**2. Methodology**

#### *2.1. Surface Modification*

As part of the experiment, the weld deposit was prepared using metallic powders and rare Earth oxides (CeO2, Y2O3, La2O3) (Pol-Aura, Olsztyn, Poland). Nickel-based powders (COB-ARC, Chorzow, Poland), iron-based powders (COB-ARC, Chorzow, Poland), and powders containing chromium and tungsten carbides (COB-ARC, Chorzow, Poland) were used to produce the deposits. The weld metals were then applied on S355 steel (Hut-Trans, Katowice, Poland) using metal active gas (MAG) welding in combination with plasma arc welding (PAW). Metallographic specimens were prepared from the collected samples for microscopic observation of microstructural changes. For this purpose, a Phenom XL scanning electron microscope (Thermo Fisher Scientific /Phenom-World, Eindhoven, The Netherlands) was employed. Representative images of the pads made of metallic powder on a nickel matrix (chemical composition: 0.6% C, 3% Fe, 11% Cr, 3.8% Si, the rest Ni) are shown in Figure 1. The modification changed the morphology and arrangemen<sup>t</sup> of dendrites, which was reflected in the change of wear resistance.

**Figure 1.** Microstructure of the Ni-based pad weld on the S355 steel: (**a**) non-modified and modified: (**b**) CeO2, (**c**) La2O3, (**d**) Y2O3.

#### *2.2. Tribological Tests*

Tribological tests under dry friction and fluid friction with the addition of SiO2 were carried out for the prepared variants, in which tribological characteristics (friction coefficient, linear wear) and wear indices (maximum wear track depth, track area) were determined.

The following tests were performed for all the welds:

• hardness test:

	- - micro combi tester MCT<sup>3</sup> ANTON PAAR (Anton Paar, Corcelles-Cormondreche, Switzerland),
	- - initial loading force 30 mN,
	- - final loading force 15,000 mN
	- - loading/unloading rate = 59,979.8 mN/min,
	- - Rockwell indenter
	- - indenter radius 100 μm.
	- - tribometer TRB3 Anton Paar (Anton Paar, Corcelles-Cormondreche, Switzerland),
	- - reciprocating motion,
	- - amplitude: 10 mm
	- - frequency: 1 Hz
	- - number of cycles: 10,000
	- - friction type: dry friction/fluid friction (water solution 10% SiO2)
	- - temperature: 23 ± 1◦
	- - humidity: 50 ± 1%
	- - optical profilometer: Leica DCM8 (Leica, Wetzlar, Germany)
	- - the maximum track depth and the track area measured from the surface profile were taken as measures of the sample wear.

The tribological tests allowed determining wear resistance of the welds. Table 1 shows sample results from the experiments performed.

#### *2.3. Exploratory Data Analysis*

The data analysis was performed in three steps:


In the first stage, exploratory data analysis (EDA) was carried out, which included description and visualisation of the data without assuming any initial hypotheses. The description and visualisation of the data made it possible to identify trends, patterns, missing data, outliers, etc.

Prior to exploratory data analysis, the following questions were generated:



**Table 1.** Compilation of sample test results.

The first thing to do with any data set is to read it. This is done not only to ge<sup>t</sup> to know all the data collected, but also to reduce the workload during analysis. The initial data investigation is known as exploratory data analysis or EDA and it primarily focuses on visually inspecting the data. The main aim of EDA is to understand what data you have, what possible trends there are, and therefore which statistical tests will be appropriate to use [28].

In the EDA process, descriptive and visualisation analyses were performed, including data set description (number of samples, number of not e number ( NaN )values), the removal of columns with a large number of empty NaNs, the insertion of missing data using strategy = mean, descriptive analysis (mean, standard deviation, min, max, median, 1st quartile, 3rd quartile), the visualisation of elements in individual classes, the identification of outliers, unsupervised learning using clustering, heat maps showing Pearson's correlations between features, and the visualisation of strong positive and negative correlations divided into 4 classes.

The following tools and libraries were used (open source):


Explanation of the methods used:


In preparing the dataset for analysis, new columns were introduced, the abbreviations of which are shown in Table 2.

The set was divided into two parts:


A NaN—Not a Number analysis was performed for the data set, Table 3.

Due to the small number of records (49), selected columns were removed (a large number of NaN values), i.e., Ni, Mo, Mn Co, B, W, V, WC. The remaining columns were completed with the mean values for each column using the SimpleImputer function. Tables 4 and 5 show the first five elements of both sets with the added mean values.

The descriptive information shown in Table 6 is then presented for the dry friction set, which shows the calculated values of mean, standard deviation, minimum, maximum value, and first, second, and third quartiles. Similar calculations were performed for fluid friction, as shown in Table 7.


#### **Table 2.** Description of abbreviations.

**Table 3.** Analysis of NaN values, before and after the removal of selected columns.



**Table 4.** Five elements of the set for dry friction with the added means.

**Table 5.** Five elements of the set for fluid friction with the added means.


**Table 6.** Basic information for the set—dry friction.


**Table 7.** Basic information for the set—fluid friction.


In order to demonstrate the correctness of the analyses carried out with regard to the number of tests performed with various modifiers (rare Earth oxides) and their effect on tribological properties, a class chart was prepared. For the tests conducted, the lack of balance between the individual classes may influence the real assessment. Figure 2 shows the number and percentage of the elements per class.

**Figure 2.** Elements in each class.

#### **3. Results and Discussion**

Figure 3 shows the dependence of disc wear on track area for each class.

Figure 4 shows the cumulative disc wear vs. track area. After removing the outliers, it can be seen that the data follow a linear dependence.

**Figure 4.** Dependence of dw1 on ta1 by class.

In the next step, a cluster analysis was carried out using two methods (K-means, Hierarchical). The analysis showed a high similarity between the two methods used. These are unsupervised classification methods of unsupervised learning.

Figure 5 shows the analyses for dry friction (column on the left) and fluid friction (column on the right).

**Figure 5.** Cluster analysis for dry and fluid friction. Determination of optimal number of clusters using: (**<sup>a</sup>**,**b**) Elbow method; (**<sup>c</sup>**,**d**) clusters with centroids determined by K-means algorithm; (**<sup>e</sup>**,**f**) determination of optimal number of clusters for Hierarchical method using dendrograms; (**g**,**h**) clusters determined by Hierarchical algorithm.

The first row shows the optimal number of clusters determined using the so-called Elbow method. For both sets, three clusters were determined by the breakpoint. The second row shows the visualisation of the cluster analysis for both cases with the indication of the centroids for all clusters. The next line shows the dendrogram plots for dry and fluid friction on the basis of which the optimal number of clusters for the Hierarchical method was calculated.

The two heatmaps shown above are for the dry friction and fluid friction sets (Figures 6 and 7).

Pearson's correlations show that in the case of dry friction, a very strong negative correlation occurs between C-cof, C-mwd1, and C-ta1 and a very strong positive correlation occurs between vh-ih and ta1-mwd1. Pearson's correlation coefficient is a measure of linear correlation between two sets of data. In contrast, for fluid friction, a very strong negative correlation occurs between C-cof with a very strong positive correlation between ta2-mwd2. The results are summarised in Table 8. The correlation values are shown in Table 9.

**Figure 6.** Heatmap for dry friction.

**Figure 7.** Heatmap for fluid friction.



**Table 9.** Strength of association.


Several strong correlations can be observed from the heatmaps for dry and fluid friction and for the pairwise correlations between these sets. For dry friction, the C index shows a very strong negative correlation with cof, mtd, and ta, whereas for fluid friction, only a very strong negative correlation with cof is observed. A strong negative correlation was found for ih and ym against the indices from mwd and ta for dry friction. In contrast, this correlation was not observed for fluid friction. For both sets, there is a very strong positive correlation between mtd and ta (0.98—for dry friction, 0.93—for fluid friction). Ym is strongly positively correlated with vh and simultaneously strongly negatively correlated with mtd and ta.

To confirm the correlations discussed above, they are presented in the form of relationships between the variables (Figures 8–10).

**Figure 8.** Relationships between the indices and carbon content.

**Figure 9.** Maximum track depth versus track area—dry friction (positive correlation (0.98)).

**Figure 10.** Maximum track depth versus track area—fluid friction (very strong positive correlation (0.93)).

The graphs for dry friction show very strong negative correlations (−0.74, −0.80, −0.74):

Figures 8–10 show the graphs in which the layers are assigned to classes, i.e., nonmodified surface (class 1) and modified surfaces (classes 2, 3, 4). The differences between the individual lines corresponding to the classes are visible. Especially for class 4 (Y2O3), we observe a different slope of the obtained straight lines. Analysis does not reveal a quantitative but a qualitative relationship, indicating the effects of the additives on the parameters determined.

Exploratory data analysis showed dependencies between individual parameters. The proportionality of the carbon content in the welds with rare earth oxides to their mechanical properties was demonstrated. It was confirmed that its increase resulted in an increase in hardness. This is due to the formation of hard carbides in their microstructure and changes in the morphology of padding welds modified with rare Earth metals. The increase in hardness lowered the coefficients of friction "cof", which directly translated into the reduction of the surface of the track wear areas and the wear track depths. A slightly different nature of wear was demonstrated for dry friction and fluid friction. It was shown that despite the increase in hardness and the decrease in the friction coefficient, the remaining parameters in the form of the wear track area and depth were not so strongly correlated in the case of fluid friction. SiO2 particles were used in the latter case, which changed the nature of the wear into tribocorrosion wear. The analyses confirmed both the complexity of the effect that parameters such as chemical composition or test environment have on wear processes, and the different nature of relationships between the parameters.
