Validation of the Optimal Points of Tribological Systems at Different Temperatures Determined by the DOE Method Using Lubricating Oil Doped with Nano-ZrO₂ Particles ^†

Abstract

In this study, the design of experiments (DOE) method is used to find the optimum values of the tribological system in a 40–120 °C range with 0.1–1 wt% zirconia nanoadditives in a base oil. Significant factors were identified. The studied parameters include friction absolute integral, static friction, the wear scar diameter and the wear volume of the specimens. The measurements were carried out on a tribometer. The results were pre-estimated using statistical software; then, validation measurements were made using the estimated optimum point. The results show that the FAI value differed by 0.008, the COF value by 0.017, the WSD value by 4 μm and the WV value by 110,000 μm³. At 1 wt%, zirconia can have a positive effect at high temperatures. As temperatures increase, wear parameters decrease and friction values remain stable.

1. Introduction

In recent decades, nanotechnology has become a new field of research. Its primary motivation has been environmental protection, sustainability and cost reduction in line with rising energy prices. Results show that metal–ceramic nanoparticles mixed with lubricating oil can significantly reduce wear and friction, which is particularly important in the automotive sector [1]. The use of nanoparticles allows the lubricating oil to maintain its optimum performance for a more extended period, thus reducing the frequency of oil and, eventually, component changes in an environmentally friendly way. Nanoadditives can also be used in bio-lubricants [2].

The design of experiments (DOE) method simplifies study design, data analysis, visualization, modeling factor interactions, and predicting unknown ranges. It improves resource utilization, productivity and product quality while reducing costs and time by predicting tribological values [3]. Correlations can also be observed after testing.

Since base oils alone do not provide sufficient friction and wear reduction in operating conditions where a suitable fluid film has not yet formed, additives can be a solution. Researchers have studied the tribological effects of different nanoceramics. The application of nanoceramics is driven by their nanoscale (1–100 nm) and material quality. Peña-Parás et al. have found a correlation between nanoparticle size and the surface roughness of the contact surface. They found that these particles are effective when their diameter is smaller than the surface’s average roughness. Particles with larger diameters cannot be absorbed into surface roughness valleys, leading to three-body abrasion [4]. Various working mechanisms have been reported in the literature to explain the observed results, like rolling (or ball bearing) mechanisms; mending mechanisms; filling up the surface roughness grooves; polishing and the forming of a protective layer (or tribofilm) [5]. Ma et al. added 6–7 nm zirconia nanopowder to low-flammability cyclopentane oil and studied its effect on friction and wear with an Optimol SRV tribometer. At 2 wt% zirconia, the load-bearing capacity increased at all tested temperatures, wear volume was significantly reduced and a ceramic tribofilm formed on contact surfaces during friction with the additive [6]. Ouyang et al. studied yttria-stabilized zirconia composites, examining several mixtures, including graphite and molybdenum disulfide, to form a lubricating film. These additives reduced friction at low temperatures due to chemical and structural degradation. [7]. Li et al. used an experimental design to investigate the parameters of the plasma spray process for yttria-stabilized zirconia coatings. They determined that third-order regression equations were the most suitable for identifying the effects of the examined process parameters [8]. Cyriac et al. studied the impact of temperature change on organic additives in lubricating oils. They tested ZDDP and GMO additives at 90 and 140 °C, which showed positive effects at high temperatures [9]. The paper’s aim will be achieved if the doped oil sample shows a positive result, and validation is accurately estimated using statistical software. A commonly used parameter for measuring friction is the coefficient of friction (COF), the maximum friction value during a stroke. This is calculated by measuring normal force and friction force. The friction force is measured using piezoelectric sensors. Continuous recording of these values during a stroke creates a curve, and the area under it is the friction absolute integral (FAI) value. These values can be used to represent the friction of a system.

2. Materials and Methods

The required measurements for this article were carried out at the University of Győr. The research aimed to determine the tribological effect of specific parameters on the system using zirconia-doped oil. Two parameters were changed during the tests and investigated by their tribological effects. Temperature is a relevant environmental effect that can alter the properties of the oil being applied, and concentration percentage is an element that can be varied to determine the effect of the additive used. Lubricating oil samples were prepared with different concentrations for the measurements. The range of the measurements was determined to be between 0.1 wt% and 1 wt%, while the temperature was interpreted to be between 40 °C and 120 °C. The design of experiments (DOE) method determines the exact position of several points within the measurement range. This article used a face-centered central composite design. This design has no extended region, and the measurements are written in squares. The measurements were designed and analyzed using statistical software. The measuring points were realized at 0.1 wt%, 0.55 wt% and 0.1 wt% zirconia content, each at 40 °C, 80 °C and 120 °C. These points (9) were used for the analysis. Four measurements were made at each point.

The lubricating oil samples should be prepared at 0.1 wt%, 0.55 wt% and 0.1 wt%. Group III 4 cSt base oil, toluene (CAS 108-88-3) and surface-activated zirconia were mixed during the preparation. Zirconia content was determined at the percentages specified above (error in accuracy is around ±0.01 g), and toluene was determined by multiplying the number of measurements by five times the desired additive percentage. Zirconia was treated with the surface activation mentioned earlier, meaning that an ethyl oleate layer formed on its surface. This reduced undesirable size growth and agglomeration formation and increased the lifetime and stability of the oil sample. Surface-activated nanoceramics were prepared based on a paper by Tóth et al. [10]. The lubricating oil samples were mixed on a magnetic stirrer for 16 h before measurement and on an ultrasonic stirrer for 15 min immediately before starting measurements.

A disk specimen and a ball specimen were used for the tribological measurements that slide on each other. The material properties of these are shown in

Table 1. Material properties of the specimens used.

Specimen	Disk	Ball
Size	⌀24 mm; 6.8 mm height	⌀10 mm
Material grade	100Cr6 (1.3505)	100Cr6 (1.13505)
Rockwell scale	62 ± 1 HRC	60 ± 2 HRC
Surface roughness (Ra)	0.047 ± 0.003 μm	0.025 ± 0.005 μm

. Before each measurement, the test specimens were cleaned in an ultrasonic cleaner at 50 °C for 15 min.

Lubricating oil samples and specimens are tested on an Optimol SRV5 tribometer equipped with an oscillating module. The disk and ball specimens are placed in the machine in this measurement. The part that grips the disk is fixed while the ball is fitted to the oscillating frame so that the ball moves on the disk’s surface, creating wear. The measurement programs have been prepared in accordance with ISO 19291:2016 [11]. The measurement time for each measurement was 2 h and 30 s, of which the measurement started with a 50 N preload for 30 s, followed by applying a force of 100 N. The measurements were made at a stroke length of 1 mm and at a frequency of 50 Hz, with an oiling rate of 225 mL/hour. The tribometer can directly measure the friction absolute integral (FAI) and stiction (COF) values. The FAI value is the area under the curve of the friction coefficient values measured over the entire stroke length recorded at a 25 kHz frequency:

$$\mathrm{F}\mathrm{A}\mathrm{I}={\displaystyle \frac{1}{s_{max}}}{\int }_{s_0}^{s_{max}}\left|\mu \left(s\right)\right|ds$$

(1)

where ‘s’ is the stroke and ‘μ’ is the coefficient of friction. The COF is the maximum coefficient of friction per stroke. In an oscillating motion, it is typically given at the dead center.

The results were further investigated by measuring the ball specimen’s wear scar diameter (WSD) using a Keyence VHX-1000 digital microscope (Osaka, Japan) and the disk specimen’s wear volume (WV) using a Leica DCM 3D confocal microscope (Wetzlar, Germany).

3. Results

The results of the measured values were analyzed using statistical software. The software results contain a contour plot, Pareto analysis and regression equation. In the contour diagram, red colors represent tribologically unfavorable values and green colors represent favorable ones. These values have not been assigned an exact range but have been scaled based on the values tested in the system. A Pareto analysis examines the parameters that significantly affect the system. A significance level of 5% (commonly used) was applied, shown as a red dashed line. A two-sided confidence level of 95% was used.

First, the results of the friction absolute integral (FAI) values are presented. The Pareto analysis in Figure 1 shows that the FAI value is significantly influenced by the zirconia concentration percentage (%), temperature (T) and the linear effect of these two parameters. The quadratic effect of temperature is also not negligible. The contour plot shows that the most favorable value at the system level is achieved at high concentration percentages (>0.6 wt%).

By examining the coefficient of static friction (COF) values, it can be concluded that the system is significantly affected by the zirconia content in the oil, the temperature and the squared effect of the temperature, as shown in Figure 2. Also, the chosen nanoceramics show the best enhancement effect at a high weight percent in terms of COF values. The enhancing effect can be already observed at the lowest level of doping.

Summarizing the friction contour plots:

• Similar trends can be observed;
• Lowering the amount of nanoadditives at high temperatures correlates with increased friction;
• Selecting a specific temperature shows that friction in the system can be reduced with increasing nanoparticle concentrations;
• At a high (1 wt%) zirconia concentration, the tribological system’s friction is less responsive to temperature changes; friction remains relatively stable despite temperature variations;
• Nanoscale zirconia may function effectively as a friction-reducing additive.

For the wear scar diameter (WSD) values, the effect of zirconia weight percent and the combined linear effect of the two examined parameters exceeds the significance level. Figure 3. shows that high percentages represent the smallest, most favorable values for the wear scar diameter. The results show that the lowest WSD value at the system level is above 75 °C.

The wear volume (WV) measured with a confocal microscope is analyzed. Zirconia weight percentage, temperature and the squared effects of temperature have a statistically significant impact on the wear volume. Of these, the most important is the zirconia concentration. The response surface diagram (Figure 4) shows a favorable value at 120 °C and a zirconia content of 1 wt%. Generally, in terms of WV, it reaches its tribologically most unfavorable value at around 75 °C in the investigated system. The wear values show that using zirconia can reduce wear in the system under test.

The results were validated using a multi-variable optimization approach using statistical software, minimizing all four parameters together (with compromises). The software predicted an optimum point of 1 wt% zirconium content and 109 °C. Three validation measurements were performed in these settings, and the estimated results were compared with the actual measurements. The differences between the software-estimated values and the validation results can be seen in

Table 2. Comparison table for estimated and validated results (1 wt% zirconia and 109 °C).

Parameter	Estimated	Validated	Abs. Difference	Rel. Difference
FAI	0.137	0.129	0.008	5.8%
COF	0.209	0.192	0.017	8.1%
WSD	469 μm	466 μm	3 μm	0.7%
WV	219,422 μm3	108,626 μm3	110,796 μm3	50.5%

. The DOE method has been used to identify the region where the most favorable values can be achieved at the system level. The FAI, COF and WSD values are accurately estimated within an 8.1% difference. For WV, the absolute difference is acceptable, but the relative deviation from the software-calculated value is large. The wear volume depends on several factors, most of which are still unknown and which are to be explored in the future.

4. Conclusions

In conclusion, it can be stated that using zirconia nanoceramics in Group III base oil can have an enhancing tribological effect even at high temperatures and high concentrations. Using the DOE method, it was found that temperature significantly impacts friction and wear volume. Zirconia has the most significant effect on friction and wear results. The results show that oil samples with 1 wt% zirconia have the most favorable values. The friction and wear-reducing effect of zirconia nanoparticles has been confirmed. Validating measurements at 109 °C with a 1 wt% zirconia nanoparticle additive has reduced friction by 5.8–8.1% and wear diameter by 0.7%, as estimated by the design of experiments (DOE) method. The relative difference in wear volume was 50.5%, reflecting the substantial reduction in wear due to very low absolute wear values (0.1–0.2 mm³).

The research provides a better understanding of the effect of a parameter, aiding result analysis beyond one-dimensional bar charts, and reveals temperature’s and zirconia content’s impact on wear and friction. The authors’ plans include investigating different parameters effects (even combined) (e.g., load and frequency) and eventually testing nano-doped oils in real-world conditions as a long-term plan. With the studies carried out so far, it is not yet possible to determine the effects of these oils under real conditions.