limits are higher at smaller edge radii, higher preheating workpiece temperature and positive rake angles.     

单晶锗纳米切削过程应力场分布的分子动力学研究

为了进一步研究单晶锗的微纳米切削机理,首次采用分子动力学方法研究了材料原子的应力场分布以及不同刀具角度对应力分布的影响。采用近邻平均法计算了切削过程中不同时刻的hydrostatic应力和von Mises平均应力值。结果表明,在单晶锗的纳米切削过程中,最大平均应力集中于刀具尖端的亚表面区域,最大应力值为8.6Gpa。在切屑中也有很高的应力值,在4.2GPa左右。此外,刀具的角度也对应力场的分布有很大影响,绘制了不同刀具角度的切削力曲线。发现,刀具前角对切削力有显著影响。刀具采用负前角切削时切削力最大,而刀具后角对切削力没有影响,这与宏观切削理论相一致。     

Simulation of 3D chip shaping of aluminum alloy 7075 in milling processes

By adopting an equivalent geometry model of machining process and considering thermo-plastic properties of the work material, a finite element method（FEM） to study oblique milling process of aluminum alloy with a double-edge tool was presented. In the FEM, shear flow stress was determined by material test. Re-meshing technology was used to represent chip separation process. Comparing the predicted cutting forces with the measured forces shows the 3D FEM is reasonable. Using this FEM, chip forming process and temperature distribution were predicted. Chips obtained by the 3D FEM are in spiral shape and are similar to the experimental ones. Distribution and change trend of temperature in the tool and chip indicate that contact length between tool rake face and chip is extending as tool moving forward. These results confirm the capability of FEM simulation in predicting chip flow and selecting optimal tool.     

Analytical modeling and experimental validation of micro end-milling cutting forces considering edge radius and material strengthening effects

This paper presents a novel micro end-milling cutting forces prediction methodology including the edge radius, material strengthening, varying sliding friction coefficient and run-out together. A new iterative algorithm is proposed to evaluate the effective rake angle, shear angle and friction angle, which takes into account the effects of edge radius as well as varying sliding friction coefficient. A modified Johnson–Cook constitutive model is introduced to estimate the shear flow stress. This model considers not only the strain-hardening, strain-rate and temperature but also the material strengthening. Furthermore, a generalized algorithm is presented to calculate uncut chip thickness considering run-out. The cutting forces model is calibrated and validated by NAK80 steel, and the relevant micro slot end-milling experiments are carried out on a 3-axis ultra-precision micro-milling machine. The comparison of the predicted and measured cutting forces shows that the proposed model can provide very accurate predicted results. Finally, the effects of material strengthening, edge radius and cutting speed on the cutting forces are investigated by the proposed model and some conclusions are given as follows: (1) the material strengthening behavior has significant effect on micro end-milling process at the micron level. (2) Cutting forces predicted increase with the increase of edge radius. (3) Considering varying sliding friction coefficient can enhance the sensitivity of the predicted cutting forces to cutting speed.     

A new thermomechanical model of cutting applied to turning operations. Part I. Theory

In this paper, an analytical approach is used to model the thermomechanical process of chip formation in a turning operation. In order to study the effects of the cutting edge geometry, it is important to analyse its global and local effects such as the chip flow direction, the cutting forces and the temperature distribution at the rake face. To take into account the real cutting edge geometry, the engaged part in cutting of the rounded nose is decomposed into a set of cutting edge elements. Thus each elementary chip produced by a straight cutting edge element, is obtained from an oblique cutting process. The fact that the local chip flow is imposed by the global chip movement is accounted for by considering appropriate interactions between adjacent chip elements. Consequently, a modified version of the oblique cutting model of Moufki et al. [Int. J. Mech. Sci. 42 (2000) 1205; Int. J. Mach. Tools Manufact. 44 (9) (2004) 971] is developed and applied to each cutting edge element in order to obtain the cutting forces and the temperature distributions along the rake face. The material characteristics such as strain rate sensitivity, strain hardening and thermal softening, the thermomechanical coupling and the inertia effects are taken into account in the modelling. The model can be used to predict the cutting forces, the global chip flow direction, the surface contact between chip and tool and the temperature distribution at the rake face which affects strongly the tool wear. Part II of this work consists in a parametric study where the effects of cutting conditions, cutting edge geometry, and friction at the tool–chip interface are investigated. The tendencies predicted by the model are also compared qualitatively with the experimental trends founded in the literature.     

Upper bound analysis of oblique cutting: improved method of calculating the friction area

This paper describes further development of the upper bound analysis of oblique cutting with nose radius tools described previously by Adibi-Sedeh et al. [[1]] by incorporation of an improved method for calculating the friction area at the chip-tool interface. Previously, the friction area was obtained from the shear surface area assuming that the ratio of these areas is the same as in orthogonal machining. Our results showed that this led to overestimation of the effect of friction on the chip flow angle, thereby resulting in smaller changes in the chip flow angle with inclination angle as compared to experimental data. In the new approach, the chip-tool contact length is obtained from the length of the shear surface assuming that the ratio of the lengths is the same as in orthogonal machining and the friction area is calculated using this length. The chip flow angle predicted using the new approach shows much better agreement with experimental data. In particular, the dependence of the chip flow angle on the inclination angle is accurately reproduced. Upper bound analysis of oblique cutting using this new model for the friction area provides an elegant explanation for the relative influence of the normal and equivalent rake angles on the cutting force.     

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.     

A new thermomechanical model of cutting applied to turning operations. Part II. Parametric study

In Part I of this work, Molinari and Moufki [Int. J. Mach. Tools Manufact., this issue], an analytical model of three-dimensional cutting is developed for turning processes. To analyse the influences of cutting edge geometry on the chip formation process, global effects such as the chip flow direction and the cutting forces, and local effects such as the temperature distribution and the surface contact at the rake face have been investigated. In order to accede to local parameters, the engaged part in cutting of the rounded nose is decomposed into a set of cutting edge elements. Thus each elementary chip, produced by a straight cutting edge element, is obtained from an oblique cutting process defined by the corresponding undeformed chip section and the local cutting angles. The present approach takes into account the fact that for each cutting edge element the local chip flow is imposed by the global chip movement. The material characteristics such as strain rate sensitivity, strain hardening and thermal softening, the thermomechanical coupling and the inertia effects are considered in the modelling. A detailed parametric study is provided in this paper in order to analyse the effects of cutting speed, depth of cut, feed, nose radius and cutting angles on cutting forces, global chip flow direction and temperature distribution at the rake face. The influence of friction at the tool–chip interface is also discussed.     

A novel methodology to characterize tool-chip contact in metal cutting using partially restricted contact length tools

A novel methodology to map the friction and normal stress distribution on the rake face using Partially Restricted Contact Length Tools in orthogonal cutting tests is proposed. The influence of cutting speed, feed and coatings on tool-chip friction when machining AISI 1045 is analysed. The results demonstrate that the new methodology can replace the more difficult to use and less robust split-tool method. They confirm two clearly different contact zones: i) the sticking region, governed by the shear flow stress of the workpiece and ii) the sliding region, where the friction coefficient is higher than 1.     

Upper bound analysis of oblique cutting with nose radius tools

A generalized upper bound model for calculating the chip flow angle in oblique cutting using flat-faced nose radius tools is described. The projection of the uncut chip area on the rake face is divided into a number of elements parallel to an assumed chip flow direction. The length of each of these elements is used to find the length of the corresponding element on the shear surface using the ratio of the shear velocity to the chip velocity. The area of each element is found as the cross product of the length and its width along the cutting edge. Summing up the area of the elements along the shear surface, the total shear surface area is obtained. The friction area is calculated using the similarity between orthogonal and oblique cutting in the ‘equivalent’ plane that includes both the cutting velocity and chip velocity. The cutting power is obtained by summing the shear power and the friction power. The actual chip flow angle and chip velocity are obtained by minimizing the cutting power with respect to both these variables. The shape of the curved shear surface, the chip cross section and the cutting force obtained from this model are presented.     

The transient beginning to machining and the transition to steady-state cutting

Knowledge of the physics behind the separation of material at the tip of the tool is of great importance for understanding the mechanisms of chip formation. How material separates along the parting line to form the chip and cut surface is still not well understood, yet it is of great importance for improving the robustness, enhancing the predictability and extending the application of currently existing finite element computer programs. This paper attempts to provide some answers to these issues by means of a combined numerical and experimental investigation of the transient beginning to machining and the transition to steady-state orthogonal metal cutting. Numerical modelling was performed by means of an updated-Lagrangian approach based on the finite element flow formulation and experiments were carried out on lead specimens under laboratory-controlled conditions. Forces and displacements are given for the initial indentation phase during which material is displaced up the rake face of the tool. Ductile damage begins to accumulate, eventually leading to separation at the tool tip. This marks the onset of a second stage during which further displacement of material along the rake face is accompanied by separation of material at the tool tip (i.e. cracking), which now continues in all subsequent deformation. The displaced material, although not yet attaining its fullest extent, now begins to take on the appearance of a continuous chip. A third stage begins when the material, which up till now has been in intimate contact with the rake face, develops curvature and leaves the tool. This does not, however, mark the beginning of steady-state cutting, because chip curl continues to increase until a steady value is attained. During this period, the contact length with the tool then reduces somewhat, before settling down to a steady value. The thrust force is a maximum at the point of greatest chip contact length. The paper demonstrates that material separation is caused by shearing rather than tension. The specific distortional energy is an appropriate criterion for evaluating ductile damage in shear and the onset of separation ahead of the cutting edge. In turn this determines the value of the fracture toughness in shear.     

Influence of the direction and flow rate of the cutting fluid on tool life in turning process of AISI 1045 steel

High-pressure coolant (HPC) delivery is an emerging technology that delivers a high-pressure fluid to the tool and machined material. The high fluid pressure allows a better penetration of the fluid into the tool–workpiece and tool–chip contact regions, thus providing a better cooling effect and decreasing tool wear through lubrication of the contact areas.The main objective of this work is to understand how the tool wear mechanisms are influenced by fluid pressure, flow rate and direction of application in finish turning of AISI 1045 steel using coated carbide tools.The main finding was that when cutting fluid was applied to the tool rake face, the adhesion between chip and tool was very strong, causing the removal of tool particles and large crater wear when the adhered chip material was removed from the tool by the chip flow. When cutting fluid was not applied to the rake face, adhesion of chip material to the face did occur, but was not strong enough to remove tool particles as it moved across the face, and therefore crater wear did not increase.