FE-based simulation on micro cutting temperature

In recent years, modelling and simulation of micro cutting has been studied by many researchers. However, very few investigations have been carried out on the micro cutting temperature and heat generation which has different effects from those of conventional cutting. Moreover, the simulation study of micro cutting temperature is quite challenging because the meshing elements are badly distorted even when adaptive meshing is used during the simulation. The consequent errors with model definition always exists when solving the heat transfer equation. However, FE-based modelling and simulation is needed due to the difficulty and complexity of the real micro machining in some cases. Consequently, accurate modelling needs to improve until inherent micro cutting mechanisms have been accurately modeled and simulated. Generation of micro cutting temperature in diamond turning is caused by very low temperature and generated heat, and, subsequently, thermal effects. Thus, there is a need to carefully study the modeling of micro cutting temperature in oder to accurately simulate the cutting temperature.

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6.2.1 Material Constitutive modelling

In order to model and characterise the cutting temperature in micro cutting, accurate material modelling is very important and represents the actual changes of physical propertires during machining. Thus, the Johnson-cook model is employed (Duan, et al., 2009; Liu & Melkote, 2007; Zong, et al., 2007). It is expressed as the flow stress which is a function of strain, strain rate and temperature in terms of the functional equation below.

̅ [ ̅ ] [ ( _̇ ̇)] [ (

) ] (6.1)

Where ̅ is the equivalent stress, ̅ is the equivalent plastic strain, ̇ is the plastic strain rate, ̇ is the reference strain rate (1.0 s-1_),

is room temperature,

is the melting temperature, A is the initial yield stress (MPa), B is the hardening modulus, n is the work-hardening exponent, C is the strain rate dependency coefficient (MPa), and m is the thermal softening coefficient. Physical properties and material constants of Johnson-cook model for diamond tool (Zong, et al., 2007) and aluminium AA6082-T6 are presented in Table 6.1 and 6.2. (Özel & Karpat, 2007)

Table 6.1 Physical properties of AA6082-T6 and diamond tool

E(Gpa) ν c(J/kgºC) (kg/m3) K(W/mºC)

AA6082-T6 70 0.33 896 2,700 180

Diamond tool 1,050 0.1 420 3,520 1,000

Where E is Young’s modulus, υ is Poisson’s ratio, c is specific heat, is material density, and K is thermal conductivity respectively.

Table 6.2 Johnson-cook constitutive material model parameters for AA6082-T6

A B C n m ̇

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6.2.2 Modelling of the chip separation criteria

In order to simulate the seperation of chip i.e., chip formation phenomenon, a dynamics failure model is also employed for the Johnson-cook model. The Johnson-cook damage parameter is based on the value of the equivalent plastic strain at element integration points. The failure is assumed to occur when the damage parameter D exceeds 1:

∑ ( ̅

̅ ) (6.2)

Where ̅ is the increment of equivalent plastic strain, ̅ is the strain at failure which is assumed equal to

̅ [ ( )] [ ( ̇

̇ )] (

) (6.3)

Where d1-d5 are failure parameters namely including Initial failure strain, Exponential factor, Triaxiality factor, Strain rate factor, and Temperature factor respectively. The damage parameters for Johnson-cook model are presented in table 6.3 (Zhou, et al., 2013).

Table 6.3 Johnson-cook failure model parameters for AA6082-T6

d1 d2 d3 d4 d5

0.0164 2.245 -2.798 0.007 3.658

6.2.3 Conditional equation on heat and temperature distribution

The temperature and heat distribution during the cutting process is modelled and simulated. The main sources of generated heat are the plastic work and the friction at the tool-chip interface which are converted into heat. A three- dimensional thermal conduction analysis (Fang & Zeng, 2005; Mamalis, et al., 2001; Marusich & Ortiz, 1995) is then developed and coupled into the cutting

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model. Thus, the governing differential equation for thermal conduction is given by

[ ] [ ] ̇ (6.4)

Where k is the thermal conductivity, ρ is the density, c is the specific heat, and ̇ is the volumetric generation rate. During the cutting process, the heat generated from both plastic work and friction can be calculated by

̇ ∫ ̅̇ ∫ ̇ (6.5) Where ̅̇ is the effective plastic strain rate, is the friction stress, ̇ is the tangential velocity component at the chip–tool interface, and V is the element volume.

The same cutting conditions as the experimental setups as shown in the next section (section 6.3) are used. Thus, a comparison of FE-based simulation associated with cutting experimetal results and discussions are given in sections 6.2.4 and 6.6 respectively.

6.2.4 Simulation results

The micro cutting temperature can be modeled with the Johnson-cook constitutive Material modeling as previously mentioned. In order to correct the cutting temperature results and avoid the distortion of mesh elements which causes errors whilst solving heat transfer equations in the simulation procedure, optimising the three main parameters that directly influence the cutting temperature is needed. The optimisation of three influencing parameters can be conducted by trial and error method. They particularly include friction coefficient

(µ) between diamond tool and workpiece’s surfaces as being used under

condition of the constant friction model (Tan, 2002) which was applied in this FE model and simulation, damage evolution (D) of material, and mesh sizes of tool (Mt) and workpiece (Mw). In the simulation process, the workpiece is divided as

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a small strip at the interaction areas with the cutting tool tip so that chips can be formed. Thus, damage evolution will be D for the strip and the rest of the workpiece’s elements, i.e, Ds and Dw respectively. Finally, the optimum parameters for validation of the cutting experimental results can be illustrated in Figure 6.1., and the simulation and experimental validation and comparison can also be found in section 6.6.

Figure 6.1 The simulation results of micro cutting temperautre and generated heat illustatation by Abaqus/explicit (µ = 0.3)

6.3 Experimental and measurement setup on cutting temperature and heat