Comprehensive evaluation of surface parameter correlation in running-in wear process

The first wear process is running-in, which is a stage of each machine system must go through. The friction pair’s surface topography is an important feature of the running-in process. After running-in, the surface topography directly affects the performance in stable working state. The wear performance of the contact pair was focused on by mostly existing studies after a time; however, we should consider the correlation of the surface topography before and after running-in. In fact, exploration of this problem is significantly important to extend the service life of machine parts and improve the running performance. Based on the three-dimensional (3D) surface topography parameter evaluation method, in this study, experiments were designed to analyze the effect of the unworn surface topography on that after running-in, and investigated the correlation of 3D surface topography parameters. The results demonstrated that the topography characterization parameters, i.e., Sa, Sq, Sv, Sdc, Str, Sdq, and Sdr under different working conditions maintained a strong autocorrelation (the correlation coefficient of the same parameter). Moreover, the cross-correlation (the correlation coefficient between different parameters) among height parameters (Sq), hybrid parameters (Sdq, Sdr), and functional parameters (Sdc, Sk) was strong. The results of the surface roughness parameters found in this study can be used as input and output feature selection research based on working conditions and surface topography prediction after the modeling research of running-in surface topography.


Introduction
Immediately after the beginning of sliding contact between the new, unworn solid surfaces, modification in coefficient of friction (COF), thermal phenomenon, and wear rate are usually observed [1,2].
The running-in process is the first stage that all workpieces must go through in their entire servicelife.This stage has an important impact on the wear characteristics of the workpiece, and huge complexity is encountered during the process.The types of wear in the running-in process are complex, and include adhesive wear [3], abrasive wear [4], corrosion wear [5], and fretting wear [6].According to different materials, types of friction pairs, and lubrication conditions, the COF changes in the running-in process show different trend curves [1].In many cases, the time to arrive the everlasting of friction is different from the wear rate, and the ending standard of the running-in process is also different due to different materials of friction pair [1].At the same time, the surface topography changes significantly during the running-in process, and the changing trend involves the optimization of the performance of load support by changing the microstructure of the surface topography.According to many experimental studies, researchers proposed the concept of equilibrium surface roughness [7].The completion of running-in can be defined in terms of the change of surface topography [7]; therefore, the study of surface topography is very important in deciding the internal mechanism of this process.
Many studies on this behavior are built on surface roughness parameters, highlighting how surface topography affects the friction-related characteristics of the running-in process, including wear characteristics [8][9], friction characteristics [10], lubrication characteristics [11], and surface topography characteristics [12].The surface topography of the friction pair has a significant effect on the running-in wear characteristics.
Surface topography not only acts as the initial participation factor of the running-in process, but also affects several characteristics of the running-in process together with many working conditions.Based on the different characteristics of the surface profile, Ghosh and Sadeghi presented a model of surface wear to simulate the effect of roughness parameters on the rate of wear in the wear stage process and stable wear stage.They showed that surface topography parameters are important indicators to highlight the wear characteristics of friction pairs [13].
At the same time, with the change of working conditions, the impact of surface roughness on components has also changed.As one of the important characteristics of friction pairs, surface roughness always participates in the entire friction and wear process of the workpiece: as an input of this process, characterization of the intermediate state of this process, results of this process, and an important factor in the wear stage and stable friction.The surface roughness values at both ends of running-in are two key important nodes, and it is very important to establish their relationship for understanding and optimizing the running-in process.
The main surface topography parameter of this study was 2D roughness parameter Ra.Based on the various types of statistical parameters of the 3D surface topography, Meireles et al. analyzed the change in surface characteristics of human teeth in the process of wear, and found that the sensitivity of different parameters to wear characteristics was inconsistent, which highlights the importance of parameter selection in the research of wear process [8].Wear research based on different types of surface 3D parameters is the correct direction to deepen the research on simple 2D profile roughness wear.
In this study, based on the comprehensive evaluation parameters of 3D surface topography by the areal method, the correlation of roughness parameters was studied by using surface topography with different characteristics, which was analyzed from three aspects of amplitude variation, autocorrelation and cross-correlation.At the same time, through the correlation analysis of different types of morphological parameters, the understanding of the degree of morphological changes in the running-in process is enhanced, thereby improving the control of running-in quality, and finally optimizing the control of friction and wear characteristics.This has practical significance for the control of friction characteristics and the prediction of wear life.

Evaluation methods of surface topography parameters
A surface is characterized by the following three parameters: roughness, waviness, and surface shape error.Surface roughness refers to the distance between two peaks or two valleys (wave distance) on the machined surface is very small (less than 1 mm), which is a microscopic geometric shape error.The lower the value of surface roughness, the smoother the surface.Surface roughness is generally caused by external factors such as mechanical processing or machine tool vibrations.Surface roughness affects the wear resistance, fatigue strength, corrosion resistance, and stability of the parts.The performance and life of a machine exhibit a very important impact.Thus, it is one of the most important and accurate indicators for evaluating the surface quality of mechanical parts.
Currently, the evaluation methods of surface quality can be mainly divided into the following two categories; one is based on 2D surface profile analysis, and the other on the 3D surface topography.The 3D surface characterization method is better for evaluate the surface topography.Methods for evaluating the regional surface topography use the 3D surface topography of an object obtained from the regional surface instead of the contour trajectory.Some of its characterizing parameters can be derived from the description of the profile, whereas the remaining are regional parameters specially designed to describe the performance of the surface structure.Therefore, the 3D evaluation parameters of the areal method can be used to evaluate the surface topography closer to the real surface, and can provide an intuitive image of the evaluated surface and sufficient information concerning the surface shape.
In general, the 3D evaluation parameters of the areal method can provide sufficient and reliable information for the effective analysis of the surface topography.Table 1 summarizes that the areal method involves multiple types of 3D parameters.Among the surface topography evaluation parameters involved in the areal method, Sq represents the average height of the surface topography and is an important parameter in surface topography characterization; Sv is the maximum pit height; Sdc is the height difference; Str is the texture aspect ratio; and Sdq denotes the gradient of the surface topography, and is affected by the height and spatial characteristics of the topography.When the value of Sa is constant, the larger the Sdq, the finer the surface texture interval, thus Sdq can be employed to effectively distinguish different surface texture features.Sdr is usually related to the surface coating characteristics.The core roughness (Sk) represents the improvement of surface support performance during running-in process, which is observed in terms of the numerical change of parameter Sk.

Correlation analysis
Correlation is a non-deterministic interdependence of objective phenomena and its purpose is to explore the network of correlations that exist in data.The correlation method refers to the analysis of two or more variable elements, in order to obtain a correlation coefficient that determines the closeness of the correlation between the two variables.It can be calculated as follows: X is the surface topography parameter before wear and Y is the surface topography parameter after wear.
Correlation coefficient r quantitatively describes the degree of correlation between X and Y.The correlation between two variables is usually determined according to the following ranges: very weak correlation or no correlation.

Experiment
For the sliding experiment, four surface morphologies with different characteristics were designed to participate in the running-in experiment under different working conditions.Herein, a surface profile comprehensive measuring instrument was used to measure the surface topography before and after running-in wear, and the areal method surface topography roughness parameter was used to evaluate the surface topography.In this way, a collection of the evaluation parameters of the surface topography was obtained.Furthermore, the changes in parameter amplitude were compared, and the correlation coefficient of the autocorrelation analysis and cross-correlation analysis were calculated.
Finally, the overall surface topography parameter changes and correlation characteristics of the process were obtained.

Experimental design
Herein, a running-in experiment was designed to systematically analyze the effects of different working conditions, surface topography, and texture on the characteristics of surface topography after running-in wear, as well as the correlation between surface topography characteristics at both ends of running-in.
The traditional conclusion concerning the surface topography after running-in wear is that the surface roughness is only related to the conditions, and different surface roughness can be obtained under different running-in conditions.According to literature studies [7], load and speed are the most important factors affecting the topography.In order to ensure the stability of running-in conditions, four types of surface morphologies were used to evaluate the characteristics of sliding friction and wear under low rotating speed (20 r min1, 40 r min1, and 60 r min1) and low contact pressure (20 N, 30 N, and 40 N).In this experiment, four kinds of surface morphologies and nine kinds of working conditions were combined to obtain 36 experiments.
The wear process was performed using a universal friction and wear testing machine with pin-disk friction pairs (WWM-1).The testing machine can produce different working conditions through lever loading and a motor drives the rotating pin to rotate on a fixed plate to perform surface abrasion.Herein, the pin-disc friction pair was used to realize the three pin heads sliding along the circular track on the friction disc using the universal friction and wear testing machine WWM-1.The working range of the friction and wear testing machine was 0-1000 N, the measuring range of the friction torque was 0-2500 N mm, the temperature control range was room temperature-300 C, the spindle speed range was 10-2000 r min1, and the time control range was 1 s-9999 min.The equipment can apply load to the lower friction plate through a lever, and the upper motor can drive the pin holder to rotate, enabling circumferential sliding of the upper pin head on the friction plate.
In the experiment, the pin head material was 45# steel (ASTM1045).The material of the friction disc was bearing steel (ASTME52100).The pin head was processed into a cylinder with a diameter of 3 mm and a length of 17 mm, and heat treatment made the hardness reach 31-36 HRC.The friction disc was processed into a disc with a diameter of 54 mm and a thickness of 10 mm, and heat treatment made the hardness reach 59-62 HRC.The pin head could slide along a circular track and the diameter of friction disk is 46 mm.During sliding friction, the pin-disk friction pair was immersed in lubricant.The lubricant used herein was diesel engine oil, whose density is 0.886 g cm3 and its kinematic viscosity is 80 mm2 s1 at 20 C.The yield strength of ASTM1045 was 355 Mpa.The nominal contact pressure under the condition of 40 N was 1.88 Mpa.Considering the actual land area may be smaller than the nominal land area, then the actual pressure becomes larger.Even if the pressure increases by 100 times, it is only about half of the yield limit.At the same time, in order to avoid the temperature rise caused by the extremely high rotating speed, which affects the material properties, low-speed sliding was used herein.
Due to the complexity of running-in, multiple output factors, including COF and rate of wear, undergo drastic change until they gradually stabilize.The completion of the running-in stage is mainly determined by the stability of output factors; thus, there is no unified standard to indicate the completion of the process.To eliminate the influence of completion criterion on the experimental results, in this study, the COF running-in process was simulated.The changes with time of the COF and wear rate of the multimodal texture surface with a large surface height under a load of 40 N are presented in Figure 1.In fact, according to the resulting change trend of the COF, in all cases, the COF was stabilized after 6 min.

Surface topography acquisition
All surface morphological characteristics involved in this study were measured with PGI830 surface topography comprehensive measuring instrument.Because the surface profile comprehensive measuring instrument (PGI830) for precision engineering surface is used to measure and analyze the roughness, waviness and shape of plane, spherical surface, aspheric surface and free surface, which is applicable to surface quality evaluation and process analysis.The device uses a contact probe to scan the surface, and the surface topography is finally measured by laser interference generated by the displacement of the probe.The horizontal measurement length of PGI830 was 200 mm, the vertical measurement length was 8 mm, and the measurement accuracy was 0.8 nm.In the running-in experiments performed on training samples, the total measurement area was 1 mm 2 , and the interval of sampling was 10 μm.After each measurement, plane fitting was used to remove the shape error.Then, a robust Gaussian filter was used to separate the waviness and roughness, the cut-off wavelength was 0.25 mm.Finally, the pin head was described based on the surface evaluation parameters of the areal method.were prepared to go through running-in.Figure 1 shows the surface morphologies, exhibiting different characteristics.Surface topography presented in Figure 2(a) shows valleys share the same direction with ridges.This kind of surface topography is commonly seen on general machining surfaces.Surface topography presented in Figure 2(b) shows pits spread on the flat top.As a type of surface topography with excellent load support performance, this surface exhibits good oil storage and lubrication performance.Surface shown in Figure 2(c) is dominated by peaks.This surface is mostly used in scenarios where the adhesion of the surface is improved or the friction of the friction pair is increased.Figure 2(d) shows the appearance of multi-direction valleys on the surface, which is a very representative type of surface topography.It is widely used as a type of functional surface that effectively improves the lubricating performance.

Surface topography characteristics
First, four different surface morphologies were evaluated by using the areal method surface topography parameters.Second, in order to eliminate the effect of the dimension, the evaluation data were standardized.Finally, some representative parameters were selected from the standardized areal method surface morphologies parameters to characterize the four different unworn morphologies, as shown in Figure 1.Combined analysis of Figure 2 indicate that the four different surface morphologies used in this experiment exhibit obvious differences.

Results
Boxplots were used to show the changes in parameter amplitudes.Through autocorrelation analysis, the parameters which maintain strong correlation when ignoring the difference caused by different speeds and different loads were obtained.On this basis, we analyzed the cross-correlation of these parameters, and obtained the correlation of different types of parameters.

Change of parameter amplitude after running-in
Boxplots including the median value and range of the surface texture parameters of the worn surface and wear free surface are shown in Figure 3.The boxplot reveals that the mean value and range of the surface texture parameters decrease after running-in.

Autocorrelation analysis
Under the premise of ignoring the difference caused by different speeds, the Pearson correlation analysis was used to analyze the autocorrelation for each parameter based on four different surface morphologies and three different loads.The results of autocorrelation analysis are presented in Table 2.According to the correlation criterion, when the absolute value of r is larger than 0.6, the correlation is considered as strong.Table 2 summarizes that: (1) when the load was 20 N, nine parameters, namely: Sa, Sq, Sv, Str, Sdq, Sdr, Sk, Sr2, and Sdc, were found to maintain a strong correlation; (2) when the load was 30 N, there were 13 parameters that maintained a strong correlation; these parameters include Sa, Sq, Sv, St, Sz, Str, Sal, Sdq, Sdr, Spk, Svk, Sk, and Sdc; and (3) when the load was 40 N, there were 13 parameters, namely: Sa, Sq, Sv, Sku, Sz, Str, Sal, Std, Sdq, Sdr, Svk, Sk, and Sdc that maintained a strong correlation.

MEIE-2023
Table 2 summarizes the autocorrelation analysis results, indicating that if the difference of load is not considered, there are eight parameters, namely, Sa, Sq, Sv, Sdc, Str, Sdq, Sdr, and Sk that maintain a strong correlation.Table 3 summarizes that: (1) when the speed was 20 r min1, there were eight parameters that maintained a strong correlation, and these parameters include: Sa, Sq, Sv, Str, Sdq, Sdr, Sdc, and Svk; (2) when the speed was 40 r min1, 17 parameters, including Sa, Sq, Sv, St, Sz, Str, Sdq, Sdr, Svk, Sk, Sdc, Sbi, Sci, Svi, Sp, Ssk, and Sku maintained a strong correlation; and (3) when the speed was 60 r min1, 15 parameters maintained a strong correlation, and these parameters include: Sa, Sq, Sv, Sku, Sz, Str, Sal, Std, Sdq, Sdr, Svk, Sk, Sdc, Sr2, and Sp.
Similarly, the autocorrelation analysis results presented in Table 3 indicate that if the difference of speed is not considered, eight parameters, namely Sa, Sq, Sv, Sdc, Str, Sdq, Sdr and Svk, maintain a strong correlation.
Both Sq and Sa characterize the average height of surface topography and their numerical values were found to be similar, in the following analyses, Sa will be not used to characterize the surface.The changes of topography parameters Sq, Sv, Sdc, Str, Sdq, Sdr, Sk, and Svk were further analyzed.Figure 4 exhibits the following results: (1) the correlation of the parameter Sq is positively associated with the load.This parameter exhibits an extremely strong correlation under small-speed and medium-speed conditions, and a strong correlation under high-speed conditions.It proves a strong correlation under different working conditions; (2) the parameter Sv is strongly correlated under small load or high-speed, and the overall correlation is extremely strong; (3) the correlation of the direction parameter Str is slightly affected by load and speed, and the overall correlation is extremely strong; (4) the correlation of the parameter Sdq shows positive association with the load.This parameter exhibits a strong correlation under medium-speed and high-speed conditions and a strong correlation under low-speed conditions.It exhibits a strong correlation under different working conditions.The parameter Sdc also exhibits this law; (5) the parameter Sdr is positively correlated with the load.This parameter exhibits an extremely strong correlation under different working conditions; (6) the correlation of the parameter Sk exhibits a medium intensity correlation under low-speed conditions, a strong correlation under a medium or small load, and a strong correlation under a medium-speed and high-speed or a large load.Furthermore, it also exhibits a strong correlation under different working conditions; and (7) the parameter Svk shows positive correlation with the load.This parameter is strongly correlated at low-speed and extremely strongly correlated at medium-speed and high-speed, and the parameter proves a strong correlation under different working conditions.

Cross-correlation analysis
The cross-correlation analysis was carried out to analyze the combination correlation of any two topography parameters based on the result of analysis mentioned above.Thus, 30 cases were obtained by correlation analysis of any two topography parameters.Owing to the abnormal performance of Svk, it was analyzed separately.The cross-correlation analysis results of extracted surface characterization parameters after removing Svk are presented in Figure 4.  Through cross-correlation analysis, the correlation coefficients between the parameter Svk before running-in and the parameters Sq*, Sdc*, Sdq*, Sdr*, and Sk* are 0.679, 0.523, 0.633, 0.629, and 0.527, respectively.Nevertheless, the correlation coefficients between the parameter Svk* and the parameters Sq, Sdc, Sdr, and Sk before running-in are 0.805, 0.808, 0.8, 0.779, and 0.765, respectively.Thus, the correlation between the parameter Svk before running-in and the other five parameters was further analyzed under different working conditions.The analysis results are shown in Figure 5. Figure 6 shows that: (1) the correlation between the parameter Sq* and the parameter Svk is positive with the load.Moreover, the parameters Sdq* and Sdr* also show this similar relationship; (2) the parameter Sdc* and the parameter Svk exhibits a weak correlation under small-and medium-load conditions, but exhibits an extremely strong correlation under high-load conditions.This similar relationship is also represented by the parameter Sk; (3) the correlation between the parameter Sdc* and the parameter Svk decreases with the increase of the speed, and the overall correlation is of medium intensity; (4) the correlation between the parameters Sq*, Sk*, Sdr*, Sdq*, and the parameter Svk, respectively, changes with the speed and follows a similar trend, and the correlation between the four parameters and the parameter Svk, respectively, is stronger when the speed is 40 r min1 than that for the other two speeds.

Conclusions
In this study, different experiments were designed to analyze the effect of different working conditions and unworn surface topography on the surface topography after wear.Based on the experiments, the conclusions were obtained: The topography after this process is relative to the working conditions and the unworn topography, which confirms the correlation of the surface topography parameters.There are eight parameters, namely, Sa, Sq, Sv, Sdc, Str, Sdq, and Sdr that maintain a strong autocorrelation under different working conditions.Moreover, the height parameter Sq exhibits a strong correlation with some hybrid parameters after running-in.The hybrid parameter Sdq and Sdr are highly correlated with the height parameters, functional parameters, and hybrid parameters (Sdr*, Sdq*).The function parameters Sdc and Sk are highly correlated with the hybrid parameters, height parameters, and functional parameters (Sdc*, Sk*).Through cross-correlation analysis, the coefficients of correlation between the parameter Svk* the parameters (Sq, Sdc, Sdr, and Sk) are all larger than 0.7.Nevertheless, the correlation coefficients between the parameter Svk and the parameters (Sq*, Sdc*, Sdq*, Sdr*, and Sk*) are abnormal.
Running-in wear is a complex process, involving a large number of working conditions and surface topography features.If the running-in process can be used as a black box model to perform reverse modeling of input and output, different discoveries may be brought about.In general, the more the input features of the model, the more the comprehensive information the model needs; however, at the same time, the complexity of the model is increased, and the ac-curacy of the model is reduced.Thus, selection of the input features is required.At the same time, the number of output variables needs to be reduced to avoid insufficient input dimensions, resulting in a decrease in output accuracy.How to make a selection to reduce input and output features requires special care to avoid important features being removed and unimportant features being retained.Therefore, in the future study, some parameters before wear can be employed to predict some parameters after it, and then the surface topography after running-in can be predicted from the results based on unworn surface topography.Thus, a modeling direction for surface topography parameter prediction based on the unworn topography can be achieved.At the same time, it is of great significance to optimize the surface topography of the sliding friction pair, improve its performance, and extend the service life.

Figure 1 .
Figure 1.Wear rate (left) and typical changes of friction coefficient (right) during running-in.

Figure 2 .
Figure 2. Initial topography of the four surfaces used in the running-in experiments and characterized by parameters.According to the running in experiment designed above, the surface morphology was measured at the 6th minute during the experiment to obtain the surface morphology of the friction coefficient running in and wear rate running in.In this study, four types of surface morphologies with different textures

Figure 3 .
Figure 3. Boxplots for surface texture parameters comparing worn and wear-free surface.

Figure 4
Figure 4 presents the analysis results of the autocorrelation coefficients of extracted parameters under different working conditions.

Figure 4 .
Figure 4. Autocorrelation coefficient of extracted parameters under different working conditions.

Figure 5 .
Figure 5. Cross-correlation of extracted characterizing parameters under different working conditions.

Figure 6 .
Figure 6.Cross-correlation coefficient of the parameter Svk before running-in and the other five parameters after running-in under different working conditions.

Table 1 .
Parameters for surface topography evaluation by the areal method.

Table 2 .
Autocorrelation coefficients based on different loads.

Table 3 .
Autocorrelation coefficients based on different speeds.