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

Authors: Bin Hu; Jianhai Han; Junhua Wang
Journal: International Journal of Optics
 (2022)

---

## Abstract

With the aim of investigating the cladding geometry characteristics by a wide-band fiber laser with coaxial rectangular nozzle, and optimizing the powder efficiency and deposition speed for economy efficiency, Fe-based alloy powder was deposited on AISI 1045 substrate by a 3000 W fiber laser in this study. Laser power (P), scan speed (V), and powder feed rate (F) were selected for a factorial design. The effects of the three process parameters on the geometry characteristics and economic efficiency 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 efficiency, and deposition speed). A process map was developed with the track shape and key economic indexes as boundaries. A flat-top feature of the track profile was found and can be utilized to achieve good cladding evenness. The process map showed that the powder efficiency and deposition speed were higher than 50% and 20 mm3/s, respectively, when selecting process parameters in the as-built operation window.


---

## Body

## 1. Introduction

Laser cladding technology coats materials on substrates via a high-energy laser beam for the aim of surface modification. The process has more advantages than other surface modification technologies due to its concentrated energy, small heat-affected zone (HAZ), and rapid solidification; thus, small thermal deformation and a fine microstructure can be achieved. The CO2 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 efficiency. High-power diode lasers have been studied in recent years due to their fast deposition speed and low dilution [1–3]. Fiber laser pumped by a semiconductor diode has a high photoelectric efficiency and good beam quality; it is mainly used for elaborate processing with low power. However, there is little research on high-energy fiber 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 influenced by scanning direction and have an asymmetric track; a coaxially symmetrical powder nozzle can solve these deficiencies [6, 7].Laser cladding should ensure cladding quality and geometric accuracy. Many studies concentrated on revealing the influences of process parameters on cladding characteristics. Goodarzi et al. [7] found that the shape of the melted substrate was affected by the powder feed rate; a deep and symmetric melt zone could be generated by a low powder feed rate, and vice versa. They also revealed that laser power was the main factor affecting 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 significant influences on dilution [10, 11]. Low input energy and high scan speed can accelerate the solidification 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.The aim of optimization is to choose proper process parameters for the desired cladding layer. The optimization objects mainly include geometric characteristics and mechanical properties, which can be divided into single-objective optimization and multiobjective optimization. The 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), finally 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 fitted 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. The 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, 16–18]. 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 mm2) of the track cross-section, Oliveira et al. [6] adopted the same limitations as Costa et al. [16]. The 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 efficiency and deposition speed with respect to the economic efficiency of laser cladding. For this reason, this paper focuses on the economy and efficiency 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 fiber 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 efficiency of single-track clad. A linear regression model was established between the combined parameter PαVβFγ and the cladding features of interest. A process map of track height was developed with the track shape, powder efficiency, and deposition speed as limitations. It is hoped that the process window can provide a reference for high-power fiber laser cladding as well as other similar setups or materials.


## 2. Experimental Methods

### 2.1. Materials

AISI 1045 plate with dimensions of 300 × 100 × 10 mm3 was employed as the substrate, which was polished and cleaned with alcohol and acetone. An Fe-based alloy powder was adopted as cladding material. The powder was prepared by gas atomization method, which has spherical shape and 53–150 μm particle size. The 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 fluidity [3].Table 1
Chemical composition of AISI 1045 and Fe-based powder (wt.%).
MaterialsCCrNiMnMoSiBFeFe-based powder0.152213—24.51.6Bal.AISI 10450.420.20.250.65—0.3—Bal.


### 2.2. Experimental Setup

Figure1 shows the experimental setup of the laser cladding system used in this work. A 3000 W fiber laser (Precitec) with a wavelength of 1080 nm was employed. The laser head was fixed 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. The 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.Figure 1
Schematic diagram of the laser cladding system.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. The spot size and defocusing distance were 6 × 2 mm and 330 mm, respectively. The nozzle outlet size was 6 × 1.6 mm, and the tilt angle was 76°(Figure2). Experiencing blowing and diverging, a rectangular powder spot was projected onto the substrate, where a narrow melt pool was generated (Figure 3).Figure 2
Structure of the laser head.Figure 3
Schematic diagram of single-track cladding.


### 2.3. Experimental Design and Analysis Method

Three 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 different groups (Table2), 27 single-clad tracks were deposited on the substrate; the length of each track was 50 mm. The flow rates of powder feeding gas and shielding gas were constant at 20 l/min and 10 l/min, respectively. The stand-off distance between the laser head and substrate was adjusted to 18 mm where the powder flow intersected to obtain the highest catchment efficiency [19].Table 2
Geometry parameters, corresponding powder efficiency (η), and deposition speed (Ds) of all the 27 clad tracks at different process parameters.
NoProcess parametersGeometry parameters of cross-sectionEconomical indexesP (W)V (mm/s)F (g/min)Wb (mm)Hb (mm)Ab (mm2)θ (°)η (%)Ds (mm3/s)1#1800816.55.560.522.05153.546.8716.42#18001016.55.430.261.08151.530.8710.83#18001216.55.220.240.88163.530.1810.564#2100816.55.810.421.78153.240.7014.245#21001016.55.730.341.48158.842.3014.86#21001216.55.580.230.93151.031.9011.167#2400816.55.940.462.01156.645.9616.088#24001016.55.910.351.61156.946.0216.19#24001216.55.830.271.26159.643.2215.1210#1800822.55.610.542.23155.037.3917.8411#18001022.55.460.41.57157.532.9115.712#18001222.55.290.291.11161.027.9213.3213#2100822.55.910.562.48141.941.5819.8414#21001022.55.740.421.85154.938.7818.515#21001222.55.560.321.32161.233.2015.8416#2400822.56.090.582.65151.344.4421.217#24001022.55.900.442.03151.342.5520.318#24001222.55.710.371.62155.640.7519.4419#1800828.55.580.732.93146.238.7923.4420#18001028.55.410.511.94156.632.1019.421#18001228.55.130.361.34159.326.6116.0822#2100828.55.810.692.97149.439.3223.7623#21001028.55.620.502.08148.034.4220.824#21001228.55.450.411.63153.532.3719.5625#2400828.56.120.793.54144.446.8628.3226#24001028.56.020.602.64150.743.6926.427#24001228.55.680.441.88153.337.3322.56All the tracks were cut transversely to 20 × 15 × 10 mm3 blocks with a wire cutting machine. Each specimen was cleaned, polished, and etched. The 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 (Hb), track width (Wb), cross-section area (Ab), and cladding angle (θ) (Figure 4).Figure 4
Schematic diagram of the track cross-section.


## 2.1. Materials

AISI 1045 plate with dimensions of 300 × 100 × 10 mm3 was employed as the substrate, which was polished and cleaned with alcohol and acetone. An Fe-based alloy powder was adopted as cladding material. The powder was prepared by gas atomization method, which has spherical shape and 53–150 μm particle size. The 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 fluidity [3].Table 1
Chemical composition of AISI 1045 and Fe-based powder (wt.%).
MaterialsCCrNiMnMoSiBFeFe-based powder0.152213—24.51.6Bal.AISI 10450.420.20.250.65—0.3—Bal.


## 2.2. Experimental Setup

Figure1 shows the experimental setup of the laser cladding system used in this work. A 3000 W fiber laser (Precitec) with a wavelength of 1080 nm was employed. The laser head was fixed 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. The 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.Figure 1
Schematic diagram of the laser cladding system.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. The spot size and defocusing distance were 6 × 2 mm and 330 mm, respectively. The nozzle outlet size was 6 × 1.6 mm, and the tilt angle was 76°(Figure2). Experiencing blowing and diverging, a rectangular powder spot was projected onto the substrate, where a narrow melt pool was generated (Figure 3).Figure 2
Structure of the laser head.Figure 3
Schematic diagram of single-track cladding.


## 2.3. Experimental Design and Analysis Method

Three 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 different groups (Table2), 27 single-clad tracks were deposited on the substrate; the length of each track was 50 mm. The flow rates of powder feeding gas and shielding gas were constant at 20 l/min and 10 l/min, respectively. The stand-off distance between the laser head and substrate was adjusted to 18 mm where the powder flow intersected to obtain the highest catchment efficiency [19].Table 2
Geometry parameters, corresponding powder efficiency (η), and deposition speed (Ds) of all the 27 clad tracks at different process parameters.
NoProcess parametersGeometry parameters of cross-sectionEconomical indexesP (W)V (mm/s)F (g/min)Wb (mm)Hb (mm)Ab (mm2)θ (°)η (%)Ds (mm3/s)1#1800816.55.560.522.05153.546.8716.42#18001016.55.430.261.08151.530.8710.83#18001216.55.220.240.88163.530.1810.564#2100816.55.810.421.78153.240.7014.245#21001016.55.730.341.48158.842.3014.86#21001216.55.580.230.93151.031.9011.167#2400816.55.940.462.01156.645.9616.088#24001016.55.910.351.61156.946.0216.19#24001216.55.830.271.26159.643.2215.1210#1800822.55.610.542.23155.037.3917.8411#18001022.55.460.41.57157.532.9115.712#18001222.55.290.291.11161.027.9213.3213#2100822.55.910.562.48141.941.5819.8414#21001022.55.740.421.85154.938.7818.515#21001222.55.560.321.32161.233.2015.8416#2400822.56.090.582.65151.344.4421.217#24001022.55.900.442.03151.342.5520.318#24001222.55.710.371.62155.640.7519.4419#1800828.55.580.732.93146.238.7923.4420#18001028.55.410.511.94156.632.1019.421#18001228.55.130.361.34159.326.6116.0822#2100828.55.810.692.97149.439.3223.7623#21001028.55.620.502.08148.034.4220.824#21001228.55.450.411.63153.532.3719.5625#2400828.56.120.793.54144.446.8628.3226#24001028.56.020.602.64150.743.6926.427#24001228.55.680.441.88153.337.3322.56All the tracks were cut transversely to 20 × 15 × 10 mm3 blocks with a wire cutting machine. Each specimen was cleaned, polished, and etched. The 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 (Hb), track width (Wb), cross-section area (Ab), and cladding angle (θ) (Figure 4).Figure 4
Schematic diagram of the track cross-section.


## 3. 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. Table2 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.Figure 5
All of the 27 single-track cross-sections. For each powder feed rate (F), the scan speed (V) increases from left to right and the laser power (P) increases from top to bottom.


### 3.1. Analysis on the Relationship between Process Parameters and Track Cross-Section

#### 3.1.1. Track Width

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 toP=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, Wb and P present a positive and linear relationship approximately, where Wb 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 Wb increasing. Compared with Figure 6(a), 6(b), and 6(c), it is found that F has little effect on Wb, while P and V are the main factors affecting Wb.Figure 6
Variation of track width with laser power and scan speed at given powder feed rate. (a)F = 16.5 g/min; (b) F = 22.5 g/min; (c) F = 28.5 g/min.
(a)(b)(c)


#### 3.1.2. Track Height

Figure7 depicts the variation trend of Hb with F and V. Hb increases as F increases; there is an approximate linear positive correlation between them, and Figure 7(b) presents a perfect linear relationship. Hb 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%. Hb 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 effects on Hb, 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 effect on Hb.Figure 7
Variation of track height with powder feed rate and scan speed at given laser power. (a)P=1800 W; (b) P=2100 W; (c) P=2400 W.
(a)(b)(c)


#### 3.1.3. Cladding Angle

The cladding angleθ is related to the track shape and should be large enough to avoid pores and cracks in laser cladding [13]. The data in Table 2 are the average values for left and right θ. Figure 4 indicates that θ decreases with Hb increases when Wb keeps constant. As mentioned earlier, Wb changes little (close to 6 mm) in contrast to Hb, thus Hb is the main factor affecting θ, it means that F and V are the main 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.


### 3.2. Analysis of Profiles of the Track Cross-Section

In order to improve cladding efficiency, the tracks generated by wide-band laser are wider than round spot laser (Figure3), so the profiles 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 different process parameters. Hb varies more remarkable and has much larger increasing rate (261%) than Wb (119%), therefore the former has more significant effect on track shape.Considering the influence ofWb and Hb, the ratio of Wb to Hb [10, 15] (R) was adopted to characterize the track profile in this paper. As shown in Figure 7, nine samples were chosen to explain the evolution of the track profiles. No. 19# sample has the smallest R due to the highest Hb, it also has the most remarkable arc profile. When R is 13.7 (14# in Figure 8), it becomes to appear a flat-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 Hb is too low to meet cladding requirements. Taking the simplicity of calculation and different contexts into consideration, many research adopted arc or parabolic for profile fitting [20, 21], but it is not applicable in this paper. As shown in Figure 9(a), ellipse fitting is performed on the same photographs in Figure 8. Apparently, ellipse fits 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). The minor axis gradually decreases with Hb decreases, and finally the major and minor axis approximately equal to Wb and 2Hb, respectively. Meanwhile, the track cross-section can be treated as a trapezium rather than a part of an ellipse due to the flat-top (Figure 9(b)).Figure 8
Contours of the track cross-section with different R (the ratio ofWb to Hb). The upper right number of each photograph is consistent with Table 2.Figure 9
Ellipse fitting of the track cross-section. (a) Ellipses of different tracks (the upper right number of each photograph is consistent with Table2); (b) the deformation tendency of the fitting curves.
(a)(b)Observing Figure5, it is found that the flat-top feature is more predominant with high scan speed, P and F have little effect on the flat-top feature. The underlying mechanism of the flat-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. The relevant content will be presented in section 3.4.


### 3.3. Analysis of Key Economy Indexes

Powder efficiency 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 efficiencyη can be expressed as(1)η=ρAbVF×100%,where ρ is the powder density (7.86 g/cm3), Ab is area of the track cross-section (mm2). The 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. This 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 efficiency, 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 efficiency. 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 significant effect on η maybe due to the fact that the amount of powder melted in the melt pool is gradually saturated. η decreases significantly with V increases means that V has greater negative effects on η than F.Figure 10
Effect of process parameters on powder efficiency (η) and deposition speed (Ds). (a, c) are at a constant power 1800 W. (b, d) are at a constant power 2400 W.
(a)(b)(c)(d)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 density of different materials and it has been widely accepted by many researchers [13]. The deposition speed Ds (mm3/s) can be expressed as(2)Ds=dVbdt=Ab×V,where Vb is track volume (mm3). As formula (2) depicts, Ds increases with V, but when P is constant, Ds reduces rapidly as V decreases (Figures 10(c) and 10(d)); therefore, V has a negative effect on Ds. Both Hb and Wb decrease with V (Figures 6 and 7), resulting in a smaller Ab, so Ds will decrease quickly, and the positive effects 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 Ds. Figures 10(c) and 10(d) also shows that when V is constant, Ds increases sharply with F because more powder are trapped in the melt pool. It can be concluded that Ds depends strongly on the geometric characteristics of clad tracks, and P, V, and F all have significant effects on Ds.


### 3.4. Process Optimization for Economy Efficiency

#### 3.4.1. Empirical Model

As discussed earlier, bothη and Ds 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 efficiency [13]. Therefore, according to the method proposed by Benjamin et al. [13], an empirical model was established between combined parameters and economic efficiency as well as the geometric characteristics of the clad tracks. The linear regression expression of the model is y=aPαVβFγ+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 γ represents the significance on y; a and b are slope and intercept of the linear equation, respectively. In this work, linear fitting was performed between combined parameters PαVβFγ and Hb, R, η and Ds, the results are shown in Figure 11.Figure 11
Linear fitting relationship between combined parameters and the bead characteristics: (a)Hb. (b) R. (c) η. (d) Ds.
(a)(b)(c)(d)As shown in Figure11(a), in equation y = 0.653x-0.315, where y represents Hb, x represents combined parameters V−3/4 F3/5, P is not included because it has little effect on Hb. The exponent of V is negative means that V has a negative effect on Hb, likewise, F has a positive effect on Hb due to the positive exponent. The combined parameters and Hb have a good fitting degree R2 = 0.92. In Figure 11(b), the combined parameters also do not include P, indicating that P has no significant effect on R, V has a positive effect on R and F has a negative effect 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 effects on R. Since R2 of Hb and R are impressive enough, it can be concluded that P, V, and F are the key process parameters affecting the geometric characteristics.F has a negative effect onη and is far less significant than P and V (Figure 11(c)); this coincides well with the analysis of 3.3. The R2 of η is 0.76 indicating a low fitting degree, probably because there are other significant process parameters not been considered, such as stand-offdistance between nozzle and substrate, flow rate of delivery gas, structure of powder feeder and so on [6, 19, 20]. Ds has linear relationship with P2/5V−2/5 F3/4 (Figure 11(d)), V has negative effect on Ds, which coincides well with Section 3.3, the fact that F has the highest exponent means it has the most significant effect on Ds. R2 of η and Ds are not as impressive as Hb and R, this will be discussed later.


#### 3.4.2. Development of Process Map

The first step in developing a process map is to define 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 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 fiber laser with a wide-band laser, so unlike other studies, this work did not consider dilution as a boundary any more. The 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 efficiency is significant for reducing the costs of additive manufacturing. Additionally, increasing deposition speed is an effective means to reduce production costs, which is more urgent for additive manufacturing. Therefore, η and Ds were determined as optimization objects. Hb 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 defined as track shape boundaries, η = 50% and Ds = 20 mm3/s were chosen as the lowest limitations of economic efficiency. As P has positive effects on η and Ds (Figure 11(c) and 11(d)), so a constant value 2800 W was determined. Then, 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 contour lines of Hb = 0.3, 0.5, and 0.8 mm were painted according to the corresponding linear model.As shown in Figure12, the left zone of the contour η = 50% has a higher powder efficiency than 50%, and the upper zone of the contour Ds = 20 has a higher deposition speed than 20 mm3/s. The three curves R = 6, η = 50%, and Ds = 20 formed a triangular zone (i.e., an operation window) where arbitrary points can be chosen to obtain high powder efficiency 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 different points (P1, P2, and P3 marked in Figure 12) chosen in the operation window. It should be emphasized that the curve Hb = 0.3 completely locates outside of the operation window; high Ds can be achieved with high V value but resulting in low η. Both Hb = 0.5 and Hb = 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 Hb is [0.5, 0.8].Figure 12
Process map for optimization of deposition speed and powder efficiency atP=2800 W.Table 3
Optimization results of different points (P1, P2, and P3) chosen in the operation window of Figure12.
NO.V (mm/s)F (g/min)Hb (mm)Ds (mm3/s)Η (%)P17.731.40.8>2050%P24.416.7>0.8>20>50%P37.8190.520>50%


## 3.1. Analysis on the Relationship between Process Parameters and Track Cross-Section

### 3.1.1. Track Width

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 toP=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, Wb and P present a positive and linear relationship approximately, where Wb 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 Wb increasing. Compared with Figure 6(a), 6(b), and 6(c), it is found that F has little effect on Wb, while P and V are the main factors affecting Wb.Figure 6
Variation of track width with laser power and scan speed at given powder feed rate. (a)F = 16.5 g/min; (b) F = 22.5 g/min; (c) F = 28.5 g/min.
(a)(b)(c)


### 3.1.2. Track Height

Figure7 depicts the variation trend of Hb with F and V. Hb increases as F increases; there is an approximate linear positive correlation between them, and Figure 7(b) presents a perfect linear relationship. Hb 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%. Hb 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 effects on Hb, 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 effect on Hb.Figure 7
Variation of track height with powder feed rate and scan speed at given laser power. (a)P=1800 W; (b) P=2100 W; (c) P=2400 W.
(a)(b)(c)


### 3.1.3. Cladding Angle

The cladding angleθ is related to the track shape and should be large enough to avoid pores and cracks in laser cladding [13]. The data in Table 2 are the average values for left and right θ. Figure 4 indicates that θ decreases with Hb increases when Wb keeps constant. As mentioned earlier, Wb changes little (close to 6 mm) in contrast to Hb, thus Hb is the main factor affecting θ, it means that F and V are the main 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.


## 3.1.1. Track Width

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 toP=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, Wb and P present a positive and linear relationship approximately, where Wb 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 Wb increasing. Compared with Figure 6(a), 6(b), and 6(c), it is found that F has little effect on Wb, while P and V are the main factors affecting Wb.Figure 6
Variation of track width with laser power and scan speed at given powder feed rate. (a)F = 16.5 g/min; (b) F = 22.5 g/min; (c) F = 28.5 g/min.
(a)(b)(c)


## 3.1.2. Track Height

Figure7 depicts the variation trend of Hb with F and V. Hb increases as F increases; there is an approximate linear positive correlation between them, and Figure 7(b) presents a perfect linear relationship. Hb 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%. Hb 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 effects on Hb, 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 effect on Hb.Figure 7
Variation of track height with powder feed rate and scan speed at given laser power. (a)P=1800 W; (b) P=2100 W; (c) P=2400 W.
(a)(b)(c)


## 3.1.3. Cladding Angle

The cladding angleθ is related to the track shape and should be large enough to avoid pores and cracks in laser cladding [13]. The data in Table 2 are the average values for left and right θ. Figure 4 indicates that θ decreases with Hb increases when Wb keeps constant. As mentioned earlier, Wb changes little (close to 6 mm) in contrast to Hb, thus Hb is the main factor affecting θ, it means that F and V are the main 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.


## 3.2. Analysis of Profiles of the Track Cross-Section

In order to improve cladding efficiency, the tracks generated by wide-band laser are wider than round spot laser (Figure3), so the profiles 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 different process parameters. Hb varies more remarkable and has much larger increasing rate (261%) than Wb (119%), therefore the former has more significant effect on track shape.Considering the influence ofWb and Hb, the ratio of Wb to Hb [10, 15] (R) was adopted to characterize the track profile in this paper. As shown in Figure 7, nine samples were chosen to explain the evolution of the track profiles. No. 19# sample has the smallest R due to the highest Hb, it also has the most remarkable arc profile. When R is 13.7 (14# in Figure 8), it becomes to appear a flat-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 Hb is too low to meet cladding requirements. Taking the simplicity of calculation and different contexts into consideration, many research adopted arc or parabolic for profile fitting [20, 21], but it is not applicable in this paper. As shown in Figure 9(a), ellipse fitting is performed on the same photographs in Figure 8. Apparently, ellipse fits 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). The minor axis gradually decreases with Hb decreases, and finally the major and minor axis approximately equal to Wb and 2Hb, respectively. Meanwhile, the track cross-section can be treated as a trapezium rather than a part of an ellipse due to the flat-top (Figure 9(b)).Figure 8
Contours of the track cross-section with different R (the ratio ofWb to Hb). The upper right number of each photograph is consistent with Table 2.Figure 9
Ellipse fitting of the track cross-section. (a) Ellipses of different tracks (the upper right number of each photograph is consistent with Table2); (b) the deformation tendency of the fitting curves.
(a)(b)Observing Figure5, it is found that the flat-top feature is more predominant with high scan speed, P and F have little effect on the flat-top feature. The underlying mechanism of the flat-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. The relevant content will be presented in section 3.4.


## 3.3. Analysis of Key Economy Indexes

Powder efficiency 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 efficiencyη can be expressed as(1)η=ρAbVF×100%,where ρ is the powder density (7.86 g/cm3), Ab is area of the track cross-section (mm2). The 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. This 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 efficiency, 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 efficiency. 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 significant effect on η maybe due to the fact that the amount of powder melted in the melt pool is gradually saturated. η decreases significantly with V increases means that V has greater negative effects on η than F.Figure 10
Effect of process parameters on powder efficiency (η) and deposition speed (Ds). (a, c) are at a constant power 1800 W. (b, d) are at a constant power 2400 W.
(a)(b)(c)(d)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 density of different materials and it has been widely accepted by many researchers [13]. The deposition speed Ds (mm3/s) can be expressed as(2)Ds=dVbdt=Ab×V,where Vb is track volume (mm3). As formula (2) depicts, Ds increases with V, but when P is constant, Ds reduces rapidly as V decreases (Figures 10(c) and 10(d)); therefore, V has a negative effect on Ds. Both Hb and Wb decrease with V (Figures 6 and 7), resulting in a smaller Ab, so Ds will decrease quickly, and the positive effects 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 Ds. Figures 10(c) and 10(d) also shows that when V is constant, Ds increases sharply with F because more powder are trapped in the melt pool. It can be concluded that Ds depends strongly on the geometric characteristics of clad tracks, and P, V, and F all have significant effects on Ds.


## 3.4. Process Optimization for Economy Efficiency

### 3.4.1. Empirical Model

As discussed earlier, bothη and Ds 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 efficiency [13]. Therefore, according to the method proposed by Benjamin et al. [13], an empirical model was established between combined parameters and economic efficiency as well as the geometric characteristics of the clad tracks. The linear regression expression of the model is y=aPαVβFγ+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 γ represents the significance on y; a and b are slope and intercept of the linear equation, respectively. In this work, linear fitting was performed between combined parameters PαVβFγ and Hb, R, η and Ds, the results are shown in Figure 11.Figure 11
Linear fitting relationship between combined parameters and the bead characteristics: (a)Hb. (b) R. (c) η. (d) Ds.
(a)(b)(c)(d)As shown in Figure11(a), in equation y = 0.653x-0.315, where y represents Hb, x represents combined parameters V−3/4 F3/5, P is not included because it has little effect on Hb. The exponent of V is negative means that V has a negative effect on Hb, likewise, F has a positive effect on Hb due to the positive exponent. The combined parameters and Hb have a good fitting degree R2 = 0.92. In Figure 11(b), the combined parameters also do not include P, indicating that P has no significant effect on R, V has a positive effect on R and F has a negative effect 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 effects on R. Since R2 of Hb and R are impressive enough, it can be concluded that P, V, and F are the key process parameters affecting the geometric characteristics.F has a negative effect onη and is far less significant than P and V (Figure 11(c)); this coincides well with the analysis of 3.3. The R2 of η is 0.76 indicating a low fitting degree, probably because there are other significant process parameters not been considered, such as stand-offdistance between nozzle and substrate, flow rate of delivery gas, structure of powder feeder and so on [6, 19, 20]. Ds has linear relationship with P2/5V−2/5 F3/4 (Figure 11(d)), V has negative effect on Ds, which coincides well with Section 3.3, the fact that F has the highest exponent means it has the most significant effect on Ds. R2 of η and Ds are not as impressive as Hb and R, this will be discussed later.


### 3.4.2. Development of Process Map

The first step in developing a process map is to define 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 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 fiber laser with a wide-band laser, so unlike other studies, this work did not consider dilution as a boundary any more. The 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 efficiency is significant for reducing the costs of additive manufacturing. Additionally, increasing deposition speed is an effective means to reduce production costs, which is more urgent for additive manufacturing. Therefore, η and Ds were determined as optimization objects. Hb 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 defined as track shape boundaries, η = 50% and Ds = 20 mm3/s were chosen as the lowest limitations of economic efficiency. As P has positive effects on η and Ds (Figure 11(c) and 11(d)), so a constant value 2800 W was determined. Then, 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 contour lines of Hb = 0.3, 0.5, and 0.8 mm were painted according to the corresponding linear model.As shown in Figure12, the left zone of the contour η = 50% has a higher powder efficiency than 50%, and the upper zone of the contour Ds = 20 has a higher deposition speed than 20 mm3/s. The three curves R = 6, η = 50%, and Ds = 20 formed a triangular zone (i.e., an operation window) where arbitrary points can be chosen to obtain high powder efficiency 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 different points (P1, P2, and P3 marked in Figure 12) chosen in the operation window. It should be emphasized that the curve Hb = 0.3 completely locates outside of the operation window; high Ds can be achieved with high V value but resulting in low η. Both Hb = 0.5 and Hb = 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 Hb is [0.5, 0.8].Figure 12
Process map for optimization of deposition speed and powder efficiency atP=2800 W.Table 3
Optimization results of different points (P1, P2, and P3) chosen in the operation window of Figure12.
NO.V (mm/s)F (g/min)Hb (mm)Ds (mm3/s)Η (%)P17.731.40.8>2050%P24.416.7>0.8>20>50%P37.8190.520>50%


## 3.4.1. Empirical Model

As discussed earlier, bothη and Ds 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 efficiency [13]. Therefore, according to the method proposed by Benjamin et al. [13], an empirical model was established between combined parameters and economic efficiency as well as the geometric characteristics of the clad tracks. The linear regression expression of the model is y=aPαVβFγ+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 γ represents the significance on y; a and b are slope and intercept of the linear equation, respectively. In this work, linear fitting was performed between combined parameters PαVβFγ and Hb, R, η and Ds, the results are shown in Figure 11.Figure 11
Linear fitting relationship between combined parameters and the bead characteristics: (a)Hb. (b) R. (c) η. (d) Ds.
(a)(b)(c)(d)As shown in Figure11(a), in equation y = 0.653x-0.315, where y represents Hb, x represents combined parameters V−3/4 F3/5, P is not included because it has little effect on Hb. The exponent of V is negative means that V has a negative effect on Hb, likewise, F has a positive effect on Hb due to the positive exponent. The combined parameters and Hb have a good fitting degree R2 = 0.92. In Figure 11(b), the combined parameters also do not include P, indicating that P has no significant effect on R, V has a positive effect on R and F has a negative effect 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 effects on R. Since R2 of Hb and R are impressive enough, it can be concluded that P, V, and F are the key process parameters affecting the geometric characteristics.F has a negative effect onη and is far less significant than P and V (Figure 11(c)); this coincides well with the analysis of 3.3. The R2 of η is 0.76 indicating a low fitting degree, probably because there are other significant process parameters not been considered, such as stand-offdistance between nozzle and substrate, flow rate of delivery gas, structure of powder feeder and so on [6, 19, 20]. Ds has linear relationship with P2/5V−2/5 F3/4 (Figure 11(d)), V has negative effect on Ds, which coincides well with Section 3.3, the fact that F has the highest exponent means it has the most significant effect on Ds. R2 of η and Ds are not as impressive as Hb and R, this will be discussed later.


## 3.4.2. Development of Process Map

The first step in developing a process map is to define 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 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 fiber laser with a wide-band laser, so unlike other studies, this work did not consider dilution as a boundary any more. The 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 efficiency is significant for reducing the costs of additive manufacturing. Additionally, increasing deposition speed is an effective means to reduce production costs, which is more urgent for additive manufacturing. Therefore, η and Ds were determined as optimization objects. Hb 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 defined as track shape boundaries, η = 50% and Ds = 20 mm3/s were chosen as the lowest limitations of economic efficiency. As P has positive effects on η and Ds (Figure 11(c) and 11(d)), so a constant value 2800 W was determined. Then, 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 contour lines of Hb = 0.3, 0.5, and 0.8 mm were painted according to the corresponding linear model.As shown in Figure12, the left zone of the contour η = 50% has a higher powder efficiency than 50%, and the upper zone of the contour Ds = 20 has a higher deposition speed than 20 mm3/s. The three curves R = 6, η = 50%, and Ds = 20 formed a triangular zone (i.e., an operation window) where arbitrary points can be chosen to obtain high powder efficiency 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 different points (P1, P2, and P3 marked in Figure 12) chosen in the operation window. It should be emphasized that the curve Hb = 0.3 completely locates outside of the operation window; high Ds can be achieved with high V value but resulting in low η. Both Hb = 0.5 and Hb = 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 Hb is [0.5, 0.8].Figure 12
Process map for optimization of deposition speed and powder efficiency atP=2800 W.Table 3
Optimization results of different points (P1, P2, and P3) chosen in the operation window of Figure12.
NO.V (mm/s)F (g/min)Hb (mm)Ds (mm3/s)Η (%)P17.731.40.8>2050%P24.416.7>0.8>20>50%P37.8190.520>50%


## 4. Discussion

Confined to the laser spot size,Wb is close to 6 mm in this paper. The laser spot width used to be wider than 10 mm in order to improve the cladding speed [3, 23]. Hc 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 Ds can be improved by increasing Ac at constant F and V; thus, η and Ds 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 Ds.Ellipse fitting coincides well with the profile of the single-track cross-section, but there still exists a little deviation due to the flat-top feature (Figure9). Some researchers strove to predict the profiles 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 profiles were subjected to simple functions such as arc, parabolic, hyperbolic, or sinusoidal [3, 20–24]. The 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 effective method is to solve the integration of powder instantaneous concentration against melting time [20, 25].It is worth noting that the R2 values of η and Ds are not so impressive as expected. There 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. This part of the powder is blown away by the feeding gas or bounced off the substrate; the more this part of powder, the lower the powder efficiency. Therefore, factors that influence the powder concentration must be taken into account for powder efficiency. Powder convergence is mainly decided by the geometric parameters and stand-off distance of the powder nozzle. As for a coaxially symmetric rectangular nozzle, exit width, chamber length, and inclination angle all have effects on the powder flow distribution and convergence [26], and the highest powder concentration emerges at the intersection of the powder flow [27]. Powder concentration will decrease as the laser head leaves from the substrate, and a high feeding gas flow is beneficial to powder aggregation [27]. The low powder efficiency 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 effect on DS (exponent is 3/4 in Figure 11(d)); given that P, V, and F are held constant, there is no doubt that Ds can be improved by increasing η. Therefore, the factors influencing η also act on Ds indirectly, resulting in a low R2 of Ds. For the sake of high powder efficiency and deposition speed, it is equally vital to optimize the process parameters (P, V, and F) and geometric parameters of the powder nozzle.


## 5. Conclusions

According to DOE and statistical analysis, a linear regression model was established between the combined parameters (PαVβFγ) and the clad geometry (Hb, R) as well as economic efficiency (η, Ds). The exponent of P, V, and F means significance and positive or negative association. R2 of each function (Hb, R, η, and Ds) was 0.91, 0.92, 0.76, and 0.89, respectively. R2 of η and Ds were not impressive because the geometric parameters of powder nozzle also had significant effects on powder concentration. Enhancing powder convergence not only can improve powder efficiency 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 efficiency could reach more than 50%, and the deposition speed could reach more than 20 mm3/s.



---

*Source: 6373772-2022-12-14.xml*