Physics based modelling of interface temperatures in machining with multilayer coated tools at moderate cutting speeds

International Journal of Machine Tools & Manufacture 44 (2004) 889–901 www.elsevier.com/locate/ijmactool

Physics based modelling of interface temperatures in machining with multilayer coated tools at moderate cutting speeds W. Grzesik
, P. Nieslony Department of Manufacturing Engineering and Production Automation, Technical University of Opole, P.O. Box 321, Opole 45-271, Poland Received 10 September 2003; received in revised form 12 February 2004; accepted 19 February 2004

Abstract A new thermal model is presented for turning with tools with multilayer coatings. In the previous paper [Int. J. Mach. Tools Manuf. 43 (2003) 1311] devoted to the thermal problems in dry turning of steels with tools treated with multilayer coatings with an intermediate Al2O3 layer new analytical models for estimating the heat partition to the chip and the average interface temperature were derived and the predictions were compared with experimental results. In this paper, a physics based modelling concept has been applied to both the individual layer and the composite layer approach to develop an estimate of the average and the maximum steady-state chip-tool interface temperatures in orthogonal turning. Different approaches for determining the heat partition coefficient for sliding bodies of defined thermal properties were tested. Experiments using the work and the tool as the thermocouple pair have verified that the proposed models accurately predict the temperatures for uncoated and coated tools for a range of cutting speeds. As a result a new computational algorithm, for predicting with reasonable accuracy the average and peak values of the temperatures at the chip-coating/substrate interface at cutting speeds up to 200 m/min, has been recommended. # 2004 Elsevier Ltd. All rights reserved. Keywords: Machining; Steels; Multilayer coatings; Interface temperatures

1. Introduction A combination of higher cutting speeds with dry process conditions have recently been recognized as an effective way for achieving higher productivity and lower production costs. This combined technology requires specially heat-protected cutting tools, obtained mainly by means of the deposition of proper coatings, in order to guarantee the best performance for the given tool life. According to many professional sources [2], in continuous turning operations the temperature of v the insert frequently goes up to 700 C or even substantially more. It is well-known that the application of cutting tools treated with advanced tool coatings enables this thermal obstacle to be overcome and high hardness to be remained due to substantial changes in friction and heat partition to the chip, and consequently a visible reduction in the cutting temperature is observed.
Corresponding author. Tel.: +48-77-4006290; fax: +48-774006342. E-mail address: [email protected] (W. Grzesik).

0890-6955/$ - see front matter # 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmachtools.2004.02.014

The author’s own and many other studies indicated that the prediction of the tool-chip interface temperatures should be made using the thermophysical properties of the sliding tool and chip materials including the thermal conductivity, thermal diffusivity and heat transfer coefficient or more complex indicators such as the Peclet and Fourier numbers [1,3,4]. This is due to the fact that in most industrial machining processes, which differ from the mostly used orthogonal case, the application of higher cutting speeds and feed rates change substantially the contact conditions and cause the interface temperatures to increase. It was clear that for modelling purpose, the assumption of constant thermal properties for a range of cutting parameters was not acceptable. According to Jen et al. [5], the error incurred in using the constant thermal property assumption on the maximum temperature calculations was about 25%, and 6% for the cutting tools made of high-speed steel and tungsten carbide for the heat flux range of 25–50 MW/m2. Especially, the effect of temperature dependent thermal properties may become important for cases when very steep temperature gradient can be generated.

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In general, the modelling concept proposed is based on the well-known principle of the simultaneous action of two independent heat sources, which suggests that the total heat flux is generated by aggregation the plastic deformation and sliding friction effects. There are the shear zone (primary deformation zone-PDZ) and frictional heat sources (secondary deformation zoneSDZ). The main difference from other existing models is that it incorporates actual values of the thermal properties and heat partition coefficients as a function of temperature in one comprehensive model. It was revealed [1] that the heat partition coefficient differs for uncoated carbide tools and when multilayer coatings include an intermediate Al2O3 ceramic layer and relevant values of R were found to range from 0.5 to 0.6 and from 0.65 to 0.8, respectively. Moreover, it was documented that the classical solution for heat partition to the chip (RSH) proposed by Shaw [4] does not provide acceptable results for advanced multilayercoated tools due to the fact that it always predicts the coefficient of heat partition for such composite structure at the level of 0.9 and neglects the well-documented in the literature heat isolating (thermal barrier) effect [3,6]. In consequence, in this study the steadystate temperature response at the tool-chip interface is calculated using the corrected heat flow model, which accounts for this effect and generalize Loewen and Shaw’s temperature model for a rectangular moving heat source [4]. In particular, a few different solutions for heat balance between the chip and the coated tool were included into computation algorithm in order to predict presumably near-real thermal features of the interface occurring at varying cutting conditions. Recently, a composite coating layer with equivalent thermophysical properties has been proposed for estimation and simulation of such process outputs as the chip geometry, cutting forces, contact length and steady-state tool temperature [7,8]. Balaji and Mohan [7] have suggested that Oxley’s predictive model [9] which accounts for the high strainrate/high temperature flow stress and thermal properties of the work material is capable of predicting the tool-chip contact length in 2-D machining but the tool material properties and their effects were neglected in this analysis. When they incorporated the combined action of different coating layers of different thicknesses in the form an effective cutting tool thermal conductivity parameter, the new model predicts the tool-chip contact length for TiN/Al2O3/TiC coated tools in conjunction with a plain carbon steel more accurately in relation to experimental data. On the other hand, Yen et al. [8] have also introduced the equivalent heat capacity into the FEM package to obtain the steady-state solution of temperature in the three-layer coated tool. It is concluded based on simulations performed for AISI 1045 steel and TiN/

Al2O3/TiC (1 lm-TiN, 3 lm-Al2O3, 6 lm-TiC) coating that two methods applied using individual coating layers with intrinsic properties and a composite layer with equivalent properties provided results for the interface temperatures consistent with the experimental values obtained by Grzesik [3,10,11]. As reported, differences between the predicted and measured values of the average interface temperature were within 5–11%. The purpose of this report is to generalize some most frequently used analytical heat transfer and temperature models and account for coatings effects by considering a uniform stack of layers with temperature dependent equivalent thermal properties, namely the thermal conductivity, heat capacity and thermal diffusivity.

2. Modelling concept 2.1. Thermal properties of the tool and workpiece materials In previous research on the cutting performance when using various coated cutting tools authors have collected and refined data from different literature sources, which concern fundamental thermal properties of the tool (substrate and coatings) and workpiece materials used, first of all, the thermal conductivity, heat capacity and thermal diffusivity [1,3,4,12]. When considering the individual layer concept, all these properties are defined separately for each layer in the multilayer structured coatings. It should be noted based on the experimental evidence that in the case of three- and four-layer coatings tested the dominant role plays an intermediate Al2O3 ceramic layer with extremely low thermal conductivity and diffusivity at real interface temperatures. The diagrams showing the dependence of the thermal conductivity and diffusivity for some frequently used materials can be found in previous author’s papers, as for example in [1,3]. In the composite layer concept, in which all components are replaced by one homogeneous thick layer, the equivalent thermal properties are introduced. As mentioned in Section 1 this concept previously, but for different modelling tasks, was applied by Balaji and Mohan [7] for prediction of the tool-chip contact and Yen et al. [9] for computer simulation of an orthogonal cutting using the finite element method (FEM). The equivalent (effective) thermal conductivity for a multilayer structure depends on the thickness of each component and the number of coating layers. For three and four layer coatings used, it can be determined using the well-known in thermodynamics expression [13], as follows: Pt x1 x2 xt 1 xi ¼ þ þ  þ ð1Þ keq k1 k2 kt

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where xi is thickness value of the selected i-layer i ¼ 1; 2; . . . t), ki is thermal conductivity of i-layer, Rxi is total thickness of the stack (composite layer), keq is the equivalent thermal conductivity of the composite layer and t denotes the top (outer) layer. Fig. 1 presents values of the thermal conductivity for P20 sintered carbide (WC) and four individual layers involved in TiC/Al2O3/TiN and TiC/Ti(C,N)Al2O3/ TiN multilayer coatings and computed values of keq for one composite layer. In calculation, the thicknesses of individual layers were assumed to be equal to 6 lm (TiC), 3 lm (Al2O3) and 1 lm (TiN) for three-layer coatings and 4 lm (TiC), 2 lm (Ti(C,N)), 6 lm (Al2O3) and 1 lm (TiN) for four-layer coatings. As can be seen from Fig. 1, both aggregate thermal properties represented by courses 3L and 4L change similarly to an Al2O3 ceramic layer, but the effect of reduction of thermal conductivity is more pronounced for four-layer coatings due to the thicker ceramic layer. This effect explains the previously reported substantial reduction of the interface temperature when using these coatings as a heat isolating for the carbide substrate [3,4]. Calculations of the heat partition coefficient require values of the thermal diffusivity to be known for actual contact temperatures [1]. It can be determined as the ratio of the equivalent thermal conductivity to the equivalent volumetric heat capacity (Ceq). The proper formula can be derived by summing volumes of the individual layers Vi to obtain the total coating. For example, in the case of a three-layer coating it can be written as follows: V ¼ V1 þ V2 þ V3

ð2aÞ

By considering adequate thicknesses (xi) and densities (qi) of all coating layers and replacing the density by qi = Ci/cpi (where cpi is the specific heat of i-layer),

the final equation can be expressed in the form: Pt x1 q1 cp1 x2 q2 cp2 xt qt cpt 1 ðxi qi cpi Þ ¼ þ þ  þ Ceq C1 C2 Ct

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ð2bÞ

where 1 denotes the first layer adjacent to the substrate and t identifies the top layer. After simple transformations, Eq. 2b can be rewritten in a more comprehensive form as: Pt 1 ðxi Ci Þ ð2cÞ Ceq ¼ P t 1 xi For example, assuming the average values of the thickness for individual layers in the three-layer stack to be equal to 6, 3 and 1 lm for TiC, Al2O3 and TiN layer, respectively, the equivalent heat capacity at v 600 C calculated from Eq. 2c is equal to 2:97  v 106 J=ðm3 CÞ. For a four-layer coating (4 lm-TiC, 2 lm-Ti(C,N), 6 lm-Al2O3 and 1 lm-TiN), this value v was found to be about 3:10  106 J=ðm3 CÞ. The computed values of the equivalent diffusivity for the temv perature rise within the range of 400–1000 C for a single Al2O3 layer, and two composite structures considered are shown in Fig. 2. 2.2. Determination of the heat partition coefficient In this study, prediction of partition of the heat flux which flows into the chip, i.e. for body with a moving heat source, was based on the determination of the heat partition coefficient (Rch), which defines the percentage of the heat entering the moving chip. It should be noted that fraction ð1  Rch Þ provides the percentage of the dissipated energy going to the tool, i.e. the member that is stationary relative to the heat source. For the modelling purpose, three different

Fig. 1. Dependence of the thermal conductivity on temperature for tungsten carbide (WC) and typical layers (a) and composite layer (b).

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contact area. The expression proposed by Kato and Fujii [15] was originally defined for conventional surface grinding and in this study modified version is used [1]: RKF ¼

1 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi    1þ cp qk T cp qk W

ð4Þ

It should be noted that in Eq. (4) triple products, named also as the heat transmission ratios, for work (W) and tool (T) materials are introduced. The third formula uses generally both Peclet and Fourier number in order to consider the sliding velocity and duration of frictional heat source [1]. The adequate expression can be given by Fig. 2. Dependence of the thermal diffusivity on temperature for ceramic Al2O3 layer and composite layer for three (3L) and fourlayer (4L) coatings.

methods of calculations of the heat partition coefficient are used, namely those proposed by Shaw [14], Kato and Fujii [15] RKF, and Reznikov [12] RR. The value of RSH coefficient can be estimated as RSH ¼

1   pffiffiffiffiffiffiffi 1 þ ð0:754ðkT =kW ÞÞ= Aa NT

ð3Þ

In Eq. (3), thermal conductivities of work (kW) and tool (kT) materials, thermal number (NT) and area shape factor (A) describe the thermal and geometrical features of the interface. The thermal number is given by NT ¼ vch lc =2aW

ð3aÞ

where vch is chip (sliding) velocity, lc ¼ lnc is natural contact length and aW is the diffusivity of work (chip) material. The shape factor (A) is determined as follows [14,16,17]: – for estimating the average temperature corresponding average value of factor A in Eq. (3) is equal to 

  m 2 l 1 m 1 Aa ¼ sinh þ sinh p l l m



1  m 2 1 l 1 l þ þ  3 l 3 m 3 m #  m   m 2 0:5 þ 1þ ð3bÞ l l – the maximum value of factor A is   m m 2 l sinh1 þ sinh1 Am ¼ p l l m

ð3cÞ

In Eqs. 3b and 3c width of the contact zone m ¼ ap (ap is depth of cut) and ratio m/l is aspect ratio of the

RR ¼

1  pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 þ ð3kT =2kW Þ PeT FoW

ð5aÞ

On the other hand, the version proposed, Eq. (5b) includes besides thermal conductivities (kT and kW) also adequate diffusivities (aT and aW) of both sliding materials. RR ¼

1 h pffiffiffiffiffiffiffiffiffiffiffiffiffiffii 1 þ ð3kT =2kW Þ aW =aT

ð5bÞ

In the author’s opinion, this expression better describes the thermal behaviour of the heat source and its geometry than the two other formulae used, i.e. Eqs. (3) and (4). 2.3. Calculation of temperature rise resulting from frictional heat source According to Shaw [14], the temperature increment due to the action of the frictional heat source can be determined as f ¼ DH

0:377Rqlc pffiffiffiffiffiffiffi kW N T

ð6Þ

where q is heat flux, lc is contact length and NT is thermal number determined by Eq. (3a). For the maximum rise of the interface temperature DHfmax constant in Eq. (6) is 0.565 [14]. On the other hand, Reznikov [12] proposes to calculate these quantities using the following formulae: pffiffiffiffiffiffiffiffiffi W lc  f ¼ 4q paffiffiffiffiffiffiffiffi ð7aÞ DH ffi Ka ðuÞ 3kW pvch pffiffiffiffiffiffiffiffiffi 2q aW lc ð7bÞ DHfmax ¼ pffiffiffiffiffiffiffiffiffi Km ðuÞ kW pvch In Eqs. (7a and b), values of the shape factors Ka(u) and Km(u) were assessed as functions of parameter pffiffiffiffiffiffi u ¼ ðb=lÞ Pe, where b ¼ m, Peclet number Pe ¼ ðvch  lc Þ=aW , based on special nomograms available in [12]. Under the thermal conditions generated at cutting speeds applied, for which parameter u is greater than

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10, the values of shape factors Ka(u) and Km(u) are equal to 0.86 and 1, respectively. Originally, the type of the heat source considered was denoted by Reznikov [12] as ðð2P2=UFSÞP2Þ, where 2P2 is two-dimensional rectangular plane slider, UF is uniformly distributed (U) and fast moving (F) heat source over a plane (P) adiabatic surface, 2-boundary conditions of the second order, S is steady-state process.

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 f ), the mean temperature rise due to friction (DH namely t ¼ H  s þ DH f H

ð11aÞ

By analogy, the maximum interface temperature (Hmax) is the effect of proper temperature peaks, namely: Hmax ¼ Hsmax þ DHfmax

ð11bÞ

2.4. Calculation of temperature rise due to plastic deformation in the PDZ The computation scheme used in this part of calculations consists of three steps. In the first one, the thermal number R is calculated using the Boothroyd’s formula [18]. The next two steps of computations are based on the theory of similarity elaborated for metal cutting purpose by Silin [19]. This enables the estimation of the maximum and mean temperatures occurring at the shear plane. It should be noted that the theory of similarity enables to calculate this temperature more accurately than Oxley’s theory [9] because more calculation formulae are proposed depending on the value of the product R  tanU. The thermal number is calculated as follows: R¼

cp q  vc  h kW

ð8Þ

where vc is cutting speed, kW is thermal conductivity of work material and undeformed chip thickness h ¼ f (f ¼ feed rate). Maximum temperature at the shear plane can be computed as: rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ssh RtanU erf Hsmax ¼ ð9Þ 4 cp qtanU where ssh is shear flow stress, A is shear angle and erf is error function. Then, the mean temperature at the shear plane is equal to [19]: for R tanU 5

 s ¼ 0:685ðR tanUÞ0:07 Hsmax H

ð10aÞ

 s ¼ 0:620ðR tanUÞ0:13 Hsmax ð10bÞ for 5 R tanU 20 H  s ¼ 0:820ðR tanUÞ0:04 Hsmax for R tanU  20 H

ð10cÞ

2.5. Calculation of average and maximum interface temperatures  t ) is defined as The average interface temperature (H  s ) and the sum of the mean shear-plane temperature (H

3. Computation procedure As mentioned in Sections 1 and 2, in order to characterize the performance of the two principal heat sources localized in the primary deformation (PDZ) and secondary deformation (SDZ) zones the corresponding values of the process variables were selected and a number of thermal properties including Peclet and Fourier numbers required for estimating heat partition and interface temperatures were computed. According to the flow chart shown in Fig. 3, the computational procedure consists of five subsequent steps as follows: Step 1. It allows the determination of three different heat partition coefficients denoted as RSH, RKF and RR. The appropriate equations used are given in Section 2.2. Step 2. The maximum temperature resulting from plastic deformation occurring in the PDZ and, as a result, the average temperature along the shear plane are calculated taking into account three boundary values of the product R  tanU (where R is thermal number and A is the shear angle). Step 3. In this step, the appropriate values of both maximum and mean temperature rises due to friction action at the interface were estimated. It should be noted that different heat partition coefficients were selected for uncoated and coated tools. This is due to the fact the coatings changed the heat partition and mitigated the temperatures observed. This specific evidence was confirmed by many experimental results [3,4]. Step 4. Consequently, the average and maximum interface temperatures were predicted by summing the components obtained in Steps 2 and 3. For example, the average interface temperature is the sum of the  s ) and the mean temmean shear-plane temperature (H  f ). perature rise due to friction (DH Step 5. The predicted values of the mean interface temperatures were compared with the corresponding values measured.

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Fig. 3.

Flow chart for prediction the heat partition coefficient and peak and average tool-chip interface temperatures.

4. Experiments In this study, the cutting experiments were conducted using two multilayer with an intermediate ceramic P layer: CVD-CVD-TiC=Al2 O3 =TiN- 10 lm and P TiC=TiðC; NÞ=Al2 O3 =TiN- 13 lm coated flat-faced inserts consisting of ISO-P20 cemented carbide substrate. In order to compare the experimental results, the substrate was also examined as a tool material. The insert geometry was ISO-TNMA 160408 with a clearv ance angle equal to 0 . The orthogonal cutting tests were carried out on a precision lathe using a thinwalled tube as the workpiece. The cutting was performed dry. The thickness of the tube wall was equal to 2 mm and the outer diameter of the tube was set at 80 mm. The work materials used in this study was AISI 1045 carbon steel. During experiments, cutting parameters were selected as follows: the cutting speed

vc ¼ 50 210 m=min, feed rate f ¼ 0:16 mm=rev, the depth of cut ap ¼ 2 mm. The measuring techniques were essentially similar to those used in previous author’s studies on cutting tool coatings [1,4,10]. The cutting forces Fc and Ff were measured using a two-component strain-gauge dynamometer fixed on the tool post of a lathe. The thermal EMF signals were recorded in the classical tool-work thermocouple circuit and converted into equivalent temperature values [20]. In order to store the data in the computer memory, on-line measurements were accomplished by a multichannel data acquisition software. In the thermocouple experiments, up to 10% variation (sporadically it was increased to 20% when turning with distinct chatter marks on the machined surface) in the thermoelectric EMF measurement was observed in the various sets of test data.

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After cutting, the contact parts of the tool rake faces were measured with a PC-based optical image processing system described in [10]. It included a CCD camera, high resolution colour display and a Corel Photo Paint v.7.0 graphics package. As a result, the tool-chip contact area and its length were estimated with high accuracy.

5. Computation results and discussion The analytical methodology developed in this study was used to predict the thermal behaviour of the toolchip interface including the heat partition and the average and peak temperature rise on the rake face of the inserts tested. The chip contact geometry corresponding to the cutting conditions for each inserts was obtained experimentally. This was used to model the heat contact zone as described previously. The effects of the cutting speed on the average temperature rise are then used to simulate the thermocouple experiments. The differences between measured and predicted values of cutting temperature were primarily due to the combination of experimental errors and the assumptions of the thermal properties. 5.1. Heat partition Fig. 4 shows changes of the heat partition coefficient computed for multilayer coated tools (courses 3L and 4L) when machining AISI 1045 carbon steel based on individual (a) and composite layer (b) assumptions using RR, RKF and RSH partition coefficients represented by cases A, B and C, respectively. It was found

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that for both models proposed the heat partition coefficient calculated from Shaw’s version (case C) is higher than 0.9 when using multilayer coated tools like for uncoated carbide tools and it increases slightly with the cutting speed rise up to the maximum value of about 200 m/min. In contrast, when using the RR value 0.55–0.6 (Fig. 4b) or 0.62–0.68 (Fig. 4a) of the dissipated heat flows to the chip depended on the modelling concept used. This implies that the use of multilayer coated tools can cause that at most about 40% of heat generated during the cutting process at higher cutting speeds is transferred into the tool body due to the heat isolation effect. As shown in [1] in such cases, the substantial change of the heat partition coefficient observed for the maximum speed applied reduces the interface temperature for multilayer coatings with an intermediate Al2O3 v ceramic layer from 700 to 630 C. 5.2. Interface temperatures The results of computations carried out in this investigation are shown successively in Figs. 5–10. The presentation scheme used includes comparisons between measured values of the interface temperatures and both the average temperature rise from the frictional heat source and the predicted total average temperature rise calculated from Eq. (11a). Moreover, this comparison was extended to the maximum interface temperatures computed from Eq. (11b). It should be noted that in all cases the process variable was the cutting speed, which is the most important parameter controlling thermal behaviour of the cutting process.

Fig. 4. Influence of cutting speed on the heat partition coefficient for individual layers (a) and composite layer (b). A—after Reznikov, B—after Kato and Fujii, C—after Shaw. 3L, 4L-three- and four-layer coatings, respectively.

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Fig. 5. The average temperature rise from the frictional heat source (a) and the average interface temperature (b) vs cutting speed. Workpiece— AISI 1045 carbon steel, tool-ISO P20 uncoated carbide. Cutting conditions: feed rate ¼ 0:16 mm=rev, depth of cut ¼ 2 mm. 1—thermocouple measurements, 2—after Shaw, 3—after Shaw and using RKF, 4—after Shaw and using RR, 5—after Reznikov.

The predicted values of the components of the average interface temperature obtained for the P20 cemented carbide tools are shown in Figs. 5a and 5b. As expected, the best prediction for the average interface temperature was achieved when the heat partition was estimated by means of the classical Shaw’s formula (Eq. 3) and the temperature increment resulting from

the sliding friction was determined from Eq. (6). It is characteristic for the relationship hav–vc that better agreement between predicted and measured results occurs when the cutting speed increases above 100(120) m/min. Consequently, modelling effects concern the friction components of the average interface temperature

Fig. 6. The average temperature rise from the frictional heat source vs cutting speed. Workpiece–AISI 1045 carbon steel, coating-TiC/Al2O3/ TiN. Cutting conditions: feed rate ¼ 0:16 mm=rev, depth of cut ¼ 2 mm. 1—thermocouple measurements, 2—after Shaw, 3—after Shaw and using RKF, 4—after Shaw and using RR, 5—after Reznikov.

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Fig. 7. The average temperature rise from the frictional heat source vs cutting speed. Workpiece—AISI 1045 carbon steel, coating-TiC/TiCN/ Al2O3/TiN. Cutting conditions: feed rate ¼ 0:16 mm=rev, depth of cut ¼ 2 mm. 1—thermocouple measurements, 2—after Shaw, 3—after Shaw and using RKF, 4—after Shaw and using RR, 5—after Reznikov.

obtained for three- and four-layer coated tools and individual layers (a) and a single composite layer (b) are presented in Figs. 6 and 7, respectively. It is worth nothing that in relation to uncoated carbides three pre-

diction versions 3–5 applied also for multilayer coatings provide something higher temperature rises resulting from friction. These differences are about v 40–60 C depending on the coating structure and

Fig. 8. The average interface temperature vs cutting speed. Workpiece—AISI 1045 carbon steel, coating-TiC/Al2O3/TiN. Cutting conditions: feed rate ¼ 0:16 mm=rev, depth of cut ¼ 2 mm. 1—thermocouple measurements, 2—after Shaw, 3—after Shaw and using RKF, 4—after Shaw and using RR, 5—after Reznikov.

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Fig. 9. The average interface temperature vs cutting speed. Workpiece—AISI 1045 carbon steel, coating-TiC/TiCN/Al2O3/TiN. Cutting conditions: feed rate ¼ 0:16 mm=rev, depth of cut ¼ 2 mm. 1—thermocouple measurements, 2—after Shaw, 3—after Shaw and using RKF, 4—after Shaw and using RR, 5—after Reznikov.

generally they are lower for a four-layer coating. When compared prediction version 2 for uncoated and version 4 for coated tools adequate differences of temperav tures caused by friction are in the range of 50–175 C depending on the cutting speed used. This evidence strengthens the well-investigated phenomenon of reduction of friction at the tool-chip interface when using coated tools, as reported in [3,16]. On the other hand, higher temperature rises in the shear zone observed for coated tools suggest that the thermal

Fig. 10. The predicted (av) and measured (m) average and maximum predicted (max) interface temperatures vs cutting speed. Workpiece— AISI 1045 carbon steel. Cutting conditions: feed rate ¼ 0:16 mm=rev, depth of cut ¼ 2 mm. 1—ISO P20, 2—TiC/Al2O3/TiN, 3—TiC/ Ti(C,N)/Al2O3/TiN.

softening effect can be weaker than this occurring for uncoated carbides. Concerning the composite layer, the computation results shown in Figs. 6b and 7b revealed lower values of the friction component of the average interface temperatures calculated from Eq. (6) with application of RKF and RR heat partition coefficients and Eq. (7a). Figs. 8 and 9 show that after summing the friction and shearing components of the interface temperature its average value fits the measured one reasonably well when using the combination of Eqs. (6) and (5). This conclusion is valid for both multilayer structures tested. In particular, the best fitting of the predicted results to measurements was achieved for the composite layer (Figs. 8b and 9b) and higher cutting speeds (especially for three-layer coating denoted by course 4 in Fig. 8b). Calculation results dealing with the average and maximum interface temperatures obtained for uncoated and coated tools are completely shown in Fig. 10. It should be noted that for uncoated P20 carbide tools the maximum interface temperature ranges from 740 to v 1025 C depending on the cutting speed employed. On the other hand, the peak temperature changes from 650 v v to 830 C and from 670 to 790 C for three- and fourlayer coatings, respectively. For comparison, the average interface temperature for the couple of multilayers v used increases from 460 to 660 C and from 480 to v 630 C. It can also be concluded that the maximum interface temperatures calculated can be used to support the choice of coated inserts for defined machining parameters in order to avoid excessive thermal loading of the tool. In the future, the predictions will be

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extended to the variable feed rate. The selected computational and measured results are listed in Appendices A and B for both modelling concepts used.

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layer coated tools (Fig. 11a and c) and for higher cutting speeds when uncoated carbide was replaced by a three-layer coated competitor (Fig. 11b).

5.3. Validation of computation results The charts in Fig. 11 compare the predicted average interface temperatures to the measured results for all cutting tool inserts tested and nine different cutting speeds applied. It is of primary importance that the prediction errors for the average interface temperature are not higher than 10% for uncoated and three-layer coated tools and do not exceed 15% for four-layer coating, as shown in Fig. 11a–c. It should be noted that the maximum prediction errors were obtained for lower cutting speeds when using uncoated and four-

Fig. 11. Validation of modelling vs measuring results for the average interface temperature. Cutting speed:1—51.37 m/min, 2—62.34 m/ min, 3—72.24 m/min, 4—89.06 m/min, 5—103.20 m/min, 6—124.69 m/min, 7—144.48 m/min, 8—178.13 m/min, 9—206.40 m/min.

6. Conclusions . In this study physics-based models for the average and peak temperatures at the tool-chip interface for both uncoated carbide tools and those coated with multilayer coatings with intermediate Al2O3 layer are provided. . It is possible to predict with a reasonable accuracy the average interface temperature based on the equivalent thermal conductivities and diffusivities of the deposited coating materials and the application of the adequate heat partition coefficients. It can be observed that the analytical solutions are in good agreement with the thermocouple experiments both in the trend and the absolute values. . Substantially lower temperature rises due to friction were revealed for multilayer coatings. In this case, adequate differences dealing with the reduction of v friction are in the range of 50–175 C depending on the cutting speed used. On the other hand, the temperature rises due to shearing in the PDZ were found to be, in general, slightly higher than for uncoated tools. . For both coatings used maximum interface temperav tures calculated are approximately 170–200 C higher than their average values. On the other hand, for uncoated tools these differences are about 220– v 250 C. Analytical solutions performed for the cutting speed of 200 m/min have placed peak temperav tures at approximately 1025, 830 and 790 C for uncoated, three- and four-layer coated tools, respectively. . Prediction errors for the average interface temperatures are relatively small in relation to the thermocouple results. They do not exceed 10–15% depending on the type of tool material used. In particular, for the three-layer coatings when cutting speeds are ranging from 100 to 200 m/min the percentage errors were determined to be not higher than 2%. . In the future, the physics-based predictions will be extended to the variable feed rate and the zone of much higher cutting speeds, up to 330 m/min. Moreover, the finite element prediction of interface temperatures that accounts for the composite layer concept will be developed for various cutting conditions.

900

W. Grzesik, P. Nieslony / International Journal of Machine Tools & Manufacture 44 (2004) 889–901

Appendix A. Data for the individual layer concept

Tool material

Cutting speed m/min

ISO—P20

51.37 62.34 72.24 89.06 103.20 124.69 144.48 178.13 206.40 TiC/Al2O3/ 51.37 TiN—3L 62.34 72.24 89.06 103.20 124.69 144.48 178.13 206.40 TiC/ 51.37 Ti(C,N)/ 62.34 Al2O3/TiN— 72.24 4L 89.06 103.20 124.69 144.48 178.13 206.40

Measured Predicted average temperature, v temperature C v Hm , C Dhf Dhs hav

Predicted maximum v temperature, C Dhf max

Dhs max

hmax

587.62 608.49 624.92 649.09 666.70 690.07 708.88 736.56 756.72 547.00 559.15 568.62 582.39 592.31 605.34 615.71 630.82 641.69 435.80 457.95 475.57 501.75 521.05 546.91 567.94 599.22 622.26

286.77 318.32 343.83 382.40 411.48 451.83 486.52 537.10 603.33 244.70 270.00 290.04 319.24 339.91 365.91 385.14 409.68 424.00 231.04 252.41 269.67 295.29 313.72 337.01 353.96 373.70 381.55

457.78 469.40 474.80 476.70 473.82 465.23 455.18 437.02 422.44 442.75 462.28 474.41 486.77 491.66 493.14 490.68 482.36 473.69 468.44 481.42 488.40 493.38 493.21 488.58 481.83 468.32 456.80

744.55 787.72 818.62 859.10 885.30 917.06 941.70 974.12 1025.77 687.45 732.27 764.46 806.00 831.57 859.05 875.83 892.04 897.69 699.48 733.83 758.06 788.67 806.93 825.60 835.79 842.02 838.35

187.43 208.54 225.62 251.47 270.96 298.00 321.22 355.12 399.10 163.28 180.16 193.53 213.01 226.81 244.16 256.99 273.36 282.91 154.16 168.42 179.94 197.03 209.33 224.88 236.18 249.35 254.59

337.79 352.31 361.00 371.21 377.94 382.70 383.53 381.01 377.23 327.22 347.10 360.53 377.78 390.20 402.76 409.80 415.85 417.59 345.51 360.80 370.50 381.79 390.37 398.08 401.53 402.99 402.04

525.22 560.85 586.62 622.68 648.90 680.70 704.75 736.12 776.33 490.50 527.26 554.06 590.79 617.00 646.92 666.79 689.21 700.50 499.67 529.22 550.44 578.82 599.70 622.95 637.71 652.34 656.63

Relative error %

10.62 7.83 6.13 4.07 2.67 1.36 0.58 0.06 2.59 10.33 5.70 2.56 1.44 4.17 6.87 8.30 9.26 9.16 14.65 15.56 15.74 15.36 15.09 13.90 12.29 8.86 5.52

Dhf, temperature rise from frictional heat source (SDZ). Dhs, temperature rise from shearing (PDZ).

Appendix B. Data for the composite layer concept

Tool material

ISO— P20

Relative error %

Cutting speed m/min

Measured Predicted average temperature temperature, v C v Hm , C Dhf Dhs

hav

Dhfmax

Dhsmax

hmax

51.37 62.34 72.24 89.06 103.20 124.69 144.48 178.13 206.40

587.62 608.49 624.92 649.09 666.70 690.07 708.88 736.56 756.72

525.22 560.85 586.62 622.68 648.90 680.70 704.75 736.12 776.33

286.77 318.32 343.83 382.40 411.48 451.83 486.52 537.10 603.33

457.78 469.40 474.80 476.70 473.82 465.23 455.18 437.02 422.44

744.55 787.72 818.62 859.10 885.30 917.06 941.70 974.12 1025.77

187.43 208.54 225.62 251.47 270.96 298.00 321.22 355.12 399.10

337.79 352.31 361.00 371.21 377.94 382.70 383.53 381.01 377.23

Predicted maximum v temperature, C

10.62 7.83 6.13 4.07 2.67 1.36 0.58 0.06 2.59

W. Grzesik, P. Nieslony / International Journal of Machine Tools & Manufacture 44 (2004) 889–901

TiC/ Al2O3/ TiN—3L

51.37 62.34 72.24 89.06 103.20 124.69 144.48 178.13 206.40 TiC/ 51.37 Ti(C,N)/ 62.34 Al2O3/ 72.24 TiN—4L 89.06 103.20 124.69 144.48 178.13 206.40

547.00 559.15 568.62 582.39 592.31 605.34 615.71 630.82 641.69 435.80 457.95 475.57 501.75 521.05 546.91 567.94 599.22 622.26

137.17 151.38 162.66 179.14 190.86 205.67 216.69 230.89 239.31 135.73 148.10 158.11 173.02 183.80 197.53 207.66 219.75 224.92

327.22 347.10 360.53 377.78 390.20 402.76 409.80 415.85 417.59 345.51 360.80 370.50 381.79 390.37 398.08 401.53 402.99 402.04

464.40 498.48 523.19 556.92 581.06 608.43 626.50 646.74 656.89 481.24 508.90 528.61 554.80 574.17 595.61 609.19 622.73 626.96

205.577 226.864 243.772 268.474 286.035 308.232 324.752 346.034 358.643 203.415 221.954 236.952 259.294 275.449 296.039 311.213 329.328 337.082

442.75 462.28 474.41 486.77 491.66 493.14 490.68 482.36 473.69 468.44 481.42 488.40 493.38 493.21 488.58 481.83 468.32 456.80

648.326 689.139 718.185 755.242 777.693 801.370 815.435 828.398 832.332 671.856 703.375 725.349 752.673 768.660 784.624 793.038 797.648 793.881

901

15.10 10.85 7.99 4.37 1.90 0.51 1.75 2.52 2.37 10.42 11.12 11.15 10.57 10.19 8.90 7.26 3.92 0.76

Dhf, temperature rise from frictional heat source (SDZ). Dhs, temperature rise from shearing (PDZ).

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