Estimation of cutting forces in CNC slot-milling of low-cost clay reinforced syntactic metal foams by artificial neural network modeling Free

Metallic foams are advanced materials and are divided into two groups: open and closed cells (Chen et al., 2014). Recently, due to their spongy structure and lightweight, these interesting materials have been selected by many researchers for real components like automobile crash boxes, aircraft fuselage equipment and core materials of sandwich laminates. Metallic syntactic foams (MSFs) can be expressed as a subgroup of closed-cell foams. Certain versions can reach up to 60% porosity and attract attention due to their lightweight, specific strength, total elongation and energy absorption capacity (Öchsner and Gr´cio, 2005). Concordantly, these versatile foams are used in many areas such as automotive, aerospace, defense, construction, medical and marine (Thalmaier et al., 2022). On the other side, if the latest trends in the material and manufacturing sciences are thought, lightweight/high-performance design ideas using the MSFs can provide a positive effect in terms of low energy consumption, less CO₂ emissions and minimum chemical activities. High porosity not only reduces the total construction/component weight but also improves fuel efficiency and environmental friendliness.

Al, Ti, Mg, Zn and Fe-based alloys are used as the matrix material of MSFs (Sánchez de la Muela et al., 2022). However, Al is the most preferred material because it is easily castable, has high corrosion resistance and can be heat-treatable (Yavuz et al., 2023). Considering fillers, ceramic-based granules (Al₂O₃, SiC and SiO₂) are noticed from micron to millimetric scales (Maróti and Orbulov, 2023). Additionally, micro-scale glass balloons and hollow glass spheres are also utilized (Anbuchezhiyan et al., 2017). Besides, expanded glass, fly-ash cenospheres, expanded perlite and volcanic pumice have also been tried as alternative options (Bolat and Gökşenli, 2020).

MSF manufacturing is generally classified with two fundamental processes: stir casting and infiltration casting (Liu and Ma, 2021). Besides, powder metallurgical ways and additive manufacturing are also tried by different research teams (Afolabi et al., 2020; Myers et al., 2015). In stir casting, the matrix is melted and preheated fillers are added to the liquid metal to blend the matrix/reinforcement system. Blending-oriented methodology is a relatively simple and has low-cost equipment. However, this technique possesses certain handicaps like the risk of sphere breakage due to the rotation-based mixing. As for the infiltration, owing to comfortable implementation, gravity-assisted infiltration, pressure casting, gas-vacuum infiltration and backward infiltration are the most popular methodologies (Bolat et al., 2021). Although these techniques require high-cost equipment, uniform reinforcement distribution can be obtained with the proper optimization. Further, infiltration techniques are more controllable than the stir casting, and this circumstance makes them easy to be optimized for uniform pore structure in the matrix metal (Orbulov and Dobranszky, 2008; Anbuchezhiyan et al., 2017).

Although there are valuable studies on the physical/mechanical properties of syntactic foams, the manufacturing challenges is still unsolved and only a few efforts can be ascertained when the archives are scanned. If the sophisticated shapes of the real components (crash boxes in the cars, pillar parts of the vehicles and wing parts consisting of sandwich foam laminates) and their inevitable assembly need are thought, the machining issue becomes considerably crucial after the casting. At this point, the limited number of works are seen while this inclination has begun to change lately. Thomas et al. (2022) made a simulation study on the alumina/AA6061 foams and pointed that as the volume of the fillers raised calculated cutting forces also climbed. Kannan et al. (2020a) showed that finer microballoons in the Mg enhanced the shear strength of the metal matrix. Bolat et al. (2022) conducted machining work on the pumice-reinforced foams and concluded that cutting force values diminished depending on the increasing cutting speeds due to the thermal softening of the matrix and the fragile nature of SiO₂-based particles. Kannan et al. (2020b) tended to cryogenic machining of the AZ31 syntactic foams and enounced that better surfaces could be achieved through low-temperature cutting. The same team offered a mechanistic model to explicate the load/deformation transfer between AZ91 foam constituents (Kannan et al., 2021). Szalóki and Viharos (2018) emphasized the difference in the surface characterization of the plain metal specimens and syntactic foams by milling.

Recently, artificial neural networks and deep learning models have become substantially attractive for investigators because of their robust capability for output prediction and adaptability to numerous engineering disciplines. Although the basic interest in the artificial neural network studies accumulates in the computer and software sciences, other applied research branches like mechanical, materials and manufacturing engineering can also be qualified as other potential applications. Concordantly, depending on the intense and fast demand from metal casting, welding, machining, powder metallurgy, additive manufacturing and other unconventional production ways, neural network-based solutions have become considerably significant instruments for different manufacturing firms. With this versatile technique, it is possible to set a strong interaction between the input and output in the mechanical and manufacturing systems.

In this paper, different from the previous investigations, axial forces emerging in the milling of the low-cost expanded clay-added Al-Zn alloy foams were estimated with a neural network approach for the first time in the literature. When the industry-oriented die-casting implemented in this study is also considered, secondary computer numerical control (CNC)-milling and model-based analyses for the cutting forces will provide a broad perspective for the mass production of complex-shaped foams. Glancing at the developments that appeared in machine learning, artificial intelligence plays a pivotal role in the engineering sciences due to its outstanding prediction ability and potential for rapid development. In this point, with the motivation of solving the main problem of the foam manufacturers, this investigation aims to incorporate the actual manufacturing/design requirements with the estimation capacity of neural network.

Zn-based aluminum alloys are preferred frequently by aerospace and aviation sectors due to their high yield strength, good corrosion resistance, low density and fatigue endurance. Besides, this alloy can be improved in terms of mechanical responses through age hardening. Metal blocks were procured from Güray Aluminum Company (Istanbul, Turkey). Chemical composition of the matrix can be seen in Table 1 according to the supplier firm.

To provide the syntactic characteristic and to create the inner porosity, low-cost and eco-friendly cellular clay particles were used. These particles (2–4 mm LECAT^®) were supplied from Söğüt Toprak Madencilik Sanayi (Ankara, Turkey). Because of its cheapness and low bulk density (0.613 g/cm³), clay granules can be evaluated as strong alternatives in syntactic foam applications. In Table 2, and Figure 1, chemical composition taken from the supplier firm and microviews of the particles can be seen.

In this effort, newly offered industrial-focused automatic cold chamber die casting technology was applied to produce the samples. Firstly, the shot sleeve and steel die were heated to 230 °C after the lubrication (Trewa-S grease oil) of the mold. Subsequently, an aluminum foil was placed on the die inlet. Then, the clay granules were poured into the die. Before this stage, particles were preheated to 400 °C for 20 min. The preheating process was conducted via Protherm PLF 110/6 (Ankara, Turkey) furnace. Following the filling, the cylindrical mold (45 mm diameter and 80 mm height) was closed with a steel lid via pins. Afterward, the initiation position of the injection cylinder was adjusted. When the casting system was ready to be run, the crucible was taken from induction furnace and molten metal at 800 °C was poured into the shot chamber to be injected into the mold cavity with 30 bar pressure. In Figure 2, casting flowchart can be seen. For all fabricated samples, the average density value is calculated as 1.91 g/cm³ with 0.015 standard deviations (SD) and the average porosity is 34.9% (SD: 0.46).

For milling operations, a computer-controlled setup depicted in Figure 3 was installed. Prior to the machining, samples were truncated through an ATM Brillant 220 (Mammelzen, Germany) model cutter to obtain flat prismatic geometry. Force signals were collected via a digital piezoelectric dynamometer and delivered to related software. Detailed equipment and tool information can be followed in Table 3. In addition, milling forces and tool geometry are depicted in Figure 4 where F_y is the force in the feed direction, F_x is the force in the step direction, f_z is the feed per tooth and a_c is the uncut chip thickness.

While F_x and F_y forces are measured according to the dynamometer coordinates, tangential (F_t) and radial (F_r) forces can be derived using Equation 1 (Sheikh-Ahmad et al., 2021). Besides, φ represents the rotation angle of the tool.

in Equation (2), the rotational angle is decisive also on the uncut chip thickness together with the feed speed (F) and spindle speed (N) (Sheikh-Ahmad et al., 2021).

Machining variables like cutting speed, feed rate and depth of cut are the major parameters influencing the operation outputs such as cutting force, surface roughness and dimensional accuracy. Therefore, in this research, all cutting process parameters were evaluated in the light of previous technical efforts (Szalóki and Viharos, 2018; Boswell et al., 2017; Karabulut, 2015; Das et al., 2022) and were selected as shown in Table 4.

Cutting speed, lubricant condition and depth of cut were appointed as the input variables while F_x and F_y were the outputs. Figure 5 demonstrates the neural architecture adopted in this work.

In artificial networks, the information coming from the outer environment enters the input layer. These datasets are significant knowledge which desired to be learned by the designed network (Kara et al., 2015). The net input is a sum of multiplications of the input variables with the relevant weights. In Equation 3, the relationship between the net input and inputs (x) with their weights (w) can be seen.

where i and j can be named as processing elements, w_ij is the weight interactions among the elements, n defines the number of processing elements, w_b shows the weight of biases, x_j relates to the output elements and NET_i is the weighted summation of the inputs. Here, the function of logistic sigmoid transfer was utilized with the form stated in the literature (Zain et al., 2010), and the mathematical relation is shared in Equation 4.

As solution approaches, three models were utilized: Levenberg–Marquard (LM), scaled-conjugated-gradient (SCG) and Bayesian regularization (BR). To develop the foreseeing ability of the network, a five-fold learning was executed.

With the influences of the inputs, to analyze the effect of the methodological differences in neural models, three strategies were tried in the learning and training. LM is a hybrid method that uses both the Gauss–Newton and the steepest descent method (Mukherjee and Routroy, 2012). Marquardt parameter decides which method will be used for learning. SCG method doesn't use the line search method in every iteration. Instead, it implements the trust region method. With this approach, the model's training cost is minimized and faster analyses can be done (Othman and Salih, 2021). In BR method, before the training, there is a pre-distribution of model parameters and this encodes the value of the parameter before seeing the data (Pillonetto et al., 2022).

If the plastic-deformation strength of the matrix is relatively high as happened in this study (approximately 105 MPa and 500 MPa with aging), estimation of the cutting forces and force-induced tool life may become more sophisticated. Right at this point, the importance of reliable prediction tools like artificial neural network emerges due to their comprehensive analysis ability.

Figures 6 and 7 indicate the cutting forces of the milling tests according to input variables. From these results, it is propounded that the depth of cut has a negative effect both on F_x and F_y. This outcome may stem from the increasing contact surface area between the tool and the workpiece. Also, when the depth of cut rises, the possibility of facing the hard and rigid clay particles for the tool increases too. Especially for the medium and high cutting forces, if the depth of cut is above 2 mm, measured cutting forces escalate sharply and this case supports the contact area phenomenon.

While the lowest milling force values of 68.5 N (x-axis) and 65.6 N (y-axis) are seen in the experimental outcomes, the highest average cutting force values can reach up to 240 N for both F_x and F_y. Typically, for plain metals, cutting force values are prone to drop based on the ascending cutting speed owing to the thermal softening and decreasing hardness of the workpiece (Kara et al., 2015). From Figures 6 and 7, this standard relation is not noticed and force fluctuates with the altering cutting speeds. This observation can be explained by the existence of the porous/cellular clay particles, the formation of localized clustered clay zones in the matrix after the casting (in Figure 8 with orange circles) and the narrow geometry of the machining slot-line not having enough area to compensate for these handicaps. During the milling operation, broken hard clay fragments can't be evacuated easily and any increase in the cutting speed values stimulates a difficulty in the chip evacuation.

In some investigations (Kannan et al., 2020a) trying micron-scale fillers in the matrix, chip evacuation can be relatively easy, but this case is notably difficult for the millimeter-scaled clay particles. The stated observation is due to the presence of big-sized broken fragments in the tool outfall channel, and cellular pores with columnar struts. Additionally, deformation instability and low fracture toughness of the particles lead to small-sized crack-sensitive zones in the matrix and cause abrupt changes in the chip width. These cases contributing to difficult chip evacuation were observed in the chip analyses (Figure 9). In this work, those kinds of circumstances were also realized, and the presumable impacts of the lubricant on the force results were monitored. Indeed, lubricant usage has an affirmative effect to dwindle the thrust force and this impact was observed for all parameter sets. However, mentioned influence is more dominant at the lower cutting speeds making rapid and easy chip evacuation possible. In practice, the effective penetration of the lubricant between the workpiece and the tool surface is critical. In this study, at lower cutting speeds, the anti-frictional and coolant properties of the lubricant are noticed evidently. Therefore, low speed, small depth of cut and proper lubrication have a useful synergy to drop the cutting forces and consumed energy for MSFs.

For quantitative factors, real numeric values were used while the terms “yes” or “no” were appointed for the lubricant condition. Accordingly, experimental data were gathered and categorized in Table 5.

To train the models, the input and output data must be between 0 and 1 for normalization. In Table 6, the normalized dataset can be found. At the cutting force and the cutting depth column, 0–1 normalization has been made. In the lubricant side, the value of “no” has been reassigned as 0 and the value of “yes” has been reassigned as 1. At the column of F_x and the column of F_y, max normalization has been applied.

For the background of the statistical calculations on the training and testing data, terms of the root mean square error (RMSE), coefficient of determination (R²) and mean error percentage (MEP) values were kept in the frontline. These terms were detected with Equations 5, 6 and 7.

in Equations 5, 6 and 7, terms t, p and o are the target value, the number of patterns and the output value, respectively.

To determine the best architecture, a comparative statistical approach was implemented between five to ten neurons at the hidden layer. Similar applications were also tried on the metal alloys in the literature (Kosarac et al., 2022), and the number of neurons was assigned in this direction. Table 7 shows the statistical results of the training and testing dataset depending on the neuron numbers and algorithms.

From Table 7, the best results were obtained with eight neurons architecture with the LM method. Looking at the statistical analyses, it can be asserted that LM has been more successful to estimate the axial forces in comparison with SCG and BR. However, the poorest prediction results were obtained with ten neurons architecture with the BR method even though SCG exhibited the lowest performance in terms of the average of all neuron combinations. In artificial neural networks, it is essential to maintain a balance in the number of neurons. If the number of neurons is insufficient or relatively less, it results in an underfitting issue. When the number of neurons is high, it can lead to overfitting problems. In the models offered in this paper, neuron numbers range between 5 and 10 at the hidden layer. For optimal outcomes, it is recommended to aim for the median. Herein, it should be noted that the LM method is a hybrid approach that combines both the steepest descent and Gauss-Newton methods. By utilizing the Marquardt parameter, the method determines which approach to use. If this parameter is too high, it opts for the steepest descent method, while if it is too low, it employs the Gauss-Newton. Therefore, optimization efforts made via the LM method outperform SCG and BR optimizations. Further, compared to the LM, the BR model can be counted as a time-consuming way owing to its need of posterior data distribution and SCG has some difficulties for the functions that cannot be derived. In addition, the strongest regression analysis for training (0.98951) and the best regression analysis for testing (0.99081) are shown in Figures 10 and 11.

When the experimental dataset is analyzed, it is seen that both F_x and F_y values range in a wide scale interval depending on the cutting parameters. This case stems majorly from the pore structure of the composite foams, particle distribution homogeneity and the existing density gradient of the solid sample. In addition, the random gap structure of the clay particles triggers this circumstance. At this point, the importance of the rapid, practicable and cost-efficient predictive models emerges, and this work indicates that LM methodology is the best way to foresee the force results. Figures 12 and 13 illustrate the evident compatibleness between predicted F_x/F_y values with the LM at second fold and collected experimental results. On the other side, from the findings, there is no direct relationship between the neuron number and error levels. The lowest error levels can be found for the intermediate neuron numbers. Similar observations are also noted by the literature efforts (Kara et al., 2015) and presumably resulted from the oscillating dataset collected from the real experiments. Thanks to that kind of dataset behavior, overfitting/memorization issue can be dropped.

Analyzing the best prediction, related mathematical statements can be derived for F_x and F_y in Equation 8 and 9. To get these equations, Equation 3 and 4 were benefited. On the other side, weights and biases between the inputs and the hidden layer are shown in Table 8. Further, weights and biases between the hidden layer and the outputs can be glanced at in Table 9.

From the findings underlined in this paper, it is true to express that low-cost granular clay-added Al-Zn series metallic foams can be machined in the style of slot milling via an exhaustive optimization work based on a neural network approach. Among the algorithms, SCG was the weakest in the average results whereas the LM approach was highly successful in foreseeing the axial cutting forces. Thanks to the k-fold design, the best algorithm layout was found, and this case was realized at the second fold in the LM model. As for the input variables, an increase in the depth of cut entailed the cutting forces and this circumstance was more obvious at the higher cutting speeds. This means that making the slots in a single pass have more height values with high cutting speeds is risky for tool life and total energy consumption. In addition, used lubricant played a positive role in reducing the consumed machining force but its contribution can be qualified as partial owing to the existence of the clay particles in the matrix leading to difficult chip evacuation and elasticity gradient in the deformation region of the tool.

The findings revealed in this effort indicate that neural network-based solutions carry a promising potential to minimize the time-consuming, provide process optimization and block human-induced undesired errors.

The authors thank the staff working in Pamukkale University's Advance Technology Application and Research Centre and the Söğüt Toprak Madencilik Sanayi for their kind interest.