Modeling and Measurement of Cutting Temperatures ...

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ScienceDirect Procedia CIRP 46 (2016) 173 – 176

7th HPC 2016 – CIRP Conference on High Performance Cutting

Modeling and measurement of cutting temperatures in milling Umut Karaguzela*, Mustafa Bakkala, Erhan Budakb a

Mechanical Engineering Department, Istanbul Technical University, 34437 Istanbul, Turkey b Faculty of Engineering and Natural Sciences, Sabanci University, 81474 Istanbul, Turkey

* Corresponding author. Tel.: +902122931300; fax: +902122450795. E-mail address: [email protected]

Abstract Milling is the one of most common cutting operations in industry. Interrupted nature of the milling process allows use of higher speeds which in turn improves productivity. Cutting temperature is one of the key factors to be investigated in process optimization. In milling, cutting temperature analysis is harder compared to turning due to experimentation difficulties and transient characteristics. In this study, a new experimental technique is proposed to measure the face milling temperatures which are used to verify the analytical model developed. Results indicate a good agreement between the model predictions and dry cutting experiments at different cutting speeds. ©©2016 Authors. Published by Elsevier B.V This is an open access article under the CC BY-NC-ND license 2016The The Authors. Published by Elsevier B.V. (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the International Scientific Committee of 7th HPC 2016 in the person of the Conference Chair Prof. Peer-review under responsibility of the International Scientific Committee of 7th HPC 2016 in the person of the Conference Chair Matthias Putz. Prof. Matthias Putz Keywords: Milling; Cutting Tool; Temperature; Measurement

1. Introduction Machining operations can be divided into two fundamental groups as continuous and interrupted cutting. Milling is an interrupted cutting operation which is used to generate a flat or a three-dimensional free-formed surface. In case of any machining operation high temperatures occur due to excessive amount of plastic deformation and friction between tool, chip and workpiece [1]. It is stated that most of the power (90-95%) generated in a machining operation is converted to heat [2]. Generated heat dissipates into tool, workpiece and chip which determines the tool life and the surface integrity of the finished part as well as the machined part quality. Thus, in order to improve productivity, thermal analysis of machining operation is worth to investigate scientifically. It requires great effort to measure and predict the temperatures experienced in machining due to characteristics of the operation such as high speeds, number of parameters, size of the heat generation zone etc. Process modeling of cutting temperature contributes to determine the effects of cutting parameters and select them to achieve more effective

production. On the other hand measuring cutting temperature can provide useful data to verify the proposed models, and can also be used in online monitoring. In the machining literature the majority of the work is on continuous cutting whereas there is only limited number of studies on interrupted cutting. Chakraverti et al. [3] proposed a unidimensional model to predict tool temperature distribution during intermittent cutting in which the heat flux is assumed as a periodic rectangular wave. It was found in the study that thermal stresses increase as amplitude of temperature fluctuation increases. Palmai [4] claimed that in interrupted cutting, temperature increases with cutting speed up to a certain limit and this relationship can be defined with an empirical formula. Stephenson and Ali [5] developed an analytical model using Green’s functions to calculate the tool temperatures during interrupted cutting. In order to validate their model, they performed a series of experiments and measured cutting temperature by tool-workpiece thermocouple technique. They concluded that the temperatures in interrupted cutting are lower than those obtained in continuous cutting. Another analytical model was proposed by Radulescu et al. [6]. In their study,

2212-8271 © 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the International Scientific Committee of 7th HPC 2016 in the person of the Conference Chair Prof. Matthias Putz doi:10.1016/j.procir.2016.03.182

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Umut Karaguzel et al. / Procedia CIRP 46 (2016) 173 – 176

cutting temperatures on tool are calculated by using prescribed heat flux taking into account the convection to surrounding air. The proposed model could be used for both interrupted and continuous cutting. Islam et al. [7] introduced a finite difference model which can calculate transient and steady state temperatures in chip, tool and workpiece.

as equal to room temperature.

Workpiece Tool

Measuring cutting tool temperature is a significant challenge in milling operation due to tool rotation. Wang et al. [8] used a garter spring pickup and thermocouples located in the inserts to measure the tool temperature. They investigate the effect of number of teeth on the temperature, and concluded that increasing number of inserts caused increased cutting temperature. McFeron et al. [9] measured the average tool-chip interface temperatures using a tool-workpiece thermocouple. Ueda et al. [10] developed a technique which includes a twocolor pyrometer and two optical fibers one is rotating with tool insert and the other one is stationary located in tool spindle to measure the tool temperature. Kerrigan et al. [11] used a wireless telemetric system which is designed with tool holder to measure the cutting temperatures during milling of CFRP composites by a coupled thermocouple. This paper presents a novel experimental technique to measure transient tool temperatures in dry milling operation with a K type thermocouple. Additionally, an analytical model is proposed which uses Green’s functions to solve the 3D transient heat conduction problem. The proposed experimental technique was used to verify the results obtained by the model. 2. Cutting tool temperature model Generated heat in cutting operation can be predicted by calculated cutting forces. Heat generation Q can be calculated as follows by assuming that all the mechanical work done in machining operation is converted into heat energy [1]: Q

Where FR is the resultant cutting force, Vc is the cutting speed. Assuming that thermal properties of cutting tool are homogeneous and independent of time, three dimensional heat diffusion equation in Cartesian coordinates is derived as: U c p wT k

wt

(2)

where k is the thermal conductivity of the tool material, ρ is the density, cp is the thermal capacity and T is the temperature field . In milling operation, a cutting insert is exposed to cyclic heating and cooling periods, the heated area which is the toolchip interface during cutting, is seen in Fig. 1. Hence the boundary condition for the problem in Eq. (2) is determined as: k

wT wz

q( x, y, t ) z

0; 0 d x d Lx , 0 d y d Ly

(3)

where Lx and Ly are the dimensions of the heat source area which can be seen in Fig. 1 and q(x,y,t) is the heat flux applied on the xy surface. The other boundary surfaces are assumed as insulated and the initial temperature for the body is considered

Y Flank face

Rake face

Z

Ly X

Lx

Fig. 1. Geometrical representation of tool temperature model

Eq.(2) can be solved either analytically or numerically. According to Stephenson [5], Green's functions can be used to solve this equation analytically if the cutting tool is assumed to be as a semi-infinite rectangular volume heated from its corner. Then, the Green function θG , which represents the temperature at the location (x, y, z) at time t, due to an instantaneous heat point source, located at x = xp, y = yp, z = 0, and releasing its energy at time t=τ. TG

ª z2 º exp « 2 » ( S .D ) ¬D ¼ 2

( x, y , z , x p , y p ,0, D )

3

(1)

FR .Vc

w 2T w 2T w 2T wx 2 wy 2 wz 2

Insert

ª § ( x x p ) 2 · § ( x x p ) 2 · º . «exp ¨ exp ¨ ¸¸ » ¸ 2 ¨ ¸ ¨ D D2 «¬ © ¹ © ¹ »¼

(4)

ª § ( y y p ) 2 · § ( y y p ) 2 · º . «exp ¨ ¸¸ » ¸¸ exp ¨¨ 2 ¨ D D2 «¬ © ¹ © ¹ »¼

where D

2 [D (t W )]

The temperature field for the tool can be obtained by using heat flux function and integrating Eq. (4) over time, Lx and Ly. T ( x, y , z , t )

D k

t

Lx

³³ ³ 0 0

Ly

0

TG ( x, y, z, x p , y p ,0, D).Q( x p , y p ,W )dy p dx p dW

(5) The integration of θG over Lx and Ly can be denoted as θGR and can be solved as follows: TGR ( x, y, z , Lx , Ly , D)

Lx

³ ³ 0

Ly

0

TG ( x, y, z, x p , y p ,0, D) dy p dx p

ª z2 º exp « 2 » TGU ( x, Lx , D).TGU ( y, Ly , D) 2 SD ¬D ¼ 1

(6)

175


where T GU (u , L, D ) erf §¨ L u ·¸ erf §¨ L u ·¸ © D ¹ © D ¹

400

By substitution of Eq. (6) in Eq. (5), temperature field for cutting tool insert is derived in Eq.(7). D k

t

³T 0

GR

( x, y, z, Lx , Ly , D).q(W )dW

(7)

Eq. (7) includes two different expressions which are function of time, θGR and q(τ) . Therefore, Eq. (7) can be solved by convolution of time. a)

200 150 100

Vc=100m/min

50

Vc=200m/min

0

0.5

1

1.5

2

Time (sec)

600 Fig. 3. Effect of convection on tool temperature

400

Fig.3 shows the effect of convection coefficient on tool temperature where the other cutting parameters are kept constant as it is seen from the figure that up to a certain value the effect can be negligible. Therefore, in Section 4, the adiabatic boundary conditions are assumed in the calculations.

200

1.2

600

Temperature o C

250

Vc=300m/min

o

Temperature C

800

300 Temperature o C

T ( x, y , z , t )

h=10W/mK h=100W/mK h=1000W/mK h=10000W/mK

350

1.4 1.6 Time (sec)

b)

1.8

3. Experimental study full immersion 50% immersion 25% immersion

500 400 300

In order to verify the proposed model, a series of cutting experiments have been performed to measure the tool temperature. Measuring transient temperatures occurred in milling operation is a significant challenge. To overcome this problem a novel experimental setup is developed and applied to milling operation.

200 100 Cutting tool

0 2.4

2.6

2.8

3 3.2 Time (sec)

3.4

3.6

Data aqusition system Workpiece

Fig. 2. Effect of (a)cutting speed and (b)radial depth of cut on tool temperature

Fig. 2 shows the solution of Eq. (7) with results of different parameters where the other parameters are as follows: upmilling, depth of cut 1mm, feed per tooth 0.15 mm and kTool 65 W/mK. In Fig. 2a effect of cutting speed on tool temperature is demonstrated. As the cutting speed increases, the elapsed time for one revolution of tool decreases. However , tool temperature increases due to increasing in generated heat. Additionally, Fig. 2b shows the effect of radial depth of cut on tool temperature. Radial depth of cut determines the elapsed time during heating and cooling cycles. The heating cycles become longer whereas cooling time reduces with immersion. The model described above has adiabatic boundary conditions. Thus, a more realistic analytical model which includes convective boundary conditions is also developed which again uses Green's function to solve related partial differential equations.

Connector Thermocouple Insert

Dynamometer

Fig. 4. Experimental setup

Fig. 4 shows the experimental setup used in milling tests. The setup includes a miniature data acquisition system (DAS) rotating with tool holder during cutting mounted by screws, a connector and a K type thermocouple located at x=1mm, y=2mm and z=0.3 mm. The thermocouple is embedded to the cutting insert and located near the cutting zone. The details of the cutting insert can be seen in Fig. 5. The DAS is an off-theshelf-item with 500k sampling rate. The measured data is stored in the device during cutting operation.

176


Φ 0.8 mm

Thermocouple 0.3 mm

Tool holder

Temperature o C

200 150 100 50

simulation experiment

0 2.6

Fig. 5. Details of cutting insert and thermocouple

In milling tests 1050 steel was used as workpiece whereas cutting insert was uncoated carbide insert with a grade AP20F. Two different cutting speeds were selected whereas feed per tooth and depth of cut were kept constant as 0.15 mm/rev and 1 mm, respectively. The cutting has 80 mm diameter, only one cutting tooth was used during experiments. Additionally cutting forces were measured by a 3 axis dynamometer. 4. Results and discussion The novel experimental setup described above is used to verify the proposed 3D transient heat conduction model. Fig.6 shows the comparison between experimental results and simulation at a cutting speed of 50 m/min. It can be seen from this figure that there is a good match between prediction and measurement results. This cutting speed leads to a time period of 0.3 sec. due to it’s a full immersion test whereas heating and cooling periods are both 0.15 sec. In the analysis average cutting force is used to calculate the heat flux which is 866 N and the partition ratio into tool is 9.6%.

Temperature o C

200 150 100 simulation experiment

50 0 2.2

2.4

2.6 2.8 3 3.2 Time (sec) Fig. 6. Experimental verification of model at Vc=50m/min

Another test was performed under 75 m/min cutting speed where other cutting parameters were kept constant. Fig. 7 shows the comparison between experiment and simulation results where the average cutting force is 742 N and the partition ratio is 10.3%. Like previous condition, there is a good match especially between maximum and minimum temperatures. However the trend of temperature variation is slightly different which is believed due to the bandwidth of the thermocouple. Interpretation of Fig.6 and Fig.7 shows that tool temperature increases with cutting speed and this can be predicted by the proposed model. Additionally, the developed experimental setup is capable of measuring transient temperatures in milling operations.

2.8

3 Time (sec)

3.2

3.4

Fig. 7. Experimental verification of model at Vc=75m/min

5. Conclusions This paper presents an analytical model based on Green’s functions. Effect of convective boundary condition is added to the model. The proposed model shows that the effect of convection is negligible under dry cutting conditions. It is also presented that the developed experimental method to verify the model is capable of measuring transient temperature occurred in milling operation. Further study will cover the heat distribution on cutting zone and measurement of temperatures during cutting of different materials under various parameters. Acknowledgement The authors would like to thank the BAP, the project funding office of Istanbul Technical University. References [1] Abukhshim NA, Mativenga PT, Sheikh MA. Heat generation and temperature prediction in metal cutting: A review and implications for high speed machining. International Journal of Machine Tools and Manufacture 2006;46/7:782-800. [2] Sato M, Tamura N, Tanaka H. Temperature variation in the cutting tool in end milling. Journal of Manufacturing Science and Engineering 2011;133/2: 021005. [3] Chakraverti G, Pandey PC, Mehta NK. Analysis of tool temperature fluctuation in interrupted cutting. Precision engineering 1984;6: 99-105. [4] Palmai Z. Cutting temperature in intermittent cutting. International Journal of Machine Tools and Manufacture 1987;27/2: 261-274. [5] Stephenson DA, Ali A. Tool temperatures in interrupted metal cutting. Journal of Manufacturing Science and Engineering 1992;114/2: 127-136. [6] Radulescu R, Kapoor SG. An analytical model for prediction of tool temperature fields during continuous and interrupted cutting. Journal of Manufacturing Science and Engineering 1994;116/2: 135-143. [7] Islam C, Lazoglu I, Altintas Y. A three-dimensional transient thermal model for machining. Am. Soc. Mech. Eng. (ASME), J. Manuf. Sci. Eng. 2015 Accept. Publ. Doi:10.1115/1.4030305. [8] Wang KK, Shien-Ming W, Iwata K. Temperature responses and experimental errors for multitooth milling cutters. Journal of Manufacturing Science and Engineering 1968;90/2: 353-359. [9] McFeron DE, Chao BT. Transient interface temperatures in plain peripheral milling. ASME, 1956. [10] Ueda T, Hosokawa A, Oda K, Yamada K. Temperature on flank face of cutting tool in high speed milling. CIRP Annals-Manufacturing Technology 2001;50/1: 37-40. [11]Kerrigan K, Thil J, Hewison R, O’Donnell G. E. An integrated telemetric thermocouple sensor for process monitoring of CFRP milling operations. Procedia CIRP 2012; 1, 449-454.