Modeling and Monitoring of the Tool Temperature During Continuous and Interrupted Turning with Cutting Fluid

Abstract

In metal cutting, a large amount of mechanical energy converts into heat, leading to a rapid temperature rise. Excessive heat accelerates tool wear, shortens tool life, and hinders chip breakage. Most existing thermal studies have focused on dry machining, with limited research on the effects of cutting fluids. This study addresses that gap by investigating the thermal behavior of cutting tools during continuous and interrupted turning with cutting fluid. Tool temperatures were first measured experimentally by embedding a thermocouple in a defined position within the tool. These experimental results were then combined with simulations to evaluate temperature changes, heat partition, and cooling efficiency under various cutting conditions. This work presents novel analytical and numerical models. Both models accurately predicted the temperature distribution, with the analytical model offering a computationally more efficient solution for industrial use. Experimental results showed that tool temperature increased with cutting speed, feed, and cutting depth, but the heat partition into the tool decreased. In continuous cutting, cooling efficiency was mainly influenced by feed rate and cutting depth, while cutting speed had minimal impact. Interrupted cutting improved cooling efficiency, as the absence of chips and workpieces during non-cutting phases allowed the cutting fluid to flow over the tool surface at higher speeds. The convective cooling coefficient was determined through inverse calibration. A comparative analysis of the analytical and numerical simulations revealed that the analytical model can underestimate the temperature distribution for complex tool structures, particularly non-orthogonal hexahedral geometries. However, the relative error remained consistent across different cutting conditions, with less error observed in interrupted cutting compared to continuous cutting. These findings highlight the potential of analytical models for optimizing thermal management in metal turning processes.

1. Introduction

During metal cutting, considerable heat is generated due to intense friction between the tool and workpiece, as well as the plastic deformation of the workpiece material in the cutting zone. Thermomechanical studies conducted by Taylor and Quinney revealed that only a small fraction of plastic work is stored as internal energy in the metal, with the majority dissipated as heat [1]. Extensive experimental studies have demonstrated that approximately 90% of the mechanical work is converted to heat during metal cutting [2]. Part of this heat transfers to the tool, causing a rapid temperature rise near the tool tip. Elevated temperatures can reduce the hardness and strength of the tool material, promote chemical reactions like oxidation and diffusion between the tool and workpiece materials, and accelerate tool wear [3]. For the workpiece, high cutting temperatures combined with mechanical stresses can lead to surface damage, including oxidation, corrosion, phase transformation, and recrystallization. Liu et al. [4] examined the effects of temperature on the workpiece surface through entropy changes. Further details on temperature effects on workpiece quality are available in review papers [5,6]. In interrupted cutting or when using cutting fluid, tool temperature can fluctuate significantly, leading to thermal fatigue and potentially causing tool fracture or failure [3]. Furthermore, high temperatures in the cutting area also negatively affect the surface quality of the workpiece. Therefore, understanding heat generation and transmission in metal cutting is crucial for improving workpiece quality and tool life.

To investigate the impact of cutting temperature on machining outcomes, various methods have been developed. Early approaches began with the balance (calorimetric) method, introduced in 1949 [7]. In this method, chips formed in the cutting zone are collected in a calorimetric vessel filled with water. By applying the energy conservation law and thermal balance, the temperature difference is measured between the vessel with water alone and the vessel with water and chips. Although applicable to any workpiece and tool materials, this method is now largely of historical interest due to its low accuracy and only approximate estimations of mean chip temperatures [8]. With advancements in sensor technology, modern temperature measurement techniques for machining processes are primarily categorized into infrared (IR) radiometry and thermocouple measurements [9]. Infrared radiometry detects surface-emitted radiation, enabling temperature estimation via the Stefan–Boltzmann law. This method offers fast response times and direct temperature distribution measurement without contact. Heigel et al. [10] used high-speed thermography during orthogonal cutting of titanium alloys, finding that peak temperature increased with cutting speed, while cutting and thrust forces remained unchanged. Similar results were observed by Soler et al. [11] in AISI 4140 cutting tests. Soloer et al. [11] also employed high-speed thermography to measure tool flank temperatures, achieving less than 3% deviation in numerical simulations of tool/chip contact temperatures under varying cutting conditions. Recent findings by Barzegar et al. [12] indicated that increasing the cutting edge radius significantly raises the temperature. While infrared thermography offers significant advantages, it also has limitations. Accurate measurements depend on precise surface emissivity data, which requires temperature calibration of the machined surface. In addition, not all machine tools and machining processes are optically accessible for radiometric measurements, especially those that work with cutting fluids.

A solution for overcoming optical accessibility issues in temperature measurement is to embed a thermocouple or pyrometer fiber directly into the cutting insert, which is typically installed into small holes in the cutting tool made via Electrical Discharge Machining (EDM). Chen et al. [13] investigated the dry turning of AISI 52100 using a CBN tool with an embedded thermocouple. Their measurements, combined with numerical modeling, revealed that the peak temperature on the machined surface in hard turning occurs along the intersection of the cutting edge and the machined surface. Kryzhanivskyy et al. [14] introduced a method to embed multiple thermocouples simultaneously, enabling reverse derivation of the tool temperature distribution and quantifying heat inflow during dry turning. Similarly, Zhang et al. [15] used multiple thermocouples to study the effect of tool coating on temperature during turning. Similar methods can also be applied to pyrometers. Han et al. [16] embedded a ratio pyrometer fiber into the tool to examine the impact of wear on tool temperature, finding that tool wear increased significantly with rising cutting temperatures. However, ratio pyrometers are only effective at temperatures above 150 °C. Current research demonstrates that the embedded multiple thermocouple technique is robust and adaptable to various cutting conditions, including those involving cutting fluids. The main limitation of thermocouples is their response time, with the fastest thermocouples requiring 10 milliseconds or more, making them unsuitable for capturing rapid temperature fluctuations during interrupted cutting or transient temperature changes. Additionally, since thermocouples provide point measurements, estimating the overall temperature field requires inverse derivation using a reliable temperature model.

Point temperature measurements can be used to calibrate temperature models, allowing for the inverse determination of temperature distribution. Transient temperature models are typically categorized into numerical and analytical approaches. Norouzifard et al. [17] embedded K-type thermocouples in the tool holder to measure temperatures at various locations during the machining of AISI 1045 and AISI 304. Their numerical models accurately predicted temperature distributions, showing strong agreement with experimental data. Sharma et al. [18] utilized thermography to measure temperatures during dry machining and thermocouples for turning AISI 304 steel with cutting fluid. By inversely calculating the heat transfer into the tool from dry machining temperatures and applying computational fluid dynamics (CFD) simulations, they achieved an error margin of 5.79% between simulation and experiment. Yi et al. [19] measured tool temperatures with K-type thermocouples and simulated them using finite element (FEM) software, reporting a 4.04% discrepancy between simulated and experimental results. Existing studies demonstrate that numerical simulations can accurately model tool temperature during the turning process, even when accounting for the effects of cutting fluids. However, such simulations often require commercial software, substantial computing resources, and expertise in simulation, which can significantly limit their applicability, particularly in industrial environments.

Analytical temperature models provide a faster and more user-friendly alternative to numerical models, as they typically do not require specialized software. These models simulate temperature variations caused by non-uniform and intermittent heat sources through the superposition of point heat sources. Karaguzel et al. [20] validated the analytical model for tracking rapidly changing tool temperatures during face milling using miniature thermocouples. Oliveira et al. [21] further advanced the analytical model by considering the effects of tool coatings on tool temperature during orthogonal cutting. More recently, the authors of this paper have introduced a transient model that incorporates convective conditions for orthogonal cutting and improves the prediction accuracy of the temperature distribution under the cutting fluid in both continuous and interrupted cutting scenarios [22]. Despite their advantages, analytical models simplify tool geometry, often assuming a rectangular parallelepiped shape, which can lead to inaccuracies for non-rectangular geometries. Additionally, no temperature model currently accounts for convective cooling during turning. This work aims to address this research gap.

In this study, steady-state tool temperature during continuous and interrupted turning of AISI 1045 steel was measured under various cutting and cooling conditions using thermocouples embedded in carbide inserts. These measurements helped determine heat transfer to the tool and the average convective cooling coefficient of the cutting fluid on the tool surface via a numerical model. Additionally, a new transient analytical turning tool temperature model was developed. This research project is intended to answer the following questions: What is the relationship between heat partition to the tool and cutting conditions? How does this relationship vary between continuous and interrupted cutting? How accurate is the analytical model in simulating turning tool temperature, given the assumption of a rectangular parallelepiped tool geometry? The scope of this paper is limited to the temperature of the tool and the heat transferred to it and does not cover chip formation mechanisms or the overall temperature distribution in the cutting area.

The next section outlines the principles of the temperature measurement experiments and describes the tools and workpieces used. Section 3 details the principles and parameters of the numerical and analytical models. The derivation of the analytical model is presented in Appendix A. Section 4 compares the relationship between heat partition and cutting parameters derived from the models, highlighting differences between numerical and analytical results. This paper concludes with a summary of the main findings and suggestions for future research.

2. Experimental Setup for Model Validation

In this study, external longitudinal turning of AISI 1045 steel was performed using carbide tools under various process parameters and cooling conditions. Tool temperature and process force components were measured during the turning process with the application of cutting fluid. The experimental results serve as a dataset for validating numerical and analytical models. This section provides a detailed description of the experimental setup for temperature measurements and the characteristics of the tools and workpieces used.

2.1. Experimental Setup for Temperature Measurement in Longitudinal Turning

The tool temperature is a key parameter in quantifying convective cooling with cutting fluid. The heat distribution along the cutting edge depends on the tool’s geometry and engagement conditions. In the turning process, varying chip thickness along the cutting edge results in uneven heat distribution and shifts in the temperature gradient. The measurement method depicted in Figure 1 was employed to capture this temperature distribution.

The temperature profile was measured at two points on the tool, as shown in Figure 1a. To position the sensors, a 0.5 mm diameter hole was drilled using Electrical Discharge Machining (EDM), located 1.8 mm from the top surface and 0.8 mm from the tool flank face. Two thermocouples were placed 2 mm apart along the main cutting edge. The choice of thermocouples was determined by the required measuring range and rate. Previous measurements in orthogonal cutting [22] showed that the tool temperature near the cutting edge rises by over 200 °C within one second, reaching a steady state after about 5 s. To measure both transient and steady-state temperatures, a Type K thermocouple from TC Mess- und Regeltechnik GmbH (Mönchengladbach, Germany) was selected, offering a measuring range of 0 to 1100 °C and a 15 ms response time. The thermocouple has a diameter of 0.25 mm. Data acquisition was conducted using the NI 9214 acquisition card from National Instruments GmbH (Austin, TX, USA), which features 16 channels for synchronized recording of multiple sensor signals.

Machining tests were performed on a DMG NEF-600 CNC lathe from DMG Mori AG (Bielefeld, Germany), as shown in Figure 2. PCLNR-type ISO tool holders Sandvik Tooling Deutschland GmbH (Düsseldorf, Germany), featuring a cooling channel and a nozzle for rake face cooling, were used and mounted on a Kistler (Sindelfingen, Germany) 9129B piezoelectric dynamometer for cutting force measurements. Cutting fluid was supplied by a ChipBLASTER (Leonberg, Germany) WVHP6-60 high-pressure unit, with a bypass valve for pressure regulation. The cutting fluid used was Vasco TP 519, a water-soluble coolant from Blaser Swisslube AG (Rüegsau, Switzerland), at an 8% concentration, specifically optimized for machining carbon steels and nickel-based alloys.

The thermocouple was initially secured with a sensor holder, as shown in Figure 2d. The holder includes two guide channels to direct the measuring probe to the cutting insert and serves two main functions: protecting the thermocouple from chips and cutting fluid, and preventing the measuring probe from slipping out. The thermocouple was then routed to the cutting insert through the EDM-drilled hole and lubricated with thermally conductive paste to ensure reliable contact with the tool. Subsequent experiments confirmed that this setup securely fixed the sensor in place.

The tests used an indexable insert with C geometry, made of H13A carbide, which is suitable for both finishing and roughing over a wide range of parameters. H13A carbide is specifically designed for machining ISO S (heat-resistant superalloys) and ISO M (stainless steels). This tool material was selected for two main reasons: its thermal properties were previously measured by the author [22], facilitating modeling, and it is widely used in wear studies [23,24,25], enabling straightforward comparison with other research findings. The large corner angle (${ϵ}_r$ = 80°) also facilitated the accurate positioning of measurement sensors. The workpiece material was AISI 1045 carbon steel, with its physical properties summarized in Figure 3. Both microstructure and hardness were measured along the central axis and radially at various points, confirming a homogeneous distribution.

A solid shaft with a 250 mm diameter was used for the continuous turning. For the interrupted turning, a VDI 3324-standard fixture was employed, as illustrated in Figure 4. This fixture securely clamps four 55 mm wide AISI 1045 workpiece bars.

2.2. Experimental Procedure and Test Plan

The experimental procedure was divided into two groups: dry machining and machining with cutting fluid. Each group was further subdivided into continuous and interrupted turning. Initially, machining tests were conducted under dry conditions to measure tool temperature. These results were used both to determine heat partitioning under different cutting conditions and as a reference for assessing the impact of cutting fluid. Subsequently, tests with cutting fluid were performed using the same cutting parameters. The cooling effect was evaluated by comparing tool temperatures between tests with and without cutting fluid.

For continuous cutting, a cutting fluid pressure of 80 bar was selected, which corresponds to the typical cutting fluid supply pressure in modern CNC lathes. The experimental results are in good agreement with industrial production conditions. For interrupted cutting, a lower pressure of 10 bar was used. This choice was based on the fact that during the non-cutting phases of interrupted cutting, the cutting fluid cools the tool sufficiently, and the intermittent nature of the process results in short chips that do not require high pressure for effective chip breaking. The investigated parameters are summarized in

Table 1. Cutting parameters for temperature analysis.

${\mathit{v}}_{\mathit{c}}$ /m/min	f /mm	${\mathit{a}}_{\mathit{p}}$ /mm	Cutting Fluid	Process Type
70	0.1; 0.2; 0.3	0.8; 2.5	Dry	Continuous
120	0.1; 0.2; 0.3	0.8; 2.5	Dry	Interrupted
70	0.1; 0.2; 0.3	0.8; 2.5	80 bar	Continuous
120	0.1; 0.2; 0.3	0.8; 2.5	10 bar	Interrupted

.

The test plan includes both continuous and interrupted cutting, with two cutting speeds ($v_c$), three feed rates (f), and two cutting depths ($a_p$), each conducted under dry conditions and with cutting fluid. For both continuous and interrupted cutting, there are 24 combinations (2 × 3 × 2 × 2), totaling 48 test conditions. Each condition is tested twice to ensure statistical reliability. This design evaluates the influence of process parameters and cutting fluid on tool temperature and heat partitioning. The empirical results will later support the evaluation and validation of simulation models.

3. Model Setup for Tool Temperature Simulation

This paper presents two models for simulating tool temperature during turning with cutting fluid: an analytical model and a numerical model. As discussed in the introduction, the numerical model accurately accounts for the actual tool geometry and predicts tool temperature distribution with an error margin of less than 10%. Therefore, it is used to determine heat flow into tool and derive the temperature distribution within the tool. The numerical simulation results serve as a benchmark for evaluating the accuracy of the analytical model developed in this paper. The following subsections outline the principles of both models and the steps involved in calculating the temperature field.

3.1. Numerical Model for Temperature Simulation Considering the Cutting Fluid

This work developed a numerical model using the commercial FEM software ABAQUS version 2021. The geometric 3D model of the tool was first measured with an Alicona (Raaba, Austria) Infinite Focus G5 microscope and then imported into the simulation software via a STEP file. The heat source on the tool surface corresponded to the contact area between the tool and the chip, determined through a Keyence (Neu-Isenburg, Germany) VHX optical microscope based on the color change of the tool surface, as shown in Figure 5.

In machining processes, heat is generated mainly in three zones: the primary shear zone, the tool–chip interface, and the tool-workpiece interface. The primary shear zone produces heat due to plastic deformation as the material shears to form a chip. At the tool–chip interface, known as the secondary deformation zone, friction between the tool and chip generates significant heat. Additional heat arises at the tool flank face, or the tool-workpiece interface, due to friction with the newly machined surface [26]. Among these zones, the tool–chip interface is the main point where heat transfers to the tool, as this area has the largest contact surface and highest temperature gradient. However, heat in this zone is not uniformly distributed. The heat flux decreases from the cutting edge toward the boundary of the contact area, influenced by variations in friction, contact pressure, and surface topography. With a contact length of less than 0.5 mm, which is very short relative to the cutting tool width of 127 mm, the model was simplified by treating the heat source as uniformly distributed.

On the major flank face of the cutting tool, heat is generated due to friction between the workpiece and the rear surface of the tool. This contact distance is relatively small when the tool is new, but it gradually increases with tool wear, especially as flank-face wear expands. In this study, the tool and experimental conditions were based on an unworn tool, so the heat source distribution on the flank face was minimal compared to that on the rake face. To reduce model complexity and improve calculation efficiency, the heat source distribution on the flank face was therefore ignored.

The cutting fluid primarily cooled the tool rake face, while the rest of the tool remained shielded by the workpiece and did not receive direct cooling. The top surface of the tool (highlighted in Figure 5) was modeled as a convective boundary, and the major and minor flank faces were treated as adiabatic boundaries. Contact heat transfer occurred between the lower and rear surfaces of the cutting tool, which were in contact with the tool holder. The tool holder was maintained at room temperature. Given that the tool holder is made of stainless steel, a heat transfer coefficient of 3.8 kW/m²·K between the cutting insert and holder was assumed [27]. Frekers et al. [28] experimentally observed that, under contact pressures below 10 MPa, the heat transfer coefficient between contacting carbon steels is typically less than 5 kW/m²·K, supporting the validity of this assumption. To further improve simulation accuracy in future studies, this assumption should be experimentally verified as proposed in [28]. An implicit solver was used for the temperature simulation, with an initial time increment of 6 × 10⁻⁴ s, a maximum increment of 0.6 s, and a minimum increment of 6 × 10⁻⁶ s. Time increment control was set to automatic. This step size selection is based on the results of stability tests. To accurately capture the tool’s geometric details, a tetrahedral unstructured mesh (DC3D4) with a global mesh size of 0.1 mm was applied, totaling 2,169,379 elements. The mesh configuration follows standard guidelines for cutting simulations to ensure high-resolution temperature distribution [29].

Table 2. Properties of H13A carbide (at 27 °C) [22].

Specific Heat Capacity	Density	Thermal Conductivity
${\mathit{c}}_{\mathit{p}}$/J/(kg·K)	$\mathit{\rho }$/kg/m3	$\mathit{\kappa }$/W/(m·K)
198	14,800	116

summarizes the physical parameters of the tool materials used in the simulation.

3.2. Analytical Model for Temperature Simulation Considering the Cutting Fluid

The analytical model in this paper assumes the cutting tool to be a rectangular, three-dimensional block heated by a square heat source, as shown in Figure 6. This simplification enables direct integration of the governing equation without requiring a numerical simulation solver. Like the numerical model, the analytical model focuses on cooling of the rake face, applying convective boundary conditions to the upper surface, while the major and minor flank faces are exposed to room temperature air and act as adiabatic boundaries.

The tool connects to the tool holder in the X, Y, and Z directions, effectively treating it as a semi-infinite body. This boundary condition differs from that in the numerical simulation, which excludes heat transfer between the tool and holder. Since the tool holder remains at room temperature, heat flows continuously through the underside of the cutting tool, approximating an infinite boundary—a common simplification in analytical models [22,30]. However, as ABAQUS 2021 does not support infinite boundary conditions, the numerical model instead applies a contact heat transfer condition. While these boundary differences affect model results, the impact on error is minimal. The evaluation focuses on the steady-state temperature, and the underside of the tool is sufficiently far from the heat source, resulting in a small temperature difference with the surrounding area. The influence of boundary conditions will be explored further in future work.

Equation (1) describes the tool’s temperature, where $\dot{q}\left(\tau \right)$ represents time-varying heat sources, $\alpha$ is the thermal diffusivity, $\kappa$ is the thermal conductivity, and h is the convection coefficient. Appendix A provides the derivation of Equation (1).

$$\begin{array}{cc}\hfill T\left(x,y,z,t\right)={\displaystyle \frac{\alpha }{\kappa }}·{\int }_0^t& {\displaystyle \frac{1}{4}}·\dot{q}\left(\tau \right)·\left\{{\displaystyle \frac{2}{\sqrt{4\pi \alpha \left(t-\tau \right)}}}exp\left[-{\displaystyle \frac{z^2}{4\alpha \left(t-\tau \right)}}\right]-{\displaystyle \frac{h}{\kappa }}exp\left[{\displaystyle \frac{h}{\kappa }}z+\alpha {\displaystyle \frac{h^2\left(t-\tau \right)}{{\kappa }^2}}\right]·\right.\hfill \\ & \left.erfc\left({\displaystyle \frac{z}{\sqrt{4\alpha \left(t-\tau \right)}}}+{\displaystyle \frac{h}{\kappa }}{\left[\alpha \left(t-\tau \right)\right]}^{{\displaystyle \frac{1}{2}}}\right)\right\}·\left\{-erf\left({\displaystyle \frac{y-a_p}{\sqrt{4\alpha \left(t-\tau \right)}}}\right)+erf\left({\displaystyle \frac{y+a_p}{\sqrt{4\alpha \left(t-\tau \right)}}}\right)\right\}·\hfill \\ & \left\{-erf\left({\displaystyle \frac{x-h_e}{\sqrt{4\alpha \left(t-\tau \right)}}}\right)+erf\left({\displaystyle \frac{x+h_e}{\sqrt{4\alpha \left(t-\tau \right)}}}\right)\right\}\mathrm{d}\tau +T_r\hfill \end{array}$$

(1)

The temperature distribution was determined by integrating the equation over time, resulting in a first-order integral with a single variable. A key advantage of this simulation model was its simplicity, allowing for temperature distribution calculations at any time without requiring commercial software. In this study, the Python SciPy version 1.14 integrator solved the model, with solution times of approximately 1 min for a 10-s continuous cutting process and around 3 min for interrupted cutting. In contrast, numerical simulations required about 2 h for continuous cutting and 72 h for interrupted cutting. The numerical simulation in this paper uses an industry-standard scheme, though it is not the most efficient from a research perspective. Research by Ulutan et al. indicates that the finite difference method can significantly increase computational efficiency in numerical temperature simulations [31]. However, as this method requires programming or specialized software, it can be challenging for industry to adopt. In the following sections, both numerical and analytical models are used to analyze tool temperature during turning.

4. Experimental and Simulation Results and Discussion

This section discusses the experimental and simulation results in two subsections. First, the process force components and tool temperatures during continuous turning under varying cutting conditions are analyzed. By combining the simulation model with measured temperature data, the heat input to the tool and the heat partition in the cutting zone are determined. The model also accounts for convective cooling, allowing the convective cooling coefficient on the tool rake face from the cutting fluid to be inversely derived from the temperature measurements. The second subsection examines heat transfer and convective cooling during interrupted turning. The constantly changing loads on the tool during interrupted cutting significantly affect the heat input and temperature fluctuations. In addition to analyzing the thermomechanical loads on the tool, the results of both numerical and analytical models are compared, and possible reasons for discrepancies are discussed.

4.1. Results of Continuous Turning

During cutting, the cutting force not only indicates the mechanical load on the tool but also directly influences the temperature in the cutting zone. Approximately 90% of the mechanical energy generated during metal cutting is converted into heat [2]. This mechanical energy can be quantified by the product of the cutting force and cutting speed. Figure 7 illustrates the process force components during continuous turning under various cutting parameters, comparing dry machining with the use of a $p_{cf}=$ 80 bar cutting fluid supply.

The force measurement results show that the cutting force increased significantly with higher cutting depth $a_p$ or feed rate f in both dry and fluid-assisted machining. This is due to the larger material removal rate and uncut chip cross-section, both of which require greater energy for chip formation. However, when cutting depth and feed rate were held constant, the influence of cutting speed on the cutting force was minimal. This can be explained by the fact that cutting force is primarily influenced by the uncut chip cross-section, material removal rate, and friction at the tool–chip interface. At higher cutting speeds, thermal softening of the material can occur, facilitating easier material shearing and counteracting any potential force increase, leading to a relatively constant cutting force.

The use of cutting fluid generally reduced cutting force by lowering friction and decreasing the load on the cutting edge. This reduction became more pronounced at lower cutting speeds and greater depths of cut. At lower speeds, the longer contact time allowed the cutting fluid to penetrate the cutting zone more effectively, thereby reducing friction. In contrast, at higher speeds, shorter contact times limited the fluid’s effectiveness. Similarly, at greater depths of cut, increased friction and heat generation made the friction-reducing properties of the cutting fluid more critical. In shallow cuts, the lower friction resulted in a less pronounced effect from the cutting fluid.

Figure 8 illustrates the maximum contact thickness ($h_e$) and contact area (A) between the tool and workpiece under various conditions, measured with an optical microscope (see Figure 5). The maximum tool–chip contact thickness generally increased with feed rate, displaying a consistent trend across conditions. The results show that the contact thickness was approximately 2.5 times the feed. At a feed rate of f = 0.1 mm, the contact thickness remained relatively stable with increasing speed. However, at feed rates of f = 0.2 mm and 0.3 mm, the contact thickness decreased notably.

The reduction in contact thickness with increasing cutting speed occurred due to several factors. Higher speeds generated more heat at the tool–chip interface, causing thermal softening of the workpiece material. This softening reduced the material’s strength, making it easier to shear, which decreased chip compression and shortened the contact length. Additionally, the elevated temperature reduced adhesion between the tool and chip, allowing the chip to slide more easily over the tool surface. Together, thermal softening and reduced adhesion explained the observed decrease in contact thickness at higher speeds, particularly at feed rates of f = 0.2 mm and 0.3 mm.

The orange bars in Figure 8 represent the measured tool–chip contact area, corresponding to the second shear zone. This zone generated significant heat due to friction between the tool and chip. The pressure distribution in this area was uneven, leading to a non-uniform distribution of frictional and contact heat transfer. However, since this contact area was very small (less than 1.8 mm²) compared to the entire tool surface, the model analysis in this paper assumed uniform heat distribution within this zone. At a cutting depth of $a_p$ = 0.8 mm, the entire contact area remained confined to the tool corner. At $a_p$ = 2.5 mm, the main cutting edge engaged with the workpiece over a larger area, making the feed rate more influential on the contact area due to geometric factors.

Cutting parameters influenced both the contact thickness and the chip shape. Figure 9 illustrates the chip morphology during dry machining under various cutting conditions. At a shallow cutting depth $a_p$ = 0.8 mm and a low feed rate f = 0.1 mm, the chip was thinnest, and due to its low ductility and strength, helical chip segments formed. When the cutting depth remained at $a_p$ = 0.8 mm but the feed rate increased to f = 0.2 mm, long helical chips were produced. At a greater cutting depth $a_p$ = 2.5 mm and a feed rate below f = 0.1 mm, long spiral and snarled chips appeared.

Increasing the feed rate promoted chip breakage as thicker chips formed, leading to higher stress concentrations at the tool–chip interface. The resulting increase in stress and strain rate caused fracture due to enhanced shear forces and ductile sliding fracture. At greater depths of cut, upward-curved spiral chip segments formed because the corner radius had minimal influence, allowing the chip to flow almost orthogonally to the chip groove geometry in the tool corner, causing it to curve upward. Conversely, at lower depths of cut, the corner radius had a stronger effect, resulting in pronounced lateral curvature of the chip and the formation of predominantly helical chips [32].

The cutting force closely related to the temperature in the cutting area, as the product of cutting force and cutting speed represented the total mechanical work of the cutting process. Approximately 90% of this mechanical work converted into heat during cutting [2]. In this study, the heat transferred to the tool was determined indirectly by measuring the tool temperature. Observation points were first defined in the simulation model, corresponding to the thermocouple positions used in the experiment. The heat source was assumed to be uniformly distributed across the tool–chip contact area, as illustrated in Figure 5. The heat source intensity was then iteratively adjusted until the simulated temperature matched the measured temperature. Once this match was achieved, the heat source represented the heat transferred to the tool (${\dot{Q}}_{Tool}$). Comparing this value to 90% of the total mechanical work, as described in Equation (2), allowed for the calculation of the heat partition into the tool $B_{Tool}$.

$$\begin{array}{c}\hfill B_{Tool}={\displaystyle \frac{{\dot{Q}}_{Tool}}{90\%·P_{Mech}}}={\displaystyle \frac{{\dot{Q}}_{Tool}}{90\%·F_c·v_c}}\end{array}$$

(2)

Figure 10 presents the measured temperatures alongside the numerical and analytical model results. The temperature $T_1$, located near the tool nose, was significantly higher than $T_2$, which was positioned 2 mm away. This occurred because the area near the tool nose was closer to the heat source, where heat accumulated and dissipated less efficiently, leading to higher temperatures. As cutting speed increased, the temperature rose due to increased heat generation. Similarly, increasing the feed rate or cutting depth raised the cutting force, resulting in a higher material removal rate and further elevating the temperature. Guimaraes et al. observed similar trends, noting that tool temperature increased with both cutting speed and cutting depth [33]. However, due to differences in measurement methods, a direct quantitative comparison with the results in this paper was not possible.

A comparison between experimental and simulated temperatures shows that both models accurately captured the temperature differences between the two measurement points, confirming that both the analytical and numerical models effectively represented the temperature distribution near the cutting area. However, the numerical model incorporated detailed tool geometry, while the analytical model simplified it to an orthogonal hexahedron, potentially leading to deviations in estimating heat input to the tool.

Figure 11 illustrates the heat partition to the tool. As the feed rate increased, the heat partition decreased. Similarly, greater cutting depth at the same speed and feed rate further reduced the heat partition to the tool. Overall, the analytical model predicted higher heat input to the tool than the numerical model for the same temperature distribution. This discrepancy arose because the numerical model accounted for the tool rake angle and chip breaker geometry, while the analytical model assumed a flat surface with a 0° rake angle. Additionally, the numerical model used an 80° tool nose, whereas the analytical model assumed 90°. The sharper corners and narrower geometric features in the numerical model led to localized heat buildup, requiring less heat input to match the temperature distribution. The relative difference in heat partition between the two models was around 40%. Specific heat source intensity values are provided in

Table 3. Heat source intensity q as determined by numerical simulation.

$v_c$	70	70	70	120	120	120	70	70	70	120	120	120
f	0.1	0.2	0.3	0.1	0.2	0.3	0.1	0.2	0.3	0.1	0.2	0.3
$a_p$	0.8	0.8	0.8	0.8	0.8	0.8	2.5	2.5	2.5	2.5	2.5	2.5
q	164	168	144	287	223	189	118	97	84	164	120	107

Unit: $v_c$: m/min, f: mm, $a_p$: mm, q: W/mm².

.

To reduce temperature and promote chip fracture, cutting fluid is commonly used. In this study, a cutting fluid supply pressure of $p_{cf}$ = 80 bar was applied, which is a level typically achievable with the internal pumps of modern CNC machine tools. The cutting fluid influences chip formation through two main mechanisms. First, it reduces friction in the secondary shear zone, increasing chip curvature. Second, it helps dissipate some of the heat generated in the cutting area. The top of the chip is effectively cooled, while the bottom remains mostly unwetted due to close contact with the tool rake face. This creates a temperature gradient that enhances the bending resistance of the chip compared to dry machining, making it more likely to collide with the cutting edge and fracture [3]. Additionally, the force of the cutting fluid jet plays an important role. When directed into the gap between the rake face and the chip, the fluid creates a pressure wedge that lifts the chip, potentially causing it to break off [29].

Figure 12 shows the chip shapes under cutting fluid application, using the same cutting parameters as in dry cutting. With cutting fluid supply, all chips broke into small segments. At a cutting depth of $a_p$ = 0.8 mm and a feed rate of f = 0.1 mm, the chip size was approximately 2 mm. As the feed rate increased, the chip size increased slightly. At a cutting depth of $a_p$ = 2.5 mm, chips at feed rates of f = 0.1 mm and 0.2 mm were similar, forming spiral chips with a radius of about 1 cm. However, when the feed rate increased to f = 0.3 mm, the chips became smaller and broke into spiral segments and discontinuous chips.

The frequency and size of chip breakage are directly related to the cooling efficiency of the cutting fluid. When chips broke, the fluid was no longer obstructed by the chip and could flow freely through the cutting area, cooling the cutting area more effectively. Additionally, as the chip curvature increased, the angle between the chip and the tool grew, further facilitating fluid flow in the cutting area and improving cooling performance.

Figure 13 shows the tool temperature at the measurement point when cutting fluid is applied. Compared to the dry cutting temperatures in Figure 10, there is a significant overall decrease in tool temperature. The relationship between tool temperature and cutting parameters follows a similar trend to dry cutting, with temperature increasing as feed rate, cutting depth, and speed rise. In the simulation, the heat partition into the tool was assumed to remain the same as in dry cutting, with only the convective cooling coefficient on the tool surface adjusted. The results indicate that the simulation effectively reflected the temperature distribution under the influence of cutting fluid.

The cooling efficiency of cutting fluid was evaluated using the convective cooling coefficient determined through simulation. Figure 14 presents the convective cooling coefficient obtained via inverse calibration. Both numerical and analytical models showed higher convective cooling at smaller cutting depths, with a slight decrease as the feed rate increased. Smaller cutting depths and feed rates produced smaller chips, which obstructed the cutting fluid less, allowing more effective cooling. As cutting depth or feed rate increased, chip size grew, and chip curvature decreased, covering more of the tool surface and restricting fluid access to the cutting zone, thereby reducing cooling efficiency. The analytical model indicated a greater cooling effect than the numerical model. This discrepancy occurred because the analytical model tended to overestimate the heat transferred to the tool, requiring a stronger cooling effect to match the measured tool temperatures. Nonetheless, the analytical model accurately captured the influence of different cutting parameters on cooling efficiency, and the differences between the two models remained consistent across various conditions.

Simulation methods were also be used to analyze the overall temperature distribution of the tool. Figure 15 shows the temperature of the tool rake under the influence of cutting fluid. Both numerical and analytical simulations show similar temperature distributions, with high-temperature areas concentrated in the contact zone between the tool and the chip. Outside this zone, the tool remained close to room temperature due to the cooling effect. Although the measurement point was less than 1.8 mm from the tool surface, the maximum surface temperature was significantly higher than the measured value at this point. These findings suggest that simulations provide a solid foundation for assessing the overall temperature load on the tool, enabling process optimization based on temperature management. Additional temperature distribution results are provided in Appendix B.

While the temperatures between the analytical and numerical models appear to be in good agreement, this agreement is primarily due to the inverse calibration used to fit the measured temperature data rather than any fundamental similarity in the behavior of the models. In particular, each model makes different assumptions about heat partitioning ratios (as shown in Figure 11) and convection coefficients (as shown in Figure 14), resulting in different interpretations of the thermal behavior. The analytical model simplifies the tool–chip interface by applying a uniform heat source distribution and a generalized convective cooling factor, whereas the numerical model incorporates a more complex boundary condition with variable heat transfer parameters that more accurately reflect specific geometric and material interactions. Thus, while the inverse calibration produces similar temperature outputs, this does not imply physical congruence between the two models. Instead, it highlights how each model uniquely balances thermal inputs and boundary conditions to achieve comparable temperature results, and underscores the importance of understanding these differences when interpreting model accuracy and application limitations.

4.2. Results of Interrupted Turning With and Without Cutting Fluid

During interrupted cutting, the tool periodically disengages from the workpiece. This prevents the formation of long continuous chips and allows the tool to be effectively cooled during the non-cutting phase. The aim of investigating interrupted cutting is twofold: to assess its impact on tool forces and temperatures, and to evaluate the accuracy of temperature analysis using simulation and analytical models.

Figure 16 shows the process force components measured during interrupted cutting. Both the magnitude of the forces and their relationship to the cutting parameters are similar to those observed in continuous cutting. This suggests that the cutting force components are primarily determined by the uncut chip geometry, with the interruptions having barely any effect. Although the cutting fluid fully wets the tool during the non-cutting phase, the process forces do not indicate improved lubrication. This is partly because the 8% emulsion Vasco TP 149519 from Blaser Swisslube AG (Rüegsau, Switzerland) is primarily for cooling rather than lubrication. In addition, any lubricating effect is minimal because the cutting process quickly removes the lubricating layer from the tool surface.

During interrupted cutting, heat generation is intermittent, resulting in fluctuating temperature rises, as shown in Figure 17. Due to the response time of the thermocouple, it captures the temperature fluctuations but cannot fully reflect the actual fluctuation range, making direct temperature comparisons difficult for assessing the heat input into tool. After 8 s of process time, the temperature fluctuation range stabilizes, and the average temperature remains constant. This stabilization time aligns with that measured by Han et al. using a pyrometer [34]. Therefore, the midpoint of the fluctuation range was used for model calibration in this study. Figure 17 compares the calibrated simulated temperatures with the measured data, showing that the simulated temperature fluctuation range is significantly larger than the measured values, which may more accurately reflect the real temperature profile.

Figure 18 shows the range of temperature fluctuations at the measurement points during dry cutting. The mean temperature at the tool tip increases with cutting depth, speed, and feed rate due to greater heat generation during the cutting process. The mean temperature at point $T_1$, near the tool corner, is higher than at point $T_2$, reflecting heat accumulation.

In terms of fluctuation range, the range at $T_2$ is significantly smaller than at $T_1$, with both points showing larger fluctuations at higher cutting depth. This indicates that the temperature fluctuation range is greater the closer the point is to the heat source. Additionally, when comparing fluctuation at different cutting speeds, increasing speed slightly reduces the fluctuation range.

A comparison of simulation and experimental results shows that both numerical and analytical simulations accurately capture the median temperature value. However, the simulation results exhibit a significantly larger fluctuation range than the measured values, which is likely due to the previously discussed response time of the temperature sensor. Additionally, the analytical model shows a noticeably larger fluctuation range than the numerical model. This is because the analytical simulation simplifies tool geometry and ignores details of the tool rake face, requiring more heat to reach the same temperature, leading to larger temperature fluctuations.

Differences in the consideration of geometric details lead not only to variations between the analytical and numerical models in terms of temperature fluctuations but also in the amount of heat required to reach the same temperature, as shown in Figure 19. The analytical model requires more heat than the numerical model to achieve the target temperature, which is consistent with the results for continuous cutting. However, for discontinuous cutting, the difference between the heat partition in the analytical and numerical models is within 4%, which is significantly less than for continuous cutting. This suggests that the omission of geometric details in discontinuous cutting has less effect on the heat partition than in continuous cutting.

Geometric details of a tool, such as rake angles, flank angles, and chip breaker, influence how heat accumulates, dissipates, and distributes across the tool’s body. In continuous cutting, where heat generation is sustained, these details play a crucial role in temperature distribution. Constant heat input without interruptions leads to a thermal equilibrium where temperature gradients become more pronounced around geometric features, especially those that face higher frictional or cutting forces. As a result, areas like tool edges or corners may experience higher localized temperatures, making the geometric details significantly impactful in controlling temperature behavior.

In contrast, with alternating temperature loads as seen in interrupted cutting, the tool experiences periodic cooling phases between cuts, allowing much of the accumulated heat to dissipate before the next cutting phase. This intermittent cooling diminishes the impact of geometric features on heat retention because each cooling phase moderates the temperature rise across these areas, preventing extreme temperature gradients from forming. The temperature load oscillates rather than accumulating continuously, so the geometric details have less time to impact heat distribution and are less likely to become localized hotspots. For these reasons, geometric details play a lesser role in the thermal dynamics of discontinuous cutting than they do in continuous cutting. This difference is a result of the physical characteristics of heat generation and dissipation unique to each cutting mode, rather than merely a simplification choice in modeling.

Interrupted turning allows the tool to be effectively cooled by the cutting fluid during the non-cutting phase, resulting in a significantly lower overall tool temperature compared to continuous turning. Figure 20 shows the range of tool temperature fluctuation at a cutting fluid pressure of $p_{cf}$ = 10 bar. The experimental results indicate that the mean tool temperature at both measurement points is below 100 °C. At a cutting depth of $a_p$ = 0.8 mm, both points are cooled to near room temperature during the non-cutting phase, with minimal temperature fluctuations. However, at a cutting depth of $a_p$ = 2.5 mm, the temperature fluctuation range increases.

The convective cooling coefficient in the numerical simulation was determined inversely based on temperature data. The simulated mean temperature aligns well with the experimental results. Compared to dry cutting, the difference between the simulated and experimental temperature fluctuation ranges is minimal. To further compare the analytical and numerical models, the analytical model uses the same convective cooling coefficient as the numerical model. In general, the analytical model tended to overestimate the temperature. However, at lower cutting depths the difference was small, at around 10 °C. At a cutting depth of $a_p$ = 2.5 mm, the difference increases with higher speed and feed rate, but the maximum difference in mean values is only about 30 °C. The temperature fluctuation range in the analytical model is also slightly larger than in the numerical model, though the difference is much smaller compared to dry cutting.

Figure 21 shows the convective cooling coefficient determined through numerical simulation. Compared to continuous cutting, the convective cooling coefficient is significantly higher under the same cutting parameters. This is because, during the non-cutting phase, the tool is fully cooled by the cutting fluid. The cutting depth directly affects the convective coefficient: when the depth is large, part of the tool corner is covered by the workpiece, restricting fluid flow into the cutting area and reducing cooling efficiency. Since only small, similarly shaped chips are generated during interrupted cutting, feed rate and cutting speed have little impact on the convective cooling coefficient. A photograph of the chips is provided in Appendix C. Thus, it can be concluded that cooling efficiency in interrupted cutting under flood cooling is primarily influenced by the cutting depth, with minimal effect from cutting speed and feed rate.

The analysis of interrupted cutting in this subsection reveals that thermocouples cannot fully capture the rapid temperature changes of the tool. To address this issue, the actual temperature fluctuations can be derived inversely using the simulation method outlined in this paper. Additionally, at low cutting depth and feed rates, the difference between the analytical and numerical model results is minimal. As the analytical model is less computationally intensive than the numerical simulation, it shows great potential for use in interrupted cutting analysis.

5. Conclusions and Outlook

This study provides a comprehensive investigation into the tool temperature behavior during both continuous and interrupted turning processes using cutting fluid. The integration of experimental thermocouple measurements with numerical and analytical simulations allowed for a detailed assessment of heat generation, heat partition, and cooling efficiency under varying cutting conditions.

Key findings include the confirmation that thermocouples are effective at capturing steady-state tool temperatures but fall short in detecting rapid fluctuations, particularly in interrupted turning operations. Both numerical and analytical models demonstrated good accuracy in predicting temperature behavior, especially at low cutting depth and feed rates, with the analytical model being computationally more efficient.

The convective cooling coefficient, critical for optimizing tool cooling, was derived from the inverse calibration of experimental data. Interrupted cutting proved advantageous in cooling efficiency, as the tool had opportunities to cool during non-cutting phases. However, the study also highlighted that the analytical model tends to overestimate heat partition, especially when tool geometry complexities are simplified.

In calculating the convective cooling factor, it was assumed that heat partition in the cutting area remains unaffected by the cutting fluid. However, in interrupted cutting with coolant, the wetting effect of the fluid may impact this assumption. The cutting fluid could act as a lubricant between the chip and rake face, altering frictional work and heat generation in the chip, which may affect the accuracy of the cooling coefficient. Additionally, tool temperature under coolant action reflects both heat outflow induced by the cutting fluid and heat inflow from the cutting area. Thus, evaluating the coolant’s effect on heat partition based solely on tool temperature remains a complex and unresolved scientific challenge.

The results highlight the potential of analytical models for industrial applications due to their lower computational requirements. However, the numerical model remains more accurate for scenarios requiring detailed geometric considerations. The analytical model proposed in this paper is suitable only for cutting tools with shapes approximating an orthotropic hexahedron; its accuracy diminishes significantly for tools with complex geometries. Additionally, the model cannot calculate the temperature of worn cutting tools, as it does not account for heat sources on the tool flank face. This limitation presents an avenue for future model development. Furthermore, the reliability of the thermocouple-based measurement used in this study requires validation across a broader range of cutting conditions.

Future research should focus on enhancing these models for greater accuracy in complex geometries and transient thermal conditions. First, as discussed in Section 3.1, a systematic comparison and analysis of temperature effects under varying boundary conditions is essential. Additionally, model accuracy could be improved by refining the heat source region to account for changes in tool–chip contact, particularly near the tool edge radius as chip load decreases, which requires a precise mathematical description of heat source distribution. Employing 3D optical scanning, such as with an Alicona microscope, could further enhance accuracy by providing detailed measurements of the contact surface shape.

Accurately defining the heat source on the tool flank face is crucial for analyzing tool temperature under wear conditions. Expanding the model to include complex material properties and wear mechanisms will enhance its relevance in real-world machining. Additionally, this study focuses solely on the tool temperature model, but the method presented can be extended to simulate workpiece and chip temperatures, enabling analysis of overall temperature distribution in the chip region and contact heat transfer between the chip and tool.