A Thermal Model to Predict Tool Temperature in Machining of Ti–6Al–4V Alloy With an Atomization-Based Cutting Fluid Spray System

Despite wide application of titanium alloy components in aerospace and biomedical industries, cooling during machining of Ti and its alloys has always remained a highly challenging problem due to high heat generation and extremely localized temperatures. Atomization-based cutting fluid (ACF) spray system is being sought as an alternative to cooling processes currently used for machining difficult-to-cut materials such as titanium alloys [1]. The ACF spray system generates a stream of monodispersed droplets of cutting fluid that are entrained using a high-velocity gas flow to form a focused axisymmetric jet of droplets. During machining, this jet penetrates the small region of the tool–chip interface that helps in lubrication and cooling of the interface. The system is also environmental friendly as it uses cutting fluid less than 100 ml/min, considerably less than that used in flood cooling [1]. In comparison to other cooling techniques such as high-pressure cooling and cryogenic cooling, ACF spray system uses much less energy, thus making it energy efficient. Initial studies by Hoyne et al. [1,2] and Nath et al. [3] have reported that the ACF spray system improves machining performances including tool life and reduced temperature in turning of Ti-alloys. The process is known to involve several complex phenomena such as droplet–surface interaction and film formation [1], which are influenced by cutting fluid and spray characteristics, viz., droplet size, droplet diameter, and droplet velocity. Therefore, for the effective use of the ACF spray in machining, it is imperative to carry out a physics-based modeling of the process in order to have a fundamental understanding of the impingement behavior of the cutting fluid and the heat transfer mechanism at the tool–chip interface and its role on increasing the tool life.

Modeling and simulation of machining of Ti alloys with/without cutting fluids received significant attention in the research community. Li and Shih [4] modeled the turning of titanium alloy in 3D to predict the cutting forces and temperatures and showed a direct correlation with cutting speed and chip–tool interface temperature. A finite element (FE) study using Johnson–Cook model was also performed by Karpat [5] to predict the temperature of the chip. Pervaiz et al. [6] conducted a finite element (FE) simulation coupled with computational fluid dynamics (CFD) simulation to predict the temperature distribution in tool during machining of Ti–6Al–4V in the presence of dry air. While the FE simulations were used to model the heat generation during machining, the CFD model was used to incorporate the convection due to the flowing air. All the above models provide insightful information on temperature prediction of tool during titanium alloy machining, but they all deal with dry cutting. Hadzley et al. [7] developed a finite element machining model for high-pressure jet-assisted machining of Ti–6Al–4V alloy. The model was used to simulate interactions between the fluid and solid structure in order to study the effect of coolant pressure on chip formation, cutting force, and cutting temperature. The heat transfer was accounted in the model using convective heat transfer coefficient of the fluid. Finite element machining model has also been developed under the application of cryogenic cooling based on Johnson–Cook flow stress model and a constant convective heat transfer coefficient to account for the heat absorption by the cryogenic fluid. Duchosal et al. [8] carried out modeling of machining under the application of minimum quantity lubrication (MQL) coolant process using an unsteady Reynolds-average Navier–Stokes (RANS) formulation. The model was used to simulate the liquid film formation using a multiphase Lagrangian model for the droplet–surface interaction process, while the heat transfer was ignored.

Although there exist several modeling efforts to simulate machining of Ti-alloys under various cutting conditions, the heat transfer is commonly accounted using a convective heat transfer coefficient that is usually constant for a cutting fluid at a given temperature. However, during the application of ACF spray as a coolant in machining of Ti-alloys, the mechanism of cooling is significantly different from conventional cooling techniques that involve complex mechanisms such as spray–surface interaction and boiling of droplets. Therefore, a model specifically targeted to understand the heat transfer mechanism taking place at the tool–chip interface with the application of ACF spray system is required.

The objective of this research is to determine the temperature reduction due to impingement of the droplets from the ACF spray system on the heated surface of the tool. This work involves the development of a thermal model that is specific to the ACF spray system used in the machining process. Since the temperature of the tool during machining of Ti-alloys is very high (>600 °C) [2,9], which is much beyond the Leidenfrost point of cutting fluid, the heat transfer mechanism is governed by the film boiling of the impinging droplets. The model is used to estimate the convective heat transfer during the application of ACF spray. This is further used in the machining model where the spray–tool interaction is accounted using a convective boundary condition. In addition, spray–surface interaction model is used to design the ACF spray-system. Experiments are also carried out to validate the model results and to understand the role of carrier gas in the ACF spray system.

The rest of the paper is organized as follows. Section 2 reviews the principle of ACF spray application in machining. The methodology for the thermal model used for estimating the tool temperature is described in Sec. 3. Section 4 presents the model validation and a discussion on the experimental and simulation results is presented in Sec. 5. In Sec. 6, the conclusions of the work are summarized.

Figure 1 shows the schematic of the ACF spray system. It consists of an ultrasonic atomizer at one end that generates monodispersed spray droplets. There are two coaxial nozzles in the system, the droplet nozzle, and the gas nozzle. The low-velocity droplets formed from the atomizer flow through the droplet nozzle are then entrained by the high-velocity gas (air/CO₂) flowing through the gas nozzle. This produces a focused axisymmetric jet of droplets that are impinged at the tool–chip interface. Upon impingement, the droplets interact with the heated tool/chip surface leading to heat transfer and vaporization of droplets that result in cooling the tool/chip surface.

In Eq. (1), v, d, μ, ρ, and σ represent the normal component of velocity, diameter, dynamic viscosity, density, and surface tension of the droplet, respectively. For We < 10, the droplet sticks to the surface. The spreading regime occurs for We > 10 and K_m < 55.7 [10], in which the impact inertial forces dominate and cause spreading of the droplet. For values of K_m > 55.7, the impact inertial forces are so high that splashing occurs and the droplet breaks up into tiny droplets. Splashing is undesirable in machining as it would lead to a reduction in air quality. Therefore, the spray parameters and fluid properties need to be selected appropriately to be able to achieve the spreading regime that will allow the cutting fluid to enter the cutting interface.

The variation of We and K_m with droplet's normal velocity at different droplet diameters is shown in Figs. 2 and 3, respectively. In the figures, threshold values of the spreading regime are indicated by horizontal lines for We = 10 and K_m = 57.7. For droplet size of 12.5 μm, the droplet velocity between 6 m/s and 40 m/s can ensure the spreading regime. For 30 μm droplet size, the droplet velocity range is from 4.2 m/s to 24 m/s. Similarly, for droplet size of 80 μm the range is from 3 m/s to 14 m/s. It is observed that the range of droplet velocities that correspond to the spreading regime is very narrow for the 80 μm sized droplet. This shows that droplet diameter sizes from 12.5 to 30 μm could be used to utilize their wider range of spreading regime velocities, with smaller droplet size providing a greater range of velocities for the spreading regime.

To achieve the droplet velocity for a given droplet size, the ACF spray system parameters including gas nozzle pressure and the distance of spray from the impingement point (Fig. 1) need to be determined. A CFD approach has been used to model the ACF spray system using the spray model and determine the spray distance for a range of spray parameters. In the model, the gas velocity and the consequent droplet velocity are evaluated using the Navier–Stokes and continuity equations. Figure 4 shows the droplet velocities along the spray distance for 12.5 μm and 30 μm size droplets. It is found from the simulation that for droplet diameter of 12.5 μm to be within the spreading regime, the spray distance has to be set at a minimum of 55 mm at 344.7 kPa gas nozzle pressure and 100 mm at 2068.5 kPa, respectively. For 30 μm droplet size, the spray distance has to be set at a minimum of 70 mm for 344.7 kPa and greater than 140 mm for 689.5 kPa and 2068.5 kPa, respectively. The obtained spreading regime velocity is used as an input to the thermal model described below in determining the spreading length of the droplet.

In machining Ti–6Al–4V, the temperature can reach up to 600 °C [2] with cooling using cutting fluid. As a result, it is highly possible that boiling heat transfer takes place at the cutting interface. However, boiling involves different heat transfer regimes including nucleate and film boiling depending on the surface temperature. In order to identify the mechanism that is taking place during machining, a controlled experiment where the WC tool is placed on a hot plate and the cutting-fluid is sprayed on the rake face of the tool is carried out. The plate is gradually heated to over 300 °C and the temperature of the plate/tool is measured with a K-type thermocouple. It is seen that a film is formed for the first few minutes (see Fig. 5(a)). However, with time, nucleate boiling is seen to occur near the cutting edge (Fig. 5(b)) and after 15 min when the temperature is over 300 °C, the droplets impinged from the ACF spray system are seen to be skittering around indicating that Leidenfrost point has been reached and the film boiling may be occurring (Fig. 5). Since the maximum temperature (300 °C) reached in this experiment is much lower than the tool temperature observed during machining Ti–6Al–4V (600 °C), film boiling is expected to occur during the cooling process.

Furthermore, the spray used in this work is a low-dense spray. This is justified by the experimental observations of spray characteristics by Nath et al. [3] under similar experimental conditions as carried out in this work. The spray angle was reported to be in the range of 36.9–46.66 °C. The corresponding diameter of spray cross section at a spray length of 55 mm can be obtained as 36.69–47.44 mm. Due to such large values of spray diameter at the impingement point, the spray can be assumed to be a low dense spray. Therefore, droplet–droplet interaction during spray impingement can be ignored. It can be safely assumed that the heat transfer during the spray cooling process is governed by film boiling of the impinging droplets. The model is not only applicable to Ti and its alloys, but can also be applied to all those materials that involve high cutting temperatures. However, note that this model is only valid for low-dense sprays.

A flowchart of the modeling approach is shown in Fig. 6. It begins with the development of a ACF spray-tool heat transfer model to estimate the heat absorbed by the impinging spray during machining. The heat transfer is characterized by the convective heat transfer coefficient that depends on the spray characteristics and the surface temperature. The obtained heat transfer coefficient along with the heat generated due to the cutting action in machining are used in the FEM-based machining model as convective heat loss from the tool surface and heat generation at the cutting edge, respectively. Lastly, the FEM-based machining model is solved to obtain the tool temperature profile.

A numerical model based on FEM using COMSOL Multiphysics is developed to estimate the temperature profile near the tool–chip interface. The 2D model is a reasonable approximation of the 3D machining process as the tool width is much larger than the depth of cut. The tool geometry taken into account and the boundary conditions used are shown in Fig. 7. The machining parameters are listed in Table 1. The heat generated due to the cutting action in machining is represented as a surface heat flux (q₀) at the tool chip-interface. A convective heat transfer coefficient of 20 W/m² is used at boundaries that are exposed to ambient air. At the far ends of the tool, an adiabatic boundary condition is used.

where F_c, F_t, and b are the cutting force, thrust force, and cut width, respectively.

The convective heat flux boundary condition is applied at the spray-contact zone. The evaluation of the convective heat flux due to the application of ACF spray is described in Sec. 3.3.

In order to estimate the convective heat flux due to the ACF spray, a modeling of heat transfer between the impinging droplets and the tool surface is carried out. When the droplet impinges on the heated tool surface, the liquid in contact with the high temperature surface vaporizes immediately, forming a vapor film. Subsequently, owing to the weight of the liquid above the vapor, some of the vapor molecules escape out. However, the continuous heat transfer between the hot surface and the liquid ensures continuous generation of vapor, and hence, the film is maintained. The heat transfer from the tool surface now occurs through the vapor film. As a result, determination of the vapor film thickness will provide an estimate of the heat flux, $q″$ absorbed by the impinged droplet.

The configuration of the ACF spray droplet on the heated surface is shown in Fig. 8, which depicts an axisymmetric droplet floating on a vapor film of thickness, δ due to the Leidenfrost effect. The surface temperature is designated as T_s and the liquid is assumed to be at the normal boiling temperature, T_b. The surface at the interface of liquid and vapor is denoted by S_BC and is assumed to be flat. The spreading droplet is assumed to be a spherical cap with base diameter, D. The heat flux through the vapor film can be written as

where k_v is the thermal conductivity of the vapor film.

The transient problem of heat transfer of a spreading droplet is simplified into a quasi-steady-state problem. The heat flux is determined using the quasi-steady vapor film thickness, δ, which is evaluated using the model of Myers and Charpin [13]. The governing equations for vapor phase can be written as [13]:

where v represents axial component of vapor velocity in the film, ρ_v is the vapor density, ρ_l is the liquid density, ds/dt represents the surface (S_BC) recession rate due to evaporation.

It is assumed that the liquid is at a constant temperature equal to the boiling temperature. ρ_l is the liquid density, L_v is the latent heat of vaporization. Equation (13) represents the Stefan's condition that describes evaporation due to the heat flux from liquid to vapor.

where df/dt represents the evaporation rate over the surface S_BAC. Since evaporation on surface S_BAC is very small compared to that of vaporization at the liquid–vapor interface, it is ignored.

The evaluation of base diameter of the droplet, D in Eq. (19) is discussed in Sec. 3.4.

Due to the spreading nature of the droplet, its diameter continuously varies. The droplet diameter reaches its maximum spreading length when all of its kinetic energy is converted into surface energy. This is schematically shown in Fig. 9. However, due to viscous forces, the droplet is compressed. As a result, the droplet diameter oscillates.

Substituting for ζ_max from Eq. (21) into Eq. (20), the value of α is obtained, which is then used in determining ζ_max and hence, the maximum spreading length, D_max. Subsequently, the value of D can be obtained and the vapor film thickness (δ) can be evaluated using Eq. (19). Finally, the heat flux (⁠$q″$⁠) at the droplet-tool surface can thus be obtained using Eq. (5).

Experiments are conducted to collect the temperature data of machining Ti-alloy using tungsten carbide (WC) cutting inserts. A Mori Seiki lathe machine is used for turning operation of the Ti–6Al–4V alloy. Cutting conditions used are shown in Table 2. The tests were carried out for one cutting pass of length equal to 2 cm. The setup used for measuring the temperature of the tool is shown in Fig. 10. A K-type thermocouple is placed inside the WC tool through a slot machined using electrical discharge machining (EDM) and the temperatures at various distances for the cutting edge are measured. Figure 11 shows the positions of the slots in the WC tool insert. The slot is perpendicular to the tool flank, allowing thermocouple placement as close as 0.15 mm from the cutting edge without risk of breakage of the thermocouple wire during machining operations. Slot distances 0.15 mm, 0.25 mm, 0.35 mm, and 0.45 mm from the cutting edge are used for the experiments. The distance from the engaging cutting edge to the thermocouple tip was fixed at 0.15 mm for all the measurements. The cutting fluid used in the ACF spray system is S-1001 at 10% dilution in water. The properties of the fluid are given in Table 3. Flow-rate of 20 ml/min is used for the fluid. CO₂ gas and/or air are supplied to the front of the nozzle using a gas supply tube. Gas pressure is kept at 344.7 kPa and spray distance at 55 mm. The temperature data is collected after a sufficiently long time when the machining process is close to steady-state conditions so that the data can be used for a fair comparison with the 2D steady-state model developed in this work.

To calculate q₀, the secondary shear zone heat source is considered as described in Ref. [12]. Tool-chip contact lengths for these conditions are used from the experimental work by Hoyne et al. [2] is used to calculate the cutting interface area over which the net heat flux acts. Table 2 also shows the contact lengths for the different cutting conditions. The tool faces that are exposed to surrounding gas have convective surface boundary conditions with convective heat transfer coefficient of 20 W/m². Thermal conductivity and specific heat capacity of the WC tool are taken to be 88 W/m K and 292 J/kg K, respectively. The net heat flux boundary is applied to the cutting interface. The tool domain is divided into finite elements of the size of 0.05 mm and the conduction equation is solved for each of the nodes created to generate the temperature field of the tool during cutting. Figure 12 shows the contour plot of the predicted temperature field in the tool. The horizontal axis represents the length along the rake face and the vertical axis represents the thickness of the tool.

Figure 13 shows the temperature of the tool predicted by the thermal model as well as mean measured temperature ±std. dev. for replicated trials along the cutting edge for the three cutting conditions. The data shows that the predicted temperature profiles follow the decreasing trend as the one created by the discrete measured values. Also, the model predictions match reasonably well within the experimental measurements taken beyond 0.15 mm from the cutting edge and lie within the limits of experimental errors. Note that Hoyne et al. [2] who employed a tool-work thermocouple method to measure temperature reported similar temperatures at distances away from the cutting edge. However, the temperature at the cutting edge is seen much higher than predicted from the model. As reported in Ref. [2], it is not well understood if the tool-work thermocouple method yields correct temperature gradient from the cutting edge. Nevertheless, the model could under-predict due to the assumption of uniform heat flux at the tool–chip interface. In reality, the heat generation will be highest at the cutting edge and decreases away from it along the rake face. Further improvements in the machining model with consideration to a more accurate heat generation close to the cutting edge may also result in higher values of temperature at the cutting edge. The vapor formation from droplet evaporation close to the cutting edge may also be a curtailing factor during the cooling process.

Note that the model predicts the results with a reasonable accuracy. However, it assumes that the droplet–droplet interaction on the tool surface that can lead to the formation of a blanket of liquid-film layer over the tool surface is negligible. Typically, this would be the case for large droplets or for a dense spray. However, for a microscopic droplet and a low dense spray, the proposed model would be perfectly applicable as is the case in ACF spray system.

Figure 14 shows the temperature profile of the tool from the cutting edge for different spray and cutting conditions. It is observed that the tool temperature at the cutting edge is as high as 1200 °C for dry cutting at a feed-rate of 0.2 mm/rev and speed of 80 m/min. This high temperature is due to the high strength and poor conductivity of Ti-alloy. However, using ACF spray system with high-velocity air shows a considerable decrease in the tool temperature. The drop in temperature is even higher when CO₂ is used. The temperature drop at the cutting edge is 40 °C higher for CO₂ as a carrier gas as compared to that of air. This may be because of expansion of CO₂ when released from initial high-pressure supply. The expansion causes the gas to cool down and lowers the temperature of the gas. The experimentally measured temperature values of CO₂ and air at 55 mm for the spray parameters used in this work are −10 °C and 18 °C, respectively. This results in a higher cooling effect of CO₂ than air. Therefore, ACF spray system with CO₂ as the carrier gas has an advantage over using air due to an increased cooling effect.

The predicted tool temperatures when cutting conditions are varied with the ACF-CO₂ spray is also shown in Fig. 14. It is seen that the temperature at the cutting edge is lowest with feed-rate of 0.15 mm/rev and speed of 80 m/min, and highest with feed-rate of 0.2 mm/rev and speed of 110 m/min. This shows that the temperature increases with an increase in both the feed-rate and/or speed, although it is not as high as that for dry cutting. Also, there is a decreasing trend in the temperature for all cutting conditions at distances away from the cutting edge. However, for the most conservative cutting conditions, the thermal gradient between 0.2 mm and 0.3 mm is slightly larger than those for the other two conditions. This could be attributed to the small tool-chip contact length (see Table 2) associated with the cutting conditions of 0.15 mm/rev and 80 m/min. This also suggests that although the temperature may not be as high as the values for other conditions, there is a possibility of thermal degradation due to this steeper thermal gradient.

The model is also extended for finish turning of titanium alloy. In finishing operation, the most important aspect is the quality of surface finish. If the tool is worn out, the surface will have higher roughness. Since high temperature reduces the lifespan of the tool, it will also affect the surface finish of the workpiece. Figure 14 shows the temperature profile for finish turning at 0.06 mm/rev and 80 m/min predicted by the model. For finish turning operations, low feed-rates are desired to achieve a better surface finish. The contact length for finish turning at the specified cutting conditions was obtained from extrapolating data in Table 2. It is observed that the overall temperature is low compared to other cutting conditions described. This data verifies that at low feed-rates, the temperature rise in the tool is relatively small. Therefore, the ACF spray system provides a cooling effect to keep the cutting temperature below 550 °C. Above 550 °C, titanium starts to react with tool materials [16] and cause degradation of the tool. Hence with the ACF spray system, the carbide tool wears slowly and has longer tool life.

In this study, a thermal model to predict the tool temperature under the application of ACF spray coolant is developed considering the phenomena of droplet impingement dynamics and film boiling of droplets. Additionally, a spray model to determine the minimum spray distance to ensure droplets spread on the heated surface has been formulated. Based on the analysis made from the model results, the following conclusions can be drawn.

1. (1)

   Boiling is one of the principal heat transfer mechanisms that takes place during ACF spray cooling. With tool temperature much above 600 °C, film boiling is the dominant mechanism that occurs at the cutting edge.

2. (2)

   The predicted temperature profiles follow the decreasing trend as also seen for the measured data. Also, the model predictions match reasonably well within the experimental measurements and lie within the limits of the experimental errors.

3. (3)

   Cutting conditions including feed-rate and speed influence the maximum temperature at the cutting edge for machining with ACF spray cooling. However, the temperatures are not as drastically high as in dry cutting.

4. (4)

   In finish turning of titanium alloy, the ACF spray system provides a cooling effect to keep the cutting temperature below 550 °C. As a result, the carbide tool can survive longer without having any significant wear.

5. (5)

   Droplet size range of 12.5–30 μm has been observed to be suitable for providing a large range in spray distance in the ACF spray system. Increasing the droplet size will narrow the velocity range required for spreading of the droplet.

6. (6)

   The minimum spray distance for a droplet of sizes 12.5 μm and 30 μm to be in the spreading regime are evaluated as 55 mm and 70 mm, respectively, for a pressure of 344.7 kPa.

The authors are thankful to the National Science Foundation (NSF) for supporting this research under the Grant No. NSF CMMI 12-33944.