An inverse estimation scheme to measure steady-state tool–chip interface temperatures using an infrared camera

International Journal of Machine Tools & Manufacture 41 (2001) 1015–1030

An inverse estimation scheme to measure steady-state tool– chip interface temperatures using an infrared camera P. Kwon *, T. Schiemann, R. Kountanya Department of Materials Sciences and Mechanics, Michigan State University, East Lansing, MI 48824-1226, USA Received 20 February 2000; accepted 5 October 2000

Abstract A new technique is developed to estimate the average steady-state chip–tool interface temperature during turning. An infrared (IR) video camera attached on the carriage of the lathe measures the transient cooling behavior on the rake surface of an insert after the feed motion is halted. This allows the zero heat flux boundary condition, where the transient Laplace heat conduction problem can be solved numerically to obtain the temporal and spatial temperature distribution. With the experimentally determined transient temperature distribution, the one-dimensional ellipsoidal model is used to estimate the average steady-state chip–tool interface temperature during machining. The results on turning gray cast iron (GCI) and AISI 1045 steels with various coated and uncoated K313 carbide inserts are presented.  2001 Elsevier Science Ltd. All rights reserved. Keywords: Steady-state crater temperature; Temporal and spatial temperature mapping; Inverse scheme; 1D elliptical model; Infrared imaging; Coated tools

1. Introduction The chip–tool interface temperature in metal cutting directly influences the wear behavior of the cutting tool [1–4]. The first attempt to measure cutting temperature was developed by Shore [5] using the tool–work thermocouple method. However, the technique has to be calibrated for every combination of tool and work materials. Other methods include embedded thermocouples/sensors [6,7], thermovision or infrared (IR) systems [8–10] and metallographic techniques [11–13]. The metallographic techniques relate the cutting temperature with the change

* Corresponding author. E-mail address: [email protected] (P. Kwon).

0890-6955/01/$ - see front matter  2001 Elsevier Science Ltd. All rights reserved. PII: S 0 8 9 0 - 6 9 5 5 ( 0 0 ) 0 0 1 1 3 - 9

1016

P. Kwon et al. / International Journal of Machine Tools & Manufacture 41 (2001) 1015–1030

in the microstructure of the tool material. Kato et al. [12] used the consolidation temperature of powders embedded in tool materials to estimate the cutting temperature. More recently, an infrared pyrometer system has been used [2,9] to measure the tool temperature a short distance away from the cutting edge. The results obtained were found to be in good agreement with the metallographic results [11]. With the radiation method using an IR camera, the temperature at the chip–tool interface cannot be measured directly during machining due to the chip covering the interface. Only the temperature distribution on flowing chips was measured directly during cutting using an IR video camera [8]. Because of the difficulties in directly sensing the chip–tool interface temperature, numerous attempts have been made to solve the cutting temperature problem analytically [14–18]. However, the interface temperature cannot be determined because the heat flux at the tool–chip interface is not known precisely. Yen and Wright [19] proposed to simplify the problem of estimating cutting temperatures based on the analytical one-dimensional (1D) elliptical model. The temperature distribution problem on a tool is relatively simple with well-defined tool geometry and boundary conditions. Their solution was found to be in good agreement with experimental observations [12]. In the present work, commercial gray cast iron (GCI) and AISI 1045 steel were turned with various coated and uncoated cemented carbide inserts under various cutting conditions. An infrared video camera attached to the carriage focuses on the insert to measure the temperatures on the rake surface after the feed motion is halted. The chip removed by halting the feed creates a uniform boundary condition on the insert, thereby making a simple solution to the Laplace equation. The homogeneous boundary condition can be achieved on the cutting tool after neglecting the clamps and the boundary between the inserts and the tool-holder. The cooling of an insert as observed by an infrared camera gives quantitative data of the transient temperatures in the vicinity of the chip–tool interface and hence can be related to a non-dimensional numerical solution of the Laplace equation. Considering the steep temperature gradients in the cutting tool, the removal of heat sources homogenizes the temperatures in the cutting tool, which can be visualized through an infrared camera. A transient temperature model was developed based on the 1D ellipsoidal model of [19]. Hence, a numerical simulation of the transient temperature distribution as a function of the initial conditions can estimate the interface temperatures. The interface temperature can then be obtained as a numerical interpolation of the solution and the experimentally observed temperatures. The uniqueness of this work is in determining both temporal and spatial temperature fields in the cutting tool using the technique presented. 2. Background Heat generation in metal cutting processes is primarily due to shear deformation of the work material during chip formation. The temperatures of the tool body, however, are mainly increased due to the heated chip passing over the chip–tool interface. The heat input into the cutting tool is traditionally modeled as a constant flux or a constant temperature boundary condition [19]. The 1D temperature model [19] used in the subsequent numerical calculations is briefly introduced. The motivation to use the ellipsoidal model is its flexibility in simulating the actual cutting condition [20]. In the general ellipsoidal model, the dimension of one-eighth of the base ellipsoid

P. Kwon et al. / International Journal of Machine Tools & Manufacture 41 (2001) 1015–1030

1017

can be chosen to fit the real chip–tool contact area by a proper selection of the semi-axes a, b and c, as shown in [20]. In addition, the isothermal surfaces on the cutting inserts also fit to the one-eighth of the base ellipsoid as shown in Fig. 1. In the special case where c=0, the base ellipsoid degenerates into a planar ellipse, which simulates an oval-shaped planar heat source in the chip–tool contact area of a cutting tool. Here, a and b can be properly chosen to fit any combination of feed and depth of cut. The solution of this ellipsoidal model is expected to be approximately close to the real cutting temperature distribution in the tool [19]. The general Laplace equation in ellipsoidal coordinates can be simplified to the special case of a one-dimensional steady-state problem, where the temperature distribution is only a function of the radial coordinate, x, in the 1D ellipsoidal model (mm2). Using the dimensionless relative temperature defined by ⌰=(Tx⫺T⬁)/(TR⫺T⬁), where TR is the steady-state chip–tool interface temperature (°C), Tx is the temperature at the location determined by x (°C) and T⬁ is the ambient temperature (°C), the final equation is

冉 冊

d⌰ d Rx ⫽0, dx dx

(1)

where Rx=√(a2+x)·(b2+x)·x and a and b are parameters describing the base ellipse (mm). The boundary conditions assumed here are: all side faces are insulated (heat convection=0, as revealed by a simple calculation of the Biot number); thermophysical properties of the tool material, l, cp and r are constant; the tool is rigid; tool wear is negligible; and uniform TR and T⬁. With mathematical manipulation [20], a function for ⌰ can be expressed as

冕冑 x

a ⌰(x)⫽1⫺ · 2K(m)

1

(a2+x)·(b2+x)x

dx,

(2)

0

where m=(a ⫺b )/a , K(m) is the complete elliptic integral of the first kind and x is the integration variable (mm2). Given the special case of a=b, a closed-form solution of Eq. (2) can be found by a simple integration. Although the experimental data [12] agree well with the prediction [19] with the special case of a=b, a and b were considered to be different in this investigation. This led to a more complicated mathematical solution, which is shown along with the development of 2

2

2

Fig. 1.

Base ellipse and isothermal surface in the 1D ellipsoidal model [20].

1018

P. Kwon et al. / International Journal of Machine Tools & Manufacture 41 (2001) 1015–1030

the transient temperature model. Moreover, the separate consideration of a and b is supported by the chip–tool interfaces on the inserts in our machining experiments.

3. Experiments 3.1. Machining experiments The experiments were conducted on a Clausing Metosa C1545 lathe in the Engineering Research Complex at Michigan State University. The turning experiments were performed dry and, before the experiments, the outer oxidized skins of the bars were removed. Because the interface temperature is known to stabilize within a few seconds of cutting [9,21], the steadystate temperature distribution is reached within the region of interest after a sufficient cutting time (a minimum of 76 s). Then, the feed was stopped to allow an unhindered view of the tool’s rake face. It was impossible to measure the temperatures of the rake face of an insert during cutting owing to the adulterating effect of the flowing chips, whose temperatures are much higher than the tool surface. Hence, this investigation attempts to get the IR images after the feed was stopped. For all cuts, the depth of cut and the feed rate were kept constant at 2.54 mm and 0.51 mm/rev, respectively. However, machining with the uncoated insert was not successful with the AISI 1045 steel due to excessive wear and stringy chip flow. As shown in Fig. 2, an aluminum fixture was built for the infrared camera, which was mounted on the carriage. The camera assembly on the fixture has a telescope and “downlooker” that focuses the IR camera down on an insert. The whole assembly travels with the carriage to obtain the IR images on the insert containing both spatial and temporal temperature data. Each frame of an IR image contains the spatial temperature information and the streams of IR images contain the temporal temperature information of the rake face of an insert. The IR images will be interpreted into the temperature information, which is then used to estimate the average chip–tool interface temperature.

Fig. 2. Set-up of machining experiments.

P. Kwon et al. / International Journal of Machine Tools & Manufacture 41 (2001) 1015–1030

1019

3.2. Inserts The cutting experiments were conducted with three types of C2–C4 grade carbide insert, with the ISO specification SPGN 190412 tools. Each of the two coated inserts had a single layer of TiN or TiAlN, while the other one was uncoated. An integral chip breaker was intentionally avoided for the sake of simplicity in modeling the tool temperatures using the 1D ellipsoidal model. The assembled tool characteristics are: the end relief angle of 4°42⬘, the side relief angle of 0°, the back rake angle of 0°, the side rake angle of 4°42⬘, the end cutting edge angle of 15° and the side cutting edge angle of 15°. The inserts were mounted on a standard CSRPR-856D tool-holder (clamp mounted). 3.3. Work materials In the machining experiments, medium carbon AISI 1045 steel (hot-rolled) and gray cast iron (GCI) class 40 grade were used, whose hardness values were 129 VHN and 165 VHN, respectively. The work materials were bar stocks with the following dimensions: for AISI 1045 steel, the diameter and length were 76.2 mm and 482.6 mm, respectively; for GCI, the diameter and length were 88.9 mm and 673.1 mm, respectively. 3.4. Infrared imaging technique The infrared camera IR 600 L (Inframetrics Inc.) consisted of an infrared detector, the scanning unit and the electronics. High sensitivity and fast response time are the distinctive properties of photon detectors. The outgoing video signal consists of video frames at a frequency of 30 Hz. To enable the system to measure temperatures, a thermal reference target is viewed regularly inside the scanner. This information is converted into a stream of visible images, which can be recorded on a video system as black and white images representing the thermal information. An accuracy of 0.78°C per gray scale level in the case of a temperature range of 200°C and an image resolution of approximately 0.165 mm/pixel were attained. The Reference Emittance Technique described in the manual of the infrared camera was used to determine the emittance values of the tool inserts employed. The emittance value of the black paint, ereference, was 0.92. Before the experiments, the emittance values, einsert, of the employed tool inserts were determined. With these data the emittance value of the insert surface can be calculated and the values of the emissivity obtained are 0.101, 0.443 and 0.357 for TiN-coated, TiCN-coated and uncoated inserts, respectively. 4. Results 4.1. Transient temperature model The transient temperature model describes the cooling phenomenon of the insert without heat input after stopping the feed. The prediction made by the model can be used to compare with the experimental results from the IR camera. Because the cooling phenomenon is of interest, the

1020

P. Kwon et al. / International Journal of Machine Tools & Manufacture 41 (2001) 1015–1030

initial condition for the model is represented by the steady-state temperature distribution in the tool body. The steady-state temperature is reached after a sufficient time of cutting (heat input⬎0). This steady-state temperature distribution obtained by solving Eq. (2) is represented by the following expression obtained by the symbolic computation in Mathematica: −i·F(arcsin{冑−x/b2}, b2/a2) , ⌰(x, t⫽0)⫽1⫺ K(m)

(3)

where m=(a2⫺b2)/a2, ⌰=(Tx⫺T⬁)/(TR⫺T⬁), K(m) is the complete elliptic integral of the first kind (dimensionless) and F(⌽, n) is the elliptic integral of the first kind (dimensionless). Steady-state isotherms on the rake face of a cutting tool obtained from the 1D ellipsoidal model are displayed in Fig. 3 for a=2.63 mm and b=1.18 mm. The ellipsoidal shape of the isothermal surfaces is distinct only in the close field of the chip–tool interface. At the locations far away from the contact area, they approach the shape of quarter circles. To transform the radial coordinate, x, into the distance from the chip–tool interface, r, on a 45° diagonal on the rake face of the insert, the following formula was obtained:

冪1/(a +x)+1/(b +x)⫺冪1/a +1/b ,

r(x)⫽

2

2

2

2

2

2

(4)

where r is the distance from the chip–tool interface on a 45° diagonal on the rake face of the insert (mm). In the subsequent analysis, we used the relative temperature distribution on the 45° diagonal

Fig. 3. Steady-state isotherms (relative temperature) as provided by Eq. (3); a=2.63 mm, b=1.18 mm.

P. Kwon et al. / International Journal of Machine Tools & Manufacture 41 (2001) 1015–1030

1021

as shown in Fig. 4 for the steady-state case. Here, a value of r=12 mm corresponds approximately to the distance between the base ellipse and the center of the insert’s rake face. To obtain the transient characteristics, the governing differential equation in ellipsoidal coordinates for the case of steady-state temperatures, Eq. (1), had to be augmented with the time derivative of the heat diffusion equation as follows:

冉 冊

4 ∂ ∂⌰ 1 ∂⌰ ·R · Rx ⫽ , 2 x x ∂x ∂x a ∂t

(5)

where Rx=√(a2+x)·(b2+x)·x and a=l/cp·r, t is the time (s), a is the thermal diffusivity of the tool material (mm2/s), l is the thermal conductivity (W/m K), cp is the specific heat (J/g K) and r is the density (g/cm3). To solve this differential equation with its initial condition, Eq. (3), Mathematica’s numerical scheme was used after assigning values for a, b, a, l, cp and r, which are predetermined by the physical experimental environment. 4.2. Determination of parameter values The length of the base ellipse, a, represented by the chip–tool contact length can be calculated based on the depth of cut (2.54 mm), which stayed constant throughout the experiments. Furthermore, an end cutting edge angle, Ce, of 15° has to be taken into account. Thus the value of a is 2.63 mm after the depth of cut was divided with cos 15°. The calculated length of the base ellipse, a, compared well with the experimentally observed values of the cutting edges. The width of the base ellipse, b, was estimated by using averaged values of the diagonal of the chip–tool interface

Fig. 4. Relative temperature with the distance from the chip–tool interface on the 45° diagonal of the rake face for steady-state case; a=2.63 mm, b=1.18 mm.

1022

P. Kwon et al. / International Journal of Machine Tools & Manufacture 41 (2001) 1015–1030

which corresponds to the characteristic value of the base ellipse, R, plus the value for the nose radius correction (see Fig. 5). To calculate b from Raverage, the following equation was applied: b⫽

冑2/(R

1 +0.50 mm)2−1/a2

,

(6)

average

where b is the width of the base ellipse (mm), Raverage is the average of the characteristic values of the base ellipse (mm) and a is the length of the base ellipse (mm). The characteristic values of the chip–tool interface, R, were measured for each cutting edge. It was measured as average values for the two work materials separately owing to their different fracture toughness, which influences the tool–chip contact area [2]. Eq. (6) yields that the width of the base ellipse is 1.18 mm for AISI 1045 steel (bs) and 1.08 mm for gray cast iron (bg). The thermal diffusivity can be calculated to be 31.5 mm2/s for the carbide inserts used in our experiment. 4.3. Numerical computation of transient temperature model Based on Eqs. (3)–(6), two numerical computations were conducted in Mathematica for both work materials. Due to the singular point at x=0 mm2, the domain of computation was taken

Fig. 5.

Geometry and characteristic distances on the rake face of the cutting tool.

P. Kwon et al. / International Journal of Machine Tools & Manufacture 41 (2001) 1015–1030

1023

beyond x=0.001 mm2. Each computation resulted in an interpolating function, which was evaluated between the time interval of 0 to 2 s in steps of 0.033 s and at a distance between 0 and 11.7 mm from the chip–tool interface. Fig. 6 displays the calculated relative temperature, ⌰, as a function of the distance from the chip–tool interface, r, for certain values of the time, t. It shows the following observations: 1. The trend of the temperature profiles is similar for all t⬎0 s (shown in Fig. 6). For t→⬁ the profiles flatten and the temperature becomes constant as r reaches 0. 2. The temperature gradient at r=0 mm for all profiles, except for t=0 s (the initial steady-state temperature distribution), is close to zero (shown in Fig. 6). 3. Temporal changes in temperature are less at a location further away from the chip–tool interface. For instance, the temperatures for t⬍200 ms and r⬎7 mm remain almost the same. 4. The temperatures for the case of bg=1.08 mm (numerically computed temperature profile was not shown here) drop slightly faster than for the case of bs=1.18 mm. 5. In both cases, the temperature at r=0 mm (chip–tool interface temperature, TR) drops very quickly. After 133 ms, only 20% of its initial value was attained. 6. At a location away from the chip–tool interface, the initial temperature drops very slowly within the first 200 ms (the curves in Fig. 6 when r is between 7 and 11.6 mm), whereas at closer locations the temperature drops very fast in the beginning (the curves in Fig. 6 when r is between 0 and 2 mm). The observations #2 and #4 above are intuitive considering that the thermal capacitance of the material volume at r=0 mm is very small in comparison to the material volume far outside the chip–tool interface. A high value of the thermal diffusivity, a, provides a rapid equalization of

Fig. 6. Numerically computed temperature profiles across the rake face of the tool body for certain times t after stopping the heat input; case bs=1.18 mm.

1024

P. Kwon et al. / International Journal of Machine Tools & Manufacture 41 (2001) 1015–1030

temperatures in small volumes. Furthermore, observation #2 promotes the idea of a uniform chip– tool interface temperature, TR, at least for the period of cooling. Observation #6 suggests an approximation of the temperature decay curve at close locations by a function of the type: ⌰(t)⫽⌰0 e−t/t,

(7)

where ⌰ is the relative temperature (dimensionless), ⌰0 is the initial relative temperature at t=0 (dimensionless), t is the time (s) and t is the time constant (to be fitted) (s). Fig. 7 illustrates the temporal development of temperature for certain distances from the chip–tool interface, r. In summary, the developed transient temperature model and its specific solution deliver the valuable information on the transient temperature distribution in a square tool insert. In both continuous cutting and interrupted cutting, the measurement technique described in this paper can provide further insights into temperature and wear issues. Different tool properties and cutting conditions can be considered by conducting the numerical computation with appropriate values of a, b and a. 4.4. Results of machining experiments As mentioned earlier, the focus in this investigation is the quantitative analysis of the IR images at the end of each cut after the feed was stopped. The IR images were recorded on videotape, and were analyzed subsequently by using the software Image Pro Plus (IPP). The Multiframe Acquire feature was applied to select the first image right after the chip of workpiece material had left the field of view completely. In addition two more images, 1 s apart, were captured at each cut. Fig. 8 shows typical images obtained in the experiments (see Table 1 for their respective machining conditions on Cut E and K). The white background in the image of Cut E is due to hot chips, which piled up underneath the tool-holder. In contrast, the cuts with gray cast iron produced small, segmented chips that were not as hot as the chips produced with AISI 1045 steel. A line profile of each image was taken across the rake face on a 45° diagonal from the cutting

Fig. 7.

Temporal development of temperature for the case bs=1.18 mm.

P. Kwon et al. / International Journal of Machine Tools & Manufacture 41 (2001) 1015–1030

1025

Fig. 8. Infrared images immediately after chips have left the field of view. Table 1 Predicted chip–tool interface temperatures TR on AISI 1045 and GCI Cut

Workpiece

Coating

Cutting speed (m/min)

TR (°C)

A B C D E F G H I J K L M N O

Steel AISI 1045

TiN TiAlN TiN TiAlN TiN TiAlN TiN TiAlN Uncoated TiN TiAlN Uncoated TiN TiAlN Uncoated

157 146 87 80 51 58 183 172 113 105 97 78 72 65 47

1546 426 981 478 857 550 –a 303 400 298 546 387 –a 532 238

a

Gray cast iron

Measurement data were found to be unreliable, see subsequent explanation.

edge to the center point according to Fig. 6. The half of the diagonal is 12.98 mm determined from the tool geometry. It also contains the characteristic value of the base ellipse, shown as R in Fig. 6. Regarding the emittance values of the chip–tool interface area after cutting, a further investigation was undertaken. Interpreting the IR images on the chip–tool interface, we found that the emittance values changed significantly due to the alteration of the surface texture of the chip– tool interface area. The temperature profile in the chip–tool contact area shows clearly the scatter in the data, which is intolerably high in the region of the chip–tool interface (r⬍0 mm). The variations in emittance values in the chip–tool interface seem to have distorted the measured temperatures. Due to these difficulties, the IR image data at the chip–tool interface cannot be taken directly for further evaluation. Therefore, the portion corresponding to the characteristic value of the base ellipse, R, was removed from the profile length for further analysis. Consequently, the transient temperature model had to be developed for this purpose.

1026

P. Kwon et al. / International Journal of Machine Tools & Manufacture 41 (2001) 1015–1030

The numerical computation also required fixing the origin of the distance from the chip–tool interface, r, at the boundary line of the interface. This problem bears a direct semblance to the difficulty experienced in [8]. They had used variable emittance values corresponding to those measured on work material samples quenched at different temperatures. However, a very small piece of a work material can adhere to the chip–tool interface during machining and change the emittance value locally. The inserts after the experiments show that the approximation of the chip–tool contact area by a quarter ellipse is very close. The characteristic values, R, were different for each cutting edge and, therefore, measured separately by using a toolmaker’s microscope. The temperature profiles drop with time rapidly at locations close to the chip–tool interface and at a much slower rate at locations away from the contact area. However, due to the time delay of the first image captured, the temperature profile at the interface does no longer reflect the steady-state temperature distribution. During this time delay, the temperature at the locations close to the chip–tool interface has already dropped significantly. It is therefore incorrect to assume the temperature at r=0 mm of the first image to be the steady-state interface temperature. Since the mentioned time delay seems to have a decisive impact even on the temperature profile of the first image, this issue is examined further in more detail. Considering the temporal circumstances at the end of each cut, an important fact has not been addressed yet. Stopping the feed, as it was practised in the experiments, does not result in an instant stop of chip flow. Rather, one additional revolution of the workpiece exists, where the tool is still cutting even without any feed. During this time of an additional revolution, the chip width decreases to zero and the insert may be on its way for cooling. The exact time that it takes for this process is determined by the spindle speed. The subsequent calculation is based on the lowest spindle speed used in the experiments (430 rev/min) in order to obtain the maximum value of the time delay. By adding the maximum time of 33 ms for taking the first image, the total maximum time delay between the feed stop and the first image, tmax, can be calculated as follows: tmax⫽

1 ⫹0.033 s⫽0.173 s. 430 rev/min

(8)

The first accessible images in all cuts were taken within a maximum time delay of 0.173 s. As stated earlier, due to the variation in emittance, it was not possible to obtain the steady-state temperature of the chip–tool interface directly from the experimental data. The transient temperature model was therefore necessary for this purpose. 4.5. Application of the transient temperature model to experimental data In the first step, the modeled steady-state temperature distribution represented by Eq. (3) was approximated by a simpler function in order to use it in the subsequent regression analysis. The relative temperature was approximated with a function with five terms (N=5) and nine parameters using a curve-fitting software: ⌰(r)⫽A1⫹A2· e−B2r⫹A3· e−B3r⫹A4· e−B4r⫹A5· e−B5r,

(9)

where ⌰ is the relative temperature (dimensionless) and r is the distance from the chip–tool

P. Kwon et al. / International Journal of Machine Tools & Manufacture 41 (2001) 1015–1030

1027

interface (mm). Here, the independent variable is the distance from the chip–tool interface, r. Since the steady-state temperature distribution is different for different values of b (width of base ellipse), the curve-fitting process had to be applied on both the curve with bs=1.18 mm and the curve with bg=1.08 mm. Hence, two different sets of parameter values were obtained. In both cases, the relative deviation of the function was less than 1.2% from the original curve. These functions were used in a regression analysis of the experimental temperature profiles. As derived in the previous section, it is incorrect to take the entire profiles into account due to the temperature drop caused by the time delay of the clearing chip. In consideration of the previously calculated maximal time delay, tmax=0.173 s, and the numerically computed profiles such as Fig. 6, only the temperature data in 7 mm⬍r⬍12 mm were suitable in the regression analysis, since these locations are characterized by a minimal change of temperature within 0.173 s. The regression analysis of the measured temperature data was undertaken in absolute temperatures in units of °C: T(r)⫽(TR⫺T⬁)·⌰(r)⫹T⬁,

(10)

where ⌰ is the relative temperature (dimensionless) and r is the distance from the chip–tool interface (mm), T(r) is the temperature at the location determined by r (°C). As mentioned before, T⬁ is specified as the temperature at infinity or the ambient temperature. In general, this means that T⬁ represents the temperature of the surrounding air, for example 25°C in the experiments conducted. However, a first regression analysis using this value in general showed a poor correspondence of the experimental and numerical data. Hence, it was decided to execute the regression analysis with T⬁ as a free parameter, as well as TR. In all cases, this led to values of T⬁ that were slightly higher than 25°C. T⬁ for Cut K was found to be the highest temperature, at 45.16°C. The temperature T⬁ turned out to be a key variable in the conducted regression analysis. The physical interpretation of its meaning is that T⬁ is a representative value in a certain experimental set-up corresponding to the thermophysical properties and geometry at the far field of the tool insert, i.e., the tool-holder and the carriage. So far the properties and geometry of the tool-holder or carriage have not been taken into account at all, although they influence the temperature distribution at the region of the cutting edge as well. Therefore, treating T⬁ as a free parameter allows the consideration of differences between the temperature model and the actual experimental set-up. The temperature data of all cuts were processed by means of a regression analysis as mentioned before. The values obtained for the chip–tool interface temperature, TR, are shown in Table 1. By analyzing the temperature profiles, it was found that the scatter in the data was highest in the cases of the TiN-coated inserts. The extremely low emittance value of the TiN coating must have caused the errors in the measurements. It is the main source of measurement errors, while the errors due to the regression analysis were insignificant. However, small measurement errors in the region of 7 mm⬍r⬍12 mm lead to higher errors in estimating TR due to the stiff slope of the curve at this point. However, if the temperature measurements are precise, the regression analysis is reliable provided that the modeled temperature distribution reflects the actual conditions in the tool. Furthermore, this idea is supported by the fact of multiple data points per temperature profile, which allows consideration of temperature gradients, in contrast to single point measurement methods such as the infrared pyrometer technique. More evidence is given when comparing the experimental temperature profiles with the profiles of the transient model. To do so, the relative

1028

P. Kwon et al. / International Journal of Machine Tools & Manufacture 41 (2001) 1015–1030

Fig. 9. Experimental and numerical temperature profiles across the rake face of the tool body for certain times t after the feed stop; Cut K.

temperatures of the numerical data had to be transformed into absolute temperatures by taking the estimated chip–tool interface temperature, TR, and the temperature at infinity, T⬁, into account. This was done representatively for the case of Cut K. Fig. 9 illustrates the experimental and numerical profiles. The estimated steady-state temperatures presented in Table 1 show a good agreement with the equation developed by Cook [22] as presented in Fig. 10. The equation is known to agree well with many experimental works including thermocouple. This proves the

Fig. 10. Comparison of measured temperature, TR, and the prediction by Cook [22].

P. Kwon et al. / International Journal of Machine Tools & Manufacture 41 (2001) 1015–1030

1029

validity of the present work. The other measurements and detailed procedures not presented here due to space constraint are elaborated in [24].

5. Conclusions Direct measurement of the chip–tool interface temperature using an infrared camera is not possible due to the flowing chips covering the chip–tool interface during cutting and the alteration in the local emissivity at the tool–chip interface due to adhesion of work material. Therefore, the IR images were obtained after the feed was stopped and the inverse estimation scheme had to be utilized. However, the important ramification of the technique introduced in this paper is that even the temperature variation within the tool–chip interface can be determined if the local emissivity on the tool–chip interface can be mapped. The transient temperature distributions were measured on the rake face of cutting tool inserts. Using the 1D ellipsoidal model of [19], a transient temperature model for the cooling of the inserts was developed and two numerical computations were conducted independently for the 1045 steel and GCI with the initial condition and the necessary constants. The attained temperature profiles and decay curves deliver meaningful information on the transient temperature distribution in a square tool insert. The temperature data at a distance between 7 and 12 mm did not change during the time when the chip thickness is vanishing to zero, which were then used to predict the average steady-state cutting temperature. A good agreement was observed between the experimental and numerical profiles in respect to both the local temperature distribution and the temporal temperature decay (see Fig. 7). This proves that the transient temperature model is a close approximation to the real distribution of temperatures in the cutting tool. However, the errors in temperature measurements, which occur preferentially at the surfaces of low emittance values, propagate and increase the errors of estimated chip–tool interface temperatures. We did not always observe the increasing trend with cutting speed. It should be pointed out that the measurement of the r dimension, which was crucial, could have affected the inverse estimation. There can be also other problems in using an average value of b for the solution of the transient Laplace’s equation. However, since the trends were specific only to the TiAlN coating, it was more an error due to the coating texture rather than an error in the modeling as a whole. It is also possible that the emittance of the surface changed considerably at an elevated temperature which, however, cannot be accounted for in the present work. Another observation from the interface temperature data was that the temperatures were lower for the GCI than for the steel. This conforms to the usual notion that materials with a lower specific work of plastic deformation, in general, have lower interface temperatures [23]. However, other parameters such as the capacitance and thermal conductivity are also bound to affect the interface temperature.

References [1] B.M. Kramer, P. Kwon, J. Vac. Sci. Technol. A3 (6) (1985) 2439. [2] P. Kwon, R. Kountanya, Tribol. Trans. 42 (2) (1999) 265. [3] P. Kwon, J. Tribol. 122 (1) (2000) 340.

1030 [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24]

P. Kwon et al. / International Journal of Machine Tools & Manufacture 41 (2001) 1015–1030 E.G. Herbert, Proc. Inst. Mech. Eng. 1 (1927) 289–329. H. Shore, S.M. thesis, MIT, Cambridge, MA, 1924. G.S. Reichenbach, J. Eng. Ind. 80 (1958) 525. A.H. Quereshi, F. Koenigsberger, Ann. CIRP 14 (1966) 189. L. Wang, K. Saito, I.S. Jawahir, Trans. NAMRI/SME XXIV (1996) 87. J. Lin, S.-L. Lee, C.-I. Weng, J. Eng. Mater. Technol. 114 (1992) 289. G. Boothroyd, Proc. Inst. Mech. Engrs 177 (29) (1963) 789. P.K. Wright, E.M. Trent, J. Iron Steel Inst. 211 (1973) 364. S. Kato, K. Yamaguchi, Y. Watanabe, Y. Hiraiwa, J. Eng. Ind. 98 (1976) 607. S. Ramalingham, E.D. Doyle, D.M. Turley, J. Eng. Ind. 102 (1980) 177. B.T. Chao, K.J. Trigger, Trans. ASME 80 (1958) 311. M.P. Lipman, B.E. Nevis, G.E. Kane, J. Eng. Ind. 89 (1967) 333. A.O. Tay, M.G. Stevenson, G. De Vahl Davis, Proc. Inst. Mech. Engrs 188 (55) (1974) 627. P.K. Venuvinod, W.S. Lau, Int. J. Machine Tool Design Res. 26 (1) (1986) 1. S. Raman, A. Shaikh, P.H. Cohen, Comput. Meth. Mater. Proc. 39 (1992) 181. D.W. Yen, P.K. Wright, J. Eng. Ind. 108 (1986) 252. D.W. Yen, Ph.D. thesis, Carnegie-Mellon University, Pittsburgh, PA, 1984. D.A. Stephenson, J. Eng. Ind. 115 (1993) 432. N. Cook, J. Eng. Ind. 95 (1973) 931. M.C. Shaw, Metal Cutting Principles, Oxford Science Publications, Oxford, UK, 1989. T. Schiemann, Diploma thesis, Rheinish-Westfalische Technische Hochschule Aachen/Michigan State University, 1998.