Trends in Lubrication Research on Tapered Roller Bearings: A Review by Bearing Type and Size, Lubricant, and Study Approach

Abstract

A tapered roller bearing (TRB) is a specialized type of bearing with a high load-to-volume ratio, designed to support both radial and axial loads. Lubrication plays a crucial role in TRB operation by reducing friction and dissipating heat generated during rotation. However, it can also negatively impact TRB performance due to the viscous and inertial effects of the lubricant. Extensive research has been conducted to examine the role of lubrication in TRB performance. Lubrication primarily influences the frictional characteristics, thermal behavior, hydraulic losses, dynamic stability, and contact mechanics of TRBs. This paper aims to collect and classify the scientific literature on TRB lubrication based on these key aspects. Specifically, it explores the scope of research on the use of Newtonian and non-Newtonian lubricants in TRBs. Furthermore, this study analyzes research based on TRB size and type, considering both oil and grease as lubricants. The findings indicate that both numerical and experimental studies have been conducted to investigate Newtonian and non-Newtonian lubricants across various TRB sizes and types. However, the results highlight that limited research has focused on non-Newtonian lubricants in TRBs with an Outer Diameter (OD) exceeding 300 mm, i.e., those typically used in wind turbines, industrial gearboxes, and railways.

1. Introduction

Bearings are mechanical components designed to minimize friction and support loads during mechanical motion, such as the rotation or linear movement of shafts in machines. They ensure stable motion and enhance the lifespan of mechanical systems. Bearings are classified into various categories based on the type of load they support. One such type is the tapered roller bearing (TRB), which features tapered inner and outer raceways with cone-shaped rollers. These rollers are arranged so that their axes converge at the bearing axis. This unique design enables TRBs to support both high radial and axial loads.

There are two primary types of TRBs: single-row and double-row. The single-row TRB supports radial and axial loads in one direction, whereas the double-row TRB, due to its additional set of tapered rollers, accommodates higher radial and axial loads in both directions [1]. These configurations are illustrated in Figure 1.

In TRBs, the line contact between the rollers and raceways can lead to significant Load-Dependent Power Losses $\left(P_{LB}\right)$. If the lubricant film thickness in the contact zone is insufficient, asperity contact may occur, leading to increased stresses, heat generation, and a negative impact on the thermal stability, dynamic performance, and fatigue life of the bearing. Proper lubrication is therefore essential for enhancing efficiency and ensuring smoother operation. It helps reduce heat generation due to $\left(P_{LB}\right)$ while simultaneously dissipating heat to maintain the bearing temperature within the designed range.

However, lubrication can also have adverse effects on TRB performance by increasing Load-Independent Power Losses $\left(P_{L{B}_o}\right)$, also known as hydraulic power losses. These losses result from the viscous (drag) and inertial (churning) effects of the lubricant interacting with moving components within the bearing [2].

Generally, two types of lubricants are used in TRBs: oil and grease. The choice of lubricant depends on the bearing’s operating conditions. Due to its free-flowing nature, oil is well suited for high-temperature and high-speed applications. Its low viscosity facilitates easy circulation within the TRB. In contrast, grease provides better leakage control, prevents dry starts, and remains within the bearing for an extended period. However, grease exhibits complex non-Newtonian behavior, making its flow characteristics more challenging to predict and understand. Proper lubrication can only be achieved if the tribological behavior of lubricants inside the TRB is thoroughly analyzed and optimized [3]. Additionally, additives are often used to enhance the lubricating properties of the lubricant, while contaminants can negatively impact its viscosity and lubricity [4].

TRBs, as mentioned above, supports both radial and axial loads; therefore, they are used in mechanical systems that involve both radial and axial loads. These bearings are commonly used in industrial and automotive applications, particularly in gear trains, rails axles, and wind turbines. TRBs have the ability to accommodate shaft misalignments and shock loads; therefore, their applications in heavy transport vehicles, i.e., trucks, trains, etc., are common. TRBs also have a very critical role in supporting loads in renewable energy systems, as they are widely used in wind turbines. Large scale double-row TRBs are used in direct-drive wind turbines to maintain operational stability under varying load conditions [5].

Both numerical and experimental studies have been conducted to analyze the role of lubrication in TRB performance. This paper aims to systematically review the scientific literature on lubrication in TRBs. The reviewed studies examine the effects of lubrication on dynamic stability, thermal and frictional characteristics, fatigue life, and hydraulic losses in TRBs. The objective of this review is to develop a comprehensive understanding of research trends regarding lubrication in TRBs, particularly in the context of Newtonian and non-Newtonian lubricants used in different sizes of TRBs.

The structure of this paper is as follows: Section 2 describes the methodology used for identifying and categorizing relevant research articles. Section 3 presents the classification of research articles. Section 4 compiles and discusses the results under relevant subtopics. Finally, Section 5 provides the conclusions of the study.

2. Methodology and Materials

A systematic review of the literature on lubrication in TRBs has been conducted to gain an in-depth understanding of the topic. The Scopus database was used to retrieve relevant scientific papers. Section 2.1 explains the keywords and search methodology applied in the Scopus querying system. Section 2.2 provides an overview of the retrieved scientific papers and their categorization.

2.1. Literature Selection Using the Scopus Database

To perform a systematic search in the Scopus database, a suitable combination of keywords was employed using Boolean operators. These keywords were specifically related to lubrication in TRBs.

By constructing appropriate search strings in the database, the most relevant scientific literature was identified. The search results were filtered based on article titles, keywords, and abstracts, while no restrictions were imposed on the year of publication. This initial search yielded 357 research publications. However, some articles were written in languages other than English, while others focused solely on the design characteristics of TRBs without discussing lubrication. Additionally, some studies investigated bearings other than TRBs. To refine the selection, further screening was performed by carefully reviewing the titles, abstracts, conclusions, and, in some cases, the entire papers. After this process, 100 research articles were deemed most relevant to the scope of this review.

As stated in the previous section, this review focuses on trends in lubrication research on TRBs. Therefore, the primary and most relevant search string used to retrieve literature on TRBs was as follows:

TRB OR “tap* roll* bear*” OR “tap* bear*”

The first phrase, “TRB”, was used to identify research papers explicitly containing this term. However, in some cases, authors may use “taper” instead of “tapered” or “rolling” instead of “roller.” To account for these variations, the asterisk (*) symbol was applied after “tap”, “roll”, and “bear”, ensuring that the search captured all possible suffix variations.

To further refine the search towards the focus of this study, an additional string was introduced to include keywords related to lubrication:

“lubr*”

By applying this second filter, all research studies relevant to lubrication in TRBs were identified.

2.2. Classification of Selected Research Articles

The classification of selected research articles has been conducted based on different aspects to clearly understand the nature of the research papers.

The following aspects are used according to which classification has been made:

• Type of TRB, i.e., single-row, double-row;
• The approach of publication, whether a numerical analysis or experimental approach;
• Type of lubricants, i.e., oil or grease;
• Target of the study, i.e., the role of lubrication in geometric and dynamic stability, fatigue life, frictional characteristics, design, thermal behavior, $P_{L{B}_o}$, roller profile, contact behavior, and lubrication systems in TRBs.

This classification has been summarized in the following section under the cluster of approaches of publication.

3. Results of Classification of Research Articles

This section shows the results of the classification of research articles cited in conducting this review. Different groups of research articles are made based on the approach of publication, as mentioned in the above section. These results are summarized in

Table 1. Classification of research articles using an experimental approach.

Target of Study		Type of TRB	Type of Lubricant	References
Role of Lubrication	Geometric and Dynamic Stability	Single Row	Oil	[6,7,8,9,10,11,12]
			Grease	[6,7,13,14]
		Double Row	Oil	-
			Grease	-
	Fatigue Life	Single Row	Oil	[15,16,17,18,19]
			Grease	[15,20]
		Double Row	Oil	-
			Grease	-
	Frictional Characteristics	Single Row	Oil	[21,22,23,24,25,26,27,28,29]
			Grease	[30]
		Double Row	Oil	-
			Grease	-
	Design	Single Row	Oil	[31,32,33]
			Grease	[34,35]
		Double Row	Oil	-
			Grease	-
	Thermal Behavior	Single Row	Oil	[36,37]
			Grease	[38,39,40,41,42,43]
		Double Row	Oil	-
			Grease	-
	Load-Independent Power Losses	Single Row	Oil	[44,45,46,47,48]
			Grease	-
		Double Row	Oil	-
			Grease	-
	Roller Profile	Single Row	Oil	-
			Grease	-
		Double Row	Oil	-
			Grease	-
	Contact Behavior	Single Row	Oil	[49,50,51,52,53]
			Grease	[54,55,56]
		Double Row	Oil	-
			Grease	-
	Lubrication System	Single Row	Oil	[57,58,59]
			Grease	[59]
		Double Row	Oil	-
			Grease	-

Note: “-” indicates no study available in that category.

and

Table 2. Classification of research articles using a numerical approach.

Target of Study		Type of TRB	Type of Lubricant	References
Role of Lubrication	Geometric and Dynamic Stability	Single Row	Oil	[7,60,61,62,63,64,65,66]
			Grease	[7,67,68,69,70,71]
		Double Row	Oil	-
			Grease	-
	Fatigue Life	Single Row	Oil	[16,18,72,73]
			Grease	[74]
		Double Row	Oil	[75]
			Grease	-
	Frictional Characteristics	Single Row	Oil	[21,23,25,27,76,77,78]
			Grease	-
		Double Row	Oil	[79]
			Grease	-
	Design	Single Row	Oil	[31,33,80,81,82,83]
			Grease	[84]
		Double Row	Oil	[85]
			Grease	-
	Thermal Behavior	Single Row	Oil	[36,86,87]
			Grease	[39,88,89,90]
		Double Row	Oil	[91,92]
			Grease	[93]
	Load-Independent Power Losses	Single Row	Oil	[44,45,46,47,48,94]
			Grease	-
		Double Row	Oil	[95]
			Grease	-
	Roller Profile	Single Row	Oil	[96,97,98,99]
			Grease	-
		Double Row	Oil	-
			Grease	-
	Contact Behavior	Single Row	Oil	[49,51,100,101,102,103]
			Grease	[54,104,105]
		Double Row	Oil	[106]
			Grease	-
	Lubrication System	Single Row	Oil	-
			Grease	-
		Double Row	Oil	-
			Grease	-

Note: “-” indicates no study available in that category.

.

4. Outcomes from Literature and Discussion

This section presents the outcomes of the literature that has been studied in the formulation of this review paper. These outcomes are compiled under their respective headings. The headings are chosen in such a way that the respective articles studied the lubrication in TRBs in relation to these factors.

4.1. Outcomes from Literature

4.1.1. Geometric and Dynamic Stability

TRBs have high stiffness and load capacity but have limited speed capability. Gartner et al. [6] performed an experimental study where they replaced the spindle bearing in the test rig with a radially loaded TRB and analyzed the effect of lubrication on the speed capability of the bearing in terms of the outer ring temperature and vibrational level in the test rig. The vibrational level was measured by using a piezoelectric acceleration sensor, and a resistance thermometer was used to measure the outer ring temperature. Two lubricants, i.e., oil–air and grease, were used on different rotational speeds in TRBs. It has been found that, with grease as a lubricant, the bearing could reach up to 6000 rpm, whereas with oil–air lubrication, the bearing could reach up to 10,000 rpm. Under varying radial loads, the, grease-lubricated TRB failed when it reached to 10,000 rpm and the outer ring temperature exceeded the limit of 80 °C.

Roller skewness is an important parameter in the design optimization of bearings. Skewness generates due to the tangential friction force that exists between rib–roller end contact. This force depends upon load, lubrication properties, speed, etc. Majdoub et al. [7] numerically and experimentally studied the skewness of rollers in TRBs. A TRB was chosen with an axial load of 1300 daN, and the speed was varied between 1000 and 5000 rpm. Inductive proximity sensors (IPSs) were used in the holes of the outer raceway to measure the alignment rotation of the roller. These results were then used in numerical friction law to numerically obtain results. It was found that the skewness of the roller increased with the rotational speed. At low velocities, skewness increased with the increase in axial load, whereas, at high velocities, skewness decreased with the increase in axial load. This was also studied by Jamison et al. [8].

Jakubek et al. [9,10] performed an experimental study to analyze the effect of the kinematic viscosity of oil on the vibrational levels in TRBs. A test rig was developed in which 10 new TRBs of type CBK-171 were tested under the use of 12 oils with different kinematic viscosities. Bearing loads of 30 N and 55 N were applied in the radial and axial directions, respectively. The rotational speed of the shaft and bearing inner ring was set to be 1450 rpm. Furthermore, 120 tests were performed in the test rig. The results showed that oil with greater kinematic viscosities had reduced the vibration amplitude in the bearing. The optimum viscosity for the oil was estimated to be in the range of 22–32 mm²/s.

It was also found in another experimental study performed by Zhou et al. [11] that the internal clearance of TRB had a great effect on the bearing vibration and thus its life. It was evident from the results that larger clearance could caused high vibration during the operation of the bearing. This caused the difference between the real ball pass frequency of the outer raceway and the theoretical one, which increased with the clearance.

Jakubek et al. [12] correlated the lubrication with the amplitude and frequency of the forms of vibroacoustic signals under different lubrication conditions, as lubrication affects the vibration and noise levels in any rotating mechanical operation.

Yang et al. [13] performed experiments to study the effect of lubrication on the skewing of the rollers in the TRBs. Special capacitance probes were used to measured the potential difference between the probe and roller surface. Probes were installed in the housing and outer race. The results showed that roller skewing increased with the lubrication of large end of roller ends and with the bearing rotational speed.

The skew angle of the roller elements in TRBs was studied by Yang et al. [14]. They varied the bearing torque, load, rotational speed, and viscosity of the lubricant in the bearing and studied its effect on the roller skew angle. It has been found that there is a variation of between 0.15° and 0.6° in the skew angle. It was witnessed that the roller skew angle depends upon the frictional force at the roller–rib interface.

A numerical study was conducted by Deng et al. [60] to analyze the whirling of the cage and dynamic properties of rollers in TRBs based on roller skew and tilt. It was assumed for the study that the roller and cage had six degrees of freedom, there was constant speed rotation of the inner ring, the outer ring was fixed, and the EHL model was used for friction analysis. Dynamic differential equations were solved by using the Adams–Bashforth–Moulton multi-step method. The results showed that there was a direct relation of the roller skew angle with the rotational speed and axial load. It was noted that the whirling of the cage occurred in all cases. However, higher rotational speeds and axial loads had a better effect on the cage stability. When the radial and axial loads were applied, the roller skew angle increased with the radial load. Also, the loaded zone experienced greater roller skew angles than the unloaded zone. Flange friction also increased the cage whirl. Sakaguchi et al. [61] obtained almost the same results for the whirling of the cage of the TRBs. Crecelius et al. [62] also put forward the study of dynamic and thermal characteristics for the high-speed TRBs.

Nelias et al. [63] also numerically predicted the roller skewing in TRBs based on the rotational speed, ring misalignment, and temperature of the lubricant. It was found that the roller skew angle was significantly affected by the traction at the roller–flange contact point and that this increased with the increase in traction.

Zihao et al. [64] studied the effect of lubrication on the dynamic performance of the TRBs. The contact area of the larger side of the roller and inner ring rib was analyzed. Contact models were studied with and without lubrication. The backward difference method and Newton–Raphson iterative algorithm were used to analyzed the model. The results showed that the increase in inner ring speed increased the vibration in the bearing, and that the lubrication made the axial motion of the inner ring smoother and smaller as compared to the condition of without lubrication. It has been shown that acceleration due to the vibration of the inner ring in the radial direction could be reduced by the use of a lubricant from 1.71 to 2.07 db in different roller end spherical radii and rib inclination angles. Therefore, it was suggested to carefully select the spherical radius and rib inclination angle. It was also found that by increasing the number of rollers from 12 to 20, the minimum film thickness for the inner ring raceway and inner ring rib could be increased by 7.97% and 4.43%, respectively.

Xia et al. [65] numerically discovered a correlation in the vibration characteristics of TRBs with the crowning of rollers using ANSYS. Vibration acceleration was calculated for various values of crowning for rollers. It was found that vibrational acceleration for rollers without crowning was higher and that its approaching time to stability was greater too. On the other side, when the crowning of rollers was complete, the vibrational acceleration and stability time reduced greatly. However, it is worth noting that crowning significantly affected the vibrational acceleration; therefore, the crowning value must be carefully chosen.

Li et al. [66] numerically studied the transient vibration in TRBs generated by the local damage. A three-dimensional non-linear vibration model was developed. It was found that local damage in the bearing may generate vibrations and ultimate failure in the bearing. It was evident that local damage occurred due to insufficient lubrication, impact load, rolling fatigue, etc.

Grease lubrication in the TRB is greatly affected by the shaft deflection. Wu et al. [67] numerically studied the effect of shaft deflection on the lubrication of TRBs. A model was developed in which the interaction loads and linear and angular displacements of bearing parts were involved. The deflected shaft affects the load carrying capacity of the TRB. It has been found that when the shaft was deflected, the contacts of the rollers deviated from the normal state and an irregular film shape and pressure profile developed. The weakening of the effectiveness of the crowning profile of rollers was due to the shaft deflection. Significant pressure spikes and necking features were witnessed at the roller end as well. In comparison with the outer race, the film thickness and pressure peak are thinner and greater in the inner raceway under loading conditions. This model could be used for oil-lubricated bearings. In this paper, the replenishment and starved lubrications were not studied.

The effect of the geometrical position of the rollers, like crowning, tilting, sliding, and skewing, on grease lubrication is significant. Wu et al. [68] analyzed the effect of these parameters on grease lubrication and traction action. In this paper, using the basis of the power law rheological model of greases, a model of grease thermal lubrication between the roller and raceway was developed, combining the energy equation of grease film and the heat conduction equation of the roller/raceway. It has been shown that for the Lundberg crowned rollers, the minimum film thickness and film pressure peak were thicker than that of cut-off crowned rollers. Film thickness decreased and pressure peak increased when considering the temperature effect. There was a reduction in the minimum film thickness and an increase in the film pressure due to the tilting motion of the roller. The tilting motion of the roller also produced necking at the main loaded end. It has been found that there was no significant effect of skewing on the grease film thickness and pressure distribution. The bearing sliding first increased the traction effect at the roller–raceway pair and then gradually decreased.

In grease-lubricated TRBs, the dynamic stability of the cage has great importance. Wu et al. [69], in their study, discussed the dynamic characteristics of the TRBs. In this study, they developed a multi-body dynamic contact model of TRBs based on the models of geometric interaction and grease elasto-hydrodynamic lubrication principles. It has been found that the loading on the bearing has a direct relationship with the roller skew angle and is inversely proportion to the roller tilt angle. The significance of bearing slip, roller tilt, and skewness became more pronounced when the speed of the bearing increased. A reduction in bearing slip was witnessed with the bearing pre-load, but this increased the roller tilt and skew angle. The grease plastic viscosity had an inverse relationship with the roller tilt angle and bearing slip, while it was directly proportion to roller skew angle. Motions of the roller and cage were somewhat independent of the grease yield stress.

Wu et al. [70] numerically studied the dynamic stability of the grease-lubricated high TRB based on the theory of grease elastohydrodynamic lubrication (EHL) and squeeze film lubrication. Taking into account the equivalent stiffness and damping of the lubricant film, a dynamic model was developed for TRBs. The cage dynamic characteristics were analyzed based on the effect of speed, load, and preload using the fourth-order Range–Kutta method. By changing the material of the cage in this study, i.e., copper, nylon, or steel, its dynamics stability was analyzed. The results showed that in comparison with the pocket contact force, there exists a greater contact force between the cage and guide ring. Even in the running state, the sliding rate of the roller was greater than that of the cage. There was a direct relationship between the sliding rate of the cage and roller and the speed. However, the sliding rate decreased with the increase in load or preload. It has been shown that the dynamic stability of the cage was better and the smaller pocket contact force was smaller when the clearance occurred in the pocket. Similarly, the contact force between the cage and guiding surface was smaller when the clearance between the guiding surface was smaller, but the dynamic stability was then poor. There is a direct relationship between the dynamic stability of the nylon cage and copper cage and the bearing rotational speed. The stability of the steel cage was less than that of the nylon and copper cage at high rotational speeds.

Mohammadpour et al. [71] studied the effect of the dynamic behavior of the TRBs on the vibration and noise characteristics of the gear pair differentials. In this study, a tribo-dynamic model was developed to analyze the lubricated bearing and gear contacts. Non-Newtonian thin lubricant film conditions were incorporated in the model. The results showed that the transmitted vibration spectra was dominated by the bearing frequencies. Vibration refinement can be achieved by pre-loading the bearing at a very high level, but this can also decrease the transmission efficiency.

4.1.2. Fatigue Life of TRBs

The effect of lubrication on the fatigue life of TRBs was studied by Takata et al. [15]. In their study, they carried out various tests by varying the rotational speeds, load, lubricants, temperature, and material of the bearings. The results showed that the fatigue life of the roller bearings depend upon the LAMBDA value, which is the ratio of calculated elastohydrodynamic film thickness to composite surface roughness. It was witnessed that if this ratio was below certain a threshold value. which was defined as the “transitional film parameter of fatigue life”, then the fatigue life of the bearing decreased significantly. The effects of grease and oil as a lubricant on the fatigue life of bearings were observed to be the same if the EHL film thickness was estimated precisely.

The literature shows that bearing fatigue life can be calculated based on the Lundberg and Palmgren theory [107]. Takahashi et al. [16] studied the effects of axial clearance on surface-initiated flaking in TRBs. It was evident that flaking damage took place before the rated life. This flaking might be due to contaminants in the lubricants. In this study, experiments were performed on TRBs by varying axial clearances. To analyze the relationship between the flaking area and axial clearance, the surfaces of the bearings were examined before and after the tests. It was evident from the results that when the axial clearance was greater, the flaking area was tilted more towards the side of the large diameter of the outer raceway. The bearing life and axial clearance were in an inverse relationship with each other.

Littmann et al. [17] studied the role of lubrication in the propagation fatigue cracks in the TRBs. Mineral oils and synthetic fluid were used in the bearings, and tests were performed. It was observed that the any debris or contaminants in the lubricant may increase stress for the nucleation of fatigue cracking in the bearing. It was declared that any surface stress concentration and the smaller film thickness both promoted contact fatigue. Low-viscosity lubricants promoted the quick propagation of fatigue cracks.

Nixon et al. [18] also experimentally studied the effect of contaminants in lubricants on the bearing life. They found adverse effects on the bearing life which may lead to the premature failure.

Cantley [19] studied the effect of the presence of water in lubricating oil used in TRB. In this study, experiments were performed on 32 bearings, maintaining the operating conditions as follows: compressive stress of 294 ksi at 2700 rpm and an operating temperature at 43 °C. SAE 20 oil was used as a lubricant. The water concentrations used were 25, 100, and 400 ppm. The results showed that bearing fatigue life significantly decreased with the increase in the water concentration of the lubricating oil. This variation was more significant when the concentration was increased from 25 to 100 ppm.

Errichello et al. [20] studied the bearing failure in the wind turbine. The bearing element failed due to the micro-structural changes developed by white etching areas and white etching cracks. Experimental tests were carried out by using through-hardened and carburized material for the bearing. It was found that the through-hardened bearing developed cracks and failed, while the carburized bearing sustained. It was concluded that carburized bearings with a low carbon content, a high nickel content, higher retained austenite, and higher compressive stress performed better and had high fracture resistance.

Researchers have also studied the effects of contaminants on the lubrication and ultimately on the rated life of the TRBs. Such a study was performed by Fitzsimmons et al. [72,73], in which they discussed both solid and liquid contaminants in the lubricants and also studied their origin. The effects on the bearing life were studied in detail.

The scuffing resistance of roller bearings is one of the important parameters that can be incorporated into its performance. Muralidharan et al. [74] performed the study to evaluate the scuffing resistance of precisely manufactured TRBs. The results showed that the TRBs were made to operate at 15 to 20 m/s rib speeds but witnessed no incidents of scuffing. The speeds at which they were operated were greater than the speeds which were recommended, i.e., 5 to 10 m/s.

In another study, Kim et al. [75] numerically studied the thermo-mechanical effect on the fatigue life of double-row TRBs. A quasi-static model and thermal network method were used to study the mechanical and thermal behavior of the TRB. Lubrication conditions were correlated with the temperature of the bearing and hence with the thermal expansion. The results showed that with the increase in rotational speed, there was a decrease in the fatigue life. It was also confirmed that with the inadequate supply of lubricant, there was an increase in the temperature of the bearing, and thus, thermal expansion happened. Due to this, an interference fit took place and the fatigue life decreased significantly. A large initial clearance could give rise to the imbalance in load distribution, which negatively affected the fatigue life. The sliding friction could be controlled by adjusting the roller end sphere radius.

4.1.3. Frictional Characteristics

The advancement in technology has made it possible to have less frictional and other losses in the mechanical process when transmitting load, but there are still power losses. The frictional losses in the rolling bearing are still major contributors to the total power loss in any mechanical process. A multibody simulation (MBS) model was developed by Wingertszahn et al. [21] to predict the frictional torque in TRBs with low levels of lubrication. This multibody simulation model runs under the program name LaMBDA. This model incorporated contact calculation, damping models, and friction models to wholly estimate the friction torque developed in the TRB. The simulated frictional torque was then validated with the experimentally measured one. The experiments were performed on the test rig of the machine elements, gears, and tribology (MEGT). The results showed that frictional torque increases with the increase in rotational speed when the bearing is preloaded axially alone as well as for the combination of axial and radial load, while, for the bearing loaded radially, frictional torque decreases with the increase in rotational speed. It was also witnessed that there is an inverse relationship between the frictional torque and temperature of the lubricant. The MBS model was validated as the simulated and measured results showed great coherence.

Manjunath et al. [22] conducted an experimental study to determine the frictional rolling torque and thermal inlet shear in TRBs. These sets of experiments were performed by using the vertical shaft roller bearing tribometer. Thermocouples were installed to measure the temperature at the inlet and outlet of the lubricant supply manifold and at the bearing outer raceway. The TRBs were heavily loaded with pure axial load and under the fully flooded lubrication conditions. The experiments were performed at different rotational speeds (200 to 2200 rpm), different supply oil temperatures (35 °C to 65 °C), and two contact loads (9.6 and 12.85 kN). First, the effect of the oil flow rate on the frictional torque and temperature was determined. It was witnessed that with the increase in the oil flow rate, there is a consequent increase in the frictional torque as well as a decrease in the temperature of the bearing and oil outlet temperature. It was also shown that sliding friction torque and drag torque were uniform with increasing speed, while rolling frictional torque increased with an increase in rotational speed; hence, its contribution to total frictional torque also increased. The results also showed that there is an inverse relation between the shear heating and friction rotational torque.

Experimental and analytical studies were performed by Karna [23] to predict the coefficient of the friction of the large rib roller end in the TRB. Axially loaded bearings with rollers in dynamic equilibrium were considered for the study. It was shown that the performance of the rib was greatly affected by the lubrication conditions. The torque produced by the rib was very small when the lubrication condition was hydrodynamic.

Matsuyama et al. [24] developed a TRB with less friction torque in their study. They used the fact that rolling resistance and agitating resistance should be reduced in order to reduce the friction torque. Therefore, they studied the influence of internal geometry and oil flow control on friction torque. The results showed that rolling resistance had a direct relationship with the number of rollers, the effective length of the rollers, and the crowning radius of the raceways. By decreasing these parameters, the contact area between the raceway and roller was reduced, and thus, the rolling resistance was also reduced. Agitating resistance was reduced by limiting the clearance between the cage and cone rib. It restricted the oil inflow to the bearing. It was shown that the discharging of oil should be carried out quickly to avoid any oil stagnation inside the bearing. The developed TRB was better in performance than the double-row angular contact ball bearing. Zhou et al. [25] developed a test rig to measure the torque of the bearing. This test rig was able to measure the torque of each individual component of the bearing, i.e., raceway rolling, raceway moments, and the frictional force of rib–roller contact. The numerical and experimental results were in good agreement with each other.

Hatazawa et al. [26] conducted a study in which they performed experiments to analyze the friction characteristics of the TRBs. Experiments were performed at different operating conditions by changing the speed, load, and lubricant viscosity. The test rig consisted of magnetized rollers and coils, which were used to measured the rpm of rollers, and the electric current flow was used to observe the contact between the rollers and raceway. The results showed that there were three different load regions for the TRB, i.e., a lower-load region, intermediate load region, and higher-load region. In the lower-load region, hydrodynamic lubrication conditions were present. For the intermediate load region, there existed EHL conditions, while mixed-lubrication conditions existed for the higher-load region. It was witnessed that frictional torque was proportional to the bearing load in the power of one-half for hydrodynamic conditions, while the rate decreased for EHL conditions. Frictional torque was nearly proportional to the bearing load in mixed-lubrication conditions.

Maccioni et al. [27] presented numerical and experimental approaches in their study to analyze the oil-lubricated TRBs. In their study, they presented methods for the computational fluid dynamics study of the lubrication in the TRBs used in OpenFOAM^®. It was suggested that these methods would reduce the computational time, and a detailed study can be conducted by using these methods, e.g., calculating flow rates, friction torques, etc. The results of these numerical approaches can then be validated with the experimental approach. In this paper, the PIV technique was studied to validate the CFD-based numerical results.

Mori et al. [28] and Evans et al. [29] developed the low viscosity oil as a lubricant for TRBs. It is a combination of a phosphorous anti-wear agent and a sulfurous extreme pressure agent. This lubricant has low viscosity, which reduced the torque loss in the bearing while maintaining the good anti-wear properties and operation in high-pressure conditions.

Gonclaves et al. [30] experimentally studied the torque produced by the friction force in grease-lubricated roller bearings and then optimized SKF’s rolling bearing friction torque model considering the experimental results. Differently formulated grease, i.e., M2, M5, MLi, and MLiM, were formulated in this work. These greases were different in terms of thickener type, thickener content, base oil nature, and several other properties. Different experiments were performed to measure friction torque for the mentioned greases at temperatures of 50, 60, and 80 °C. Generally, there is an inverse relation between the friction torque and rotational speed. The results showed that there were higher friction torques when lithium-thickened greases were used, specifically for the grease MLiM. For the lithium-thickened grease, the number of speeds tested were limited at constant temperatures of 50 and 60 °C. It was due to the fact that these greases generated more heat because their base oil was of high viscosity. The polymer greases M2 and M5 showed smaller frictional torque compared to lithium-thickened greases.

Hatazawa et al. [76,77] in other theoretical studies analyzed the friction characteristics for TRBs. Hydrodynamic lubrication conditions and low load were applied to the bearing. The results showed that friction torque increased with the increase in the rpm and viscosity of the lubricant. It was also observed that the speed ratio was almost independent of the bearing load, rotational speed, and viscosity of the lubricant.

Leibersperger [78] studied the oil-lubricated TRBs. Using the laminar boundary layer theory, a study was performed for analysis. It was predicted that the viscosity, density of oil, and rotational speed and geometry of the bearing held influence on the friction torque, fluxes, and heat generated.

Xu et al. [79] numerically studied the friction torque of the TRB. A mechanical numerical method was used to determine the effect of axial pre-deformation, internal radial clearance, and angular misalignment on friction torque. The results showed that friction torque increases with the increase in axial pre-deformation and angular misalignment while decreasing with the increase in radial clearance.

4.1.4. Design of TRB

Denkena et al. [31] in their study analyzed the machining strategies for the production of dimples on TRBs. Dimples encourage better lubrication into the contact zone and reduce friction. In this study, a simulation was used for the material removal to model the milling process. The results showed that in using the advanced machining process, uniform lubrication dimples could be machined for better lubrication.

Aihara et al. [32] studied the effect of the surface roughness of the raceways of TRBs on the rolling friction that results due to the viscous nature of the lubricants. It was concluded that raceways with more roughness resulted in lower elastohydrodynamics rolling resistance.

The geometry of the raceways of the TRB also affect the friction torques and thus the lubrication conditions. Liu et al. [33] studied the effects of the convexities of the raceway friction torque of the TRB. They used theoretical and experimental approaches for their study. The elastohydrodynamic lubrication condition of oil was used for the bearings during the operation. They varied the convexities of the inner and outer raceways (2–6 micron) and the roughness of the inner and outer raceways (0.10–0.30 Ra), and its effects were estimated on the friction moments. The results showed that friction torque decreased with the increase in raceway convexity when it was less than 4 microns. The convexity value was restricted by the contact stress and should not cross 6 microns. The friction moment also decreased with the increase in the roughness of the raceways and rim.

TRBs can experience starved lubrication conditions during their operation. As previously discussed, the dimples on the TRB surface can improve the lubrication in the bearing. Wang et al. [34] experimentally studied the effect of dimples on the performance of TRBs during starved lubrication conditions. A vertical universal friction wear tester was used as a test rig. The dimples were manufactured on the outer ring by the use of a laser machine. The dimples were formed with different geometric parameters, i.e., diameter (60 microns, 100 microns, or 200 microns), depth (5 microns, 10 microns, or 2 microns), and density (6, 12, and 24%). In terms of the coefficients of friction and wear losses, it was found that they were significantly less than the non-dimpled TRB. It is also worth mentioning that for dimple diameters of 100 microns and a density of 24%, the coefficients of friction and wear losses were lowest. They were reduced by 35.6% and 62.5%, respectively, when compared with the non-dimpled TRB under the same operating conditions. In [35], they also confirmed that a surface with dimples could also reduce the noise and vibration of TRBs during operation.

Fujiwara et al. [80] studied TRBs to estimate the optimized radius of the large end faces of rollers. A numerical model was developed based on EHL considering asperity contact and roller skewing. It was concluded that the optimum radius of large ends of rollers was about 85% of the rib face conical surface for a thicker film formation. The convexity of rollers was studied by Wang et al. [81] using a finite element method.

Leaver et al. [82] studied the topography of the rollers in the TRBs and coupled it with the mixed lubrication. They excluded asperity contact contribution wavelengths greater than the Hertzian width to the friction torque that took place during rotation. The statistical properties of the surfaces were made based on their condition.

Senthil Kumaran et al. [83] studied the recent trends, challenges, and methods to improve the useful life of TRBs. They discussed the design, developments, and testing to improve bearing life. They specifically focused on the lubrication, and it was suggested that bearing life can be improved by sufficient amounts of lubrication.

The surface morphology of rolling elements has a great influence on effective lubrication. Wang et al. [84] has completed numerical simulations of non-Newtonian elastohydrodynamic lubrication between tapered rolling elements and inner-ring axle box bearings in a high-speed train. The input conditions, i.e., velocity, acceleration, and plastic viscosity, were changed, and the effects on the film-forming characteristics were studied. It has been found that during the acceleration and braking process, there is mixed lubrication in the bearing. A method of optimizing the surface morphology was adopted to improve lubrication. It has been shown that when the surface roughness of the rolling elements was less than 0.1 micrometers, the mixed lubrication was transformed to full-film lubrication, but when it was less than 0.03 microns, it is less useful to improve lubrication. Less fluctuations of film thickness were witnessed for kurtosis—less than three. Skewness has little effect on the film-forming characteristics of lubricant when it is negative. However, it had effects in reducing the maximum film pressure.

There is another CFD-based study of lubrication in double-row TRBs performed by Zhu et al. [85]. In this study, TRBs with two different rib structures were analyzed under the loss of lubrication process. The two rib structures were the outer ring rib structure and the inner ring rib structure. It was experimentally found that when TRBs with two different rib structures were tested for 40 min, the outer ring rib structure TRB operated normally with no signs of failure, while the inner ring rib structure TRB was observed to be failed. Its cage had became black, and the small roller cage was fractured. These incidents were then explained by performing CFD simulations to analyze the distribution of the lubricant. The volume of the fluid multiphase flow model was used to incorporate both the phases, i.e., oil and gas. As the TRB was operating at high rotational speeds, turbulence was significantly present. To effectively incorporate the turbulence into the flow field, the RNG k-$\mathsf{\epsilon }$ model was adopted. Furthermore, as in TRBs, the outer ring is stationary and the inner ring, roller, and cage are in motion. So, there are static and dynamic regions present. To convert the transient flow state into a steady flow state, a multiple reference frame (MRF) model was used in this study. The results showed that, generally, outer ring rib structure TRBs performed better than the inner ring rib structure in terms of internal lubrication conditions. In fully flooded conditions, the outer ring wall of TRBs with an inner rib structure had 11.296 times less lubricant than that of the outer ring rib structure. The outer ring rib structure efficiently blocked the lubricant from going out of the bearing cavity. Similarly, in the loss of lubrication process, the outer ring rib structure still had twice the amount of lubricant than that of the inner ring rib structure.

4.1.5. Thermal Behavior

Winer et al. [36] experimentally and analytically studied the thermal behavior of TRBs and ultimately estimated the thermal resistance of the bearing. An apparatus was constructed to experimentally measure the temperature and, thus, the thermal behavior. An infrared scanner and thermocouples were used to measured temperatures. Shaft heating was provided steadily at 30 W. It was shown that frictional heat generated by the bearing was 15.2 W. The thermal resistance of the bearing from shaft to housing was estimated to be of the order of 1 K/W.

Mccoy et al. [37] suggested in their study that water jackets should be manufactured in the housing for heat transfer from the TRB. It was shown that 80–90% of the heat generated during operation could be removed from the bearing by these water coolants. The temperature of the bearing was controlled by the thermostat, and the water coolant flowed when the temperature exceeded the threshold.

Tsuji et al. [38] studied the effect of load and shaft rotational speed on the temperature increase in TRBs. In this study, a TRB with a bore diameter of 343 mm and an outside diameter of 457 mm was studied. Thermocouples were used to measured the temperature at the inner and outer raceways, retainer, and guide flange. It was concluded that temperature increases in the inner and outer raceways and retainers were a strong function of the rotational speed, while the temperature rise in the guide flange was a strong function of the load.

Yan et al. [39] also numerically and experimentally studied the temperature distribution and heat generation of the grease-lubricated TRBs. The finite element method was implemented by the APDL program in ANSYS to observe the thermal behavior of the bearing. For the experimental study, a test rig was developed which included two axle boxes, two roller bearings, and a test axle. It was concluded that the highest temperature existed in the rollers and that the lowest temperature existed in the outer ring. The rib experienced high temperatures in the inner ring. The small end of the roller was in a high-temperature zone. With the increasing radial force and speed of rotation, the heat generation of the rib and raceway increased.

TRBs have the capability to operate at high speeds. Lieser et al. [40] found that TRBs with grease as a lubricant were suitable for operating at speeds of even 160 mph in their study. However, due to the greater heat generation by the rubbing lip seals at high speed, they should be replaced with clearance seals. It was found that the use of highly stable soap-thickened grease as a lubricant in the bearing did not need any re-lubrication, even when operating it for 200,000 miles. It was also found that grease deterioration and a reduced ability to lubricate may be witnessed when the grease was excessively filled due to the high temperature rise.

Parker et al. [41,42] investigated the performance of a 120.65 mm bore diameter of TRBs lubricated with oil at high speeds, i.e., up to 15,000 rpm. In this study, the effects of the rotational speed, radial and axial loads, the flow rate of the lubricant, and its temperature on the temperature distribution and heat generation of the bearing were evaluated. Two methods were used for injecting the lubricant, i.e., through holes directly into the cone–rib contact point or through jets at the small end side of the roller. It was evident that the former method had a positive effect on the performance of the bearing, resulting in lower cone-face temperatures and power loss, as well as consuming less lubricant compared to the latter. The bearing temperature increased with the increase in speed and decreased with the quantity of oil. Bearing power losses increased with increases in the lubricant flow rate.

Hoeprich et al. [43] studied TRBs with nine different combinations of thickeners and oil viscosity greases. The bearing was loaded with small thrust loading and rotational speeds of 1800 and 3600 rpm. For 30 days, or after the rib temperature reached 150°, the bearing was operated. Grease film thickness was observed by using the IR technique, and then it was compared with the theoretical calculated film thickness. The results showed that stability in the temperature was achieved with the increasing viscosity, as could be witnessed in fully flooded lubrication.

Yu et al. [86] numerically studied the temperature distribution of the oil-lubricated TRBs. In their study, they tracked the temperature distribution of oil and analyzed the thermal elastohydrodynamic behavior of oil. They used the column-by-column method technique to find the temperature behavior. It was witnessed that, along the film thickness, the temperature profile was symmetrical and that the middle layer was experiencing the highest temperature. The bearing and applied load had directly affected the temperature of the middle layer of oil.

Zhang et al. [87] studied the thermal properties and lubrication performances of the TRB installed in the dual clutch transmission. As it operates with high speed and carries a large load, its failures are therefore more obvious than others. In this study, roller’s spinning motion was investigated for the effects it had on the performance of lubrication in the bearing.

Bearings operating at high rotational speeds generate greater heat, and, therefore, temperature rises take place. This temperature rise leads to the unstable thermal expansion of the bearing parts, which ultimately lead to its failure. Kletzli et al. [88] studied these thermally induced failures inside the TRBs. A finite element method was used in ABAQUS to develop the transient thermal and static structural models. The thermal-mechanical transient time responses, as a function of the seal type, speed, and lubricant starvation, were predicted using these models. It was assumed that the bearing had loads only due to the temperature rise and had no external loads. The results showed that at a speed of 100 mph, there were chances of failure due to the instability in the growth of the load, and this was due to the grease starvation and heat flux from the contact seals, which ultimately increased the rib temperature. However, for rotational speeds equivalent to 80 mph, the temperature was under the limit; therefore, the bearing operated normally and no instabilities were reported.

There is a strong dependence of the performance of TRBs on the rheology of the lubricant. Karnizanm et al. [89] performed a study to analyze the relationship between the performance of the TRB and the rheology of lubricant, i.e., grease. The KRL thrust bearing rig was used to analyze the regimes of lubrications as explained by the Stribeck–Hersey curve. In this study, they discovered a relationship between the bearing performance and the temperature dependence of Gibbs energy. Consequently, from this correlation, they described the lubrication regimes according to the load and grease type.

Both high and low temperatures affect the properties of grease, e.g., viscosity, vapor pressure, etc. It has been found that the greases used in roller bearings that are operated at low temperature have high starting friction moments. Lindenkamp et al. [90] performed a study about the grease-lubricated roller bearings at low temperatures. It was found in this study that the TRBs had higher starting friction moments than the bearings with better kinematics, i.e., angular contact ball bearings.

The bearing life is directly related to the lubricant distribution in the bearing cavity. One of the reasons the bearing fails is a loss of lubrication (LOL). Due to the LOL, the temperature of the bearing increases, so much so that it crosses the maximum limit and the bearing fails. Li et al. [91] numerically studied the temperature dependency during the loss of lubrication process in double-row TRBs. The CFD approach was used to develop a two-phase flow model (oil–air) for double-row TRBs and calculated the volume fraction of oil on the surface of the bearing. In this paper, temperature distributions during the LOL process were studied on small and large rollers and the raceway surface. The results showed that the temperature variation inside the bearing had a significant relationship with the lubrication, especially in the loss of lubrication process. It was witnessed that there were worse lubrication and temperature distributions on the large roller side. If the number of lubricant inlets were increased, it was found that the temperature could be reduced by 25%.

Xu et al. [92] used the finite element model in ANSYS for the estimation of temperature distribution in the inner ring, outer ring, and rollers. These temperature fields affect the critical speeds of TRBs, as this would generate thermal stresses and will ultimately affect the vibrational behavior of the bearing. It was found that the steady-state temperature distribution had more significant effects on the low-order critical speed than the high-order critical speed. The optimum design of bearings was proposed in this study.

Ai et al. [93] studied the temperature rise in grease-lubricated double-row TRBs using the thermal network method based on generalized Ohm’s Law. In this study, the effect of different bearing speeds, grease filling ratios, and roller large end radii on the bearing temperature were investigated. The results showed that with the increasing of the rotational speed of the bearing and grease filling ratio, there was an increase in the temperature increase in the bearing. It was noted that with the increase in the filling grease ratio, the loss due to viscous drag became more significant, which ultimately became the reason for high temperature increases. Different roller end spherical radii, ranging from 50 mm to 500 mm, were examined for temperature rises in the bearing. It was found that the minimum temperature was appropriate and, thus, heat generation occurred for the roller end spherical radius of 400 mm.

4.1.6. Load-Independent Power Losses $\left(P_{L{B}_o}\right)$

Maccioni et al. [44] numerically and experimentally studied the effect of different operating temperatures and geometries of oil reservoirs on load-independent power losses $\left(P_{L{B}_o}\right)$ in fully flooded lubricated TRBs. The experimental study was performed by developing the test rig which offered three different configurations (right, left, and center) in terms of the test bearing. The 32,208 TRB was tested experimentally. These configurations allowed them to observed the oil reservoir geometry on $\left(P_{L{B}_o}\right)$. Temperatures of 50 and 60 °C and rotational speeds of 1000, 3000, 4500, and 6300 rpm were used to obtain the results. The experimental conditions were reproduced numerically by implementing the CFD model in OpenFOAM^®. As the lubrication condition was fully flooded, the cyclic symmetry was therefore exploited. Three different meshes were developed to perform simulations by varying the number of cells. The results showed that mesh M3, which had a lower number of cells, had lesser simulation time and greater speed compared to meshes M2 and M1. Load-independent power losses $\left(P_{L{B}_o}\right)$ for rollers, cages, and shafts were obtained at different operating conditions. It was witnessed that contributions made by the roller and cage towards the $P_{L{B}_o}$ were almost the same (70 to 75%) and that the similarity could be better visualized at higher temperatures. It was clear from the results that the shaft contributed less than the cage and roller to the $P_{L{B}_o}$. These losses were further distinguished in terms of the inertial and viscous effects. It was shown that $P_{L{B}_o}$ due to the cage was due to the inertial effects, while $P_{L{B}_o}$ due to the shaft was emerging due to the viscous effects. The roller contribution to $P_{L{B}_o}$ was due to both inertial and viscous effects. It was also evident from the results that $P_{L{B}_o}$ increased at high rotational speeds.

Gonda et al. [45] also performed a numerical and experimental study to estimate the hydraulic power losses, i.e., load-independent power losses, in rolling bearings. They estimated the affect of different working parameters like viscosity, speed, and flow rate on the magnitude of hydraulic power losses.

Liebrecht et al. [46,47] performed the experimental and numerical approach to estimate the drag and churning losses inside the TRBs. The CFD simulations were carried out to analyze the magnitude and identify the type of hydraulic losses that each bearing components contribute. Due to this, they obtained clear division between the drag and churning losses inside the bearing. They also derived some empirical relations with which to determine these hydraulic power losses.

Cruz et al. [48] studied the power loss of a rear axle gear transmission. They performed the study experimentally and numerically. TRBs were used to support pinion shaft and crown assembly. The main focus was to find the power loss due to crown wheel churning and lubricant squeezing from the pre-loaded TRB. It was found that almost 74% of the total power loss was due to the TRB.

The study of two phases, i.e., the oil–air interface, has also been carried out by researchers. For instance, Wang et al. [94] performed a study about the flow field of oil-lubricated TRBs by developing the simulation model. They used the multiple reference frame (MRF) to examine the physical motion of the bearing and volume of fluid (VOF). A two-phase flow model was used to examine the flow field of the oil–air interface in the TRB. A VOF model can accurately determine the position and shape of the two-phase interface. The numerical simulation indicated that as the geometric gap distance between the inner race way and roller element decreased, the frictional losses occurring in the churning phase were at the inner raceway and the rolling elements. It was observed that the frictional torque increased, with increases in the inner ring speed and lubrication viscosity making a significant contribution to the rolling element, which was around 50% of the total power loss. In this paper, they optimized the cage structure and found that the frictional torque could be reduced by 29.2% due to this optimization. By reducing the roller half-cone angle, frictional torque was reduced by 26.2%.

Bearing power losses significantly contribute to the total power losses in any mechanical equipment. Bearing power losses are classified as load-dependent power $\left(P_{LB}\right)$ losses and load-independent power losses $\left(P_{L{B}_o}\right)$. There are numerous techniques to estimate load-dependent power losses $\left(P_{LB}\right)$. But there are limited methods that estimate the load-independent power losses $\left(P_{L{B}_o}\right)$. Maccioni et al. [95] completed a study where they estimated load-independent power losses $\left(P_{L{B}_o}\right)$ in oil-lubricated double-row TRBs. This study was performed by developing a numerical tool based on the computational fluid dynamics in OpenFOAM^®. A back-to-back (O-configuration) double-row TRB was used in this study. Two lubrication conditions, i.e., fully flooded (FLO-L) and feed lubrication (FEED-L), were modelled. A single-phase model was used for FEED-L, and a two-phase model was used for FLO-L. The simulations were performed at different operating conditions in terms of rotational speed, viscosity, and flow rate. The results showed that in FEED-L, the outer raceway (having minimum velocity) was the region in which a significant amount of lubricant was present. Load-independent power losses $\left(P_{L{B}_o}\right)$ were analyzed, and it was observed that they were considerably less in the FEED-L condition than in the FLO-L condition. A major contribution to load-independent power losses $\left(P_{L{B}_o}\right)$ in FEED-L was made by inertial effects (up to 99%), while in FLO-L, it was 70% due to the viscous effects. It was also shown that the flow rate of the lubricant and load-independent power losses $\left(P_{L{B}_o}\right)$ had a direct relation with each other.

4.1.7. Roller Profile

Cao et al. [96] numerically studied the crowning profile in the TRBs and its influence on the mixed-lubrication conditions in the nearing. Generally, the profile of rollers in TRBs are straight. In this study, the profile was changed into the crowned profile in order to culminate the pressure spike that is normally generated in elastohydrodynamic lubrication. A quasi-static model and mixed-lubrication model were used to analyze the load distribution and EHL conditions in TRBs, respectively. Regarding internal load distributions, it was found that with the increase in radial load on the TRB, the bottom roller could withstand higher loads, while the rollers at the top could withstand lighter loads. The internal load distributions were independent of the bearing speed; however, the EHL condition was a strong function of the bearing speed. The roller profiles were then modified with dub-off, logarithmic, and running-in optimized profiles. The results showed that in the rolling direction, there was almost the same contact pressure for all the three profiles. While the contact pressure had differences in the axial direction for the three profiles, for the dub-off profile, the contact pressure increased at the edges. Similarly, for the logarithmic profile, there was still a pressure spike, which presents in EHL. For the optimized profile, a smooth uniform pressure distribution was observed in the contact region.

Duan et al. [97] also studied the influence of the roller profile on the film-forming capacity of the lubricant. In this study, the logarithmic crowned profile roller was used with a gauge point located at 0.79 times the distance from the center to the end of the roller. Three different roller profiles with the modification coefficients k of 1.33, 4.00, and 6.65 were used in this study. A quasi-static model and EHL model were used to analyze the load distribution and lubrication conditions in TRBs. The results showed that the load distribution in TRBs could not be influenced by the crown drop of the roller, but it significantly affected the load variation in the axial direction of the roller. Asymmetric profiles of film thickness and film pressure were witnessed for the tapered roller–cup and roller–cone contact. The film pressure was greater in the smaller end of the roller than that of the larger end.

Fanghua et al. [98] also numerically studied the effect of logarithmic profile of the roller on the elastohydrodynamic lubrication in TRBs. In this study, the logarithmic roller profile were analyzed under an EHL model, and the film thickness, pressure distribution, and von Mises stress were obtained. The results showed that there were neither high pressure nor stress concentration at the ends when the logarithmic roller profile was used. It is also worth mentioning that regions of minimum film thickness were witnessed at the ends and thinner film thickness at the smaller end. Due to the logarithmic profile, the minimum film thickness was increased, and consequently, the lubrication was found to be better than straight profiles.

In the conventional EHL model, the effect of free ends were not considered, due to which the pressure peak and film thickness are estimated with some errors. Chen et al. [99] developed the improved EHL model for TRBs considering the effects of free ends. A quasi-dynamic model was used to determine the forces on roller contact, and then the improved EHL model was used to determine the pressure distribution and film thickness. The results showed that the pressure distribution and film thickness were more stable and uniform when using the improved EHL model. The effect of the free ends decreased with the decrease in load, while it increased with the decrease in the distance between the two neighboring free ends. The roller fillet radius and length should be properly designed in order to reduce the pressure peak and increase the minimal film thickness for proper lubrication.

4.1.8. Contact Behavior

A study was performed by Maccioni et al. [49,50] to analyze the lubricant fluxes in fully flooded oil-lubricated TRBs. This study was completed experimentally as well as numerically. Particle image velocimetry was used for the experimental study, and these results were reproduced numerically by completing the simulation in OpenFOAM^®. For the experimental study, a special test rig was constructed, in which the outer ring was made of sapphire. Castrol Syntrans 75W-85 was used as a lubricant with fully flooded conditions by without aeration lubrication. Different rotational speeds up to 2500 rpm were maintained in the test rig for measurements. The axial and tangential components of the velocity field and external flow rate were examined using the PIV technique. These results were reproduced in OpenFOAM^®. The numerical model was developed for a single sector, i.e., between two rollers. Two single-phase isothermal, i.e., laminar and turbulent (SST k-$\mathsf{\omega }$), models were used for simulation. The results showed that the external flow rate for the low rotational speed (500 rpm) was less than that for the high rotational speed (2500 rpm). Therefore the internal flow could not be neglected, especially for the low rotational speed. There was more than 70 percent of lubricant flow from the external side of the cage, but a portion of this flow rate passed through the external part under study in this paper. It was found that the tangential oil velocity $U_x$ was greater than the average cage velocity $U_{x0}$ in the majority of the region. There is an inverse relationship between the ${\mathsf{\omega }}_s$ and the difference between the average tangential velocity of fluid $U_x$ and that of the cage $U_{x0}$. A squeezing effect was observed in the region of contact between rollers and the outer raceway, especially at low rotational speeds. It has been observed that there is a direct relationship between the velocity and axial flow in the region of study, which lead to an increase in the average axial velocity. Therefore, the flows in the downward direction were less effective in the region of study.

Rolling element bearings experience aeration due to the interaction of air–lubricant, and this significantly affects the lubrication mechanism. Maccioni et al. [51] performed their study to analyze the influence of aeration in TRBs on the mechanisms of lubrication. The study was performed numerically by implementing a new solver that incorporated aeration into the OpenFOAM^® environment. The Hirtz aeration model was implemented in OpenFOAM^®. It was then reproduced and validated experimentally via PIV measurements. A test rig, whose outer ring was made of sapphire, was developed to have optical access to the inner environment. The results were obtained at different rotational speeds in terms of the tangential, axial, and radial velocities. The results showed that at low rotational speeds, i.e., 300 and 600 rpm, there was no significant aeration and the standard solver and the solver with the aeration model provided similarresults, which were comparable to the PIV experimental measurements. As the rotational speed was increased to 900 rpm—at which speed, aeration is observed—it was witnessed that the tangential velocity that was obtained by the use of the new solver (with aeration) was in good agreement with the experimental PIV measurements, while the standard solver (without aeration) provided a poor approximation of the results. The radial and axial velocity fields were also approximated effectively by the new solver, although they were not similar to the PIV measurements. When the aeration phenomenon dominated, i.e., at 2100 rpm, the new solver again approximated the tangential velocity in close agreement with the PIV results, and the same was the case for radial velocity as well. The standard solver failed to incorporate the aeration phenomenon and, consequently, its effect on the flow field.

The performance of lubricants can be improved by adding additives to it. Many studies have been conducted in this regard. Bercea et al. [52] studied the addition of polyethylene to mineral oils as a lubricant in TRBs. The effects of the polymer concentration, temperature, and speed on the lubricant viscosity and film-formation capability were studied. It was observed that when low-density polyethylene was added to oil at a concentration of 0.5%, it produced a highly viscous and thick lubricant film, ultimately leading to better lubrication.

Moyer [53] experimentally tested the ball bearings, TRBs, and cylindrical bearings with debris in lubricants and identified the seven key factors that affect the performance of bearings when the debris are present in the lubricants. These factors are debris size and distribution, lubricant system, film thickness, material of bearing, contact size of bearing, and filtering level.

Zhang et al. [54] investigated roller bearings lubricated with grease. In this paper, grease-lubricated roller bearings were studied in terms of bleeding behavior and film thickness evolution with time. The thick solid layer and bleed oil were modeled as two different film formations. Therefore, the porous thin layer model was used to investigate thickener-rich layer, and a multiphase bleeding model was used to simulate oil bleeding. These models were validated by the experimental results. The results showed that, due to contact pressure, there was a sideways flow of base oil from the thickener-rich layer. This increased the thickener fraction and made it more viscous, becoming a solid-like layer. The oil that came out from the thickener-rich layer was due to the capillary action. The reduction in the permeability of the thickener was observed during operation, and it significantly affected the base oil flow rate from the thickener-rich layer. It has been found that the thickener-rich layer was difficult to form in greases with a rough texture and a small amount of thickener. These type of greases show greater permeability and thus have a high bleeding rate of oil.

Several studies are performed to study the performance and characteristics of the grease during the mechanical operation. For instance, Ninos [55] performed an experimental study to evaluate the performance of the grease inside TRBs in an automotive wheel. Five candidate greases were tested under high accelerated conditions in a pair of TRBs. The tested speed was set at 800 rpm, and the radial load was applied continuously at a level equivalent to 150% of the vehicle curb weight, while the axial load was applied for 0.5–1 min after every 5 min at a level equivalent to 30% of the radial load. The ratings of these greases were made on the basis of experimental life, residual grease, and the condition of contact surfaces.

The intervals for grease relubrication were studied for roller bearings by Bengtsson et al. [56]. They performed tests for a time period of 8 years. Lithium soap-based greases were used, and they were tested for changes in acidity, consistency, and wear debris. It was found that the relubrication intervals for deep groove bearings, cylindrical roller bearings, and TRBs could be extended to factors of 5, 10, and 20, respectively.

Luo et al. [100] studied the radial stiffness of the contact pair in the TRBs. It was found that, with an increase in the contact load, the equivalent radial contact stiffness increased. Oil film significantly affected the radial contact stiffness when the applied radial load was small. However, this effect decreased when the radial load became higher.

Wang et al. [101] numerically studied elastohydrodynamic lubrication for TRBs. The rotational speed, load, length, and entraining angle were varied, and their effects on the lubrication film thickness were analyzed. The results showed that, at high entraining speeds and/or light loads, the lubrication film thickened. It was suggested that the entraining angle should be equal to 90°.

Yamashita et al. [102] performed a load analysis of the TRBs by using the fluid film lubrication model based on the EHL findings. Both the radial and axial loads were applied on the bearing, and the pressure distribution and film thickness were studied. Barreled isosceles trapezium conjunctions were used for TRBs. The results showed that the pressure distribution and film thickness were asymmetrical and different from those of the elliptical conjunctions.

In elastohydrodynamic lubrication, the film thickness of the lubricant is considered to be formed by the sufficient supply of the lubricant. However, as the roller bearings operate at high speeds, starvation may occur. There are several numerical and analytical models that are used to analyze the effect of starvation on the lubricant boundary film thickness and its distribution inside the bearings. Centrifugal effects and surface tension are the two main phenomenons, in addition to others that have significant effects on the lubricant distribution inside the TRBs. Van Zoelen et al. [103] performed a numerical study to predict the effect of centrifugal forces on the film thickness inside the TRB. A model was developed to estimate the lubricant film decay due to the centrifugal effect. It was assumed for the study that equipartition took place for two layers between the roller and raceway.

Jiang et al. [104] studied the contact between the rib and roller end by considering the non-Newtonian lubricants. The elastohydrodynamic theory was used to analyze the two geometric configurations: the tapered rib/spherical roller and spherical rib/spherical roller end. The lubrication temperature, film thickness, and friction torque were calculated at various speeds and loads.

Wang et al. [105], in another mathematical study, used the piezo-viscous effect of lubricant to analyze the lubrication of the TRB. The results showed that the viscosity and density of the lubricant changed with the application of pressure, and due to this phenomenon, better lubrication was witnessed for the thick film. It was also observed that the load carrying capacity of the bearing increased with the increase in the entraining speed of lubricants. The higher the piezo-viscosity coefficient of the lubricants, the greater the load carrying capacity.

Lang et al. [106] analyzed the contact behavior between the inner ring flange and roller large end, studying the effect of the roller large end spherical radius on the lubrication phenomenon. This was completed by simulating the contacts formed between them and determining the location of the contact point. The sliding velocities of the roller large end and inner ring flange were obtained from the spinning and orbital speed of the rollers. The contact forces were then calculated for the roller outer raceway, roller inner raceway and roller large end flange.

4.1.9. Lubrication System

Anon [57] developed a system in which a two-phase lubricant mixture and evaporative cooling were used. Lubricating oil was used with Freon. Freon was condensed and returned to the bearing by use of a heat exchanger. So, in this way, evaporative cooling was achieved, and the bearing temperature was controlled.

Hammell [58] studied the lubrication systems for the high-speed rolling elements and proposed improvements for it. Lube curve characteristics were studied, and lubricant/air delivery systems were refined for the optimum supply of lubricant to the bearing. Mist, standard terminating, and termination with air purge systems were compared in this study.

Wagenknecht [59] studied different lubrication systems that may be used for TRBs. He suggested various lubrication systems, i.e., an oil and grease lubrication system, immersion splash, and a force feed oil mist lubrication system. He also extended his studies to evaluate the influence of contaminants and additives for better lubrication.

4.2. Discussion

In this part of the paper, the selected scientific literature will be discussed based on the type and size of TRB using Newtonian, i.e., oil, and non-Newtonian, i.e., grease, lubricants.

Table 3. Overview of experimental research articles categorized by the outer diameter (OD) of studied TRBs.

Target of Study		Type of TRB	Type of Lubricant	Size of TRB
				OD < 100 mm	100 mm < OD < 200 mm	200 mm < OD < 300 mm
Role of Lubrication	Geometric and Dynamic Stability	Single Row	Oil	[6,9,10,11,12]	-	[7,8]
			Grease	[6,13,14]	-	[7]
		Double Row	Oil	-	-	-
			Grease	-	-	-
	Fatigue Life	Single Row	Oil	[15,18,19]	-	[18]
			Grease	[15]	-	[20]
		Double Row	Oil	-	-	-
			Grease	-	-	-
	Frictional Characteristics	Single Row	Oil	[22,25,29]	[21,23,24,27]	-
			Grease	[30]	-	-
		Double Row	Oil	-	-	-
			Grease	-	-	-
	Design	Single Row	Oil	-	[31,32,33]	-
			Grease	-	[34,35]	-
		Double Row	Oil	-	-	-
			Grease	-	-	-
	Thermal Behavior	Single Row	Oil	[36]	-	-
			Grease	-	[42,43]	[39]
		Double Row	Oil	-	-	-
			Grease	-	-	-
	Load-Independent Power Losses	Single Row	Oil	[44,45,46,47,48]	-	-
			Grease	-	-	-
		Double Row	Oil	-	-	-
			Grease	-	-	-
	Roller Profile	Single Row	Oil	-	-	-
			Grease	-	-	-
		Double Row	Oil	-	-	-
			Grease	-	-	-
	Contact Behavior	Single Row	Oil	[51,52,53]	[49,50]	-
			Grease	[54,55,56]	-	-
		Double Row	Oil	-	-	-
			Grease	-	-	-
	Lubrication System	Single Row	Oil	-	[57,58,59]	-
			Grease	-	[59]	-
		Double Row	Oil	-	-	-
			Grease	-	-	-

Note: “-” indicates no study available in that category.

and

Table 4. Overview of numerical research articles categorized by the outer diameter (OD) of studied TRBs.

Target of Study		Type of TRB	Type of Lubricant	Size of TRB
				OD < 100 mm	100 mm < OD < 200 mm	200 mm < OD < 300 mm
Role of Lubrication	Geometric and Dynamic Stability	Single Row	Oil	[63,64]	[60,61]	[7,62]
			Grease	[70,71]	-	[67,69]
		Double Row	Oil	-	-	-
			Grease	-	-	-
	Fatigue Life	Single Row	Oil	[72,73]	-	-
			Grease	[74]	-	-
		Double Row	Oil	[75]	-	-
			Grease	-	-	-
	Frictional Characteristics	Single Row	Oil	[25,76,77,78]	[21,23,27]	-
			Grease	-	-	-
		Double Row	Oil	-	[79]	-
			Grease	-	-	-
	Design	Single Row	Oil	[80,82]	[31,33]	-
			Grease	-	-	[84]
		Double Row	Oil	-	[85]	-
			Grease	-	-	-
	Thermal Behavior	Single Row	Oil	[36]	[86,87]	-
			Grease	-	-	[39,88,89]
		Double Row	Oil	-	-	[91,92]
			Grease	-	[93]	-
	Load-Independent Power Losses	Single Row	Oil	[44,45,46,47,48,94]	-	-
			Grease	-	-	-
		Double Row	Oil	-	[95]	-
			Grease	-	-	-
	Roller Profile	Single Row	Oil	-	[97,98,99]	[96]
			Grease	-	-	-
		Double Row	Oil	-	-	-
			Grease	-	-	-
	Contact Behavior	Single Row	Oil	[51,101,102]	[49,103]	-
			Grease	[54,104,105]	-	-
		Double Row	Oil	-	[106]	-
			Grease	-	-	-
	Lubrication System	Single Row	Oil	-	-	-
			Grease	-	-	-
		Double Row	Oil	-	-	-
			Grease	-	-	-

Note: “-” indicates no study available in that category.

show the papers that have studied the role of lubrication in different sizes of TRBs both experimentally and numerically, respectively.

4.2.1. Small-Sized TRBs (OD < 100 mm)

A comprehensive review of the existing literature reveals that the majority of research efforts have been concentrated on small-sized tapered roller bearings (TRBs) with an outside diameter of less than 100 mm. Within this size category, both numerical simulations and experimental investigations have been conducted to study the effects of lubrication. This review identifies a total of 44 studies focused on small-sized TRBs, indicating a strong research emphasis on this group. Oil has predominantly been used as the lubricant in these studies, while only 14 studies have specifically explored the use of grease. Notably, no experimental study has been found investigating double-row TRBs in this size range, and only a single numerical study has addressed this configuration, as shown in Table 3 and Table 4, respectively.

4.2.2. Medium-Sized TRBs (100 mm < OD < 200 mm)

In contrast, research on medium-sized TRBs, defined by an outside diameter between 100 mm and 200 mm, appears to be less extensive. A total of 29 studies were identified within this category, reflecting a moderate level of research activity. Similarly to small-sized TRBs, oil remains the dominant lubricant, with only five studies specifically focusing on grease-lubricated TRBs. As with the smaller bearings, there is a lack of experimental investigations on double-row TRBs in this size range, while only two numerical studies have been reported, as summarized in Table 3 and Table 4.

4.2.3. Large-Sized TRBs (200 mm < OD < 300 mm)

Research on large-sized TRBs, with an outside diameter ranging from 200 mm to 300 mm, is even more limited. This review includes 14 studies that examine bearings within this size category, indicating a relatively modest research presence. Oil continues to be the primary lubricant in most cases, while grease has been considered in only eight studies. Importantly, no experimental studies have investigated double-row TRBs in this category, and only two numerical studies have focused on such configurations, as presented in Table 3 and Table 4.

Additionally, it is noteworthy that only two studies [38,81] have investigated single-row TRBs with significantly larger outside diameters of 457 mm and 1220 mm, respectively.

The research trend has been clearly evident from reviewing the scientific literature studying the role of lubrication in the performance of TRBs. Small-sized (OD < 100 mm) TRBs have been studied more extensively as compared to medium-sized (100 mm < OD < 200 mm) and, specifically, large-sized (200 mm < OD < 300 mm) TRBs. This reflects the relative simplicity involved in conducting experiments and numerical simulations at a smaller scale. This shows a lack of research for large-sized TRBs, which are widely used in heavy-duty applications, such as wind turbines, railways, and industrial gearboxes.

Oil, as a lubricant, dominates the research studies that have been reviewed in this study. Oil is best suited for high-speed applications, having good heat dissipating and lubricating properties. However, grease is best suitable in large-sized bearings where heavy loads and longer operations are required due to its smaller number of relubrication cycles and better sealing properties. Grease (non-Newtonian fluid) has complex rheological behavior under loading conditions. Therefore, the gap in research must be filled in order to better predict the performance of systems that use grease as lubricant.

Double-row TRBs are widely used in heavy load applications, i.e, wind turbines and gearboxes, due to their high load carrying capacity. They support axial and radial loads in multiple directions. However, a severe lack of research has been observed in this study. This leads to a limited understanding of lubrication physics and its interaction between two rows of TRBs.

5. Conclusions

In this paper, the Scopus database was used as a search engine for the identification of the scientific literature that studied TRBs with respect to lubrication. The screened articles have been classified based on different aspects, i.e., (1) the approach of the study, (2) type of TRB, (3) type of lubricant, and (4) target of the study. The results of this classification are summarized in Section 3 under the cluster based on the approach of study, i.e., Table 1 and Table 2.

The outcomes of the research articles are presented and discussed in Section 4. There are certain significant factors that are affected by the lubrication in TRBs. Researchers have mainly studied lubrication in TRBs in terms of $P_{L{B}_o}$, thermal behavior, frictional characteristics, geometric and dynamic stability, and the contact behavior of the TRB. The results show the reviewed papers based on the type and size of TRBs using Newtonian and non-Newtonian lubricants. Research trends were clearly identified with the help of this classification. Much research has been conducted studying oil-lubricated single-row TRBs having an OD less than 300 mm.

By reviewing the literature, some advanced experimental and numerical tools were identified for studying lubrication phenomenon in TRBs. The particle image velocimetry (PIV) technique was used in some papers to study different aspects of lubrication inside the bearing when performing experimental studies. Advanced CFD models were also used in the literature, using different approaches to simulate conditions in closer proximity to the real world. These approaches included VOF models for multiphase flows, the Rigid Mesh Motion (RMM) approach to study the dynamic behavior of mesh, and the Hirtz aeration model to study the aeration phenomenon in bearings.

It has been observed in this study that the papers that have adopted a numerical approach, in particular CFD analysis, have studied a single sector of TRBs. These results were then extended to the entire bearing using symmetry. Oil-lubricated single-row TRBs have been studied experimentally and numerically in detail, but there still exists a research gap in studying grease-lubricated TRBs, particularly double-row TRBs.

It has been concluded from the systematic review of the scientific literature that limited research has been conducted studying grease as a lubricant for single-row TRBs having an OD less than 300 mm, while for ODs greater than 300 mm, except for one paper, no other study has been conducted. No study has been conducted for double-row TRBs having an OD greater than 300 mm using grease as a lubricant, which means that there is severe lack of understanding in predicting the performances of high load applications, i.e., wind turbines, industrial gearboxes, and railways. Therefore, this area presents an opportunity for future research.