Three-dimensional thermo-mechanical analysis of molybdenum wire electrode during wire EDM process
B. Mechanical analysis
3.5 Computation of temperature and stresses generated in the wire using the developed model
and the stress is represented as
1 2 3 12
23 13
(3.21)
The displacement field {u} is represented by
u
N d
(3.22) where {u} = [u v w]T and {d} is the nodal displacement degree of freedom of an element.Strains are determined by the relation
B d
(3.23) and
B N (3.24) In coupled thermo-mechanical analysis, both the temperature and stress are computed simultaneously.3.5 Computation of temperature and stresses generated in the wire using the developed
Figure 3.4 Temperature dependent thermal conductivity(Tietz and Wilson (1961)) and specific heat (Taylor and Finch(1964)) of molybdenum
Figure 3.5 Temperature dependent Young‟s modulus of molybdenum(Zhang et al. (2014))
Table 3.1 Thermal and physical properties of molybdenum(Zhang et al. (2014))
Property Value
Density(kg/m3) 10200
Poisson‟s ratio 0.3
Coefficient of thermal expansion (µm/m-ºC) 4.6
Melting point (K) 2896
Tensile testing of molybdenum wire
The yield strength and tensile strength of the wire were determined by performing a tensile test of a fresh molybdenum wire. The tensile testing of the wire was carried out on a micro- tensile machine by Deben (Deben micro test MT10081), shown in Figure 3.6. The micro tensile machine had an upper limit of up to 5 kN tensile load and maintained the crosshead speed at 0.2mm/min. The tensile testing was carried out under ambient conditions. The data from the tensile test was collected and converted into stress-strain values. The stress-strain behavior of the molybdenum wire was studied to determine the yield strength and ultimate strength of the wire. Figure 3.7 shows the stress-strain behavior of the wire during the tensile testing. The yield point of the molybdenum wire was determined to be about 600 MPa and the ultimate strength at around 1472 MPa. These values of yield stress and strain were taken from the graph to be incorporated into the numerical model.
Figure 3.6 Micro tensile testing machine
Figure 3.7 Stress vs. strain graph of a molybdenum wire
3.5.2 Process parameters used for the model
In the present model, four input parameters, viz. discharge voltage, discharge current, pulse on-time and pulse off-time were varied at different levels. The process parameters have been selected by performing extensive preliminary experiments. The trade literature and research articles have been duly referred to choose the ranges of the process parameters. The levels chosen for each process parameter are listed in Table 3.2.
Table 3.2 Process parameters and their levels Factors Level 1 Level 2 Level 3 Discharge voltage (V) 60 85 -
Discharge current (A) 4 6 8
Pulse on-time (µs) 4 8 16
Pulse off-time (µs) 2 4 6
The wire velocity (v) was kept constant at 6 m/s in the present model.
3.5.3 Overview of the process model development
Figure 3.8 shows the schematic representation of the thermo-mechanical analysis that was carried out to compute the thermal residual stresses. A three-dimensional coupled thermo- mechanical model was developed for the wire electrode. In the present study, the temperature is first evaluated during the thermal analysis and based on the temperature distributions obtained, the stresses on the wire are calculated after a single pulse at different process conditions. This model shall pave the way to estimate the total thermal load in the wire and evaluate the effects that lead to wire breakage by determining the stresses induced due to sparks during the operation.
Figure 3.8 Schematic representation of thermo-mechanical analysis
3.5.4 Finite element meshing of the wire geometry
The process model along with the boundary conditions was solved in transient mode by using ABAQUSTM, a commercial FEM solver. The wire geometry is discretized with eight-node hexahedral elements C3D8T. The elements „C3D8T‟ are especially suitable for coupled thermo-structural analysis. Figure 3.9 shows the meshed model of the wire electrode along with the incorporated boundary conditions. Mesh optimization was performed for better convergence of results in optimum time. The overall mesh size was kept at 30 µm for the wire model. The heated and nearby region was discretized using finer mesh size to get better accuracy of results. The mesh sensitivity analysis was carried out for a single process condition at discharge voltage (V) = 60 V, discharge current (I) = 6 A, pulse on-time (ton) = 16 µs, pulse off-time (toff) = 6 µs, wire velocity (v) = 6m/s. The heated region was discretized with a fine mesh of various sizes, shown in Table 3.3. It was observed that the smallest change in temperature occurs when the fine mesh size changes from 10 µm to 8 µm as compared to the other cases. Thus, the element of 8 µm size was selected as the optimum fine mesh size for the heated region to achieve better results. The moving heat source concept was used in the model to incorporate the effect of moving wire during the wire EDM machining process. The Gaussian heat flux moving at a constant velocity over the wire surface was employed using a user subroutine DFLUX. The subroutine is included in Appendix A3. The FORTRAN code was written to define the input process conditions during a single discharge phenomenon during wire EDM cutting. The movement of Gaussian heat flux over the wire surface is shown in Figure 3.9. The transient heat transfer problem was solved by applying
the heat flux at the spark location and adopting an automatic time step increment. Convection heat transfer is applied over the wire surface as shown in Figure 3.9.
Figure 3.9 Mesh model of wire electrode
Table 3.3 Mesh sensitivity analysis for the fine mesh in the heated region Serial no. Mesh size
(µm)
Temperature output (K)
Change in temperature (%)
CPU time (hrs.)
1 25 664.3 - 0.15
2 20 517.4 22.11 0.26
3 15 500.6 3.24 1.79
4 10 470 6.11 5.92
5 8 460.7 1.97 8.92