A new methodology for determining the stress state of the plastic region in machining with restricted contact tools

In rigid-plastic slip-line theory, once the geometry of the slip-line field is established, the stress state of the plastic region (including the primary and secondary deformation zones) in restricted contact machining is governed by the hydrostatic pressure P_A (at a point on the intersection line of the shear plane and the work surface to be machined) and the frictional shear stress τ on the tool rake face. Based on the recently established universal slip-line model and a detailed study of six representative machining cases, a new methodology for determining the stress state of the plastic region, i.e. maximum value principle, is presented in this paper. According to this principle, the stress state of the plastic region can be determined by giving both P_A and τ their theoretical maximum permissible values. The theoretical maximum permissible values of P_A and τ can be found by satisfying four mechanical and geometrical constraint conditions under which the universal slip-line model applies. A comprehensive assessment factor is introduced in this paper. It is shown that the three machining parameters investigated in this present study, i.e. cutting force ratio, chip thickness ratio, and chip back-flow angle can be simultaneously considered to form a comprehensive criterion to compare predicted and experimental results. The applicable range of the maximum value principle is also discussed.     

Machining with tool-chip contact on the tool secondary rake face—Part I: a new slip-line model

Given the growing number of applications of groove-type chip breaker tools in modern machining, it is becoming increasingly important to study the tool-chip contact on the tool secondary rake face. This type of tool-chip contact significantly changes not only the state of stresses in the plastic deformation region, but also changes the distribution of forces and temperatures over the tool rake face. A new slip-line model accounting for the tool-chip contact on the tool secondary rake face is proposed in this paper. The model also takes into account chip curl and incorporates seven slip-line models developed for machining during the last six decades as special cases. Dewhurst and Collins's matrix technique for numerically solving slip-line problems and Powell's algorithm of nonlinear optimization are employed in the mathematical formulation of the model. The inputs of the model include (a) the tool primary rake angle γ₁, (b) the tool secondary rake angle γ₂, (c) the tool land length h, (d) the undeformed chip thickness t₁, (e) the ratio of hydrostatic pressure P_A to the material shear flow stress k, (f) the ratio of frictional shear stress τ₁ on the tool primary rake face to the material shear flow stress k, and (g) the ratio of frictional shear stress τ₂ on the tool secondary rake face to the material shear flow stress k. The outputs of the model include (a) the cutting force F_c/kt₁w and the thrust force F_t/kt₁w, (b) the chip up-curl radius R_u, (c) the chip thickness t₂, and (d) the natural tool-chip contact length l_n.     

Slip-line modeling of built-up edge formation in machining

Extensive investigations on built-up edge (BUE) formation in machining have been conducted in the past. However, very little effort has been made to quantitatively predict the size of the BUE and its effect on chip flow and cutting forces under different machining conditions. This prediction is important because it is the key to predicting the fluctuation of cutting forces and provides better rationale for explaining various machining phenomena associated with BUE formation. A new slip-line model for machining with BUE formation and its associated hodograph are proposed in this paper. Consisting of four slip-line sub-regions, the new slip-line model meets both the stress equilibrium and velocity requirements of material flow. The new model simultaneously predicts the length and height of the BUE, cutting and thrust forces, chip up-curl radius, chip thickness, and tool–chip contact length. Dewhurst and Collins's matrix technique for numerically solving the slip-line problem is employed in the mathematical formulation of the model, with non-unique solutions being obtained. It is demonstrated that one of the four slip-line angles included in the new model directly governs the size and surface shape of the BUE. Compared with the well-known Lee and Shaffer's model, the new model predicts a much longer BUE covering a larger portion of the tool rake face. A small tool rake angle tends to generate a large BUE. The predicted trends of the variation of relevant machining parameters are consistent with experimental observations.     

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.     

A class of slipline field solutions for metal machining with slipping and sticking contact at the chip-tool interface

In the present investigation slipline field solutions for orthogonal machining are presented when the plastically stressed region in the chip/tool contact length consists of both slipping (τk) and sticking (τ=k) zones. The interface friction in the slipping region is assumed to obey Coulomb's law and the fields are analysed using the linear approximation to the above non-linear boundary value problem as suggested by Dewhurst. The range of validity of the above slipline fields is examined from the consideration of overstressing of rigid vertices in the assumed rigid regions. Results are presented for variation of cutting forces, cutting ratio, chip curl radius and contact length with variation in rake angle and interface friction coefficient. Solutions incorporating elastic effects are obtained by the method suggested by Childs. Results from the theoretical analysis are compared with experimental values reported in literature.     

Thermal modeling of the metal cutting process — Part II: temperature rise distribution due to frictional heat source at the tool–chip interface

Heat partition and the temperature rise distribution in the moving chip as well as in the stationary tool due to frictional heat source at the chip–tool interface alone in metal cutting were determined analytically using functional analysis. An analytical model was developed that incorporates two modifications to the classical solutions of Jaeger's moving band (for the chip) and stationary rectangular (for the tool) heat sources for application to metal cutting. It takes into account appropriate boundaries (besides the tool–chip contact interface) and considers non-uniform distribution of the heat partition fraction along the tool–chip interface for the purpose of matching the temperature distribution both on the chip side and the tool side. Using the functional analysis approach, originally proposed by Chao and Trigger (Transactions of ASME, 1951; 73:57–68), a pair of functional expressions for the non-uniform heat partition fraction along the tool–chip interface — one for the moving band heat source (for the chip side) and the other for the stationary rectangular heat source (for the tool side) were developed. Using this analysis, the temperature rise distribution in the chip and the tool were determined for two cases of machining, namely, conventional machining of steel with a carbide tool at high Peclet number (N_Pe≈5–20) and ultraprecision machining of aluminum with a single-crystal diamond tool at low Peclet number (N_Pe–0.5). The calculated temperature rise distribution curves on the two sides of the tool–chip interface are found to be well matched for both cases. The analytical method developed was found to be much faster, easier to use, and more accurate than various numerical methods used earlier. Further, the model provides a better physical appreciation of the thermal aspects of the metal cutting process.     

Numerical experiments on the influence of material and other variables on plane strain continuous chip formation in metal machining

Finite element simulations of metal machining chip formation have been carried out with model materials that have been given a range of thermal softening and strain hardening behaviours. For materials that are approximately perfectly plastic, predictions of slip-line field theory regarding the dependence of chip/tool normal contact stress distribution on the combination of shear plane angle, friction angle and tool rake angle are reproduced. But it has not proved possible to generate the full range of non-unique fields predicted by slip-line theory. The introduction of strain hardening causes chips to thicken but with deviations at high hardening rates from the behaviour proposed by Oxley. These observations are generally in agreement with previously published physical test data. A study of the effect of increasing the cutting edge radius confirms the important effect of that, particularly on tool thrust forces. By continually comparing the results to expectations from more simple modelling, and asking the question ‘Is that expected?’, a general problem of creating a friction law applicable to both plastically flowing high stress conditions and to more lightly loaded elastic conditions has been recognised and is the subject of continuing work.     

Statistical analysis of process parameters in drilling of AL/SICP metal matrix composite

Four micro-holes were made using micro-EDM on rake face of the cemented carbide (WC/TiC/Co) tools. MoS₂, CaF₂, and graphite solid lubricants were respectively embedded into the four micro-holes to form self-lubricated tools (SLT-1, SLT-2, and SLT-3). Dry machining tests on hardened steel were carried out with these self-lubricated tools and conventional tools (SLT-4). The cutting forces, average friction coefficient between tool and chip, and tool wear were measured and compared. It was shown that the cutting forces and tool wear of self-lubricated tools were clearly reduced compared with those of the SLT-4 conventional tool. The SLT-1 self-lubricated tool embedded with MoS₂ just exhibited lower friction coefficient between tool and chip in cutting speed of less than 100?m/min; the SLT-2 self-lubricated tool embedded with CaF₂ possessed lower friction coefficient in cutting speed of more than 100?m/min; and the SLT-3 self-lubricated tool embedded with graphite accomplished good lubricating behaviors steadily under the test conditions. It is indicated that cemented carbide inserts with four micro-holes on rake face embedded with appropriate solid lubricants on rake face is an effective way to reduce cutting forces and rake wear.     

Improved wear resistance of Si3N4 tool inserts by addition of Al2O3 platelets

In the present work, Si₃N₄ matrix composites reinforced with different amounts of Al₂O₃ platelets (0, 30 and 50vol%) were produced with the aim of increasing the tribochemical resistance in the machining of steels. Tool wear was related to the linear increase of the main cutting force (F_c) with time (dF_c/dt); a real-time parameter that can be used to assess the cutting edge damage and to stop machining before the tool fails. For all machined steels, tool wear resistance increased with increasing Al₂O₃ platelet content.     

On the contribution of primary deformation zone-generated chip temperature to heat partition in machining

In machining, the percentage of heat flux that enters the cutting tool can have a critical impact on tool wear especially in dry cutting or high speed machining. In previous work, heat partition was evaluated by iteratively reducing the secondary deformation zone heat flux to the tool until the finite element simulated temperatures matched the experimental measured rake face temperatures. This follow-on work quantifies the contribution of primary zone heat flux to heat partition in machining. In this study, an analytical model was used to evaluate the rise in chip temperature due to primary deformation zone heat source. The heat partition and thermal modelling on the rake face was then conducted with an appropriate initial rake face temperature. Thus primary zone heat loads and shear-force-derived secondary zone heat flux were applied in finite element transient heat transfer analysis to evaluate heat flux into the cutting tool. External dry turning of AISI/SAE 4140 with tungsten carbide-based multilayer TiCN/Al₂O₃-coated tools was conducted for a wide range of cutting speeds between 314 and 879 m/min. Results further support the dominance of secondary zone heat flux on heat partition. The contribution of primary zone heat generation to the cutting tool heat flux in machining was less than 9.5 %. These findings suggest that, to address the thermal problem in machining, research and development should also focus on reducing friction on the rake face (e.g. coating innovations) and reducing contact areas (e.g. rake face design) in addition to the modification of shear angle and hence primary zone heat intensity.     

Machining with applied chip tension—Part II: Experiments

Machining with applied chip tension is the basis of a process, strip peeling, for making small batches of metal special strip products. An approximate slip-line field numerical analysis of the process, related to the matrix method, is presented which shows how pulling stress and its direction affect chip thickness and curvature and tool forces. Pulling parallel to, or within 5° of, the rake face produces straight chips but results in less reduction of chip thickness and tool forces than pulling at more than 5° to the rake face. In the latter case chips are formed curled and are subsequently plastically straightened by the pulling force. Chip failure by plastic straightening and other causes is discussed and it is recommended that the pulling direction should be between 5 and 20° from the rake face. Influences of rake angle and friction stress are also considered.     

Temperature measurement in orthogonal metal cutting

Orthogonal cutting experiments were carried out on steel at different feedrates and cutting speeds. During these experiments the chip temperatures were measured using an infrared camera. The applied technique allows us to determine the chip temperature distribution at the free side of the chip. From this distribution the shear plane temperature at the top of the chip as well as the uniform chip temperature can be found. A finite-difference model was developed to compute the interfacial temperature between chip and tool, using the temperature distribution measured at the top of the chip.Nomenclature contact length with sticking friction behaviour [m] - c specific heat [J kg^–1 K^–1] - contact length with sliding friction behaviour [m] - F _P feed force [N] - F _V main cutting force [N] - h undeformed chip thickness [m] - h _c deformed chip thickness [m] - i,j denote nodal position - k thermal conductivity [W m^–2 K^–1] - L chip-tool contact length [m] - p defines time—space grid, Eq. (11) [s m^–2] - Q _C heat rate entering chip per unit width due to friction at the rake face [W m^–1] - Q _T total heat rate due to friction at the rake face [W m^–1] - Q _% percentage of the friction energy that enters the chip - q ₀ peak value ofq(x) [W m^–2] - q _e heat rate by radiation [W] - q(x) heat flux entering chip [W m^–2] - t time [s] - T temperature [K] - T _C uniform chip temperature [°C] - T _max maximum chip—tool temperature [°C] - T _mean mean chip—tool temperature [°C] - T _S measured shear plane temperature [°C] - x,y Cartesian coordinates [m] - V cutting speed [m s^–1] - V _C chip speed [m/s] - rake angle - ,, control volume lumped thermal diffusivity [m² s^–1] - emmittance for radiation - exponent, Eq. (3) - density [kg m^–3] - Stefan-Boltzmann constant [W m^–2 K⁴] - (x) shear stress distribution [N m^–2] - shear angle     

FEM INVESTIGATION FOR ORTHOGONAL CUTTING PROCESS WITH GROOVED TOOLS-TECHNICAL COMMUNICATION

Rigid-visco-plastic finite element models are used to simulate the chip formation and cracking in the turning processes with grooved tools. The Johnson-Cook constitutive equation and Johnson-Cook damage model, which are appropriate for high-speed machining, are assumed for the workpiece material properties. Thermal effects in cutting are considered. The tool material is considered as rigid, but heat-conducting, with the properties of tool material H11. The calculated chip back-flow angle, curling radius and thickness are analyzed as three typical chip shape parameters. The effects of land length and second rake angle of the grooved tool on chip formation, cracking and temperature are discussed. Some simulation results are compared with other published analytical and experimental results.     

Single-point diamond turning of CaF2 for nanometric surface

Single-crystal CaF₂ is an important optical material. In this work, single-point diamond turning experiments were performed to investigate the nanometric machining characteristics of CaF₂. The effects of tool feed, tool rake angle, workpiece crystal orientation and cutting fluid were examined. It was found that two major types of microfracturing differing in mechanism limited the possibility of ductile regime machining. The critical conditions for microfracturing depend strongly on the tool rake angle and the type of cutting fluid. The results also indicate that one type of the microfractures is caused by thermal effect, and can be completely eliminated by using a sufficiently small undeformed chip thickness and an appropriate negative rake angle under dry cutting conditions. Continuous chips and ductile-cut surfaces with nanometric roughness were generated.     

FEM INVESTIGATION FOR ORTHOGONAL CUTTING PROCESS WITH GROOVED TOOLS–TECHNICAL COMMUNICATION

Rigid-visco-plastic finite element models are used to simulate the chip formation and cracking in the turning processes with grooved tools. The Johnson-Cook constitutive equation and Johnson-Cook damage model, which are appropriate for high-speed machining, are assumed for the workpiece material properties. Thermal effects in cutting are considered. The tool material is considered as rigid, but heat-conducting, with the properties of tool material H11. The calculated chip back-flow angle, curling radius and thickness are analyzed as three typical chip shape parameters. The effects of land length and second rake angle of the grooved tool on chip formation, cracking and temperature are discussed. Some simulation results are compared with other published analytical and experimental results.     

Tool life monitoring during the diamond turning of electroless Ni–P

Diamond tools become severely worn when machining Ni–P plating materials. Tool life monitoring is therefore essential to avoid the deterioration of workpiece quality. In this paper, in order to better detect tool life while the tools are in use, detailed investigations of the cutting force and acoustic emission (AE) measured during diamond turning process have been made. The results of this tool-life testing show that the cutting force and AE supply valuable information on tool failure; the dynamic component of the thrust force fluctuates chaotically when the tool dulls. This phenomenon can be detected using the 1/f^β power spectrum with a spectral exponent of β > 1. On the other hand, the AE amplitude a tends to rise just when chipping occurs on the cutting edge. This feature can be detected by the amplitude distribution spectrum, in which the AE event rate follows the power law a^−m with a scaling exponent of m < 2. Therefore, we can conclude that a spectral exponent of β > 1 and a scaling exponent of m < 2 can be used as the criteria to gauge tool life, because it was observed at the end of the tool life that tool corner had become worn out and that chipping had occurred on the cutting edge.     

Focused ion beam-shaped microtools for ultra-precision machining of cylindrical components

Focused ion beam (FIB) sputtering is used to shape a variety of cutting tools with dimensions in the 15–100 μm range and cutting edge radii of curvature of 40 nm. The shape of each microtool is controlled to a pre-specified geometry that includes rake and relief features. We demonstrate tools having rectangular, triangular, and other complex-shaped face designs. A double-triangle tip on one tool is unique and demonstrates the versatility of the fabrication process. The FIB technique allows observation of the tool during fabrication, and, thus, reproducible features are generated with sub-micron precision. Tools are made from tungsten carbide, high-speed tool steel, and single crystal diamond. Application of FIB-shaped tools in ultra-precision microgrooving tests shows that the cross-section of a machined groove is an excellent replication of the microtool face. Microgrooves on 40–150 μm pitch are cut into 3 mm diameter polymer rods, for groove arc lengths greater than 12 cm. The surface finish of machined features is also reported; groove roughness (R_a) is typically less than 0.2 μm. Ultra-precision machining of cylindrical substrates is extended to make bound metal microcoils having feature sizes of 20–40 μm.     

Predictive model to estimate the stress–strain curves of bulk metals using nanoindentation

Many studies have shown that finite element modeling (FEM) can be used to fit experimental load–displacement data from nanoindentation tests. Most of the experimental data are obtained with sharp indenters. Compared to the spherical case, sharp tips do not directly allow the behavior of tested materials to be deduced because these produce a nominally-constant plastic strain impression. The aim of this work is to construct with FEM an equivalent stress–strain response of a material from a nanoindentation test, done with a pyramidal indenter. The procedure is based on two equations which link the parameters extracted from the experimental load–displacement curve with material parameters, such as Young's modulus E, yield stress Y₀ and tangent modulus E_T. We have already tested successfully the relations on well-known pure metallic surfaces. However, the load–displacement curve obtained using conical or pyramidal indenters cannot uniquely determine the stress–strain relationship of the indented material. The non-uniqueness of the solution is due to the existence of a characteristic point (ε_c, σ_c); for a given elastic modulus, all bilinear stress–strain curves that exhibit the same true stress σ_c at the specific true strain ε_C lead to the same loading and unloading indentation curve. We show that the true strain ε_c is constant for all tested materials (Fe, Zn, Cu, Ni), with an average value of 4.7% for a conical indenter with a half-included angle θ=70.3°. The ratio σ_c/ε_c is directly related to the elastic modulus of the indented material and the tip geometry.     

Investigation and prediction of chip geometry in diamond turning

Management of the chips generated in diamond turning is often critical, because contact between chips and the workpiece can result in superficial damage to the finished surface. Controlling chip motion is not a trivial process as the proper positioning of an oil or air stream requires an understanding of the dynamics of a diamond turned chip and the machining parameters that affect it. Work has been performed to investigate the effects of cutting speed, depth of cut, tool geometry, tool wear, and workpiece material properties on chip motion and geometry. Utilizing radius of curvature data from cutting experiments, a parameter has been proposed that can be used to predict chip radius of curvature for a wide range of machining conditions. This chip curvature parameter, χ, exhibits a power law relationship with chip radius of curvature as a function of tool geometry, depth of cut, cutting speed, and both elastic and plastic properties of the workpiece material.