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Computational-experimental investigation of milling porous aluminium
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CIRP-1580; No. of Pages 4 CIRP Annals - Manufacturing Technology xxx (2016) xxx–xxx
Contents lists available at ScienceDirect
CIRP Annals - Manufacturing Technology jou rnal homep age : ht t p: // ees .e lse vi er . com /ci r p/ def a ult . asp
Computational-experimental investigation of milling porous aluminium N. Michailidis (2)a,*, S. Kombogiannis b, P. Charalampous b, G. Maliaris c, F. Stergioudi a a
Physical Metallurgy Laboratory, Department of Mechanical Engineering, School of Engineering, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece Laboratory for Machine Tools and Manufacturing Engineering, Department of Mechanical Engineering, School of Engineering, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece c Mechatronics & Electromechanical Systems Automation Laboratory, Department of Electrical and Computer Engineering, Polytechnics School, Democritus University of Thrace, 67100 Xanthi, Greece b
A R T I C L E I N F O
A B S T R A C T
Keywords: 3D FEM modelling Milling Porous materials
Porous materials are increasingly incorporated in light-weight structures and although they are nearnet-shape fabricated, a finishing step is required to achieve the desired tolerances. Herein, a computational-experimental framework is proposed to investigate milling of porous aluminium. A FEM model was built, for the first time recorded in the literature, to simulate the milling process of the 3D closed-cell porous geometry, reconstructed by a Voronoi-based CAD algorithm. The chip evolution, traced by the developed FEM model, reveals interesting deformation mechanisms, while the chip fragmentations lead to multiple force fluctuations in a single cut, offering a good agreement with the measured forces. ß 2017 Published by Elsevier Ltd on behalf of CIRP.
1. Introduction Porous metals are among the most promising materials to use in advanced industrial applications and structures, like aerospace, medicine, automotive etc. [1–3]. This trend arises from the interesting combination of characteristics and the ease of adjusting their properties to meet the desired needs by tailoring porosity characteristics [4]. Even though porous metals are usually nearnet-shape fabricated, they often require a finishing machining stage. Due to the thin walls of the porous structure, they often yield to burr formation, which in some cases may be a critical issue [5]. Cryogenic cutting seems to be a working solution for controlling ductility of porous metals [6]. However, machining of porous materials has been rarely investigated [7,8] and even more modelling of the machining process, especially in milling, seems to be an unexploited area. The present work aims to investigate the milling of porous aluminium by computational investigations coupled with cutting force measurements. A 3D FEM model of the cutting process was established, enabling the monitoring of the chip evolution and the forces developed in milling. Some of the major challenges encountered when building the FEM model refer to the workpiece geometry complexity, which makes difficult the establishment of tool-workpiece contact, along with the simulation during densification of the porous structure and the self-contact at the workpiece. The 3D geometry of the porous structure was reconstructed employing a Voronoi-based tessellation algorithm
* Corresponding author. E-mail address: [email protected] (N. Michailidis).
developed for this purpose [9]. The results show a good correlation between experimental and computational findings, revealing that the cutting forces are fluctuating according to the pores located underneath the tool. These fluctuations of the cutting force may imply a premature fatigue damage of the tool, given that the tool is loaded multiple times per cut chip, which intensifies the fatigue initiation and fracture. The chip thickness h is pivotal in producing continuous (non-fragmented) chips and was varied to avoid burr formation and pore closures through permanent deformations of the workpiece. 2. Materials and methods 2.1. Tool and cutting details Grade K05-K20 cemented carbides, supplied by KENNAMETAL and deposited with a 5 mm-thick diamond coating by CEMECON AG [10], were applied in the milling investigations. Fig. 1 shows the cutting strategy and the experimental setup employed for measuring the cutting forces. Down milling was selected with both the radial ae and axial ap depths of cut set to 2 mm. Chip thickness h was varying from 0.2 to 0.5 mm by adjusting the feedrate, while cutting speed vc was set to 600 m/min. A KINSTLER type 9257A 3-axis piezoelectric force measurement device was engaged, supported by three signal amplifiers Kistler Type 5011 (one per axis) and a National Instruments data acquisition card NI PCI-6024E. Labview SignalExpress software package offered the platform for data acquisition. The cutting forces measured in the stationary coordinate (F x , F y, F z ) were then translated into the rotating cutting tool coordinate system (F c , F k n , F k t).
http://dx.doi.org/10.1016/j.cirp.2017.04.022 0007-8506/ß 2017 Published by Elsevier Ltd on behalf of CIRP.
Please cite this article in press as: Michailidis N, et al. Computational-experimental investigation of milling porous aluminium. CIRP Annals - Manufacturing Technology (2017), http://dx.doi.org/10.1016/j.cirp.2017.04.022
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Fig. 1. Cutting strategy and experimental setup for measuring the cutting forces in down milling of porous aluminium.
2.2. Porous aluminium macro- and micro-structure and 3D geometry reconstruction The porous aluminium work material employed in the cutting investigations was fabricated through liquid metallurgy using AlSi10 as matrix, by adding 1.3 wt.% Ca (to enhance the viscosity) and 2 wt.% TiH2 particles (as foaming agent) and stirring the melt at 620–650 8C [9]. From the obtained Al-foam with an average porosity of about 70%, plates were manufactured to a thickness of 30 mm. Fig. 2 presents images from optical and scanning electron microscopes of the produced foam, revealing both its micro- and macro-structure, respectively, after a careful grinding-polishing procedure to avoid damage of the cells. At macro scale level, pores are ellipsoidal forming a closed-cell structure with almost no interconnection with each other. At micro scale level (see detail of the cell microstructure), dendrites of primary solid solution a-Al grains and eutectic structure mainly found in the dendritic interspaces are evident. The eutectic consists of relatively coarse silicon plates dispersed in an Al-matrix (a phase). The Ti that is released from the foaming agent, as well as the Ca, remain in the Al-Si melt, forming Al4Ca and TiAl3 precipitates (not shown in the micrograph). There is no evidence that the precipitates are concentrated on or near the pore surface area, so they are considered as homogeneously dispersed all over the volume of the porous metal.
Fig. 2. Macro- and micro-structure of the produced porous Al.
The reconstruction of the porous geometry was realized employing Rhino software in combination with Grasshopper add-in, following the procedure described in [9]. Fig. 3a shows the main steps followed, involving: (i) Polyhedra generation by applying the Voronoi tessellation algorithm based on random points created inside a solid cube with an edge length of 30 mm. (ii) Scaling down of the polyhedra with respect to their centroid to create an empty space, which then is used to form the walls between the cells and smoothing to match the shape of the pores, which could be characterized as ellipsoid. (iii) A Boolean operation was performed to subtract the smoothed polyhedra from the initial cube to create the porous structure. (iv) Creation of the final geometry considering the cutting tool first cut, by removing the volume which is formed from the intersection of the workpiece with the tool when rotated and moving on the path of the feed. The porosity of the modelled structure was adjusted to approximate one of the produced foam, by tuning the number of generated polyhedra and scale ratio. A total number of 1070 polyhedra combined with a scale ratio of 0.9 resulted to a structure having a porosity of approximately 70%. To further investigate the porous macro-structure (cell size, cell shape and anisotropy) of the produced Al-foam, five cross-sections with dimensions of 30 mm 30 mm were cut employing a precision diamond saw to minimize the cell damage. A quantitative image analysis was then performed based on approximately 200 pores. The images of the cross-sections went through various preparation steps including: converting the image to black and white, enhancing the contrast and brightness, and adaptive thresholding to specified areas of interest for highlighting the pores. Once the crosssectional images were segmented, each pore was replaced by the best fitting ellipse of the same area, orientation and centroid as the original pore, by applying an appropriate algorithm. The ratio of the smallest pore axis s divided by its largest l and the mean pore
Fig. 3. (a) Reconstruction of the 3D porous geometry by the developed Voronoibased tessellation algorithm and (b) comparison of its pore characteristics with the real foam.
Please cite this article in press as: Michailidis N, et al. Computational-experimental investigation of milling porous aluminium. CIRP Annals - Manufacturing Technology (2017), http://dx.doi.org/10.1016/j.cirp.2017.04.022
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CIRP-1580; No. of Pages 4 N. Michailidis et al. / CIRP Annals - Manufacturing Technology xxx (2016) xxx–xxx
size distribution were used as shape indicators of the pores (see Fig. 3b), based on the prerequisite that the reconstructed geometry fully converges with that of the produced foam in terms of porosity, attaining the value of 70%. Most of the pores (more than 80%) possess a pore axis ratio in the range of 0.6–0.9, with the mean values for the Al-foam and the modelled geometry being 0.79 and 0.77, respectively. The pore size stochasticity is monitored by the mean pore size distribution, with more than 80% of the pores lying in the range between 1 and 3 mm. The mean size of the pores is 2.31 and 2.37 mm for the Al-foam and the modelled geometry, respectively. 3. 3D-FEM model simulating milling of porous aluminium The computational investigations were performed in DEFORM 3D software package. A representative volume (having the same geometrical characteristics with the original one) of the porous geometry reconstructed in Fig. 3, was first inserted to ANSA software package (BETA CAE Systems), to produce a fine mesh and then the meshed geometry was input to DEFORM 3D. The imported geometry is initially meshed using 1st order 3-node 2D elements (CTRIA3). This is a necessary step to successfully apply a volume determination routine, while the surface meshing is a prerequisite for the solid meshing routine which discretises the solid geometry with 4-sided solid elements (CTETRA). Fig. 4 shows the engagement of the cutting insert with the porous work material, along with the boundary conditions. During solution, remeshing was frequently performed. In DEFORM 3D the imported geometry should have a single and continuous surface. Since the modelled geometry consists of an external surface together with internal ones representing the enclosed cells, meshing or remeshing with DEFORM could lead to loss of geometric data, especially of the modelled voids. To overcome this issue, ANSA was once again employed, using a script which was specially developed for exporting the deformed geometry, remeshing in ANSA and
3
reimporting it to DEFORM as meshed geometry. Then, DEFORM transferred the solution variables from one meshing to the other, by applying an internal data interpolation routine. The number of elements of the tool were amount to 50k, while those of the workpiece to 500k. Boundary conditions consisted of: (i) movement restriction in all axis, applied on the back planar model surfaces and (ii) heat exchange with the environment in the form of heat convection with the air in contact with the workpiece and conduction with the cutting tool. Both stress and temperature fields are restricted near the contact area between the cutting tool and the workpiece. The minimum distance to the side of the extracted part that heat transfer boundary conditions were not defined, is at least 15 times larger than the extent of the thermal field, given the very limited cutting time. A rigid (tool)-plastic (workpiece) material model was set, with flow-stress data of the AlSi10 workpiece material deriving from [11]. The thermomechanical properties were calculated from equation 2.9, chapter 5.1.10 as described in [11]. The values for the parameters of the specific equation were also derived from the same reference. The table of Fig. 4 contains the flow stress values in MPa for a temperature of 200 8C. The same material model is used both for solid and porous aluminium. The size of the workpiece material is pivotal considering that it should be at the same time big enough to avoid interactions with the boundary conditions and small enough to keep the computational resources low. A sensitivity analysis was performed by running multiple solutions with different workpiece material sizes, to ensure that an appropriate size of the porous material has been selected, concluding to H W L of 15 mm 15 mm 30 mm. The results of the sensitivity analysis are presented in Fig. 5.
Fig. 5. Sensitivity analysis for selecting the size of the porous geometry.
4. Results and discussion
Fig. 4. 3D-FEM model constructed for simulating milling of the porous geometry.
Milling experiments were performed at various feedrates to vary the chip thickness h in the range between 0.2 and 0.5 mm, keeping constant the cutting speed at 600 m/min, while measuring the cutting forces. Identical cutting conditions were applied in the FEM model described in Fig. 6. For comparison reasons and in favour of the elucidation of the acting phenomena when milling the porous aluminium, the same material was prepared as solid and tested at the same conditions in milling. Fig. 6 summarizes the results of the cutting force components as measured and calculated at a chip thickness h = 0.3 mm, both for the solid and porous aluminium. When cutting the solid material, the cutting forces follow a typical course of down milling [12], having a maximum value at the beginning of the chip formation, where the chip has its maximum thickness, and gradually descending to zero. The course of the calculated force (red solid line) is in good agreement with the measured one (blue solid line). When cutting the porous material, forces are fluctuating according to the porosity. This is a stochastic effect, but if we consider a mean pore size of 2.3 mm, one should expect around 6 fluctuations of the force over the chip length lcu (=15 mm). This reasoning is validated both for the measured (blue dashed line) and the calculated (red
Please cite this article in press as: Michailidis N, et al. Computational-experimental investigation of milling porous aluminium. CIRP Annals - Manufacturing Technology (2017), http://dx.doi.org/10.1016/j.cirp.2017.04.022
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time. It is obviously shown that the smaller the chip thickness h is, the easier it breaks into smaller chips when the tool path is over a pore. This is not the case at higher chip thicknesses, i.e. at h = 0.5 mm, where the cutting forces are still present. To investigate further the chip formation mechanism, instances of the chip were selected from DEFORM when the cutting forces have a local minimum. Fig. 7b presents such instances for both chip thicknesses. On one hand, at h = 0.2 mm the chip is plastically deformed and remains on the workpiece as a burr. On the other hand, at h = 0.5 mm the chip has an almost normal evolution. The images of the workpiece at the bottom part of the figure have been taken by a stereomicroscope after milling at h = 0.2 and 0.5 mm and verify the previously described findings of the FEM simulation. 5. Conclusions
Fig. 6. Comparison of the measured cutting force components with the FEMdetermined ones at a chip thickness h of 0.3 mm.
dashed line) cutting forces. Due to the fragmentation of the chip and the increased plasticity of the porous structure, the cutting forces in milling the aluminium foam are lower than those of the solid. The chip formation is generally governed by intense plastic deformation of smaller interrupted chips in correspondence with the porous geometry. As the chip thickness h increases from 0.2 to 0.5 mm, the chip tends to become continuous, which is clearly evidenced through the cutting forces. Fig. 7a shows the FEMdetermined principal cutting forces Fc at h = 0.2 and 0.5 mm versus
Milling of porous aluminium was investigated by a realistic 3D FEM model of the cutting process coupled with cutting force measurements. The 3D geometry of the porous structure was reconstructed by a developed Voronoi-based tessellation algorithm. The cutting forces were fluctuating according to the porosity, implying fatigue problems in the cutting tool performance. An increase of the chip thickness h appeared to have a beneficial effect in avoiding burr formation and pore closures through permanent deformations of the workpiece. The developed 3D FEM model, stands as a useful tool that can be generically applied to other porous geometries and materials.
References [1] Lefebvre L-P, Banhart J, Dunand DC (2008) Porous Metals and Metallic Foams: Current Status and Recent Developments. Advanced Engineering Materials 10(9):775–787. [2] Neugebauer R, Hipke T (2006) Machine Tools with Metal Foams. Advanced Engineering Materials 8(9):858–863. [3] Michailidis N, Stergioudi F, Viglaki K, Chatzinikolaidou M (2014) Production of Novel Ceramic Porous Surfaces Tailored for Bone Tissue Engineering. CIRP Annals - Manufacturing Technology 63(1):557–560. [4] Michailidis N, Stergioudi F, Tsouknidas A, Pavlidou E (2011) Compressive Response of Al-Foams Produced via a Powder Sintering Process Based on a Leachable Space-Holder Material. Materials Science and Engineering A 528(3):1662–1667. [5] Aurich JC, Dornfeld D, Arrazola PJ, Franke V, Leitz L, Min S (2009) Burrs— Analysis, Control and Removal. CIRP Annals - Manufacturing Technology 58(2): 519–542. [6] Schoop J, Ambrosy F, Zanger F, Schulze V, Balk TJ, Jawahir IS (2016) Cryogenic Machining of Porous Tungsten for Enhanced Surface Integrity. Journal of Materials Processing Technology 229:614–621. [7] Tutunea-Fatan OR, Fakhri MA, Bordatchev EV (2011) Porosity and Cutting Forces: From Macroscale to Microscale Machining Correlations. Proceedings of the Institution of Mechanical Engineers Part B: Journal of Engineering Manufacture 225:619–630. [8] Matz AM, Kammerer D, Jost N, Oßwald K (2016) Machining of Metal Foams with Varying Mesostructure Using Wire EDM. Procedia CIRP 42:263–267. [9] Michailidis N, Smyrnaios E, Maliaris G, Stergioudi F, Tsouknidas A (2014) Mechanical Response and FEM Modeling of Porous Al Under Static and Dynamic Loads. Advanced Engineering Materials 16:289–294. [10] Skordaris G, Bouzakis K-D, Charalampous P, Kotsanis T, Bouzakis E, Lemmer O (2016) Effect of Structure and Residual Stresses of Diamond Coated Cemented Carbide Tools on the Film Adhesion and Developed Wear Mechanisms in Milling. CIRP Annals - Manufacturing Technology 65(1):101–104. [11] Spittel M, Spittel T (2011) in Warlimont H, (Ed.) Part 2: Non-Ferrous Alloys – Light Metals AlSi10, Springer-Verlag, Berlin, Heidelberg318–322. [12] Bouzakis K-D, Gerardis S, Katirtzoglou G, Makrimallakis S, Michailidis N, Lili E (2008) Increasing Tool Life by Adjusting the Milling Cutting Conditions According to PVD Films’ Properties. CIRP Annals - Manufacturing Technology 57(1):105–108.
Fig. 7. Chip formation of the porous geometry at different chip thicknesses, as monitored by (a) the FEM-calculated cutting forces and (b) the FEM-determined chip formation and pictures of the workpiece.
Please cite this article in press as: Michailidis N, et al. Computational-experimental investigation of milling porous aluminium. CIRP Annals - Manufacturing Technology (2017), http://dx.doi.org/10.1016/j.cirp.2017.04.022
CIRP-1580; No. of Pages 4 CIRP Annals - Manufacturing Technology xxx (2016) xxx–xxx
Contents lists available at ScienceDirect
CIRP Annals - Manufacturing Technology jou rnal homep age : ht t p: // ees .e lse vi er . com /ci r p/ def a ult . asp
Computational-experimental investigation of milling porous aluminium N. Michailidis (2)a,*, S. Kombogiannis b, P. Charalampous b, G. Maliaris c, F. Stergioudi a a
Physical Metallurgy Laboratory, Department of Mechanical Engineering, School of Engineering, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece Laboratory for Machine Tools and Manufacturing Engineering, Department of Mechanical Engineering, School of Engineering, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece c Mechatronics & Electromechanical Systems Automation Laboratory, Department of Electrical and Computer Engineering, Polytechnics School, Democritus University of Thrace, 67100 Xanthi, Greece b
A R T I C L E I N F O
A B S T R A C T
Keywords: 3D FEM modelling Milling Porous materials
Porous materials are increasingly incorporated in light-weight structures and although they are nearnet-shape fabricated, a finishing step is required to achieve the desired tolerances. Herein, a computational-experimental framework is proposed to investigate milling of porous aluminium. A FEM model was built, for the first time recorded in the literature, to simulate the milling process of the 3D closed-cell porous geometry, reconstructed by a Voronoi-based CAD algorithm. The chip evolution, traced by the developed FEM model, reveals interesting deformation mechanisms, while the chip fragmentations lead to multiple force fluctuations in a single cut, offering a good agreement with the measured forces. ß 2017 Published by Elsevier Ltd on behalf of CIRP.
1. Introduction Porous metals are among the most promising materials to use in advanced industrial applications and structures, like aerospace, medicine, automotive etc. [1–3]. This trend arises from the interesting combination of characteristics and the ease of adjusting their properties to meet the desired needs by tailoring porosity characteristics [4]. Even though porous metals are usually nearnet-shape fabricated, they often require a finishing machining stage. Due to the thin walls of the porous structure, they often yield to burr formation, which in some cases may be a critical issue [5]. Cryogenic cutting seems to be a working solution for controlling ductility of porous metals [6]. However, machining of porous materials has been rarely investigated [7,8] and even more modelling of the machining process, especially in milling, seems to be an unexploited area. The present work aims to investigate the milling of porous aluminium by computational investigations coupled with cutting force measurements. A 3D FEM model of the cutting process was established, enabling the monitoring of the chip evolution and the forces developed in milling. Some of the major challenges encountered when building the FEM model refer to the workpiece geometry complexity, which makes difficult the establishment of tool-workpiece contact, along with the simulation during densification of the porous structure and the self-contact at the workpiece. The 3D geometry of the porous structure was reconstructed employing a Voronoi-based tessellation algorithm
* Corresponding author. E-mail address: [email protected] (N. Michailidis).
developed for this purpose [9]. The results show a good correlation between experimental and computational findings, revealing that the cutting forces are fluctuating according to the pores located underneath the tool. These fluctuations of the cutting force may imply a premature fatigue damage of the tool, given that the tool is loaded multiple times per cut chip, which intensifies the fatigue initiation and fracture. The chip thickness h is pivotal in producing continuous (non-fragmented) chips and was varied to avoid burr formation and pore closures through permanent deformations of the workpiece. 2. Materials and methods 2.1. Tool and cutting details Grade K05-K20 cemented carbides, supplied by KENNAMETAL and deposited with a 5 mm-thick diamond coating by CEMECON AG [10], were applied in the milling investigations. Fig. 1 shows the cutting strategy and the experimental setup employed for measuring the cutting forces. Down milling was selected with both the radial ae and axial ap depths of cut set to 2 mm. Chip thickness h was varying from 0.2 to 0.5 mm by adjusting the feedrate, while cutting speed vc was set to 600 m/min. A KINSTLER type 9257A 3-axis piezoelectric force measurement device was engaged, supported by three signal amplifiers Kistler Type 5011 (one per axis) and a National Instruments data acquisition card NI PCI-6024E. Labview SignalExpress software package offered the platform for data acquisition. The cutting forces measured in the stationary coordinate (F x , F y, F z ) were then translated into the rotating cutting tool coordinate system (F c , F k n , F k t).
http://dx.doi.org/10.1016/j.cirp.2017.04.022 0007-8506/ß 2017 Published by Elsevier Ltd on behalf of CIRP.
Please cite this article in press as: Michailidis N, et al. Computational-experimental investigation of milling porous aluminium. CIRP Annals - Manufacturing Technology (2017), http://dx.doi.org/10.1016/j.cirp.2017.04.022
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CIRP-1580; No. of Pages 4 2
N. Michailidis et al. / CIRP Annals - Manufacturing Technology xxx (2016) xxx–xxx
Fig. 1. Cutting strategy and experimental setup for measuring the cutting forces in down milling of porous aluminium.
2.2. Porous aluminium macro- and micro-structure and 3D geometry reconstruction The porous aluminium work material employed in the cutting investigations was fabricated through liquid metallurgy using AlSi10 as matrix, by adding 1.3 wt.% Ca (to enhance the viscosity) and 2 wt.% TiH2 particles (as foaming agent) and stirring the melt at 620–650 8C [9]. From the obtained Al-foam with an average porosity of about 70%, plates were manufactured to a thickness of 30 mm. Fig. 2 presents images from optical and scanning electron microscopes of the produced foam, revealing both its micro- and macro-structure, respectively, after a careful grinding-polishing procedure to avoid damage of the cells. At macro scale level, pores are ellipsoidal forming a closed-cell structure with almost no interconnection with each other. At micro scale level (see detail of the cell microstructure), dendrites of primary solid solution a-Al grains and eutectic structure mainly found in the dendritic interspaces are evident. The eutectic consists of relatively coarse silicon plates dispersed in an Al-matrix (a phase). The Ti that is released from the foaming agent, as well as the Ca, remain in the Al-Si melt, forming Al4Ca and TiAl3 precipitates (not shown in the micrograph). There is no evidence that the precipitates are concentrated on or near the pore surface area, so they are considered as homogeneously dispersed all over the volume of the porous metal.
Fig. 2. Macro- and micro-structure of the produced porous Al.
The reconstruction of the porous geometry was realized employing Rhino software in combination with Grasshopper add-in, following the procedure described in [9]. Fig. 3a shows the main steps followed, involving: (i) Polyhedra generation by applying the Voronoi tessellation algorithm based on random points created inside a solid cube with an edge length of 30 mm. (ii) Scaling down of the polyhedra with respect to their centroid to create an empty space, which then is used to form the walls between the cells and smoothing to match the shape of the pores, which could be characterized as ellipsoid. (iii) A Boolean operation was performed to subtract the smoothed polyhedra from the initial cube to create the porous structure. (iv) Creation of the final geometry considering the cutting tool first cut, by removing the volume which is formed from the intersection of the workpiece with the tool when rotated and moving on the path of the feed. The porosity of the modelled structure was adjusted to approximate one of the produced foam, by tuning the number of generated polyhedra and scale ratio. A total number of 1070 polyhedra combined with a scale ratio of 0.9 resulted to a structure having a porosity of approximately 70%. To further investigate the porous macro-structure (cell size, cell shape and anisotropy) of the produced Al-foam, five cross-sections with dimensions of 30 mm 30 mm were cut employing a precision diamond saw to minimize the cell damage. A quantitative image analysis was then performed based on approximately 200 pores. The images of the cross-sections went through various preparation steps including: converting the image to black and white, enhancing the contrast and brightness, and adaptive thresholding to specified areas of interest for highlighting the pores. Once the crosssectional images were segmented, each pore was replaced by the best fitting ellipse of the same area, orientation and centroid as the original pore, by applying an appropriate algorithm. The ratio of the smallest pore axis s divided by its largest l and the mean pore
Fig. 3. (a) Reconstruction of the 3D porous geometry by the developed Voronoibased tessellation algorithm and (b) comparison of its pore characteristics with the real foam.
Please cite this article in press as: Michailidis N, et al. Computational-experimental investigation of milling porous aluminium. CIRP Annals - Manufacturing Technology (2017), http://dx.doi.org/10.1016/j.cirp.2017.04.022
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CIRP-1580; No. of Pages 4 N. Michailidis et al. / CIRP Annals - Manufacturing Technology xxx (2016) xxx–xxx
size distribution were used as shape indicators of the pores (see Fig. 3b), based on the prerequisite that the reconstructed geometry fully converges with that of the produced foam in terms of porosity, attaining the value of 70%. Most of the pores (more than 80%) possess a pore axis ratio in the range of 0.6–0.9, with the mean values for the Al-foam and the modelled geometry being 0.79 and 0.77, respectively. The pore size stochasticity is monitored by the mean pore size distribution, with more than 80% of the pores lying in the range between 1 and 3 mm. The mean size of the pores is 2.31 and 2.37 mm for the Al-foam and the modelled geometry, respectively. 3. 3D-FEM model simulating milling of porous aluminium The computational investigations were performed in DEFORM 3D software package. A representative volume (having the same geometrical characteristics with the original one) of the porous geometry reconstructed in Fig. 3, was first inserted to ANSA software package (BETA CAE Systems), to produce a fine mesh and then the meshed geometry was input to DEFORM 3D. The imported geometry is initially meshed using 1st order 3-node 2D elements (CTRIA3). This is a necessary step to successfully apply a volume determination routine, while the surface meshing is a prerequisite for the solid meshing routine which discretises the solid geometry with 4-sided solid elements (CTETRA). Fig. 4 shows the engagement of the cutting insert with the porous work material, along with the boundary conditions. During solution, remeshing was frequently performed. In DEFORM 3D the imported geometry should have a single and continuous surface. Since the modelled geometry consists of an external surface together with internal ones representing the enclosed cells, meshing or remeshing with DEFORM could lead to loss of geometric data, especially of the modelled voids. To overcome this issue, ANSA was once again employed, using a script which was specially developed for exporting the deformed geometry, remeshing in ANSA and
3
reimporting it to DEFORM as meshed geometry. Then, DEFORM transferred the solution variables from one meshing to the other, by applying an internal data interpolation routine. The number of elements of the tool were amount to 50k, while those of the workpiece to 500k. Boundary conditions consisted of: (i) movement restriction in all axis, applied on the back planar model surfaces and (ii) heat exchange with the environment in the form of heat convection with the air in contact with the workpiece and conduction with the cutting tool. Both stress and temperature fields are restricted near the contact area between the cutting tool and the workpiece. The minimum distance to the side of the extracted part that heat transfer boundary conditions were not defined, is at least 15 times larger than the extent of the thermal field, given the very limited cutting time. A rigid (tool)-plastic (workpiece) material model was set, with flow-stress data of the AlSi10 workpiece material deriving from [11]. The thermomechanical properties were calculated from equation 2.9, chapter 5.1.10 as described in [11]. The values for the parameters of the specific equation were also derived from the same reference. The table of Fig. 4 contains the flow stress values in MPa for a temperature of 200 8C. The same material model is used both for solid and porous aluminium. The size of the workpiece material is pivotal considering that it should be at the same time big enough to avoid interactions with the boundary conditions and small enough to keep the computational resources low. A sensitivity analysis was performed by running multiple solutions with different workpiece material sizes, to ensure that an appropriate size of the porous material has been selected, concluding to H W L of 15 mm 15 mm 30 mm. The results of the sensitivity analysis are presented in Fig. 5.
Fig. 5. Sensitivity analysis for selecting the size of the porous geometry.
4. Results and discussion
Fig. 4. 3D-FEM model constructed for simulating milling of the porous geometry.
Milling experiments were performed at various feedrates to vary the chip thickness h in the range between 0.2 and 0.5 mm, keeping constant the cutting speed at 600 m/min, while measuring the cutting forces. Identical cutting conditions were applied in the FEM model described in Fig. 6. For comparison reasons and in favour of the elucidation of the acting phenomena when milling the porous aluminium, the same material was prepared as solid and tested at the same conditions in milling. Fig. 6 summarizes the results of the cutting force components as measured and calculated at a chip thickness h = 0.3 mm, both for the solid and porous aluminium. When cutting the solid material, the cutting forces follow a typical course of down milling [12], having a maximum value at the beginning of the chip formation, where the chip has its maximum thickness, and gradually descending to zero. The course of the calculated force (red solid line) is in good agreement with the measured one (blue solid line). When cutting the porous material, forces are fluctuating according to the porosity. This is a stochastic effect, but if we consider a mean pore size of 2.3 mm, one should expect around 6 fluctuations of the force over the chip length lcu (=15 mm). This reasoning is validated both for the measured (blue dashed line) and the calculated (red
Please cite this article in press as: Michailidis N, et al. Computational-experimental investigation of milling porous aluminium. CIRP Annals - Manufacturing Technology (2017), http://dx.doi.org/10.1016/j.cirp.2017.04.022
G Model
CIRP-1580; No. of Pages 4 4
N. Michailidis et al. / CIRP Annals - Manufacturing Technology xxx (2016) xxx–xxx
time. It is obviously shown that the smaller the chip thickness h is, the easier it breaks into smaller chips when the tool path is over a pore. This is not the case at higher chip thicknesses, i.e. at h = 0.5 mm, where the cutting forces are still present. To investigate further the chip formation mechanism, instances of the chip were selected from DEFORM when the cutting forces have a local minimum. Fig. 7b presents such instances for both chip thicknesses. On one hand, at h = 0.2 mm the chip is plastically deformed and remains on the workpiece as a burr. On the other hand, at h = 0.5 mm the chip has an almost normal evolution. The images of the workpiece at the bottom part of the figure have been taken by a stereomicroscope after milling at h = 0.2 and 0.5 mm and verify the previously described findings of the FEM simulation. 5. Conclusions
Fig. 6. Comparison of the measured cutting force components with the FEMdetermined ones at a chip thickness h of 0.3 mm.
dashed line) cutting forces. Due to the fragmentation of the chip and the increased plasticity of the porous structure, the cutting forces in milling the aluminium foam are lower than those of the solid. The chip formation is generally governed by intense plastic deformation of smaller interrupted chips in correspondence with the porous geometry. As the chip thickness h increases from 0.2 to 0.5 mm, the chip tends to become continuous, which is clearly evidenced through the cutting forces. Fig. 7a shows the FEMdetermined principal cutting forces Fc at h = 0.2 and 0.5 mm versus
Milling of porous aluminium was investigated by a realistic 3D FEM model of the cutting process coupled with cutting force measurements. The 3D geometry of the porous structure was reconstructed by a developed Voronoi-based tessellation algorithm. The cutting forces were fluctuating according to the porosity, implying fatigue problems in the cutting tool performance. An increase of the chip thickness h appeared to have a beneficial effect in avoiding burr formation and pore closures through permanent deformations of the workpiece. The developed 3D FEM model, stands as a useful tool that can be generically applied to other porous geometries and materials.
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Fig. 7. Chip formation of the porous geometry at different chip thicknesses, as monitored by (a) the FEM-calculated cutting forces and (b) the FEM-determined chip formation and pictures of the workpiece.
Please cite this article in press as: Michailidis N, et al. Computational-experimental investigation of milling porous aluminium. CIRP Annals - Manufacturing Technology (2017), http://dx.doi.org/10.1016/j.cirp.2017.04.022