Some aspects of finite element modelling of ultrasonically aided micro-EDM of CoCr alloys

The paper deals with finite element modelling of micromachining CoCr alloys by ultrasonically aided electrical discharge machining. This hybrid machining process has two components: a thermal one due to EDM, and a mechanical one to ultrasonic assistance. Both components were modelled using Thermal and Structural Mechanics time dependent modules of Comsol Multiphysics. The results were compared with the experimental data obtained in our laboratories, proving a good agreement and offering some solutions for machining optimization.


Introduction
The mechanical properties of CoCr alloys, extremely wear resistant and also at corrosion, and biocompatibility as well, recommend their use in medical applications, injection molding and engine components [1,2].The stellite superalloys have similar using areas but also at cutting tools, components for guns etc.The C content and existence of carbides play an important part in their functional behavior [3,4].Conventional casting of CoCr alloys determines existence of metallic carbides, affecting later machining, in comparison with other nonconventional techniques like selective laser melting (SLM) or Electron Beam Melting (EBM) that assures a homogenous structure [1,2].
All increased properties of CoCr alloys determine high difficulties at conventional machining of micro-surfaces [5].Ultrasonically aided micro-electrical discharge machining (µEDM+US) is an appropriate response in terms of machining rate, precision and surface quality, supported by relative low costs [6].This hybrid process was applied for other advanced materials difficult to machine by cutting technologies [7,8].
At micro-EDM+US application, CoCr alloys thermo-physical characteristics as well as mechanical ones become critical, corresponding to their two components of this hybrid machining: thermal one due to EDM, and ultrasonically induced cavitation owed to ultrasonic assistance.In this respect, values of properties needed for modelling of EDM part are: density 8290 kg/m 3 for usual alloys, or much higher (9120-9240 kg/m 3 ) at additional alloying elements, and 8690 kg/m 3 for stellite, thermal conductivity 33W/m o K at 1000 o C, which is lower than at usual steels, heat capacity 420-460 J/kg o K, which is slight lower than at usual steels, melting range 1380-1430 o C [5,10,11], and boiling temperature around 3000 o C, taking into account the boiling points of alloy main components (Co, Cr, Mo).About mechanical characteristics of CoCr alloys, necessary for ultrasonic material removal modelling, modulus of elasticity varies between 200 -220 GPa, much higher than other alloys used in medical applications, based on Ti and Au, and ultimate tensile strength is 1300 MPa [1,2,9].Stellite alloys have higher elasticity modulus at 230 GPa, and ultimate tensile strength at 1195 MPa [3,4], in comparison with CoCr Arcam alloys with 960 MPa [2].The fatigue limit is 610 MPa at rotating beam fatigue test [2].Other values of fatigue limits of the alloys are: at bending, this is estimated in the region of 480 MPa [9]; for stents CoCr alloys, it is predicted much lower, at 207 MPa [10].

Experimental data
An experimental setup for preliminary studying the micro-EDM+US process on CoCr alloy was created, presented in fig. 1.This comprises basically an ultrasonic chain, integrating the tool its end, connected to an ultrasonic generator of 20 kHz, producing tool amplitude of around 2 µm during EDM process.CoCr alloy rectangular samples of 30 x 50 x 1 mm were machined comparatively on Romanian ELER 01 machine with US vibrations of tool (EDM+US) and without US (classic EDM).Both commanded and relaxation pulses were used provided by a special generator for finishing and micro-machining.The working parameters at commanded pulses were: current step, I=3A, positive (tool) polarity; pulse time, t i =48 µs, pause time, t 0 =24 µs; t i =8µs t 0 =8µs.At relaxation pulses, the specific working parameters were: negative polarity, capacitor step, C=10 nF, resistance step, R=0.74 kΩ (for adjusting supply current).For flushing, the lateral one was chosen with pressure, p hl =0.04 MPa.The values of consumed power on ultrasonic chain (P cUS ) were: 90 and 120 W.
The variation of total hydraulic pressure (p ht ) is calculated with the following relation, and presented in fig.2: where: During T US , commanded and relaxation pulses are delivered.At overlapping the pulses on CMS, it was noticed experimentally that the discharge is stopped due to high pressure generated by collective gas bubble implosion.Then the dielectric liquid is allowed to access the melted material by discharge, and therefore increased volume of material is removed.
The microtopographies provided by scanning electron microscope (SEM) QUANTA INSPECT F50, with field emission electron gun and resolution of 1 nm, and corresponding profile of craters average dimensions, obtained by mediation of craters diameters with their depth (Rz) given by surface roughness tester SJ411, are presented in fig. 3 -8.

Finite element modelling of micro-EDM+US process
The material removal process of µEDM+US on CoCr alloys was modelled by finite element method using Comsol Multiphysics, time dependent modules of Heat Transfer in Solids and Solid Mechanics, corresponding to EDM, and ultrasonic components.Some parametric models were created for each pulse type, using the assignation shown in fig.9.The Van Dijck and Snoeys's overheating model was considered for EDM component modelling.In this case, boiling is the main mean to remove overheated material after pulse end when pressure drops suddenly; the gas bubble formed around plasma channel lasts very long after the end of pulse, so the material melted by discharge is already solidified [6].Constant 3473 K temperature on EDM spot, thermal isolation on area covered by gas bubble, and convection cooling on workpiece periphery in contact with dielectric liquid with 313 K were setup as boundary conditions.The temperature distribution obtained around EDM spot with t i =48 µs and t 0 =24 µs is presented in fig. 10 At ultrasonic assistance, due to relative long pulse time t i =48 µs, comparable with T US , it is very high probability to its overlapping on CMS [14].So, melting becomes the main mechanism of material removal since the gas bubble around plasma channel collapses at CMS, and dielectric liquid accesses the melted material.The temperature distribution obtained in this case is presented in fig.11.a:During EDM removal, another mechanism is produced due to ultrasonic cavitation.Crater margins are removed by shear of shock waves oriented parallel to machined surface.In order to underline the volume of material removed by hydraulic mechanical effect of ultrasonic cavitation, the fatigue limit at shear pulsing cycle (τ 0 ) was calculated [11]: where: σ r is the usual ultimate tensile strength; in this case, σ r =1300 MPa, and the parameter of interest is τ o =277.76MPa.In fig.11.b, it can be observed a massive removal also from the bottom of crater, which determines the roughness increase, i.e. the depth of crater.This is confirmed by experimental data (see fig.At µEDM+US with t i =8 µs, t 0 =8 µs, the overlapping probability of pulse time on CMS, decreases very much, under 20% [6].So, classic thermal removal like in classic µEDM occurs dominantly, and the temperature distribution after pulse end is presented in fig.12: The boiling isothermal position is in agreement with experimental data from fig. 5, validating the model.Over this thermal removal mechanism is superimposed, the ultrasonic removal due to shock wave produced by CMS parallel to machined surface [6].In fig.12.b, distribution of Von Mises stress is presented, higher than shear fatigue limit, which shows IManE&E 2017 the material that is removed.The decrease of craters depth is produced, and implicitly the surface roughness, confirming the experimental data from fig. 6.b, at lower P cUS =90W.At µEDM+US with relaxation pulses, the nature of material removal mechanism is very similar with the previous working mode.The ultra-short discharge duration of relaxation pulses makes a very low probability to overlap them on CMS.So, classic thermal removal is dominant, as presented in fig.13.a, associated with ultrasonic shear of craters margins, producing lowering of craters dimensions, confirmed experimentally by data from fig. 8.

Conclusions
The FEM study of µEDM+US on CoCr alloy, not systematically treated in the state of the art yet, emphasized two types of material removal mechanism, confirmed by experimental data.At longer pulse time, comparable with ultrasonic period, the thermal mechanism of removal is dominant, and position of melting isothermal shows a spectacular increase of machining rate.At shorter pulse time, especially at relaxation pulses using, the ultrasonic hydraulic removal becomes dominant by removing the craters margins -the debris are not spherical like at melting and resolidification.Finding an optimum value of consumed power on ultrasonic chain, correlated with CoCr alloy fatigue limit, is of utmost importance in order to decrease the surface roughness in comparison with pure µEDM.

Fig. 9 .
Fig. 9. Example of assigned parameters for material removal process of µEDM+US on CoCr alloy.
, indicating close value to experimental ones (see fig. 3.b), validating the model.
4.b), explained by relative high power, P cUS = 120 W used on ultrasonic chain.Both removal mechanism determined increase of craters dimensions in comparison with pure micro-EDM, experimentally emphasized by fig. 4.
Variation of tool elongation and total pressure in the gap within TUS during EDM+US tests.
1/2 =1267.7 m/s; K=1.35x109Pa (K-bulk modulus); p hl -local hydraulic pressure [Pa], p hl =0.04MPa.At each final of ultrasonic period T US , when pressure increases, cumulative microjets stage (CMS) occurs, due to the collective implosion of gas bubbles, generating shock waves.This produces pressure of 100 MPa order of magnitude, oriented along the gap, frontal in this case -fig.2.