Multi-Objective Optimization of Laser Cladding Parameters for Remanufacturing Repair of Hydraulic Support Cylinders

Abstract

In order to obtain the optimal cladding process parameters for repairing the inner wall of the cylinder, 316L stainless steel powder was laser clad onto 27SiMn steel, which is the base material of the inner wall of the cylinder. The CCD (Central Combination 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 (intactness, dilution rate, and the micro-hardness of the cladding layer) was established. The adaptive chaotic differential evolution algorithm (ACDE) 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 1350 w, a scanning speed of 11.7 mm/s, and a powder-feeding rate of 2.5 g/min. After cladding, the macroscopic quality of the cladding layer was increased by 11.1%, the micro-hardness was increased by 7.1%, and the dilution rate was reduced by 24.7%. During the friction wear experiments, it was found that the maximum wear depth of the optimal specimen was 149.72 μm, which was smaller and more wear-resistant than the specimen in the control group. The results provide theoretical data for the repair and strengthening of the inner wall of the hydraulic support cylinder.

1. Introduction

Hydraulic support is a kind of hydraulic power device that utilizes liquid pressure to generate support force and realize automatic movement to support and manage the roof. It is an indispensable supporting equipment for comprehensive mechanized coal mining [1,2,3]. However, due to its harsh working environment, the inner wall of its cylinder is easily corroded and damaged, so it needs to be rebuilt and repaired [4,5]. Because of its high hardenability, high toughness, high strength, and good wear resistance, 27SiMn steel is widely used in the manufacturing of scenarios requiring high toughness and wear resistance and is often used in the manufacturing of coal mining equipment, hydraulic support, geological drills, automobile axles, and other parts.

Laser cladding technology has been widely used in the production and repair of large equipment reconstruction because of its efficient and clean characteristics [6,7,8]. However, the laser cladding process is influenced by the time-varying high-temperature thermal cycle and heat accumulation. Its forming mechanism is very complicated. Therefore, it is necessary to study the optimization of laser cladding parameters [9].

In the process of laser cladding, the coupling effect occurs very easily between the three phases of light, powder, and gas, leading to the selection of process parameters that directly affect the forming quality of the cladding layer. If the process parameters are not properly controlled, it will cause defects such as inner pores and micro-cracks in the cladding layer [10]. Therefore, it is necessary to select appropriate experimental design schemes, such as the Taguchi method [11], uniform design [12], the response surface method [13], etc. The central composite design scheme in the response surface method is suitable for multi-factor and multi-level experiments, and there are continuous variables that can better fit the response surface. In addition, the selection of process parameters in the laser cladding process is a complex multi-objective optimization problem. In order to achieve the best of each subset of the target at the same time, it is necessary to select a suitable intelligent algorithm [14]. Algorithms, according to the fitness function and time density, include PSO (Particle Swarm Optimization) [15], the GA (Genetic Algorithm) [16], DE (Differential Evolution) [17], etc. Various algorithms have the problems of being time-consuming and possessing a complicated calculation process, or they easily fall into local optima and cannot jump out of the global optimal solution. Principal component analysis (PCA) is used to transform multi-objectives into comprehensive indicators by using the idea of dimension reduction. The adaptive chaotic differential evolution algorithm (ACDE) introduces an adaptive chaotic operator, which is a global optimization method that tries to improve the given quality and measure through iteration. The combined principal component analysis (PCA) and ACDE method is a new attempt, especially used in laser cladding process parameter optimization and multi-channel cladding. It is simple to calculate and fast-converging, making it suitable for practical repair and surface-strengthening applications.

In this paper, the laser power (A), scanning speed (B), and powder-feeding rate (C) are used as input variables for the optimization of laser cladding process parameters, while cladding layer integrity (f₁), dilution rate (f₂), and micro-hardness (f₃) are taken as the response values of the input variables. A total of 20 groups with three factors and five levels of laser cladding are designed based on the central combination design (CCD) model. Factor Analysis (FA) [18] is used to convert the three sets of response values into a comprehensive evaluation index (Q) of the cladding layer. The Adaptive Chaotic Differential Evolution Algorithm (ACDE) is used to optimize the input variables, and the obtained optimal solution is used for experimental verification. The reliability of the optimal process parameters of laser cladding is determined, which provides a theoretical basis for broadening the application of laser cladding.

2. Experimental Conditions and Protocol

2.1. Experimental Conditions

Because of its high hardenability, high toughness, high strength, and good wear resistance, 27SiMn steel is widely used in the manufacturing of scenarios requiring high toughness and wear resistance and is often used in the manufacturing of coal mining equipment, hydraulic support, geological drills, automobile axles, and other parts. The 27SiMn steel plate, with a size of 100 × 100 × 10 mm³, was selected as the substrate, which was polished and cleaned before the experiment, and its surface roughness was measured as 6.4 μm. The cladding material was spherical 316L stainless steel powder with a powder particle size of 28–60 μm, which was dried before the experiment. The morphology of the substrate and powder under a super-depth-of-field microscope (VHX-700, Keyence, Osaka, Japan) is shown in Figure 1. The composition of the cladding substrate and powder is shown in

Table 1. Composition of the plate and powder.

Material	Ni (%)	Cr (%)	Si (%)	C (%)	Fe (%)
27SiMn steel	≤0.30	17	1.10	0.24	Remainder
316L	12.44	16.66	0.82	0.031	Remainder

. As shown in Figure 2, the experimental equipment is 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 laser cladding system is powered by a semiconductor laser (YLS-3000, wavelength 1064 nm) with a circular nozzle shape and spot diameter of 2 mm. The integrity and dilution rate are measured by an ultra-depth-of-field microscope, and the micro-hardness is measured by a HV-1000 Vickers micro-hardness tester (YiZong Precision, Shanghai, China), where the loading load was 500 gf and the pressure was 10 s. The MMW-2 multipurpose friction and wear machine (Chengwei Instrument, Shanghai, China) was used, where the load was 100 N and the test time was 900 s.

2.2. Experimental Program Design and Results

The laser power (A), scanning speed (B), and powder-feeding rate (C) are used as input variables for the optimization of laser cladding process parameters, while cladding layer integrity (f₁), dilution rate (f₂), and micro-hardness (f₃) are taken as the response values of the input variables. A total of 20 groups with three factors and five levels of laser cladding are designed based on the central combination design (CCD) model in Design-expert software 13. The horizontal coding of the central composite experimental design is shown in

Table 2. CCD experimental level coding.

Process Factor	Parameters
	−2	−1	0	1	2
A (w)	1200	1350	1500	1650	1800
B (mm/s)	9	10	11	12	13
C (g/min)	1.8	2.0	2.2	2.4	2.6

.

Through the observation of the macroscopic morphology of the cladding layer and the measurement of the line roughness by the ultra-depth-of-field microscope, the quality evaluation standard of the cladding layer is established. As shown in

Table 3. Basis for determining the integrity of laser multichannel coatings.

	Excellent 100–90	Better 90–80	Good 80–70	Moderate 70–60	Difference <60
Surface Appearance	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.	The clad layer is completely bonded with the substrate. The surface contour line of the clad section is smooth and continuous, and the slag is lesser.	The clad layer is completely bonded with the substrate. The surface contour line of the clad section is continuous and not smooth, and the slag is greater.	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.	There is a large number 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.
Cross-Sectional Integrity	No cracks, no air holes	No cracks, very few air holes	No cracks, few air holes	Tiny cracks, lots of air holes	Large cracks, lots of air holes
Line roughness/μm	<1000	1000–1300	1300–1600	1600–1800	>1800

, this is the laser multi-channel coating integrity basis.

The process parameters of the CCD experimental design and the corresponding measurement results are shown in

Table 4. CCD orthogonal experimental design and experimental results.

CCD Experimental Serial Number	Input Variables			Response Value
	Laser Power/(w)	Scanning Speed (mm/s)	Powder-Feeding Rate (g/min)	Cladding Layer Intactness (f1)	Dilution Rate f2 (%)	Micro-Hardness f3 (HV0.5)	Comprehensive Target Value Q
S1	1200	9	1.8	81	20.8	183.6	84.43
S2	1200	13	1.8	70	13.0	180.4	80.32
S3	1200	9	2.6	73	21.3	210.1	91.18
S4	1200	13	2.6	80	18.6	219.6	96.69
S5	1350	13	2.2	68	11.7	198.2	85.79
S6	1500	12	2	58	10.0	210.6	87.23
S7	1500	9	2.6	75	19.9	197.1	87.34
S8	1500	10	2.2	82	17.5	212.9	96.88
S9	1500	9	2.2	66	18.1	199.5	85.66
S10	1500	11	1.8	78	23.8	205.2	90.90
S11	1500	11	2.2	61	16.4	209.4	87.64
S12	1500	10	2.6	79	10.1	206.2	91.54
S13	1500	12	2.2	71	13.6	215.3	92.40
S14	1500	12	1.8	84	21.5	211.7	94.76
S15	1500	13	2.4	77	24.7	221.1	96.00
S16	1650	9	1.8	55	11.6	228.9	92.58
S17	1800	9	1.8	49	22.5	217.3	86.99
S18	1800	13	1.8	81	13.8	214.5	94.61
S19	1800	9	2.6	74	12.2	197.4	87.18
S20	1800	13	2.6	63	17.1	218.3	91.20

. The test used a 136-degree diamond indenter, which was pressed into the surface of the measured object through the specified test pressure, and the test force was unloaded after maintaining the loading time of 10 s. Then, the indentation diagonal of the sample surface was measured by a visual mirror, and the Vickers hardness value was obtained.

After the cladding experiment, the cross-sectional morphology of each sample under the ultra-depth-of-field microscope is shown in Figure 3.

3. Building a Laser Cladding Agent Model

The cladding layer intactness (f₁), dilution rate (f₂), and micro-hardness (f₃) are defined as three sub-goals. In the cladding process, it is expected that the heat-affected zone depth of the cladding layer section is smaller, the dilution rate is lower, and the micro-hardness is greater. Therefore, the mathematical model is

$$\left\{\begin{array}{c}{f}_1=\mathit{max}(A_i,B_i,C_i)\\ f_2=\mathit{min}(A_i,B_i,C_i)\\ f_3=\mathit{max}(A_i,B_i,C_i)\end{array}\right.\begin{array}{cc},& \begin{array}{c}1200\le A_i\le 1800,\mathrm{W}\\ 9\le B_i\le 13,\mathrm{m}\mathrm{m}/\mathrm{s}\\ 1.8\le C_i\le 2.6,\mathrm{r}/\mathrm{m}\mathrm{i}\mathrm{n}\end{array}\end{array}$$

(1)

In Formula (1), A is the laser power, B is the scanning speed, C is the powder-feeding rate, and i is any positive integer in the value interval.

3.1. FA Solves for Weighting Factors

The basic purpose of factor analysis (FA) is to use a few factors to describe the relationship between many indicators or factors, that is, several closely related variables are classified into the same category and each type of variable becomes a factor, with fewer factors to reflect most of the information of the original data, and there is a strong correlation between these factors. It can effectively transform the multi-objective problem into a single-objective problem and simplify the problem.

The basic relational equation for factor analysis is

$$X_i=a_{i1}{F}_1+a_{i2}{F}_2+\cdots +a_{im}{F}_m+{\epsilon }_i,(i=\mathrm{1,2},\cdots p)$$

(2)

In Formula (2), F is the common factor and i is called the special factor of X_i. The matrix X is imported from the data in Table 4, where a and ε are both column vectors and need to satisfy (1) m ≤ p; (2) the public factor F and the special factor ε_i are not related to each other.

The matrix algebra form of the above equation after centering is

$$X=aF+\epsilon$$

(3)

In Formula (3), the covariance matrix with respect to ε has a mean of 0, and the phase factors are independent of each other. Formula (3) takes the transpose after deformation, and then adds mathematical expectation to both sides of the formula to obtain Formula (4):

$$E\left|X{X}^T\right|=AE\left|F{F}^T\right|A^T+E\left|\epsilon {\epsilon }^T\right|$$

(4)

In Formula (4), E is the unit matrix and X^T is the rank of X. Finally, the eigenvalue formula is obtained by solving the eigenvector of matrix A, as shown in Equation (5).

$$\lambda ={\left[0.346\hspace{1em}0.285\hspace{1em}0.369\right]}^T$$

(5)

The results were fitted and analyzed by Spss software27 to obtain

Table 5. Eigenvalue parameters and check coefficient of matrix A.

Component	Feature Value	Variance Proportion	Factor Scores
1	0.346	46.5419	82.798
2	0.285	31.216	67.699
3	0.369	39.018	100
KMO	0.813	Bartlett	0.015

. The KMO test standard is that when the value is between 0.8 and 0.9, it is proven to be more suitable for factor analysis. The result of Bartlett’s sphericity test was 0.015, which is significant and the result is applicable. The value of the comprehensive target Q is obtained by using Equation (5) as the weight matrix.

3.2. RSM Construction Model and Analysis

Based on the CCD model in RSM, the data in Table 4 are sorted out, and the mathematical model between input variables (A, B, C) and comprehensive target Q value is built. After importing the data into the Design-expert software13, the multivariate quadratic regression equation is selected as the basic form of the model. Finally, the ternary quadratic polynomial derived by the software is shown in Formula (6).

$$Q=91.18+1.22\ast A+1.66\ast B+1.81\ast C+1.33\ast A\ast B-3.42\ast A\ast C+1.55\ast B\ast C-2.34\ast A^2-2.36\ast B^2+2.57\ast C^2$$

(6)

Table 6. Residual analysis of composite objective target Q.

Source	Squares	F-Value	p-Value
Model	25.94	1.67	0.0185
A-A	12.45	0.80	0.0920
B-B	35.99	2.31	0.0592
C-C	40.43	2.60	0.0380
AB	14.69	0.94	0.0541
AC	95.18	6.12	0.0329
BC	24.17	1.55	0.0409
A2	9.78	0.63	0.0461
B2	9.37	0.60	0.0556
C2	15.61	1.00	0.0401
mean variance	15.55	R2	0.9104
Adeq-Precision			9.862

shows the residual analysis of the composite objective Q. It can be seen that all the p-values of the model are 0.1, the F-value is larger, and the mismatch term is >0.1, indicating that the model is significant. R² (correlation square coefficient) = 0.9104, indicating that the fitted model can represent 91.04% of the data in the experiment, and the deviation rate of the model is only 8.96%. The accuracy of the model is up to standard and can be used as an adaptive function for subsequent intelligent algorithm optimization.

The residual diagram of the fitted model is shown in Figure 4, with 20 sets of data points distributed tightly on both sides of the straight line, according to normal probability distribution. It further illustrates the accuracy of the adaptive function.

4. Process Parameter Optimization and Result Analysis

4.1. ACDE Algorithm Optimization

The Adaptive Chaotic Differential Evolutionary (ACDE) algorithm introduces the concept of self-adaptation, which can adjust the parameters at any time according to the progress of the optimization process, so as to avoid the population falling into the local solution. On the basis of the differential evolution algorithm, the optimization ability of the algorithm is further improved, and its stability, robustness, and convergence are enhanced. The flow chart of the ACDE algorithm is shown in Figure 5.

In the process of population initialization of the traditional differential evolution algorithm, the rand function is used for random allocation, so that the population cannot be evenly distributed in the solution domain, which reduces the diversity of the population and may also lead to premature convergence of the algorithm, causing it to fall into the local optimum. The ACDE algorithm can improve the diversity of the population after adding the chaotic map. The search formula of the chaotic map is

$$z_{n+1}=\mu (1-z_n)$$

(7)

where: µ is a random number between [0,4]; z_n is any chaotic variable, and z_n $\in$ [0,1]. The evolution direction of the population is determined by the random quantity taken, and the search direction of any chaotic mapping in the space is completely unknown, so a non-different solution can be obtained within the population.

In the ACDE algorithm, the adaptive inertia weight adjustment function is introduced, and the population individual fitness update rate with the number of iteration steps is used as the feedback parameter. The adaptive mathematical model is shown in Equation (8):

$$\left\{\begin{array}{c}w\left(t\right)=\frac{1}{1+p(t)·e^{(\frac{1}{t_{max}}·\left(t-\frac{t_{max}}{2}\right))}}\\ p\left(t\right)=\frac{n_{update}(t)}{n_{max}}\\ x_{new}^i=w\left(t\right)·x_{old}^i-r_i·(x_i-F·x_{i-1})\\ f\left(x_{new}^i\right)=w\left(t\right)·f\left(x_{old}^i\right)-r_i·(x_{new}^i-x_{old}^i)\end{array}\right.$$

(8)

where: w(t) is the value of weights taken in generation t; p(t)w is the rate of updating the fitness of individuals in the population in generation t; t_max is the total number of iterations; n_update(t) is the individual with the smallest fitness value in generation t; and F is the scaling factor, which takes the value of a real number between any [0,2].

When the change of individual fitness is small or unchanged, the algorithm is more likely to fall into the local optimum. At this time, the update rate is used as the dominant parameter to increase the inertia weight and help the population jump out of the local optimum. On the contrary, when the algorithm optimization state is normal, the number of iterative steps is used as the dominant factor for regulation so that the population has a large inertia weight in the early stage of iterative computation, which ensures the global optimization ability of the algorithm.

Based on the ACDE algorithm, the parameters were set to have a population size of 40, a maximum number of iterations of 300, a crossover probability Cr of 0.85, a scaling factor F of 0.95, and the accuracy of the adaptation values was defined as 1 × 10⁻¹⁰. The parameter settings were completed, and after the ACDE algorithm was optimized, its adaptive iterative convergence curve was obtained, as shown in Figure 6. Because of the small number of populations, convergence was produced in 17 iterations, and the final comprehensive target Q value obtained is 104.83, which corresponds to the optimal parameters: a laser power of 1350 w, a scanning speed of 11.7 mm/s, and a powder-feeding rate of 2.5 g/min.

4.2. Validation and Discussion of Results

The optimal parameters are experimentally verified and the optimal specimen is named. After comprehensive consideration, the two groups of specimens (S4 and S8) with the best cross-sectional morphology and response values in the table and Figure 3 are taken as the comparison group, and the two groups of specimens are analyzed and discussed in comparison with the optimal specimen. As shown in Figure 7, the cross-sectional morphology of the three specimens is compared. There are no obvious defects in the cross-section of the cladding layer of the optimal specimen and S4. The bonding between the cladding layer and the substrate is relatively flat and without cracks, and S8 has a very small number of pores.

The parameters of the three groups of specimens (optimal, S4, and S8) were used to make 32 mm × 32 mm multi-pass cladding specimens, and friction and wear experiments were carried out. Before the experiment, the sample was weighed by a thousandth electronic scale (0.001 g), placed on the friction and wear auxiliary fixture, and the grinding pair was a 45 steel thrust ring. After the experiment, anhydrous ethanol was used to remove impurities on the surface of the sample and dry it. The friction and wear curve was generated by the friction and wear machine, and the wear morphology of the sample surface was observed by the ultra-depth-of-field microscope.

Figure 8 shows the frictional wear surface profile of the optimal specimen, S4, and S8. It can be seen that Figures (a–c) are 3D color images of the wear depths of the friction areas marked. The maximum wear depth of the optimal specimen is 149.72 μm, while the maximum wear depths of S4 and S8, respectively, are 210.16 μm and 201.17 μm. The reason for this is that the cladding layer of the optimal specimen is more closely combined with the substrate, the surface contour of the cladding layer section is smooth and continuous, there is very little slag, and there is no porosity on the cladding layer.

Comparing the micro-hardness values in Table 4, it can be found that the micro-hardness of the S4 specimen (219.6HV_0.5) is slightly larger than that of the S8 specimen (212.9HV_0.5), meaning that the wear resistance is stronger. The reason for this is that it unifies the metrics through factor analysis, constructing a mathematical model using the multiple linear regression equation by means of the ACDE method. The micro-hardness of the optimal specimen (231.6HV_0.5) is greater than that of the S4 and S8 specimens. The wear depth is smaller and the wear resistance is stronger.

As shown in Figure 8d–f are the 2D friction profiles of the three specimens at the uniform sampling point. It can be observed that the cladding layer prepared by laser-cladding technology has a certain wear resistance and there is no cracking or obvious large-area spalling after wear. The surface wear of S4 and S8 specimens is mainly in the form of adhesive wear and abrasive wear. Figure 8e,f shows multiple plastic deformations and minor scratches, as well as large areas of depressions and flaking at the edges of the scratches, which are initially caused by the unevenness of the coating surface and subsequently by scratches due to the interaction of abrasive debris with the coating. The surface of the optimal specimen did not show plastic deformation, and there were only wear points with short furrows caused by normal wear, which is a normal wear mechanism. It indicates that the optimal specimen has better wear resistance than the S4 and S8 specimens [18,19].

A comparison of the response values of the optimal, S4, and S8 samples is shown in Figure 9. After weighting the response values of the S4 and S8 specimens, it can be seen that the coating integrity of the specimen under the optimal parameters increased by 11.1%, micro-hardness increased by 7.1%, and the dilution rate decreased by 24.7%. In summary, the optimized process parameters have improved the intactness and micro-hardness, the dilution rate has been reduced, and the wear resistance has been improved, which is effective and reliable for actual production.

5. Conclusions

In this paper, laser-cladding 316L stainless steel powder on the surface of 27SiMn steel was used to explore the surface morphology, micro-hardness, and dilution rate of the cladding layer under the optimal process parameters, and the following conclusions were drawn.

(1) The optimal combination of process parameters was obtained by the adaptive differential chaotic evolution algorithm as follows: laser power of 1350 w, scanning speed of 11.7 mm/s, and powder feeding rate of 2.5 g/min, which corresponded to a response value of 90 for the degree of intactness, a dilution rate of 14.2%, and micro-hardness of 231.6HV0.5. After experimental comparison, it was found that the coating integrity improved by 11.1%, micro-hardness increased by 7.1%, and the dilution rate decreased by 24.7%.

(2) On the basis of the factor analysis method, multiple objectives were converted into a comprehensive quality Q by dimensional reduction. After discussing the residual map, uptake map, three-dimensional surface map, and contour map of the model, the accuracy of the model was obtained by residual analysis as 91.04%, meaning that the model was fully able to be used as an adaptive function of the intelligent algorithm.

(3) In the verification analysis of the specimen under the optimal parameters, it was found that the specimen had a closer bond between the fused cladding layer and the substrate in the macroscopic cross-section. The surface contour lines of the fused cladding layer cross-section were smooth and continuous, there was very little slag, and there were no air holes in the fused cladding layer. In the friction wear experiment, it was found that the maximum wear depth of the optimal specimen was 149.72 μm. Compared with the specimen in the control group, its wear depth is smaller, its wear resistance is stronger, and the wear on the surface of the specimen is mainly abrasive wear with a small number of furrows, which proves that its wear resistance has been sufficiently improved.

(4) The surface strengthening and repair of the mechanical parts require multi-track laser cladding. The optimal process parameters found by the ACDE algorithm can provide effective guidance and help for industrial applications.