3D finite element modeling of thin-wall machining of aluminum 7075-T6 alloy

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1 5 th International & 26 th All India Manufacturing Technology, Design and Research Conference (AIMTDR 2014) December 12 th 14 th, 2014, IIT Guwahati, Assam, India 3D finite element modeling of thin-wall machining of aluminum 7075-T6 alloy Gururaj Bolar 1, S. N. Joshi 2 * 1 Department of Mechanical Engineering, Indian Institute of Technology Guwahati, Guwahati, , gururaj@iitg.ernet.in 2 *Department of Mechanical Engineering, Indian Institute of Technology Guwahati, Guwahati, , snj@iitg.ernet.in Abstract This paper presents the modeling and simulation of deformation of thin-wall section using finite element method (FEM). A 3D non-linear numerical model was developed by employing Johnson-Cook material constitutive model for aluminum 7075-T6 alloy. Johnson-cook damage law was adopted to account for damage initiation and chip formation during cutting tool penetration into the work material. The deformation of thin-walled part under the action of cutting forces during milling operation was studied for a set of process conditions and the preliminary results are discussed. Keywords: Thin-wall machining, numerical simulation, deformation, aluminum 7075-T6 1 Introduction Aerospace industry needs monolithic thin-wall components to manufacture the sections of aircraft fuselage, wings, aircraft door frame, and engine blades. Monolithic parts are machined from a single block of workpiece to their final shape. Monolithic parts are preferred over the traditional riveted-welded parts due to the high set-up cost and long time of production associated with the later [Campa et al. (2007)]. During the machining of thin-wall parts, their sections deform under the action of cutting forces. This leads to geometrical errors which in turn influence the quality and accuracy of final product. The geometrical error produced during machining of a thin-wall part is shown in figure 1. The material ABCD needs to be cut away ideally. However, under the action of machining forces, the low rigidity thinwall structure deflects, which results in cutting away of material A BCD. When the cutter moves away from the milled surface, the wall elastically recovers, and material C CD remains uncut. This was a common problem observed in the machining of thinwall components. This causes the shape of the wall to be thicker atthe top and thinner atits bottom. Researchers proposed that the machining errors can be minimized either by trial and error approach or by repetitive feeding techniques. However this may lead in longer production time and higher costs. Finite element modeling can be used to simulate machining of thin-wall parts to predict the deflection and deformation of thin-walls. Literature reports research on various aspects of thin-wall machining such as deflection, deformation, machining mechanics and dynamics, error prediction and control. Ratchev et al. (2003) (2004) developed a flexible cutting force model and investigated the deflection of the low rigidity parts under the action of the calculated cutting forces. In the similar way, Tang and Liu (2008) studied the deformations of thin-walled plate under the action of static end milling forces. Figure 1 Error in thin-wall machining Tanase et al. (2010) analyzed the deformation during milling thin-walled parts. The cutting forces were determined separately based on the cutting power measured during experiments.few attempts have been reported on 3D finite element modeling of milling process. Pittalà and Monno (2010) simulated the face milling of aluminum alloy. Soo et al. (2010) 135-1

2 3D finite element modeling of thin-wall machining of aluminum 7075-T6 alloy developed a 3D finite element model for high speed ball end milling process. Wu and Zhang (2014) worked on 3D simulation of milling of titanium alloy. However it has been noted that during these reported numerical studies, the machining forces are calculated either based on the cutting force model developed[ratchev et al. (2003) (2004)] [Tang and Liu (2008)] or based on experimental values [Tanase et al. (2010)].The cutting force values are computed based on certain assumptions viz.simplification of milling force as linear load, the normal line being straight and vertical to the middle plane both before and after deformations, direct stress on the plane parallel to the middle plane etc. These assumptions limit the applications of these models. Reported 3D models reported were limited to general end milling operation [Soo et al. (2010)] [Wu and Zhang (2014)] and face milling [Pittalà and Monno (2010)]. Very scant work is reported on 3D modeling of deformation during thin-wall machining process. In this work, a 3D numerical FEM based model was developed to simulate the thin-wall machining process. The model employs the material constitutive criterion which describesthe material behavior of aluminum7075-t6 alloy and material damage law which account for chip formation.details regarding model development are presented in the next sections followed by preliminary results and conclusions. 2 Finite element modeling of thin-wall machining By using 2D orthogonal or oblique cutting models, it is not possible to simulate the interaction of helical teeth and workpiece and to predict the workpiece deformation and surface roughness. Therefore it was felt that a 3D finite element model would provide a realistic approach to simulate the thin-wall machining operation. In the present work, commercial FEM solver ABAQUS TM was used. 2.1 Geometrical modeling, boundary conditions and mesh configuration The thin-wall workpiece was modeled as an inverted cantilever structure as shown in figure 2. The workpiece was constrained at the bottom, whilst the other three ends of the thin-walled parts are not constrained as shown in figure 3. The milling tool was made to move in in the feed direction and is provided with rotation motion. The workpiece was meshed with 3D solid element C3D8R. It is 8-node linear brick element with reduced integration and hourglass control. The mesh density is kept higher at the cutting region where tool and workpiece interaction takes place. It captures accurately the chip formation process at the cutting region and minimizes the use of total numbers of elements at the non-interacting regions. This increases computational efficiency of the simulation. Figure 2 Work dimensions and boundary conditions The workpiece was discretized into elements. The cutting tool was considered to be rigid body and the suitable constraint was applied to it. The cutting tool was meshed using 4-node, bilinear quadrilateralr3d4 rigid element. The cutting tool was discretized into 4325 elements. The helical milling cutter was assumed to be having sharp cutting edges. Cutting tool parameters are listed in table 1. Figure 3 Boundary conditions and meshing 135-2

3 5 th International & 26 th All India Manufacturing Technology, Design and Research Conference (AIMTDR 2014) December 12 th 14 th, 2014, IIT Guwahati, Assam, India Table1 Cutting tool parameters [Sekiguchi et al. (2004)] Tool material Tool diameter (mm) 8 HSS Tool rake angle (⁰) 12 Tool helix angle (⁰) 30 Tool clearance angle (⁰) 15 Number of flutes Material properties and material constitutive equation Aluminum alloy 7075-T6 (A7075-T6), an aerospace material was used in the present study. It is an aluminum zinc alloy which is a primary alloy used in airframe structural applications. This alloy is used in upper wing skins of aircrafts where high strength is required [Starke and Staley (1996)]. Constitutive equation is an equation which describes the thermo-mechanical properties of a material undergoing deformation.johnson Cook (J-C) constitutive equation is used to characterize the material behavior of the workpiece. It provides the description of material behavior undergoing large strains, temperature-dependent visco-plasticity and high strain rates. The model is represented by equivalent flow stress σ as stated in the equation 1. m n ( ε ε T -T ) room σ = A+ B 1-Cln 1- T melt -T room ε0 (1) where, A (MPa) is the initial yield stress of the material, B (MPa)the hardening modulus, C the strain rate dependency coefficient, n the work-hardening exponent, mthe thermal softening coefficient, ε is the equivalent plastic strain, is the equivalent plastic strain rates and is the reference plastic strain rate, T room is the room temperature and T melt is the workpiece melting temperature. The Johnson-Cook parameter values for the present study are taken from the work carried out by Brar et al. (2009) which are listed in table 2. The workpiece material properties are listed in table 3. Table 2 Johnson cook material parameters values for A7075-T6 [Brar et al. (2009)] 2.3 Failure model A B n C m Material is said to be failed when it loses its load carrying capacity. In the present work, to simulate the chip formation phenomenon material damage criteria developed by Johnson & Cook (1985) has been employed. This model uses a damage parameter Dwhich isdefined as the sum of the ratio of the increments in the equivalent plastic strain to the fracture strain as given in equation 2. The fracture strain equation 3. ε D = ε f (2) is of the form as given in P ε ε f = D 1 + D2exp D D ln _ 4 σ ε0 T - T 1 + D 5 T melt - T room room (3) Where, - are the damage constants, P is the hydrostatic pressure and is equivalent flow stress. Constants of the J-C failure model for AA7075-T6 determined by Brar et al are tabulated in table 4. Table 3 Workpiece material properties [Matweb.com (2014)] Density, ρ 2810 Elastic modulus, E (GPa) 71.7 Poisson ratio, ν 0.33 Specific heat, 960 Thermal expansion, α (10e-6/ºC) 23.6 Thermal conductivity 130 T melt (ºC) 520 T room (ºC) 20 Table 4 Johnson Cook failure parameters for A7075-T6 [Brar et al. (2009)] When the damage parameter D exceeds unity, the material loses its load carrying capacity and failure occurs. Then the elements will be deleted by using element deletion criterion based on J-C damage law. 2.4 Contact model In the present work a modified coulomb friction model was used to define the contact between the cutting tool and the workpiece. Wu and Zhang (2014) in their work utilized the model which states that the contact between the chip and the rake surface region 135-3

4 3D finite element modeling of thin-wall machining of aluminum 7075-T6 alloy can be divided into two regions namely the sliding region and the sticking region. Sticking friction is observed occurring very near the cutting edge in contact with the workpiece and the sliding friction occurring far away from the contact area. The sliding region obeys the Coulomb friction law. In the sticking region, the shear stress τ is equal to the critical frictional stress. The modified coulomb law is defined by the equations (4) (5). τ =τ criti when µσ >τ criti (Sticking region) (4) τ = µσ whenµσ >τ (Sliding region) (5) In the present work, tool and work contact was defined using surface to surface contact. The constraint provided was master-slave kinematic control. The tangential behavior of the contact surface was defined using penalty contact with co-efficient of friction value µ of 0.3 [Wang et al. (2010)]. One of the advantages of using the modified Coulomb friction model was that the solver determines the friction state automatically according to the contact stress value during the simulation process. 3 Cutting conditions and process simulation A 3D finite element simulation of thin-wall machining of A7075-T6 workpiece using an end milling cutter is carried out. The J-C material model parameters are assigned to the workpiece which takes care of the mechanical properties during deformation. Also a J-C material damage law was applied to initiate the chip formation. The detailed cutting conditions are listed in the table 5. In the present work determination of the deflection of the workpiece under the action of cutting force is considered to be the main objective. Heat generated and temperature rise during machining are ignored for the ease of computation and memory management. In the lagrangian formulation, the finite element mesh is attached to the material and follows its deformation. Lagrangian formulation is used to analyze transient problems which undergo large deformations. The milling process involves large deformation and continuously changing contact. To handle the large amount of nonlinearity, a dynamic explicit time integration scheme is adopted. The explicit dynamic analysis procedure implements the explicit integration rule together with the use of lumped mass matrix. The explicit procedure does not require any iterations and tangent stiffness matrix. The explicit procedure integrates through time by using many small time increments. The explicit formulation advances the solution in time with the central difference scheme. The central-difference operator is conditionally stable, and the stability limit for the operator is based on the critical time step. The critical time step for a mesh is considered to be the minimum value of the element length taken over all criti the elements. This is computed by using the equation 6. l t c min d (6) ABAQUS TM explicit software was used to carry out the simulation work. Total simulation time taken was 100hrs with a 3.4GHz, 4GB RAM processor. Table 5 Cutting condition during machining Cutting condition Dry Spindle speed (RPM) 7500 Feed (mm/tooth) 0.2 Radial depth of cut (mm) 0.2 Axial depth of cut (mm) 25 5 Results and discussion The preliminary results obtained during the numerical simulation of machining thin-wall aluminum 7075-T6 alloy part are discussed in this section. The deflection measurement points are shown in figure 4. The cutter moves along X-direction from point P to V. Deflection of part along X-direction at the end of cutting process is plotted in figure 5. Figure 4 Deflection measurement points 135-4

5 5 th International & 26 th All India Manufacturing Technology, Design and Research Conference (AIMTDR 2014) December 12 th 14 th, 2014, IIT Guwahati, Assam, India ends. As a result material remains uncut at the top end. This fact has been observed by Mangalekar (2011) in his experimental studies. In figure 8, qualitative comparison of the experimental part [Mangalekar (2011)] and simulated thin-part in the present is depicted. It was observed that the due to the deflection of the part under the action of cutting forces during machining, the top portion is thicker compared to the bottom portion at the end of the process. Also the thin-wall structure undergoes permanent deformation. Thus our numerical simulation verifies the established facts. This gave us a confidence to plan for further numerical studies. Figure 5 Variation of deflection along the part length of workpiece It was observed that the maximum deflection was occurring at the two ends as compared to that occurred at the center of the thin-wall. This may be due the fact that the two ends of the workpiece are free ends which are flexible and deflect under the action of resultant cutting force. The resultant cutting force is lower at two ends when compared to the center as shown in figure 6. Figure 7 Variation of deflection along the height of workpiece Figure 6 Resultant cutting forces during along the length of workpiece Figure 7 shows the deflection of the work piece along Y-direction at various points of the surface of the work part. It can be seen that the deflection at the top edge is more as compared to the bottom portion of the work part.this may be due the fact that the inverted cantilever is just fixed at its bottom portion whilst it s top portion free and unconstrained to deflect under the action of resultant force. Also the lower stiffness value leads to more deflection of free Figure 8 Comparison of form error obtained with experiment and numerical simulation Numerical simulation can also be used to determine the surface roughness of a machined part. The surface finish of the machined thin-wall simulated part is shown in figure 9. It was observed that under the action of cutting forces, the inverted 135-5

6 3D finite element modeling of thin-wall machining of aluminum 7075-T6 alloy cantilever workpiece undergoes cyclic deflections. This was due the repeated cutter teeth engagement and disengagement with the work part. This results in non-uniform material removal and unevenly finished surface. Figure 9 Surface roughness observed in numerical simulation Conclusions In the present work 3D transient nonlinear FEM based numerical model of thin-wall milling wasdeveloped. Based on this model, a simulation of thin-wall machiningof aluminum 7075-T6 workpiece was carried out and preliminary results are discussed. The model successfully simulated the physical interaction of helical cutter teeth with the work part surface. However it took approximately 100 hours. The approach was found to be realistic as it employs the Johnson-Cook material model and damage law to define the workpiece material properties and chip formation criterion. The preliminary results were compared with those available in published experimental work. It was observed that there was a significant amount of deflection of thin-wall part due to the action of cutting forces. The prediction of work geometry was found to be agreed well with the experimental results. Based on this model, further numerical studies are planned. The work will further be extended to include the heat generation and temperature rise during machining. References Brar, N.S., Joshi, V.S. and Harris, B.W. (2009), constitutive model constants for Al7075-T651 and Al7075-T6, AIP Conference Proceedings, Vol. 1195, pp Campa, F. J. Seguy, S. López, L. N. Arnaud, L. Dessein, G. and Aramendi, G. (2007), Stable milling of thin-walled parts with variable dynamics, Proceedings of the 6 th International conference on high speed machining, San Sebastian Gang, L. (2009), Study on deformation of titanium thin-walled part in milling process, Journal of materials processing technology, Vol. 209, pp Johnson, G R. and Cook, W.H. (1983), A constitutive model and data for metals subjected to large strains, high strain rates, and high temperatures, Proceedings of 7 th International symposium on ballistics, pp Johnson, G.R. and Cook, W.H. (1985), Fracture characteristics of three metals subjected to various strain, strain Rates, temperature, and pressures, Engineering fracture mechanics, Vol. 21, No. 1, pp Mangalekar, N. (2012), Experimental studies on thinwall machining of aluminum 8011 alloy, M.Tech. thesis, Indian Institute of Technology Guwahati, India Pittalà, G.M. and Monno, M. (2010), 3D finite element modeling of face milling of continuous chip material, International Journal of Advanced Manufacturing Technology, Vol. 47, pp Ratchev, S. Govender, E. Nikov, S. Phuah, K. and Tsiklos, G. (2003), Force and deflection modeling in milling of low-rigidity complex parts, Journal of materials processing technology, Vol , pp Ratchev, S. Huang, W. Liu, S. Becker, A.A. (2004), Modeling and simulation environment for machining of low-rigidity components, Journal of materials processing technology, Vol , pp Sekiguchi, T. Kagiya, Y. and Goshima, Y. (2004), Cemented carbide end mill, U.S patent Soo, S. L. Dewes, R.C. and Aspinwall, D.K. (2010), 3D FE modeling of the cutting of Inconel 718, International Journal of Advanced Manufacturing Technology, Vol. 50, pp Starke, E. A. and Staley, J. T. (1996), Application of modern aluminum alloys to aircraft, Progress in Aerospace Sciences, Vol. 32, pp Tanase, I. Ghionea, A. and Ghionea, I. (2010), Measurement and analysis of cutting forces and deformation at milling thin parts, Proceedings in Manufacturing Systems, Vol. 5, pp Tang, A. and Liu, Z. (2008), Deformations of thinwalled plate due to static end milling force, Journal of materials processing technology, Vol. 206, pp Wang, G.N. Qin, G. H. Lu, D. and Xin, S.Q. (2010), Simulation and experimental investigation for end milling process of 7075-T7451 aluminum alloy, Advanced material research, Vol , pp Wu, H.B. and Zhang, S.J. (2014), 3D FEM simulation of milling process for titanium alloy Ti6Al4V, International Journal of Advanced Manufacturing Technology, Vol. 71, pp (accessed June 2014) 135-6