The friction mechanics model within chip-tool-workpiece dual interfaces for cutting nickel-based superalloy at the cooling and lubrication conditions of the three forms oil-on-water mist in wide temperature range

Nickel-Based superalloy has been extensively applied in the critical mechanical bearing components, such as aeroengine owing to its excellent performance at high temperature, but its machinability has always been dissatisfied. In order to improve processing efficiency, reduce cost, and decrease environmental pollution, in this paper, the friction mechanics model within chip-tool-workpiece dual interfaces was established in turning of S-type difficult-to-machine nickel-based superalloy Inconel 718 utilizing the PVD TiAlN coated carbide tool under the cooling and lubrication conditions of three forms oil-on-water mist in wide temperature range (− 30 ~ 150 ℃) (high temperature oil-on-water mist (150 ℃), normal temperature oil-on-water mist (20 ℃), and low temperature oil-on-water mist (− 30 ℃)). Meanwhile, the influence law and mechanism of the cutting speed, depth of cut, and feed on the three-way cutting forces, friction coefficient between chip-tool-workpiece dual interfaces, and normal stress and tangential stress in chip-tool interface have been studied. The results showed that the lowest and highest friction coefficient within chip-tool interface was obtained at the conditions of the high temperature oil-on-water mist (HTOoW) and the normal temperature oil-on-water mist (NTOoW), respectively. The most notable influence of the low temperature oil-on-water mist (LTOoW) on the strain hardening, strain rate hardening, and thermal softening of the materials occurred.


Nomenclature
Rake angle (degrees) Clearance angle (degrees) The friction coefficient at sliding zone a The area of sticking zone on tool rake face b The area of sliding zone on tool rake face S The area of chip-tool contact interface

Introduction
Inconel 718 (GH4169, China) is a kind of nickel-based superalloy which belongs to precipitation strengthening alloy with stable crystal structure and internal strengthening phase making the alloy has good mechanical properties [1]. It has been employed as the key component material in aerospace and other energy equipment due to its high yield strength bellow 700 °C, excellent corrosion and oxidative resistance, and high fatigue strength at high temperature [2]. There are various processing methods for such alloys, including non-traditional machining methods such as laser melting, Electrical Discharge Machining(EDM), electrochemical machining, and traditional machining, which still has been acting as the most efficient way [3][4][5][6]. However, the alloy is extremely difficult to be processed, and its machinability is as low as about 0.1 since its superb plasticity and toughness under powerful yield strength [7]. In the machining process, in order to reduce the temperature of the cutting zone, it can improve friction condition of chiptool-workpiece dual interfaces, reduce the tool wear, and promote the quality of the machined surface by means of pouring emulsion. However, it can cause such disadvantages as increased cost by 20%, pollute the environment, and harm to workers owing to pouring a large amount of emulsion in the process [10]. Therefore the research on the cooling and lubrication technology has been remaining central issue in the field of green cutting technology, resulting in the emergence of various cooling and lubrication technologies such as the dry, minimal quantity lubrication, cold air, vegetable oil, liquid nitrogen cooling, CO 2 cooling, and water vapor. There were many researches in machining of the nickelbased superalloy by utilizing different cooling and lubrication technologies in recent years. In 2004, Dudzinski et al. [8] have found that it can improve the cutting performance in machining of nickel-based superalloy by using the minimum quantity lubrication (MQL) technology, which is better than traditional method of pouring cutting fluid. In 2008, Obikawa et al. [9] have carried out the turning test of Inconel 718 under the condition of MQL with oil flow rate less than 1.0 ml/h. They discovered the machining efficiency can be improved, and has little effect on the tool wear moreover; the tool life has been extended to 47 min when the oil flow rate is 0.5 ml/h and the cutting speed is 1.3 m/s, which becomes only 1 min shorter than that by pouring cutting fluid. Next year, Silva et al. [10] have found that the MQL cooling and lubrication technology can significantly reduce the temperature in the cutting zone and obtain less tool wear in cutting of the nickel-based superalloy Inconel 718 with different cutting tools. In 2015, Fan et al. [11] have studied the tool life in turning of the Inconel 718 with the PVD TiAlN coated tools under the condition of water vapor cooling and lubrication. The research results indicated that the steam cooling and lubrication can improve the tool life. Moreover, Iturbe et al. [12] have discovered that the common cooling method is the best choice in terms of the perspective of machinability and surface integrity through analyzing the tool wear, machined surface roughness, microstructure damage, and microhardness distribution in turning of Inconel 718 by utilizing the CVD TiCN-Al2O3-TiN coated tools. In 2018, Roy et al. [13] have investigated the machinability in turning of nickel-based superalloys with the AlTiN coated carbide tool under the cooling and lubrication conditions of the dry, cold air, and MQL. The results showed that MQL is superior to the other two classes of lubrication technologies in reducing the surface roughness and tool wear. Within the year, Shokrani et al. [14] have carried out the experimental study in cutting of Inconel 718 at high speed by using an innovative hybrid cooling and lubrication system composed of liquid nitrogen and MQL based on rapeseed oil. They have found that hybrid lubrication system can almost double the tool life and produce a maximum surface roughness value of 0.4 µm compared with simple MQL. Next, Nikolay et al. [15] have discovered the temperature in the cutting zone reduces approximate 150-200 °C, and the surface roughness decreases effectively in the process of turning structural steel with cooling ionized air as a lubricating medium, when the number of ions in the cooling air increased from 10 4 to 10 5 per cubic centimeter.
In 2019, Darshan et al. [16] have investigated the surface roughness and tool wear in cutting of the nickel-based superalloy with the mixed oil mist of rapeseed oil and MoS 2 particles as the cooling and lubricating medium. The results showed that it can effectively reduce the temperature in cutting zone and improve the friction characteristics in chip-tool interface. In addition, the cooling effect of MQL based on high oleic soybean oil in milling of Inconel 718 material with the AlTiN coated tool has been investigated by Okafor et al. [17], and they discovered that high oleic soybean oil can replace mineral oil. Pereira et al. [18] have found there is higher tensile residual stress within the machined surface as turning Inconel 718 with ceramic tool by utilizing liquid nitrogen as the cooling medium; However, a larger compressive residual stress is generated within the subsurface, which can improve components fatigue life. The turning test on Inconel 718 with the cooling medium of liquid nitrogen at the parameters of 70-m/ min cutting speed, 0.2-mm depth of cut, and 0.2-mm/r feed has been carried out by Chaabani et al. [19]. The results indicated that the cooling and lubrication medium has a positive effect on reducing tool wear. Subsequently, Okafor et al. [20] have discovered that simple liquid nitrogen cooling has poor effect on reducing tool wear, and MQL combined with liquid nitrogen cooling has significant effect on reducing tool wear and machining cost. It has also been found by Pereira et al. [21] that the tool life increases by 1.2 times in milling of Inconel 718 by using carbon dioxide cooling inside the tool and MQL cooling outside compared with the independent MQL. Hafiz et al. [22] have taken the experiment of milling Inconel 718 with the PVD TiAlN coated tool in cold air and dry condition. They have concluded that the tool wear is retarded because there is no accumulation of workpiece materials at the edge of the tool at the condition of cold air. Allu et al. [23] have  considered that the cutting force becomes small and the tool wear does decrease in cutting of Inconel 718 at the cooling medium of low-temperature MQL. However, the alloy surface has been hardened and the tool becomes more prone to crack due to the effect of low temperature.
Nearly two years from now, in 2020, Mahesh et al. [24] have found that the heat dissipation conditions in dry cutting of nickel-based superalloy is poor and the temperature in the cutting zone is high, as well as the material accumulated at tool edge seriously, which can short tool life compared with dry and wet cooling methods; In addition, there is poor integrity and residual stress on the machined surface due to the high temperature in the cutting zone, which can promote crack initiation and propagation. Zahoor et al. [25] have carried out the cutting tests on nickel-based superalloy in the cooling and lubrication condition of vegetable oil-based  [26] have developed the cutting test on Inconel 718 and other hard-to-cut materials applied CO 2 as the cooling and lubrication medium, which is not better than other common emulsion in terms of the machined surface quality. Sivalingam et al. [27] have added 0.2 wt% solid lubricants such as molybdenum disulfide and graphite powder to vegetable oil as the cooling and lubrication medium to cut Inconel 718. It has been discovered that the groove wear and fracture of the tool edge become weakened effectively, the tool wear at the flank face and the surface roughness are reduced by 50-65% and 39-51%, respectively, due to the existence of solid lubricant in the chip-tool interface. De Bartolomeis et al. [28] have found that the tool wear obviously decreases in high-pressure cooling medium, compared to other cooling and lubrication methods in cutting of nickel-based superalloys. In 2021, the cooling and lubrication effects of dry type, MQL, and cold air to the machining process of the Inconel 718 with the AlTiN coated carbide tool have been investigated by Çakıroğlu et al. [29] It has been determined that the cutting speed of 70 m/min and feed of 0.05 mm/r are the best cutting parameters under the MQL. Through the experimental study of milling Inconel 718, Zhang et al. [30] have found that the chips adhering to the ceramic tool can be removed and the lubrication effect of the cutting zone greatly improves with the cooling technology of supercritical carbon dioxide combined with MQL. Danish et al. [31] have discovered that the machined surface roughness, the temperature in the cutting zone, and the tool wear can be respectively reduced by 60.6%, 37%, and 19.5% with the cooling medium of Cryo-MQL (low-temperature MQL) compared with the dry, MQL, and low-temperature MQL in turning of nickel-based superalloys. The above research findings indicated that the cooling and lubrication of MQL performs excellently in the process of machining Inconel 718. In this paper, a study aims to developed the friction mechanics model of chip-toolworkpiece dual interfaces in turning experiment of S-type difficult-to-machine nickel-based superalloy Inconel 718 with the PVD TiAlN coated carbide tool at three cooling and lubrication mediums of high temperature oil-on-water mist (HTOoW, 150 ℃), normal temperature oil-on-water mist (NTOoW, 20 ℃), and low temperature oil-onwater mist (LTOoW, − 30 ℃). And what is more, the law and mechanism of three-way cutting forces, friction  coefficient between chip-tool-workpiece dual interfaces, normal stress and shear stress between chip-tool interface affected by the developed friction mechanics mode, cutting speed, depth of cut, and feed will be all discussed in this paper.

Experimental system
The experimental system in this study was consists of three parts: cutting system, three forms oil-on-water mist in wide temperature range, and off-line measurement system composed of surface roughness instrument.

The cooling and lubrication system of oil-on-water mist in wide temperature range
The cooling and lubrication system of oil-on-water mist in wide temperature range is made up of the air compressor, gas cylinder, NTOoW and LTOoW generator (type:AR-800-OoW-55), high temperature vapor generator, and atomizing nozzle (nozzle diameter is 0.8 mm). The system can output cooling and lubrication medium of oil-on-water mist in wide temperature range (150 ~ 30 ℃) (HTOoW (150 ℃), NTOoW (20 ℃), and LTOoW (− 30 ℃)).
As shown in Fig. 1, the compound spray system can output two kinds of cooling and lubrication medium, which is named as the NTOoW (20 ℃) and LTOoW (− 30 ℃); The HTOoW (150 ℃) has been exported due to composing high temperature vapor generator and micro spray oil pump (type: YS-BPV-3000). The outlet diameter of the atomizing nozzle in the cooling and lubrication system is about 0.8 mm, and its principle of the atomization is as follows: The structure of the atomizing nozzle is shown as No. 14 in Fig. 1. The nozzle's internal space is divided into two parts separated by a hollow cylindrical core, inside of which high-speed air has been circulated, the lubricating oil and liquid water has been run at outside. The filmed liquid in the nozzle is broken into small droplets by the air, when the high-speed air does meet the liquid at the nozzle outlet. As the airflow moved towards the spray direction, the velocity of airflow at the nozzle becomes greater than the droplet because the pressure of the airflow is over than that of the liquid; With the increase of jet distance, the droplets are constantly washed by the airflow, so that the large diameter droplets at the nozzle gradually changes into smaller diameter droplets, and thus they were atomized. In the experiment, the principle of generating cooling and lubrication mediums in wide temperature range (HTOoW (150 ℃), NTOoW (20 ℃), and LTOoW (− 30 ℃)) are as follows: As shown in No. 11 of Fig. 1, the superheated steam generated by the water vapor generator is connected to the core of the atomizing nozzle. The output pressure of the steam can be controlled by adjusting the overflow valve. The other port of atomizing nozzle is connected to micro spray oil pump (type:YS-BPV-3000). The steam quickly flows through the nozzle core due to its high pressure, which reduces the pressure at both sides of the core outlet, and further decreases the pressure of the other nozzle interface. The oil enters the nozzle and forms the oil film at the nozzle outlet due to the action of the micro spray oil pump. A throttle valve and flowmeter is arranged in the pipeline where the oil flows to control the flow of the lubricating oil. The output pressure of the steam and the flow of the oil are presented in Table 1.
In the experiment, the NTOoW/LTOoW is supplied by the same set of equipment, as shown in Fig. 1. Firstly, the air compressor (No. 1) provides the stable air source to the gas cylinder (No. 2), its internal pressure is stabilized at about 0.8 MPa. The stable air source is provided by the gas cylinder to the NTOoW/LTOoW equipment (No. Fig. 2); Secondly, the atomizing nozzle in the system has three input ports, the core is utilized to input high speed airflow, and the other two inputs are used to input water and lubricating oil; Finally, when the NTOoW is required, the device for cooling (No. 4 in Fig. 1) is turned off, so that the airflow directly enters into the core of the atomizing nozzle through the air dryer (No. 3 in Fig. 1), the lubricating oil and water enters the nozzle by adjusting the overflow valve at the same time, then the oil and water is atomized and injected due to the driven of high speed airflow.

in
When the LTOoW is required, the channel of normal temperature airflow is closed and the cooling equipment (No. 4 in Fig. 1) is opened to decrease the temperature of the airflow, then the nozzle core is fed with low-temperature airflow. The airflow reaching the nozzle core can still achieve about − 30 ℃ due to its extremely low temperature, as shown in Fig. 3. Therefore, the liquid water inside the nozzle is condensed into ice crystals owing to the effect of low temperature airflow, and is injected into the cutting zone with the cold airflow and oil mist. The pressure of the nozzle outlet and the flow of the lubricating oil and the water in the NTOoW and LTOoW system are shown in Table 1.

Measurement system
The offline measurement system was consisted of surface roughness tester (type: SJ-210) as shown in Fig. 4(a), ultra depth of field microscope (type: Smartzoom5), and Scanning Electron Microscope (type: inspec F50, SEM) as shown in Fig. 4(b) and (c). The three dimensional cutting forces and the temperature of the cutting zone have been measured by online; The machined surface roughness, the machined surface morphology, and the tool wear have been measured by offline.

Workpiece material
The material in the experiment is nickel-based superalloy Inconel 718. The step of heat treatment for workpiece is as follows: First, it was heated up to 1050 ℃ in the electric furnace; Second, taken out after 1 h of holding, and then cooled in the air until about 20 ℃; Third, heated up to 720 ℃ in the electric furnace again and holding for 8 h, and then the temperature of furnace decreased by 50 ℃ per hour, and holding for 8 h until its down to 620 ℃; Finally, it was cooled in the air immediately. The average surface hardness of the workpiece is 50 ± 1 HRC. The diameter of the workpiece is 100 mm and the length is 300 mm, as presented in No. 8 of Fig. 2. The chemical composition of the workpiece is shown in Table 2.

The PVC TiAlN coated cutting tool
The tool employed in the experiment is the PVC TiAlN coated carbide tool (type: TS 2500 08 / 2 M1) produced by SECO company of Switzerland, and the matrix material of the tool is tungsten (W)-cobalt (Co) alloy. The effective geometry angles of the tool are shown in Table 3.

Experimental parameters
The experimental parameters are described in Table 4. The experiment was conducted to investigate the influences of different cutting parameters on cutting forces, friction coefficient between chip-tool-workpiece dual interfaces, and normal stress and tangential stress in chip-tool interface at three forms cooling and lubrication technologies.

Friction model
As shown in Fig. 1, f is the feed direction of the tool, and n is the main movement direction of the workpiece. During the cutting process, there was mutual extrusion and friction between the tool and the workpiece, and the force imposed on the tool was measured by the dynamometer connected to the tool handle. The three dimensional cutting forces is as follows: The feed force F x is parallel to the feed direction, the main cutting force F z is perpendicular to the cutting plane, and the radial force F y is perpendicular to F x and F z meanwhile.
The force imposed on the tool in oblique turning mainly originates in the friction of the chip-tool interface and the tool-workpiece interface (including interface between the tool flank and the workpiece transition surface, interface between the tool minor flank and the workpiece machined surface). In order to study the behavior of the friction between chip-tool-workpiece dual interfaces, three orthogonal cutting forces are converted into normal and tangential force along the tool rake and flank.
In Fig. 5, is the rake angle, is the clearance angle, ′ is the back clearance angle, r is the tool cutting edge angle, ′ r is the tool minor cutting edge angle, s is the cutting edge inclination angle. The measurement values of three dimensionally orthogonal cutting forces imposed on the tool rake face convert into the normal force F nr and tangential force F tr , and the conversion relationship are shown in formula (1). (1) The curve of relationship between the cutting force and cutting speed Fig. 7 The curve of relationship between cutting force and depth of cut The conversion relationship of the normal force F nf and tangential force F tf imposed on the tool flank face may be shown as formula (2).
The conversion relationship of the normal force F ns and tangential force F ts imposed on the tool minor flank face is shown as formula (3).
The friction coefficient on the tool rake face, flank and minor flank face is defined as rk , fk , and sc , as shown in formula (4) according to Coulomb's law of friction.
(2) Figure 6 shows the variation law of cutting force with cutting speed at the depth of cut of 0.2 mm, feed of 0.15 mm/r under the condition of three forms oil-onwater mist in wide temperature range (HTOoW (150 ℃), NTOoW (20 ℃), and LTOoW (− 30 ℃)). It can be seen in Fig. 6 that the main cutting force F z and the feed force F x in the HTOoW (150 ℃) are slightly smaller than those in the other two cooling and lubrication conditions, and Fig. 9 The graph of friction coefficient of the tool rake face in various cutting speed Fig. 10 The graph of friction coefficient of the tool flank face in various cutting speed its trend is relatively smooth with the increase of cutting speed; While the radial cutting force F y is much larger than the other two cutting forces. The chief reason is that the material hardness is too high to yield in the cutting process of extrusion deformation, and there is a separation point in the first shear deformation area where the chip on the tool rake face is separated from the workpiece [32,33]. Part of the materials is extruded into the transition surface and the machined surface by the tool flank and minor flank face, taking this separation point as the boundary. During this process, the part of the materials would recover elastically, thus resulting in a larger radial force. The trend of the radial cutting force in NTOoW and LTOoW cooling and lubrication condition is consistent, which increases firstly and then decreases slowly, and the node speed of transformation reaches 111 m/min. The radial cutting force in HTOoW increases sharply at first with increments of the cutting speed. When the cutting speed exceeds 111 m/min, it decreases firstly and then increases, and reaches 836.5 N, which is about 5 times that at 22 m/min. Figure 7 presents the variation law of the cutting force with depth of cut at a 111-m/min cutting speed and 0.15mm/r feed under the condition of three forms oil-on-water mist in wide temperature range (− 30 ~ 150 ℃). It can be discovered in Fig. 7 that the main cutting force F z increases slightly with the increase of the depth of cut in the three kinds of cooling and lubrication condition. The phenomenon indicates that the influence of depth of cut on the main cutting force becomes weakly. The feed force F x increases slowly with the increase of the depth of cut under the cooling and lubrication condition of HTOoW and LTOoW. Its tendency is upward firstly and then downward in the cooling and lubrication condition of NTOoW, in which F x reaches the maximum at 0.2-mm depth of cut. The radial cutting force F y rises quickly at the beginning, and then gradually shrinks with the increased of the depth of cut.

Cutting force
The cutting force is mainly induced from the deformation of the materials and the friction between tool and materials. In the cutting process, most of the materials deform and crack into the chips due to the extrusion of the tool rake face, and a few of them recover elastically into machined surface after the tool leaves. A conclusion can be made out: plastic deformation predominates in the deformation mechanism of the materials in the cutting zone which has both elastic and plastic deformation, and the plastic deformation of the material is related to the mechanical properties of the materials itself. In the machining process, the mechanical properties of the materials do not remain constant with the variation of cutting parameters and the cooling and lubrication medium, and yet which is related to the strain, strain rate, and the temperature of the materials deformation area, which is in agreement with the literature [34]. It can be observed from Fig. 6 that with v = 111 m/min as the node, the plastic deformation of the materials is mainly dominated by strain hardening and strain rate hardening; However, when the node is exceeded, the cutting force decreases, indicating that the thermal softening effect of the material takes dominate place after the node. Relevant literatures [35][36][37][38] indicate that the type of friction between the tool and the materials is in the form of sticking-sliding movement, and the friction is affected by many factors. The roughness of tool surface, the compressive stress in the contact surface, and the temperature in the deformation area all have a significant effect on the friction when the material of the friction pair is certain. The size of the chip-tool contact area is mainly determined by depth of cut and feed, as shown in Figs. 7 and 8. With expanding of the chip-tool contact zone, the compressive stress on the tool face diminishes. Theoretically, the influences of the two parameters on the cutting forces should show a downward trend, but only the increase in feed results in decrease of the cutting force, which indicates that increasing the material removal rate by increasing the depth of cut becomes more reasonable than increasing the feed.

Friction coefficient
In the process of oblique turning the cylindrical surface, the friction in the cutting zone is mainly existed in the chip-tool interface, the tool flank -workpiece interface, and tool minor flank -workpiece interface, and the friction characteristic within the interfaces is different. In this paper, the changes of friction coefficient with the cutting parameters and cooling and lubrication mediums were compared and analyzed. Figures 9, 10, and 11 describe the variation of the friction coefficient with the cutting speed. The friction coefficients in the chip-tool interface in the condition of HTOoW are lower than those at the other two cooling conditions, as observed in Fig. 9. Therefore, the average values of the main cutting force and feed cutting force in the same condition are lower than those in the other two cooling conditions, as found from  Fig. 6. The principal reason of the induced phenomenon as follows: the position to reach firstly is the tool rake face when the cooling medium is sprayed, and the cooling mechanism of the oil-on-water mist in different states is distinct from each other. The cooling medium difficultly enters into the interface cooling a lubricating in the chip-tool contact surface due to the great pressure, and the extremely high temperature does occur in the cutting zone. However, the water vapor molecules enter a very small gap existing within the chip-tool interface owing to its smaller volume and the capillary action, and then a boundary lubrication condition does form in the interface. Meanwhile, it is difficult for NTOoW and LTOoW to penetrate into the contact interface, resulting in dry friction; In the system of sliding friction, the tangential friction force is directly proportional to the actual contact zone of the slide joints, and the chip-tool interface is stuck due to the high pressure between the interface, which raises the actual contact zone and then increases the tangential friction force [39], leading to the value of the friction coefficient becomes greater than 1 in the condition of this kind of cooling and lubrication medium. The phenomenon can also be proved by the tool wear morphology of the tool rake face, as shown in Table 5. As shown in Table 5, in the cooling and lubrication condition of the HTOoW, the friction of sticking type on the tool rake face is not dominant role since the lubrication condition is better than the other two cooling mediums, and the chemical reaction rate improves owing to the high-temperature water vapor at the same time. The Cr 2 O 3 , Fe 2 O 3 , and Fe 3 O 4 of the oxides do generate in the cutting process to form an unstable film, which plays the role of lubrication, and inhibits chip-tool interface adhesion effectively, resulting in less adhensive wear of the tool [11,40]. It can be observed that only a small amount residues of the chip adheres to the crater of the tool rake face.
A large amount of workpiece materials are stuck on the tool rake face in the other two cooling mediums. The material is softened due to the higher temperature in the cutting zone, especially in the condition of NTOoW. In the cutting process, the coating on the tool surface is bonded and stripped owing to high pressure located in the chip-tool interface, and then the tool matrix material also is bonded and stripped. In the end of the cutting process, part of the stripped tool coating material is piled up on the tool tip, as observed from the EDS in area A in Table 5.
In the condition of LTOoW, liquid water and cold airflow (− 30 ℃) met in the atomizing nozzle and become ice crystals. Although the ice crystals mixed oil mist does not enter the capillary in the closely contact zone within tool-chip interface, a lot of heat in the cutting zone has been taken away in the process of the ice crystals melting into the gasification, and the softening effect and viscosity of the chip is weakened, thus the adhesion and peeling of the tool surface coating and matrix is weakened. In the condition of LTOoW, the phenomenon can be observed from the SEM of the tool rake face in Table 5.
It can be observed in Figs. 10 and 11, the trend of the friction coefficient in the tool flank face -workpiece interface and tool minor flank face -workpiece interface is almost consistent with increments of the cutting speed at the same cooling and lubrication medium. The friction coefficient in the tool flank face -workpiece interface and tool minor flank faceworkpiece interface gradually decreases with increments of cutting speed at HTOoW. The main reason resulting in the phenomenon is that the superheated water vapor can penetrate into the slit of the contact surface within chip-tool-workpiece dual interfaces due to its powerful molecular energy and active movement, as well as the capillary action [41,42]. The slit in the contact surface  within chip-tool-workpiece dual interfaces is equivalent to be semi-vacuum state in the cutting process. The faster the cutting speed, the lower the pressure in the slit, the more water vapor molecules penetrate, and the better the lubrication conditions, so as the friction coefficient of the contact surface decreases.
The friction coefficient at the same cutting parameters in the tool flank face -workpiece interface and tool minor flank face -workpiece interface becomes highest at NTOoW, followed by LTOoW, and lowest at HTOoW, when the cutting speed is higher than 69 m/min. It is the principal reason inducing this phenomenon that the kinetic energy of the chips increases and part of the kinetic energy is converted into heat energy when the cutting speed becomes faster. The cooling effect of NTOoW in the cutting zone is significantly weakened compared with LTOoW. Figures 12,13, and 14 present the influence of the depth of cut on the friction coefficient at cutting speed of 111 m/ min and feed of 0.15 mm/r. The friction coefficient on the tool rake face tends to be upward with the increase of depth of cut. The deformation energy of the workpiece material in the process of chip formation increases with increments of depth of cut. In addition, the chips is hindered in the process of outflow due to the negative tool cutting edge inclination angle used in the experiment, thus the chip-tool interface contacts more tightly, the friction coefficient on tool rake face increases. It is very interesting that the friction coefficient in the tool flank face -workpiece interface and tool minor flank face -workpiece interface changes gently with the depth of cut. The reason is that the split point between the chip and the material is basically constant when the  Table 6, too. As presented in the Table 6, with the increase of depth of cut, there is no serious pressing and ironing trace on the machined surface, and the ridges generated by the duplicate of the tool arc shape is still clearly visible, which may be also mutually confirmed with the wear form of the tool flank and the tool minor flank face in Table 5. In addition, in the three cooling and lubrication technologies, although the values of the friction coefficient are not significantly different at the same cutting parameters, it can still be clearly observed that the friction coefficient is the largest under the condition of NTOoW, which is consistent with the mechanism with different cutting speed. Figures 15, 16, and 17 present the change law of the friction coefficient on chip-tool-workpiece dual interfaces with increments of feed in a case of 111-m/min cutting speed and 0.2-mm depth of cut. It can be found in Fig. 15 that the change law of friction coefficientin the chip-tool interface presents as opposite with that of depth of cut at the three cooling and lubrication conditions, which appears a downward trend with the increase of feed. The main reasons inducing this phenomenon are as follows: First of all, as presented in the formulas (2), (3), and (4), the friction coefficient is directly proportional to the tangential force in the contact surfaces and inversely proportional to the normal pressure. The force on the tool rake face mainly derives from the deformation of the workpiece material. Since the tool used in this experiment has a positive rake angle being conducive to the outflow of the chips, the component force of the deformation force along the tangential direction of the rake face does not increase exponentially, while the normal pressure on the tool rake face increases ruptly; Secondly, the outflow speed of the chips along the tool rake face becomes faster with increments of the feed, leading to the increase of the temperature within chip-tool interface, and thus the softening effect of the materials is dominant; Thirdly, through the observation of the workpiece machined surface at different feeds, it has been discovered that a small piece of softened workpiece material is embedded on the machined surface at 0.08 mm/r, as shown in Fig. 21. The phenomenon indicates that there is a large build up edge on the tool tip at the feed. Therefore, the actual rake angle of the tool becomes negative as a result of a small feed, which results in the material deform difficultly, hinders the outflow of the chips, increases the cutting force, and makes the friction coefficient of tool rake face higher. Given all of that, with increments of the feed, the contact zone within the chip-tool interface expands, the chip outflow speed goes up, the temperature of the cutting zone increases, the material softening effect gradually dominates, and the friction coefficient of the chiptool interface gradually decreases.
As presented in Fig. 16, in the three cooling and lubrication conditions, the friction coefficient in the tool flank faceworkpiece interface gradually increases with the increase of feed. It reaches the maximum value of 0.83 at 0.26 mm/r in the cooling and lubrication condition of the NTOoW. It is the primary reason that the pressure on the tool flank and the transition surface of the workpiece material equivalently increases when the feed increases; When the cutting speed and depth of cut remains constant, the greater the pressure between the tool flank face -workpiece, the closer the contact between them, the more difficult it is for the cooling and   Table 7 The value of tool rake face lubrication medium to penetrate the contact interface, and the greater the friction coefficient; Therefore, the friction coefficient on the tool flank face tends to be larger with increments of feed, and finally become the largest one when utilizing the NTOoW technology. These features can be observed from the wear morphology of the tool flank and minor flank face obtained by Ultra depth of field microscope. Figures 18, 19, and 20 describe the tool wear morphology in the cooling and lubrication conditions of the HTOoW, NTOoW, and LTOoW, respectively. The shape of the most serious worn area on the tool flank is similar, as observed in this figure, thus it can be inferred that the area belongs to the tightest contact zone in the tool flank face -workpiece interface. The wear characteristics of HTOoW in this area where existed deep scratches are most similar to that of the LTOoW, which indicates that there is less bonding between the tool flank face and the workpiece materials. However, in the condition of NTOoW, the tight contact zone is the largest, and there are no tidy scratches. It is mainly characterized by the falling off of a large zone of the tool base materials, and the burning of coating material does occur at the edge of the tight contact zone, which indicates that there is more bonding within the tool flank face -workpiece in the cooling and lubrication condition. These circumstances are basically consistent with the variation law of the friction coefficient on the tool flank and the mechanisms of three kinds of cooling and lubrication (Fig. 21).
In the three kinds of cooling and lubrication conditions, the variation range of the friction coefficient on the tool minor flank face with the feed is fairly gentle, and it is basically about 0.15, but it is still the highest in NTOoW. This can also be surveyed from the outside of the tool tight contact zone of the tool wear morphology in Figs. 18, 19, 20.

Stress distribution on tool rake face
The tool wear in cutting zone is directly affected by the stress distribution in the chip-tool interface. As shown in Fig. 22, the chip-tool contact zone can be basically divided into two parts: sticking zone and sliding zone. There is a small zone between the sticking zone and the sliding zone, and its friction characteristic exists in the form of the coexistence of sticking and sliding, which is the transition zone of sticking and sliding characteristic [36]. As presented in Fig. 23, the transition area can be measured together with the sliding zone due to its narrowness and characteristic that has been difficult to be clearly measured. In this experimental, the contact zone of the tool rake face and the chip in different cutting parameters was measured. According to the literature [35][36][37][38], it is assumed that the normal stress is exponentially distributed on the tool rake face, as shown in formula (5).
In the formula, 0.2 is the yield strength of Inconel 718, and S is the chip-tool contact zone. According to the actual tool-chip contact zone of the measured shown in Table 7, the function of the macroscopic normal pressure F int−n of the tool rake face can be obtained by definite integral in the contact zone, as shown in Eq. (6). Compared with the measured actual normal pressure F nr , the normal pressure distribution curve close to the measured actual normal pressure was obtained by changing the exponent of the stress distribution function. The flow chart of calculating the exponent n is shown in Fig. 24. In different cutting conditions, the exponent n is presented in Table 7. Figure 25 presents the stress-strain curve of the Inconel 718. The size of compression sample for quasi-static compression in strain rate of 10 -3 s −1 is Φ10 mm × 16 mm. The equipment for the compression experiment is Digital Display Electronic Universal Testing Machine (type: WDW-E200D). The curve shows that the sample does not yield during compression, and the material yield limit is 0.2% stress at the plastic strain. Through the coordinate (0.2, 0), the straight line parallel to the curve of the elastic strain stage is made to intersect with the stress-strain curve. The intersection point was the plastic strain point, In order to obtain the friction coefficient and tangential stress on the tool rake face, the following assumptions are made: (i) the size of the transition zone is 0.1 times that of the sliding zone; (ii) The friction coefficient of sticking zone and sliding zone is constant, which are sticking zone st , sliding zone sl , and transition zone tr , respectively, and the friction coefficient of transition zone tr changes linearly; The characteristics of the sliding zone are similar to those of the tool minor flank face -workpiece interface by observing, thus the friction coefficient of the sliding zone is assumed (iii) s1 − sc . Then the friction coefficient and tangential stress distribution in the chip-tool interface are presented in Eqs. (7) and (8). The friction coefficient in the sticking zone st and the variation function of the friction coefficient tr in the transition area can be obtained based on simultaneous solution of Eqs. (7)-(9) and letting F int-t = F tr , in the equations, F tr is the measured actual value of the tangential stress on the tool rake face.
The variation trend of the normal stress in chip-tool interface with increments of cutting speed in three cooling and lubrication conditions is presented in Fig. 26(a), (b), and (c). The normal stress at the tool tip is the smallest in a case of 22-m/min cutting speed, as observed in this figure. Especially, at this cutting speed, the chip-tool contact zone in the cooling and lubrication condition of HTOoW is less than that in the other two cooling and lubrication conditions, which shows that lubrication effect on the cutting zone of the HTOoW is the best. As a result, it is benefit to reduce the wear of the tool rake face. In the cooling and lubrication conditions of the HTOoW and NTOoW, the normal stress on the tool rake face is the highest at 111 m/ min, indicating that the strain rate hardening of the material reaches the extreme at this cutting speed. The chiptool contact zone become the smallest, the normal stress at the tool tip and the temperature in the cutting zone reach the highest in the cooling and lubrication condition of the LTOoW in a case of 251 m/min, 0.2 mm, and 0.15 mm/r. The temperature reaches 305 ℃ through the observation by utilizing the infrared radiation thermometer, as presented in Fig. 27. As shown in Fig. 26(c), the sticking zone increases while the sliding zone decreases due to the dominant thermal softening effect of the material. Although the LTOoW can effectively promote the heat dissipation in the cutting zone, the materials should be hardened seriously due to the effect of the low temperature, which makes the chips not easy to curl. Therefore, in the same cutting parameters, the chip-tool contact zone was the largest in this cooling condition. As shown in Fig. 28(a), (b), and (c), the normal stress in the chip-tool contact zone does not increase with increments of depth of cut at the three cooling and lubrication conditions, and the relationship of each other is nonlinear. In three cooling and lubrication conditions, the normal stress in chip-tool interface is the smallest at 0.10-mm depth of cut, while the contact zone in chip-tool interface is the largest at 0.20 mm. The depth of cut should be one of the key influence factors of the material strain rate. Thus, it can have a conclusion that the depth of cut of 0.20 mm is the turning point of the strain rate in the cutting process.   The variation trend of the normal stress in chip-tool interface with feed in three cooling and lubrication conditions is presented in Fig. 29(a), (b), and (c). The tool-chip contact zone is the largest in the conditions of HTOoW and NTOoW in a case of 0.10 mm/r, while it is the largest in the condition of the LTOoW in a case of 0.08 mm/r, as can be observed in the figure. The normal stress in chip-tool interface is basically inversely proportional to the feed, which is consistent with the variation law of the coefficient in chip-tool interface. Especially, the normal stress at the tool tip in chip-tool interface is weakly affected by the variable feed due to the excellent lubrication effect of the HTOoW.   The tangential stress and normal stress in chip-tool interface conforms to Coulomb's friction law [43], so the variation law of the tangential stress can be obtained from Eq. (8). The variation trend of the tangential stress in chip-tool interface with the cutting speed in three cooling and lubrication conditions is presented in Fig. 30(a), (b), and (c). It can draw a conclusion that the variation trend of the tangential stress in chip-tool interface with movements of cutting speed is consistent with that of the normal stress in the condition of the HTOoW. In the conditions of NTOoW and LTOoW, the tangential stress is still small at a cutting speed of 69 m/min due to the small value of the friction coefficient on the tool rake face even if the normal stress is large.
The variation trend of the tangential stress in chip-tool interface with increments of depth of cut in three cooling and lubrication conditions is presented in Fig. 31(a), (b), and (c). In the HTOoW condition, the trend and magnitude of the tangential stress in chip-tool interface are basically the same at depth of cut of 0.20 mm and 0.30 mm. The normal stress and friction coefficient in chip-tool interface are basically the same in this cutting parameter, as can be observed in Fig. 31(a) and Fig. 12. When the depth of cut reaches 0.25 mm, the tangential stress of chip-tool interface becomes slightly lower than that of the other two depth of cuts. The tangential stress does not change linearly with the increase of depth of cut although the depth of cut is directly proportional to the chip-tool contact zone. The depth of cut determines the initial volume of the deformed materials during cutting process. The relationship between stress and strain becomes nonlinear in the plastic stage of material, as shown in Fig. 25. From above results, the strain hardening of the materials plays a leading role and contributes to an increase of material deformation stress in the cooling and lubrication condition of HTOoW in a case of 0.20-mm depth of cut. In the cooling and lubrication condition of the NTOoW, the tangential stress in chip-tool interface is basically the same by comparing with the results of those at 0.15 mm, 0.25 mm, 0.20 mm, and 0.30 mm, as shown in Fig. 31(b). It can be seen in Fig. 31(c), in the condition of LTOoW, the value of strain hardening turning point becomes higher due to the hardening effect of the low temperature on the materials; thus, when the depth of cut reaches 0.30 mm, the tangential stress near the tool tip is lower than the consequence of at 0.25 mm, and the turning point changes from 0.20 to 0.25 mm.
The trend of tangential stress in chip-tool interface with feed in three cooling and lubrication conditions is presented in Fig. 32(a), (b), and (c). As observed from the figures, in the three cooling and lubrication conditions, the tangential stress near the tool tip is the smallest when the feed is 0.26 mm/r, the state is consistent with the relationship between the cutting force and feed, as well as the friction coefficient between the chiptool interface and feed. Therefore, the feed can be appropriately increased to reduce the tool wear without affecting the machined surface quality.

Conclusions
Besides the friction mechanics model of chip-tool-workpiece dual interfaces was established in turning of nickel-based superalloy Inconel 718 by using the PVD TiAlN coated  Fig. 32 The effect of feed on tangential stress of tool rake face at three cooling and lubrication conditions (ac = 0.2 mm, v = 111 m/ min) carbide tool, the influences law and mechanism of the cooling and lubrication condition, cutting speed, depth of cut, and feed on the three-way cutting forces, friction coefficient in the chiptool-workpiece dual interfaces, normal stress and tangential stress in chip-tool interface have been investigated at the cooling and lubrication conditions of three forms oil-on-water mist in wide temperature range (HTOoW (150 ℃), NTOoW (20 ℃), LTOoW (− 30 ℃)). The main conclusions are as follows: (1) In the three cooling and lubrication conditions, the radial cutting forces are awesomely higher than the other two cutting forces. The main cutting force and feed force in the condition of HTOoW are smaller than those at the other two cooling and lubrication technologies. At the cooling and lubrication conditions of NTOoW and LTOoW, the variation law of the cutting force with cutting speeds is basically the same, while the influence of the depth of cut and feed on cutting forces is opposite. (2) At the three cooling and lubrication conditions, the friction coefficient within the chip-tool interface is maintained at about 0.9, and the form of the main friction is possible to be sticking-sliding mode, and the sticking is mostly emerged near the tool edge. The sticking friction in chiptool interface becomes the most serious in the cooling and lubrication condition of NTOoW, followed by LTOoW, and yet the friction coefficient of HTOoW is the lowest. (3) At the conditon of HTOoW, the friction coefficient within the tool flank face -workpiece and tool minor flank face -workpiece interfaces decreases obviously with the increase of cutting speed due to the small volume and active movement of water vapor molecules, and the capillary action of cooling and lubrication medium within tool-workpiece interface. (4) At the cooling and lubrication conditions of NTOoW and LTOoW, the variation law of the friction coefficient between the tool flank face -workpiece and tool minor flank faceworkpiece interfaces is similar, and the heat in the cutting zone is dissipated mainly in the form of water changing into steam. The heat dissipation effect of the LTOoW is the best, but the material hardens seriously due to the effect of the low temperature. (5) The friction coefficient in chip-tool interface starts from the tool tip, changes from sticking zone to transition zone and sliding zone, and then decreases in turn. The transition area is the smallest, and the phenomena of sticking and sliding exist simultaneously. (6) The influence of cooling and lubrication condition on the strain hardening, strain rate hardening, and thermal softening of materials in cutting process becomes different, and the three factors are less affected by the HTOoW and NTOoW. The threshold of strain hardening and strain rate hardening reduces at the LTOoW condition during the material deformation process. The thermal softening effect is no longer dominant in the condition of LTOoW.