Thermal Influence of Cutting Tool Coatings on Tool Life, During Orthogonal Turning Processes – Study of Two-Dimensional FEA Simulation vs. Reference Literature Findings J.W. Navan Department of Engineering and Science, Rensselaer Polytechnic Institute 275 Windsor Street, Hartford, CT 06120 USA Submitted: April 19, 2006 1 Table of Content Page(s) Table of Content Abstract Introduction Formulation Results Discussion Conclusion References Appendix (A) Analytical Solution (B) AdvantEdge™ Simulation Contour Plots Figure P1 through P9 1 2 3-6 6 - 11 11 - 14 15 - 16 16 - 17 18 - 19 20 2 Abstract This paper deals with the thermal influence of cutting tool coatings on tool life, as specifically measured by peak tool temperature. The machining process of interest is the orthogonal turning of AISI 1045 steel. The study employs the two-dimensional capabilities of the metal cutting, FEA modeling / simulation software package, AdvantEdge™ - Version 4.71, produced by Third Wave Systems, Inc. Simulations of non-coated carbide cutting tool conditions are contrasted with single, two and three layer cutting tool coatings, all conditions having been exposed to the variables of two machining speed and two machining length conditions. The balance of the work piece, tool and process parameters were held constant by choice or by software default. Completed simulation iterations are individually subjected to the Results Analysis and Visualization module, which offers FEA meshed contour plots that allow a detailed examination of the tool / workpiece interface, as well as a visual (color coded) depiction of peak tool and workpiece temperatures. Peak cutting tool temperatures for the various simulation iterations are compared and contrasted with recently published experimental, analytical, and FEA/FDM studies. In addition, and perhaps more importantly, the peak temperature of individual tool coatings and their underlying tool substrate are probed for their temperature differential. Although published studies are not entirely in agreement on the role of coatings in the reduction of peak tool temperatures, it is agreed that appropriately coated cutting tools operate at substantially lower peak temperatures than their uncoated counterparts. As a result of the lower substrate temperatures, the coated cutting tools have substantially longer lives. As such, good general correlation between the subject modeling software and the referenced literature is apparent. 3 Introduction The 18th century gave rise to the “Industrial Revolution”, and the mechanization of industry. It was during this period that Eli Whitney, arguably, developed and implemented the principal of interchangeable parts manufacture. The ability to assemble parts, without hand fitting each one drove the need for better machining processes. Ever since, new methods, machines, materials, and processes have been sought to increase machining through-put, maximize cutting tool life, and reduce overall costs. Heat, whether it was known or not, has been a principal enemy in this regard since the first chip was produced by a cutting tool. The mechanical work of a machining operation generates heat through the chips plastic deformation, and as a result of friction between the cutting tool and the work piece. The generated heat flows into the chip, cutting tool, and the work piece being cut. In addition, some heat is also lost through convection to the atmosphere and any cutting coolant / lubricant used. It is well known that as cutting tool temperatures reach elevated levels, tool life diminishes quickly, as specifically related to the softening of the tool material and or diffusion of constituents critical to the tool material strength. For example, the maximum working temperature for Titanium Nitride (TiN) is 600 deg. C, beyond which it oxidizes intensively. If a TiN coated tool experiences temperatures beyond this limit, it rapidly wears. Therefore, the cutting conditions must be selected in such a way that the predicted temperature does not exceed this limit. As such, the peak cutting tool temperature is a principal limiting factor to the cutting tools life and performance. Therefore, the control and reduction of cutting tool temperature becomes a key objective for the machining industry and a potential competitive advantage for individual machinists and / or the companies they labor for. As such, many of the early advances were obtained on an individual basis with little industry wide cooperation. The initial focus having been on feeds, speeds and coolants / lubrication, which through tribal knowledge became widespread general practice, with incremental improvements through the 20th century. The greatest advances in machining performance were driven by the need to harness, and fully utilize, the power of the new numerically controlled machines. The ability to obtain and analyze process data, including cutting tool operational characteristics, provided the information necessary to focus resources on the areas that provided the most performance payback. Cutting tool performance, as limited by temperature, was quickly identified as a critical focus. For the purposes of this paper, the focus will be on the Contact Conditions, with a principal focus on Heat Generation, Heat Flow and Heat Partition. The potential 4 influence of cutting tool / insert coatings, including the listed Contact Conditions, has been captured in Figure 1. Possible Coating Influence Contact Conditions Wear Resistance Friction Interfacial Effects Surface Integrity and Structural Effects Volume Effects Cutting Edge Sharpness Heat Generation Abrasion Crack Initiation Roughness of Working Faces Heat Flow Adhesion Scoring Residual Stresses Heat Partition TriboOxidation Plastic Deformation N - Phase Diffusion Figure 1. The Role of Coatings in the Alteration of Cutting Process performance [1] As temperature in a machining operation is developed at the cutting tool – chip interface, and the ability to transfer heat away from this area is critical to controlling heat build up in the interface, one must focus attention on tool wear, life, and surface integrity. To further exasperate the need and challenge, economical and ecological pressures of the 21st century have driven machining processes to ever faster speeds and dry (without coolant) processes. Composite materials have often been brought to bear on design problems where homogeneous materials are not capable of achieving necessary performance expectations. In recent years, this has been found to be true with cutting tools, and their cutting performance, specifically related to the control of process temperature and ultimately tool life. Coatings that provide thermal conductivity, thermal diffusivity, and heat transfer coefficient properties that complement the substrate properties, as they specifically relate to temperature buildup at the cutting tool – chip interface and conduction into the substrate material, are of particular interest. 5 It is estimated [2] that currently about 53% of all cutting tool materials are Chemical Vapor Deposition (CVD) and Physical Vapor Deposition (PVD) coated carbides, both in the form of solid tools or indexable inserts. Currently [3, 4] coatings of different structures containing layers of titanium carbide (TiC), titanium nitride (TiN), titanium carbonitride (Ti(C,N), aluminum oxide (Al2O3) and titanium aluminum nitride ((Ti, Al)N) are mostly used in metal cutting manufacturing. “Chemical Vapor Deposition, or CVD, is a thin-film coating with a chemical and metallurgical bond that results from the reaction between various gaseous phases and the heated surface of a substrate. The final product is a hard, wear-resistant coating with an extremely strong bond to the substrate. CVD is sometimes referred to as a “hot coating” because the process approaches temperatures around 1925° F. For this reason, special post-coating vacuum heat-treating processes have been developed for steel components.” [5] “Physical Vapor Deposition, or PVD, is a term used to describe a family of coating processes. The most common of these PVD coating processes are hollow cathode reactive ion plating, cathodic arc deposition, and magnetron sputtering. All of these processes occur in vacuum at roughly 10-2 to 10-4 Torr. All of these deposition methods involve the generation of positively charged ions. These ions react with gases that are introduced into the vacuum chamber to create various coating compositions. The parts to be coated are given a negative bias in order to attract the positively charged ions. The result is a very strong physical bond between the coating and the tooling substrate.” [5] A typical cross-sectional photomicrograph of a multi-layer carbide tool coating system is shown in Figure 2. The chemical or physical deposition methods employed assure intimate contact between layers, supporting Figure 2. Photomicrograph of Multi-Layer Tool Coating [6] 6 The thermal performance of coated and non-coated tools, utilized in an orthogonal turning process, will be analyzed via the metal cutting modeling / simulation software package, AdvantEdge™ (Version 4.71), produced by Third Wave Systems, Inc., and compared to reference literature for agreement. The following provides insight into the characteristics of the AdvantEdge™ code, “…the finite element model used for the plane-strain orthogonal metal cutting simulation is based on the Lagrangian techniques and an explicit dynamic, thermo-mechanically coupled modeling software with adaptive remeshing. This means that the initial mesh becomes distorted after a certain length of cut and is remeshed in this vicinity to form a rectangular mesh again.” [7] For the purposes of this study, the simulations will be conducted in 2D FEA simulation mode. The analysis of the coated tool condition will be further broken down into single and multi-layer tool coatings. Machining feeds, work piece material, and tool material types will be held constant, as necessary, for a particular iteration. Formulation Simulation Development Since the intent of the paper is to establish the degree of agreement between results found in the referenced literature, as compared to that which is obtained through the use of the simulation, a spreadsheet of reference literature studies and findings was prepared to provide the necessary focus for the simulations. The search of available research on this topic identified twelve papers that dealt specifically with the thermo-mechanical properties of cutting tools during orthogonal cutting processes. Several of those references dealt exclusively with physical experiments and / or modeling of tool coatings and their effect on thermo-mechanical performance of the system. In all, eight specific references were chosen as a body of knowledge to draw upon to compare and contrast AdvantEdge™ simulation results. As shown in Table 1., a summary of reference work is provided, including, to the degree available in the literature, workpiece, tool, coating and process parameters. Many factors determine the type and rate at which cutting tool wear occurs on the tool surfaces. The major critical variables that effect wear are tool temperature, hardness and type of tool material, grade and condition of workpiece material, tool geometry, feed, cutting fluid, and surface finish on the tool. [8] A thorough examination of the literature for these critical variables reveals that there were a number of commonalities between the studies, including the lack of definition of non-trivial parameters in several cases. As we have previously established peak tool temperature as the defining characteristic that we will use to determine tool life, the remaining critical variables need to be defined. For the purposes of this study, and a meaningful application of the simulation package, fixed and variable attributes were defined as shown in Table 2. and summarized as follows; 7 Insert Table 1 – Reference Literature 8 Insert Table 2 Attribute & Variable 9 Tool Temperature – The Peak Tool Temperature is the simulation output that we seek to associate with tool life. Tool Material and Hardness – P20 Carbide Tool Geometry – Rake & Relief - Angle/Length were fixed at 5 Deg/2 mm Tool Surface Finish – Set at default via friction coefficient Workpiece Material (Grade & Condition) – Although more exotic materials were of interest (i.e. Titanium, Nickel Alloys, Aluminum Alloys, etc.) the reference materials focused on the examination of steel, specifically AISI 1018, 1035, & 1045. AISI 1045 was chosen for commonality with the most useful and available data. Default settings allowed for condition. Cutting Fluid – Dry machining was simulated in all cases. One of the more elusive parameters that needed to be understood was that of duration, or length, of cutting. The obvious concern being, whether or not the simulation reached a steady-state temperature, and therefore, achieved a peak temperature from which to draw conclusions on tool life expectancy. Extensive AdvantEdge™ FEA work by Grzesik, [8] helped guide the decision process in this regard. “It was established based on temperature traces with tool travel that the time required to reach the steady-state temperature was 0.35 – 0.60 ms depending upon the tool material used.” One can presume that higher thermal conductivity materials will reach steady-state quicker than lower thermal conductivity materials. As AISI 1045 is the material of choice, and possessing a relatively low thermal conductivity, a goal figure of > 0.60 ms was assumed to be conservative criteria for this simulation. With an understanding of fixed and variable attributes, and the four tool coating conditions selected (non-coated, TiC, TiC/TiN, and TiC/Al2O3/TiN) the AdvantEdge™ simulations could be planned and conducted. Table 3. provides an all inclusive matrix of attributes/results. It is important to note that a review of the AdvantEdge™ user’s manual and training manual, identified several cautionary issues that needed to be accommodated. As identified by the User Manual [9], the use of very thin 2D tool coatings (< .003 mm total) has the potential of yielding erroneous results. For the purposes of this simulation, all individual coating layers were set at 0.004 mm. Simulation options include both a Rapid and a Standard simulation. Although the Rapid mode is up to five times faster it is reported to be prone to a 20% accuracy error over the Standard mode. For the purposes of this simulation all simulations were initially done in Rapid mode for development of a simulation matrix, and then repeated in Standard mode. The Standard mode results are those that are used for conclusions. Instantaneous data spikes in Peak Tool Temperature / Force vs. Time data were output to Tecplot 10 and necessarily “Force Filtered” to provide useable plots. Automatic re-sizing of the nose radius will occur unless total thickness is less than 3 microns. As such, the coating layer augments your tool dimensions, and therefore your effective edge radius defined prior will be altered. 10 Insert Table #3 11 Analytical Solution Development In the interest of completeness, the methods utilized in the reference literature to obtain an analytical solution of the heat conduction problem in a coated insert were examined for suitability to this papers work. The detailed development for the one dimensional and three dimensional analytical solution is provided in Appendix A. [10] Results Three individual cutting speed and cutting length combinations were simulated for each coating condition. Rapid simulation results were initially generated to establish a baseline, and followed with the more accurate standard simulation. The resulting peak tool temperature results were picked from generated contour plot peak tool temperatures. As previously mentioned, and as shown in Table 4., significant errors in results can be anticipated when using “Rapid” versus “Standard” simulation mode. The quoted 20% was shown to be understated, and uncoated conditions were clearly the worst offenders in this regard. This degree of error in the non-coated condition was initially thought to be counter-intuitive, but quickly understood as being a direct result of the coating additions “forced” smaller mesh size (necessary to accommodate the coating layer) versus the noncoated configuration, where mesh sizing is freer. The degree of error ranged from 77 % for the uncoated condition to 0 % for the three layer coating configuration. Table 4 - Error % - Standard vs. Rapid Simulation - Peak Tool Temperature Simulation Name Noncoated1 Noncoated1A Noncoated2 Noncoated3 TiC1 TiC1A TiC2 TiCTiN1 TiCTiN1A TiCTiN2 TiCAl2O3TiN1 TiCAl2O3TiN1A TiCAl2O3TiN2 Rapid Simulation 1310 1275 730 735 760 730 580 770 790 565 770 790 572 Standard Simulation 740 744 625 545 703 744 537 720 730 550 720 790 573 Difference 570 531 105 190 57 -14 43 50 60 15 50 0 -1 Error % 77.03% 71.37% 16.80% 34.86% 8.11% -1.88% 8.01% 6.94% 8.22% 2.73% 6.94% 0.00% -0.17% The supporting meshed peak temperature contour plots, provided via the simulations Tecplot 10 utility, have been placed in Appendix (B) as Figures P1 through P9. The plots of the tool / workpiece interface are an excellent reference, as they provide 12 temperature color coding and FEA meshing, which gives a thermo-mechanical image of the interaction. A somewhat obvious result of the analysis of cutting speeds influence on peak tool temperature is shown in Figure 3. Regardless of the coating condition, the peak tool temperatures for the 200 m/min iterations are at least 100 degrees higher than the 50 m/min iterations. Figure 3. - Cutting Speed Influence on Peak Tool Temperature 800 700 600 Deg. C 500 Uncoated TiC 400 TiC/TiN TiC/Al2O3/TiN 300 200 100 0 50 m/min 200 m/min Cutting Speed Using the software’s probe utility, the peak tool temperatures of the tool coating and tool substrate (in this case carbide) were separately probed in the Tecplot 10 contour plot. The temperature probing was conducted on the outermost edges of the tool coating and substrate, along the full length of the line of contact, so as to establish the peak tool temperature utilized in the results. The resulting probed peak tool coating and substrate temperatures are shown in Table 5. Equivalent process parameters are like color coded for convenient viewing. As can be seen in Figure 4, 5 & 6 a significant reduction in substrate temperature is evident in all coating conditions, with the exception of the uncoated condition. 13 Table 5 AdvantEdge Simulation - Probed Temperature Values - Color Coded to Indicate Equivalent Process Parameters Cutting Speed (m/min) Length of Cut (mm) Standard Run Time (ms) Maximum Probed Substrate Temp (Deg. C) Uncoated1 Uncoated1A Uncoated3 TiC1 TiC1A TiC2 200 200 50 200 200 50 3 10 3 3 10 3 0.8 2.7 3.2 0.8 2.7 3.2 742.996 760.059 577.43 664.343 688.385 514.923 742.996 760.059 577.43 726.681 736.73 550.132 0 0 0 62.338 48.345 35.209 0 0 0 1 1 1 P1 P1A P3 P4 P4A P5 TiCTiN1 TiCTiN1A TiCTiN2 TiCAl2O3TiN1 TiCAl2O3TiN1A TiCAl2O3TiN2 200 200 50 200 200 50 3 10 3 3 10 3 0.8 2.7 3.2 0.8 2.7 3.2 649.082 668.31 504.68 625.989 699.094 505.504 728.863 725.27 556.638 724.673 758.452 569.449 79.781 56.96 51.958 98.684 59.358 63.945 2 2 2 3 3 3 P6 P6A P7 P8 P8A P9 Simulation Name Maximum Probed Coating Temp (Deg. C) Delta Probed Coating vs. Substrate Coating Layers Contour Plot Figure # Peak Probed Temperature - Figure 4 50 m/min Cutting Speed & 3 mm Cutting Length 600 580 560 Deg.540 C Substrate Coating 520 500 480 460 NonCoated TiC TiC/TiN TiC/Al2O3/TiN 14 Peak Probed Temperature - Figure 5 200 m/min Cutting Speed & 3 mm Cutting Length 760 740 720 700 680 Deg. C Substrate 660 Coating 640 620 600 580 560 NonCoated TiC TiC/TiN TiC/Al2O3/TiN Peak Probed Temperature - Figure 6 200 m/min Cutting Speed & 10 mm Cutting Length 780 760 740 720 Deg. C Substrate 700 Coating 680 660 640 620 NonCoated TiC TiC/TiN TiC/Al2O3/TiN 15 Discussion As the goal of this paper is to compare and contrast AdvantEdge™ simulation results to analytical and experimental results and conclusions made in selected literature, it is prudent to include specific quotes on the Literature / Reference based results and conclusions, summarized as follows, with the direct parallels drawn to this studies findings. Selected Literature / Reference Based Results and Conclusions (A) – FEM / FDM / Analytical Conclusions Grzesik [7] concludes, “The finite element simulations performed yield the evidence of existence and localization of the secondary shear zone. In particular, it was documented that for coated tool areas with the maximum temperatures are localized near the chip and workpiece. Also the substrate under the thin coating is visibly cooler in comparison to uncoated tools.” Author’s Comments: It is apparent from the colored contour plots and the contact line probing, conducted in this study, that this is an accurate statement. Kusiak et al [10] concludes, “The presented application consists in estimating the heat flux in the tool with different types of coatings during steel turning. The obtained results show a slight heat flux diminution by Al2O3 coating whereas the others do not modify it significantly.” .Author’s Comments: It is implied that Al2O3’s superior insulating characteristics should be evident when one probes the tool temperature drops across the three coating layers (TiC/Al2O3/TiN). This is in fact true, as can be seen by probing on each layers interior and exterior edge, noting that the temperature drop across the Al2O3 layer is up to 50 % greater for equivalent layer thicknesses. Rech et al [11] concludes, “Investigations on the influence of the thermal diffusivity and of the thickness of the coating has shown that coatings do not have any capacity to insulate a substrate in continuous cutting applications.” Author’s Comments: As 0.6 ms of cutting time has been previously offered as a reasonable time to assume steady state conditions in the cutting tool, and an examination of probed temperatures for cutting times of 0.8 and 3.2 ms reveals 60 and 40 degree, respectively, temperature drop across a three layer coating, it can be concluded that insulating characteristics do exist. A check of equivalent depth into an uncoated tool reveals temperature drops that are 30 to 50 % less. Grzesik et al [12] concludes, “Analytical solutions performed for the cutting speed of 200 m/min have placed peak temperatures at approximately 1025, 830, and 790 deg. C for uncoated, three – and four-layer coated tools, respectively.” Author’s Comments: The peak tool temperatures observed in this study were not this magnitude for the uncoated and three layer coating configuration. However, as previously seen a significant temperature drop occurs between uncoated and multi-layer coating conditions. Grzesik does not make mention of several parameters in his study that may have an impact on the differences, the most important of which may be the use of Rapid vs. Standard simulations. 16 (B) - Experimental Conclusions Rech et al [13] concludes, “…that coatings mainly influence the amount of heat generated at the tool – chip interface and the tool – chip contact width, but coatings do not influence the partition of heat between the tool substrate and the chip body during turning operations.” Author’s Comments: Although it is accurate to say that coatings mainly influence the amount of heat generated at the tool – chip interface, the second conclusion regarding the partition of heat between the tool substrate and the chip body is not substantiated by this studies simulations. Grzesik et al [1] concludes, “The experimental results indicated that coatings with an intermediate ceramic layer can modify substantially the tool-chip interface behavior and thus friction and the dissipation of frictional heat. It was observed in this study that the coating system chooses itself the most convenient properties to dissipate the frictional heat from the interface.” Author’s Comments: As previously discussed, on a micro-scale the ceramic Al2O3 layer does have a greater contribution to heat dissipation than its adjacent layers, but as a three layer system does not fully exploit this characteristic. Conclusions Most important to the intent of this study is that it has been proven in all simulation cases that cutting tool substrate temperatures are substantially lower when TiC, TiC/TiN, or TiC/Al2O3/TiN coatings have been applied. Since lower cutting tool temperatures are universally accepted as being associated with longer tool life, it can be assumed that these coatings will result in longer tool life versus uncoated tools. The TiC/TiN coating systems effectiveness was most conclusive in all simulations, more so than the TiC/Al2O3/TiN results, giving cause to consider more extensive focused studies in the future. Cutting speed has been shown to have a significant influence on peak tool temperatures. The four coating scenarios (uncoated, TiC, TiC/TiN, and TiC/Al2O3/TiN), were each evaluated at 50 and 200 m/minute cutting speeds. A peak tool temperature reduction of at least 100 degrees is realized when cutting speed is reduced to 50 m/minute from 200 m/min. The reduction of cutting speed will therefore increase tool life, all other parameters being equal. The ceramic Al2O3 layer, as utilized in the three coating layers (TiC/Al2O3/TiN) system, did individually exhibit a temperature drop that was up to 50 % greater than adjacent TiN or TiC coating layers, for equivalent layer thicknesses. Cutting duration simulations of 0.8 through 3.2 ms substantiated claims that steady state was obtained beyond 0.6 ms. Defining the point below 0.8 ms at which the simulation is not at steady-state was not a goal of this study. 17 “Rapid” versus “Standard” simulation mode, quoted at a 20% potential error was shown to be understated, actually ranging from 77 % for the uncoated condition to 0 % for the three layer coating configuration. This study has clearly identified a framework for additional simulation work, including the use of more advanced simulation options. As noted in several references, identifying an appropriate coefficient of friction between tool and workpiece is perhaps the single most elusive parameter. 18 References 1. Grzesik,W., and Nieslony, P. (2004). “Prediction of Friction and Heat Flow in Machining Incorporating Thermo-physical Properties of the Coating-Chip Interface.” Wear. Vol. 256, pp 108-117. 2. Huston, M.F., and Knobeloch, (1998) “VDI Berichte”. Vol. 1399, pp 21-53 3. Klocke, F., Krieg, T., and Gerschwiler, K. (1998) “CIRP”. Vol. 47, pp 65-68 4. Prengel, H.G., Pfouts, W.R., and Santhanam, A.T. (1998) “Surface Coating Technology”, Vol.102, pp 183 – 190. 5. http://www.richterprecision.com/CVD_coatings.htm 6. http://global.kyocera.com/prdct/tool/ceratip/repert/cvd.html 7. Grzesik,W. (2006). “Determination of Temperature Distribution in the Cutting Zone Using Hybrid Analytical-FEM Techniques.” International Journal of Machine Tools & Manufacture. Vol. 46, pp 651-658. 8. Marks’ “Standard Handbook for Mechanical Engineers” (Ninth Edition) McGrawHill Book Company, pp 13-48 to 13-54 9. Third Wave Systems AdvantEdgeTMUser’s ManualVersion 4.71 http://www.thirdwavesys.com 10. Kusiak, A., Battaglia, J.L., and Rech, J.(2005). “Tool Coatings Influence on the Heat Transfer in the Tool During Machining.” International Journal of Surface & Coatings Technology. Vol. 195, pp 29-40. 11. Rech, J., Battaglia, J.L., and Moisan, A. (2005). “Thermal Influence of Cutting Tool Coatings.” Journal of Materials Processing Technology. Vol. 159, pp 119-124. 12. Grzesik,W., and Nieslony, P. (2004). “Physics Based Modeling of Interface Temperature in Machining with Multilayer Coated Tools at Moderate Cutting Speeds.” International Journal of Machine Tools & Manufacture. Vol. 44, pp 889901. 13. Rech, J., Kusiak, A., and Battaglia, J.L. (2003). “Tribological and Thermal Functions of Cutting Tool Coatings.” International Journal of Surface & Coatings Technology. Vol. 186, pp 364-371. 14. Grzesik,W., Bartoszuk, M., and Nieslony, P. (2005). “Finite Difference MethodBased Simulation Of Temperature Fields For Application To Orthogonal Cutting With Coated Tools.” International Journal of Machining Science and Technology, 9:529-546 15. Jen, Tien-Chien, and Anagonye, A., (2001). “An Approved Transient Model of Tool Temperatures in Metal Cutting.” Transactions of the ASME, Vol. 123, pp 30-37. 16. Lazoglu, I., and Altinas, Y., (2002). “Prediction of Tool and Chip Temperature in Continuous and Interrupted Machining.” International Journal of Machine Tools & Manufacture. Vol. 42, pp 1011-1022. 17. Anagonye, A., and Stephenson, D., (2002). “Modeling Cutting Temperatures for Turning Inserts with Various Tool Geometries and Materials.” Transactions of the ASME, Vol. 124, pp 544-552. 18. Grzesik,W., and Nieslony, P. (2003). “A Computational Approach to Evaluate Temperature and Heat Partition in Machining with Multilayer Coated Tools.” International Journal of Machine Tools & Manufacture. Vol. 43, pp 1311-1317. 19 19. M. Necati Ozisik. (1993). "HEAT CONDUCTION", 2nd ed., John Wiley & Sons, Inc, New York, ISBN 0-471-53256-8. 20. Bejan, A., and Kraus, A. D. (2003). “Heat Transfer Handbook.” John Wiley & Sons, Inc, New York, ISBN 1-59124-513-3. 21. “Introductory Short Course on Modeling Metal Cutting” (2001). Third Wave Systems, Inc, 7900 West 78th Street, Minneapolis, Minnesota. 22. http://www.guhring.com/downloads/CoatingS.pdf 20 Appendix (A) Analytical Solution (B) AdvantEdge™ Simulation Contour Plots Figure P1 through P9