Thermal influence of cutting tool coatings

Thermal influence of cutting tool coatings

Journal of Materials Processing Technology 159 (2005) 119–124 Thermal influence of cutting tool coatings J. Rech a,c,∗ , J.L. Battaglia b , A. Moisan...

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Journal of Materials Processing Technology 159 (2005) 119–124

Thermal influence of cutting tool coatings J. Rech a,c,∗ , J.L. Battaglia b , A. Moisan c a

LTDS, Ecole Nationale d’Ingénieurs de Saint-Etienne, 58 Rue Jean Parot, 42000 Saint-Etienne, France b LEPT, Ecole Nationale Supérieure d’Arts et Métiers, 33405 Talence, France c LABOMAP, Ecole Nationale Supérieure d’Arts et Métiers, 71250 Cluny, France Received 29 January 2003; received in revised form 21 April 2004; accepted 21 April 2004

Abstract The paper deals with the qualification of the thermal behaviour of the system “work material-coated carbide cutting tool–chip”, with the purpose of reaching a better understanding of the heat flow entering into the tool substrate during a turning operation. Heat transfer in the deposit–substrate system was analysed for a simple tip geometry. A model of heat transfer in the cutting tool has been proposed. Results shows that the coating thermal barrier does not exist in continuous cutting operations, but that seems to be significant in discontinuous cutting operation, especially performed with high cutting speeds. © 2004 Elsevier B.V. All rights reserved. Keywords: Coatings; Thermal modelling; Cutting

1. Introduction Clean and safe machining is one of the industry’s important topics. Both economical and environmental factors contribute to the recent increase in applications of machining under dry or minimal lubrication conditions. Manufacturers are looking for ways of reducing production costs and, at the same time, of avoiding the environmental problems associated with the use of cutting fluids. In order to reach these objectives, tools manufacturers are especially interested in the application of new cutting tool coatings. About 80% of all machining operations are now performed with coated tools [1]. Among the coating systems available on the market, titanium-based hard thin films have found the widest acceptance. They tend to improve the wear resistance in many cutting applications [2,3], by reducing friction, adhesion, diffusion and to relieve thermal and mechanical stresses on the substrate. Nevertheless, few works treat on the influence of coatings on the heat flux flowing into the tool during machining. The heat flux introduced into the cutting tool comes from three different sources (Fig. 1): the primary shear zone (plastic deformation and viscous dissipation), the secondary shear zone (frictional and plastic shearing energy), and the fric-

∗ Corresponding author. E-mail address: [email protected] (J. Rech).

0924-0136/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2004.04.414

tional rubbing of the cut surface on the tool insert flank. These three heat sources may diffuse either in the workpiece, or in the substrate or in the chip body. Actually, the quantification of these three sources is not clear neither in the case of uncoated tools, nor in the case of coated tools. Moreover, the influence of coating on the heat partitioning within the cutting zone is unknown. Hence, it is not clear whether coatings influence the cutting process by an insulation effect (lower heat flux transmitted into the substrate), or rather by a tribological effect (lower level of heat generated by friction). Grzesik [4] studied the cutting mechanics of various coated carbide tools. He shows that depending on the coating, the tool–chip contact area and the average temperature at the tool–workpiece interface are modified, without proving that coatings are able to insulate the substrate. In order to evaluate the heat flux transferred into the tool, some theoretical models based on FEM analysis have been investigated in the literature, but only few of these studies consider the role of the coatings [5,6]. Du et al. [5] showed that during a very short transient period, a coating with a low thermal conductivity can insulate a substrate and maintain a lower temperature inside the cutting tool. Nevertheless, none of these FEM analysis have investigated the comparison of various coatings with different thermal properties in the case of continuous cutting application such as turning with cutting times longer than 0.1 s. At time,

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Fig. 1. Possible heat sources during cutting.

it is not clear whether a coating with a low thermal conductivity is able to insulate a substrate and to relieve the heat in the chip in turning. The paper presents an analytical solution of heat diffusion in a coated tool, so as to model and to quantify the thermal influence of a coating, without considering its tribological influence. Moreover, the heat flux entering into the substrate is analysed taking into account the thermophysical properties of the deposit and its thickness.

2. An analytical solution of the heat conduction problem on a coated insert

Fig. 2. (a) 1D and (b) 3D axisymmetric configurations considered for the heat transfer modelling in a deposit–substrate system.

heat flux, as: Heat conduction modelling in a deposit–substrate system can be performed, as a first approximation, on the geometry represented in Fig. 2a. Thus let us consider a thin layer of thickness ec , thermal conductivity λc , and diffusivity αc , deposited on a substrate of thickness es , conductivity λs , and diffusivity αs . The rake face of the insert is submitted to a uniform heat flux φ0 (t). More complex heat flux distributions, that may be considered as more realistic compared to a concrete cutting application, have not been considered in this first approach. The thermal resistance at the deposit–substrate interface is denoted as Rc . It comes from the imperfect contact at the interface caused, for example, by a cramping defect of the deposit on the substrate. A more realistic configuration, 3D axisymmetric one, is presented in Fig. 2b. This model only considers a single layer of coating on the rake face of the cutting tool. Moreover, only the heat flux at the tool–chip interface has been considered, without taking into account the heat flux at the flank face/workpiece interface. Indeed, Trent [7] has shown that the energy amount at this second interface is at least 10 times smaller than the first one. Applying Laplace and Hankel integral transforms [8], respectively, on the time and on the radial space variables, as described in Section 2.1, leads to expressing the average transformed temperature (considered as homogeneous) on the rake face of the deposit, according to the transformed

T¯ 0 (αn , s) = H3D (s)φ¯ 0 (s)

(1)

where s is the Laplace variable and αn the Hankel variable. It must be noticed that, in the real machining process, the temperature varies with space at the tool–chip contact area because of sliding phenomenon. This implies that T0 (t) is viewed as the average temperature on the tool–chip contact area (heated surface), even if the literature has already reported that the local temperature at this interface is not constant [9]. 2.1. Modelling the heat transfer function Let us consider a wall of thickness e, thermal conductivity λ, and thermal diffusivity α. The heat flux on the surface at the distance x = 0 is denoted φ0 (t) as the heat flux on the opposite face, at x = e, is denoted φe (t). The one-dimensional heat transfer by conduction in the wall is described by the following equations [8]: ∂2 T(x, t) 1 ∂T(x, t) = 0, − α ∂t ∂x2

0 < x < e, t > 0

(2)

−λ

∂T(x, t) = φ0 (t), ∂x

x = 0, t > 0

(3)

−λ

∂T(x, t) = φe (t), ∂x

x = e, t > 0

(4)

J. Rech et al. / Journal of Materials Processing Technology 159 (2005) 119–124

T(x, t) = 0,

0 ≤ x ≤ e, t = 0

(5)

Applying the Laplace transform on the time variable t to the previous equations, one can obtain the classical quadrupoles formulation [8] that expresses the transformed heat flux and temperature on the front face according to the same quantities on the back face as:   T¯ 0 (s) = T¯ (x = 0, s) φ0 (s) = φ(x = 0, s)    T¯ e (s) = T¯ (x = e, s) A B = C A φe (s) = φ(x = e, s)   

(6)

X

where T (s) and φ(s) denote, respectively, the Laplace transforms of T(t) and φ(t) defined by:  ∞  ∞ T (x, s) = T(x, t) e−st dt and φ(s) = φ(t) e−st dt 0

0

(7) The components of the matrix X are: A = cosh(ke),

B=

sinh(ke) , λk

C = sinh(ke)λk (8)

with k=



s α

(9)

where s is the Laplace transform variable, and α the thermal diffusivity. Considering the deposit–substrate system shown in Fig. 2a, the quadruple approach leads to a very compact form of the solution, as:       1 Rc As Bs Ad Bd T 0 (p) = Cd Ad 0 1 Cs As φ¯ e (p)           ×

Xd

interface

T e (p)



G0 + G1 + G2 G3 + G 4 + G 5

λ s ks sinh(ks es )sinh(kd ed ) λd kd 1 G2 = h sinh(ks es ) cosh(kd ed ) λs ks +Rc cosh(ks es ) cosh(kd ed )

1 sinh(kd ed ) cosh(ks es ) + λd kd

G1 =

G3 = λd kd cosh(ks es ) sinh(kd ed ) G4 = Rc λs ks sinh(ks es )λd kd sinh(kd ed ) +λs ks sinh(ks es ) cosh(kd ed ) λd kd sinh(kd ed ) sinh(ks es ) G5 = h λ s ks +Rc λd kd sinh(kd ed ) cosh(k

s es ) + cosh(kd ed ) cosh(ks es ) Heat transfer in the 3D axisymmetric configuration represented in Fig. 2b is also modelled by using the quadrupoles approach [8]. Considering insulation on the faces at β = 0 and π/4, the elementary matrix X in Eq. (6) is achieved now by considering the governing equations of heat transfer in a cylinder. In this case the heat flux shape φ0 on the front face is applied on a disk of radius r0 . The governing mathematical equations become [8]:

∂T(r, z, t) ∂2 T(r, z, t) 1 ∂T(r, z, t) 1 ∂ r + =0 − r ∂r ∂r α ∂t ∂z2 with 0 < r < R, 0 < z < e, t > 0 (12) ∂T(r, z, t) = 0, ∂r ∂T(r, z, t) −λ = ∂z

(10)

(11)

r = 0, r = R, 0 < z < e, t > 0

φ0 (t) 0

∂T(r, z, t) = φ0 (t), ∂z

T(r, z, t) = 0,

with H1D (s) =

G0 = cosh(ks es ) cosh(kd ed ) + Rc λs ks sinh(ks es ) cosh(kd ed )

−λ

Subscripts d and s are, respectively, associated to the deposit and the substrate. The thermal resistance at the interface between the deposit and the substrate is denoted as Rc and when considering heat exchange with the ambient on the back face, that is φ¯ e = hT¯ e , where h is the heat exchange coefficient. From Eq. (10), one obtains the following relation that expresses the temperature on the front face according to the heat flux at the same location: T¯ 0 (s) = H1D (s)φ¯ 0 (s)

and

Xs

φ¯ e (p) = hT e (p)

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r ≤ r0 , r > r0

(13)

z = 0, t > 0

(14)

0 < r < R, z = e, t > 0

(15)

0 ≤ z ≤ e, 0 ≤ r ≤ R, t = 0

(16)

As previously, the Laplace and Hankel transforms are applied, respectively, on the time variable and on the r spatial variable as:  R T¯ h (αn , z, s) = T¯ (r, z, s)J0 (αn r) dr (17) 0

J0 is the Bessel function of the second kind, order 0. The transformed temperature and heat flux on the front face are expressed according to that on the back face as in Eq. (6), but now k must be replaced by:  s k= (18) + α2n α

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with

J. Rech et al. / Journal of Materials Processing Technology 159 (2005) 119–124



1 αn R ≈ π n + 4



3 1 8π n + 1/4

(19)

As in the 1D configuration, one finds the relation expressing the temperature on the front face according to the heat flux φ¯ 0 (s) as: r0 T¯ 0 (αn , s) = H1D (s, αn ) J1 (αn r0 ) φ¯ 0 (s) (20) αn    H3D (αn ,s)

Practically, the inverse Laplace transform is computed and the inverse Hankel transform is determined from: T¯ (r, z, s) =



T¯ h (αn , z, s)

n=1

J0 (αn r) 2 R /2(J0 (αn R)2 )

(21)

Asymptotic behaviour of the transfer functions for the small times (t → 0 ⇔ s → ∞) is the same for the 1D and 3D configurations: lims→∞ H1D (s) = lims→∞ H3D (αn , s) =

1 1 √ λd (ρCp )d s (22)

This function for the long durations (t → ∞ ⇔ s → 0) is given by: for the 1D configuration: lims→∞ H1D (s) =

1 es ed + + + Rc h λs λd

(23)

for the 3D axisymetric configuration: lims→∞ H3D (αn , s) 1/αn + Rc λs ed es α2n +ed es /λd (λs αn + hRc ) + hes /λs αn = αn (λd ed + λs es + Rc λd λs ed es α2n +hλd /λs (ed es ) + hRc λd ed + h/α2n )

(24)

3. Quantification of the thermal influence of cutting tool coatings In Fig. 3, the impulse response for known thermal properties of the deposit and the substrate is calculated from the transfer functions H1D (s) and H3D (s). The substrate considered for this example is a sintered tungsten carbide with a cobalt binder phase substrate, which is commonly used for cutting tools. Thermal properties of the carbide substrate have been provided by [11]. The thermal properties of coatings effectively applied on cutting tools (such as TiN, (Ti,Al)N, Al2 O3 , etc.) are very difficult to find in the literature, due to the lack of standard methodology to quantify these properties in the case of very thin layers. Generally these properties are determined by tool or coating manufacturers. Most of the time, the avoidance of explanations regarding either the real composition of the

Fig. 3. Impulse response calculated from the transfer functions H1D (s) and H3D (r = 0, z = 0, s) for deposit–substrate system without thermal contact resistance.

coating (multilayer, composite, superlattice, etc.) or the procedure being applied to obtain these results tends to induce a big scatter of the values usually reported in the literature. Facing this problem, authors have chosen values estimated for a TiN coating reported by [6,10]. The effect of the temperature on the thermal properties has not been considered in this model. The values at 500 ◦ C have been used to calibrate this model. As demonstrated in Section 2.1, the two curves in Fig. 3 are superposed for the small durations leading to the asymptotic solution in Eq. (23). The gap between the two responses occurs during heat diffusion in the substrate. Characteristic response times of each layer differ largely according to the ratio of thicknesses ec /es . Then the impulse response must be represented using a logarithmic scale with a great number of decades. Three domains of heat transfer in the system are distinguishable. The first domain, from 10−5 to 10−3 s, is concerned by the heat diffusion in the deposit. The second domain, from 10−3 s to about 10−1 s, is concerned by the heat diffusion in the substrate. For the longer times, one observe the heat loss with the ambient, characterized by the heat exchange coefficient h. The influence of the thermal diffusivity of a coating αc has been investigated for a given substrate. If we consider the ratio αc /αs , for a carbide substrate and a coating, the usual values are between 0.1 and 1 (e.g., at 500 ◦ C αc /αs = 0.5 for TiN, αc /αs = 0.2 for Al2 O3 [6]). Nevertheless, the extreme values have been investigated between 0.01 and 100 so as to evaluate the sensitivity of this parameter, even if these values are not realistic for cutting tool coatings. Fig. 4 shows that the variation of the thermophysical characteristics of the deposit only affect the diffusion at the small times with regards to the response time of the system. After this period the system behaviour remains unchanged for all the thermal diffusivities considered, which means that coatings have no influence on the heat transfer in cutting application with a long tool–chip contact duration such as turning. Neverthe-

J. Rech et al. / Journal of Materials Processing Technology 159 (2005) 119–124

Fig. 4. Impulse responses calculated from the transfer function H3D (r = 0, z = 0, s) without thermal contact resistance for different values of the ratio αc /αs .

less, coatings may insulate a substrate in application with a very short tool–chip contact duration such as milling. This result is in accordance with a previous investigation of Du et al. [5]. In order to quantify the sensitivity of heat transfer according to the deposit thickness, impulse responses for different values of the ec are computed. A large spectrum of values have been investigated (1–50 ␮m). The usual coatings applied on cutting tools have thicknesses lower than 20 ␮m. As a consequence the impulse responses plotted for bigger values are not realistic. Nevertheless they show the sensitivity of this variable on the result. Impulse responses calculated for each configuration are plotted in Fig. 5. As previously, results show that the coating thickness only affects the thermal behaviour of the system at the small times. The previous results lead to some important conclusions. The thermophysical properties and the thickness of the deposit have a significant influence on the thermal behaviour of

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a coated tool only during the small durations of the contact between the cutting tool and the chip (<10−2 s). This means that the deposit has no influence on the thermal behaviour of the tool during a continuous machining process as turning one (typical tool–chip contact duration >1 s). This result is in accordance with experimental investigations made by Rech et al. [12]. Nevertheless, they can affect the thermal behaviour during an interrupted machining process such as milling, resulting in a lower heat flux transmitted into the substrate (e.g., rotation speed: 10 000 rpm, radial depth of cut = mill diameter/4, tool–chip contact duration per tooth ∼5 × 10−4 s). A lower amount of heat is associated with a lower temperature reached by the substrate, which will preserve the mechanical properties of the substrate and improve the wear resistance of the tool. Moreover, it appears that the influence of a coating becomes even more important with the decrease of the tool–chip contact time, as it is the case for high speed milling applications. This result is in accordance with FEM investigations made by Yen et al. [6]. Fig. 5 also shows that the larger the coating thickness is the more influence it has on the heat transfer, especially in cutting applications with tool–chip contact duration around 10−2 s. As a consequence, it appears that the important variations of temperature measured by M’Saoubi [9] at the tool–chip interface in turning with various coatings can only be explained by variations in the tribological phenomenon at this interface, as it has already been reported by Rech et al. [12] and Grzesik [13].

4. Conclusions An analytical solution of heat transfer modelling has been proposed so as to characterize the influence of a coating on the heat flow entering into the tool substrate. Investigations on the influence of the thermal diffusivity and of the thickness of the coating has shown that coatings do not have any capacity to insulate a substrate in continuous cutting applications. Inversely, in interrupted cutting applications, such as in high speed milling, coatings seems to keep a larger amount of heat in the tool–chip contact zone, which can help to improve the wear resistance of the substrate. Moreover, it has been pointed out that the tribological phenomenon at the tool–chip interface is the main reason to explain the differences in the heat flux transmitted to a substrate.

References Fig. 5. Impulse responses calculated from the transfer function H3D (r = 0, z = 0, s) without thermal contact resistance for different values of the ratio ec /es .

[1] Balzers, 2002. www.balinit.balzers.com. [2] J. Rech, M.A. Djouadi, High speed gear hobbing, Wear 250 (2001) 45–53.

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[3] W. König, New approaches to characterize cutting tool coatings, Ann. CIRP 41 (1) (1992) 49–52. [4] W. Grzesik, A computational approach to evaluate temperature and heat partition in machining with multiplayer coated tools, Int. J. Mach. Tools Manuf. 43 (2003) 1311–1317. [5] F. Du, R. Lovell, T.W. Wu, Boundary element method analysis of temperature fields in coated cutting tools, Int. J. Solids Struct. 38 (2001) 4557–4570. [6] Y.C. Yen, A. Jain, P. Chingurupati, W.T. Wu, T. Altan, Computer simulation of orthogonal cutting using a tool with multiple coatings, in: Proceedings of the CIRP Workshop on Modelling of Machining Operations, Hamilton, Canada, 2003, pp.119–130. [7] E.M. Trent (Ed.), Metal Cutting, Butterworths/Heinemann, 1991.

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