1 Introduction

Thanks to their excellent corrosion resistance, weight ratios, and mechanical properties, aluminium alloys (AA) have been extensively utilized in the naval [1], aviation [2], and automotive industries [3, 4]. Specifically, the AA5083 is known for its resistance to seawater corrosion [5, 6] and tribological properties and is used broadly by the shipbuilding industry [7]. Therefore, the processing of AA5083 is of great interest in manufacturing industries, and it is processed by many cutting and diffusing–joining processes [8,9,10], for example, milling [11], turning [12], and friction stir welding [13, 14].

CNC end milling is a highly customizable material processing approach that involves rotating flute cutters to shape a workpiece until the final desired shape is achieved [15, 16]. Optimization problems in the cutting processes, such as surface finish, smoothness and flatness, are very common, especially for difficult-to-cut materials such as aluminium [17], copper [18], and titanium alloys [19,20,21], to name a few [22, 23]. Additionally, dimensional accuracy [24], wear, and tribological properties are affected by machining conditions the most, as has been observed in the literature [25, 26]. Commonly, finishing machining material removal rates are determined by surface roughness performance, which is associated with cutting build-up edge formation and chip characteristics, and, in finishing conditions, are more critical than cutting force and tool wear [27,28,29].

Therefore, even if the cutting theory has developed predictive models for static and dynamic tools [30, 31], for surface roughness parameters, when we have to deal with difficult-to-cut materials, it is prevalent to produce experimental data for specific cutters and materials varying the basic cutting parameters, i.e. the cutting speed, feed rate, and depth of cut. Debnath et al. [11] investigated five processing parameters (cutting speed, feed rate, depth of cut, tool nose shape, and number of flutes) during end milling (50 mm length slots, 8 mm cutter diameter, carbide tools, dry condition) of Al 5083-H112 and utilized the concept of desirability function analysis to determine the optimum combination of parameter values. They observed that cutting speed and feed rate contributed the most to Ra values and that increasing cutting speed or decreasing feed rate or depth of cut resulted in better Ra values. In Kalita et al. [32], a high-speed steel cutter was utilized to end mill Al1100 specimens varying cutting speed, feed rate, and depth of cut and proved that the Ra values decreased with the decrease of feed rate, cutting speed, and depth of cut.

Moreover, in the literature, the geometric cutting parameters of a two-flute cutter were optimized, varying the cutting depth, speed and feed [17, 33]. The 50% core diameter, 38° flute angle, 22° rake angle, 22° first relief angle, and 30° second relief angle were optimized for the cutting efficiency concerning the average and max depth of surface texture (Ra and Rt). Note here that optimizing the cutter geometry is of outstanding importance as it defines the cutting conditions and further the cutting forces, tool wear, cutting accuracy, process removal rates, and, consequentially, the final parts’ production cost and process planning [34].

The current work is an optimization study of cutting conditions during dry end milling of AA5083, where the optimized geometry of the two-flute cutter is manufactured by a grinding 5-axis machine, as described in detail in Kechagias et al. [17], and then the radial cutting depth, feed per tooth, and speed were tested in different dry cutting conditions. Note here that, in the literature, the majority of the research works utilized cutters from the market and not laboratory-made [35,36,37,38,39]. Therefore, the cutter geometry details were designed and optimized for the specified AA5083 alloy.

Further, in this work, the newly extracted machinability data has been analyzed by utilizing the full factorial design experimental approach, which means that all combinations of the used parameters and levels appeared in the experimental table, and three measurements have been performed in each of the twenty-seven experiments for higher experimental power [40,41,42]. The signal-to-noise ratio has been used as an objective function for the cutting condition optimization process according to the surface texture mean and max depth roughness (Ra and Rt). The theoretical basis of using the SN ratio as a performance measure to optimize the surface texture of the machined surface has to do with cutter vibrations, which affect the surface roughness in these three measurement lines in different ways and cause significant variations in Ra and Rt measurements that make optimization crucial to eliminate surface defects during the machining process [43, 44]. The proposed approach can be utilized by the manufacturing industry for better AA5083 product surface quality, corrosion performance and process planning.

2 Materials and methods

The two-flute end mill cutter (8 mm in diameter) was manufactured homemade (Hawemat 5-axis machine) as described in previous work with the optimized geometry (50% core diameter, 38° flute angle, 22° rake angle, 22° first relief angle, and 30° second relief angle) [17]. The tool geometry details can be seen in Fig. 1a. The cutting parameters are all for finish end milling conditions. As indicated in the ShopMill panel, the consuming cutting power was lower than 5% of the machine’s max power (13 kW and 14,000 rpm) in the experimental area and was not investigated. According to the finishing conditions and preliminary experimental work, the radial depth of the side cutting surfaces was decided between 0.5 and 1.5 mm, the cutting feed between 0.055 and 0.11 mm/tooth, and the cutting speed between 5000 and 7000 rpm [17]. The DMU 50 Ecoline milling 5-axis machine centre is utilized for all cuts.

The feedstock was a plate of 150 mm length × 80 mm width × 50 mm depth of AA5083 (see Fig. 1b). The composition, physical properties, and mechanical properties of a typical 5083 aluminium alloy can be seen in [33]. The G–code for the twenty-seven different cuts was prepared as a text for this experiment and fed on a 5-axis machine control unit (ShopMill). After each cut, the carbide tool geometry was inspected for wear, and no wear or build-up edges were observed for all the twenty-seven experiments, as can be seen in Fig. 1c. The cutting surfaces were 10 mm in length and 5 mm in depth, as depicted in Fig. 1d.

Fig. 1
figure 1

a Two flute end mill cutter geometry (centre cutting type), b cutting procedure, c tool inspection for wear after each cutting, and d cutting surface (5 mm depth and 10 mm length)

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The tool was tangentially imported and exported on the 10 mm length cutting surface twenty-seven times, varying the cutting radial depth of cut (RDOF, mm), feed (f, mm/tooth), and speed (S, rpm) as described in Table 1. The machined surfaces are tabulated in Fig. 2. The width of each cutting surface was 5 mm (vertical distance between the upper part edge and tool cutting edge). After machining, all cutting surfaces were measured in three different positions, as shown in Fig. 2, by a nose surface tester (4.8 mm sampling length). Therefore, three absolute arithmetic average surface roughness values (Ra1, Ra2, and Ra3; µm) and three highest distances between the maximum peak and lowest valley (Rt1, Rt2 and Rt3; µm) were measured. Last but not least, two more columns are added to Table 1 to demonstrate the signal-to-noise ratio known as SN ratio, which, in the case of Ra and Rt values (positive higher than zero values; the smaller, the better case), is calculated by Eq. 1 [45].

$$\eta=-10\;Log\left(\frac1n\sum\nolimits_1^ny_i^2\right)$$
(1)

where the SN ratio is the η (here SNRa and SNRt), n (here three times), and the number of trials measured in the performance measure y (here Ra and Rt).

Table 1 Experimental array and measurements
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The twenty-seven experiments in Table 1 were performed in three groups according to RDOC levels (0.5, 1, and 1.5 mm). In each group, a random sequence was followed to eliminate other latent factors affecting surface roughness.

Fig. 2
figure 2

Twenty-seven different combinations of end milling cutting surfaces

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3 Results and discussion

In Fig. 2, the effect on the surface texture can be observed by varying the three basic cutting parameters (RDOC, f, and S). The variation of the parameters affects the surface texture, and the different conditions are reflected in the machined surfaces for each case. Therefore, parameter optimization is necessary when the final machined parts are for high-accuracy assemblies that operate in challenging high-corrosion environments in the naval industry.

Optimal levels of the Ra and Rt can be observed by SN ratio main effect plots, as shown in Fig. 3. Main effect plots or analysis of means (ANOM) graphically show the mean values of each parameter level inside the experimental area. Therefore, the significance of each parameter’s contribution to variability (delta values) and the optimal parameters’ levels can be thoroughly seen. The 0.5 mm RDOC, 0.082 mm/tooth feed, and 6000 rpm optimize both Ra and Rt SN ratios. Note that experiment number 26 in Table 1 has slightly better SN ratios than 23, but this is due to the mean levels calculated from the values of each parameter within the experimental domain, as explained earlier.

Fig. 3
figure 3

Main effect plots of SN ratios: a SNRa and b SNRt

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The conclusions from reading the main effect plots in Fig. 3 are analyzed below:

  • Reducing the radial depth of cut minimizes the volume of material removed per unit time, the radial cutting force, and upper and lower limits of cutter vibration, resulting in thinner chips with smaller surface roughness Ra and Rt (improve SN ratios). This is consistent with the literature, and in particular, in AA5083, the results of the radial DOC on Ra and Rt parameters are of greater importance than in [43] for slot milling surfaces of aluminium blocks, where similar results were derived, even if the depth of cut proved to have lower effects on surface roughness in comparison with the spindle speed and feed rate. Moreover, the RDOC effects follow the simulated results extracted in [46] for the ball-end milling process.

  • Cutting feed gradually increases the SN ratios of Ra and Rt, but after the centre level, it rapidly reduces the SN ratios and gives the worst quality at the higher feed. The feed rate increase increases the chip volume, resulting in better quality cutting conditions for the values close to the centre point of 0.082 mm/tooth and worse for the left and right level values. The tribological conditions between the cutter and side surface improved in the centre point of the cutting feed, resulting in fewer vibrations and smoother surfaces. Note that in the orthogonal cutting theory, increasing the cutting feed increases the Rt values (static tool geometry; see [31]), but the theoretical models do not take into account the tribological conditions and vibrations but only the geometrical parameters.

  • Finally, the cutting speed increase has a similar attitude to the feed and optimizes the average roughness Ra for the centre level (6000 rpm) and the worst values for the higher speeds (7000 rpm). The centre levels reduce the vibrations having benefits on surface roughness. Note that, in orthogonal cutting theory, static and dynamic tool geometrical models were extracted (see [30, 47]), proving that the vibrations and machinability conditions (tribological and thermal) need optimization for optimal machining performance [21, 47].

Interaction plots (see Fig. 4) between the RDOC and feed show that all RDOC give almost the same SN ratios for Ra and Rt in 0.082 mm/tooth feed and considerably different for the lower and higher feeds with higher feeds, resulting in worse values for 1.5 mm RDOC. Similar results were observed between RDOC and S with the 1.5 mm RDOC and 7000 rpm, resulting in the worst SNRa and SNRt values. Finally, the f and S interactions show that the SN ratios for Ra and Rt improved smoothly at 6000 rpm for all feed values, while the 0.11 mm/tooth and 7000 rpm resulted in the worst SN ratios.

Fig. 4
figure 4

Interaction plots of SN ratios: a SNRa and b SNRt

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After the analysis of means and interaction plots, a general linear model with linear interactions cross products was applied to the SNRa and SNRt ratios (see Eq. 2; additive model; [45]).

$${SN}_{l(i,k)}=m_l+\sum\nolimits_i^{}\;(m_{l\left(i,k\right)}-m_l)+\sum\nolimits_{i\neq j}^{}\;(m_{l\left(i,k\right)}\times m_{l\left(j,k\right)}-m_l)\pm e_l$$
(2)

where l is the SN output different metric (l: Ra, Rt), i and j (i ≠ j) are the variable parameters (i, j: RDOC, f, S), and k is the level value.

In addition, the ANOVA general linear model (GLM) for SNRa and SNRt are presented in Tables 2 and 3, respectively. Radial depth of cut significantly affects the SN ratios of Ra and Rt having F-values higher than 4 (12.08 and 5.48, respectively) and p-values lower than 0.05 (0.004 and 0.032, respectively). When the RDOC increases, the radial cutting forces increase, likewise increasing the vibrations, noise, and surface defects. Feed, again, affects the SNRa ratios significantly, having an F-value higher than 4 (4.76) and p-value close to 0.05 (0.044), with centre values resulting in optimum performance while insignificantly affecting the SNRt (1.53 F-value lower than 2). Speed likewise significantly affects the SNRa (4.13 F-value higher than 4, and 0.059 p-value close to 0.05) and insignificantly the Rt (0.89 F-value lower than 2 and 0.447 p-value higher than 0.05).

The cross interactions have minor effects for SNRa as presented F-values lower than 2 for all cases, with RDOC × f interaction being higher than the RDOC × S and f × S interactions (Fig. 4). Similarly, the same observations have been made for SNRt, showing all interactions to be insignificant. Note here that the orthogonal cutting theory derives analytical models that Ra and Rt values depend mainly on cutting feed and tool geometry and not on the depth of cut [48]. Here, it proved experimentally that the RDOC significantly affects the surface texture during the end milling of an AA5083 difficult-to-cut material, followed by f and then by S.

Table 2 ANOVA: SNRa vs. RDOC; f; and S
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Table 3 ANOVA: SNRt vs. RDOC; f; and S
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The SN ratios of Ra and Rt additive models show Rsq (coefficient of determination) values of about 87.21 and 72.77%, but the residuals were tested if they followed the normal distribution, and both showed p-values higher than 0.05 (0.373 and 0.473, respectively), which means that the linear models are adequate for predicting the process performance (see Fig. 5).

Fig. 5
figure 5

Probability test for SN ratios: a SNRa and b SNRt

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Finally, the additive models are used to calculate the mean absolute percentage errors (MAPE) for all eighty-one Ra and Rt measurements, as shown in Table 4. The MAPE values for all measurements are about 15% and 23% showing good prediction performance.

Table 4 Mean absolute percentage errors (MAPE)
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Here, note that the extracted additive models cannot predict intermediate values of predictors parameters (RDOC, f, and S), and therefore, interpolation should be utilized for these cases.

4 Conclusions

The current study optimizes the cutting condition of a two-flute cutter during dry end milling of a difficult-to-cut aluminium alloy known as AA5083. The experimental data showed that the radial depth of cut (RDOC) is the dominant predictor parameter as it defines the chip removal rate, chip cross-section area and shape, and the radial cutting force. Its increase increases noise forces and vibration limits, resulting in surface defects and lower surface quality. Feed rate likewise has moderate effects on noise, and its increase higher than 0.082 mm/tooth decreases the quality (lower Ra and Rt SN ratios) in all ranges of RDOC (0.5–1–1.5 mm) and S (5000–6000–7000 rpm) according to MEP plots (Fig. 3). Note here that for the specified 0.5 mm RDOC and 6000 rpm S, the 0.082 mm/tooth feed shows slightly lower Ra and Rt SN ratios than the 0.11 mm feed (see Table 1), which means that for 0.5 mm radial depth-of-cut and 6000 rpm speed the cutting conditions become slightly better for the 0.11 mm/tooth feed. Moreover, cutting speed moderately affects the surface performance parameters Ra and Rt, and its increase to the centre point increases the quality softly and then decreases it sharply.

Last, according to the three different measurements on each of the twenty-seven machined surfaces and the SN ratio approach (SN ratio as an objective function), additive models are adequate to predict the surface quality performance according to the residual analysis and the achieved MAPE values. Intermediate values of the predictors can be observed using linear interpolation. Further investigation to identify a more sophisticated predictive model, such as suggested in [49,50,51], incorporating more parameters and utilizing dynamic models (higher order or NN models) and optimization machine learning algorithms are suggested as future work.