1. Introduction

Rolling bearings are the most widely used bearings in the vehicle transmission industry due to their advantages of less friction coefficient for rotatory movements [1]. With the future trends of vehicle transmission development shifting toward lighter and more compact designs with greater power density, the main shaft bearings are subjected to more severe demands of simultaneous shrinking size and excessive loading [2, 3]. These requirements enforce higher thermal load on the bearings. The rolling bearings under stress overload and poor heat dissipation conditions are prone to wear out easily due to metal-to-metal contact, which corrode surface of bearings.

Hence, lubrication of bearings plays a significant role in fatigue life assurance by reducing friction and wear, which ensure the safe and reliable operation of bearings. The choice of lubrication mode of rolling bearing mainly depends on load, working speed, and temperature. Grease and splash lubrication are capable enough for lowspeed rolling bearings [4], while oil-jet lubrication could better meet the requirements under heavy load, high-speed, and high-temperature conditions [5].

Fluid jet heat transfer enhances the heat transfer rates in comparison with conventional methods. In an oil-jet cooling rolling bearing, a portion of the oil is utilized to lubricate the ball bearing and form lubricant film in ball raceway

contacts. A larger film thickness is helpful to reduce the friction and the heat generation. However, for the high-speed operation, the total energy dissipated by friction is significant, leading to an excessive heat generation. To compensate for this problem, larger amounts of lubricant oil flow are required to provide sufficient cooling capability, while only a relatively small part of the oil is used to form a lubricant film [6, 7]. Besides, while a larger amount of oil mass flow may lead to a higher power loss due to the increased drag against the rotation of the rolling elements and, an insufficient oil mass flow may cause a lubrication failure.

Thus, both the power performance and the lubrication performance of a rolling bearing are considered to be significantly impacted by the flow around it, which is in typical forms of enclosed space flow or open space flow. The enclosed space flow relates to the flow inside a bearing chamber, which is a common flow state in the real operating conditions such as aero engines, etc. However, there is usually no bearing chamber design for the drivetrain applications with lightweight requirements. The flow state of these rolling bearings is an open space flow, in which the heat that determines the temperature of bearing and oil-out is generated by the drag among rolling elements.

Experimental investigations with regard to high-speed ball bearings with oil-jet lubrication have been reported by Zaretsky et al. [8], indicating a lower bearing temperature with a double-nozzle jet construction compared with a single-nozzle jet counterpart under the same given oil flow rate. Flow was simulated using the computational fluid dynamic method for acquiring working performance of the oilmist lubrication, without and with the flow inside the rolling bearing [9, 10]. The results indicate that the opening near the inner raceway is expected to be the excellent location for supplying oil-mist or oil-jet for accomplishing better lubrication and cooling of ball bearing components. Both the flow pattern around one sphere and its drag coefficient are modified when placing another sphere in its vicinity.

The lubrication performance of the rolling bearing has been investigated a lot by single-phase method [11, 12]. The bearing temperature forecast model, considering the heat transfer of the oil flow and the air flow, respectively, is mainly presented by Harris [13, 14]. The convective heat transfer coefficients are given considering the lubricant oil flow and the air flow, respectively [15]. A computer program Shaberth has been used to calculate the thermal performance of ball bearings [16]. The oil volume fraction is required for input in Shaberth, and an empirical equation was derived for the oil volume fraction value inside the ball bearing as a function of oil flow rate, shaft speed, and bearing pitch diameter. However, the flow field inside a rolling bearing with oil-jet lubrication, in reality, is far more complicated since the air entrainment in the lubricant is ineluctable while the bearing is rotating. In addition, the air flow phase and the lubricant flow phase constantly interact with each other, and their interaction is strongly affected by the rotary speed of the bearing.

As stated above, while an accurate assessment of the flow around the ball bearing is of particular importance, the experiment measurements are not enough, and the numerical studies are mainly based upon single phase and empirical equation which are incapable in reflecting the real physics. This work herein investigates the air-oil two-phase transient flow inside the ball bearing. A CFD modeling method is presented for the air-oil two-phase flow inside the rotary ball bearing. It aims to increase the understanding of the temperature effects and flow pattern of the flow field inside the oil-jet lubricated ball bearing. The results can be used to optimize the precise oil-jet lubrication design to control the amount of lubricant oil inside the ball bearing at a later stage.
