Parameter Study and Economic Efficiency Optimization for Laser Cladding with Wide-Band Fiber Laser

. With the aim of investigating the cladding geometry characteristics by a wide-band fber laser with coaxial rectangular nozzle, and optimizing the powder efciency and deposition speed for economy efciency, Fe-based alloy powder was deposited on AISI 1045 substrate by a 3000W fber laser in this study. Laser power (P), scan speed (V), and powder feed rate (F) were selected for a factorial design. Te efects of the three process parameters on the geometry characteristics and economic efciency of single tracks were statistically analyzed, and a linear regression model was established between the combined parameters and the relevant characteristics (including track height, ratio of track width to height, powder efciency, and deposition speed). A process map was developed with the track shape and key economic indexes as boundaries. A fat-top feature of the track profle was found and can be utilized to achieve good cladding evenness. Te process map showed that the powder efciency and deposition speed were higher than 50% and 20mm 3 /s, respectively, when selecting process parameters in the as-built operation window.


Introduction
Laser cladding technology coats materials on substrates via a high-energy laser beam for the aim of surface modifcation. Te process has more advantages than other surface modifcation technologies due to its concentrated energy, small heat-afected zone (HAZ), and rapid solidifcation; thus, small thermal deformation and a fne microstructure can be achieved. Te CO 2 laser has high output power and has been applied to laser cladding for many years, but its wavelength is hard to absorb for metal materials [1]. YAG solid lasers have good performance for metal processing but low photoelectric efciency. High-power diode lasers have been studied in recent years due to their fast deposition speed and low dilution [1][2][3]. Fiber laser pumped by a semiconductor diode has a high photoelectric efciency and good beam quality; it is mainly used for elaborate processing with low power. However, there is little research on high-energy fber laser cladding [4,5]. Large-area cladding could be realized by a wide-band laser beam coupled with a rectangular nozzle. As for powder feeding laser cladding, a single powder nozzle may be infuenced by scanning direction and have an asymmetric track; a coaxially symmetrical powder nozzle can solve these defciencies [6,7].
Laser cladding should ensure cladding quality and geometric accuracy. Many studies concentrated on revealing the infuences of process parameters on cladding characteristics. Goodarzi et al. [7] found that the shape of the melted substrate was afected by the powder feed rate; a deep and symmetric melt zone could be generated by a low powder feed rate, and vice versa. Tey also revealed that laser power was the main factor afecting the melting area of the substrate. Lots of studies have found that track width increases as the power increases and track height increases as the scan speed decreases or the powder feed rate increases [8,9]. Small laser scanning distances can generate homogeneous dilution and a small HAZ; a lower laser focus gap can obtain shallower dilution depths; and P and F have signifcant infuences on dilution [10,11]. Low input energy and high scan speed can accelerate the solidifcation and increase the layer hardness, but high scan speed also induces pores and unmelted defects [12].
Many studies concentrated on process parameters P, V, and F with great interest [13]. Exploring the relationship between these parameters and cladding characteristics is the premise of laser cladding optimization.
Te aim of optimization is to choose proper process parameters for the desired cladding layer. Te optimization objects mainly include geometric characteristics and mechanical properties, which can be divided into single-objective optimization and multiobjective optimization. Te design of experiment (DOE) is often adopted to establish empirical-statistical models between process parameters and optimization objects. Farahmand et al. [1] conducted multiobjective optimization of track height, HAZ depth, and microhardness via the response surface method (RSM) and central composite design (CCD), fnally obtaining a group of optimal parameters accompanied by homogeneous chemical composition, a thick clad layer, high microhardness, and a shallow HAZ. Similarly, Yu et al. [14] determined a set of parameters corresponding to maximum track width, minimum track height, and ftted dilution by the Taguchi orthogonal experiment combined gray analysis. Meng et al. [15] built a model via RSM and ANOVA (analysis of variance) to optimize the dilution, ratio of track width to track height, and microhardness. Te aforementioned studies aimed to obtain a set of optimal process parameters, but sometimes it needs to plot contour graph (i.e., process map) of interest characteristics adopting the process parameters as variables. Generally, a process map is a 2D graph whose coordinate axis is single or combined process parameters [6,13,[16][17][18]. Costa et al. [16] developed a process map of track height for coating Satellite 6 on low-carbon steel; they chose low dilution (3-5%) and a big cladding angle (>100°) as limitations. With the aim of attaining the desired area (0.25 to 5 mm 2 ) of the track cross-section, Oliveira et al. [6] adopted the same limitations as Costa et al. [16]. Te process maps developed by these studies were very convenient and effective, and they mostly concentrated on the geometric characteristics and mechanical performances, but there is a lack of research on powder efciency and deposition speed with respect to the economic efciency of laser cladding. For this reason, this paper focuses on the economy and efciency optimization of laser cladding.
Based on a full factorial experiment, this study deposited Fe-based alloy powder on an AISI 1045 substrate using a 3000 W fber laser combined with coaxial rectangular powder nozzles. A statistical analysis method was adopted to investigate the relationship between key parameters (P, V, and F) and geometric characteristics as well as the economic efciency of single-track clad. A linear regression model was established between the combined parameter P α V β F c and the cladding features of interest. A process map of track height was developed with the track shape, powder efciency, and deposition speed as limitations. It is hoped that the process window can provide a reference for high-power fber laser cladding as well as other similar setups or materials.

Experimental Methods
2.1. Materials. AISI 1045 plate with dimensions of 300 × 100 × 10 mm 3 was employed as the substrate, which was polished and cleaned with alcohol and acetone. An Fe-based alloy powder was adopted as cladding material. Te powder was prepared by gas atomization method, which has spherical shape and 53-150 μm particle size. Te chemical compositions of the substrate and the powder were depicted in Table 1. Before deposition, the powder was dried for 5 hours at 120°C to ensure good fuidity [3]. Figure 1 shows the experimental setup of the laser cladding system used in this work. A 3000 W fber laser (Precitec) with a wavelength of 1080 nm was employed. Te laser head was fxed on a 6-axis KUKA robot (KR 20) as the end operator, which was driven to move relative to the workpiece placed on the worktable. Te powder was blown into the melt pool via a double tank feeder rotating at 0-10 r/min. 99.99% argon was used as a powder feeding gas and shielding gas, which can prevent powder oxidation and invading metal vapor.

Experimental Setup.
A single-mode laser was transformed into a rectangular uniform spot. Coaxial rectangular powder nozzles were installed symmetrically on both sides of the laser beam. Te spot size and defocusing distance were 6 × 2 mm and 330 mm, respectively. Te nozzle outlet size was 6 × 1.6 mm, and the tilt angle was 76°( Figure 2). Experiencing blowing and diverging, a rectangular powder spot was projected onto the substrate, where a narrow melt pool was generated ( Figure 3).

Experimental Design and Analysis Method.
Tree key process parameters (P, V, and F) were adopted as input variables for a 3 × 3 factorial design experiment. According to the process parameters of diferent groups (Table 2), 27 single-clad tracks were deposited on the substrate; the length of each track was 50 mm. Te fow rates of powder feeding gas and shielding gas were constant at 20 l/min and 10 l/min, respectively. Te standof distance between the laser head and substrate was adjusted to 18 mm where the powder fow intersected to obtain the highest catchment efciency [19].
All the tracks were cut transversely to 20 × 15 × 10 mm 3 blocks with a wire cutting machine. Each specimen was cleaned, polished, and etched. Te cross-sections of the specimens were photographed by an electron microscope, and the geometry characteristics of the tracks were measured by ImageJ software, including track height (H b ), track width (W b ), cross-section area (A b ), and cladding angle (θ) (Figure 4).

Results
Observing the surfaces of the tracks, it was found that all the tracks were uniform and bonded closely with the substrate. Electron microscope images showed that no cracks or pores appeared at the bonding location. Table 2 lists the values of 27 groups of process parameters and the corresponding measured data. All of the single-track cross-sections are shown in Figure 5.

Analysis on the Relationship between Process Parameters and Track Cross-Section
Measured data show that the track width of all the specimens is close to the laser spot size (6 mm); the maximum and minimum values are 5.22 mm and 6.12 mm, respectively, corresponding to P � 1800 W, V � 12 mm/s, F � 16.5 g/min, P � 2400 W, and V � 8 mm/s, F � 28.5 g/min. It can be concluded that wider tracks can be formed at high power, low scan speed, and high powder feed rate. Figure 6 shows that when F is constant, W b and P present a positive and linear relationship approximately, where W b increases as V decreases at a constant P. It may be related to the linear energy density (P/V) [6], which increases with P increases or V decreases. P/V increases mean heat absorbed by the substrate and powder per unit length increases, and more material will melt to generate a larger melt pool, resulting in W b increasing. Compared with Figure 6(a), 6(b), and 6(c), it is found that F has little efect on W b , while P and V are the main factors afecting W b . Figure 7 depicts the variation trend of H b with F and V. H b increases as F increases; there is an approximate linear positive correlation between them, and Figure 7(b) presents a perfect linear relationship. H b increases dramatically, especially at high power and low scan speed (V � 8 mm/s in Figure 7(c)), and the increasing rate (maximum value/minimum value) is up to 172%. H b increases as V decreases, and the increase rate is up to 180% when V is reduced from 12 mm/s to 8 mm/s (Figure 7(c)). It can be concluded that both F and V have remarkable efects on H b , and the combined parameters F/V can give a reasonable explanation. F/V means powder feeding mass per unit length [6]. F/V increases with F increases or V decreases, so more powder could be injected into the melt pool, leading to a higher clad track. Figure 7 also shows that P has little efect on H b .

Cladding Angle.
Te cladding angle θ is related to the track shape and should be large enough to avoid pores and cracks in laser cladding [13]. Te data in Table 2 are the average values for left and right θ. Figure 4 indicates that θ decreases with H b increases when W b keeps constant. As mentioned earlier, W b changes little (close to 6 mm) in contrast to H b , thus H b is the main factor afecting θ, it means that F and V are the main  International Journal of Optics process parameters deciding θ as previous analysis. Because the track cross-section is neither a regular arc or ellipse nor is it symmetrical, the measured data are not precise enough [13], so the cladding angle is not discussed much in this work.

Analysis of Profles of the Track Cross-Section.
In order to improve cladding efciency, the tracks generated by wideband laser are wider than round spot laser (Figure 3), so the profles of track cross-sections are long and narrow, consequently θ is large enough to avoid defects. According to the photographs in Figure 5, the tracks mainly changed in bulged height with diferent process parameters. H b varies more remarkable and has much larger increasing rate (261%) than W b (119%), therefore the former has more signifcant efect on track shape. Considering the infuence of W b and H b , the ratio of W b to H b [10,15] (R) was adopted to characterize the track profle in this paper. As shown in Figure 7, nine samples were chosen to explain the evolution of the track profles. No. 19 # sample has the smallest R due to the highest H b , it also has the most remarkable arc profle. When R is 13.7 (14 # in Figure 8), it becomes to appear a fat-top feature of the contours. As R increases, the rest of the tracks almost have the same characteristic. No. 6 # sample has the biggest R but H b is too low to meet cladding requirements. Taking the simplicity of calculation and diferent contexts into consideration, many research adopted arc or parabolic for profle ftting [20,21], but it is not applicable in this paper. As shown in Figure 9(a), ellipse ftting is performed on the same photographs in Figure 8. Apparently, ellipse fts well to most of the tracks especially to which has low R value (upper photographs in Figure 9(a)). But it is worth noting that the curve doesn't stay so close to the top of the contour any more with R increasing (lower photographs in Figure 9(a)), so a variation trend was given in Figure 9(b). Te minor axis gradually decreases with H b decreases, and fnally the major and minor axis approximately equal to W b and 2H b , respectively. Meanwhile, the track cross-section can be treated as a trapezium rather than a part of an ellipse due to the fat-top (Figure 9(b)). Table 2: Geometry parameters, corresponding powder efciency (η), and deposition speed (D s ) of all the 27 clad tracks at diferent process parameters.

No
Process parameters Geometry parameters of cross-section Economical indexes P (W) V (mm/s)  Figure 4: Schematic diagram of the track cross-section.
Observing Figure 5, it is found that the fat-top feature is more predominant with high scan speed, P and F have little efect on the fat-top feature. Te underlying mechanism of the fat-top feature will not been discussed in this work, but this special characteristic can be utilized to achieve a good surface evenness if the relationship between R and the main process parameters (P,V and F) can be established. Te relevant content will be presented in section 3.4.

Analysis of Key Economy Indexes.
Powder efciency refers to the ratio of melted powder to feeding powder, assuming that the cross-sections of tracks are uniform along the scan direction, the powder efciency η can be expressed as  where ρ is the powder density (7.86 g/cm 3 ), A b is area of the track cross-section (mm 2 ). Te calculated η ranges from 20%-50% (Table 2). Lower η corresponded to small laser power and high scan speed, and higher η was derived from big laser power and low scan speed. Tis may be subjected to the relationship between P/V and F, low P/V accompanied with high F would diminish the melt pool area leads to less powder trapped in the melt pool. It not only reduces the powder efciency, but also generates powder adhesion on the track surface. On the contrary, when P/V increases or F decreases, the melt pool area would be enlarged and more powder been melted resulting in higher powder efciency. Figure 10 depicts how η changes with V and F at P � 1800 W and 2400 W, η has a downward trend as F increases. Especially when V � 8 mm/s, F increases from 16.5 g/min to 22.5 g/min, there is a remarkable reduction of η. However, F has no signifcant efect on η maybe due to the fact that the amount of powder melted in the melt pool is gradually saturated. η decreases signifcantly with V increases means that V has greater negative efects on η than F. Deposition speed represents volume or mass of cladding materials over unit time, the former representation is adopted in this paper since there is no need to consider the  International Journal of Optics density of diferent materials and it has been widely accepted by many researchers [13]. Te deposition speed D s (mm 3 /s) can be expressed as   Table 2.
International Journal of Optics 7 where V b is track volume (mm 3 ). As formula (2) depicts, D s increases with V, but when P is constant, D s reduces rapidly as V decreases (Figures 10(c) and 10(d)); therefore, V has a negative efect on D s . Both H b and W b decrease with V ( Figures 6 and 7), resulting in a smaller A b , so D s will decrease quickly, and the positive efects of V are counteracted. In addition, when P and V are constant, the laser line energy density (P/V) and powder feed weight per unit length (F/V) will decrease as V increases, as does D s . Figures 10(c) and 10(d) also shows that when V is constant, D s increases sharply with F because more powder are trapped in the melt pool. It can be concluded that D s depends strongly on the geometric characteristics of clad tracks, and P, V, and F all have signifcant efects on D s .

Empirical Model.
As discussed earlier, both η and D s mainly depend on the geometric characteristics of clad tracks; however, simple combined parameters (P/V and F/V) are not adequate to describe the relationship between process parameters and economic efciency [13]. Terefore, according to the method proposed by Benjamin et al. [13], an empirical model was established between combined parameters and economic efciency as well as the geometric characteristics of the clad tracks. Te linear regression expression of the model is y � a(P α V β F c ) + b, where y is certain respond of interest; P, V, and F represent laser power, scan speed, and powder feed rate; each value of α, β, and c represents the signifcance on y; a and b are slope and intercept of the linear equation, respectively. In this work, linear ftting was performed between combined parameters P α V β F c and H b, R, η and D s , the results are shown in Figure 11.
As shown in Figure 11(a), in equation y = 0.653x-0.315, where y represents H b , x represents combined parameters V −3/4 F 3/5 , P is not included because it has little efect on H b . Te exponent of V is negative means that V has a negative efect on H b , likewise, F has a positive efect on H b due to the positive exponent. Te combined parameters and H b have a good ftting degree R 2 = 0.92. In Figure 11(b), the combined parameters also do not include P, indicating that P has no signifcant efect on R, V has a positive efect on R and F has a negative efect on R, which is consistent with the views of Qian et al. [10] and Meng et al. [15]. Because the absolute values of the exponents belong to V and F are equal, they have the same efects on R. Since R 2 of H b and R are impressive enough, it can be concluded that P, V, and F are the key process parameters afecting the geometric characteristics.
F has a negative efect on η and is far less signifcant than P and V (Figure 11(c)); this coincides well with the analysis of 3.3. Te R 2 of η is 0.76 indicating a low ftting degree, probably because there are other signifcant process parameters not been considered, such as stand-ofdistance between nozzle and substrate, fow rate of delivery gas, structure of powder feeder and so on [6,19,20]. D s has linear relationship with P 2/5 V −2/5 F 3/4 (Figure 11(d)), V has negative efect on D s , which coincides well with Section 3.3, the fact that F has the highest exponent means it has the most signifcant efect on D s . R 2 of η and D s are not as impressive as H b and R, this will be discussed later.

Development of Process
Map. Te frst step in developing a process map is to defne the boundaries for interesting characteristics [13]. Dilution had been generally concerned by many studies because low dilution can ensure good metallurgical bonding; on the contrary, high dilution  Table 2); (b) the deformation tendency of the ftting curves. 8 International Journal of Optics usually damages the coating quality due to too much mixed substrate materials. According to Tuominen et al. [4] and Turichin et al. [5], a low dilution rate (lower than 10%) can be easily achieved by a high-power fber laser with a wideband laser, so unlike other studies, this work did not consider dilution as a boundary any more. Te convexity of a single-clad track determines the bonding quality of adjacent cladding and the surface evenness of the cladding layer. Bulging too much may cause unmelted defects or pores, and in turn, the desired layer thickness cannot be achieved if the convex is too low. So as described in Section 3.2, R was adopted as a boundary of the clad track shape. Since most powders are expensive, improving powder effciency is signifcant for reducing the costs of additive manufacturing. Additionally, increasing deposition speed is an efective means to reduce production costs, which is more urgent for additive manufacturing. Terefore, η and D s were determined as optimization objects. H b was chosen as a tailored geometry characteristic, which was usually adopted by process maps in previous studies [16,17,22]. In this work, considering the experimental results, R � 6 and R � 18 were defned as track shape boundaries, η � 50% and D s � 20 mm 3 /s were chosen as the lowest limitations of economic efciency. As P has positive efects on η and D s (Figure 11(c) and 11(d)), so a constant value 2800 W was determined. Ten, plotted 2D process map, taking V and F as the horizontal and vertical axes, respectively, whose highest values were 16 mm/s and 32 g/min. At last, the 16   contour lines of H b � 0.3, 0.5, and 0.8 mm were painted according to the corresponding linear model. As shown in Figure 12, the left zone of the contour η � 50% has a higher powder efciency than 50%, and the upper zone of the contour D s � 20 has a higher deposition speed than 20 mm 3 /s. Te three curves R � 6, η � 50%, and D s � 20 formed a triangular zone (i.e., an operation window) where arbitrary points can be chosen to obtain high powder efciency and deposition speed as well as good clad quality. Table 3 lists the coordinate values (F, V), tailored geometry values, and optimization results of three diferent points (P1, P2, and P3 marked in Figure 12) chosen in the operation window. It should be emphasized that the curve H b � 0.3 completely locates outside of the operation window; high D s can be achieved with high V value but resulting in low η. Both H b � 0.5 and H b � 0.8 curves are partly in the operation window, and the latter has a wider value range. It can be deduced that clad tracks lower than 0.5 mm cannot achieve the desired optimization aim, so the approximate tailored range of H b is [0.5, 0.8].

Discussion
Confned to the laser spot size, W b is close to 6 mm in this paper. Te laser spot width used to be wider than 10 mm in order to improve the cladding speed [3,23]. H c is mainly decided by powder feeding mass per unit length (F/V) if the powder melts well, so the thickness of the cladding layer can be controlled by altering F or V. According to formulas (1) and (2), η and D s can be improved by increasing A c at constant F and V; thus, η and D s increased impressively as P increased from 1800 W to 2400 W ( Figure 10); this means the laser should work at nominal power to achieve high η and D s . Ellipse ftting coincides well with the profle of the singletrack cross-section, but there still exists a little deviation due to the fat-top feature (Figure 9). Some researchers strove to predict the profles according to process parameters (P, V, and F) to avoid high costs and time-consuming experiments, but their numerical models were based on the premise that the profles were subjected to simple functions such as arc, parabolic, hyperbolic, or sinusoidal [3,[20][21][22][23][24]. Te functions were very applicable in their respective situations but had no universality; maybe a more accurate solution is to calculate the height of each point in the contour. An efective method is to solve the integration of powder instantaneous concentration against melting time [20,25].
It is worth noting that the R 2 values of η and D s are not so impressive as expected. Tere may be other vital factors not considered except for P, V, and F. Although the powder in the melt pool can be completely melted at optimized process parameters (P, V, and F), but inevitably there is still a part of powder that falls outside of the melt pool due to scattering. Tis part of the powder is blown away by the feeding gas or bounced of the substrate; the more this part of powder, the lower the powder efciency. Terefore, factors that infuence the powder concentration must be taken into account for powder efciency. Powder convergence is mainly decided by the geometric parameters and stand-of distance of the powder nozzle. As for a coaxially symmetric rectangular nozzle, exit width, chamber length, and inclination angle all have efects on the powder fow distribution and convergence [26], and the highest powder concentration emerges at the intersection of the powder fow [27]. Powder concentration will decrease as the laser head leaves from the substrate, and a high feeding gas fow is benefcial to powder aggregation [27]. Te low powder efciency in this work (Table 1) was not only related to P, V, and F but also subjected to the powder nozzle. F has an impressive efect on D S (exponent is 3/4 in Figure 11(d)); given that P, V, and F are held constant, there is no doubt that D s can be improved by increasing η. Terefore, the factors infuencing η also act on D s indirectly, resulting in a low R 2 of D s . For the sake of high powder efciency and deposition speed, it is equally vital to optimize the process parameters (P, V, and F) and geometric parameters of the powder nozzle.

Conclusions
According to DOE and statistical analysis, a linear regression model was established between the combined parameters (P α V β F c ) and the clad geometry (H b , R) as well as economic efciency (η, D s) . Te exponent of P, V, and F means signifcance and positive or negative association. R 2 of each function (H b , R, η, and D s ) was 0.91, 0.92, 0.76, and 0.89, respectively. R 2 of η and D s were not impressive because the geometric parameters of powder nozzle also had signifcant efects on powder concentration. Enhancing powder convergence not only can improve powder efciency but also increase deposition speed indirectly. Proper boundaries were determined to plot a 2D process map with a constant power of 2800 W. In the operation window, the powder efciency could reach more than 50%, and the deposition speed could reach more than 20 mm 3 /s.

Data Availability
Te experiment data used to support the fndings of this study are included within the article.

Conflicts of Interest
Te authors declare that there are no conficts of interest regarding the publication of this paper.