Effect of Ultrasonic Vibration in Friction Stir Welding of 2219 Aluminum Alloy: An Effective Model for Predicting Weld Strength

Abstract

Friction stir welding (FSW) is today used as a premier solution for joining non-ferrous metals, although there are many limitations in its application. One of the objectives of this study was to propose an innovative welding technique, namely ultrasonic-assisted friction stir welding (UAFSW) with longitudinal ultrasonic vibration applied to the stirring head. In this paper, UAFSW mechanical properties and microstructure analysis were performed to demonstrate that the fluidity of the weld area was improved and the strengthened phase organization was partially preserved, due to the application of ultrasonic vibration. The addition of 1.8 kW of ultrasonic vibration at 1200 rpm and 150 mm/min welding parameters resulted in a 10.5% increase in the tensile strength of the weld. The ultimate tensile strength of 2219 aluminum alloy UAFSW was analyzed and predicted using mathematical modeling and machine learning techniques. A full factorial design method with multiple regression, random forest, and support vector machine was used to validate the experimental results. In predicting the tensile behavior of UAFSW joints, by comparing the evaluation metrics, such as R², MSE, RMSE, and MAE, it was found that the RF model was 22% and 21% more accurate in the R² metric compared to other models, and RF was considered as the best performing machine learning method.

1. Introduction

The Welding Institute in the United Kingdom devised friction stir welding (FSW), a solid phase joining process, the principle of which is indicated in Figure 1. Non-ferrous metals with low melting points, such as aluminum and copper, are the most used materials for this process [1]. 2219 aluminum alloy is a precipitation-hardenable aluminum alloy with high strength, good mechanical properties, heat resistance, fatigue resistance, etc. It is one of the most widely used aluminum alloys in aerospace applications [2,3]. In previous studies, it has been found that welding process parameters play an important role in the quality of the weld and the control of the welding process [4,5,6]. The common process parameters in friction stir welding are stir tool rotation speed, stir tool transverse feed speed, stir tool inclination, press-in depth, axial force, etc. [7]. With widespread engineering application of friction stir welding, its limitations, due to the defects of its special heat generation mechanism, have been exposed. For example, the uneven distribution of temperature and flow fields leads to holes in the weld seam, weak connections at the bottom, and a lack of weld penetration. To obtain higher performance and higher quality welds, scholars have proposed methods to introduce new energy action mechanisms into the friction stir welding process, and the introduction of ultrasonic vibration into the FSW process has become a popular topic of research among scholars in recent years [8,9].

A new ultrasonic vibration enhanced FSW (UVeFSW) process was developed by Wu et al. [10] of Shandong University, in 2012, by applying an ultrasonic emission device 20 mm in front of the stirring tool. Using this device for butt joint experiments on 6061-T6 and 2024-T4 aluminum alloys, it was discovered that applying ultrasonic vibration directly to the workpiece surface might improve the welded joint’s mechanical and fluidity properties, therefore expanding the process window and increasing the surface forming quality of aluminum alloy welding. In 2017, A.A. Eliseev et al. [11] introduced a new ultrasonic loading method for ultrasonic impact treatment of the workpiece that uses a magneto-strictive transducer rigidly mounted on the free edge of the workpiece to be welded and an adaptive ultrasonic generator that provides optimal vibration transfer efficiency at 21–23 kHz. At present, scholars involved in ultrasonic-assisted friction stir welding research mainly include the influence of ultrasound on the mechanical properties and microstructure of the weld, the mechanism of action of ultrasound, etc. For example, Faraz [12] studied the changes in the organization and mechanical properties of ultrasound-assisted friction stir welding welds of AZ91-C magnesium alloy and found that ultrasonic vibration greatly improved the mechanical properties of conventional friction stir welded joints. Tian WH et al. [13] studied the effect of ultrasonic energy on friction stir welded Al/Cu welded joints and found that ultrasonic vibration caused more intense mixing of Al and Cu, effectively reduced the activation energy and flow stress of the material, stimulated stable plastic deformation near the tool, and facilitated the homogenization of the Al/Cu joint. Hu [14,15,16] analyzed the acoustic softening effect of ultrasonic vibration in friction stir welding, where high-density vacancies lead to enhanced dislocation mobility. In summary, external ultrasonic vibration greatly improves the quality of the weld joint by refining the grain, improving the flow of the metal material in the weld zone, enhancing mechanical properties (such as tensile strength, toughness, and hardness), reducing residual stresses and forming more homogenous welded joints [17]. However, few have studied the effect of different process parameters, including ultrasonic power, on the weld strength. The strength of UAFSW welding is the result of multiple parameters acting together and the relationship between the parameters is complex, so the optimal weld strength needs to be data-driven so as to be predicted.

Eliseev’s method, mentioned as literature [11] above, involves ultrasonic vibration applied to the workpiece to be welded. Its advantage is that the stirring tool structure changes have less impact on a variety of materials and have universal adaptability. However, because the ultrasonic vibration is applied to the surface of the workpiece, rather than the welding area, the transmission to the bottom of the weld has less ultrasonic energy, and improvement in the weakest mechanical qualities of the weld bottom are not visible. The new welding technology proposed in this study is ultrasonic-assisted friction stir welding (UAFSW). Ultrasonic vibration energy is applied directly to the stirring tool along the axial direction to reduce the loss of ultrasonic energy [18]. During the welding process, the high-speed rotating stirring tool is driven by high-frequency mechanical vibration to do ultrasonic frequency vibration, which makes the metal in the weld area form a dense weld tissue under the compound effect of ultrasonic action and stirring friction. The method is characterized by the improvement of material fluidity at the bottom of the weld, which is more obvious, because the ultrasonic vibration energy is applied directly to the bottom of the weld along the longitudinal direction of the weld. This, in turn, improves the thermoplastic flowability of the metal material and increases the strength of the weld [19].

In summary, the optimal process parameters for UAFSW, the prediction of the ultimate tensile strength of the weld joints, and the improved effect of ultrasound on the FSW process remain to be studied. In this study, the relationship between the typical process parameters and the ultimate tensile strength of ultrasonic-assisted friction stir welding was investigated, based on a full factorial experimental design. Traditional mathematical models and machine learning techniques were applied to predict the ultimate tensile strength of UAFSW joints. The optimal process parameters were determined by multiple regression and statistical analysis of variance. The regression equation was given and the ultimate tensile strength was predicted. Machine learning methods, such as the random forest model and support vector machine model, were used to predict the ultimate tensile strength. The benefits and drawbacks of both mathematical modeling and machine learning methods were compared for the ultrasonic-assisted friction stir welding process, and the optimal process parameters and ultimate tensile strength of UAFSW were predicted. The laws of ultrasonic vibration on the mechanical properties and microstructure of the weld were explored to verify the good effect of ultrasound on weld strength.

2. Experimental

2.1. Experimental Setup

The base material (BM) utilized in the experiment was 500 mm × 200 mm × 6 mm 2219-T6 Al alloy plates. Infrared Spectroscopy was used to determine the material composition of aluminum alloy 2219. The chemical composition of BM is listed in

Table 1. Main chemical element composition of 2219 aluminum alloy (mass fraction, %).

Cu	Si	Fe	Gu	Mn	Zn	Ti	Al
6.38	0.08	0.23	0.15	0.32	0.10	0.06	Bal

. The MTS Landmark 100 KN tensile tester and HV-5 Vickers hardness tester were used to determine the mechanical properties of the BM. The tensile strength of 2219 aluminum alloy at room temperature was about 417 MPa, its yield strength was about 345 MPa, its elongation was about 14%, and its hardness was about 130 HV.

Figure 2 illustrates the independently designed FSW1609K CNC gantry type FSW welding machine. The machine has the advantages of high welding accuracy, sensitive control, good stability during welding, and wide applicability. It can carry out the welding process of aluminum, magnesium, copper, and other materials and workpieces of various sizes and thicknesses. In this process test, the welding machine equipment was used for the welding test.

The schematic diagram of the UAFSW system designed in this study is shown in Figure 3a. The ultrasonic vibration device was added to the conventional friction stir welding platform, which was mainly composed of an ultrasonic generation device, piezoelectric ceramic, amplitude rod, and stirring tool. In operation, the ceramic piezoelectric effect converts electrical energy into small mechanical vibrations, and then the amplification of ultrasonic vibration by the variable amplitude rod is conducted to the top of the stirring tool, so the stirring tool’s top forging force produces the axial ultrasonic frequency vibration. The ultrasonic system uses a constant frequency of 20 kHz, the maximum amplitude at no load is 16 μm, the vibration mode is sine, and the ultrasonic power supply output power can be varied from 0 to 3 kW. In the actual welding process, the power supply output power is adjusted to control the amplitude.

The shape and size of the stirring tool determine the welding quality. To better resonate with the ultrasonic system, and obtain a more efficient amplitude, the UAFSW stirring tool was optimized on the conventional stirring tool with the specific dimensions and schematics shown in

Table 2. Stirring tool size.

Φ1	Φ2	Φ3	L	H
6	7	14	5.7	5.6

and Figure 3b.

Some parameters in this study were kept constant and did not change throughout the study. These parameters were:

• Stirring needle inclination angle 3°
• Stirring needle downward pressure at a speed of 0.6 mm/s
• The plunging depth of 0.2 mm

2.2. Design of Experiment

The plates were polished on both sides to remove oxide film before welding. As shown in

Table 3. Welding variables and their levels.

Parameter	Unit	Level 1	Level 2	Level 3	Level 4
Rotational speed	rpm	1000	1200	1400
Welding speed	mm/min	100	150	200
Ultrasonic power	kW	0	0.9	1.8	2.7

, in this study, the rotational speed (RS), welding speed (WS), and ultrasonic power (UP) were selected as the three factors at different levels to design a full factorial experiment to test the mechanical properties. It is worth noting that ultrasonic power = 0 represents conventional friction stir welding, without the addition of ultrasonic vibration.

After welding was completed, the welds were prepared as tensile specimens using a wire cutter, and tensile tests were conducted on all specimens. The tests were conducted by the MTS Landmark 100 KN and the tensile speed was 2 mm/min. The detailed tensile strength of each specimen is shown in

Table 4. Design of experiment and corresponding response values.

Exp. No.	RS	WS	UP	UTS (MPa)
1	1000	100	0	308
2	1000	100	0.9	315
3	1000	100	1.8	320
4	1000	100	2.7	295
5	1000	150	0	296
6	1000	150	0.9	298
7	1000	150	1.8	305
8	1000	150	2.7	303
9	1000	200	0	260
10	1000	200	0.9	245
11	1000	200	1.8	271
12	1000	200	2.7	269
13	1200	100	0	305
14	1200	100	0.9	313
15	1200	100	1.8	321
16	1200	100	2.7	312
17	1200	150	0	314
18	1200	150	0.9	325
19	1200	150	1.8	347
20	1200	150	2.7	331
21	1200	200	0	301
22	1200	200	0.9	312
23	1200	200	1.8	314
24	1200	200	2.7	313
25	1400	100	0	277
26	1400	100	0.9	281
27	1400	100	1.8	291
28	1400	100	2.7	289
29	1400	150	0	280
30	1400	150	0.9	282
31	1400	150	1.8	287
32	1400	150	2.7	285
33	1400	200	0	259
34	1400	200	0.9	262
35	1400	200	1.8	276
36	1400	200	2.7	261

. Fracture specimens of FSW and UAFSW were cut and their port morphology was observed under a TESCAN MIRA 3 FE-SEM high vacuum field emission scanning electron microscope. Transmittance samples of the base material, FSW, and UAFSW were prepared, searched for precipitated phase particles, and photographed under a TECNAI G2 F20 field emission transmission electron microscope.

3. Results and Discussions

3.1. Mean Effect and Interpretation of Experimental Results

The mean response refers to the average value of the quality characteristics of each parameter at different levels, and the analysis of the mean response of each factor at different levels of testing could lead to better parameter combinations and the analysis of the law of influence of different levels on ultimate tensile strength. The mean response of the raw data for each parameter at each level in Table 4 was calculated and compared, as shown in Figure 4.

The mean response graph shows that (1) in a certain range (1000 rpm–1200 rpm), the tensile strength increased with the increase in rotational speed. Jabraeili [20] points out that increased rotational speed increases the heat input to the welding process, allowing for a more adequate thermoplastic flow of the material. However, it should be noted that too high a rotational speed (1400 rpm) will make the material extrude from both sides, reducing the material in the weld area and reducing the mechanical properties (2). On comparison of the impact of different welding speeds on the mechanical properties of the joint it was found that the tensile strength increased with a certain range of welding speed, showing a trend of first increase and then decrease. At the higher welding speed (200 mm/min), due to insufficient heat input, the welding speed is too fast, resulting in the formation of material tissue that is not dense, making the tensile strength decrease rapidly (3). Ultrasonic power of 0 represents conventional friction stir welding, and it is clear from the figure that the introduction of ultrasonic vibration had a generally positive effect on the mechanical properties of the friction stir weld. Qian et al. [21] found that the strength and elongation of the welds increased after adding 2 kW of ultrasonic vibration to friction stir welding of 2219-T6 aluminum alloy. This study found that the tensile strength of the weld first increased and, then, decreased with increase of the introduced ultrasonic power. When adding too much ultrasonic power (2.7 kW), it was found that the mechanical properties of the welded joint “decreased rather than increased”, which indicated that the excessive ultrasonic vibration power had a counter effect on the strength of the welded joints. The analysis is that excessive vibration power makes the stirring tool axial pressure reduce, the temperature drops too much, and does not achieve a good welding state, and so the performance of the welded joint reduces. At the same time, excessive ultrasonic vibration frequency will also affect the life of the stirring tool, increasing the risk of fracture failure of the stirring tool. Comprehensive analysis could assume that the ultimate tensile strength reached its maximum value at a speed of 1200 rpm, a welding speed of 150 mm/min, and an ultrasonic power of 1.8 kW.

3.2. Effect of Ultrasonic Vibration on Friction Stir Welding

3.2.1. Fracture Behavior

Figure 5 shows a comparison of the tensile fracture locations of the FSW and UAFSW welded joints at 1200 rpm and 150 mm/min process parameters. It can be observed that there was obvious plastic deformation near the fracture, and all were oblique fractures. The section had a metallic luster, not found in the macroscopic existence of defects. Demeneghi et al. [22] analyzed in detail the fracture behavior of 2219 aluminum alloy friction stir welds and found that the weakest point in the weld cross-section was located in the heat-affected zone (HAZ). For FSW tensile specimens, the initial cracks were generated from the bottom and extended upward to the upper surface HAZ, and the cracks were located on the advancing side. For tensile specimens with a uniform cross-sectional area, fracture usually occurs in the weakest area of mechanical properties, so it can be concluded that the weakest area of mechanical properties in the FSW welded joint is located at the bottom and the advancing side of the weld, and in engineering, it has been found that the bottom and the advancing side of the upper surface of the FSW weld are the most common areas of defects. This is determined by the special action mechanism of FSW, where the bottommost layer of material is weakly subjected to thermal coupling and poor material mobility, resulting in a weak connection at the bottom. Comparison of UAFSW weld joint fractures resulted in observation of some tensile specimens with cracks near the return side, which indicated that ultrasonic vibration promoted the overall material flow in the weld area and weakened the stress concentration in the forward side area, do that the forward side area of some specimens was not a mechanically weak area. A comparison of previous data shows that tensile specimens that fracture on the return side usually have relatively high tensile strengths, which directly indicated that UAFSW improved the mechanical properties of the weld.

It can be seen that most of the crack growth appeared first at the bottom of the weld, indicating that there might be mechanically weak areas at the bottom of the weld. Scanning electron microscope photographs of the bottom of the fractured weld at 1200 rpm, 150 mm/min, and 1.8 kW parameters for FSW and UAFSW are shown in Figure 6. It can be found that even though no macroscopic imperfections were found in the weld, the micrographs of the bottom of the tensile fracture showed a smooth and tough nest-free plane, which indicated that a weak joint still existed. The analysis suggested that during the friction stir welding process, the area at the bottom of the weld in the thickness direction was subjected to minimal heat input, weak thermal coupling, insufficient thermoplastic flow, and poor diffusion of atoms between the metal interfaces, which led to the absence of a good metallurgical bond in this part. Comparing Figure 6a,b, it can be seen that the weakly connected region at the bottom of the conventional FSW joint was about 500 μm, and after the introduction of ultrasonic sinusoidal vibration, the fracture was a typical ductile fracture with the weakly connected region reduced to 300 μm. This could be explained by the acoustic softening effect of ultrasonic vibrations, which might affect the physical properties of crystalline solids, causing a reduction in the rheological stress of the material [16]. During ultrasonic vibration-assisted metal plastic processing, ultrasonic vibration could have reduced the maximum shear stress for the plastic flow of the material, and, thereby, could have made it easier for the material to enter the plastic flow state. It can be seen from the figure that ultrasonic vibration improved the mobility of the metal at the bottom of the weld, especially the strengthening of the flow behavior of the material along the thickness direction, so that the material flow intersection behavior of the metal at the top and bottom of the weld was more adequate. The thickness variation of the weak connection region at the bottom affects the local mechanical properties [23], so the homogeneity of the weld properties under the action of ultrasonic vibration was better.

3.2.2. Microstructure Analysis

Figure 7 shows the TEM images of base metal, FSW, and UAFSW stir zones. There is a high-density distribution of plate-shaped θ′ and θ″ phase precipitates in the base metal (as seen in Figure 7a), which are identified according to the electron diffraction patterns from BM (as seen in Figure 7b). All the strengthening precipitates were presented as plate-shaped with a range of 30–150 nm in diameter, decorating uniformly inside the grains of the Al matrix. As shown in Figure 7c, all the precipitates were dissolved into the matrix and large-sized particles were formed in the FSW nugget zone. While in Figure 7d, it is clear that there were lots of fine equilibrium θ precipitates, which still had a Zener pinning effect, in UAFSW. In the FSW process, the main precipitate evolution includes precipitate dissolution and over-aging [24] due to the high temperature and severe mechanical effect. In UAFSW, most of the precipitates overaged to equilibrium precipitates as proved by the presence of a large number of fine equilibrated θ particles.

The major intermetallic compound in Al-Cu alloy 2219 is Al₂Cu and the strengthening precipitates were mainly metastable plate-shaped coherent θ″, semi-coherent θ′, having parts of the stable θ phase which should be fine enough [25,26,27,28]. The precipitation sequence can be explained as: supersaturated solid solution→Guinier-Preston zones→α + θ″→α + θ′→α + θ. In the process of FSW, following the coarsening and growth of θ the phase, the solid solution strengthening effect of copper is reduced owing to the partial moving of copper from the matrix to Al₂Cu particles. Furthermore, the large-sized Al₂Cu particles lose their obstacle function. The softening in the stirred zones is mainly caused by the transformation of the metastable θ′ phase to a stable and large-sized θ phase and the dissolution of θ′ and θ″ phases.

In the process of FSW, a large amount of metastable θ″ and θ′ particles were dissolved into the matrix, and the other transformed into a stable large-sized θ phase due to the elevated temperature. Thus, these factors led to the loss of the precipitate pinning effect. While in UAFSW, a fraction of the fine equilibrium phase would form but not totally dissolve into the Al matrix, owing to the acoustic softening effect of ultrasonic vibration. After the introduction of ultrasonic vibration, the welding axial pressure becomes smaller due to the acoustic softening effect [29,30], i.e., the heat input to the stirring tool is reduced, resulting in less heat and lower temperature in the weld zone. As a result, the fine θ particles are retained due to the Zener pinning effect of the strengthening precipitates. Furthermore, the ultrasonic high-frequency vibration could break the growing particles which can cause more fine particles in the welding zone [31].

From previous research it is clear that ultrasonic vibration plays a positive role in the strength of friction stir welds, but an effective and feasible model to predict the ultimate tensile strength of UAFSW, and the corresponding optimal process parameters, is needed for practical engineering applications. In this section, both mathematical models and machine learning methods were used to predict the ultimate tensile strength of UAFSW.

3.3. Analysis of Regression for Tensile Strength

ANOVA explored the significance of each substantive parameter and its interaction, as well as the dependence of the response on each parameter. The tensile strength data were first preprocessed by Z-score normalization to eliminate the effects arising from different magnitudes. The mean squares of all experimental data were compared and the ANOVA test results were obtained, as shown in

Table 5. ANOVA for UTS.

Source	DF	Adj SS	Adj MS	F-Value	p-Value
Regression	9	30.1972	3.3552	18.16	0.000
RS	1	1.8405	1.8405	9.96	0.004
WS	1	6.1787	6.1787	33.45	0.000
UP	1	0.7612	0.7612	4.12	0.053
(RS)2	1	16.3836	16.3836	88.69	0.000
(WS)2	1	2.8828	2.8828	15.61	0.001
(UP)2	1	0.5847	0.5847	3.17	0.087
RS×WS	1	1.4673	1.4673	7.94	0.009
RS×UP	1	0.0233	0.0233	0.13	0.725
WS×UP	1	0.0751	0.0751	0.41	0.529
Error	26	4.8028	0.1847
Total	35	35.0000

DF-Degree of Freedom, Adj SS-Adjusted Sum of Squares, Adj MS-Adjusted Mean Square.

. In this study, the ANOVA test was performed at a 95% confidence level. When p < 0.05, the factor was considered to be significantly different. Therefore, the rotational speed (RS), the welding speed (WS), and the interaction of RS and WS were statistically significant, as can also be seen from the Pareto plot (Figure 8). The regression equation with the insignificant term removed is shown below. The ultimate tensile strength of ultrasonic-assisted friction stir welding could, therefore, be predicted to be 330.31 MPa, when the optimum parameters were 1200 rpm, 150 mm/min, and 1.8 kW, respectively.

Regression equation:

$$\begin{gathered} UTS=1.514-O.2293\times RS-0.4202\times WS-0.981\times {\left(RS\right)}^2 \\ -0.412\times {\left(WS\right)}^2+0.2077\times RS\times WS \end{gathered}$$

3.4. Random Forest

3.4.1. Modeling Steps

Figure 9 depicts the UAFSW data modeling flow chart. The following were the specific steps:

• Created a mechanical performance data collection for UAFSW.
  Table 4 in Section 2.2 lists the procedure parameters and tensile strength data for the UAFSW specimens. For data preprocessing, rotational speed, welding speed, and ultrasonic power were chosen as independent variables, with ultimate tensile strength as the dependent variable. To eliminate the impacts of varying magnitudes, the tensile strength data were pre-processed with Z-score normalization.
• Separated training and testing sets.
  The original data of UAFSW were $T=\left\{\left(x_1,y_1\right),\left(x_2,y_2\right),\dots ,\left(x_n,y_n\right)\right\}$. In machine learning, data segmentation is commonly used to separate all data into training and testing sets in order to validate the validity and accuracy of the proposed model [32]. The training set was used to train the model, whereas the test set was used to evaluate the model’s correctness. Since there was a moderate quantity of total data in this article, the division method was used to pick 70% of the data as the training data set and 30% as the test data set.
• Determined optimal parameters
  To ensure the model training set was not slow and error stable, $ntree=1,2,\dots ,2000,$ and $leaf=1,2,\dots ,k$ were chosen sequentially to determine the optimal $ntree$ and $leaf$ parameters.
• Model performance evaluated.
  The characteristic variables were chosen at random for generating the regression decision tree utilized for splitting. For the evaluation of model prediction results, the following metrics were used [33].

$$MSE=\left({\sum }_{i=1}^n{\left(y_t-y_p\right)}^2\right)/n$$

(1)

$$RMSE=\sqrt{\left({\sum }_{i=1}^n{\left(y_t-y_p\right)}^2\right)/n}$$

(2)

$$MAE=\left({{\displaystyle \sum }}_{i=1}^n\left|y_t-y_p\right|\right)/n$$

(3)

$$R^2=1-\frac{\sum {\left(y_p-y_t\right)}^2}{\sum {\left(\overline{y}-y_t\right)}^2}$$

(4)

where $y_t$, $y_p$ and $\overline{y}$ are the true value, predicted value, and the average value of the ith sample, respectively, and n is the corresponding sample size.

3.4.2. Optimized Model Parameters

The number of decision trees and leaf nodes in the random forest model have a direct impact on the model’s prediction accuracy. These two factors were optimized in order to produce more accurate predicted results.

(1)

Optimization of the number of decision trees

The size of the random forest model is determined by the number of decision trees ($ntree$). The random forest model’s convergence and stability are hampered if the number of decision trees is too small. When the number of decision trees is too high, the model’s convergence is slow, which is inconvenient for practical applications [34]. The $ntree$ was set at 5–2000 for modeling in this study, and the accompanying MSE values were calculated independently to establish the best $ntree$ based on the MSE values’ trend. The horizontal axis shows the $ntree$, and the vertical axis reflects the MSE value, as shown in Figure 10. When the $ntree$ was between 50 and 2000, the MSE value tended to remain steady, and when $ntree=1000$, the MSE reached a minimal value of 0.083947214. Therefore, $ntree=1000$ was chosen to be set as the optimum value for the number of decision trees for this model.

(2)

Optimization of the number of leaf nodes

The $leaf$ in this research was taken to be between (5,10,15,50). Figure 10 shows that when $leaf=50$, the model had the minimum MSE value, and, hence, this was the optimum value for the number of leaf nodes in this model.

3.4.3. Variable Importance Assessment

Figure 11 illustrates the weights of the three parameters RS, WS, and UP in the random forest model. The rotational speed contributed the most to the model, thus in the actual ultrasonic friction stir welding process, the effect of the stirrer rotational speed on the weld strength should be focused on.

3.4.4. Analysis of Prediction Results

In this research, Python was used to create a random forest model for forecasting UAFSW’s ultimate tensile strength. The model’s two parameters were set to $ntree=1000$ and $leaf=50$, respectively, as shown above. The model’s accuracy was measured using R², MSE, MAE, and RMSE. This research compared the prior multiple regression model to the support vector machine model to test the accuracy of the random forest model predictions. Figure 12 depicts a depiction showing the association between actual and predicted UTS values using three methods: a mathematical model (multiple regression) and two machine learning models (RF and SVM). The perfect line is represented by the dashed line in the illustration, which is displayed at 45°. The performance characteristics of the three models (i.e., R², MSE, MAE, RMSE) are given in

Table 6. Model Performance Evaluation.

Model	R2	MSE	MAE	RMSE
Multiple Regression	0.74	0.20	0.33	0.44
Random Forest	0.96	0.03	0.16	0.17
Support Vector Machine	0.75	0.19	0.33	0.44

for the performance evaluation of the models.

Figure 12 shows that the random forest model’s predicted values were closer to the perfect line than the multiple regression and support vector machine models, indicating a better fit with the test response. The SVM model, on the other hand, had a scatter of predicted values that deviated somewhat from the perfect line, suggesting poor prediction. Table 6 reflects this objectively as well. The random forest model had the highest R² value (0.96) and the lowest MSE value (0.03), while the traditional multiple regression model had the lowest R² value (0.74) and the highest MSE value (0.20), and the support vector machine model also performed poorly, indicating that the random forest model had the best quality performance. A plot of the relationship between UTS and the number of test datasets is shown in Figure 13. It is clear from the figure that the random forest model predictions were very close to the experimental values of the UTS, in agreement with the pattern demonstrated in Figure 12. This could be attributed to the learning capability of the random forest and the application of the learning to the prediction of the more complex friction stir weld strength nonlinear problem [35]. Since the interactions between certain variables could be detected and compared, random forest models could handle complex nonlinear problems. The prediction of friction stir weld strength is complex and therefore the random forest model was the preferred method for prediction. High R² values indicated the advantage of random forest over traditional multiple regression models in predicting the tensile strength of friction stir welds. This strong correlation could be used for tensile strength prediction, which reduces the requirement for future laboratory welding process window exploration. The random forest approach provided an excellent insight into ultrasonic-assisted friction stir welding.

3.5. Confirmation Test

Tests were conducted using optimized optimal process parameters to verify the prediction of ultimate tensile strength by different models, which were all calculated using 5% confidence intervals, which have been represented in the figure. Five validation tests were designed under the optimal process parameters, and an average ultimate tensile strength of 340.28 MPa was obtained at 1200 rpm, 150 mm/min welding speed and 1.8 kW ultrasonic power (indicated in the figure using the dashed line), and the test values were within the confidence intervals of the respective models. A comparison of the predicted results of the different prediction models is shown in Figure 14.

4. Conclusions

In this study, ultrasonic vibration was introduced on the basis of conventional friction stir welding. A full factorial experimental design was used to investigate the laws of ultrasonic influence on the mechanical properties and microstructure of friction stir welded joints. Conventional mathematical models and machine learning techniques were applied to the ultimate tensile strength prediction and process parameter optimization of UAFSW joints. The main conclusions are as follows:

(1)

Ultrasonic-assisted friction stir welding can effectively improve the tensile strength of friction stir welded joints and change the fracture location of tensile specimens. The tensile strength increased with the increase of ultrasonic power and then decreased, reaching a maximum of 347 MPa, which was 10.5% higher than that of FSW welds, but excessive ultrasonic vibration power could have a counter effect on the strength of welded joints. The fracture analysis clearly shows that the rheological stress of the material in the weld area was reduced due to the mechanism of the acoustic softening effect of ultrasonic vibration, the fluidity of the material was improved, and the weak joint area at the bottom of the weld was reduced from 500 $\mathsf{\mu }\mathrm{m}$ to 300 $\mathsf{\mu }\mathrm{m}$.

(2)

The strengthening precipitates (metastable θ″ and θ′ phase) with a range of 30–100 nm in diameter were uniformly presented with the Al matrix in the BM. After FSW, all the strengthening precipitates were dissolved into the Al matrix in the NZ. A fine equilibrium θ strengthening phase can lead to the precipitate pinning effect in the UAFSW nugget zone.

(3)

To predict the ultimate tensile strength of 2219 aluminum alloy UAFSW, three prediction models were developed, namely, a multiple regression model, a random forest model, and a support vector machine model. Based on the weight analysis of the random forest, it was found that the rotational speed of the stirring tool was the most important factor affecting the UTS, accounting for 50.7%.

(4)

The results of the three prediction models were compared, and it was found that, for the current dataset, the random forest model had better accuracy compared to the multiple regression model and the support vector machine model, with an R² of 96%, which was 22% and 21% better compared to the other models, respectively. It indicated that the optimized random forest model was more suitable for solving complex nonlinear problems, such as ultrasonic-assisted friction stir welding, providing an insight into the application of machine learning techniques in the manufacturing field.