a novel method to determine tool-chip thermal ... - IDC Technologies

J. E. Jam et al. / International Journal of Engineering Science and Technology (IJEST)

A NOVEL METHOD TO DETERMINE TOOL-CHIP THERMAL CONTACT CONDUCTANCE IN MACHINING J. E. JAM, V. N. FARD Composite Materials and Technology Center, Tehran, IRAN

Abstract In this paper thermal contact conductance of the tool-chip interface in the metal cutting process is determined using an inverse procedure. An orthogonal cutting of the AISI 1045 steel is simulated by LS-DYNA finite element code. Tool-chip interface average temperature is determined using thermo-mechanical coupled analysis of a two dimensional finite element model of the orthogonal cutting process under plane strain condition and compared with experimental measured data from literature during the inverse procedure. In thermo-mechanical coupled analysis friction condition in tool-chip interface is modeled using Coulomb’s friction law together with the shear stress limits to describe the sliding and sticking condition on the tool rake face. The work piece material behavior has been modeled using the Johnson-Cook constitutive material model. Numerical simulation results of the orthogonal cutting process consisting of temperature in the tool-chip interface and cutting forces are shown and compared with experimental data reported in literature. Also, in this paper three dimensional thermal analysis of the cutting tool is performed. Temperature distribution in three dimensional cutting tool model and thermal contact conductance of the tool-chip interface are also presented. Keywords: Thermo-mechanical coupled analysis; Thermal contact conductance; FEM; Orthogonal cutting.

1. Introduction In metal cutting processes, high temperatures are generated due to large plastic deformation of the work piece material in the cutting zones. High temperature in the tool rake face strongly affects tool wear, tool life, work piece surface integrity, chip formation mechanisms and contributes to the thermal deformation of the cutting tool [1]. Thus, determination of the maximum temperature and temperature distribution along rake face of the cutting tool is one of the interesting topics for researchers. The finite element method has particularly become the main tool for simulation of metal cutting processes in the recent decades [2, 3]. Finite element models are widely used for optimization of tool geometry [4-6], calculating the residual stresses [7, 8], determination of temperature distribution [9, 10], chip segmentation [11, 12] and optimization of new machining techniques such as high speed machining and hard turning [13-16]. Metal cutting processes can be studied faster and cheaper using finite element method comparing to time consuming and expensive experiments. A large number of input parameters are necessary for a successful modeling of the metal cutting by the finite element method such as material properties, the tool-chip friction model and thermal contact conductance of the tool-chip interface. Several constitutive material models are derived such as Johnson-Cook [17] and ZerriliArmstrong [18] models with the material constants obtained from experiments. These material models determine the work piece material behavior in high strain, wide range of strain rates and high temperatures of cutting zones. The effect of the material model constants on the orthogonal cutting simulation accuracy is also investigated in the literature [19]. Tool-chip friction model is another important input parameter for the modeling of the cutting process. Many investigations are performed to study the influence of the friction modeling on metal cutting simulation results [20-22]. In these investigations different friction models are presented and numerical simulation results are compared with experimental data. The thermal contact conductance is a consequence of contact being made only at discrete locations, rather than over the entire area. Fig. 1 shows the cross section of two contacted bodies and temperature drop in contact interface. Ideally, the contact area is the interface area of surfaces. However even in very smooth surfaces, irregularities exist which may restrict the contact area to few discrete spots irrespective of the sample size. Thus, the heat flow is constricted in the vicinity of the contact region [23].

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Vol. 3 No.12 December 2011

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Fig. 1. Contact cross section and temperature drop

This constriction is responsible for the contact resistance. Thermal contact conductance ( h ) may be defined as:

h=

q T1 − T2

(1)

in which T1 - T2 is the temperature drop across the interface between two contacting bodies and ( q ) the heat flux which is defined as:

q=

dQ dA

(2)

where ( Q ) and ( A ) are the heat flow and contact area respectively [24]. Thermal contact conductance of the tool-chip interface is an essential parameter to determine the temperature distribution in the cutting tool. This parameter is not determined for the metal cutting condition in the tool rake face yet. In numerical simulations of orthogonal cutting different values are employed for thermal contact conductance of the tool-chip interface

(10

4

)

-107 W / m 2 .°C . There are plenty of literature on

experimental measuring this value in forming processes [23-25], but no study on the value of this parameter in the cutting process [26]. Thus, the aim of this paper is to determine the thermal contact conductance of the toolchip interface using finite element method, and experimental data from literature [27]. In this paper thermal contact conductance of the tool-chip interface in metal cutting process is determined using an inverse procedure which is based comparison of the orthogonal cutting finite element analysis results and experimental tool-chip temperature data given in literature. A two dimensional Lagrangian finite element model of the orthogonal cutting process under plane strain condition is developed to determine the tool-chip interface temperature and heat flux flowing into the cutting insert. The procedure of the thermal contact conductance determination is shown in Fig. 2. In the orthogonal cutting simulation, the friction condition in the tool-chip interface is modeled using Coulomb’s friction law together with the shear stress limits to describe the sliding and sticking condition on the tool rake face. The work piece material behavior has been modeled using the Johnson-Cook constitutive material model. Numerical simulation results of the orthogonal cutting process consist of the temperature distribution in tool-chip interface is presented. Both cutting forces and the average temperature in the tool-chip interface are obtained and compared with experimental data reported in literature. Temperature distribution in three dimensional cutting tool model and calculated thermal contact conductance of the tool-chip interface are also presented. 2. The orthogonal metal cutting finite element model The heat flux in the tool-chip contact area is an essential input parameter for the cutting tool thermal analysis. In order to determine the heat flux, in this paper a two dimensional Lagrangian finite element (FE) model of orthogonal cutting process under plane strain condition is developed. There are two major FE formulations, i.e., the Lagrangian and the Eulerian formulations. In the Lagrangian method, the elements, covering the region of analysis exactly, are attached to the material and deformed simultaneously with the work piece. In Lagrangian formulation, simulation starts from transient to steady state analysis. A lagrangian finite element simulation of the orthogonal cutting process needs chip separation mechanism to separate chip from the work piece.

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Fig. 2. The thermal contact conductance calculation inverse procedure

Crack propagation and pour deformation without crack are two main concepts about chip separation mechanisms. In the present simulation, pour deformation concept is considered because of crack propagation mechanism limitations to simulate chip separation in the orthogonal cutting with negative rake angle and non sharp cutting edge. In order to simulate chip formation based on pour deformation, cutting tool is allowed to penetrate in the work piece and adaptive remeshing is performed to avoid extreme distortion of elements. The two dimensional orthogonal cutting model is presented in Fig. 3. The length and height of the work piece are 4.0 and 1.0 mm, respectively. This model is meshed using 4-node plain strain elements. Plain strain condition can be approximated in the orthogonal cutting simulation if the width of cut is more than or equal to 10 times of the undeformed chip thickness. All simulations have a cutting depth of 0.16 mm, cutting width of 2 mm and tool rake angle of -5 degrees. All cutting parameters are presented in Table 1. By assuming isotropic material behavior and Von-Mises plasticity, a constitutive model is proposed by Johnson and Cook [17] that predicts equivalent stress in various plastic strains, wide range of strain rates and different temperature conditions. Thus, equivalent stress σeq can be expressed as: (3) σ eq = A + Bε pn 1 + C ln ε∗ 1 − T ∗m

(

)(

)(

)

where A, B, C, n and m are material constants, ε p is accumulated plastic strain, ε 0 is reference strain rate, T , T0 , Tm are the actual temperature, the room temperature and the melting temperature respectively. This material model is used for determination of the work piece material flow stress. Johnson-Cook material model constants for the work piece material, AISI 1045 steel, were determined by Jaspers and Dautzenberg [28]. These constants are listed in Table 2. Cutting tool is assumed as a rigid material. In the coulomb’s updated friction law, there are two distinct regions on the rake face of the cutting tool. The first region from cutting edge is the sticking friction region and the sliding region is the second one. In the sliding region the Coulomb’s friction law with constant coefficient of friction µ is applied, whereas in the sticking region the equivalent shear stress limit is imposed. Thus, the frictional stress τ fr on the interface can

be expressed as:

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τ fr = μσ n

,

τ fr < τ max

(6)

τ fr = τ max

,

τ fr ≥ τ max

(7)


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where

σn ,

is the normal stress along the tool rake face. The equivalent shear stress limit,

determined as:

τ max =

τ max

is

σ eq

(8) 3 where σ eq , is the Von-Mises equivalent stress in the secondary shear zone.

ST SH

SC

SH

Fig. 3. Schematic of the orthogonal cutting model

In present model constant coefficient of friction ( µ = 0.65 ) is assumed for all simulations. The shear stress limit,

τ max

range is estimated from equation (8). Therefore several orthogonal cutting simulations are

performed with various shear stresses in the tool-chip contact area and suitable value for this parameter is determined by comparison of numerically calculated cutting forces with experimental data given in reference [27]. The numerical and experimental cutting forces are listed in Table 3. Table 1. Orthogonal cutting parameters

Cutting speed (m/min) Feed rate (mm) Rake angle (degree) Relief angle (degree) Edge radius (µm) Cutting width (mm)

105, 150 & 210 0.16 -5 5 33 2

Table 2. Johnson-Cook material model constants for the work piece material

A ( Mpa )

B ( Mpa )

C

m

n

553

601

0.014

1.0

0.234

Table 3. Comparison of the experimental and numerical cutting forces

τ max ( Mpa )

360

370

380

390

Experimental

Frictional Cutting Force

405 N

410 N

420 N

435 N

440 N

Orthogonal cutting is a thermo-mechanical coupled process. During the cutting process heat generation occurs as a result of plastic deformation. The deformation zones and heat generation sources in metal cutting process are shown in Fig. 4 [29].

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Fig. 4. Heat generation sources in orthogonal metal cutting

Firstly, heat is generated in the primary deformation zone due to plastic work done at the shear plane. The local heating in this zone results in very high temperatures, thus softening the material and allowing greater deformation. Secondly, heat is generated in the secondary deformation zone due to work done in deforming the chip and in overcoming the sliding friction at the tool-chip interface zone. Finally, the heat generated in the tertiary deformation zone, at the tool work piece interface, is due to the work done to overcome friction, which occurs at the rubbing contact between the tool flank face and the newly machined surface of the work piece. Thus, a thermo-mechanical coupled analysis is performed on the finite element model. Following boundary conditions are applied to the orthogonal cutting model:

(

)

•

For areas of the cutting tool which are exposed to the air, heat loss due to convection h = 20 W / m 2 . °C

•

is considered. The cutting tool boundary, which is away from the cutting zone, remains at the room temperature (T = 25 °C ) .

•

Thermal contact with thermal contact conductance is assumed for the tool-chip contact surface. The work piece boundary surfaces are assumed adiabatic. Thermal heat loss from these areas can be neglected because of the high cutting velocity of the cutting tool. The explained cutting tool thermal boundary conditions are shown in Fig. 3 and are expressed as follow: T = T∞ (on ST),

∂T = hint (T − Tc ) ∂n ∂T −k = h∞ (T − T∞ ) ∂n −k

−k

∂T =0 ∂n

(on SC) (on SH) (on the work piece boundaries)

(9)

where k is the thermal conductivity of the object considered, Tc the contact temperature of the opposite object at the tool–chip interface and n the unit vector normal to the boundary surface. 3. 3D finite element model of cutting tool Three dimensional CAD geometry and meshed model of the cutting tool are presented in Fig. 5. Thermal and mechanical properties of the cutting insert and holder material are listed in Table 4. Steady state thermal analysis is performed using ANSYS commercial finite element code. The calculated heat flux applied over toolchip contact area on the rake face of the cutting insert is the basis of the thermal analysis. Experimental data about the tool-chip contact area in the machining condition, similar to the present problem condition, are given

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in reference [27]. Fig. 5 also shows the tool-chip contact area on the rake face of the cutting insert over which the thermal heat flux is applied. Following boundary conditions are used for the model: For all areas of the cutting insert which are exposed to the air, heat loss due to convection

( h = 20 W / m . °C ) is considered. 2

Thermal contact (thermal contact conductance = 104 W / m 2 . °C ) is assumed for all interior areas of the cutting insert, shim seat and holder shank, which are in contact.

Fig. 5. CAD geometry, finite element meshed model of the cutting tool and tool-chip interface area

4. Results and discussions Fig. 6 shows the temperature distribution contours of the tool and the chip near the cutting zone in various simulation times. According to the orthogonal cutting simulation, the maximum temperature location in the chip side of the tool-chip contact area varies with the simulation time. In the beginning of the simulation, maximum temperature in the chip is located near tool tip which tends to the second deformation zone on the rake face of the cutting tool in the steady state condition. This observation is in agreement with the experimentally measured temperature distribution of the literature [29]. Average temperature of the cutting tool in contact area with the chip in various simulation times is shown in Fig. 7 for cutting speed of 105 m / min . According to this figure cutting tool temperature and thermal condition in the tool-chip interface achieve steady state condition after simulation time of 0.8 mc . Finite element simulation is also performed on the orthogonal cutting of the work piece in various cutting speeds. Table 5 lists average temperature of the cutting tool and the chip in the tool-chip interface calculated by thermo-mechanical coupled analysis. Numerical results are also compared with experimental data given in the literature [30]. According to Table 5, there are reasonable agreements between numerical simulation results of the cutting tool average temperature and the experimental measured data. Maximum shear stress distribution in deformation zones and chip morphology in various cutting speeds are shown in Fig. 8. As cutting speed increases the chip curl radius decreases, because of increasing temperature gradient in the chip thickness and bi-metal effect. Fig. 9 shows the numerical calculated cutting forces which are compared with the experimental data. As shown in Fig. 9 the numerically obtained cutting forces match the experimental data well. Consequently, a reliable simulation of cutting process is achieved. Table 4. Thermal and mechanical properties of cutting insert and tool holder

Property Material Density (kg/m3) Yang module (Gpa) Poisson’s ratio Specific heat (J/kg.°C) Thermal Conductivity (W / m.°C )

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Cutting Insert and Shim Seat Tungsten Carbide

Tool Holder AISI 1045 Steel

15000 800 0.2 203 33 + 0.015T

7850 207 0.3 452 45 – 0.0225T


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Fig. 6. Temperature counters in various simulation times (cutting speed of 210 m/min)

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Thermal heat fluxes, flowing into the cutting tool in the tool-chip interface, are listed in Table 5 for various cutting speeds calculated from thermo-mechanical coupled analysis results. The heat fluxes are calculated as: q = h(Tch − Tt ) (10)

Fig. 7. Average cutting tool temperature in tool-chip interface versus simulation time for cutting speed of 105 m/min

where h, Tch , Tt are thermal contact conductance, chip average temperature and tool average temperature, respectively. The heat fluxes are applied over the tool-chip contact area on the cutting tool rake face in the three dimensional cutting tool finite element model. Fig. 10 shows temperature distribution in the cutting insert and its holder. The average temperatures of the tool and the chip in the tool-chip contact area and calculated thermal contact conductance from equation (1) are listed in Table 6. According to the tool thermal analysis results, the thermal contact conductance of 5 × 105 W / m 2 .°C is calculated for the tool-chip contact in the orthogonal cutting condition. Comparison of the calculated thermal contact conductance for the metal cutting process obtained this paper with the measured values in the forging process reported in literature [23] verifies the accuracy of the numerical method presented in this study. Table 5. Average temperature in the tool and chip in tool-chip contact area

Cutting speed ( m / min )

Numerical

Tool Numerical

Heat Flux (FEM)

Experimental

105 150 210

670 705 750

734 753 785

585 619 672

20.9 MW/m2 24.7 MW/m2 29.4 MW/m2

Chip

Table 6. Thermal analysis results

Cutting speed ( m / min ) 105 150 210

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Average temperature in interface FEM Exp. [30] 653 684 725

670 705 750

Tool-chip contact length Exp. [27] 0.67 mm 0.60 mm 0.52 mm


Thermal contact conductance (from Eq. 1) 137 KW/m2. °C 182 KW/m2. °C 260 KW/m2. °C

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Fig. 8. Maximum shear stress counters and chip geometry in various cutting speeds

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Fig. 9. Numerical simulation of the cutting forces compared with the experimental data

Fig. 10. Temperature distribution in the three dimensional cutting tool (cutting speed is 105 m/min)

5. Conclusions In this paper, a thermo-mechanical coupled analysis was performed on the orthogonal cutting model using finite element method under plane strain condition. The orthogonal cutting simulation results such as temperature distribution contours, chip geometry and cutting forces were presented and compared with the experiment. An inverse procedure was developed and thermal contact conductance in tool-chip interface was determined for orthogonal machining process. These comparisons showed that the orthogonal cutting process was successfully simulated by the finite element analysis. A pure thermal analysis was also performed on the cutting tool in the three dimensional FE model. The heat flux from the thermo-mechanical coupled analysis was applied over the rake face of the cutting insert in the thermal model. Temperature distribution in cutting tool in 3D real dimensions was also presented in this paper. Prediction of the tool temperature in metal cutting simulations will be improved using the actual thermal contact conductance.

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