Tool Temperature in Titanium Drilling

The spatial and temporal distribution of tool temperature in drilling of commercially pure Rui Li titanium is studied using the inverse heat transfer method. The chisel and cutting edges of a spiral point drill are treated as a series of elementary cutting tools. Using the oblique Albert J. Shih cutting analysis of the measured thrust force and torque, the forces and frictional heat generation on elementary cutting tools are calculated. Temperatures measured by ther- Mechanical Engineering, mocouples embedded on the drill ﬂank face are used as the input for the inverse heat University of Michigan, transfer analysis to calculate the heat partition factor between the drill and chip. The Ann Arbor, MI 48109-2125 temperature distribution of the drill is solved by the ﬁnite element method and validated by experimental measurements with good agreement. For titanium drilling, the drill temperature is high. At 24.4 m/min and 73.2 m/min drill peripheral cutting speed, the peak temperature of the drill reaches 480°C and 1060°C, respectively, after 12.7 mm depth of drilling with 0.025 mm feed per cutting tooth. The steady increase of drill temperature versus drilling time is investigated. ͓DOI: 10.1115/1.2738120͔

1 Introduction carried out to calculate the heat partition and drill temperature ͓14͔. On the analysis of drill temperature as a finite domain, Sax- Titanium ͑Ti͒ and its alloys are lightweight, corrosion resistant, ena et al. ͓15͔ and Watanabe et al. ͓16͔ developed the finite dif- biocompatible, and high-temperature materials that have been ference method. More recently, finite element method has been widely utilized in aerospace, medical, military, and sports appli- ͓ ͔ ͓ ͔ cations. The poor machinability of commercially pure ͑CP͒ Ti and applied by Fuh et al. 17 and Bono and Ni 18,19 for the drill Ti alloys has been studied by researchers and summarized in re- temperature analysis. These studies showed limitations in accurate view papers ͓1–4͔. Because of the inherent properties of Ti, par- prediction of drill temperature. The inverse heat transfer modeling ticularly the low thermal conductivity, the tool temperature when using measured force, torque, and drill temperature as the input is machining Ti is high and concentrated at the tool tip ͓1͔. High developed to improve the accuracy in predicting the drill tempera- temperature softens the tool material and promotes rapid diffusion ture distribution for Ti drilling. wear and severe tool edge chipping ͓5,6͔. This research studies the By dividing the drill chisel and cutting edges into the elemen- ͑ ͓͒ ͔ ͓ ͔ drill temperature distribution in Ti drilling. tary cutting tool ECT 20 segments, Ke et al. 21 have devel- Although Ti drilling has been widely utilized in industry, re- oped the procedure to extract the force data acting on each ECT, search publications are still limited. Sakurai et al. ͓7–9͔ conducted which works like an oblique cutting tool during drilling. At the a series of experiments in drilling of Ti-6Al-4V. Effects of tool start of drilling, one ECT after another in the drill chisel and surface treatment, cutting speed, and feed on thrust force and cutting edges gradually engages the cutting action from center of torque ͓7͔, benefits of the vibratory motion of the drill ͓8͔, and the the drill. Using measured thrust force and torque at the start of variable feed for chip ejection ͓9͔ were studied. Other research in drilling, cutting forces in each ECT can be calculated. The chip Ti drilling included Arai and Ogawa ͓10͔ on the high pressure thickness and shear angle associated with each ECT can be mea- ͑7MPa͒ cutting fluid-assisted drilling, Dornfeld et al. ͓11͔ on the sured from the machined chip to estimate the chip speed. Based burr formation, and Cantero et al. ͓12͔ on the dry drilling tool on this cutting data, the frictional force and heat generation can be wear and workpiece subsurface damage. This review indicates determined. A heat partition factor is required to find the amount that the in-depth research of drill temperature distribution in drill- of heat transferred to the drill for thermal finite element analysis. ing of Ti is still lacking. In Ti drilling, the tool temperature is high This heat partition between the drill and chip is recognized as an ͓1–5͔. High tool temperature is critical to tool life and has been important, but difficult, parameter to determine. Earlier studies observed in high throughput drilling of Ti ͓13͔. Detailed thermal used a constant value for heat partition along the tool-chip inter- modeling and experimental investigation are important to advance face ͓14–17͔. Variable heat partition factor depending on the cut- the drill design and process parameter selection to increase the ting speed ͓22͔ has later been adopted by Bono and Ni ͓18͔ for tool life for Ti drilling. The goal of this study is to build a thermal drilling temperature prediction. More advanced modeling of vari- finite element model of the spiral point drill, which has demon- able heat partition ͓23,24͔ in the sticking and sliding contact re- strated to be effective in high throughput drilling of Ti ͓13͔,to gions has been studied for two-dimensional orthogonal cutting. investigate the drill temperature distribution and effect of cutting Because of the short length of contact region ͓1͔ relative to the speed in Ti drilling. characteristic size of finite elements and the lack of basic machin- The heat generation rate and drill temperature distribution during data of Ti to determine the model parameters, the variable heat ing Ti drilling are difficult to measure directly. Agapiou and partition in the contact regions is not used. In this study, the cut- Stephenson ͓14͔ have reviewed the analytical modeling of tem- ting speed-dependent heat partition model ͓22͔ is adopted for drill perature distribution in the drill, which was represented as a semi- temperature prediction. infinite body. The empirical force equations from a series of turn- In this paper, the experimental setup for Ti drilling tests is first ing ͑oblique cutting͒ tests were used to calculate the heat source. introduced. The drill solid modeling, elementary cutting tools, fi- A transient heat transfer analysis in the semi-infinite domain was nite element thermal model, oblique cutting mechanics in ECT, calculation of heat generation rate, and inverse heat transfer analysis are discussed in Sec. 3. Experimental results, model validation, Contributed by the Manufacturing Science Division of ASME for publication in the JOURNAL OF MANUFACTURING SCIENCE AND ENGINEERING. Manuscript received June and drill-temperature distributions are presented in the following 1, 2006; final manuscript received April 1, 2007. Review conducted by Yung C. Shin. three sections.

Downloaded 05 Sep 2007 to 141.212.132.84. Redistribution subject to ASME license or copyright, see http://www.asme.org/terms/Terms_Use.cfm Fig. 1 Experimental setup with workpiece in the spindle and drill in a vertical tool holder

2 Experimental Setup The Ti drilling experiment was conducted in a Mori Seiki TV 30 computer numerical control vertical machining center. Figure 1 shows the experimental setup with the stationary drill and the Ti workpiece driven by a spindle. The drill was stationary so four thermocouples embedded on the flank face could be routed through coolant holes in the drill body to a data acquisition system during drilling ͓14͔. The drill and machine spindle axes were aligned by a test indicator installed in the spindle. The location of the drill was adjusted in the horizontal plane until the eccentricity was less than 10 ␮m. The tilt of the drill was adjusted so that two planes, which were 5 cm apart in height, both had less than 10 ␮m eccentricity. Under the drill holder was a Kistler 9272 dynamometer to measure the thrust force and torque. Fig. 3 Solid model of the spiral point drill: „a… side view and „b… The workpiece was a 38 mm diam grade two CP Ti bar. The top view with seven marked ECTs drill was a 9.92 mm diam spiral point drill, Kennametal K285A03906, with a S-shaped chisel edge. Compared to a conventional twist drill, the chisel edge of the spiral point drill had lower negative rake angle. Therefore, the web could participate in cutting, not just indenting like the conventional twist drill. This grade K715͒. The spiral point drill has proven to perform well in reduces the thrust force and makes the drill self-centering ͓25͔. high-speed Ti drilling with peripheral speeds over 180 m/min The tool material was WC in a 9.5 wt % Co matrix ͑Kennametal ͓13͔. The chips were collected after drilling and chip thickness was measured to estimate the shear angle of each ECT. The aver- age of three repeated measurements was used to represent the chip thickness. Figure 2 shows the spiral point drill and locations of four thermocouples on the drill frank surface. The top view of a new drill with two flutes and two coolant-through holes is shown in Fig. 2͑a͒.AnXTYT coordinate system with the XT-axis parallel to the tangential of the apex of the curved cutting edge is defined. The tips of 0.127 mm dia type-E thermocouples ͑OMEGA 5TC-TT-E- 36-72͒ were installed at the edge of hand-ground slots on the drill flank face. Four thermocouples, denoted as TC1, TC2, TC3, and TC4, are arranged at different locations on the flank surface, as shown in Fig. 2͑b͒. The XTYT coordinates of the four thermocouples are listed in Fig. 2. The close-up view of TC1 and TC2 is illustrated in Fig. 2͑c͒. TC1 is located close to the cutting edge and away from the drill center. TC2 is placed close to the flute and away from the drill center. TC3 and TC4, as shown in Fig. 2͑d͒, both near the cutting edge, are close to and away from the drill center, respectively. Thermocouples were covered with cement ͑Omega OB-400͒ to secure the position and prevent the contact with workpiece. In this research, three drilling experiments were conducted at three rotational speeds, 780 rpm, 1570 rpm, and 2350 rpm, which Fig. 2 The spiral point drill and thermocouple locations in the corresponded to 24.4 m/min, 48.8 m/min, and 73.2 m/min drill peripheral cutting speeds, respectively. The feed remained fixed at drill flank face: „a… original drill, „b… drills with thermocouples embedded, „c… close-up view of TC1 and TC2, and „d… close-up 0.051 mm/rev or 0.025 mm for each tooth of the two-flute drill. view of TC3 and TC4 All experiments were conducted dry, without cutting fluid.

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Downloaded 05 Sep 2007 to 141.212.132.84. Redistribution subject to ASME license or copyright, see http://www.asme.org/terms/Terms_Use.cfm Fig. 4 Rake angle, inclination angle, and angle between drill Fig. 5 Mesh for the 3D ﬁnite element thermal model: „a… side axis and ECT cutting edge view and „b… top view

3.2 Elementary Cutting Tools (ECT). As shown in Fig. 3 Spiral Point Drill Geometry and Finite Element 3͑b͒, two ECTs are used to represent half of the chisel edge ͑web Thermal Modeling of the drill͒ and five ECTs are used to model the cutting edge. The The thermal finite element model of the drill is established for whole drill point is composed of 14 ECTs. Each ECT has a inverse heat transfer and temperature analysis. The solid modeling straight cutting edge. The length of cutting edge of the ECT is of the spiral point drill, elementary cutting tools, thermal finite 0.71 mm and 0.85 mm in the chisel and cutting edge, respectively. element modeling of the drill, oblique cutting mechanics in ECT, Figure 4 shows the rake angle, inclination angle, and angle be- calculation of heat generation rate, and inverse heat transfer mod- tween drill axis and ECT cutting edge of the seven ECTs. These angles were obtained from the drill solid model since there is no eling are discussed in Sec. 3.1–3.6. existing formula to calculate these angles of the spiral point drill. 3.1 Drill Solid Modeling. The spiral point drill has more The rake angle in the chisel edge is equal to −29 deg and −9 deg complex geometry than the conventional twist drill. To develop a for ECTs 1 and 2, respectively. Compared to the conventional three-dimensional ͑3D͒ finite element mesh for thermal analysis, twist drill with a 118 deg point angle and −59 deg rake angle ͓26͔, the solid model of the drill was established in three steps. First, the spiral point drill has less negative rake angles. the drill cross-section profile ͑DCSP͒ perpendicular to the axis of Oblique cutting mechanics is applied to analyze the cutting the drill was measured using an optical tool-maker microscope. forces ͓18,26͔ in each ECT. Cutting forces in each ECT are ob- Then, a CAD software, SOLIDWORKS™, was applied to generate the tained from experimentally measured thrust force and torque at drill body by sweeping the DCSP along a spiral curve with the the onset of drilling, before the full engagement of the drill tip specified pitch and helix angle. Finally, the trajectory of grinding with the workpiece. wheel to generate the spiral drill point with S-shaped chisel edge 3.3 Finite Element Thermal Model. The drill solid model is was simulated to remove unwanted material and create the solid exported to ABAQUS™, the finite element analysis software used in model of drill tip geometry. The drill grinding parameters were this study, for mesh generation. Figure 5 shows the finite element provided by Kennametal. The solid model of the spiral point drill mesh of the drill, which is modeled by 68,757 four-node tetrahe- is illustrated in Fig. 3. Key parameters of the drill are a 30 deg dral elements. As shown in the top view in Fig. 5͑b͒, 13 nodes are helix angle, 135 deg point angle, 1.9 mm point length, 1.4 mm located on the chisel edge and 11 nodes are placed on each cutting coolant hole diameter, 52 deg chisel edge angle, 7 deg clearance edge to achieve reasonable resolution in the analysis of drill tem- angle at cutting corner, 0.43 mm width of margin, 1.4 mm chisel perature distribution in Ti drilling. edge radius, and 1.8 mm chisel edge length. The drill was ground The initial condition of finite element analysis is a uniform using a grinding wheel with 150 mm diam and 1.1 mm corner temperature of 20°C in the drill. Because the drill does not rotate radius. in the experiment, the free convection boundary condition is ap-

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Downloaded 05 Sep 2007 to 141.212.132.84. Redistribution subject to ASME license or copyright, see http://www.asme.org/terms/Terms_Use.cfm the workpiece. Assuming the thrust force and torque on each ECT do not change, the thrust force and torque contributed by each ECT can be found by identifying the incremental increase of measured thrust force and torque at the time when an ECT is fully engaged with the workpiece ͓21͔. Figure 6 shows the oblique cutting model of an ECT. Five angles including the inclination angle ␭, normal rake angle ␣, angle between the drill axis and ECT cutting edge ␪, chip flow angle ␩, and shear angle ␾ are defined. According to Stabler’s rule ͓28͔, the chip flow angle ␩ is assumed to be equal to the inclination angle ␭. The uncut chip thickness and chip thickness are marked as a and ac, respectively. An orthogonal coordinate system with the X-axis in the cutting direction and the Z-axis perpendicular to the plane determined by the X-axis and the straight cutting edge is defined for each ECT. The Y-axis is perpendicular to the X- and Z-axes to form a right-handed coordinate system. The torque, denoted as T, generates a force component Fc along the X-axis direction. The Fc =T/r, where r is the distance from the drill axis to the center of the ECT. The component of resultant Fig. 6 Oblique cutting model of an ECT force in the Y-axis is Fl and in the Z-axis is Ft. The thrust force, denoted as FTh, is parallel to the drill axis and can be decomposed to Ft and Fl ͓18͔, plied to the whole drill inside ͑fluid hole͒ and outside surfaces. cos ␪ ͱcos2 ␭ − cos2 ␪ ͑ ͒ The heat flux of a vertical wall due to free convection in air is FTh =−Fl + Ft 2 cos ␭ cos ␭ applied on the drill surface ͓27͔ The resultant force on an ECT can also be decomposed to the Љ ͑ ͒1.25 ͑ ͒ qconv = B T − Tϱ 1 force components normal and parallel to the rake face, denoted as 2 1.25 where B=1.8 W/m K and Tϱ =20°C. The boundary condition Fn and Ff, respectively. Ff is the friction force in the direction of on the bottom surface at the end of the drill, opposite from the chip flow on the tool rake face. Because the resultant force lies in drill tip, is assumed to be maintained at 20°C. the plane defined by Fn and Ff, Fl is related to Fc and Ft by ͓29͔ The heat generation in drilling is applied as a line heat source F ͑sin ␭ − cos ␭ sin ␣ tan ␩͒ − F cos ␣ tan ␩ ͓ ͔ F = c t ͑3͒ on the cutting edges. As reported in 1 , the contact between tool l ␭ ␣ ␩ ␭ and chip is narrow in Ti machining. Compared to the 0.0254 mm sin sin tan + cos feed per tooth, the characteristic length of the elements at the Fc, Fl, and Ft are related with Fn and Ff by ϳ cutting edges is much larger, 0.4 mm. This allows the use of F cos ␭ sin ␭ 0 −1 0 0 0 sin ␩ line heat source at the cutting edge in finite element thermal l ␭ ␭ ␣ ␣ ␩ analysis. For the chisel edge, because the characteristic length of ΆFc · = ΄sin cos 0 ΅΄ 0 sin cos ΅΄0 cos ΅ ␣ ␣ elements is shorter than the chip contact length, a parabolic heat Ft 00 10 cos − sin 1 0 source along the contact length is applied ͓22͔. F ϫͭ n ͮ ͑4͒ 3.4 Oblique Cutting Mechanics in ECT. The oblique cut- F ting analysis is utilized to calculate the friction force and chip f velocity along the chip flow direction on the ECT rake face. Start- From Eq. ͑4͒, Ff can be calculated as ing from the ECT 1 at the drill tip, the ECT sequentially engages ͑cos ␣ cos ␭͒F + sin ␣F F = t c ͑5͒ the workpiece at the start of drilling. After the drill moves a dis- f ␭ ␩ ␣ ␭ ␩ tance equal to the drill point length, 1.9 mm into the workpiece cos cos + sin sin sin for the drill used in this study, all seven ECTs are engaged with Ft can be solved by substituting Eq. ͑2͒ into ͑3͒.

F ͑sin ␭ sin ␣ tan ␩ + cos ␭͒ cos ␭ + F ͑sin ␭ − cos ␭ sin ␣ tan ␩͒ cos ␪ Th c ͑ ͒ Ft = 6 ͱcos2 ␭ − cos2 ␪͑sin ␭ sin ␣ tan ␩ + cos ␭͒ + cos ␣ tan ␩ cos ␪

The chip velocity Vc along the chip ﬂow direction is also re- a cos ␣ tan ␾ = ͑8͒ quired to calculate the frictional heat generation. Vc is calculated ␣ ac − a sin from the cutting speed V=␻r, where ␻ is the drill rotational speed ͓ ͔ 30 where a= fd sin ␪, in which fd is the feed per tooth and ␪ is the angle between the drill axis and ECT cutting edge. 3.5 Heat Generation Rate. On the ECT cutting edge, the cos ␭ sin ␾ friction force and chip velocity are multiplied to calculate the heat ͑ ͒ Vc = V 7 generation rate by friction, q =F V . Deﬁning K to be the heat cos ␩ cos͑␾ − ␣͒ f f c partition factor determining the ratio of heat transferred to the The chip thickness ac corresponding to each ECT is experimen- tool, the heat generation rate on the ECT qtool=Kqf. tally measured and applied to determine the shear angle ␾ ͓5͔ In this study, the cutting speed dependent K is applied ͓22͔

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Downloaded 05 Sep 2007 to 141.212.132.84. Redistribution subject to ASME license or copyright, see http://www.asme.org/terms/Terms_Use.cfm embedded on the drill flank surface as the input to predict the heat generation rate at the drill chisel and cutting edges. s is solved using an optimization method. The flowchart for inverse heat transfer solution is summarized in Fig. 8. By assuming a value for s, the l, K, and qtool are calculated and applied to nodes on the cutting and chisel edges of ECT. The spatial and temporal temperature distribution of the drill can then be found. The inverse heat transfer method is applied to solve s by minimizing an objective function determined by the experimentally measured and finite element modeled temperature at specific thermocouple locations, as shown in Fig. 2, on the drill flank face. The discrepancy Fig. 7 Thermal conductivity of the WC-Co tool between the experimentally measured temperature at thermo- ti͉ couple j at time ti,Tj exp, and finite element estimated temperature at the same thermocouple location and time, T ti͉ , deter- −1 j est k ␲d mines the value of the objective function K =1−ͩ1 + 0.45 t ͱ w ͪ ͑9͒ kw Vcl

where kt and kw are the thermal conductivities of WC-Co tool and Ti workpiece material, respectively, dw is the diffusivity of Ti, and ni nj l is the tool-chip contact length. All thermal properties are tem- ͑ ͒ ͑ ti͉ ti͉ ͒2 ͑ ͒ Obj s = ͚ ͚ T j exp −Tj est 11 perature dependent. The tool thermal conductivity kt is shown in i=1 j=1 Fig. 7. For CP Ti, kw and dw, are obtained from Ref. ͓31͔. The tool-chip contact length l was assumed to be twice the chip thickness in previous drill thermal modeling ͓17͔. In this study, where ni is the number of time instants during drilling and nj is ͑ ͒ the number of thermocouples selected to estimate the objective l = sac 10 function. where s is the ratio of the tool-chip contact length to the chip 3.7 Validation. After finding the value of s, the finite element thickness. The value of s is assumed to be the same across the chisel and cutting edges and is determined by the inverse heat modeling can be applied to calculate temperatures at locations of transfer solution. thermocouples not used for inverse heat transfer analysis. The drill temperature predicted from the finite element modeling at 3.6 Inverse Heat Transfer Solution. Inverse heat transfer TC2 and TC4 is compared to experimental measurements to vali- utilizes the temperature measured by thermocouples TC1 and TC3 date the accuracy of proposed method.

Fig. 8 Flowchart of the inverse heat transfer solution of drill temperature

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Downloaded 05 Sep 2007 to 141.212.132.84. Redistribution subject to ASME license or copyright, see http://www.asme.org/terms/Terms_Use.cfm 4 Experimental Results The experimentally measured chip thickness, thrust force, and torque are applied to calculate the shear angle, ECT cutting forces, frictional heat generation, and heat partition factor. 4.1 Chip Morphology, Thickness, and Shear Angle. The morphology of the Ti chips generated at all three drilling speeds has the same shape, which is an initial spiral cone followed by a folded long ribbon. An example of the chip machined at 73.2 m/min peripheral cutting speed is shown in Fig. 9͑a͒. The spiral cone, as shown in the close-up view in Fig. 9͑b͒, is formed by the gradual engagement of chisel and cutting edges at the drill tip. After the drill tip fully engages the workpiece, the chip morphology changes to the ribbon type. Folding of the ribbon chip is due to the resistance caused by chip ejection ͓21͔. At the end of the spiral cone, a cross section of the chip, as marked by the line in Fig. 9͑b͒, determines the variation of chip thickness across the chisel and cutting edges at the moment when the drill tip makes the full engagement with workpiece. The sym- bol C in Fig. 9͑b͒ represents the center of the drill. A picture of the chip cross section and the corresponding ECT and thickness along the line in Fig. 9͑b͒ are shown in Fig. 9͑c͒. The chip generated by the chisel edge is thicker, due to the negative rake angle. This is consistent with the anticipated rake angle effect on chip thickness. Measured chip thicknesses ac and calculated shear angles ␾ at seven ECTs under three peripheral cutting speeds are summarized in Fig. 10. Consistently, the chisel edge generates higher chip thickness and lower shear angle, compared to those of the cutting edge. Along the cutting edge, the chip thickness increases and the shear angle decreases. Under the same cutting speed, the rake angle ␣ and the angle between drill axis and cutting edge ␪ of each ECT affect the chip thickness and shear angle. Large ␣ usu- ally decreases the chip thickness and increases the shear angle, Fig. 9 Ti chip at 73.2 m/min peripheral cutting speed where as large ␪ increases the uncut chip thickness as well as the „2350 rpm rotational speed…: „a… the spiral cone followed by the chip thickness. Along the cutting edge, ␣ increases and ␪ is about folded long ribbon chip morphology, b close-up view of the ͑ ͒ „ … the same Fig. 4 . The combination of these two effects results in spiral cone chip at the start of drilling, and „c… chip cross sec- a lower chip thickness in the cutting edge, as shown in Fig. 10. tion and chip thickness variation of ECT „C: chip close to the center of drill… 4.2 Thrust Force and Torque on ECT. Figure 11 shows the thrust force and torque measured at three drilling speeds. In the first 1.9 mm of drilling, the force and torque gradually increase until the drill tip makes full engagement with workpiece. Incre- ments in force and torque are assumed to be contributed by the sequential participation of ECTs in cutting. The vertical dash line and the number above it in Fig. 11 represent the drilling depth and the corresponding ECT fully engaged the workpiece, respectively. After the drill tip fully engages the workpiece, the thrust force and torque both reach a more stable level. The speed has a significant effect on the torque and changes the thrust force only slightly after the full engagement of drill tip. High torque at high cutting speed is mainly due to the increasing difficulty in chip ejection ͓21͔. The FTh and T of each ECT, as shown in Fig. 12, are calculated from the incremental increase of thrust force and torque as each ECT engages in drilling ͑Fig. 11͒. Although ECTs 1–3 generate high thrust force, their value relative to other ECTs is small in comparison to a conventional twist drill ͓26͔. Similar to a conventional twist drill, the ECTs at the cutting edge of the spiral point drill has a major contribution to the torque. 4.3 Solution of the s, K, and Heat Generation Rate. The measured temperatures at TC1 and TC3 at three peripheral cutting speeds are shown in Fig. 13. By minimizing Obj͑s͒ using the measured temperature at TC1 and TC3 as input, the value of s is solved as 6, 6, and 4 for 24.4, 48.8, and 73.2 m/min peripheral cutting speed, respectively. The Golden Section optimization method ͓32͔ was used for solution. Using the temperature-dependent material properties, the heat partition factor K varies both spatially and temporally. The K after 1.9 mm depth of drilling, i.e., the stage when the whole cutting edge engages the workpiece, is shown in Fig. 14. The lower K at Fig. 10 Chip thickness and shear angle of seven ECTs

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Downloaded 05 Sep 2007 to 141.212.132.84. Redistribution subject to ASME license or copyright, see http://www.asme.org/terms/Terms_Use.cfm Fig. 11 Thrust force and torque versus drilling depth

higher cutting speed represents that a larger portion of heat gen- Fig. 12 Thrust force and torque of seven ECTs erated at the tool-chip interface is carried away by the chip at higher cutting speed. This is a well-known phenomenon at high cutting speed ͓5͔. Because of the cutting speed effect, ECTs at the erms p = ͑13͒ cutting edge have a higher K than those on the chisel edge. Tj͉peak To compare the heat transfer to each ECT, the qtool is divided by the length of ECT cutting edge to calculate the heat generate rate where N is the number of temperature measurements, j is the Ј Ј thermocouple, and Tj͉peak is the peak measured temperature. The per unit length of contact, denoted as qtool. Results of qtool after 1.9 mm depth of drilling are shown in Fig. 15. Consistently, due absolute temperature scale is used to calculate p. to the higher torque, ECTs at the cutting edge have a much higher The erms and p at four thermocouples are listed in Table 1. The qЈ than those at the chisel edge. At 73.2 m/min peripheral cut- erms increases at high cutting speeds due to the high tool tempera- tool ture at high cutting speed. In general, the e and p at TC2 and ting speed, the qЈ increases along the cutting edge toward the rms tool TC4 are comparable to those of TC1 and TC3. At all three cutting outside of the drill. This trend is altered at 24.4 m/min and speeds, pϽ5%, which is a considerable improvement from the 48.8 m/min cutting speeds at which qЈ at ECT 7 is lower than tool previous drill temperature study ͓18͔. In summary, the low e that at ECTs 5 and 6. This is because the torque of ECT 7 is higher rms and p and good match of experimentally measured and finite ele- than that of ECTs 5 and 6 at 73.2 m/min cutting speed but lower ͑ ͒ ment modeled temperatures at four thermocouples throughout the at 24.4 m/min and 48.8 m/min cutting speed Fig. 12 . At lower drilling process validates the proposed method to predict drill peripheral cutting speed, i.e., lower rotational speed, the effect of temperature. strain rate hardening at ECT 7 is not high enough to compensate ͑ ͒ the effect of high rake angle Fig. 4 , which generates lower cut- 6 Drill Temperature Distributions ting forces Fc. The peripheral cutting speed has a significant effect on the heat The spatial distribution of temperature near the tip of the spiral generation rate at the cutting edge. As the cutting speed increases point drill after 12.7 mm depth of drilling is shown in Fig. 16. The Ј drilling time was 19.2 s, 9.6 s, and 6.4 s at 24.4 m/min, from 24.4 m/min to 73.2 m/min, qtool increases by more than 100% for most of the ECTs on cutting edge. 48.8 m/min, and 73.2 m/min peripheral cutting speeds, respectively. High temperature is concentrated along the cutting edge at the drill tip. High peripheral cutting speed generates high tempera- 5 Validation of Drill Temperature Modeling tures in the drill. The peak temperature increases from 480°C to The finite element prediction of drill temperature is validated 1060°C when the drill peripheral cutting speed is increased from by the comparison to experimentally measured temperatures at 24.4 m/min to 73.2 m/min. The peak temperature is located on thermocouples TC2 and TC4. As shown in Fig. 13, a good match the cutting edge near the drill margin for all three cutting speeds. of temperature can be seen at TC2 and TC4. The temperature at This study shows the high drill temperature and cutting speed TC2 is lower and the discrepancy is higher than the other three effect in drilling Ti. thermocouples because TC2 is the furthest away from the cutting Figure 17 shows cutting speed effect on distributions of tem- edge. Generally, the simulation underestimates the temperature at perature along the chisel and cutting edges after 12.7 mm depth of the beginning of drilling. This is likely due to the effect of grooves drilling. At three peripheral cutting speeds, the pattern of tempera- carved on the drill flank face used to install thermocouples. These ture distribution is the same: low at the chisel edge and high near grooves were not considered in the finite element modeling. the margin. As the cutting speed increases, the location of peak To quantify the discrepancy between the experimental and temperature moves outside toward the drill margin. ͑ ͒ ͓ ͔ At the highest peripheral cutting speed, 73.2 m/min, after drill- modeling results, the root mean square rms error erms 33 and the percentage error p are defined ing for 0.2 s, 0.5 s, 0.8 s, 1.0 s, 6.4 s, 20 s, and 50 s, the temperature distributions along the chisel and cutting edges of the drill are N 1 shown in Fig. 18. The location of peak temperature on the drill ͱ ͑ ti ti ͒2 ͑ ͒ erms = ͚ T j͉exp −Tj͉est 12 cutting edges is moving with respect to the time of drilling. In this N i=1 746 / Vol. 129, AUGUST 2007 Transactions of the ASME

Downloaded 05 Sep 2007 to 141.212.132.84. Redistribution subject to ASME license or copyright, see http://www.asme.org/terms/Terms_Use.cfm Fig. 13 Comparison of the measured and modeled temperature at four thermocouple locations

case using the spiral point drill for Ti, the location of peak tem- at 50 s drilling time, which corresponds to a 102 mm depth of perature gradually moves from the drill center toward the drill drilling. The rate of increase in drill temperature gradually drops margin. But, even at long drilling time, the peak temperature does at higher drilling depth. not occur at the outmost point of the cutting edge ͑drill margin͒. The temporal analysis of drill temperature shows the steady state 7 Concluding Remarks was not achieved. The drill temperature keeps rising with the increase of the drilling depth. The peak temperature reaches 1750°C This study quantified the level of high temperature and effects of cutting speed and cutting time on drill temperature distributions in dry drilling of Ti. The complete temporal and spatial distributions of the drill temperature can be analyzed accurately and validated experimentally. This was based on the work of many researchers in drilling study in the past years. A finite element thermal model combined with inverse heat transfer analysis, which used experimentally measured thrust force, torque, chip thickness, and temperature as inputs, was validated with reason- ably good agreement. An accuracy of Ͻ5% discrepancy between experimentally measured and numerically predicted drill temperature was achieved. This study showed that the cutting edge had a lower heat partition factor and higher heat generation rate per length than the chisel edge. The peak temperature of the drill increased from 480°C to 1060°C as the peripheral cutting speed increased from 24.4 m/min to 73.2 m/min after 12.7 mm depth of drilling. The location of peak temperature moved outside toward the drill margin as the peripheral cutting speed increased. The modeling results also showed the drill temperature did not Fig. 14 Heat partition factor K at seven ECTs after 1.9 mm reach the steady state after a long, 50 s, drilling time. depth of drilling The research in Ti drilling is ongoing on several fronts. The proposed method can be expanded to the drilling condition with the supply of cutting fluid, which is important for the high throughput drilling of Ti. Using the predicted drill temperature

Table 1 Root mean square „rms… and percentage errors Peripheral cutting speed ͑m/min͒ TC1 TC2 TC3 TC4

͑ ͒ 24.4 erms °C 10.8 9.5 15.3 12.9 p͑%͒ 2.1 1.9 2.9 2.5 ͑ ͒ 48.8 erms °C 18.2 11.8 22.1 17.7 p͑%͒ 2.9 2.2 3.5 2.8 ͑ ͒ 73.2 erms °C 24.9 29.6 27.2 23.6 Ј Fig. 15 Heat generation rate per unit length qtool at seven ECTs p͑%͒ 3.6 4.8 3.9 3.4 after 1.9 mm depth of drilling

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Downloaded 05 Sep 2007 to 141.212.132.84. Redistribution subject to ASME license or copyright, see http://www.asme.org/terms/Terms_Use.cfm distribution and cutting forces, the coupled thermal and mechanical stress analysis of the deformation and stress distributions of the drill can be performed. This study can also be expanded for the drill selection, drill geometry design, and optimization of drilling process parameters to further enhance the productivity of drilling Ti and other advanced engineering materials.

Acknowledgment A portion of this research was sponsored by the Heavy Vehicle Propulsion Systems Materials Program, U.S. Department of En- ergy. Assistances from Parag Hegde of Kennametals and Dr. Ray Johnson of Oak Ridge National Laboratory are greatly appreci- ated.

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