1 Introduction

The extension of human life expectancy in our era has led to an increase in the demand for artificial implants in dental and orthopaedical field, with a predicted request of only hip and knee implants revisions of 3.48 billion by 2030; as underlined in the work of Sarraf et al. [1]. Moreover, Hao et al. [2] observed that prostheses are required to endure in the human body, without accomplishing failures, for a long time. Hence, to ensure this durability, Heimann [3] found that prosthesis materials must possess, at the same time, several characteristics, such as the extreme resistance to corrosive phenomena typical of a living environment with aggressive, often changing conditions, as in the human body. Moreover, good wear and fatigue resistance, high strength together with low density and elastic modulus are required [4]. Focusing on metallic biocompatible materials, the most employed are stainless steels, cobalt-chromium, and titanium alloys. Amongst these latter, Ti-6Al-4V was indicated by Aghili et al. [5] as the most widely used for biomedical applications, in particular for joints and bones replacement, and dental implants. The high degree of diffusion of Ti-6Al-4V alloy in biomedical field is due to the combination of its biocompatibility, corrosion resistance and mechanical properties. Considering the need of patience-tailored implant design, AM results to be of great and strategic importance. This technology, in fact, allows to produce specific implants having optimized shapes [6], porosity ratios [7], and bone-comparable elasticity modulus able to profitably interact with the body, hel** cells growth and osseointegration, at relatively low costs [8]. Selective laser melting (SLM) and electron beam melting (EBM), both belonging to the powder bed fusion (PBF) methodology, have been revealed by the study of Tong et al. [9] as the most adopted AM techniques to manufacture Ti-6Al-4V components. SLM exploits the thermal power of a laser source to melt powder particles, while the heating source in EBM is an electron beam. Due to this difference, SLM is performed in an inert gas (Ar or He) environment at room temperature with higher powers than EBM process, that is carried out in vacuum at high temperatures. Consequently, SLM is characterized by the use of lower particle sizes and printing speeds, and higher cooling rates with respect to EBM, resulting in different microstructures, tensional states, mechanical properties, and surface qualities [10]. More in detail, SLM products have smaller grain size, elongation percentage, surface roughness, and higher residual stress, ultimate tensile stress than the EBM ones [2]. Even if AM is considered a net-shape process, research conducted by Abeni et al. [11] and Filiz et al. [28]. The micro-milling test corresponding to the CCD central point, with VC = 40 m/min and fZ = 3.0 μm/tooth*rev was repeated three times with the aim of increasing the reliability of the statistical analysis [29]. Figure 5 shows the values of the selected process parameters for each typology of manufacturing process of the specimens. In this manner, 11 machining tests were performed for as-received, SLM, and EBM samples, leading to a total number of 33 experiments.

Fig. 5
figure 5

Summary of the employed micro-milling parameters by the related CCD representation

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The cutting speed range was selected according to the values suggested in the manufacturer’s datasheet, while the designated range of feed per tooth was bounded to the adopted values because unexpected tool breakage was observed at higher fZ values.

In order to avoid undesired effects on the final achieved surface related to tool wear occurrence, the tool was substituted after each channel micro-milling.

At the end of each machining test, the three-dimensional surface roughness parameters Sa was measured with the optical microscope Mitaka PF60 (Mitaka Kohki.Co.,Ltd., Japan). According to ISO 25178 standard for three-dimensional parametric definition of surface texture, the mean height of surface irregularities Sa can be calculated using Eq. (1):

$${S}_a=\frac{1}{LB}\int_0^L\int_0^B\left|\eta \left(x,y\right)\right| dxdy$$
(1)

where η(x,y) is the deviation of the surface irregularities from the base plane, L is the length, and B is the width of the given section of surface. The adopted scanning size for the optical imaging was of 0.245 × 2.3 mm2 positioned at the central point of the micro-machined surface, with minimum and maximum focusing points of the height of the surface sample, and a magnification of 400×. The image processing for obtaining the Sa values was performed by using the Digital Surf MountainsMap Premium software version 8 (Digital Surf, Besançon, France). Figure 6 depicts an example of the resulting measurement for the SLM specimen machined with VC = 40 m/min and fZ = 0.30 μm/tooth*rev, while in Table 3, the acquired Sa measurements for all the tests are presented.

Fig. 6
figure 6

Example of the acquired Sa measurement (VC = 40 m/min, fZ = 30 μm/tooth*rev)

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Table 3 Summary of the Sa experimental values for all the tests
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3 Results and discussion

In order to investigate the effects of the variation in process parameters, and which ones are the most impactful, on surface roughness, an analysis of variance (ANOVA) of Sa values was performed for the three cases, namely as-received, SLM, and EBM. The reliability of the results analysis, and the related derived regression models, is strictly correlated to their normality [30]. Hence, in order to check the normal distribution of the acquired Sa data, their probability plots, in which the percentage of the normal probability of the data residuals are represented, were computed (Fig. 7). Referring to these plots, the straight central line represents the cumulative probability, while the two curves highlight the 95 % confidence interval (CI) boundaries. The data respect the normality assumption when they are enclosed between the CI curves and closely positioned to the cumulative probability line.

Fig. 7
figure 7

Probability plots of Sa for a as-received, b SLM, and c EBM specimens

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The probability plots of as-received (Fig. 7 a) and EBM (Fig. 7 c) Sa values are in accordance with the previously presented normality definition, while SLM (Fig. 7 b) ones are not normally distributed. Therefore, a normalization of these latter is mandatory. As suggested in [29], a Johnson transformation can be utilized for this purpose. Following this, the SLM Sa values were normalized by the application of Eq. (2):

$${S}_{a\_ SLM norm}=0.392249+0.550540\bullet \ln \left(\frac{S_{a\_ SLM}-0.196534}{0.320174-{S}_{a\_ SLM}}\right)$$
(2)

where Sa_SLM are the experimental Sa values, and Sa_SLMnorm are the normalized ones. Figure 8 illustrates that Sa_SLMnorm values are normally distributed, thus the resulting statistical analysis can be considered reliable.

Fig. 8
figure 8

Probability plots of Sa_SLMnorm

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3.1 As-received Sa values analysis

The results of the ANOVA for the Sa values of as-received specimens are shown in Table 4. The Source column gives the process parameters that have been analyzed, where it can be seen that not only their individual effects on the surface roughness behavior were considered, but also their interaction and their squared contribution. In the other columns the number of degrees of freedom (DoF) are given for each source, together with, the adjusted sum of squares (Adj. SS), the adjusted mean of squares (Adj. MS), the F-value, and the p value. In the common practice, for assessing if a determined source parameter has a significant influence on the final response, in this case the surface roughness Sa, the p value is the most useful parameter. Whenever the p value is lower than a predefined threshold value, also known as significance level, the null hypothesis H0, that states that there is no relation between the source and the outcome, is rejected. The significance level for the p-value depends on the CI. Since, for the presented analysis, CI = 95 %, the significance level is equal to 1 – 95 % = 0.05. Consequently, if the p value is smaller than 0.05, the alternative hypothesis H1 is considered correct, concluding that there is a statistically significant relation between the source and the outcome [30].

Table 4 ANOVA results for Sa of as-received specimens
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The ANOVA results of Table 4 do not reveal any influence of neither feed per tooth nor cutting speed on micro-machined surface roughness values. In fact, there are no p-value lower than 0.05. This first outcome is quite suspicious as unexpected. By ANOVA the presence of an outlier was discovered. An outlier is defined as a value of the response having a standard residual higher than the standard deviation of the other values distribution. It may be either caused by an error in calculation or data coding, or by a measurement error. In the case of outliers having a standard residual higher than 3 times the standard deviations, they can be excluded from the analysis without compromising its significance. The standard residual of the Sa value related to VC = 35 m/min and fZ = 3.5 μm/tooth*rev is equal to 2.12, which results to be greater than 3 times the standard deviation of as-received data, equal to 0.05236. Thus, it has been removed from the analysis, and a new ANOVA, whose results are visible in Table 5, was performed.

Table 5 ANOVA results for Sa of as-received specimens without outlier
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The ANOVA outcomes of Table 5 underline that cutting speed and its interaction with the feed per tooth variation, significantly affect the evolution of Sa for the as-received material. In particular, as depicted in the main effects plots of Fig. 9, if VC increases the surface quality is enhanced, meaning that Sa value decreases. The same trend is observable for the variation of fZ, although a statistical correlation of it with Sa was assessed. The surface and contour plots of Fig. 10 summarize the clear effect of the VC-fZ interaction, and again indicate that the way in which fZ influences Sa is not clear, since at low VC an increase of fZ lead to an augmentation of Sa, while at high VC the inversion of the Sa trend is detected. Considering these outcomes, the fZ effect needs to be further investigated.

Fig. 9
figure 9

Main effects plots of as-received Sa respect to a VC and b fZ

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Fig. 10
figure 10

a Surface and b contour plots for as-received Sa

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3.2 SLM Sa values analysis

The results of the ANOVA performed on the normalized values of Sa for SLM specimens are summarized in Table 6.

Table 6 ANOVA results for normalized value of Sa for SLM specimens
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It can be clearly seen that the most affecting parameters on the evolution of Sa values in case of SLM specimens are VC and fZ, while their interaction and squared contribution are negligible. A reduction of both VC and fZ increases the value of machined surface roughness, as described by the variation trends shown in the main effects plots of Fig. 11. This trend is visible in the related surface and contour plots of Fig. 12 as well.

Fig. 11
figure 11

Main effects plots of SLM normalized Sa respect to a VC and b fZ

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Fig. 12
figure 12

a Surface and b contour plots for SLM normalized Sa

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3.3 EBM Sa values analysis

The ANOVA performed on the surface roughness data obtained from micro-milled EBM specimens yields the results shown in Table 7.

Table 7 ANOVA results of Sa values for EBM specimens
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The only influencing parameter on the Sa value is the cutting speed. Also in this case, when VC decreases, surface roughness increases, and this behavior is described by the negative slope of the VC plot in the main effects diagrams in Fig. 13. Moreover, similar behavior is detectable for the effect of fZ, but as observed in the case of as-received samples, it has no influence, and its final contribution needs to be further examined. The surface and contour plots of Fig. 14 show the great impact of VC on Sa for EBM specimens and, in addition, the neglectable effect, especially at higher cutting speed value, of fZ.

Fig. 13
figure 13

Main effects plots of EBM Sa respect to a VC and b fZ

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Fig. 14
figure 14

a Surface and b contour plots for EBM Sa

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3.4 RSM regression models

With the intent of analyzing the effects of different micro-milling parameters on the surface roughness value, numerous studies have been developed. A summary of them is reported in Table 8, where the machined workpiece (WP) material, the evaluated roughness parameter (SP), the analyzed micro-milling process parameters (MMP), and the model derivation source are indicated.

Table 8 Summary of studies on surface roughness in micro-milling processes
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Most of the studies of Table 8 had analyzed the behavior of roughness parameter Ra in the case of specimens not produced by AM processes and with different materials respect Ti-6Al-4V investigated in this work. Therefore, to better evaluate the effects of production process type, the development of mathematical models of surface roughness considering this aspect, results to be a profitable task. To develop mathematical models capable of reliably predicting the evolution of micro-milled surface roughness as a function of the variation of the employed machining parameters and the production process, the response surface methodology (RSM) was applied to the experimental measurements of Sa. By means of RSM, a regression model was derived for each type of manufacturing process applied to sample preparation. This methodology conveys to the formulation of Eq. (3), Eq. (4), and Eq. (5) for as-received (Sa_AR), SLM normalized (Sa_SLMnorm), and EBM (Sa_EBM) Sa values, respectively.

$${S}_{a\_ AR}=1.9+0.79{f}_Z+0.060{V}_c+0.022{f}_Z^2+0.000023{V}_c^2-0.023{f}_Z{V}_c$$
(3)
$${S}_{a\_ SLMnorm}=12.1-0.78{f}_Z-0.304{V}_c-0.264{f}_Z^2+0.00089{V}_c^2+0.027{f}_Z{V}_c$$
(4)
$${S}_{a\_ EBM}=0.23-0.041{f}_Z+0.011{V}_c+0.023{f}_Z^2-0.000068{V}_c^2-0.003{f}_Z{V}_c$$
(5)

To check the validity of the regression models obtained, a comparison between the experimental and calculated values was carried out. Due to the Johnson transformation applied to the Sa_SLM data, to correctly achieve the parallel, an inverse transformation must be applied to the Sa_SLMnorm estimated values. Hence, by reversing Eq. (2), Sa_SLM can be expressed by Eq. (6).

$${S}_{a\_ SLM}=\frac{0.320174\bullet {e}^{\frac{S_{a\_ SLM norm}-0.392249}{0.550540}}+0.196534}{1+{e}^{\frac{S_{a\_ SLM norm}-0.392249}{0.550540}}}$$
(6)

Finally, by using Eq. (3), Eq. (6), and Eq. (5), the value of Sa for each combination of process parameters, and for each manufacturing process of the specimens were calculated. The measured and estimated Sa values, with indication of the percentage error e% between them, are summarized in Tables 9, 10, and 11.

Table 9 Comparison between experimental and estimated values of Sa for as-received specimens and related percentage errors in calculation
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Table 10 Comparison between experimental and estimated values of Sa for SLM specimens and related percentage errors in calculation
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Table 11 Comparison between experimental and estimated values of Sa for EBM specimens and related percentage errors in calculation
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3.5 Discussion

ANOVAs performed on the different types of specimens, produced via the three different processes described above, reveal that, regardless of the specimen preparation process, the cutting speed has a strong influence on the quality of the final part surface. In particular, when VC is decreased, the roughness value of the machined surface increases, and, following the investigation of Kiswanto et al. [46], this can be explained by the effect of vibrations induced by the non-homogeneous properties of the material and by the formation of built-up edges at lower cutting speeds. The significance of feed rate has been observed only for SLM specimens, while its interaction with VC appreciably affects the surface roughness of as-received samples. The influence of fZ on components produced with SLM can be justified by the higher brittleness associated with these specimens. This feature derives from the microstructure resulting from the higher cooling rate induced by the SLM technique, which leads to a more pronounced shear cutting mode, from which traces of the tool passage remain on the surface, as observed by Gorsse et al. [47]. On the other hand, Rafi et al. [48] highlighted that due to the more ductile microstructure associated with as-received and EBM specimens, the high contribution of the ploughing mode improves surface plastic deformation by reducing path traces. Furthermore, an increase in fZ has been indicated by Roushan et al. [49] as a reducing factor for vibrations, with a related decrease in surface roughness. Nevertheless, for better understanding the misty effect of fZ on both as-received and EBM samples, further analysis is mandatory.

Regarding the total surface roughness values for the different types of specimens, these values appear to be lower for SLM samples than EBM, while the highest values were observed for as-received. This can again be attributed to the different microstructures. In fact, higher ductility causes the material to adhere to the radius corresponding to the cutting-edge, negatively affecting Sa, while brittle behavior leads to less burr formation [50].

Without considering the percentage error of 56 % in Table 9, which is related to an outlier identified in the Sa measurement of as-received specimens, the maximum computational error of the mathematical models derived from RSM is around 11 % (Tables 9, 10, and 11). These outcomes highlight the reliability of the developed models when estimating the resulting micro-milling surface roughness, allowing, depending on the type of material, both to predict the achievable surface roughness value once the cutting parameters have been selected and to optimize the range of process parameters once the desired Sa value has been identified. The results of the micro-milling tests performed did not identify a combination of material, manufacturing process, and processing parameters that could achieve the required surface roughness values for optimal osseointegration for dental applications (Sa = 1.5 μm). Therefore, for this field of application the use of shot blasting still remains the most convenient and suitable process. Medium and low Sa values, in a range between 0.200 and 0.500 μm, are instead reachable, making micro-milling suitable for bone plates and screws, or ball joints (Fig. 1). In consideration of this, and exploiting Eqs. (3–6), a set of proposed optimized values of process parameters as a function selected values of three-dimensional surface roughness are proposed in Table 12.

Table 12 Process parameters values optimized by Eqs. (3–6) for selected Sa values
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However, as previously acknowledged by Kemény et al. [51], it is worth pointing out that the detection of the most suitable surface roughness value for osseointegration enhancement is also affected by surface chemistry and morphology, resulting in the need for a more complex analysis to allow optimal conditions. Moreover, different biomedical applications, such as dental or orthopedic implants, have different requirements, hence it is not possible to draw general conclusions for quantitative optimal surface roughness for all biomedical applications [52]. In general, surface roughening is beneficial for osseointegration, while a smooth surface provides higher fatigue resistance and fretting corrosion resistance [53].

Further investigation of micro-milling processes should be carried out to analyze the possibility of using only machining techniques without post-processing. However, the values achieved are usable for prosthetic implants and cell cultures.

4 Conclusions

In this work, a series of mathematical models were presented for the evaluation of surface roughness aimed at improving the osseointegration of prosthetic implants, resulting from the process of micro-milling applied on parts made of Ti-6Al-4V resulting from three different manufacturing processes. These models have been derived from RSM analysis of experimental measurements of Sa three-dimensional surface roughness parameter of machined material achieved by conventional rolling process (as-received), SLM and EBM additive manufacturing techniques. To achieve this target, an extensive experimental campaign consisting of a series of micro-milling tests was carried out. Comparison between the experimental results and those calculated by the models are in good agreement, highlighting the ability of the derived equations to estimate the final surface quality. Considering the initial material conditions, the SLM samples showed higher surface roughness values than the as-received and EBM ones, and this can be ascribed to the specific microstructures resulting from the different cooling rates associated with the manufacturing technique used. SLM technique, characterized by higher cooling rates, led to a microstructure characterized by higher brittleness than that of the other specimens, thus promoting a shearing cutting mode. This particular condition produces more pronounced path traces on the machined surface with respect to materials with higher ductility, where an important contribution is given by the mechanism of the ploughing cutting. In addition, an ANOVA of the experimental results allowed the investigation among the process parameters, thus understanding which ones influence surface roughness. As a result, it was possible to show that cutting speed is the most influential parameter for all production methods, while feed per tooth has a significant impact only on SLM samples. In general, an increase of Sa has been observed when both VC and fZ decrease, and this is again ascribable to the microstructure-dependent cutting mechanism. However, it should be noted that further analysis will be needed to clearly assess the contribution of fZ. Establishing the optimal surface roughness value, in fact, remains a challenging task. Indeed, it involves understanding a phenomenon that is not only a function of the manufacturing process, but also of the final implant application, the chemistry and topology of the material surface, and the mechanical and corrosion resistance properties that may affect good and durable osseointegration of the prosthesis, as summarized in Figs. 1 and 2. Consequently, in addition to the exploitation of the proposed models, further studies, and at least in-vitro osseointegration tests, are needed to identify the optimal topography that can adequately combine all requirements.