A study of high-performance plane rake faced twist drills. Part II: Predictive force models

Predictive cutting models for the thrust, torque and power in drilling operations using modified plane rake faced twist drills are presented and discussed. The models are based on the mechanics of cutting approach incorporating the many tool and cutting process variables and have been assessed by numerically analysing the predicted trends and by comparing with the experimental data. It is shown that the model predictions are in excellent agreement with the experimental results with an average deviation of about 5%. Simpler “empirical-type” thrust, torque and power equations are also established for use as an accurate alternative to the complex predictive models to facilitate practical applications.     

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.     

An investigation into the mechanics of cutting using data from orthogonally cutting Nylon 66

Cutting force data for Nylon 66 has been examined in terms of various different models of cutting. Theory that includes significant work of separation at the tool tip was found to give the best correlation with experimental data over a wide range of rake angles for derived primary shear plane angle. A fracture toughness parameter was used as the measure of the specific work of separation. Variation in toughness with rake angle determined from cutting is postulated to be caused by mixed mode separation at the tool tip. A rule of mixtures using independently determined values of toughness in tension (mode I) and shear (mode II) is found to describe well the variation with rake angle. The ratio of modes varies with rake angle and, in turn, with the primary shear plane angle. Previous suggestions that cutting is a means of experimentally determining fracture toughness are now seen to be extended to identify the mode of fracture toughness as well.     

A model for cutting forces generated during machining with self-propelled rotary tools

In this paper, a force model for self-propelled rotary tool is presented. Conventional oblique cutting force predictions were reviewed and extended to predict the cutting forces generated during machining with the self-propelled rotary tools. The model presented is based on Oxley's analysis and was verified by cutting tests using a typical self-propelled tool. Good agreement was obtained between the predicted and the experimentally measured forces under a wide range of cutting conditions. The effect of different cutting conditions on the friction coefficient along the chip/tool interface and tool rake face normal force were also presented and discussed.     

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.     

Prediction of cutting forces in three and five-axis ball-end milling with tool indentation effect

Simulation of multi-axis ball-end milling of dies, molds and aerospace parts with free-form surfaces is highly desirable in order to optimize the machining processes in virtual environment ahead of costly trials. This paper presents a mechanics model that predicts the cutting forces in feed (x), normal (y) and axial (z) directions by modeling the chip thickness distribution, and cutting and indentation mechanics. The shearing forces are based on commonly known cutting mechanics models. The indentation of the cutting edge into the work material is modeled analytically by considering elasto-plastic deformation of the work material pressed by a rigid cutting tool edge with a positive or negative rake angle. The distribution of chip thickness and geometry of indentation zone are evaluated by considering five-axis motion of the tool along the toolpath. The proposed model has been experimentally validated in plunge indentation, as well as in three and five-axis ball-end milling of free-form surfaces. The prediction of axial (z) cutting forces is shown to be improved significantly when the proposed indentation model is integrated into the mechanics of ball-end milling.     

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.     

A new methodology for designing a curve-edged twist drill with an arbitrarily given distribution of the cutting angles along the tool cutting edge

The present study aims at the development of a new methodology for designing a curve-edged twist drill with an arbitrarily given distribution of the cutting angles along the tool cutting edge. The new methodology consists of 81 major mathematical equations and is developed using a method of mapping relevant planes and straight lines of a cutting tool (such as the cutting plane and the cutting edge) as corresponding image points and image lines on a projection plane. The developed methodology is used to intuitively and graphically analyze and determine the relationship between the orientation of the cutting edge and the cutting angles at each point on the cutting edge. A set of image points and image lines is established to calculate the cutting angles on the cutting edge of a twist drill, including the working tool rake angle, the working tool inclination angle, the working cutting edge angle, and the working normal rake angle. Three computer case studies are provided to show curved cutting edges that correspond, respectively, to a linear distribution of the working tool rake angle, a combined linear and uniform distribution of the working tool rake angle, and a linear distribution of the working tool inclination angle along the tool cutting edge. Finally, a set of metal drilling experiments is performed to compare the drilling torque and the thrust force between a conventional straight-edged twist drill and a new curve-edged twist drill that has a combined linear and uniform distribution of the working tool rake angle along the tool cutting edge. The experimental results show that the new curve-edged drill reduces the drilling torque by 28.5% and the thrust force by 24.6% on average.     

A thermo-mechanical model of dry orthogonal cutting and its experimental validation through embedded micro-scale thin film thermocouple arrays in PCBN tooling

Cutting temperature and its distribution in the cutting zone are a critical factor that significantly affects tool life and degrades part accuracy during metal removal operations. However, issues surrounding their modeling and experimental validation in the immediate cutting zone still remain an unresolved issue. A major impediment is the unavailability of adequate temperature measurement methods with sufficient temporal and spatial resolution to measure actual temperatures and validate predictive models. In this paper, a model for the dry orthogonal cutting process with thermo-mechanical coupling effects, i.e., interactions between the stress state, strain rates and the temperature softening of material in the plastic deformation zone, is proposed to predict cutting temperature distribution in the cutting zone. The feasibility and prediction accuracy of the model is verified by experimental measurements through Thin Film Thermocouple (TFTC) arrays embedded at the immediate vicinity of the cutting zone into Polycrystalline Cubic Boron Nitride (PCBN) tooling. The experimental verification is performed under hard turning conditions. It has been shown that the predictions of the proposed model are in very close agreement with the experimentally measured results including the cutting forces, chip thickness and cutting temperature distributions on the rake and flank faces in the cutting zone. Furthermore, the modeling results have also provided an essential understanding on the stress distributions at the tool/chip and work/tool interfaces as well as of the nature of the chip flow velocity along the rake face of the cutting tool.     

Implementation of a process and structure model for turning operations

The consideration of the dynamic interaction between the machine tool structure and the cutting process is a prerequisite for the simulative prediction and optimization of machining tasks. However, existing cutting force models are either dedicated to already examined manufacturing operations or require extensive measurements for the determination of cutting coefficients. In this context this paper outlines a modular, analytical cutting force model applicable to common turning processes. It takes into account the dynamic material behavior, nonlinear friction ratios on the rake face as well as heat transfer phenomena in the deformation zones. On the part of the machine tool structure a parametric model based on the Finite Element Method (FEM) is implemented. Both models are coupled for the simulation of process and structure interactions, whereas the influence of the control system is considered as well. The simulation results were verified experimentally on a turning center.     

An application of the finite element method to the prediction of cutting tool performance

In metal cutting tools the are close to the tool point is the single most important region and conditions at the tool point must be carefully examined if improvements in tool performance, through changes in tool design and material, are to be achieved. The paper describes an analysis of cutting tool performance through a determination of the stress distribution within, and at the boundaries of, the tool wedge. The stressanalysis was based on a two-dimensional model as encountered in orthogonal cutting, using a range of cutting geometries including tools with double rake angles. A finite element technique was employed which can be effectively utilised in the solution of metal cutting problems once the boundary conditions have been established. The results presented demonstrate the significance of the chosen boundary conditions to the analysis of metal cutting. Finally it is argued that the deformation of the cutting edge, especially at the clearance face under the stress field set up in the tool, may well be a determining factor in establishing tool life as based on the flank wear criterion.     

High-speed rotary cutting of difficult-to-cut materials on multitasking lathe

This paper aims to realize the high-speed rotary dry cutting of an Inconel 718 at 500 m/min on a multitasking lathe which has an additional milling spindle with an X/Y/Z-axis and inclination control. A series of experiments were conducted and are discussed with respect to the tool face temperature analysis by FEM. It was verified that it is necessary to select an optimum inclination angle, tool rotation speed and tool diameter so as to enable the main cutting force direction to align with the highest rigidity direction of an applied rotary tool. Under preferable cutting conditions, the average tool rake face temperature measured by a thermograph camera was about 300 °C even at a high cutting speed of 500 m/min under dry cutting conditions, and the tool wear decreased dramatically compared with the conventional tools.     

The mechanics of continuous chip formation in oblique cutting with single-edged tool—part II. Experimental verification of the theory

Experimental results obtained during oblique cutting of annealed steel Ck 45 (SAE-AISI 1045) with a single-edged tool are presented. Extensive measurements of forces, cutting ratio, chip flow angle etc. have been carried out under a wide range of cutting conditions. The measured data obtained from these cutting tests are used to test assumptions proposed in the first part of this work. In relation to previous works dealing with oblique cutting problems the present one extends to tools with angles of tool obliquity ranging from 30° to 70° and having a large negative rake angle.     

Mechanics of high speed cutting with curvilinear edge tools

High speed cutting is advantageous due to the reduced forces and power, increased energy savings, and overall improved productivity for discrete-part metal manufacturing. However, tool edge geometry and combined cutting conditions highly affects the performance of high speed cutting. In this study, mechanics of cutting with curvilinear (round and oval-like) edge preparation tools in the presence of dead metal zone has been presented to investigate the effects of edge geometry and cutting conditions on the friction and resultant tool temperatures. An analytical slip-line field model is utilized to study the cutting mechanics and friction at the tool-chip and tool–workpiece interfaces in the presence of the dead metal zone in machining with negative rake curvilinear PCBN tools. Inserts with six different edge designs, including a chamfered edge, are tested with a set of orthogonal cutting experiments on AISI 4340 steel. Friction conditions in each different edge design are identified by utilizing the forces and chip geometries measured. Finite-element simulations are conducted using the friction conditions identified and process predictions are compared with experiments. Analyses of temperature, strain, and stress fields are utilized in understanding the mechanics of machining with curvilinear tools.     

Practical implementation of cutting force model for step drill using 3D CAD data

As an extension of the cutting force model, which was developed by analyzing the forces on rake and relief face, a practical method of cutting force model is suggested. By a calibration test, cutting coefficients are determined, including the information on tool geometry, work material and cutting conditions such as cutting speed and feed rate. As inputs for the force model, normal rake angle and normal relief angle were obtained by a new method from the measured angles using a 3D CAD machine. This practical force model can be applied for machining CFRP successfully, which was proved from the experiments.     

A new approach to the modeling of oblique cutting processes

A new upper-bound model that incorporates force equilibrium parallel to the cutting edge is proposed for oblique cutting operations. The energy approach is framed in terms of the normal shear angle and two new fundamental variables that characterize the energy requirements of the oblique cutting process. SLIP is a kinematic variable and is defined as the ratio of the shear velocity imparted to the chip on the shear plane parallel to the cutting edge, to the incoming velocity in the same direction. RATIO is a force-based variable and is defined as the ratio of the friction force on the rake face to the resultant shear force in the shear plane. Calibration of the model for either real time identification purposes or for process planning/optimization requires experimental force data but no shear angle data, making it very suitable for the analysis of cutting operations with non-straight cutting edges. The relationships between SLIP, chip flow angle, and RATIO are shown to be remarkably consistent over a very wide range of inclination and normal rake angles. Finally, the authors demonstrate the success of the model using existing experimental data.     

Design of hob cutters for generating helical cutting tools with multi-cutting angles

This paper studies the design of hob cutters for generating the multi-cutting angles (radial rake angle, relief angle, and clearance angle) of helical cutting tools in one hobbing process. The current manufacturing process can be greatly improved if the cutting edges in the normal section profile, the rack profile, of a hob cutter are designed with several cutting edges with different pressure angles, so that the helical cutting tools with multi-cutting angles can be formed in one generating process. This paper, therefore, designs a rack profile of a hob cutter consisting of three straight cutting edges with different pressure angles and a curved cutting edge. By applying the equations of designed rack profiles of hob cutters, the principle of coordinate transformation, the theory of differential geometry, and the theory of gearing, the mathematical models of the helical cutting tool can be derived. In addition, the formulas for the radial cutting angle, relief angle, and clearance angle can be derived. Meanwhile, solid modelling of the helical cutting tool can be carried out with computer graphics programming. The results of this paper will contribute to the improvement of the design technology of hob cutters, to enhance the manufacturing processes of helical cutting tools, and to assist tool-related industries in upgrading their technology and competitive abilities.     

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].     

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].     

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。