1 Introduction

Metal machining process involves the coupling effects of metal physical behaviors, including large strain, high strain rate, and extreme temperature. Plastic deformation of the workpiece can dramatically produce heat at cutting regions in machining difficult-to-cut materials [1, 2]. Extreme temperature not only affects surface quality of workpiece but also contributes to the thermal deformation and failure of the cutting tools [3]. In order to guarantee the superior performance and longer service lifetime of cutting tools and to achieve lower costs and higher productivity in cutting process, the super-hard materials have been attracted so much attention in cutting tools applications [2].

Cubic boron nitride (cBN) is the second most thermally conductive and the second hardest material comparable to diamond. Additionally, cBN has high thermal stability and excellent chemical inertness against ferrous materials at temperatures up to 1200 °C, but diamond reacts with ferrous metal at 600 °C [2, 4]. The versatile combination of the remarkable physical and chemical properties of cBN renders it the most promising solution in machining difficult-to-cut ferrous components harder than 45 HRC such as hardened steel and hardened ductile iron [2, 5, 6]. Currently, the commercially available cBN cutting tools can only be fabricated by using cBN powders synthesized by high-pressure high-temperature (HPHT) method, which is costly and difficult to achieve complex geometries. The cBN-coated cutting tools by employing coatings technique (e.g., PVD and CVD) have higher flexibility and lower cost than polycrystalline cBN (PcBN) tools fabricated by HPHT [4].

Up to now, cBN coatings, however, have not been used in industrial cutting tools because of the difficulty in the deposition process including limitations of coating thickness and insufficient mechanical stability, which resulted from considerable compressive stress and poor adhesion between coatings and substrates [4]. Only a few works on laboratory level, mainly devoted to the research on deposition and cutting performance of cBN-coated cutting tools, have been addressed. Among these works, most of them focused on deposition of cBN-coated cutting tools but still lacked the evaluation of performance by implementing cutting experiments [7,8,9,10]. Although several works investigated the cutting performance of cBN-coated cutting tools, they merely focused on the cutting force and tool wear [11,12,13]. Unfortunately, the research on cutting temperature of cBN-coated cutting tools remains an unexploited territory. The limited success of these attempts in the evaluation of performance for cBN-coated tools motivated us to explore the temperature distributions, and we expected to complement this drawback.

In our previous work, the 2.2-μm-thick cBN coatings have been successfully deposited on Si3N4 cutting tools via boron-doped diamond (BDD) buffer layers by the electron cyclotron resonance microwave plasma chemical vapor deposition (ECR MPCVD) technique [14]. And the mechanical and friction wear performances of cBN-coated Si3N4 cutting tools have been evaluated by comparison with TiAlN coatings [14]. Since cBN, diamond, and Si3N4 are all electrical insulator [15], the infrared thermography methods were introduced to measure the cutting temperature in our turning experiments. This method can measure temperature without physical contact, and also, it is of fast response and high capability of providing the thermal fields [16, 17]. However, the temperature distributions of micron-thickness coatings on cutting tools are very difficult to be captured by infrared thermography methods owing to the micro-scale coatings and the rapid response of heat transfer. The finite element method (FEM) has been an alternative and helpfully complementary technique to better understand the temperature field distribution for machining process [18, 19].

In this paper, a series of experimental and numerically simulated studies were carried out to investigate the influence of cutting parameters on the temperature distribution of cBN/diamond–coated Si3N4 cutting tools. FE model of cBN/diamond–coated tools was built and validated by turning experiments. In addition, FEM simulations of the temperature distribution of cBN/diamond coatings on Si3N4 cutting tools with various cutting speed and tool rake angle were implemented. This study may provide a guideline for further exploring the temperature distribution in experimental machining difficult-to-cut ferrous materials by applying cBN-coated cutting tools.

2 Experimental and modelling

2.1 Experimental procedure

The cylindrical workpiece used in the cutting experiments was made from hardened ductile iron (QT900) with a hardness of ~ 54 HRC obtained by heat treatment process. Ductile iron has outstanding properties including extreme strength, high toughness, and excellent wear resistance. Thus, it has been extensively employed as an important engineering material for the fabrication of tribological components such as crankshafts, wind turbine elements, gear, railway brake discs, and motor frames [20,21,22,23]. The as-deposited cBN/diamond–coated Si3N4 cutting tools were employed. Additionally, the commercial TiAlN-coated Si3N4 cutting tools were selected as references which have excellent thermal stability and cutting performance in machining ferrous metals, as reported by [24,25,26,27]. Cutting experiments were carried out on a CA6140 lathe employing cylindrical turning under dry conditions. During the experiments, the cutting tools were mounted on tool holders (CRSNR2525M12, ZCCCT, Co., Ltd., China), and combination of the cutting tools and holders resulted in an effective negative rake angle of 5° and an effective clearance angle of 5°. A triaxial piezoelectric force sensor (Kistler 9265B) with a data acquisition system was used to continuously monitor cutting forces components. The temperatures during cutting process were measured by an infrared thermometer (Thermovision A20). The cutting parameters employed in the cutting experiments are displayed in Table 1.

Table 1 Cutting parameters employed for cutting experiments
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2.2 Finite element modelling

The two-dimensional thermo-viscoplastic cutting simulation model was conducted for the two coated cutting tools by using a commercial Abaqus/Explicit software. The proposed finite element model is illustrated in Fig. 1. In the finite element model, each coating layer is represented by separate layer of respective thickness, cBN (2 μm)/diamond (4 μm) and TiAlN (4 μm) on top of the Si3N4 substrate, see Fig. 1. The bottom surface of the workpiece is fixed in all directions. The cutting tool is assumed as a rigid body and is moved forward with the cutting speed (vc). The cutting simulation is performed at ambient temperature assuming the initial temperature is equal to 25 °C.

Fig. 1
figure 1

Configuration of tool-workpiece for the FEM simulation

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The Coulomb friction model is the most widely used in the simulation of metal cutting process [28, 29]. To express the friction contact between tool rake face, flank, and workpiece, the extended Coulomb friction model is adopted in this study. The relationship between shear stress and friction coefficient of the tool-chip contact is described by the following [30, 31]:

$$ \tau =\left\{\begin{array}{c}\mu {\sigma}_n\\ {}{\tau}_{\mathrm{max}}\end{array}\right.{\displaystyle \begin{array}{c},\mu {\sigma}_n\prec {\tau}_{\mathrm{max}}\\ {},\mu {\sigma}_n\ge {\tau}_{\mathrm{max}}\end{array}} $$
(1)

where τ is shear stress, μ is friction coefficient, σn is the normal contact pressure, τmax is the shear limit stress, \( {\tau}_{\mathrm{max}}=\frac{\sigma_{M\mathrm{ises}}}{\sqrt{3}} \), and σMises is the Mises yield stress. In this study, the friction coefficient of cBN coatings and TiAlN coatings with the workpiece was set to be 0.17 and 0.3, respectively.

The physical parameters of workpiece and coated cutting tools are displayed in Tables 2, 3, 4, and 5.

Table 2 Physical properties of the workpiece [21, 32]
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Table 3 Thermal expansion of the workpiece [21, 32]
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Table 4 Specific heat capacity of the workpiece [21, 32]
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Table 5 Physical properties of the cutting tools [14, 15, 33,34,35,36,37,38]
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Providing the physical and thermal parameters of the workpiece, cutting tools, and coating materials is of great importance to obtain reliable results from the finite element solution. Most importantly, these materials undertake the behavior of high strain, strain rate and extreme temperature in cutting process [29]. The Johnson-Cook material model is suitable for describing high rate deformation of materials and can produce excellent results for chip formation [39, 40]. The workpiece material was modeled as isotropic thermal-elastic plastic body expressed by

$$ \sigma =\left(A+B{\varepsilon}^n\right)\left[1+C\ln \left(\frac{\overset{\cdotp }{\varepsilon }}{\overset{\cdotp }{\varepsilon_0}}\right)\right]\left[1-{\left(\frac{T-{T}_r}{T_m-{T}_r}\right)}^m\right] $$
(2)

where A, B, n, C, and m are material parameters, i.e., A is the yield stress, B is the strain hardening factor, n is the strain hardening index, C is the strain rate sensitivity parameter, m is the thermal softening index; σ is equivalent stress, εn is equivalent plastic strain, and \( \overset{\cdotp }{\varepsilon } \) and \( \overset{\cdotp }{\varepsilon_0} \) are equivalent plastic strain rate and reference strain rate, respectively; and T is the homologous temperature and Tr and Tm are reference ambient temperature and material melting temperature, respectively. The Johnson-Cook parameters for workpiece materials are listed in Table 6.

Table 6 Johnson-Cook parameters of workpiece [39, 40]
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The Johnson-Cook damage initiation law is employed to define material failure process in the FE model [41], as given by

$$ {\overline{\varepsilon}}_D^{pl}=\left[{d}_1+{d}_2\exp \left({d}_3\frac{\sigma_p}{\sigma_{\mathrm{Mises}}}\right)\right]\left[1+{d}_4\ln \frac{\overline{\xi}}{\overline {\xi_0}}\right]\left[1+{d}_5{\left(\frac{T-{T}_r}{T_m-{T}_r}\right)}^m\right] $$
(3)

where σp is the hydro static pressure, σMises is Mises stress, \( \overline {\xi_0} \) is reference strain rate, generally equals to 1, \( \overline{\xi} \) is equivalent plastic strain rate, \( {\overline{\varepsilon}}_D^{pl} \) is equivalent plastic strain of damage initiation, and d1–d5 are failure parameters and the values for workpiece are displayed in Table 7. The cutting parameters employed for simulation are listed in Table 8.

Table 7 Failure parameters of workpiece [41]
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Table 8 Cutting parameters employed for simulation
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3 Validation of the finite element model

The cutting force and cutting temperature of finite element results are compared with cutting experiments results to verify the effectiveness and correctness of finite element model proposed.

3.1 Cutting force

Figure 2 depicts the radial force simulated and experimental dependent on depth of cut (ap) for TiAlN- and cBN-coated cutting tools at vc of 63 m/min. It can be found that the cutting force increases with the increase of ap for each cutting tool. And cBN-coated tools show lower cutting force than TiAlN-coated tools. It could be attributed to the lower friction coefficient and higher hardness of cBN coatings than TiAlN coatings, which have been demonstrated in our previous study [14]. For cutting tools, low friction coefficient can decrease the friction forces between tools and workpieces and evacuate effectively the chips from the tool rake face; high hardness can enhance the wear resistance against tool wear and maintain the superior cutting performance reported by Davim [2]. The relative errors of simulated and experimental results are lower than 18% of both cBN- and TiAlN-coated tools. The errors could be attributed to the applied friction law in finite element modelling [28, 42].

Fig. 2
figure 2

Radial force simulated and experimental dependent on depth of cut for TiAlN- and cBN-coated cutting tools at vc of 63 m/min

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Figure 3 shows that the radial force decreases with the increase of cutting speed (vc) for TiAlN- and cBN-coated cutting tools at ap of 0.25 mm. This could be ascribed to the effect of increasing in temperature. Ucun et al. [28] and Ng et al. [37] have demonstrated that with the increase of vc, cutting temperature at the first deformation zone increases but the yield strength of the workpiece decreases, leading to the decrease of cutting force. Additionally, cBN-coated tool shows the lower cutting force than TiAlN-coated tools. It is attributed to the lower fiction coefficient and excellent wear resistance of cBN coatings. And the relative errors of simulated and experimental results are low than 12% for both cBN- and TiAlN-coated cutting tools.

Fig. 3
figure 3

Radial force simulated and experimental dependent on cutting speed for TiAlN- and cBN-coated cutting tools at ap of 0.25 mm

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3.2 Cutting temperature

Figure 4 shows the simulated and experimental cutting temperature as a function of cutting speed (vc) for TiAlN- and cBN-coated cutting tools at ap of 0.25 mm. Figure 5 illustrates the simulated and experimental cutting temperature, and Fig. 5b is the infrared images obtained from turning procedure by using cBN-coated cutting tools at vc of 239 m/min. The inset is the image of turning operation. The cutting temperature increases with the increase of vc (as shown in Fig. 4). This can be ascribed to the workpiece plastic deformation and chip sliding. With the increase of vc, the workpiece plastic deformation rate and the chip sliding velocity are increased, which induce a more rapid heat formation, thus resulting in the increase of cutting temperature demonstrated by Ucun et al. [28], Ng et al. [37], and Khalili et al. [43].

Fig. 4
figure 4

Cutting temperature simulated and experimental dependent on cutting speed for TiAlN- and cBN-coated cutting tools at ap of 0.25 mm

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Fig. 5
figure 5

Cutting temperature of a simulated results and b experimental results obtained infrared image from turning procedure by using cBN-coated cutting tools at vc of 239 m/min. The inset is turning operation

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Moreover, the cutting temperature obtained by using cBN-coated tool is lower than that by TiAlN-coated tools (as depicted in Fig. 4). The main reasons are the lower fiction coefficient and higher thermal conductivity of cBN coatings. The research results of Ng et al. [37], Kone et al. [44], and Grzesik [45] have demonstrated that the properties of coatings on cutting tools have significant influence on heat generation and dissipation, although the heat dissipation by tools is less than that by the chips. Lower friction coefficient induces less friction; higher thermal conductivity yields more rapid heat dissipation under identical conditions. Additionally, the relative errors of simulated and experimental results are low than 14% for both cBN- and TiAlN-coated tools.

The relative errors of simulated and experimental results for cutting force and cutting temperature are acceptable and reasonable in some extent. The temperature at tool-chip contact region, where the maximum temperature is produced, cannot be measured by infrared method in cutting experiments. Thus, the experimental cutting temperature is lower than that of simulated results. Together with the above results verified that the proposed FM model is effective and correct. Therefore, the finite element model can be employed to predict coated tools temperature distribution and evolution at various cutting parameters.

4 Simulated results and discussion

4.1 Comparison of cutting temperature distribution by using TiAlN- and cBN-coated tools

Among the cutting parameters, involving cutting speed (vc), feed rate (f), and depth of cut (ap), the vc has the most significant effect on the cutting temperature reported by Davim [2]. Thus, the influence of vc on cutting temperature is studied mainly in this paper.

The distributions of cutting temperature by using cBN- and TiAlN-coated tools at vc of 150 m/min are shown in Fig. 6. The temperatures for both cutting tools and chips show the obvious gradient distribution. The maximum temperature occurs at the chips particularly the contact region between tools and chips, since the heat generation sources are mostly from the intensive friction of tool-chip interfaces and the large plastic deformation of chip under extreme conditions is demonstrated by Ucun et al. [28]. Additionally, the cutting temperature obtained by applying cBN-coated tools is lower than that by TiAlN-coated tools, indicating the less heat generation during turning by cBN-coated tools. It is noted that the temperature distribution of tool flank face-workpiece is not shown in Fig. 6. Under the cutting conditions of negative rake angle 5° and positive clearance angle 5°, the rake face and chips experienced the more intensive friction and deformation which is the mainly source of cutting heat, as demonstrated by Fig. 5b.

Fig. 6
figure 6

Cutting temperature simulated by using a TiAlN- and b cBN-coated cutting tools at vc of 150 m/min

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4.2 Effect of cutting speed on TiAlN- and cBN-coated tools temperature

Generally, the temperature in the cutting tools is lower than the temperature resided in chips. This can be ascribed to following two aspects. Firstly, the chips experience not only the intensive friction but also the plastic deformation generated by the extrusion of cutting tools. But the cutting tools only undergoes the friction resulted from the chips and workpiece due to its higher hardness than workpiece. Additionally, the thermal contact conductance of tool-chip interface affects heat transfer; thus, the cutting heat transferred to the cutting tools is reduced [28, 46, 47]. More importantly, the heat transferred to the tools can greatly affect the cutting performance of the tools demonstrated by Grzesik [48, 49]. Therefore, it is indispensable to investigate the temperature distribution in the coated tools. Figure 7 shows the maximum temperature of TiAlN- and cBN-coated cutting tools obtained by FEM simulation as a function of cutting speed at ap of 0.50 mm. It is revealed that the temperature is increased with the increase of cutting speed for both TiAlN- and cBN-coated cutting tools.

Fig. 7
figure 7

Tool maximum temperature obtained simulation dependent on cutting speed for TiAlN- and cBN-coated cutting tools at ap of 0.50 mm

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In order to better understand the heat distribution and dissipation of each coating with substrates, we mainly studied the temperature variation of coatings regions under enlarged view conditions. Figure 8 depicts the temperature distribution of TiAlN- and cBN/diamond–coated Si3N4 cutting tools. It is shown that maximum temperature of cBN/diamond–coated tools is significantly lower than TiAlN-coated tools, which indicates the less heat generation of cBN coatings. Cubic BN coatings have lower coefficient than that of TiAN coatings, which has been demonstrated by implementing friction and wear experiments in our previous study [14], thus contributing to less heat generation during cutting process. Moreover, each coating and tool substrate shows relatively obvious gradient distribution of temperature. The heat dissipation in cBN/diamond coating regions is more rapid than TiAlN coatings under the same conditions. The disparity is mainly attributed to the thermal conductivity of coating and substrate material. For coating materials, higher thermal conductivity enables a rapid heat dissipation illustrated by Grzesik [45]. Furthermore, maximum temperature is resided in the rake face and decreased with the increase of depth in cutting tools. Coatings for both TiAlN and cBN/diamond, as the heat-isolation layers, maintain the tool substrate a relatively low temperature. This is ascribed to the disparity from thermal conductivity of materials and thermal contact conductance of coating-tool substrate interfaces reported by Courbon et al. [47] and Grzesik [48].

Fig. 8
figure 8

Temperature distribution simulated of a TiAlN- and b cBN/diamond–coated Si3N4 cutting tools at vc of 250 and 290 m/min

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In combination of the above simulated results, it is found that the maximum temperature occurs at tool rake face. The rake face not only undergoes extreme temperature but also experiences intensive friction from chips, thus leading to severe tool wear. In addition, the thermal stability of TiAlN coatings and cBN coatings are 800 °C and 1200 °C, respectively[4, 14, 50]. Considering the temperature, rake face wear, and thermal stability of coatings, we concluded that the preferred cutting speed among employed cutting parameters is below 250 m/min for TiAlN-coated cutting tools while cBN-coated cutting tools has a wide range of cutting speed to be adopted.

4.3 Effect of rake angle on TiAlN- and cBN-coated tools temperature

Tool geometry has a significant influence on the cutting temperature, cutting force, and tool life during turning process. Generally, the negative rake angle (γ0) and positive clearance angle (ɑ0) are recommended for machining difficult-to-cut materials (above 47 HRC) such as hardened steels, tool steels, and hardened ductile iron reported by Davim [2].

Figure 9 shows the maximum temperature in TiAlN- and cBN-coated tools as a function of the rake angle with the constant vc of 270 m/min and constant clearance angle of 5°. It is noted that the temperature decreases with the increase of rake angle, indicating the proper increase of tool rake angle can reduce the tool temperature. Hu et al. [51] have demonstrated that relatively large rake angle not only can improve friction state of tool surface but also can reduce chip deformation during turning process, thus leading to less heat generation. Additionally, the temperature of cBN-coated cutting tools is decreased by approximately 20.4–28.6% than that of TiAlN-coated cutting tools. This is ascribed to the lower friction coefficient of cBN coatings than TiAlN coatings demonstrated in our previous study [14].

Fig. 9
figure 9

Tool maximum temperature obtained simulation dependent on rake angle for TiAlN- and cBN/diamond–coated Si3N4 cutting tools with the constant clearance angle of 5° and the constant vc of 270 m/min

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Figure 10 shows the temperature distributions of TiAlN- and cBN/diamond–coated cutting tools with different rake angles at constant clearance angle (5°) and constant cutting speed (270 m/min). The temperatures show the obvious gradient distribution for TiAlN and cBN/diamond coatings with tool substrates. And the maximum temperature occurs at rake face, then it propagates and decreases with the increase of depth in cutting tools. Furthermore, the dissipation of cBN/diamond coatings is more rapid than TiAlN coatings under identical conditions. It should be attributed to the higher thermal conductivity of cBN and diamond, rendering the rapid heat dissipation. When the rake angle was increased to be − 2°, the temperature is decreased for both TiAlN- and cBN/diamond–coated cutting tools. And the maximum temperature still resides in rake face, but its rich region transfers to near the tool nose. The decreasing of temperature could be ascribed to the larger rake angle improves friction status of between tool rake face and chips and reduces intensive chip deformation [51].

Fig. 10
figure 10

Tool temperature distribution simulated of a TiAlN- and b cBN/diamond–coated Si3N4 cutting tools at rake angle of − 8° and − 2° and the constant clearance angle of 5° and constant vc of 270 m/min

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Considering the temperature, rake face wear, and thermal stability of coatings, we concluded that the preferred tool rake angle among selected cutting parameters is above − 4° for TiAlN-coated cutting tools. But the cBN-coated cutting tools have a wide range of tool rake angle to be used.

5 Conclusion

Finite element method simulation was introduced to determine the temperature distribution of cBN/diamond–coated Si3N4 cutting tools. The FE model of cBN/diamond–coated tools was built and validated by turning experiments. Based on the developed FE model, the effects of cutting speed and tool rake angle on temperature distribution of cBN/diamond–coated tools were investigated compared to TiAlN coatings. The results show that the temperature is increased with the increase of cutting speed while decreased with the increase of tool rake angle. The maximum temperature occurred at the rake face and then decreased dramatically with the increase of tool depth. The temperature of cBN-coated tools is decreased by approximately 20.4–28.6% than TiAlN-coated tools under identical conditions. Additionally, the preferred cutting speed and rake angle were obtained among employed cutting parameters in consideration of the temperature, rake face wear, and thermal stability of coatings. The results showed that the use of advanced cBN coatings can significantly improve the performance of cutting tools with distinctly lower temperature than the commercial TiAlN coatings.