Additive manufacturing offers the advantage of infinite freedom to design and fabricate complex parts at reduced lead-time. However, the surface quality of additively manufactured parts remains well behind the conventionally processed counterparts. This paper aims to systematically investigate the impact of varying surface inclination angles with respect to the build direction on the resultant surface textures. A bespoke metal truncheon artifact with inclination angles varying from 0 deg to 180 deg was built by selective laser melting. Focus variation microscopy was used to measure the topography of inclined surfaces with a tilt angle of up to 132 deg. The measurement data were then analyzed to characterize the staircase effect and the particles adherent to the artifact surface. Areal surface texture parameters, including height parameters, spatial parameters, functional parameters, and feature parameters, were explored to quantify the general surface topography, the staircase effect, and the particle features. The areal surface texture characterization and particle analysis reveal the resulted surface topographies are strongly correlated with the surface inclination angles.
Additive manufacturing (AM) is the process of adding thousands of minuscule layers of feedstock materials to fabricate an end-product. Selective laser melting (SLM) and electron beam melting (EBM) are leading the advanced metal AM processes . Metal AM uses powder (steels, titanium, aluminum, nickel-based superalloys, metal, and ceramic-based matrix composites) dispersed in layers, which is being selectively melted by a focused beam of a heat source to form a three-dimensional (3D) final part [2–5]. AM process offers many advantages over conventional manufacturing methods such as infinite freedom to design and fabrication of complex parts without any supporting tools at reduced lead-times . Metal AM is growing exponentially compared to other AM processes due to its higher potential of meeting market demands and cost-effective product development especially in aerospace, automotive, and biomedical applications . Fabrication of bionics, light-weight cellular, or lattice-type structures, and a new paradigm shift from mass production to the mass customization of parts are the potential trends of AM applications [7–9]. In addition, multiple materials that are used to build multirange products would become a possible solution to optimize the overall component’s properties .
Even though AM offers greater flexibility in the production of intrinsic parts, poor manufacturing repeatability and restricted dimensional tolerance or precision are the two technological drawbacks that are limiting the further advancement of AM process . Another limiting factor of AM technology is its failure to achieve the surface quality to meet the industrial standards. In terms of part functionality, the surface texture is one of the critical properties because surface texture contributes up to 10% of the part failure rate in conventionally fabricated parts . This is anticipated to be even higher in the case of AM processed parts . As a matter of fact, the AM process often induces variable and uneven rough surfaces as compared to conventional processes. Metal AM like SLM undergoes complex thermophysical phenomena consisting of various heat transfer mechanisms and molten melt flow that results in poor surface quality . It is extremely difficult to control the surface finish of melt tracks. The inevitable metallurgical defects, such as balling, ripple effect, or formation of humps like structures, hot spatters and powder spatters, porosities, cracks formed due to residual thermal stresses, are the major contributors to the poor surface quality of AM melt tracks [14–20]. The staircase effect due to the layer-by-layer nature of the AM process is equally responsible for the higher surface roughness of AM part with inclined surfaces [21,22]. It is worth noting that good surface quality is a prerequisite for an optimized AM process, as it acts as a determinant factor of the final part quality [23,24]. To achieve a better surface roughness, one or more forms of surface post-process treatment are essential , especially for the components exposed to extreme working conditions, e.g., aerospace applications. However, post-processing is time-consuming and expensive . It is of significant importance to address the prevailing conditions associated with the surface quality of AM components.
The present research work deals with an investigation to link the impact of the formation of diverse surface irregularities with respect to the various inclination angles on both up-skin and down-skin surfaces. SLM fabricated truncheon artifact built with different inclination angles was adopted to measure and characterize its surface texture per the areal surface texture parameters. The targeted useful parameters comprise height parameters (Sa, Sq, Ssk, and Sku), hybrid parameters (Sdq and Sdr), functional parameters (Vmp), spatial parameters (Sal and Str), and feature parameters (Spd). In addition, equal importance has been given for the feature-based analysis to quantify the geometrical characteristics of particle features, including the number of particles, particles density, particles coverage percentage, and peak material volume.
2 State of the Art
2.1 Impact of Additive Manufacturing Process Parameters on Surface Quality.
The surface quality of metal AM parts is an important property that affects dimensional accuracy and product functionality. The surface texture of metal AM parts is influenced by a number of factors, namely, power of heat source beam, layer thickness, scan speed, hatch spacing, angle of laser interaction with the powder bed, part orientation, and the powder particle size distribution . In addition to the other process parameters, layer thickness is the most critical parameter that defines the very important surface feature, i.e., staircase effect (see Fig. 1(a)), especially in the case of inclined or curved AM parts. The stair-stepping effect induces higher surface roughness that leads to the low surface quality of AM parts. The staircase effect could be minimized by adaptively decreasing the layer thickness between the melt track layers, depending on the surface orientation  (Fig. 1(b)).
Many researchers have attempted to investigate the correlation between process parameters and the resultant surface texture [28,29]. Charles et al. carried out a systematic experimental investigation to examine the interrelation between the different process parameters and their surface roughness (Sa). It was found that the obtained surface roughness is highly dependent on the process parameters interplay. However, interplay effects might be varied depending on the applied levels, because the interrelationship between the process parameters depends on the energy absorbed by the powder particles . Eidt et al. attempted to understand the significance of laser powder bed fusion (L-PBF) process parameters on the surface roughness of (only) the vertical surfaces and the downward-facing angle instead of considering a whole sample. They also conducted experiments to determine the L-PBF process optimization relationship with fatigue performance and dimensional tolerance . It was pointed out that contouring parameters are responsible for controlling vertical surfaces. This phenomenon is attributed to the increase in the contour laser power that leads to a decrease in surface roughness. Similarly, a lower surface roughness pattern was observed for the down-skin parameter while increasing the laser power .
It is well known that hump types of protruded structures are caused by the ripple effect, and the stair-stepped effect is commonly observed on both the surfaces of curved or inclined AM components [14,30]. These phenomena give rise to a higher surface roughness of AM parts, which adversely affect the final part quality. At a very high scan speed, the input heat energy is not sufficient to completely wet the surrounding powder particles resulting in the formation of balling . An extreme case of balling leads to the formation of humps or ripple effect . The humping or ripple effect is caused due to Plateau-Raleigh capillary instability . Yadroitsev et al. studied the single-track formation of 316 L stainless steel samples processed using the SLM process. According to their findings, too low laser fluence and/or extremely high scan speed resulted in balling . Strano et al. studied the surface roughness of varying surface inclination angles for the SLM process. From their research findings, balling or ripple effect obstructs the molten melt pool flow at the edges of melt track resulting in a rougher up-skin surface. Consequently, gravity forces of the unsupported layers also play a significant role in yielding extremely poor surface finish on the down-skin surfaces as compared to up-skin surfaces. This poor surface finish is due to improper heat distribution rates over the powder, as compared with the underlying substrate or with the already solidified supporting layers of melt tracks . Chen et al. evaluated the correlation between the scan parameters and surface roughness. They obtained the different surface roughness values for the identical laser parameters located at the different locations on the building substrate. According to their hypothesis, the difference in surface roughness was attributed to varying powder particle size distribution of the powder bed resulting from the combined action of the re-coater arm and the inert gas flow. In addition, they concluded that part orientation and projected shape of laser beam interaction with the powder is another aspect for generating varying surface roughness results . Spatters dispersed across the powder bed were also identified, which was accredited to the gas flow .
As soon as the focused heat source beam moves forward, each melt layer starts to solidify, surrounding unmelted or partially melted powder particles stick to the edge or corner of the melt track layer also contributes to the higher surface roughness of AM parts [35,36]. As a matter of fact, the surface roughness of the PBF fabricated parts found to be in the range of powder particle size. The main reason for the higher surface roughness could be related to the formation of partially melted particles, with the only exception of the surfaces built perpendicular to the build direction [37,38]. It is worth noting that along with surface roughness, a subsurface feature is another important characteristic linked to the part quality that needs to be addressed as well . In addition to the surface and subsurface features, re-entrant features, which are common facets of AM processes, need to be taken into consideration . Zhu et al. studied the link between areal surface texture with process parameters, porosity (subsurface porosity and re-entrant features), and mechanical properties of high-speed sintered parts . They adopted the surface texture parameters (Sa, Sq, and Sv) as the indicators to link with porosity, as well as to differentiate up-skin/down-skin and side surfaces. Similarly, Ssk and Sku parameters were used to connect the subsurface porosity and re-entrant features. Consequently, the surface texture parameters were further used to correlate mechanical properties. It was concluded that energy input was the prime variable that was responsible for causing the inconsistent scales of porosities and different surface topographies .
2.2 Surface Roughness Prediction Models for Inclined Surfaces.
Most of the existing surface roughness prediction models often use the staircase effect formed on inclined or curved surfaces to predict the surface quality [28,38,42]. In addition to conducting experiments to interrelate AM process parameters with surface roughness Sa, Charles et al. studied the surface roughness predictive model for down-skin surfaces. Their prediction model for the optimization of process parameters revealed that minimizing the obtained Sa value in 45 deg and 35 deg down-skin surface, individually, was achieved with an average error percentage of 5% and 6.3% respectively . Rausch et al. examined a predictive simulation of process windows for the PBF AM process, with the main aim to investigate the significance of powder size distribution . The primary objective of their research was to identify the single layer or multiple layer binding faults, which cause porous structures between the melt-tracks. They also attempted to achieve minimum possible surface roughness of the final part and thus lower the efforts required for the surface post-processing . Based on their combination of porosity and surface roughness predictive simulation model, it was found that the higher surface roughness leads to increased porosities. The increased porosities were a result of balling- and wetting-related effects which triggered uneven surface defects on the subsequent layers . Kaji et al. evaluated the critical drawback of AM parts and the staircase effect based on empirical modeling . They demonstrated an empirical model for the surface roughness distribution which was based on actual observations and modeling of cusp geometry under different setup and processing conditions. In view of the fact the profiles at corners or edges are critical to the surface quality, their developed model was used to directly predict the surface quality of the final part . Bacchewar et al. examined the empirical modeling and process optimization of the AM process. Central rotatable composite design (CCD) was used for the design of experiments; analysis of variance (ANOVA) was adopted to investigate the impact of process parameters on surface roughness . It was revealed that build orientation had a significant impact on surface roughness. Furthermore, layer thickness and laser power played a major role in achieving higher roughness of down-skin surfaces. It was found that the predicted results were in good agreement with experimental findings especially in the range of 10−70 deg , beyond this range their model needed correction.
Campbell et al. studied the theoretical model to quantify the variation in relation to the orientation of the model surface. Comparing their measured values, it was found that for most AM processes, e.g., stereolithography (SLA), fused deposition modeling (FDM), and laminated object manufacturing (LOM), there was at least a range of angles where surface roughness could be reasonably predicted . FDM results revealed that between 45 deg and 180 deg was the range where roughness was predictable. Similarly, the roughness of LOM was reasonably predicted, and its measured values compromised the theoretical model . Strano et al. studied the accurate surface roughness prediction model for the staircase effect generated on various inclined surfaces . In addition, they developed a mathematical model that takes into consideration of the particles present on the top surface. Surface roughness (Ra) recorded for the top surface (0 deg) and the vertical surface (90 deg) was ∼9 µm and 14 µm respectively. The predicted roughness of the horizontal surface was ∼16 µm, as the inclination angle increased the roughness gradually decreased until it reached 0 µm at 90 deg. The results showed that the predicted surface roughness model was in good agreement with the experimentally measured values .
2.3 Surface Texture Characterization.
Measurement and characterization of surface topography of metal AM components is extremely important because it is helpful to assess the surface quality as well as it acts as a reliable tool to investigate the behavior of the manufacturing process [45,46]. Cabanettes et al. investigated the areal multiscale topographies (form and roughness) for both up-skin and down-skin surfaces of SLM built samples with respect to various inclination angles . Sdq and Sfq were found to be proportional to inclination angles. Also, Ssk was found to be positive for the up-skin surface, whilst being negative for the down-skin surfaces. Sdq, Sfd, and Ssk behaved in sinusoids with the inclination angles; hence, they concluded that they were able to differentiate the staircase effect inside the topography measurement . Sidambe studied three-dimensional surface topography characterization for three different surface finishes (0 deg, 55 deg, and 90 deg) . Their resulting surface topographies revealed a considerable difference in numerical values of areal surface texture parameters. Sa for 0 deg displayed smoother surface (Sa 15.8 µm), while inclined surface (55 deg) and vertical surface (90 deg) recorded rougher surface roughness with Sa 36.8 µm and 54.3 µm, respectively. The higher surface roughness of the inclined and vertical surface was attributed to the staircase effect and adherent powders. They concluded that different surface characteristics were due to the anisotropic melting of powders in the PBF AM process . Newton et al. explored a combined approach consisting of areal surface texture and feature-based characterization of EBM fabricated parts with varying surface inclinations . The authors developed the feature-based characterization to identify, isolate, and quantify spatters and other particles embedded on the as-built surfaces and investigated the variation of these feature-based characteristics in accordance with the surface orientation. They also compared areal surface texture parameters of the original surface topography and the feature-deprived topography .
A considerable number of researchers have attempted to study the surface texture characterization of metal AM parts [38,42,47–49]. However, the investigation in terms of the surface asperities such as staircase effect, spatters, and unmelted/partially melted powder particles presented on the different surface inclinations and the selection of suitable parameters to characterize these features are very limited. Thus, this research more focuses on investigating the impact of distinct surface irregularities or asperities that form on the various surface inclinations of the SLM component. To quantify these formed surface asperities, the areal surface texture characterization and the advanced features-based particle analysis were studied. This consolidated investigation would be beneficial to a better understanding of the surface texture characteristics of metal AM surfaces especially SLM surfaces.
As aforementioned, most of the researchers in the literature followed the general surface texture characterization procedures to obtain the surface texture parameters but necessarily complied with the ISO 4288  and ISO 25718−3 . A summary of the profile/areal surface texture measurement and characterization available from the existing literature is given in Table 1. It is interesting to note that different measurement lengths/areas and cutoff wavelengths (λc—the cutoff wavelength to separate the waviness from the roughness, λs—the cutoff wavelength to separate the roughness from the shorter wavelength components) were adopted and various surface texture parameters were studied. For example, Triantaphyllou et al. adopted cutoff wavelength (λc) of 8 mm and noise cutoff wavelength (λs) of 8 µm . Cabanettes et al. used λc 250 µm to isolate the welding tracks at 0-deg inclination . Newton et al. used λc of 70 µm to remove larger-scale topographic formations (i.e., long spatial wavelengths), i.e., any feature potentially larger than a particle or spatter formation . In general, the measurement area/length and cutoff wavelengths should be selected upon the surface roughness scale [52–54]. ISO 4288 recommended suitable sampling lengths and cutoff wavelengths corresponding for each roughness range . However, the AM surface topography displays a different nature from the conventionally machined surfaces. It is unsure whether the current ISO standards apply to AM surfaces. This leads to the attempts on choosing various measurement areas/lengths and cutoff wavelengths as evidenced by Table 1.
A spectrum of areal surface texture parameters employed in this research to characterize the surface topographical features of inclined AM surfaces are listed in Table 2. These targeted potentially useful parameters include height parameters (Sa, Sq, Ssk, and Sku), hybrid parameters (Sdr and Sdq), functional parameters (Vmp), and feature parameters (Spd). Further details of specific surface texture parameters can be found in ISO 25178-2:2012 . The surface texture parameters characterization was further complimented by feature-based particle analysis with the application of the threshold segmentation approach.
3 Experimental Setups
3.1 Additive Manufacturing Artefact Design and Fabrication.
The bespoke truncheon artefact was produced by the Renishaw AM400 SLM machine using 316 L stainless steel alloy powder. The commercially available 316 L alloy stainless steel powder with particles mostly spherical in shape (supplied by Renishaw plc Stone, Staffordshire, UK) was selected to build the test artefact. The 316 L alloy is austenitic stainless steel (SS) mainly iron alloyed along with the presence of other important elements like chromium, nickel, and molybdenum with mass fraction of 18%, 14%, and 3%, respectively . The Renishaw SLM machine is fitted with a fiber-laser that generates pulsed laser waves with a maximum power out of 400 W. The following default process parameters were employed, laser power 110 W, scan speed 5000 mm/s, hatch spacing 110 µm, and layer thickness 50 µm. The build chamber was filled with 99.99% purity level inert gas (argon), whereas oxygen content was maintained at less than 0.1 vol% during the AM process.
The truncheon artifact was built in a horizontal direction aligned perpendicular to the build direction (z-axis). The fabricated truncheon artifact consists of 31 square sections with various inclination angles from 0 deg to 180 deg with increments of 3 deg (Fig. 2(a)). At 0 deg orientation, the surface is parallel to the horizontal plane; at 90 deg inclination, the surface is parallel to the build direction. The surfaces ranging from 0 deg to 90 deg inclination angles were considered as the up-skin, whist the surfaces from 90 deg to 180 deg were deemed as down-skin. However, the down-skin surface measurement was restricted to a 132-deg position, beyond which resulted in extremely rugged surface damaged by supporting structures. Additionally, it is well known that the surface topography of up-skin differs from the down-skin surfaces. As aforementioned, the main reason for these differed surface topographies is the presence of supporting structures that leads to significantly higher surface roughness rather impractical. In contrast, the lack of sufficient supporting structures would result in AM part being distorted or eventually lead to complete failure.
3.2 Measurement Strategy.
Alicona G4 focus variation microscope (FVM) was employed to measure the areal surface topography of the truncheon artifact. The FV measurement configuration parameters are listed in Table 3. The magnification and measurement area were selected aiming to capture the representative portion of the surfaces, suitable for both the identification and quantification of a large number of particles and spatter formations, and the characterization of the staircase effect. The ring light was used because it can not only avoid excessive illumination but also captures the sharp flank characteristics. The measurement readings for each incremental angle surface were taken at three different positions (Fig. 2(b)), followed by the computation of the mean values and the standard deviation. The measurement taken at 0 deg was repeated four times to verify the repeatability error. The average deviation of Sa was found to be equal to 4.87 nm, and a standard deviation was equal to 6.1 nm.
3.3 Data Processing and Surface Texture Parameters Characterization.
Digital Surf MountainsMap software  was employed to analyze the gathered surface texture data. The analyzed surface texture results promote to characterize the staircase effect and particle features. The imported measurement data are first processed by filling the non-measurement points, followed by least-square leveling. The resulted data was then filtered by the S-filter (the λs filter) with the nesting index 5 µm to remove the short spatial wavelength components, comprising the measurement noise and the fine surface details which are out of interest of this research. Similarly, to separate the features of the particle from the underlying staircase surface, the robust Gaussian filter with the nesting index of 80 µm was applied due to its robustness against outliers . The data processing procedure is illustrated in Fig. 3.
4 Surface Roughness Prediction Model
5 Results and Discussions of Selective Laser Melting Artefact
5.1 Visual Inspection of Staircase Effect.
Figure 5 illustrates the optical images of truncheon surfaces measured by 5× lens to gain a larger measurement area (2 mm × 10 mm) for the visual inspection of surface patterns. Please note the images were trimmed off to reduce their sizes for a better exhibition. At 0 deg, the surface looks like a typical metal AM surface, with the presence of ripple characteristics caused by the fast-moving laser topped by a few unwanted particles. The linear patterns visible at 3 deg and 6 deg are predominantly formed by solidified melt track stripes stacked between the stair steps induced by the staircase effect (related to the layer thickness and the inclination angles). The melt track stripes and staircase effect are dominant especially between the 3 deg and 6 deg surface inclinations in such a way that the chessboard laser scan strategy is clearly evident. Moving forward, as the inclination increases from 6 deg to 9 deg, a steady decrease in the width of the constituting staircase effect can be noticed. The visibility of the linear patterns of melt tracks becomes less significant after 9 deg. It is evident that unmelted/partially melted particles and spatters attach to the edges of the stair steps. Further increase in the inclination angle (12−15 deg) resulted in a gradual decrease in the width of the stair steps (Fig. 12 for more details), and the scan pattern that existed in previous inclinations becomes almost indistinguishable.
Figure 6 shows the comparison of the up-skin and down-skin surface pairs at the matching angles, 48 deg (132 deg), 60 deg (120 deg), 72 deg (108 deg), and 90 deg up-skin (90 deg down-skin; vertical built component has two side surfaces at 90 deg, i.e., the left and the right, marked as 90 deg+ and 90 deg− hereafter). It is physically visible that the color of the fabricated down-skin surface has changed evidently compared to the up-skin surfaces. The number of particles on the up-skin has changed significantly with the change of inclination angle, while the down-skin surface has very little changes, regardless of the number of particles covering the area.
5.2 Height Parameters.
Sa and Sq values of the primary, staircase, and predicted surfaces for both up-skin and down-skin surfaces built with respect to different inclination angles are shown in Figs. 7(a) and 7(b). The Sa and Sq trend resemble identical throughout for all the inclination angles. A higher uncertainty near 0 deg in Sa and Sq values are observed, which is attributed to the combination of inevitable ripple effect features induced by the fast-moving laser beam, in addition to the presence of solidified melting tracks stripes and powder spatters. As the surface inclination increases from first the measurement point (0 deg), an abrupt increase in both Sa and Sq were recorded (between 3 deg and 6 deg). This quick rise in surface roughness on the inclined surfaces is attributed to the staircase effect. In addition to the staircase effect, the SLM process is designed in such a way that the lasers melt/re-melt only the horizontal surfaces, but not the inclined ones . Lack of laser re-melting leads to the formation of unmelted/partially melted particles attaching to the inclined surfaces. The surface roughness decreases steadily between 6 deg and 45 deg surface inclinations, and the region between 51 deg and 60 deg experiences a slight increase in the trend, which can be attributed to the transition of staircase effect to the dominance of accumulated particles on the surface. The notable increase in roughness between 51 deg and 60 deg is still well below the roughness values obtained at 3 deg and 6 deg inclination angles. A steady trend can be noticed between 70 deg and 90 deg. This is the zone/area where the accumulation of partially melted/unmelted powder particles are at the maximum level, by dominating the staircase, and eventually replacing the staircase effect as the inclination angle reaches 90 deg (up-skin surfaces). The staircase effect can be clearly observed between 3 deg and 45 deg; above 45 deg, the staircase effect slowly started to disappear, which was finally replaced by particle features at 90 deg.
An interesting point to be noted here is the difference in measured Sa and Sq values taken at 90 deg for both up-skin and down-skin surfaces. The observed surface roughness on the down-skin surfaces generally tends to be significantly higher than up-skin surfaces, e.g., about 140% higher than that of the up-skin surface at 90-deg location. On further exploring the 3D view of their surface topographies, it is found that there is an obvious accumulation of buildup stripes (perpendicular to the build direction) on the down-skin surface, whilst the buildup stripes on the upper surface are not obvious (Figs. 8(a) and 8(b)). The rationale behind this exploration is that the heat dissipation through the inclined surfaces resulted in elevated temperatures in down-skin surfaces. These higher temperatures led to the distortion and warping of down-skin surfaces. Additionally, the combination of intermittent heat transfer mechanism and the re-appearance of the staircase effect on the down-skin surfaces (90−132 deg) lead to the increasing trend of Sa and Sq values. The intermittent heat transfer along the down-skin surface contributes to the unnecessary adhesion of unmelted/partially melted particles on the surface, which eventually leads to higher surface roughness. In fact, Sa and Sq of the down-skin surfaces are higher than their matching angles of the up-skin counterparts.
The sudden change of predicted Sa and Sq from 0 deg to 3 deg is caused by the transition from a purely flat surface to a strong staircase presented surface, while a constant declining trend observed between 3 deg and 90 deg is attributed to the reducing strength of the staircase effect. This is followed by an increasing trend after 90 deg due to the re-formation of the staircase effect in the opposite direction. The Sa and Sq trends of the measurements for all cases tend to closely follow the theoretical mathematical model (Figs. 7(a) and 7(b)). By comparing the Sa and Sq values of the primary, staircase, and predicted surfaces, it was found that the changes in Sa and Sq are primarily caused by the staircase effect, whereas the impact of the particle features is less significant.
Ssk defines the unique distribution of height values above or below the mean plane, which is generally indicated by a positive or negative value, respectively. The majority of the recorded Ssk remained to be positive for all the up-skin surfaces. This signifies that the height distribution of the up-skin surface has a longer tail at the upper side of the mean/reference plane, indicating peaks dominate the surface (Fig. 9(a)). The reason for the Ssk value close to zero at 24 deg and 45 deg surface inclinations could be related to the random deep valleys, but overall, the characteristics of the up-skin surface are mainly dominated by surface peaks. However, the noted Ssk trend for the down-skin surfaces (90−132 deg) tends to be unstable. The Ssk becomes negative for all surface inclinations after 114 deg. The unstable skewness is accredited to deep valley features and redundant peak features caused by the presence of a large number of protruded particles consisting of unmelted/partially melted particles adhered to the down-skin surfaces. A similar result has been found in the literature . The Ssk of the primary surface is found to be larger than the staircase surface for almost all the surface inclinations, except for 3 deg, 6 deg, and 9 deg, but the overall trend is almost the same between primary and staircase surface. However, in the prediction model, the values of Ssk are nearly zero, because the number of peaks and valleys is considered to be the same. The surfaces at 0 deg, 90 deg, and 180 deg do not display any stair steps, and thus, the resultant Ssk values are close to infinity.
Sku is described by the probability of distribution of height values. It usually indicates whether the distribution of height values has sharp peaks (Sku > 3) or short and widespread (Sku < 3). The calculated Sku value for all the surface inclinations was slightly above the nominal value of 3 (Fig. 9(b)). This gives a clear indication that the surface height distribution is basically spiky-natured normal distribution. It is also found that the Sku values of the staircase surface resembles as that of the primary surface, which only drops a little at a partial tilt angle, but almost all the results are greater than 3. The predicted surface displays a Sku value lesser than 3 for all the surface inclinations. Similarly, there are no peaks and valleys at 0 deg, 90 deg, and 180 deg; therefore, Sku is considered to be infinite in these cases.
Figure 10 presents a further investigation of both Ssk and Sku by considering the surface height distributions at three different inclination angles, i.e., 0 deg, 90 deg, and 132 deg. For 0 deg and 90 deg, the height distributions are skewed below the mean plane, see Figs. 10(c) and 10(d), which implies positive Ssk values. In comparison, the height distribution of 132 deg appears to be skewed above the mean plane, indicating a negative Ssk (Fig. 10(e)). The shapes of three height distributions were found to be sharper than that of the normal distribution (Sku = 3), and thus, their recorded Sku values are all positive (Figs. 10(c)–10(e)). These findings are all consistent with the Ssk and Sku values displayed in Fig. 9.
5.3 Spatial Parameters.
Sal is defined by the minimal correlation length of the new location with respect to the original location. Sal is related to the periodicity of the surface, which is dominated by the melt track stripes (at 0 deg), and staircase effect (above 3 deg). Sal displays a general decline trend for the up-skin surfaces, and a strong rising trend for the down-skin surfaces (Fig. 11). This is consistent with the characteristic of the staircase effect. As the angle of inclination increases, the distance between the edges of stair steps decreases (Fig. 12). Overall, the Sal plot for the staircase surface follows an oscillating pattern. A possible explanation could be Sal is sensitive to short-wavelength periodical features. If part of particle features remains on the staircase surface, it can introduce significant turbulences to the Sal trend.
The predicted surface displays a very interesting Sal trend consisting of a sharp step peak at 3 deg, and a gradual decline to become flat at 90 deg. Based on the prediction model, Sal decreases with the increase of the inclination angle, which completely aligns with the reduction of the step width illustrated in Fig. 12. The predicted surface at 0 deg presents a purely flat surface (no consideration of melt tracks); thus, Sal is zero. This is same for 90 deg (no staircase at all). Sal of predicted down-skin surface maps the changing trend of the up-skin surface by reflection in terms of 90 deg.
Str (texture aspect ratio) is a measure of uniformity of the surface texture . Figure 13 illustrates the trend of Str with respect to different surface inclination. The Str plot for particle surface displays a more or less stable trend overall (except between 0 deg and 27 deg surface inclinations) with the values approaching 1, which evidences the isotropic nature of particle features. In comparison, the Str trends of staircase surface and primary surface exhibit many fluctuations, in a similar pattern to Sal. Overall, Str for both staircase and primary surfaces display close to 0, which signifies the anisotropic characteristics of these surfaces. It is evident from the graph that the staircase is the main factor that affects Str.
5.4 Hybrid Parameters.
Sdr is useful in the applications of surface coating, adhesion, lubricant, and heat exchanger applications, where the functional performances are highly linked with the surface area. Sdr values for up-skin and down-skin primary surfaces with respect to different inclined angles are shown in Fig. 14. Sdr increases with the rise in the inclination angle. By comparing the Sdr results of the primary surface and the staircase surface, it is found that their trends and specific values are very close, which implies the staircase effect has fewer impacts on Sdr. The key factor affecting Sdr is the particles attached to the surface.
Sdq is usually employed to distinguish surfaces with similar roughness. As displayed in Fig. 7, the recorded changes for Sa and Sq values from 60 deg−90 deg and 90 deg−117 deg are relatively smooth. However, comparing Sdq in the same regions, it is found that Sdq increases gradually with the rise of the inclination angle, see Fig. 15. In general, Sdq in the range from 0 deg to 90 deg increases slowly in a minor oscillation pattern. In contrast, the down-skin surface exhibits a V-shaped trend between 90 deg and 132 deg. Overall, the changing trend of the up-skin surface Sdq is relatively uniform, whilst that of the down-skin surface is more turbulent.
5.5 Functional Parameters.
Functional parameters were developed to characterize the common functional properties, such as wear and tribological related characteristics. The volume parameters are obtained by splitting the material ratio curve into three zones by applying two material ratio thresholds Mr1 10% and Mr2 80%, with the default assumption that the peak materials embrace 0−10% of the material ratio whilst the core material/void ranges cover 10–80% and void valley ranges from 80% to 100% of the material ratio . However, it should be noted that Mr1 and Mr2 can be set flexibly upon the requirement of a specific application. The peak material volume parameter (Vmp) was employed in this study to analyze the particle features on the truncheon surface topography. Instead of using the default Mr1 ratio of 10%, it is found that material ratio thresholds Smr1 and Smr2 derived from the Sk parameters are more suitable for the analysis of PBF topography features, e.g., particles and subsurface pores .
The Vmp results with respect to Smr1 are shown in Fig. 16. As the inclination angle increases, Vmp of the up-skin surface generally increases, while the Vmp of the down-skin surface exhibits an irregular changing pattern. The steady increase in Vmp for all up-skin surfaces (0−90 deg) is credited to the increase in the amount of unmelted/partially melted powders and spatters attached to the edges of the steps. In comparison, the down-skin surfaces (90−132 deg) do not display so many interesting facts; instead, the trend appears to be flat with a large standard deviation. This phenomenon is attributed to the unmelted powders in the down-skin surface occupying the whole down-skin surface which presents a more irregular surface topography in comparison with the up-skin surface. The irregularity of the down-skin surface is even deteriorated by residual heat energy and the tendency of molten metal liquid moving downward due to gravity effects. Similar results are also observed in particle analysis (see Sec. 5.7).
5.6 Feature Parameters.
Spd, indicating the density of peaks, is based on the watershed segmentation of surface topography with 5% Wolf pruning . Figure 16 presents Vmp and Spd of the particle surface with respect to the inclination angle. On the up-skin surfaces, as the inclination angle increases, the number of peaks steadily increases between 3 deg and 90 deg. It is worth noting that Spd decreases significantly between 0 deg and 3 deg. This is ascribed to the presence of numerous spatters attached to the surface at 0 deg. The down-skin surface presents a slow decrease of Spd, which forms a certain reflection symmetry to the up-skin surfaces but showing more variations due to the random nature of the down-skin surface topography. An interesting fact was found by comparing the trend of down-skin surface Spd and Vmp: Spd decreases as the down-skin inclination increases, whereas it is the polar opposite in the case of Vmp. This implies as the down-skin tilt angle increases, the number of large particles or large protrusions on the bottom surface increases.
5.7 Particle Analysis.
Complimentary to Spd, a height threshold segmentation approach is applied to the particle surface (the staircase effect has been excluded). The particles are identified by comparing the surface height with a pre-defined height threshold. If the surface portion is above this threshold, it is regarded as a particle feature. The determination of this threshold is critical for the accurate identification of particles. To keep the consistency of the particle volume density analysis in the case of Vmp, this threshold is selected as the surface height corresponding to Mr1 of the material ratio curve, which is used to separate the peak zone and the core zone (the peak zone represents the particle features). A similar approach can be found in Ref. . Furthermore, the number of particles, the particle coverage, and the particle density are calculated, respectively, to provide a quantitative characterization of particles.
These three parameters basically show similar trends (Figs. 17 and 18). Six examples of particle identification and associated particle coverage ratio and numbers are illustrated in Fig. 19. The three particle characterization parameters of the up-skin surface rise slowly, while those of the down-skin surfaces show a flatter pattern. On the up-skin surface, the number of stair steps increases as the inclination goes up, while the corresponding width of these steps gradually decreases. This causes a rising number of particles to adhere to the edges of the steps . On the contrary, the number of particles and the particle coverage rate on the down-skin surface remain relatively steady (Fig. 17). During the melting of the down-skin surface, the residual heat is accumulated, resulting in the expansion of the melt pool; and melt metal liquid moves downward due to the gravity effect. All of these contribute to the irregularity of down-skin surface and the adherence of particles.
6 Conclusions and Future Work
The influence of various build inclinations angles on the surface topography of the SLM processed artifact was investigated. In addition, a surface texture prediction model based on the trigonometric functions was acclimated to compare the measured texture parameters results with the predicted ones. Suitable surface texture parameters were utilized to quantify the prevailing surface irregularities (staircase effect, un-melted/partially melted powders, and spatters) with respect to different surface inclinations.
Sa and Sq of inclined surfaces are dominantly influenced by the staircase effect, whereas the impact of the particles is less significant. Sa and Sq trends for all cases tend to closely follow the prediction model. Sa and Sq of the down-skin surfaces generally tend to be higher than those of the up-skin surfaces due to intermittent heat transfer. A similar pattern of Ssk was recorded for both up-skin and down-skin surfaces, with the majority of Ssk being positive, indicating the surface is dominated by peak features. Sku was slightly higher than nominal value 3, which implies that the surface height distribution is basically a spiky-natured normal distribution.
Sal generally decreases as the surface inclination approaches 90 deg, which is consistent with the fact that the decline in staircase width is evident with the growth of the inclination angle. Sal is mainly determined by the staircase effect but could be influenced by the remaining particle portions on the staircase surface.
Sdr and Sdq of the primary surface and the particle surface both present strong upward trends, along with the increase of surface inclination. It was found that the particle features are the major contributors to the increase of surface area and general surface slope, while the impact of the staircase effect is insignificant.
Vmp (with the threshold ratio set to Smr1) is dedicated to characterizing the volume density of particle features. It shows a general rising trend against the surface inclination, which indicates that the surfaces with more inclination have a larger total volume of particles.
Spd of the particle surface displays a strong rising trend for the up-skin surfaces, indicating the growth of particle features, while the down-skin surfaces show an opposite trend.
The values of particle descriptors derived from the particle analysis exhibit a steady rising trend for the up-skin surfaces, followed by a relatively stable pattern for the down-skin surfaces. All descriptors display a consistent trend.
In future, the present work will be further expanded to quantify the internal surfaces, subsurface porosity, and re-entrant features. Another key future work is to investigate the inhomogeneity of surface roughness across various locations on the inclined surface.
S. Lou would like to acknowledge the support of UK’s Engineering and Physical Sciences Research Council (EPSRC) via New Investigator Award (Grant No. EP/S000453/1) and Catapult Researcher in Residence scheme (Grant No. EP/R513520/1), and the support of the 3M Buckley Innovation Centre via 3M BIC Fellowship. From the University of Huddersfield, the authors gratefully acknowledge EPSRC funding of the Future Advanced Metrology Hub (Grant No. EP/P006930/1). The authors also thank Digital Surf for providing the MountainsMap software.
Conflict of Interest
There are no conflicts of interest.
Data Availability Statement
The data sets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request. The authors attest that all data for this study are included in the paper. Data provided by a third party are listed in Acknowledgment.