**3. Results**

## *3.1. Ball-on-Disk Wear*

Wear rate as a function of surface roughness for all EM greases is shown in Figure 2a. For smooth surfaces, the wear rates of the four greases are similar, although the lowest wear is observed for the MP. In contrast, there is more differentiation between the greases on rougher surfaces, where the ML consistently exhibits the lowest wear rate. In addition, for these testing parameters, greases with mineral base oil have lower wear rate than the synthetic base greases.

**Figure 2.** Wear results from EM grease ball-on-disk tests. (**a**) Wear rate as a function of roughness and (**b**) change in wear rate with roughness at 100 ◦C. (**c**) Wear rate as a function of temperature and (**d**) the change in wear rate with temperature at 35 nm Ra (composite Ra of 40 nm) for MP and ML.

The sensitivity of wear rate to changes in roughness was quantified as the slope of a linear fit to the data. Although this analysis is based on an assumption that wear rate increases linearly with roughness, the approach enables direct comparison of the greases. The slope calculated from a linear fit to the wear rate versus roughness data is shown in Figure 2b. This analysis indicates that wear rate with the ML grease is the least dependent on surface roughness. In addition, of the tested greases, greases with mineral base oil have less wear-roughness dependence than the synthetic base greases.

Wear rates at different temperatures are shown in Figure 2c. At 40 ◦C, there is no observable wear for any of the greases. The lowest wear rate at 100 ◦C is observed for the ML grease and, at 150 ◦C, is found for the SL grease. Additionally, at 100 and 150 ◦C, for the greases tested here, lithium thickened greases have a lower wear rate than their polyurea counterparts.

The temperature dependence of the wear rate is very different for synthetic versus mineral based greases. Specifically, the wear rate increases approximately linearly between 100 and 150 ◦C for the mineral greases, but is nearly constant for the synthetics. Due to this behavior, the linear approximation cannot be used to quantify the change of wear rate with temperature for the synthetic greases. However, the linear fit was performed for the mineral greases as shown in Figure 2d. The wear rate is less dependent on temperature for the ML grease than the MP grease.

## *3.2. Ball-on-Disk Friction*

Friction results for each grease are shown in Figure 3. On average, friction increased with surface roughness for all greases (see Figure 3a). In addition, on most surfaces, friction was lowest for the SL grease. On the rougher surfaces, the ML also exhibited low friction behavior. For these tests, the lithium based greases had lower friction than the polyurea greases, except on the smoothest surfaces where the friction coefficient was below 0.08 for all greases.

**Figure 3.** Friction results from EM grease ball-on-disk tests. Friction coefficient (**a**) as a function of surface roughness at 100 ◦C and (**b**) as a function of temperature at 35 nm Ra (composite Ra of 40 nm).

Friction at three different temperatures is shown in Figure 3b. At 40 ◦C, the lowest friction was exhibited by the SP grease whereas, at 100 ◦C, the SL grease had the lowest friction. At both 40 and 100 ◦C, the friction was lower for synthetic greases than their mineral counterparts. At 150 ◦C, the friction coefficient was comparable for all four greases.

The friction trends with respect to roughness and temperature are not linear. This is primarily because both roughness and temperature affect the lubrication regime. Further, increasing temperature can promote grease bleed such that the degree of starvation decreases with increasing temperature [16]. So, the effect of these parameters on friction cannot be quantified using a simple linear fit. Instead, these trends will be analyzed in the context of the Stribeck curve, as discussed later.

## *3.3. 4-Ball Test*

Results from the 4-ball tests are shown in Figure 4. ML had the lowest wear across all three bearing configurations. The performance of ML might be attributable to thicker lubricating films that provide more separation between interacting surfaces or better antiwear film formation. For the SS<sup>3</sup> and NS<sup>3</sup> configurations, average wear increased as ML < MP < SP < SL. However, this trend cannot be directly explained since the 4-ball test is primarily measuring anti-wear behavior, and the additive composition of these commercial greases is unknown. For the SN<sup>3</sup> configuration, wear was high for all four greases, and large error bars precluded direct comparison between the greases.

**Figure 4.** Wear area for four greases and three bearing configurations measured using the 4-ball test. Representative wear patterns (from left to right): SS<sup>3</sup> circular wear scar on steel ball, NS<sup>3</sup> circular wear scar on steel ball, and SN<sup>3</sup> elliptical wear scar on ceramic ball.

Comparing the different material combinations, for all greases, the lowest average wear was observed for NS3, followed by SS<sup>3</sup> and then SN3. The observation that wear for NS<sup>3</sup> was lower than that for SS<sup>3</sup> is consistent with previous reports that grease life with hybrid bearings is longer than with standard bearings [26]. Lower wear for NS<sup>3</sup> is also consistent with experimental and anecdotal observations that sugges<sup>t</sup> longer lives for hybrid bearings than estimated by the Lundberg-Palmgren equations [30].

In contrast, the SN<sup>3</sup> configuration consistently had very high wear. This configuration also exhibited qualitatively very different behavior than the other two material pairs. As shown in the insets to Figure 4, the wear scars for the SS<sup>3</sup> and NS<sup>3</sup> configurations are circular, while those for the SN<sup>3</sup> are elliptical. The wear mechanism of the rotating elements determine and may cause non-circular wear scars of the stationary balls [39]. Therefore, the difference may be attributable to the hardness of the rotating element. For SN3, the steel ball is the rotating element attached to the spindle (upper ball), while the three lower balls are silicon nitride. Material hardness affects material wear; a softer steel ball rotating on a harder ceramic ball causes the wear scar to elongate with increasing material deformation, thus causing relative displacement between the upper and lower balls.

## **4. Analysis & Discussion**

*4.1. Lubrication Regime Analysis*

The friction results shown in Figure 3 suggests that changing either roughness or temperature caused a transition between lubrication regimes. The lubrication regime can be determined by the lambda ratio:

$$\lambda = \frac{h}{\left(Ra\_{ball}^2 + Ra\_{disk}^2\right)^{1/2}},\tag{1}$$

where *h* is the film thickness, *Raball* is the average roughness of the ball, and *Radisk* is the average roughness of the disk. Although the exact values of *λ* corresponding to transitions between lubrication regimes vary in the literature, they are often defined by *λ* - 3 for full film lubrication, 1 *λ* 3 for mixed lubrication, and *λ* 1 for boundary lubrication [34,40,41]. However, these transition values are not absolute, and studies have shown that full film or mixed lubrication is possible even in cases where *λ* would typically sugges<sup>t</sup> boundary lubrication (e.g., *λ* 1) [41].

For bearings, the *λ* ratio also affects contact fatigue life. Low *λ* ratios are associated with surface deformation and distress [2]. In the context of the conditions studied here, small surface roughness and low temperature conditions that correspond to higher *λ* ratios will have lower contact fatigue and longer life.

To calculate *λ*, we first had to determine film thickness. It is known that the film thickness of a grease may be larger or smaller than the film thickness for its base oil, depending on the operating conditions [12,34]. However, there is no standard equation or method of calculating grease film thickness that is applicable for all conditions. Therefore, as a first order approximation, we calculated film thickness using the Hamrock and Dowson equation [2] for central film thickness with parameters for the base oil:

$$h \approx h\_{\varepsilon} = 2.69 R \left(\frac{1 l \eta}{ER}\right)^{0.67} (aE)^{0.53} \left(\frac{W}{ER^2}\right)^{-0.087} (1 - 0.61 \varepsilon^{-0.73k}),\tag{2}$$

where *U* is the speed, *R* is effective radius, *E* is effective elastic modulus, *α* is the pressureviscosity coefficient, *η* is the ambient viscosity, *W* is the load, and *k* = 1 for a spherical geometry. Most of these parameters are constant for the ball-on-disk tests. However, the ambient viscosity and pressure-viscosity coefficient were calculated for each test based on the rheological properties of the base oil and the temperature. Table 2 summarizes the film thickness and *λ* ratio for each EM grease, temperature, and roughness case considered in this study.

The friction measured from the ball-on-disk tests is plotted as a function of the calculated *λ* ratio to create a Stribeck curve in Figure 5. The large *λ* cases correspond to tests run on smooth surfaces and at lower temperatures. Conversely, rough surfaces and high temperatures lead to small *λ* ratios. The general shape of the Stribeck curve in Figure 5 indicates that our tests included the mixed regime, where friction decreases with *λ*, and the full film regime, where friction increases with *λ*.


**Table 2.** EM grease calculated film thickness (*hc* in nm) and lambda (*λ*) ratio at all tested composite roughness and temperature combinations.

The greases clearly exhibit full film at larger lambda ratios. In this regime, the lowest friction was exhibited by the SP and SL (synthetic greases). The mixed regime is clearly observed at small *λ* ratios. Here, as composite roughness increases, *λ* values decrease, and friction tends to increase. In mixed lubrication, the lowest friction was observed for the ML and SL (greases with lithium thickener). Across most of the lubrication regimes measured, SL had the best friction performance.

**Figure 5.** Stribeck curve based on measured friction and calculated *λ* ratios for four greases tested across all roughness and temperature conditions.

The transition between the full film and mixed lubrication regimes is important because both friction and wear are higher in the mixed regime due to asperity contacts in the interface. Therefore, it is desirable to remain in the full film regime as long as possible. To identify the *λ* ratio at which the full film-mixed transition occurs for each grease, we found the intersection of a linear fit to the data in the mixed regime and a linear fit to the data in the full film regime. The two largest *λ* ratios for each grease were fit for full film, and the three smallest *λ* ratios were fit for the mixed regime. Figure 6 shows the linear fits and their intersection which was identified as the transition lambda (*λt*). The *λt* values for each grease were found to be: SP at *λt* = 0.48, MP at *λt* = 0.47, ML at *λt* = 0.37, and SL at *λt* = 0.58.

The ML grease had the lowest *λ<sup>t</sup>*, indicating that the interface would remain in the full film regime the longest with increasing temperature or roughness. However, it is important to note that ML also has higher friction in this transition region. So, ML's lower *λt* suggests the lubricant is able to maintain a thicker lubrication film than the other greases, but this comes at a cost of higher viscous friction. On the other hand, SL has a larger *λt* value but considerably lower friction than the rest of the tested greases in this transition range. In fact, despite having a larger *λt* value, SL maintained lower friction at most test conditions. This analysis shows there is a compromise between low friction in full film lubrication and how long the interface will remain in that regime before the onset of mixed lubrication.

**Figure 6.** Independent linear fits performed for the mixed and full film regimes for (**a**) SP, (**b**) MP, (**c**) ML, (**d**) SL. The intersection of the two lines corresponds to the transition lambda *λt*.

#### *4.2. Predicted Lubrication Regime Transitions*

The *λ* ratio determines lubrication regime, as well as contact fatigue. In our study, this critical ratio is determined by surface roughness, grease properties and temperature. So, for a given grease, roughness, and temperature, the *λ* value can be calculated, and the conditions at which the lubrication regime transitions to mixed can be predicted.

Surface roughness affects this calculation directly, as it appears in the denominator of Equation (1). Temperature indirectly affects the film thickness as calculated using Equation (2) through its effect on *η* and *α*. The grease itself determines the values of *η* and *α* and their temperature dependence. To predict *λ* for any temperature *T*, we used a linear equation for *α*(*T*) and the Vogel equation [2] for *η*(*T*), both fit to available grease data. Then, *λ* was calculated directly using the equations for *α*(*T*) and *η*(*T*), combined with Equations (1) and (2).

This analysis was performed for each grease at temperatures ranging from 30 to 200 ◦C and composite roughness values from 20 to 200 nm Ra. The predicted *λ* values are shown as color contour plots in Figure 7. In addition, shown are horizontal planes corresponding to *λ<sup>t</sup>*, the ratio at the transition between mixed and full film lubrication, identified from the friction data for each grease in Figure 6. The intersection between this plane and the surface predicted as described above indicates the temperature and surface roughness at which the interface will transition from full film to mixed lubrication. Such an approach

can be used as part of the design process to guide selection of a grease, surface roughness specifications, or prescribed limits on operating conditions.

**Figure 7.** Contour plots with predicted *λ* ratios for each of the four commercially available EM greases: (**a**) SP, (**b**) MP, (**c**) ML, and (**d**) SL. The transition between full film and mixed lubrication (*λt*) is shown as a horizontal plane.

## *4.3. Grease Evaluation*

The four greases evaluated in this study exhibited varying levels of performance at different surface roughness and temperature conditions. These observations are summarized briefly here.

As observed in Figure 2a, MP had the lowest wear rate on smooth surfaces, while ML had the lowest wear on rough surfaces. ML was also found to exhibit the least dependence of wear rate on surface roughness. On average, greases with mineral base oil had lower wear rate and roughness dependence than the synthetic base greases. In high temperature tests (150 ◦C), the lowest wear rate was found for the SL grease. In addition, the wear rate of the synthetic greases did not change with temperature at high temperatures, while an increase in wear rate with temperature was observed for the mineral greases. In the 4-ball tests, ML had the lowest wear across all the various bearing configurations. For the SS<sup>3</sup> and NS<sup>3</sup> configurations, average wear increased as ML < MP < SP < SL. Larger wear rates increase material debris, which can have implications, such as artificial surface roughness, reduced lubricating capabilities, and abrasion/erosion, so low wear is extremely important.

In terms of friction, on most surfaces, friction was lowest for the SL grease. For rougher surfaces, the lithium greases generally had lower friction than the polyurea greases. On very smooth surfaces, the synthetics had lower friction than the mineral based greases. In terms of temperature, at 40 ◦C, the lowest friction was exhibited by the SP grease whereas, at 100 ◦C, the SL grease had the lowest friction. At both 40 and 100 ◦C, the friction was lower for synthetic greases than their mineral counterparts. The friction data was also used to determine transitions between the full film and mixed lubrication regime. This analysis showed that under these testing parameters, ML had the lowest *λ<sup>t</sup>*, indicating that the interface would remain in the full film regime the longest with increasing temperature or roughness. However, ML also had higher friction in this transition region indicating that the lubricant maintained a thicker lubrication film at a cost of higher viscous friction. In contrast, SL had a larger *λt* ratio but considerably lower friction than the rest of the tested greases in this range.

While the comparisons between greases in terms of individual performance metrics are valuable, they need to be combined to determine which grease is best for a given application. Therefore, it is necessary to develop a grease evaluation and comparison method to assess these commercially available greases. Performance metrics included are low temperature (40 ◦C) friction, low surface roughness (10–60 nm Ra) friction and wear, high surface roughness (120–200 nm Ra) friction and wear, high temperature (100–150 ◦C) friction and wear, wear dependence on surface roughness, and NS<sup>3</sup> (best represents EM hybrid bearings) wear from the 4-ball tests. The ranking system was developed with EM bearing applications in mind, so high temperature friction and wear were given twice the weight of the other metrics. The greases were ranked 1 through 4 (or 8 for high temperature parameters), where 4 (or 8) was best. The results are shown as radar plots in Figure 8.

The individual rankings for each grease were summed to give an overall score, shown next to the radar plots in Figure 8. Based on the overall score, for the testing parameters used here, the two lithium greases outperformed the two polyurea greases (SL = 34 > ML = 31 > SP = 25 > MP = 22). The overall score can also be separated into a friction rating and a wear rating, both of which are reported next to the radar plots in Figure 8. In terms of friction performance, the results indicate that the synthetic greases had better overall friction performance than the mineral based greases (SL = 19 > SP = 14 > ML = 10 > MP = 7). Consistent with the overall rating, SL exhibited the best friction performance, particularly at high temperatures. However, different trends are observed for wear, and the overall wear scores indicate that mineral greases outperformed their synthetic counterparts (ML = 21 > SL = 15, MP = 15 > SP = 11). The ML exhibited the best wear performance and, particularly, the least dependence of wear on surface roughness. MP and SL were tied for the second-best, but the good rating of SL was largely due to its low wear at high temperature whereas MP outperformed SL in all other wear metrics, particularly wear at low surface roughness.

Generally, the overall ratings, along with the radar charts themselves, serve as guidelines with which a designer can evaluate each grease based on metrics important for the application being considered. However, it should be noted that long duration and high speed bearing/grease life tests would be useful as another metric to include in this type of analysis for grease evaluation for EM applications.

**Figure 8.** Grease ranking system based on a 1 to 4 scale (or 1 to 8 for high temperature parameters). A ranking of 4 (8) corresponds to best and 1 to worst. Low temperature is 40 ◦C, high temperature is 100–150 ◦C, low Ra is from 10–60 nm Ra, and high Ra from 120–200 nm Ra.
