Prediction of cutting forces and machining error in ball end milling of curved surfaces -II experimental verification

This paper presents the results of a series of experiments performed to examine the validity of a theoretical model for evaluation of cutting forces and machining error in ball end milling of curved surfaces. The experiments are carried out at various cutting conditions, for both contouring and ramping of convex and concave surfaces. A high precision machining center is used in the cutting tests. In contouring, the machining error is measured with an electric micrometer, while in ramping it is measured on a 3-coordinate measuring machine. The results show that in contouring, the cutting force component that influences the machining error decreases with an increase in milling position angle, while in ramping, the two force components that influence the machining error are hardly affected by the milling position angle. Moreover, in contouring, high machining accuracy is achieved in “Up cross-feed, Up cut” and “Down cross-feed, Down cut” modes, while in ramping, high machining accuracy is achieved in “Left cross-feed, Downward cut” and “Right cross-feed, Upward cut” modes. The theoretical and experimental results show reasonably good agreement.     

Investigation of subsurface damage considering the abrasive particle rotation in brittle material grinding

This paper presents the feasibility study of potential application of recently developed surface defect machining (SDM) method in the fabrication of silicon and similar hard and brittle materials using smooth particle hydrodynamics (SPH) simulation approach. Simulation study of inverse parametric analysis was carried out to determine the Drucker-Prager (DP) constitutive model parameters of silicon by analysing the deformed material response behaviour using various DP model parameters. Indentation test simulations were carried out to perform inverse parametric study. SPH approach was exploited to machine silicon using conventional and surface defect machining method. To this end, we delve into opportunities of exploiting SDM through optimised machining quality, reduced machining time and lowering cost. The results of the conventional simulation were compared with the results of experimental diamond turning of silicon. In the SPH simulations, various types of surface defects were introduced on the workpiece prior to machining. Surface defects were equally distributed on the top face of the workpiece. The simulation study encompasses the investigation of chip formation, resultant machining forces, stresses and hydrostatic pressure with and without SDM. The study reveals the SDM process is an effective technique to manufacture hard and brittle materials as well as facilitate increased tool life. The study also divulges the importance of SPH evading the mesh distortion problem and offer natural chip formation during machining of hard and brittle materials.     

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.     

An exploration of friction models for the chip–tool interface using an Arbitrary Lagrangian–Eulerian finite element model

A better understanding of friction modeling is required in order to produce more realistic finite element models of machining processes to support the goals of longer tool life and better surface quality. In this work an attempt has been made to explore and evaluate various friction models used in numerical metal cutting simulations. A finite element model, based on the ALE approach, was developed for orthogonal machining and used to study the conditions prevailing at the chip–tool interface for hardened steel. The ALE approach does not require any chip separation criteria and enables an approximate initial chip shape to smoothly evolve into a reasonable chip shape, while maintaining excellent mesh properties. The results, for a wide range of feed values, were obtained using different friction models and are compared to previously published experimental findings. A reasonable agreement was obtained between the measured and predicted forces with some discrepancy between the cutting and feed force depending on the friction model: if agreement with the cutting forces was good, then the feed force was underestimated; if the feed force agreed well, then the cutting force was overestimated. In all cases the chip thickness was well estimated but the chip–tool contact length was underestimated.     

Thermoviscoplastic modelling of oblique cutting: forces and chip flow predictions

A modelling of oblique cutting for viscoplastic materials is presented. The thermomechanical properties and the inertia effects are accounted for to describe the material flow in the primary shear zone. At the tool–chip interface, a temperature-dependent friction law is introduced to take account of the extreme conditions of pressure, velocities and temperature encountered during machining. The chip flow angle is calculated by assuming that the friction force is collinear to the chip flow direction on the tool rake face. Due to the temperature dependence of the friction law at the tool–chip interface, the chip flow angle predicted by the model, is affected by the cutting speed, the undeformed chip thickness, the normal rake angle, the edge inclination angle and the thermomechanical behavior of the work material. This dependence and the trends predicted by the present approach are confirmed by experimental observations. Effects of cutting conditions on the cutting forces are also presented and compared to experiments.     

Mechanistic modelling of the milling process using complex tool geometry

Mechanistic models of the milling process must calculate the chip geometry and the cutter edge contact length in order to predict milling forces accurately. This task becomes increasingly difficult for the machining of three dimensional parts using complex tool geometry, such as bull nose cutters. In this paper, a mechanistic model of the milling process based on an adaptive and local depth buffer of the computer graphics card is compared to a traditional simulation method. Results are compared using a 3-axis wedge shaped cut – a tool path with a known chip geometry – in order to accommodate the traditional method. Effects of cutter nose radius on the cutting and edge forces are considered. It is verified that there is little difference (1.4% at most) in the predicted force values of the two methods, thereby validating the adaptive depth buffer approach. The numerical simulations are also verified using experimental cutting tests of aluminium, and found to agree closely (within 12%).     

TYPOLOGY OF MODELS AND SIMULATION METHODS FOR MACHINING OPERATIONS

This paper presents a new modeling approach, based on Oxley's predictive model, for predicting the tool–chip contact in 2-D machining of plain carbon steels with advanced, multi-layer coated cutting tools. Oxley's original predictive model is capable of predicting machining parameters for a wide variety of plain carbon steels, however, the tool material properties and their effects are neglected in the analysis. In the present work, the effect of the tool material, more particularly, the effect of multiple coating layers and the individual coating thicknesses on the tool–chip contact length in orthogonal machining is incorporated. The results from the model predict the tool–chip contact length with respect to major cutting parameters such as feed and rake angle, work material parameters such as the carbon content in the steel, and varying thicknesses and combinations of coating layers. This model enables more precise cutting tool selection by predicting the relative tribological impact (in terms of tool–chip contact length) for a variety of multi-layer coated tools.     

NUMERICAL SIMULATION OF TITANIUM ALLOY DRY MACHINING WITH A STRAIN SOFTENING CONSTITUTIVE LAW

In this study, the commercial finite element software FORGE2005®, able to solve complex thermo-mechanical problems is used to model titanium alloy dry machining. One of the main machining characteristics of titanium alloys is to produce a special chip morphology named “saw-tooth chip” or serrated chip for a wide range of cutting speeds and feeds. The mechanism of saw-tooth chip formation is still not completely understood. Among the two theories about its formation, this study assumes that chip segmentation is only induced by adiabatic shear band formation and thus no material failure occurs in the primary shear zone. Based on the assumption of material strain softening, a new material law was developed. The aim of this study is to analyze the newly developed model's capacity to correctly simulate the machining process. The model validation is based on the comparison of experimental and simulated results, such as chip formation, global chip morphology, cutting forces and geometrical chip characteristics. A good correlation was found between the experimental and numerical results, especially for cutting speeds generating low tool wear.     

A universal slip-line model with non-unique solutions for machining with curled chip formation and a restricted contact tool

A universal slip-line model and the corresponding hodograph for two-dimensional machining which can account for chip curl and chip back-flow when machining with a restricted contact tool are presented in this paper. Six major slip-line models previously developed for machining are briefly reviewed. It is shown that all the six models are special cases of the universal slip-line model presented in this paper. Dewhurst and Collins's matrix technique for numerically solving slip-line problems is employed in the mathematical modeling of the universal slip-line field. A key equation is given to determine the shape of the initial slip-line. A non-unique solution for machining processes when using restricted contact tools is obtained. The influence of four major input parameters, i.e. (a) hydrostatic pressure (P_A) at a point on the intersection line of the shear plane and the work surface to be machined; (b) ratio of the frictional shear stress on the tool rake face to the material shear yield stress (τ/k); (c) ratio of the undeformed chip thickness to the length of the tool land (t₁/h); and (d) tool primary rake angle (γ₁), upon five major output parameters, i.e. (a) four slip-line field angles (θ, η₁, η₂, ψ); (b) non-dimensionalized cutting forces (F_c/kt₁w and F_t/kt₁w); (c) chip thickness (t₂); (d) chip up-curl radius (R_u); and (e) chip back-flow angle (η_b), is theoretically established. The issue of the “built-up-edge” produced under certain conditions in machining processes is also studied. It is hoped that the research work of this paper will help in the understanding of the nature and the basic characteristics of machining processes.     

Dynamic cutting force modeling and experimental study of industrial robotic boring

In this paper, a new approach based on industrial robotic boring is proposed to solve problems associated with intersection holes during aircraft assembly. A model is established to predict the dynamic cutting force of a robotic machining system. The robot stiffness coupling, chip deformation, and plowing interference affecting the cutting force are considered using the principles of cutting mechanics and the Oxley orthogonal cutting model. By solving a numerical solution of motion differential equation, the cutting force components in the radial, tangential, and feed directions are obtained by the model. In addition, an advanced curve intersection method is developed to identify the instantaneous uncut chip area and cutting edge contact length. Verification tests were performed on an ABB-IRB6600-175/2.55 robot for titanium alloy TC4 to determine the accuracy of the predictions. The results show that the simulated and measured cutting forces were in good agreement under different cutting conditions. By analyzing simulated and experimental results, we show that the model can be applied to predict the occurrence of vibration and has application value in terms of suppressing vibration during robotic boring.     

An explicit finite element model to study the influence of rake angle and friction during orthogonal metal cutting

A fundamental understanding of the tribology aspects of machining processes is essential for increasing the dimensional accuracy and surface integrity of finished products. To this end, the present investigation simulates an orthogonal metal cutting using an explicit finite element code, LS-DYNA. In the simulations, a rigid cutting tool of variable rake angle was moved at different velocities against an aluminum workpiece. A damage material model was utilized for the workpiece to capture the chip separation behavior and the simultaneous breakage of the chip into multiple fragments. The friction factor at the cutting tool–workpiece interface was varied through a contact model to predict cutting forces and dynamic chip formation. Overall, the results showed that the explicit finite element is a powerful tool for simulating metal cutting and discontinuous chip formation. The separation of the chip from the workpiece was accurately predicted. Numerical results found that rake angle and friction factor have a significantly influence on the discontinuous chip formation process, chip morphology, chip size, and cutting forces when compared to the cutting velocity during metal cutting. The model was validated against the experimental and numerical results obtained in the literature, and a good agreement with the current numerical results was found.     

Numerical investigations of optimum turning parameters—AA2024-T351 aluminum alloy

Aerospace aluminum alloys have gained the prime significance due to their excellent machining characteristics. Numerous experimental and numerical studies have been conducted to establish the optimum cutting parameters of these alloys. In the numerical cutting models, the authenticity of computational results is suspected particularly because of the complex interaction at tool–chip interface, which involves a high material strain rate and thermal processes. The fidelity of cutting simulation results is appraised by a parametric sensitivity analysis and actual experimentation. In this research, the orthogonal turning of AA2024-T351 aluminum is simulated in Abaqus/Explicit by using a thermoviscoplastic damage model and Coulomb friction model for the contact interfaces. A parametric sensitivity analysis is performed to comprehend the chip morphology, tool–chip interface temperature, reaction force, and strain. Different simulations are performed with varied cutting speeds (200, 400, 600, and 800 m/min), rake angles (5°, 10°, 14.8°, 17.5°), feeds (0.3, 0.4 mm), and friction coefficients (0.1, 0.15). It is observed that an increased rake angle decreases the cutting force and increases tool–chip interface temperature. Similarly, the cutting depth has prominent effect on chip–tool interface temperature as compared to the friction. The computational results are found in close approximation with the published experimental data of AA2024-T351.     

Efficient Chip Breaker Design by Predicting the Chip Breaking Performance

As machining technology develops toward the unmanned and automated system, the need for chip control is considered increasingly important, especially in continuous machining such as in the turning operation. In this study, a systematic chip breaking prediction method is proposed using a 3D cutting model with the equivalent parameter concept. To verify the model, four inserts with different chip breaker parameters were tested and their chip breaking areas were compared with those obtained from the model. Finally, a new type insert (MF1) for medium-finish operations with variable parameters was designed by modifying the commercial one. The chip breaking region predicted by using the modified 3D cutting model for the above insert agrees with the one obtained experimentally. The newly designed insert showed better chip breaking ability than the base model, and other performance tests such as surface roughness, cutting force and tool wear also showed good results.     

A novel chatter stability criterion for the modelling and simulation of the dynamic milling process in the time domain

The modelling of the dynamic processes in milling and the determination of chatter-free cutting conditions are becoming increasingly important in order to facilitate the effective planning of machining operations. In this study, a new chatter stability criterion is proposed, which can be used for a time domain milling process simulation and a model-based milling process control. A predictive time domain model is presented for the simulation and analysis of the dynamic cutting process and chatter in milling. The instantaneous undeformed chip thickness is modelled to include the dynamic modulations caused by the tool vibrations so that the dynamic regeneration effect is taken into account. The cutting force is determined by using a predictive machining theory. A numerical method is employed to solve the differential equations governing the dynamics of the milling system. The work proposes that the ratio of the predicted maximum dynamic cutting force to the predicted maximum static cutting force can be used as a criterion for the chatter stability. Comparisons between the simulation and experimental results are given to verify the new model.     

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.     

Geometry of chip formation in circular end milling

Machining along continuous circular tool-path trajectories avoids tool stoppage and even feed rate variation. This helps particularly in high-speed milling by reducing the effect of the machine tool mechanical structure and cutting process dynamics. With the increase in popularity of this machining concept, the need for detailed study of a valid chip formation in circular end milling is becoming necessary for accurate kinematic and dynamic modeling of the cutting process. In this paper, chip formation during circular end milling is studied with a major focus on feed per tooth and undeformed chip thickness along with their analytical derivations and numerical solutions. At first, the difference in the feed per tooth formulation for end milling along linear and circular tool-path trajectories is presented. In the next step, valid formulation of the undeformed chip thickness in circular end milling is derived by considering an epitrochoidal tooth trajectory with a wide range of the tool-path radius. The complex transcendental equations encountered in the derivation are dealt with, by a case-based approach to obtain closed-form analytical solutions. The analytical solutions of undeformed chip thickness are validated with results of numerical simulations of tool and tooth trajectories for circular end milling and also compared to the linear end milling. The close resemblance between analytical and numerical calculations of the undeformed chip thickness in circular end milling suggests validity of the proposed analytical formulations. As a case study, the cutting forces in circular end milling are calculated based on the derived chip thickness formulations and an existing mechanistic model. The calculation results reiterate the need of taking into account adjusted feed per tooth and valid chip thickness formulations in circular end milling, especially for small tool-path radii, for more realistic process modeling.     

基于有限元数值模型和进给速度优化的薄壁件侧铣变形在线控制

为实现在加工过程中对薄壁件侧铣产生的较大切削变形进行在线控制,提出基于有限元数值模型和进给速度优化的在线控制策略。根据薄壁件切削过程的有限元仿真结果,建立数控机床进给速度、切削力、工件切削变形间的数值模型,进而确定用于控制变形的最优目标切削力。在具有开放式模块化的数控系统平台上开发了切削力信号实时采集、滤波功能和基于Brent-Dekker算法的进给速度在线优化策略,并根据滤波后的切削力及相应算法在加工过程中实时调整机床进给速度,保证切削力逐渐接近最优控制目标而实现切削变形的在线控制。试验结果表明,经过进给速度在线优化后的切削过程可将薄壁件侧铣变形控制在规定范围内,同时提高了切削效率。     

高速切削温度动态变化规律的数值模拟

切削温度与刀具磨损、工件加工表面完整性及加工精度密切相关,其变化规律反映出高速切削过程本质的重要方面。本文应用数值模拟,对高速切削加工过程中切屑、工件和刀具三方面的温度随切削速度、进给量、切削深度的动态变化进行了研究,探讨了其变化规律,其结论有助于优化高速切削工艺及建立高速切削数据库。     

A SLIPLINE FIELD ANALYSIS OF FREE-CHIP ORTHOGONAL MACHINING WITH ADHESION FRICTION AT RAKE FACE

The paper presents slipline field solutions for metal machining assuming adhesion friction at the chip-tool interface. The field is of “indirect” type and is analyzed by the matrix method suggested by Dewhurst, Dewhurst and Collins. The range of validity of the proposed solutions is examined from the consideration of overstressing of rigid vertices in the assumed rigid regions. Rake angle and rake friction are found to be the most important variables that influence the deformation process in machining. Variation of cutting forces, chip thickness ratio, chip curvature and contact length with rake angle and friction parameters is investigated. It is observed that cutting and thrust forces and cutting ratio decrease as rake angle increases but increase as coefficient of friction increases. However, tool-chip contact length decreases as rake angle increases. As a result the average normal and shear stresses on the tool face increases as rake angle increases though, the cutting and thrust forces decrease. Results indicate that friction coefficient cannot be uniquely determined by the rake angle alone, but may have a range of allowable values for a particular value of rake angle. The theoretical results are compared with experimental data available in literature and also with those obtained by the authors from orthogonal cutting tests.     

Thermal modeling of the metal cutting process — Part III: temperature rise distribution due to the combined effects of shear plane heat source and the tool–chip interface frictional heat source

This paper is Part III of a 3-part series on the Thermal Modeling of the Metal Cutting Process. In Part I (Komanduri, Hou, International Journal of Mechanical Sciences 2000;42(9):1715–1752), the temperature rise distribution in the workmaterial and the chip due to shear plane heat source alone was presented using modified Hahn's moving oblique band heat source solution with appropriate image sources for the shear plane (Hahn, Proceedings of the First US National Congress of Applied Mechanics 1951. p. 661–6). In Part II (Komanduri, Hou, International Journal of Mechanical Sciences 2000;43(1):57–88), the temperature rise distribution due to the frictional heat source at the tool–chip interface alone is considered using the modified Jaeger's moving-band (in the chip) and stationary rectangular (in the tool) heat source solutions (Jaeger, Proceedings of the Royal Society of New SouthWales, 1942;76:203–24; Carlsaw, Jaeger. Conduction of heat in solids, Oxford, UK: Oxford University Press, 1959) with appropriate image sources and non-uniform distribution of heat intensity. The matching of the temperature rise distribution at the tool–chip contact interface for a moving-band (chip) and a stationary rectangular heat source (tool) was accomplished using functional analysis technique, originally proposed by Chao and Trigger (Transactions of ASME 1955;75:1107–21). This paper (Part III) deals with the temperature rise distribution in metal cutting due to the combined effect of shear plane heat source in the primary shear zone and frictional heat source at the tool–chip interface. The basic approach is similar to that presented in Parts I and II. The model was applied to two cases of metal cutting, namely, conventional machining of steel with a carbide tool at high Peclet numbers (≈5–20) using data from Chao and Trigger (Transactions of ASME 1955;75:1107–21) and ultraprecision machining of aluminum using a single-crystal diamond at low Peclet numbers (≈0.5) using data from Ueda et al. (Annals of CIRP1998;47(1):41–4). The analytical results were found to be in good agreement with the experimental results, thus validating the model. Using relevant computer programs developed for the analytical solutions, the computation of the temperature rise distributions in the workmaterial, the chip, and the tool were found. The analytical method was found to be much easier, faster, and more accurate to use than the numerical methods used (e.g., Dutt, Brewer, International Journal of Production Research 1964;4:91–114; Tay, Stevenson, de Vahl Davis, Proceedings of the Institution of Mechanical Engineers (London) 1974;188:627). The analytical model also provides a better physical understanding of the thermal process in metal cutting.