Optimization of Multi-Track Laser-Cladding Process of Titanium Alloy Based on RSM and NSGA-II Algorithm

Abstract

Titanium alloy is an important material in the 21st century and its consumption in the aerospace and energy fields is increasing. In the production and repair of titanium alloy, the problem of energy saving and consumption reduction is becoming increasingly important. Laser-cladding technology with optimized parameters can bring great economic benefit. In order to obtain the best process parameters of laser-cladding TC4 alloy powder, a method of laser-cladding parameters’ optimization based on the RSM and NSGA-II Algorithm is proposed. The BBD (Box–Behnken Design) experiment scheme was designed by the response surface method. A surrogate model between input variables (laser power, scanning speed, and powder-feeding speed) and response values (macroscopic quality, microhardness, and average friction coefficient) was established. The second generation non-dominant sorting genetic algorithm (NSGA-II) was used to optimize the process parameters and the optimization results were verified by experiments. The results show that the optimum parameters are a laser power of 2600 W, scanning speed of 19.1 mm/s, and powder-feeding rate of 12.2 g/min. The samples prepared with the best process parameters show mainly abrasive wear, accompanied by a small amount of adhesive wear. Its wear depth is 7.71 μm and the average friction coefficient is 0.293. After cladding, the macroscopic quality of the cladding layer is increased by 5.8%, the microhardness is increased by 10.1%, and the average friction coefficient is reduced by 27.6%.

1. Introduction

Titanium alloy has the advantages of low density, high specific strength, and corrosion resistance [1]. Additionally, titanium and titanium alloys are superior to steel, aluminum, and other most-modern building materials in terms of physical and mechanical properties, and manufacturability [2]. Therefore, it is widely used in high-tech industries, including aircraft and rockets, shipbuilding, nuclear energy, chemical industry, and medicine. As an excellent additive manufacturing technology, laser cladding has been widely used in the production and repair of titanium alloy products [3,4].

The laser-cladding technology uses a high-energy laser beam to remelt the substrate and the alloy powder material rapidly, forming a new alloy functional coating and effectively improving the surface wear-resistance, corrosion-resistance, and oxidation-resistance of the metal-part materials. It can realize the repair and reconstruction of mechanical parts in the form of wear and tear, and the effect of material saving and energy saving is remarkable and the economic benefit is good [5,6,7]. However, the laser-cladding process is influenced by the time-varying high-temperature thermal cycle and the thermophysical properties of heterogeneous materials (substrate and powder) [8]. If the process parameters are not properly controlled, the surface unevenness of the cladding layer will be increased and the defects, such as the inner pores and micro-cracks, will be induced [9,10]. Therefore, it is necessary to study the optimization of laser-cladding parameters.

In laser multi-channel cladding, each parameter has an effect on the cladding and there is a multi-coupling effect. Therefore, the quality and performance of laser cladding is not a simple linear relationship with laser-cladding process parameters; thus, it is necessary to solve the problem by reasonable optimization methods [11,12]. The experimental design optimization methods, such as the orthogonal method [13], Taguchi method [14], and response surface method (RSM) [15,16], and intelligent algorithms, such as the evolutionary algorithm (EA) [17,18] and Neural Network (NN) [19,20], are often used to optimize the laser-cladding process parameters. In order to optimize the parameters of laser cladding, it is necessary to select an algorithm. Algorithms, according to the fitness function and time density, include Particle Swarm Optimization (PSO) [21], the Genetic Algorithm (GA) [22], the Pareto Evolutionary Algorithm (SPEA) [23], etc. In contrast, the second-generation non-dominated sorting genetic algorithm (NSGA-II) with elite strategy is used to fit the relation between the factor and response, with a non-deflection degree cubic polynomial. The influence of each factor on the response and the interaction of multiple factors on the response are analyzed and the optimal combination form is found [24,25]. It can be seen that the NSGA-II algorithm has the advantages of high speed and high searching precision, and it is more algorithmic for the multi-channel process-parameter optimization of laser cladding. For the multi-channel process-parameter optimization of laser cladding, it reduces the precision reduction caused by quadratic fitting.

In view of this, in this paper, the laser power (A), scanning speed (B), and powder-feeding rate (C) are taken as input variables for the optimization of laser-melting process parameters, while macroscopic quality (F₁), microhardness (F₂), and the average friction coefficient (F₃) of the melted layer are taken as response values of the input variables, and 17 groups with 3 factors and 3 levels of melting are designed based on the Box–Benhnken model in RSM. The NSGA-II algorithm is applied to obtain the Pareto solution set by the global optimization of the input variables and the experimental verification of the preferred process parameters is carried out to determine the effectiveness of the optimal process parameters for laser cladding. Through the experimental verification, it can be found that the results are very reliable. Due to the superiority of the algorithm, the complexity of the fitting process is reduced and the accuracy of the optimization result is guaranteed. The accuracy of the coating comprehensive evaluation system is also verified.

2. Experimental Conditions and Protocol

2.1. Experimental Conditions

The TC4 plate (GB/T13810-2017), with a size of 120 mm × 120 mm × 15 mm, was selected as the substrate, which was polished and cleaned before the experiment, and its surface roughness was measured as 0.64μm. The main elements contained in the titanium alloy plate were Al (4.5%–5.5%), V (3.5%–4.5%), Fe (0.03%), C (0.01%), N (0.05%), H (0.01%), O (0.2%), and Ti (remainder).

The coated substrate was spherical TC4 alloy powder with a particle size of 30–60 μm, which was dried before the experiment. The powder was prepared by electrode-atomization. The powder contained less non-metallic inclusions, had higher purity, had a higher packing density, and had a vibration density. Its oxygen content was low, the chemical composition of the powder particles was the same and uniform, and there was no segregation phenomenon. The morphology of the substrate and powder under a super depth-of-field microscope (VHX-7000, Keyence, Osaka, Japan) is shown in Figure 1.

The equipment selected for this experiment was a 3 kW power fiber laser-cladding machine (Tianyuan, Xi’an, China). It consisted of a cladding head (ZF-KDDPZ-001A), a water-cooling device (CWFL-3000), and a powder-feeding device (RH-DFOM-01). The concentration of the powder supply gas and protection gas of the cladding system were both 99.99%/Ar and the coaxial-cladding synchronization of the optical powder was realized by ABB(ABBIRB2600) operator programming, as shown in Figure 2.

2.2. Program Design

The experimental design scheme was set as 3 factors and 3 levels, and the Box–Benhnken model (BBD) was used. The BBD model can better fit the response surface by selecting low-level factors and can effectively reduce the design of the experimental array and reduce the experimental cost. In the BBD experiment, the corresponding coding value of each input variable was successive: laser power (2100/2400/2700), scanning speed (18/20/22), and powder-feeding speed (1.2/1.4/1.6). Each molten sample after the experiment is shown in Figure 3.

In the experimental design, the macroscopic quality evaluation was determined by the macroscopic surface quality, and the evaluation criteria are shown in

Table 1. Basis for determining the macroscopic quality of the coating.

Score Interval	Surface Appearance	Cross-Sectional Integrity	Line Roughness/µm
Excellent (100–90)	The clad layer is completely bonded with the substrate. The surface contour line of the clad section is smooth and continuous, and there is very little slag.	No cracks, no air holes	<1000
Better (90–80)	The cladding layer is completely combined with the substrate. The surface contour line of the cladding section is smooth and continuous, and the slag is lesser.	No cracks, very few air holes	1000–1300
Good (80–70)	The cladding layer is completely combined with the substrate. The surface contour line of the cladding section is continuous and not smooth, and the slag is greater.	No cracks, few air holes	1300–1600
Moderate (70–60)	The cladding layer is not fused with the substrate in a small amount. The surface contour line of the cladding layer section is continuous and not smooth, and there are many slags.	Tiny cracks, lots of air holes	1600–1800
Difference (<60)	There is a large amount of unfused components between the clad layer and the substrate. The surface contour line of the clad layer section is discontinuous and unsmooth, and there is a great amount of slag.	Large cracks, lots of air holes	>1800

. The macroscopic quality of the coating was determined by the surface morphology, section integrity, and line roughness. The metallurgical bonding of the specimens was observed by a high-magnification microscope to check whether there were cracks and pores. The linear roughness, which is an accurate measurement value, was introduced to further prove the reliability of coating macroscopic quality determination.

Microhardness was measured by HV-1000 Vickers hardness. The average friction coefficient was measured by the MMW-2 friction tester. The input variables of the BBD experimental design and their corresponding response values are shown in

Table 2. Input variables and their response values for the BBD experimental design.

BBD Experimental Serial Number	Input Variables’			Response Value
	Laser Power/w	Scanning Speed (mm/s)	Powder-Feeding Rate (g/min)	Macro Quality	Microhardness	Average Friction Coefficient
S1	2100	18	14	68	396.5	0.370
S2	2100	20	12	80	429.5	0.374
S3	2100	22	14	75	410.5	0.325
S4	2100	20	16	77	441.4	0.320
S5	2100	18	12	85	389.6	0.294
S6	2400	20	16	57	447.9	0.337
S7	2400	22	12	63	441.9	0.327
S8	2400	22	16	61	432.7	0.339
S9	2400	20	14	82	389.8	0.393
S10	2400	18	16	56	384.5	0.340
S11	2400	20	12	50	415.9	0.345
S12	2400	18	14	60	419.8	0.361
S13	2700	22	14	81	469.6	0.362
S14	2700	20	16	78	415.6	0.379
S15	2700	20	12	72	462.7	0.359
S16	2700	18	1.4	65	419.6	0.373
S17	2700	22	16	69	404.2	0.378

.

3. Building a Laser-Cladding Agent Model

Proxy models are constructed to use limited data to construct models that tend to be realistic by fitting relationships between input variables and response values. Data collation and function-fitting of the regression model was performed using Design-Expert software for the input variables and response values in Table 1, and a second-order polynomial regression function was used as a proxy model for laser cladding. In order to verify the usability of the developed proxy model, an analysis of variance (ANOVA) was performed and residual plots were made to prove its reliability.

The basic form of the multiple linear regression model is

$$y_a={\beta }_0+{\beta }_1{x}_{1a}+{\beta }_2{x}_{2a}+\dots +{\beta }_k{x}_{ka}+{\epsilon }_a$$

(1)

In the formula, β₀, β₁, β₂, ..., β_k, is the parameter to be determined. $\epsilon$_a is the random variable and k is the number of independent variables.

The ternary quadratic polynomial describing the functional relationship between the input variables (A, B, and C) and the response values (F₁, F₂, and F₃) constructed by the BBD experiment is

$$\{\begin{array}{l}{F}_1=11.69A^2-6.55B^2-6.73C^2+3.24AB+3.24AC\\ +0.18BC-2.42A+2.7B-0.61C+69.95;\\ F_2=9.16A^2-6.1B^2+5.73C^2+3.26AB-20.49AC\\ -2.0BC+8.87A+13.3B-5.53C+418.82;\\ F_3=-6.664\times {10}^{-3}{A}^2+4.073\times {10}^{-4}{B}^2-0.045C^2\\ +2.901\times {10}^{-3}AB+0.031AC-3.715\times {10}^{-3}BC\\ +0.033A-8.901\times {10}^{-4}B-0.015C+0.37.\end{array}$$

(2)

In the formula, F₁ is the macroscopic quality of the molten layer, F₂ is the microhardness of the molten layer, F₃ is the average friction coefficient of the molten layer, A is the laser power, B is the scanning speed, and C is the powder-feeding rate.

To verify the accuracy of the proxy model, the difference between the predicted and experimental values of the model, the probability distribution of the residuals, the types of errors, and the presence of outliers were investigated and analyzed in the paper. The ANOVA results of the three response values are shown in

Table 3. Analysis of variance of response values.

Source of Variance	Response Value
	Macro Quality	Microhardness	Average Friction Coefficient
Models	1207.1	7328.2	16.8
F Value	53.84	9.81	0.49
p-value	<0.0001	<0.0001	<0.0001
Loss of proposed items	0.4926	0.4231	0.4625
R2	0.8316	0.8173	0.8912
Signal to noise ratio	17.540	9.548	18.84

. It can be seen that the p-values of the macroscopic quality of the molten layer, microhardness, and average friction coefficient are less than 0.0001; the F-values are larger; and the values of the misfit terms are all greater than 0.1, which indicates that the confidence intervals were reasonably chosen and the model is significant. The decision coefficient was used to further verify the reliability of the fit. For example, R² = 0.8316 for the macroscopic quality model of the melt layer, meaning that 83.16% of all the experimental data can be explained by this model. The signal-to-noise ratio of all three response values is greater than 4, which indicates that the experimental results are reliable [26,27].

The residual plots corresponding to the macroscopic quality of the molten layer, microhardness, and average friction coefficient are shown in Figure 4. All points are distributed around a straight line and the closer their normal distribution probabilities are to the straight line, the better the fit. In summary, the constructed proxy model for laser cladding maps a non-linear relationship between the input variables and the response values close to the true one, which has good significance and high prediction accuracy [28].

4. Discussion and Analysis of the Results

4.1. Process-Parameter Optimization

The laser multi-pass cladding process was studied under an actual production background. The macroscopic quality of the cladding layer is required to be large. If it is too small, it will lead to internal cracking of the cladding layer, resulting in a large number of pores or cracks. As one of the indexes to measure the mechanical properties of the cladding layer, the microhardness of the cladding layer is required to be higher. A low friction coefficient indicates that the coating has good wear resistance and a long service life.

The three simultaneous search-adaptive functions are F₁, F₂ and, F₃. They are required to reach their expected values when they are coupled to each other at some point in the search space. Thus, the definition is

$$\{\begin{array}{c}{F}_1=(A_i,B_i,C_i)\to \max \\ F_2=(A_i,B_i,C_i)\to \max \\ F_3=(A_i,B_i,C_i)\to \min \end{array}\begin{array}{ccc},& \begin{array}{c}2100\le A_i\le 2700\\ 18\le B_i\le 22\\ 1.2\le C_i\le 1.6\end{array}& \end{array}$$

(3)

The NSGA-II algorithm is a new algorithm based on the first generation of the genetic algorithm by introducing the concept of non-dominated ranking and aggregation distance. Among them, the non-dominated ranking functions to form the non-dominated set by applying the concept of domination on the same plane to rank the points with merit and the non-dominated set (P) must satisfy the following:

$$\{\begin{array}{l}{M}_{x\subset \{x_1,x_2,x_3,\dots ,x_n\}}Q=P\\ \forall i,j\in \{1,2,3,\dots ,n\}\mathrm{and}i\ne j,x_i\cap x_j=\varnothing \\ x_1>x_2>x_3\dots >x_n,\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\\ \mathrm{That} \mathrm{the} \mathrm{individuals} \mathrm{in} x_{k+1} \mathrm{are} \\ \mathrm{dominated} \mathrm{by} \mathrm{the} \mathrm{individuals} \mathrm{in} x_k\end{array}$$

(4)

Based on the concept of non-dominance, the species’ population is defined as N and divided into n mutually disjoint subpopulations satisfying the above conditions, which meets the requirements of the spatial distribution of the solution set of the algorithm. In order to satisfy the diversity of the populations, the concept of aggregation distance is again used for sorting among the dominant planes, which follows the principle of

$$Q_{[i]}=(Q_{[i+1]}\times f_1-Q_{[i-1]}\times f_1)+(Q_{[i+1]}\times f_2-Q_{[i-1]}\times f_2)$$

(5)

where Q is the position of the offspring in two-dimensional space, f₁ is the displacement on the horizontal axis of space, and f₂ is the displacement on the vertical axis of space. When the population evolves, thus sorting by aggregation distance, more regions in the space can be searched to ensure that the best individuals continue to participate in the next generation of evolution.

After performing multiple-sorting, the set of Pareto solutions is concentrated on a frontier surface, which reduces the operation time and complexity. The elite strategy, based on the first generation, puts the parents and children together for merit selection, which expands the population size, improves the efficiency of the merit-seeking process, and avoids settling into local optimal solutions. The flow chart of the NSGA-II algorithm is shown in Figure 5 [29].

Based on the NSGA-II algorithm, the population size is set to 100 and the number of iterations is set to 200, and the optimized Pareto front is shown in Figure 6. Among them, there are 41 points that meet the requirements, and the macroscopic quality of 85, microhardness of 473.3 Hv_0.5, and average friction coefficient of 0.293 μm are selected as the results of the global optimal parameters, which correspond to the following parameters: laser power of 2600 w, scanning speed of 19.1 mm/s, and powder-feeding rate of 12.2 g/min. This combination of parameters is the global optimal process-parameter combination.

4.2. Experimental Validation and Analysis

In order to determine the effectiveness of the optimized optimal process parameters for laser cladding, validation experiments were conducted. A comprehensive comparison was performed in terms of coating macroscopic quality, frictional wear characteristics, and microhardness.

The specimen named S18 was prepared according to the global optimal process parameters. Specimen S18 was compared with Specimen S2, with the best response value in Table 2, as shown in Figure 7.

Compared with S2, the clad layer of Specimen S18 is more tightly bonded to the substrate, and the surface contour line of the clad section is smooth and continuous; there is very little slag and there are no pores in the clad layer. In other words, the macroscopic morphology and the cross-section of the clad layer of the specimen with the optimal parameters are better than those of all the specimens in Table 2.

The average friction coefficients of Specimens S2 and S18 are shown in Figure 8. It can be seen that under the optimal parameters, the average friction coefficient of the specimen is smaller, the fluctuation is smaller, and the friction process enters the stable period more quickly. In the experiment, the time was set to 900 s, and you can see the curve rising to a gradual plateau; this avoids the chance of too few experiments [30].

Figure 9 shows the wear section profile curves of Specimens S2 and S18. The deeper furrows can be found in Figure 9a, which proves that the coating experienced severe wear, and the cladding layer in contact with the pin is the most severely worn. From the contour curve in Figure 9b, it can be seen that the wear profile of Specimen S2 has a deeper furrow and the wear of the cladding layer is more serious, while the contour curve of the wear section of Specimen S18 has a good continuity, which means that the surface of the cladding layer is worn uniformly. The wear depth of Specimen S2 is 74.54 μm and the wear width is 2459.64 μm, while the wear depth of Specimen S18 is 56.64 μm and the wear width is 1884.79 μm, indicating that the optimized process parameters can improve the wear resistance of the material [31].

The surface morphology of Specimens S2 and S18 after wear is shown in Figure 10. As shown in Figure 10a,c, the cladding layer prepared by laser-cladding technology has certain wear resistance and there is no cracking or obvious large-area spalling after wear. In addition, the wear surface of the cladding layer is rougher and the plough grooves parallel to the sliding direction are formed on the surface, indicating that there is abrasive wear. However, the plough grooves on the surface of Specimen S2 are deep and large, and the abrasive wear is more serious on the surfaces of Specimens S2 and S18. Local plastic deformation occurred on the surfaces of Specimens S2 and S18, and some materials were shed as abrasive chips in the sliding process, thus forming adhesive wear, while the adhesions on the surface of Specimen S2 are greater in quantity and larger, and the adhesive wear is more serious [32].

Considering that the coating microstructure obtained at the powder-feeding speed of S2 and S18 is composed of a small amount of acicular martensite α′ phase, compared to the coating microstructure obtained at the condition of S18, there are a large number of spicle-like martensite α′ arranged in a herringbone pattern and the hardness of each phase of titanium alloy is α′ > α > β; thus, the hardness of Specimen S18 is the highest, its friction performance is the best, and the surface-wear profile is shallow [33].

A comparison of the response values of S2 and S18 is shown in Figure 11. It can be seen that the macroscopic quality of the clad layer is improved by 5.8%, the microhardness is increased by 10.1%, and the average mean friction coefficient is reduced by 27.6% for the optimum parameters. In summary, the macroscopic quality and microhardness of the optimized process parameters are improved, the average mean friction coefficient is reduced, and the wear resistance is improved, which is a beneficial result for practical production.

5. Conclusions

In this paper, laser-cladding TC4 alloy powder on the surface of titanium alloy substrate was used to explore the surface morphology, microhardness, and friction coefficient of the cladding layer under the optimal process parameters, and the following conclusions were drawn.

(1)

The implicit function is approximated by the ternary quadratic polynomial fitted by the response surface. The p-value, F-value, coefficient of determination, and SNR are all reliable, and the regression effect is remarkable in the range of engineering applications.

(2)

Through algorithm optimization, the best parameter set was obtained as a laser power of 2600 w, scanning speed of 19.1 mm/s, and powder-feeding rate of 12.2 g/min. After experimental comparison, it was found that the macroscopic quality of the clad layer improved by 5.8%, microhardness increased by 10.1%, and the average friction coefficient decreased by 27.6%.

(3)

The surface wear of the clad layer of Specimen S2 is mainly in the form of adhesive wear and abrasive wear. Specimen S18 is a normal-wear mechanism with a small amount of adhesive wear; its wear depth is 30.71 μm and the average friction coefficient is 0.293. A large number of acicular martensite α′ are arranged in a herringbone pattern in the coating structure of Specimen S18. Specimen S18 has better wear resistance.

(4)

The surface strengthening and repair of the mechanical parts require multi-track laser cladding. The optimal process parameters found by the NSGA-II algorithm can provide effective guidance and help for industrial application.