Modelling for prediction of time-varying heat partition coefficient at coated tool-chip interface in continuous turning and interrupted milling

International Journal of Machine Tools & Manufacture 147 (2019) 103467

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International Journal of Machine Tools and Manufacture journal homepage: http://www.elsevier.com/locate/ijmactool

Modelling for prediction of time-varying heat partition coefficient at coated tool-chip interface in continuous turning and interrupted milling Zhao Jinfua, b, Zhanqiang Liu a, b, * a

School of Mechanical Engineering, Shandong University, China Key National Demonstration Center for Experimental Mechanical Engineering Education, Key Laboratory of High Efficiency and Clean Mechanical Manufacture of MQE, Jinan, 250061, Shandong, China

b

A R T I C L E I N F O

A B S T R A C T

Keywords: Time-varying heat partition coefficient Coated tool Metal cutting

Knowing heat partition coefficient at tool-chip interface is important for accurate estimating the distribution of heat flux and temperature field in metal cutting process. The heat partition coefficient in steady metal cutting has been widely analyzed. However, the time-varying effect of heat partition coefficient is rarely investigated in metal cutting with coated tool. In this research, a novel model for prediction of the transient heat partition coefficient at coated tool-chip interface was proposed. The time-varying heat partition coefficient was quanti­ tatively calculated. The new proposed model fully considered the coating thickness and material thermal properties compared with current models including Shaw’s model, Kato-Fujii’s model and Reznikov’s model. The time-varying heat partition coefficients in continuous turning and interrupted milling process were compara­ tively analyzed. Results showed that the time needed for attaining quasi-steady-state of heat partition was about tens of milliseconds. The heat partition coefficient was mainly dependent on tool coating and workpiece thermal properties rather than tool substrate thermal properties. The heat partition coefficient was decreased with the increase of interrupted cutting speed. The new proposed model was verified accurate compared with former research and cutting experiment. The proposed methodology can guide for design and selection of coated tool in metal cutting production.

1. Introduction Coating has been commonly deposited on cutting tools due to its superior thermal barrier effect [1] and antifriction effect [2]. Heat partition coefficient RW is presented as the proportion of heat flux dissipated into chip from the coated tool-chip interface. The heat flux distribution in metal cutting process can affect the tool life and machined workpiece quality [3,4]. Determining the heat partition RW at coated tool-chip interface is beneficial for accurate estimation of heat flux distribution and cutting temperature in metal cutting process. Analytical prediction of heat partition RW in steady metal cutting with coated tool has been researched. Grzesik and Nieslony [5] calcu­ lated the heat partition RW in steady turning 1045 steel with TiC/A­ l2O3/TiN and TiC/Ti(C,N)/Al2O3/TiN coated tool (substrate carbide K10) with Loewen-Shaw’s model [6], Kato-Fujii’s model [7] and Reznikov’s model [8]. Loewen-Shaw’s model [6], Kato-Fujii’s model [7] and Reznikov’s model [8] for calculation of heat partition RW were determined with Eq. (1), Eq. (2) and Eq. (3), respectively.

RW ¼

1 � � pffiffiffiffiffi �� 1 þ 0:754ðλT =λW Þ Aa NT

(1)

RW ¼

1 pffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ ðλT =λW Þ αW =αT

(2)

RW ¼

1 pffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ 3=2ðλT =λW Þ αW =αT

(3)

Average turning temperatures calculated with above models [6–8] were compared with the average turning temperature measured with natural thermocouple method. The results showed that the Reznikov’s model [8] was proper for describing the heat partition RW in steady metal turning with coated tool. Loewen-Shaw’s model [6] was proper for describing the heat partition RW in steady metal turning with un­ coated tool. Grzesik and Nieslony [9] analyzed the influences of thermal properties of two contacted bodies on heat partition RW in steady turning process. The heat partition RW was calculated as 0.77 and 0.71

* Corresponding author. School of Mechanical Engineering, Shandong University, Jingshi Road 17923, Jinan, 250061, PR China. E-mail addresses: [email protected] (J. Zhao), [email protected] (Z. Liu). https://doi.org/10.1016/j.ijmachtools.2019.103467 Received 12 June 2019; Received in revised form 16 September 2019; Accepted 16 September 2019 Available online 19 September 2019 0890-6955/© 2019 Elsevier Ltd. All rights reserved.

J. Zhao and Z. Liu

International Journal of Machine Tools and Manufacture 147 (2019) 103467

for turning 1045 steel by TiC/Al2O3/TiN three-layer coated tool with Kato-Fujii’s model [7] and Reznikov’s model [8]. The heat partition coefficient was calculated as 0.51 using Loewen-Shaw’s model [6] when turning 1045 carbon with uncoated tools. It was illustrated that the existence of coating can increase the heat flux dissipated into chip in metal cutting process. Zhang et al. [10] established the semi-analytical model for investigating the heat partition RW at coated tool-chip inter­ face. The results showed that the increase of coating thickness induced smaller heat partition RW. The coating thermal conductivity was the main influencing factor on heat partition RW. Rech et al. [11] established the 1-D and 3-D axisymmetric analytical models of coated tool to analyze the thermal effects of coating on heat transfer in metal cutting. The results showed that the thermal effects of coating thermal diffusivity and coating thickness were dominant in high speed interrupted cutting, while they were inessential in continuous cutting. Finite element (FE) simulation and experiments were also applied to estimate the heat partition RW in steady metal cutting with coated tool. Ceretti et al. [12] measured the temperature within TiN coated tool with the embedded thermocouple in dry cutting AISI 1045. The FE simulation based on ALE method was applied to inversely determine the heat partition at coated tool-chip interface in steady metal cutting. Puls et al. [13] proposed a FE model for predicting heat partition RW in dry cutting AISI 1045 steel by using TiAlN and TiN coated tools. The results showed that the coating thermal properties have great influences on heat partition RW. Akbar et al. [14,15] utilized FE simulation and cutting experiment to predict heat partition RW in steady turning AISI 4140 steel with uncoated tool, TiN and (Ti,Al)N coated tools. The cutting temper­ ature in steady turning process was measured with IR camera. TiN and (Ti,Al)N coated tools increased the heat partition RW compared with uncoated tool. (Ti,Al)N coated tool increased the heat partition RW compared with TiN coated tool in HSM, but decreased the heat partition RW compared with TiN coated tool at conventional cutting speed. Bon­ net et al. [16] and Zemzemi et al. [17] developed a novel tribometer to simulate the heat partition RW in dry cutting AISI 316 L steel and AISI 4142 steel with TiN coated carbide tool, respectively. The effect of sliding speed on the heat partition RW was analyzed with the sliding experiments and FE simulations. They found that the heat partition RW was increased with the sliding speed. Zemzemi et al. [18] made a further prediction of heat partition at coated tool-chip interface during sliding of Inconel 718 with TiAlN coated tools using the developed tribometer [16,17]. The results showed that the experimental heat partition RW was lower than that calculated with Kato-Fujii’s model [7]. It was illustrated that Kato-Fujii’s model [7] was not enough accurate by only considering coating and workpiece thermal properties. Some researchers also analyzed the heat partition RW in metal cut­ ting with coated tool using tribometers [16,17]. Eguilaz et al. [19] characterized the effect of steel’s inclusions on heat partition RW in dry machining of AISI 4140 steel with TiN coated tool in the developed tribometer [16,17]. There was no evident effect of the inclusions on heat partition RW. Mondelin et al. [20] predicted heat partition RW in cutting AISI 4140 steel with TiN coated tool under various lubrication mode in the developed tribometer [16,17]. The straight oils cannot modify the heat partition RW, but emulsions can evidently decrease heat partition RW. Rech et al. [21] applied the tribometer [16,17] to analyze the heat partition RW for machining various workpiece with TiN coated tool under different lubrication conditions. They found that the thermal properties of workpiece influenced the heat partition RW. Melkote et al. [22] reviewed the research advances of material and friction for modelling metal machining. The effects of workpiece and tool thermal properties on modelling friction and heat partition RW of different machining process should be considered. However, the time-varying effect of heat partition RW in metal cut­ ting with coated tools has been rarely discussed due to the difficulty in the transient heat transfer modelling in metal cutting with coated tools. In addition, the influences of coating thickness and tool substrate on heat partition RW are neglected in previous research, as shown in

Table 1. In our research, the transient coated tool-chip interface heat partition model was proposed. The time-varying heat partition coeffi­ cient in metal cutting with coated tools was quantitatively predicted. The influences of coating thickness and tool substrate on time-varying heat partition RW(t) were quantitatively analyzed in continuous and interrupted metal cutting process, respectively. The new proposed model was verified with former research results and cutting experiment. 2. Model and solution of time-varying heat partition RW at coated tool-chip interface in metal cutting process Metal cutting can be simplified as the model shown in Fig. 1, due to the great difficulty of modelling complex actual 3-D continuous and interrupted cutting process. It should be noted that the heat partition exists when chips contact with tool rake face. The microelement is proposed to capture the key feature of coated tool-chip interface in Fig. 1 (a). The workpiece and coated tool body are assumed as semi-infinite body within short duration time. The qinter is assumed as the heat flux induced at coated tool-chip interface. The heat flux in metal cutting process could be determined with the cutting experiment and two-stage inverse calculation method [23]. The transient coated tool-chip inter­ face heat partition model ignores the thermal resistance at the tool-chip contact interface, as shown in Fig. 1(b). No additional thermal resistance is generated at coating-substrate interface. The upper and bottom boundaries are assumed as adiabatic with the consideration of main heat transfer direction along x-axis. As illustrated in former research [24], the solution of temperature distribution within coated tool body was developed. Explicit solutions have been depicted in the Appendix. The rake face temperature of coated tool can be calculated with Eq. (4) when the coordinate x is equal to zero. T Coated x¼0

tool

¼ ð1

(4)

RW ðtÞÞ⋅qinter ⋅Aðx1 ; kc ; αc ; ks ; αs ; tÞ þ T∞

where RW(t) is the time-varying heat partition coefficient. A(x1, kc, αc, ks, αs, t) is the time-varying variable considering coating thickness x1, coating thermal conductivity kc, coating thermal diffusivity αc, substrate thermal conductivity ks, substrate thermal diffusivity αs, which can be calculated with Eq. (5). T∞ is the environment temperature. # rffiffiffi ( " pffiffiffiffi ∞ 4 αc X t ðn þ 1Þ2 x21 ðjcjÞnþ1 ⋅ Aðx1 ; kc ; αc ; ks ; αs ; tÞ ¼ ⋅ exp ⋅ kc n¼0 π t⋅αc rffiffiffiffiffiffiffi �) ðn þ 1Þx1 2 t⋅αc pffiffiffiffiffiffiffi þ t⋅αc kc π

� erfc

(5) where c is the intermediate variable, which can be defined with Eq. (6). Table 1 Thermal properties of coating, substrate and workpiece (500 � C). Symbol

Material

Thermal conductivity k (W/(m⋅K))

Thermal diffusivity α (�10 6 m2/s)

C1

(Ti,Al)N coating [25] Al2O3 coating [26] TiC coating [26] TiN coating [26] Substrate (Ken2210) [25] Substrate (M10) [27] Substrate (P10) [27] Inconel 718 [28] H13 steel [29]

15.41

10.59

14.00

4.90

24.00 21.00 68.14

9.80 5.50 14.48

40.15

9.80

37.70

14.00

19.75 37.00

4.64 8.47

C2 C3 C4 S1 S2 S3 W1 W2

2

J. Zhao and Z. Liu

International Journal of Machine Tools and Manufacture 147 (2019) 103467

Fig. 1. (a) Microelement of metal cutting with coated tools; (b) Transient coated tool-chip interface heat partition model.

c¼

pffiffiffiffi pffiffiffiffi kc αs ks αc pffiffiffiffi pffiffiffiffi kc αs þ ks αc

3.1. Effects of thermal properties of coating, workpiece and substrate on time-varying heat partition RW with coated tools

(6)

The temperature of chip side can be determined with Eq. (7) when coordinate x is equal to zero. T Workpiece ðtÞ ¼ RW ðtÞ⋅qinter ⋅BðkW ; αW ; tÞ þ T∞ x¼0

The variations of calculated heat partition RW with duration time for several combinations in continuous and interrupted machining were depicted in Fig. 2(a) and (b). As shown in Fig. 2(a), the heat partition RW increased rapidly within initial tens of milliseconds. The heat partition RW then attained a quasi-steady-state in continuous cutting process. The finding was consistent with that from former research [30]. Komanduri et al. [30] found that the time required for attaining the quasi-steady-state of sliding heat source was around 0.01–0.1s in continuous metal cutting process. However, there was no quasi-steady state of heat partition RW in interrupted metal cutting process with high cutting speed 100 m/min as shown in Fig. 2(b). Each rotation period was 60 ms determined with Eq. (10) in interrupted metal cutting by using a single coated tool insert at cutting speed 100 m/min. Duration time for tool-chip contact was 6 ms determined with Eq. (11) during each rotation period. As shown in Fig. 2(a), the heat partitions RW in continuous cutting Inconel 718 by using Al2O3, TiC and TiN coated tools (substrate carbide Ken-2210) were 12.63%, 20.53% and 27.30% lower than that of (Ti,Al) N coating at duration time 100 ms, respectively. As shown in Fig. 2(b), the maximum heat partitions RW in interrupted cutting Inconel 718 by Al2O3, TiC and TiN coated tools (substrate carbide Ken-2210) were 11.95%, 17.68%, and 24.62% lower than that of (Ti,Al)N coating. The influence of tool coating on heat partition RW was significant in metal cutting process. The heat partition RW was the highest when cutting Inconel 718 by (Ti,Al)N coated tool with Ken-2210 substrate carbide compared with that by other Al2O3, TiC and TiN coatings. The lowest heat partition RW was obtained in cutting Inconel 718 by TiN coated tool with Ken-2210 substrate carbide. Fig. 2(a) showed that the heat partition RW in continuous cutting Inconel 718 by (Ti,Al)N coated tool (substrate carbide Ken-2210) was 12.43% lower than that of H13 at duration time 100 ms. As shown in Fig. 2(b), the maximum heat partition RW in interrupted cutting Inconel 718 by (Ti,Al)N coated tool (substrate carbide Ken-2210) was 13.30% lower than that of H13. Higher heat partition coefficient could be ob­ tained in cutting H13 with (Ti,Al)N coated tool compared with that of Inconel 718. It was illustrated that the thermal conductivity and thermal diffusivity of H13 was 87.34% and 39.34% higher than that of Inconel 718, respectively. More heat flux was dissipated into the chip of H13 in the cutting process, which led to higher heat partition RW. As shown in Fig. 2(a), the heat partition RW in continuous cutting Inconel 718 by (Ti,Al)N coated tool with substrate carbide M10 was 4.77% and 3.14% lower than that of carbide Ken-2210 at duration time 5 ms and 10 ms, respectively. The heat partition RW in continuous cut­ ting Inconel 718 by (Ti,Al)N coated tool with substrate carbide P10 was 6.55% and 4.34% lower than that of carbide Ken-2210 at duration time

(7)

where B(kW, αW, t) is the time-dependent coefficient considering work­ piece thermal conductivity kW, workpiece thermal diffusivity αW, which can be calculated with Eq. (8). rffiffiffiffiffiffiffiffiffi 2 t⋅αW BðkW ; αW ; tÞ ¼ (8) kW π As referred in a former research [8], the relative sliding between workpiece and coated tool should be considered in calculation of heat partition RW in cutting process. By analogy, the time-varying heat partition RW should be modified as Eq. (9). RW ðtÞ ¼

Aðx1 ; kc ; αc ; ks ; αs ; tÞ Aðx1 ; kc ; αc ; ks ; αs ; tÞ þ 3=2BðkW ; αW ; tÞ

(9)

3. Computed results Thermal properties of several coatings, substrates and workpieces were summarized in Table 1. The material thermal conductivity and thermal diffusivity were assumed constants at temperature 500 � C. Specific symbols were applied to represent the summarized materials. The combination parameter (Cx-Sx-Wx) illustrated the metal cutting (workpiece Wx) with coated carbide tool (coating Cx, carbide Sx). The time-varying heat partitions RW(t) in continuous and interrupted cutting with coated tool (coating thickness of 5 μm) were predicted, respectively. One representative case of interrupted milling process was utilized in our research. Each rotation period was determined with Eq. (10) in the interrupted metal milling using a single coated tool insert. Duration time for coated tool-chip contact (Δt) was determined with Eq. (11) during each rotation period in the interrupted metal cutting using a single coated tool insert. Δtrotation period ¼ 1000

60π d ðmsÞ vc

Δt ¼ Δtrotation period η ðmsÞ

(10) (11)

where vc was the cutting speed in interrupted metal cutting process (m/ min). d was the diameter of milling cutter, which was 1/10π (m). η was the ratio for cutting time/(cutting time þ non-cutting time) during each rotation period, which was 1/10.

3

J. Zhao and Z. Liu

International Journal of Machine Tools and Manufacture 147 (2019) 103467

Fig. 2. Variation of calculated heat partition RW with duration time for several combinations: (a) Continuous metal cutting; (b) Interrupted metal cutting with cutting speed 100 m/min. Variation of time-varying heat partition RW with coating thickness: (c) Continuous metal cutting; (d) Interrupted metal cutting with cutting speed 100 m/min. (e) Time-varying heat partition RW vs. cutting speed in interrupted metal cutting.

5 ms and 10 ms, respectively. The influence of tool substrate on heat partition RW was insignificant with the increase of duration time in continuous cutting process. As shown in Fig. 2(b), the maximum heat partitions RW in interrupted cutting Inconel 718 by (Ti,Al)N coated tool with substrate carbide M10 and P10 were 4.26% and 5.86% lower than that of carbide Ken-2210, respectively. The highest heat partition RW was obtained in cutting Inconel 718 by (Ti,Al)N coated tool with sub­ strate carbide P10 compared with other carbide M10 and Ken-2210. The lowest heat partition RW was obtained in cutting Inconel 718 by (Ti,Al)N coated tool with substrate carbide Ken-2210 compared with other car­ bide M10 and P10.

The influence of thermal property of coating and workpiece on heat partition RW was dominant in continuous and interrupted cutting pro­ cess. While, the influence of thermal property of tool substrate on heat partition RW was significant in the transient stage (within initial tens of milliseconds). 3.2. Effect of coating thickness on time-varying heat partition RW with coated tool Fig. 2(c) and (d) showed the transient heat partition RW with coating thickness for continuous and interrupted cutting Inconel 718 with (Ti, 4

J. Zhao and Z. Liu

International Journal of Machine Tools and Manufacture 147 (2019) 103467

Al)N coated tool (carbide Ken-2210). Each rotation period was 60 ms determined with Eq. (10) in interrupted cutting Inconel 718 by using a single (Ti,Al)N coated tool insert at cutting speed 100 m/min. Duration time for tool-chip contact was 6 ms determined with Eq. (11) during each rotation period. As shown in Fig. 2(c), the heat partition RW decreased 7.52% and 3.01% when the (Ti,Al)N coating thickness increased from 1 μm to 7 μm at duration time 10 ms and 50 ms, respectively. The influence of coating thickness on heat partition RW decreased gradually with the increase of duration time. Zhang et al. [10] also found that the thicker coating thickness decreased the heat partition RW. As shown in Fig. 2(d), the maximum heat partition RW decreased by 10.33% when the (Ti,Al)N coating thickness increased from 1 μm to 7 μm. The increase of coating thickness decreased heat partition RW in metal cutting. It was illustrated by that more heat flux was required for a thicker coating for reaching the same rake face temperature compared with a thin coating, thus decreasing heat partition RW.

Fig. 2(e) showed the transient heat partition RW versus cutting speed in interrupted metal cutting. The maximum heat partitions RW were 0.536, 0.523, 0.513 and 0.504 at the interrupted cutting speed 50, 100, 150, 200 m/min, respectively. The maximum heat partition RW decreased by 5.97% when the interrupted cutting speed increased from 50 m/min to 200 m/min. 4. Validation 4.1. Validation with former research To validate the new proposed model, the calculated heat partition RW and predicted average machining temperature were compared with the research result of Grzesik and Nieslony [5]. A CVD-TiC/Al2O/­ TiN-⅀10 μm multilayer coated tool (substrate carbide K10) was applied for machining AISI 1045 steel. The temperature-dependent thermal properties of multilayer coating, substrate carbide K10 and 1045 steel were depicted in Refs. [5,9,25,31,32]. The comparison of calculated heat partition RW between the new proposed model and former prediction models [6–8] was depicted in Fig. 3(a). It was illustrated that the heat partition RW calculated with the new proposed model was slightly lower than that calculated with Reznikov’s model [8]. It was due to the ignorance of coating thickness and substrate thermal properties in the prediction of heat partition RW calculated with Reznikov’s model. The comparison of predicted average machining temperature be­ tween new proposed model and former prediction models [6–8] was

3.3. Effect of cutting speed on time-varying heat partition RW in interrupted cutting with coated tool Each rotation period was 120, 60, 40 and 30 ms determined with Eq. (10) in interrupted cutting Inconel 718 using (Ti,Al)N coated tool at cutting speed 50, 100, 150 and 200 m/min, respectively. Duration time for coated tool-chip contact (Δt) was 12, 6, 4 and 3 ms determined with Eq. (11) during each rotation period at cutting speed 50, 100, 150 and 200 m/min, respectively.

Fig. 3. Comparisons between predicted models and measured temperature in machining 1045 with TiC/Al2O3/TiN multilayer coated tool (a) Heat partition RW; (b) Average machining temperature; (c) Relative error (d) Accumulative relative errors. 5

J. Zhao and Z. Liu

International Journal of Machine Tools and Manufacture 147 (2019) 103467

depicted in Fig. 3(b). The average cutting temperature predicted with new proposed model and Reznikov’s model [8] could obtain higher accuracy compared with the measured temperature than that of Loe­ wen-Shaw’s model [6] and Kato-Fujii’ model [7]. The relative error and accumulated relative error of four predicted models compared with experimental value at specific cutting speed were depicted in Fig. 3(c) and (d). The accumulated relative error of the new proposed model was the lowest one compared with that of other models. It illustrated that the new proposed model was verified accurate.

maximum tool-chip interface temperature and the experimental value was depicted in Fig. 5(b). Fig. 5(c) showed the relative errors of the predicted model compared with experimental value. The new proposed model had the lowest relative error of 11.04% compared with other former models, which showed that the proposed model was more ac­ curate to predict the heat partition. 5. Conclusions In this study, a new model for predicting transient heat partition RW at coated tool-chip interface in metal cutting process was developed and verified. Several conclusions are summarized as the followings.

4.2. Experimental validation As depicted in Fig. 4, a two-color thermometer was used for measuring the maximum temperature of the chip flowed from the cut­ ting zone during orthogonal cutting Inconel 718 with using (Ti,Al)N coated carbide tools (Ken-2210 carbide, coating thickness 2 μm). The measuring principle of two-color thermometer has been illustrated in Ref. [28]. The maximum tool-chip interface temperature was calculated ac­ cording to Grzesik and Nieslony [5]. Parameters required for calculation included the measured cutting forces, chip thickness, tool-chip contact width as well as length, and material thermal properties. These calcu­ lation parameters have been summarized in Fig. 4 and Table 1. The specific heat capability and density of Inconel 718 were approximately 516.45 J/(kg⋅K) and 8240.00 kg/m3, respectively. The heat partition RW was calculated with the former three models [6–8] and the proposed model. The heat partition RW calculated with the mentioned four models was summarized in Fig. 5(a). The comparison between the calculated

➢ The time needed for attaining quasi-steady-state of heat partition RW was around tens of milliseconds in continuous cutting. However, there was no evident quasi-steady state of heat partition RW in high speed interrupted cutting. ➢ The heat partition RW was mainly influenced by the thermal prop­ erties of coating and workpiece. The highest heat partition RW for cutting Inconel 718 was obtained with (Ti,Al)N coated carbide tool compared with that of TiN, Al2O3 and TiC coated carbide tool. The maximum heat partition RW in interrupted cutting Inconel 718 with (Ti,Al)N coated tool (substrate carbide Ken-2210) was lower about 13.30% than that of H13 at the cutting speed 1000 m/min. ➢ Coating thickness and substrate material properties also influence heat partition RW. The maximum heat partition RW for interrupted cutting Inconel 718 with (Ti,Al)N coated tool decreased 10.33% when coating thickness increased from 1 μm to 7 μm at the cutting speed 100 m/min. The heat partition RW was the lowest when cutting

Fig. 4. Orthogonal cutting experiment of Inconel 718 with (Ti,Al)N coated tool under cutting speed 50 m/min and feed 0.1 mm/r. 6

J. Zhao and Z. Liu

International Journal of Machine Tools and Manufacture 147 (2019) 103467

Fig. 5. Comparisons between predicted models and experimental value: (a) Heat partition RW; (b) Maximum tool-chip interface temperature; (c) Relative error.

Inconel 718 by (Ti,Al)N coated tools with substrate carbide Ken2210 compared with other substrate carbide M10 and P10. ➢ The heat partition RW decreased with cutting speed in interrupted cutting with coated tools. The maximum heat partition RW for interrupted cutting Inconel 718 with (Ti,Al)N coated tool decreased 5.97% when the cutting speed increased from 50 m/min to 200 m/ min.

Acknowledgement This research was funded by National Natural Science Foundation of China (grant numbers 51425503 and 91860207), and Taishan Scholar Foundation, the National Key Research and Development Program of China (grant number 2018YFB2002201), and Shandong Provincial Natural Science Foundation of China (grant number ZR2019MEE073).

Appendix Explicit solutions of temperature distribution within coated tool have been listed as the followings as referred to literature [24]. The one-dimensional transient heat transfer model of monolayer coated tool was depicted with right section in Fig. 1(b). The following as­ sumptions (a) - (f) were made to establish the explicit solutions of model. (a) Specific heat flux q0 was applied on coated tool rake face. (b) No additional thermal resistance was generated at coating-substrate interface. (c) The tool body was assumed as semi-infinite body. (d) The model boundary conditions were assumed as adiabatic; (e) The material thermal properties were assumed constants; (f) Tool wear was neglected. For the monolayer coated tool, the excess temperature was set as θ(1) ¼ T(1)-T∞ in the coating layer and θ(2) ¼ T(2)-T∞ in the substrate, respectively. Heat conduction partial derivative equations for the one-dimensional transient heat transfer model of monolayer coated tool were expressed with Eqns. (1a) and (2a).

∂θð1Þ 1 ∂θð1Þ ¼ ; 0 � x � x1 ; t � 0 ∂x2 αc ∂t

(1a)

∂θð2Þ 1 ∂θð2Þ ¼ ; x � x1 ; t � 0 ∂x2 αs ∂t

(2a)

where αc and αs were the coating thermal diffusivity and substrate thermal diffusivity, respectively. Outer boundary conditions were expressed with Eqns. (3a) and (4a). kc

∂θð1Þ j ¼ q0 ; x ¼ 0; t � 0 ∂x x¼0

(3a) (4a)

θð2Þ ðx; tÞ ¼ 0; x→∞; t � 0

7

J. Zhao and Z. Liu

International Journal of Machine Tools and Manufacture 147 (2019) 103467

where kc was the coating thermal conductivity. Initial condition was expressed with Eq. (5a). (5a)

θð1Þ ðx; tÞ ¼ θð2Þ ðx; tÞ ¼ 0; t ¼ 0 Continuity conditions at coating-substrate interface were expressed with Eqns. (6a) and (7a).

(6a)

ð1Þ

θ ðx1 ; tÞ ¼ θð2Þ ðx1 ; tÞ kc

∂θð1Þ ∂θð2Þ jx¼x1 ¼ ks j ∂x ∂x x¼x1

(7a)

where ks was the substrate thermal conductivity. Considering the Laplace transform expressed with Eqns. (8a) and (9a), the transform processes were obtained with Eqns. (10a)–(15a). Z ∞ θðx; pÞ ¼ L½θðx; pÞ� ¼ θðx; tÞe st dt 0

�

�

∂θðx; pÞ ¼ pθðx; pÞ ∂t

L

ð1Þ

∂θ ∂x2

p

(9a)

θðx; 0Þ

¼ 0; 0 � x � x1 ; t � 0

(10a)

¼ 0; x � x1 ; t � 0

(11a)

∂θ q0 j ¼ ; x ¼ 0; t � 0 ∂x x¼0 p

(12a)

αc

ð2Þ

∂θ ∂x2

p

αs

θ

θ

ð1Þ

ð2Þ

ð1Þ

kc

(13a)

ð2Þ

θ ðx; pÞ ¼ 0; x→∞; t � 0 ð1Þ

(14a)

ð2Þ

θ1 ðx1 ; pÞ ¼ θ2 ðx1 ; pÞ ð1Þ

kc

ð2Þ

∂θ ∂θ ¼ ks j j ∂x x¼x1 ∂x x¼x1

(15a)

The general solutions of Eqns. (1a) and (2a) were obtained with Eqns. (16a) and (17a). �rffiffiffiffi � �rffiffiffiffi � p p ð1Þ ⋅ x þ B1 exp ⋅x θ ¼ A1 exp

αc

θ

(8a)

ð2Þ

αc

�rffiffiffiffi � �rffiffiffiffi � p p ⋅ x þ B2 exp ⋅x ¼ A2 exp

αs

(16a) (17a)

αs

where A1, B1, A2, and B2 were constant variation coefficients. Coefficient A1 was expressed with Eq. (18a). � qffiffiffi � c⋅exp 2 αpc ⋅x1 pffiffiffiffi 1 q α � �⋅ 0 c A1 ¼ 3=2 ⋅ ffi ffi ffi q p kc 1 c⋅exp 2 αpc ⋅x1

(18a)

where the intermediate variable c was defined with Eq. (19a) for clear representation. pffiffiffiffi pffiffiffiffi kc αs ks αc c ¼ pffiffiffiffi (19a) pffiffiffiffi kc αs þ ks αc � qffiffiffi � Considering exp 2 αpc ⋅x1 , it was difficult to invert the Laplace transform of Eq. (18a), the Taylor series expansion was used to perform the calculation as shown in Eq. (20a). 2 � rffiffiffiffi � p ⋅x1 c⋅exp 2 pffiffiffiffiffi 6 pffiffiffiffi αc 1 q0 αc 1 q0 α1 6 � A1 ¼ 3=2 ⋅ ¼ 3=2 ⋅ rffiffiffiffi �⋅ 6 p kc 4 kc p p 1 c⋅exp 2 1 ⋅x1

αc

pffiffiffiffi (X ∞

¼

1 q0 αc ⋅ p3=2 kc

n¼0

� ðjcjÞnþ1 ⋅exp

2ðn þ 1Þ

rffiffiffiffi p

αc

3 � c⋅exp

1

rffiffiffiffi � p 2 ⋅x1

αc

�) ⋅x1

Similar calculations of B1, A2 and B2 were obtained with Eqns. (21a)–(23a). 8

7 7 17 5

(20a)

J. Zhao and Z. Liu

International Journal of Machine Tools and Manufacture 147 (2019) 103467

pffiffiffiffi (

B1 ¼

pffiffiffiffi 1 q0 αc 1 q0 αc ⋅ þ 3=2 ⋅ kc p3=2 kc p

∞ X

� ðjcjÞnþ1 ⋅exp

rffiffiffiffi p ⋅x1 2ðn þ 1Þ

�) (21a)

αc

n¼0

(22a)

A2 ¼ 0 � rffiffiffiffi pffiffiffiffi rffiffiffiffi � 1 q0 αc p p ⋅x1 þ ⋅x ⋅ ⋅exp kc αc αs 1 p � pffiffiffiffi ( ∞ rffiffiffiffi rffiffiffiffi �) 1 q0 αc X p p nþ1 þ 3=2 ⋅ ⋅x1 þ ⋅x1 ðjcjÞ ⋅exp ð2n þ 1Þ kc α α p c s n¼0 � pffiffiffiffi ( ∞ rffiffiffiffi rffiffiffiffi �) 1 q0 αc X p p ⋅x1 þ ⋅x þ 3=2 ⋅ ðjcjÞnþ1 ⋅exp ð2n þ 3Þ kc αc αs 1 p n¼0

B2 ¼

3=2

(23a)

Consequently, the transient temperature distributions of the coating and substrate considering excess temperature (θ ¼ T-T∞) were obtained with Eqns. (24a) and (25a). � pffiffiffiffi ( ∞ rffiffiffiffi rffiffiffiffi �) q0 αc X p p ð1Þ nþ1 ⋅x þ ⋅x θ ¼ ðjcjÞ ⋅exp ð2n þ 1Þ αc 1 αc kc p3=2 n¼0 � pffiffiffiffi ( ∞ rffiffiffiffi rffiffiffiffi �) q0 αc X p p (24a) ⋅x1 ⋅x ðjcjÞnþ1 ⋅exp 2ðn þ 1Þ þ 3=2 αc αc kc p n¼0 � rffiffiffiffi � pffiffiffiffi q0 αc p þ 3=2 exp ⋅x ; 0 � x � x1 αc kc p � pffiffiffiffi ( ∞ rffiffiffiffi rffiffiffiffi rffiffiffiffi �) q0 αc X p p p nþ1 ⋅x þ ⋅x ⋅x θ ¼ ðjcjÞ ⋅exp ð2n þ 1Þ αc 1 αs 1 αs kc p3=2 n¼0 � pffiffiffiffi ( ∞ rffiffiffiffi rffiffiffiffi rffiffiffiffi �) q0 αc X p p p þ 3=2 ⋅x1 þ ⋅x1 ⋅x ðjcjÞnþ1 ⋅exp ð2n þ 3Þ αc αs αs kc p n¼0 pffiffiffiffi � � rffiffiffiffi rffiffiffiffi rffiffiffiffi �� q0 αc p p p þ 3=2 exp ⋅x1 þ ⋅x1 ⋅x ; x � x1 αc αs αs kc p ð2Þ

(25a)

Convolution theorems of Eqns. (26a) - (28a) were used to obtain the final explicit solutions. 2 3 pffiffi � 2 1 a 7 exp a p 6 L½f1 ðtÞ� ¼ L4pffiffiffiffie 4t 5 ¼ pffiffi p πt

L½f2 ðtÞ� ¼ L½1� ¼

L

1

pffiffi �� a p

� exp

p3=2 Z

¼ 0

t

1 p

1 pffiffiffiffiffi⋅e

πτ

(27a) 1

¼L

pffi t

Z

a2 4τ

dτ ¼

8 > a2 pffi 2 < ¼ pffiffiffi y⋅e 4y2 j0 t π> :

(26a)

1 pffiffiffi⋅e

a2 4y2

π

0

Z a

Z t pffiffi � � a p 1 ⋅ ¼ f1 ðtÞ*f2 ðtÞ ¼ f1 ðτÞ⋅f2 ðt pffiffi p p 0

� exp

u2

∞

ffi

e

a p 2 t

8 > > 2 < 4ya22 pffit dy ¼ pffiffiffi y⋅e j0 π> > :

8 > 2 π> : ; 9 > =

Z 0

pffi t

2

a ⋅e 2y2

a2 4y2

τÞdτ

9 > > = dy > > ;

(28a)

9 � �> a = a⋅erfc pffi 2 t > ;

The explicit solutions of temperature distribution within coated tool were characterized with Eqns. (29a) and (30a) with Laplace’s transformation

using convolution theorem. rffiffiffi � � ��) � � pffiffiffiffi ( ∞ q0 αc X t D2 D pffi T ð1Þ ¼ ⋅ exp ðjcjÞnþ1 ⋅2 erfc kc π 4t 2 t n¼0 ( rffiffiffi � � ��) � � pffiffiffiffi ∞ q0 αc X t E2 E nþ1 pffi þ ðjcjÞ ⋅2 ⋅ exp erfc kc π 4t 2 t n¼0 � pffiffiffiffi � rffiffiffi q0 αc t ⋅exp þ 2 kc π

x2 4αc t

�

rffiffiffiffi 1

αc

� ⋅x⋅erfc

(29a)

�� x pffiffiffiffiffiffi þ T∞ ; 0 � x � x1 2 αc t

9

J. Zhao and Z. Liu

International Journal of Machine Tools and Manufacture 147 (2019) 103467

rffiffiffiffi � 1 ⋅x1 D ¼ 2ðn þ 1Þ

αc

rffiffiffiffi � 1 ⋅x

αc

(30a)

rffiffiffiffi rffiffiffiffi � � 1 1 ⋅x1 þ ⋅x E ¼ 2ðn þ 1Þ

αc

αc

The coated tool rake face temperature can be determined with Eq. (31a) by assuming x ¼ 0. # rffiffiffi ( " rffiffiffiffiffiffiffi � �) pffiffiffiffi ∞ 4 αc X t ðn þ 1Þ2 x21 ðn þ 1Þx1 2q0 t⋅αc ð1Þ nþ1 pffiffiffiffiffiffiffi erfc ⋅ exp þ T∞ T x¼0 ¼¼ q0 þ ⋅ ðjcjÞ ⋅ t⋅αc kc n¼0 π t⋅αc kc π

(31a)

¼ q0 Aðx1 ; kc ; αc ; ks ; αs ; tÞ þ T∞

References

[18] F. Zemzemi, J. Rech, W.B. Salem, A. Dogui, P. Kapsa, Identification of friction and heat partition model at the tool-chip-workpiece interfaces in dry cutting of an Inconel 718 alloy with CBN and coated carbide tools, Adv. Manuf. Sci. Technol. 38 (1) (2014) 5–22. [19] E.R. De Eguilaz, J. Rech, P. Arrazola, Characterization of friction coefficient and heat partition coefficient between an AISI4140 steel and a TiN-coated carbide–influence of (Ca, Mn, S) steel’s inclusions, P. I, Mech. Eng. J-J. Eng. 224 (10) (2010) 1115–1127. [20] A. Mondelin, C. Claudin, J. Rech, F. Dumont, Effects of lubrication mode on friction and heat partition coefficients at the tool–work material interface in machining, Tribol. Trans. 54 (2) (2011) 247–255. [21] J. Rech, P.J. Arrazola, C. Claudin, C. Courbon, F. Pusavec, J. Kopac, Characterisation of friction and heat partition coefficients at the tool-work material interface in cutting, CIRP Ann. - Manuf. Technol. 62 (1) (2013) 79–82. [22] S.N. Melkote, W. Grzesik, J. Outeiro, J. Rech, V. Schulze, H. Attia, P.-J. Arrazola, R. M’Saoubi, C. Saldana, Advances in material and friction data for modelling of metal machining, CIRP Ann. - Manuf. Technol. 66 (2) (2017) 731–754. [23] V. Kryzhanivskyy, V. Bushlya, O. Gutnichenko, R. M’Saoubi, J.-E. Ståhl, Heat flux in metal cutting: experiment, model, and comparative analysis, Int. J. Mach. Tool Manuf. 134 (2018) 81–97. [24] S.J. Zhang, Z.Q. Liu, Analytical and numerical solutions of transient heat conduction in monolayer-coated tools, J. Mater. Process. Technol. 209 (5) (2009) 2369–2376. [25] J.F. Zhao, Z.Q. Liu, Q.Q. Wang, J.M. Jiang, Measurement of temperaturedependent thermal conductivity for PVD Ti0.55Al0.45N ceramic coating by time domain thermo-reflectance method, Ceram. Int. 45 (7) (2019) 8123–8129. [26] W. Grzesik, C.A. van Luttervelt, An investigation of the thermal effects in orthogonal cutting associated with multilayer coatings, CIRP Ann. - Manuf. Technol. 50 (2001) 53–56. [27] S.J. Zhang, Z.Q. Liu, An analytical model for transient temperature distributions in coated carbide cutting tools, Int. Commun. Heat Mass Transf. 35 (2008) 1311–1315. [28] J.F. Zhao, Z.Q. Liu, B. Wang, Y. Hua, Q.Q. Wang, Cutting temperature measurement using an improved two-color infrared thermometer in turning Inconel 718 with whisker-reinforced ceramic tools, Ceram. Int. 44 (15) (2018) 19002–19007. [29] E.G. Ng, D.K. Aspinwall, D. Brazil, J. Monaghan, Modelling of temperature and forces when orthogonally machining hardened steel, Int. J. Mach. Tool Manuf. 39 (1999) 885–903. [30] R. Komanduri, Z.B. Hou, Analysis of heat partition and temperature distribution in sliding systems, Wear 251 (2001) 925–938. [31] W. Grzesik, W.P. Nieslony, Thermophysical-property-based selection of tool protective coatings for dry machining of steels, J. Manuf. Sci. Eng. 125 (2003) 689–695. [32] W. Grzesik, The influence of thin hard coatings on frictional behavior in the orthogonal cutting process, Tribol. Int. 33 (2000) 131–140.

[1] W. Grzesik, Experimental investigation of the cutting temperature when turning with coated indexable inserts, Int. J. Mach. Tool Manuf. 39 (1999) 355–369. [2] S.M. Lee, H.M. Chow, F.Y. Huang, B.H. Yan, Friction drilling of austenitic stainless steel by uncoated and PVD AlCrN and TiAlN-coated tungsten carbide tools, Int. J. Mach. Tool Manuf. 49 (1) (2009) 81–88. [3] L. Chen, B.L. Tai, R.G. Chaudhari, X. Song, A.J. Shih, Machined surface temperature in hard turning, Int. J. Mach. Tool Manuf. 121 (2017) 10–21. [4] G.K. Dosbaeva, M.A. El Hakim, M.A. Shalaby, J.E. Krzanowski, S.C. Veldhuis, Cutting temperature effect on PCBN and CVD coated carbide tools in hard turning of D2 tool steel, Int. J. Refract. Met. H. 50 (2015) 1–8. [5] W. Grzesik, P. Nieslony, Physics based modelling of interface temperatures in machining with multilayer coated tools at moderate cutting speeds, Int. J. Mach. Tool Manuf. 44 (9) (2004) 889–901. [6] M.C. Shaw, Metal Cutting Principles, Clarendon Press, Oxford, 1989. [7] T. Kato, H. Fujii, Energy partition in conventional surface grinding, ASME Trans. J. Manuf. Sci. Eng. 121 (1999) 393–398. [8] A.N. Reznikov, Thermophysical Aspects of Metal Cutting Processes, Mashinostroenie, Moscow, 1981. [9] W. Grzesik, P. Nieslony, A computational approach to evaluate temperature and heat partition in machining with multilayer coated tools, Int. J. Mach. Tool Manuf. 43 (2003) 1311–1317. [10] X. Zhang, T. He, H. Miwa, T. Nanbu, R. Murakami, S.B. Liu, J. Cao, Q.J. Wang, A new approach for analyzing the temperature rise and heat partition at the interface of coated tool tip-sheet incremental forming systems, Int. J. Heat Mass Transf. 129 (2019) 1172–1183. [11] J. Rech, J.L. Battaglia, A. Moisan, Thermal influence of cutting tool coatings, J. Mater. Process. Technol. 159 (1) (2005) 119–124. [12] E. Ceretti, L. Filice, D. Umbrello, F. Micari, ALE simulation of orthogonal cutting: a new approach to model heat transfer phenomena at the tool-chip interface, CIRP Ann. - Manuf. Technol. 56 (1) (2007) 69–72. [13] H. Puls, F. Klocke, D. Veselovac, FEM-based prediction of heat partition in dry metal cutting of AISI 1045, Int. J. Adv. Manuf. Technol. 86 (2016) 737–745. [14] F. Akbar, P.T. Mativenga, M.A. Sheikh, An evaluation of heat partition in the highspeed turning of AISI/SAE 4140 steel with uncoated and TiN-coated tools, P. I, Mech. Eng. B-J. Eng. 222 (7) (2008) 759–771. [15] F. Akbar, P.T. Mativenga, M.A. Sheikh, On the heat partition properties of (Ti,Al)N compared with TiN coating in high-speed machining, P. I. Mech. Eng. B-J. Eng. 223 (4) (2009) 363–375. [16] C. Bonnet, F. Valiorgue, J. Rech, C. Claudin, H. Hamdi, J.M. Bergheau, P. Gilles, Identification of a friction model—application to the context of dry cutting of an AISI 316L austenitic stainless steel with a TiN coated carbide tool, Int. J. Mach. Tool Manuf. 48 (11) (2008) 1211–1223. [17] F. Zemzemi, J. Rech, W.B. Salem, A. Dogui, P. Kapsa, Identification of a friction model at tool/chip/workpiece interfaces in dry machining of AISI4142 treated steels, J. Mater. Process. Technol. 209 (8) (2009) 3978–3990.

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