Finite element simulation of tool wear in machining of nickel-chromiumbased superalloy

Andrea Abeni. Department of Mechanical and Industrial Engineering, University of Brescia, V. Branze 38, Brescia, 25123, Italy Corresponding author: Andrea Abeni. E-mail address: andrea.abeni@unibs.it Cristian Cappellini. Faculty of Science and Technology, Free University of Bolzano, P.zza Università 5, Bolzano, 39100, Italy Aldo Attanasio. Department of Mechanical and Industrial Engineering, University of Brescia, V. Branze 38, Brescia, 25123, Italy


Intr Introduction oduction
Nickel-chromium based superalloys, and in particular Inconel 718, are widely used in high temperature and extremely corrosive environments, such as jet engines parts, gas turbine components, and rocket motors in the aerospace industry, due to their ability to maintain proper mechanical characteristics also in extreme conditions [1]. The retain of these properties, combined with low thermal conductivity, high chemical affinity with cutting tool materials, and the presence of abrasive carbide particles, makes Inconel 718 a difficult-to-cut material, and it brings to a very pronounced tool wear [2,3]. The amount of tool wear heavily affects machining forces, cutting efficiency, residual stresses and surface roughness of the machined product, and the tool life itself [4][5][6]. Moreover, when drilling is considered, due to its internal machining nature and to the higher difficulty of the chip to be removed from the cutting zone, stronger mechanical and thermal loads on tool and workpiece are generated if compared with external machining (turning and milling) [7], making the tool wear control more prominent. The evolution of tool wear can be assessed by means of several experimental tests, but these are expensive and time consuming [8]. To overcome this costly approach, Finite Element Methods (FEM) can be utilized. The capability of FEM to predict cutting forces, torques, and surface integrity as a function of process parameters and tool geometry for different machining operations has been demonstrated by numerous research [7][8][9]. The limits of the commercial software for Finite Element Analysis (FEA) are related to the impossibility of updating the geometry of the worn tool, and consequently the effects of it on forces and workpiece quality are not foreseeable [10]. In order to surmount this lack, in this work, a self-released subroutine able to modify the tool geometry in DEFORM 3D simulations by considering the volume reduction of the tool is presented.
The validation of the model has been performed by the comparison of simulation results with the experimental data obtained by drilling tests of Inconel 718 with conventional metal working fluids (MWF) lubrication [11]. The resulting simulated worn tool geometry, in agreement with the real tool geometry, has been used to perform FEM drilling simulations and to predict how torque changes as a function of the tool wear. The good comparison between simulated and experimental values demonstrated that, in a predictive maintenance perspective, the model can be profitably   The three dimensional CAD geometries of tool and workpiece are illustrated in Figure 1. The helicoidal drill design ( Figure 1a) must comply with the actual tool shape. The workpiece (Figure 1b) is modeled as a cylinder with a hole which replicates the profile of the drill. In DEFORM-3D, the FEM modelling of the chip formation is based on the chip separation criterion [12]. The fracture criterion defines a variable and a critical value of breakage. The contact between the tool cutting edge and the workpiece determines a crack in an element of the mesh if the variable reaches the critical value. Tools can be modeled as a rigid body while workpieces visco-plastic behavior can be defined as flow stress dependent on strain, strain rate and temperature. The software allows to select the fracture criterion between various models [13]. They include the Cockcroft-Latham criterion, which is defined by the Equation 1.
where ̅ is the effective strain; 1 is the maximum principal stress; D is a material constant. The thermal proprieties of the workpiece, the tool and the coating materials were defined in terms of thermal conductivity, heat capacity, emissivity and thermal expansion. The relative movement between tool and workpiece is achieved by assigning a feed speed and a rotation speed to the tool. The workpiece is fixed by adding a constrain to the nodes of mesh which belongs to the external side surface of the cylinder. FEM simulation of drilling requires the definition of the friction between tool and workpiece. Several researchers adopted shear model in machining [14,15], which is defined by Equation 2.
where is the tangential stress, k is the shear yield stress and m is the shear friction factor. It must be determined through tribological test or it can be assumed by literature. The FEM analysis considers also the heat exchange between objects. The simulator requires the heat conduction coefficient hcond across the tool-workpiece interface and the convection coefficient hconv to perform the thermal simulation. In machining, a high value of hcond is usually used to reach steady state in a short time [16]. Furthermore, hconv strongly depends on the cutting fluid proprieties and temperature and it can be experimentally determined.

T Tool w ool wear modeling ear modeling
The simulation of tool flank wear (VB) is performed by using a subroutine written in Fortran language [10]. It iteratively calculates the incremental wear (ΔVB) and subsequently it reconstructs the worn tool flank. The procedure includes a preliminary Lagrangian simulation to reach the thermo-mechanical steady state. At the beginning of the chip formation mechanism, the contact area with the tool surface increases. The increasing is limited by the chip curvature.
It determines the separation between chip and the rake surface of the drill.  Once the ΔVBMAX is known, it can be used to calculate the width of the wear on flank along the entire cutting edge.
Different computation strategy can be adopted in order to calculate different morphology of the worn flank. The procedure to update the tool mesh as function of VB(r)i is the most critical part of the subroutine. The mesh nodes which belongs to the flank, the rake and the cutting edge must be identified in order to calculate the local rake angle (γ) and the local clearance angle (α). As the wear VB, also γ and α depends on the distance r. The subroutine calculates the angles with the purpose to compute a local wear volume (LWV) in correspondence of each node of the cutting edge [10]. Since the LWV depends on the local VB, α and γ, the FEM is capable to compute the actual loss of volume due to wear on flank. Finally, the subroutine deletes all the nodes contained in the LWV. A new tool geometry is extrapolated by the updated mesh and it is used for the further iteration.

Stud Study case y case
An experimental study case was used to test the reliability of the procedure. In particular, the study case was designed with the purpose to simulate different profile of wear on flank and to compare them with the experimental profile.
The drilling tests were performed by Chen and Liao [11] with a multi-layer TiAlN PVD coated tungsten carbide drills manufactured by Guhring. An optical microscope and a scanning electronics microscope (SEM) were utilized to inspect the tool wear condition.
The SEM images allowed to evidence the development of micro-cracks distributing along the chipping area. The propagation of the cracks determined a progressive damage of the cutting edge. A crater wear was formed on the tool rake and the flank wear gradually increases. Finally, the wear rate increases drastically until the end of the tool life. Figure 3a shows the worn flank after 600 seconds of machining. The width of the wear lip was periodically measured on the curved section of the cutting edge, where it was maximum (VBMAX). The trend of VBMAX is illustrated in Figure   3b. For the first ten minutes, the wear rate was constant, and it was equal to 4.4·10 -4 mm/s. At the end of the drilling tests, the wear rate increased to 1.2·10 -4 mm/s. The drilling tests were simulated with the FEM model described in section 2. The tool was modeled as a rigid body and meshed with 200k tetrahedral elements, setting a maximum size of 0.3 mm. The elements with minimum size were located around the cutting edge and the ratio between minimum size and maximum size was set equal to ten.
The multi-layer TiAlN PVD coating was added. The workpiece was meshed with more than 100k elements with a size ranging from 0.05 to 0.5 mm. The thermo-viscoplastic behavior of Inconel 718 was selected from the DEFORM database, such as the proprieties of the materials which constitutes the tool [10]. Table 2 summarizes the critical value D of the Cockcroft-Latham criterion. The table expresses also the shear friction factor m and the convention coefficient hconv of the lubricant. The first was determined through tribological tests [10], while the second was calculated by Outeiro et al. [7].
T Table 2

R Results and discussion esults and discussion
The thermo-mechanical steady-state was reached after a drill rotation equal to 180°. The temperature of the tool cutting edge and the torque rapidly increase during the first 45°. Subsequently the torque reaches an equilibrium point at 10.7 Nm. The cutting edge temperature reached a peak of 320°C in the correspondence of the most stressed nodes. Moreover, the wear increases as the distance from the drill center increases also along the curved section of the cutting edge as a consequence of the cutting speed increasement (Figure 4c). The actual tool [11], visible in Figure 3a, shows a good correspondence with the geometry showed in Figure 4a.   The model can predict also the increment of the tool temperature determined by tool wear. Fig. 6 shows the cutting edge, the flank and the face of one cutting flute in different wear conditions. The increment of the red-colored high temperature zone around the tool corner is well visible. The maximum value of temperature progressively increased from 320°C to 349°C after 360 s ( Fig.6a and Fig.6b). The tool heating becomes faster for larger tool wear and the temperature reaches an absolute maximum of 393 °C. Also the tool face and flank temperature is affected by tool wear.

Conclusion Conclusion
In this paper, the development and application of a self-released subroutine, in DEFORM-3D FE simulation software, capable to modify the tool geometry as a function of the volume reduction due to wear has been presented. Its Bibliogr Bibliograph aphy y