5.1 Validation of the numerical model
The aluminum honeycomb structure is made of fragile 5056 aluminum sheets considered as shell elements in the numerical simulation. As mentioned earlier, aluminum is often modeled by the Johnson-Cook (JC) law. The latter consists of three terms representing the effect of strain hardening, strain rate and thermal softening. In some cases, Johnson Cook's (JC) law can be used in a reduced form where one of the two terms representing the strain rate effect or the temperature effect is neglected [26]. In order to determine the appropriate mechanical behavior law for the numerical simulation of the milling of aluminum honeycomb structures. A numerical study was approached to compare the two mechanical behaviors of Johnson-Cook and Johnson-Cook simplified in terms of cutting force and under the same cutting conditions used in the experimental phase. To do this, four rotational speeds were examined, namely: 2000, 10000, 15000 and 23000 rpm with a feed rate of around 3000mm/min. The depth of cut is equivalent to that used for the numerical simulation ap= 6 mm. The numerical results issued by the numerical model were compared with the results determined by the experiment [12, 27]. The obtained results are grouped together in Fig. 5 and Fig. 6.
By comparing the results obtained, we noticed that the proposed behavior laws reproduce the same mechanical behavior of milling of aluminum honeycomb structures so that the cutting forces decrease with high rotational speeds. This is observed for all the components of the cutting forces. However, the Fy component remains far from experimental reality. This is due to the loss of contact between the thin walls of the honeycomb structure and the tooth of the cutting tool. Furthermore, we found that both mechanics behaviors are nearly associable with experimental results, showing that thermal softening does not have a significant effect on cutting forces. In this regard, many studies have shown that the heat transfer is negligible in the case of impact and perforation tests of aluminum plates with a thickness of less than 20 mm at high speed [28]. Moreover, numerical studies have been shown that heat transfer by conduction is a slow process and the temperature increase in plastic zones is mainly adiabatic [28–30]. Based on these studies, we therefore assume that the effect of increasing temperature is negligible on the yield strength and ultimate stress. In our study, walls of the aluminum honeycomb were represented by highly chopped shell elements. The cutting of the latter is done in a particular way. As a result, the thin walls come into point contact with the tool teeth at each revolution, reducing the area and contact time between the wall and the cutting tool. In view of these results and to better predict and analyze the machinability of honeycomb structures, it is preferable to use the simplified Johnson Cook's law because this model is recommended for several reasons. The first is due to the difficulty encountered in identifying the thermal softening coefficients, the second is related to the influence of the thermal parameters on the overall CPU calculation time. Thus, the simplified Johnson Cook's law makes it possible to correctly simulate the machining of aluminum honeycomb structures while respecting the reasonable calculation time.
5.2 Analysis of the number of teeth on the machinability of the aluminum honeycomb structure
Experimental trials are very expensive in terms of its implementation. Consequently, the experimental procedure fails to study the influence of the geometric parameters of the cutting tool on the machinability of aluminum honeycomb structures. To this end, numerical simulation represents a very important tool for highlighting all the physical and technical phenomena of machining. Using the proposed numerical approach and the Johnson Cook behavior law simplified (JCS) it is interesting to study the effect of geometric parameters in terms of number of teeth on the machinability of the aluminum honeycomb structure. In the present work, the tool used is always composed of two parts: the shredder and the toothed cutting blade. However, we kept the same dimensions of the cutter (shredder) presented previously, while we modified the number of teeth blade. In this work, the accent is put on the effect of the number of teeth cutting blade on the cutting forces, the accumulation of the material or the size of the chips and the surface quality produced. To do this, four configurations were studied, namely the 30-tooth cutting blade, 40-tooth cutting blade, 50-tooth cutting blade and 60-tooth cutting blade. (Fig. 7). Feed rate, rotational speed and depth of cut (2000 rpm; 3000 mm/min; 6 mm) are prescribed as cutting conditions for all cases tested. The numerical simulations were carried out for 0.05s, this means that the lateral depth ae is of the order of 2.5 mm.
5.2.1 Effect of number of teeth on material accumulation and chip size
In order to analyze the number of teeth of the cutting tool on the accumulation of the material (chips size), numerical simulations were carried out and under the same machining conditions mentioned above. Indeed, the orthogonal cutting of the aluminum honeycomb structure is done in the same way as traditional materials such as the toothed blade cuts the thin walls of the aluminum. The latter float on the upper surface of the toothed blade until it reaches the cutter to shred them. The chips obtained for each simulation were collected and analyzed. Figure 8, Fig. 9 and Fig. 10 present the size of the chips according to the number of teeth of the cutting tool, namely, 30 teeth, 40 teeth and 50 teeth.
In view of the results obtained and based on a visual examination, it can be concluded that the size of the chips and the accumulation of the material are closely sensitive to the number of teeth of the cutting tool. In this sense, we found that the accumulation of material is more pronounced for the low number of teeth. By increasing the latter, the accumulation of material in front of the cutting tool is completely removed. The toothed blade with a minimum number of teeth does not manage to cut the aluminum walls correctly. Thus, the minimum number of teeth and the ductility of the aluminum causes the accumulation of material to appear in the form of large chips (Fig. 8). By increasing the number up to 40 teeth, we have found that cutting thin walls is done well. Thus, the chips accumulate in front of the cutting tool become quite small (Fig. 9). In the same way, the milling process is repeated for a cutting tool carrying a count of 50 teeth. In this case, we found that the small chips completely disappeared (Fig. 10). Although, the ductile behavior of aluminum favors the accumulation of material in front of the cutting tool, however the cutting tool carrying a maximum number of teeth (50 teeth) is able to cut aluminum walls correctly and shred them easily. Therefore, the tool carrying a number of 50 teeth generates chips of small sizes and considerably reduces the wear of the cutting tool.
5.2.2 Effect of the number of teeth on the cutting forces
In this study, we want to quantify the sensitivity of the numerical model with respect to the number of teeth on the cutting forces. For this purpose, four toothed blade were examined, namely, 30-tooth, 40-tooth, 50-tooth and 60-tooth knives. The numerical simulations were carried out in the same cutting conditions indicated above. The obtained results are shown in the Fig. 11 and Fig. 12.
Looking at the evolution of the cutting force as a function of the number of teeth, we see that the higher the number of teeth, the more the cutting force decreases. This is noticed for all components of the cutting force (Fx, Fy and Fz). Regarding the advance component of the cutting force Fx, a significant drop in cutting force is observed between 30 and 40 teeth while a regular drop is observed between 40 and 60 teeth. The reduction in cutting force is associated with the accumulation of material in front of the cutting tool, i.e. the large number of teeth reduces the cutting forces in the direction OX. The same trend is observed for the component of the cutting force Fy. In this case, the large number of teeth decreases the point contact between the tooth and the thin wall of the aluminum honeycomb structure. Consequently, the values of the cutting force in the direction OY decrease. In addition, we noticed that the high values of the cutting forces were recorded for the cutting component Fy this is explained by the strong point contact between the surface of the walls of the cells forming the honeycomb structure and the tooth of the cutting tool. Thus, the ductile behavior of the thin aluminum walls and the punctual teeth favor the increase of the cutting forces along the OY axis. Similarly, we noticed that the number of teeth has an influence on the crushing component Fz so that the high number of teeth reduces the cutting forces in the direction of compression OZ. This shows that the large number of teeth decreases the permanent contact between the clearance surface of the toothed blade and the surface of the honeycomb structure. In view of these results, our advice to the industrial sector is to take into consideration the number of teeth of the blade to prevent premature wear of the cutting tool.
5.2.3 Effect of the number of teeth on generated surface quality
To optimize the influence of the number of teeth of the cutting tool on the quality of the generated surface, numerical simulations were carried out under the same machining conditions mentioned above. Indeed, the most pronounced machining defects during milling of the aluminum honeycomb structure are the folding of the walls causing burrs and the deformation of the cells [12, 27]. Given that the walls forming the honeycomb structure are modeled by thin shell elements of the S4R type, the burrs drawn by an excess of material on the walls of the cells are impossible to visualize by the numerical model. On the contrary, the burr generated by the folding of the walls is observed thanks to the modeling and the consideration of the plastic deformation of the machined cells. The Fig. 13 and Fig. 14 show the quality of the machined surface as a function of the number of teeth of the cutting tool, namely 40 teeth and 50 teeth.
In view to the results obtained and based on a visual examination, it can be concluded that the quality of the machined surface is closely sensitive to the number of teeth of the cutting tool. Generally, the digital modeling reveals three machining defects, the folding of the walls, the plastic deformation of the cells and the tearing of the walls. The Folding and tearing of the walls is less pronounced for the 50-tooth tool, while cell deformation appears only for the 40-tooth tool. Thus, milling by the cutting tool having a number of 50 teeth improved the quality of the generated surface. In the end, to properly optimize the quality of the aluminum honeycomb surface after milling, it is essential to take into consideration the number of teeth of the cutting tool.