Development of a Lubricant Temperature Prediction Model

As described in NSK Technical Review No. 2603, “Lubrication Life Formula (Lubrication Pentagon Theory),”¹⁾ NSK is developing a technology for theoretically predicting lubrication life in order to achieve both lower torque and longer life in rolling bearings. The Lubrication Pentagon Theory interrelates bearing torque, lubricant temperature, lubricant degradation, viscosity, and oil-film thickness, thereby representing the process by which the oil film becomes thinner and the lubrication condition changes over time. Here, the oil film is a thin layer of lubricant formed at the contact areas inside the bearing; it helps prevent direct metal-to-metal contact. Fig.1 shows the structure of the lubrication life formula.

This article presents our efforts to develop a prediction model for lubricant temperature, one of the components of the theory. Bearing temperature is generally represented by the outer-ring temperature because it is relatively easy to measure. In grease-lubricated bearings, however, the temperature of the lubricant that actually lubricates the contact areas may be higher than the outer-ring temperature. Oxidative degradation of the lubricant, changes in viscosity, and oil-film thickness are all strongly affected by temperature. Consequently, evaluating lubrication performance and lubrication life using the outer-ring temperature may underestimate the actual lubricant temperature and thus overestimate lubrication life. On the other hand, directly measuring the lubricant temperature inside a bearing is challenging.

A method for predicting lubricant temperature from operating conditions is therefore important. More accurate determination of the lubricant temperature inside a bearing can help achieve both lower torque and longer bearing life by preventing premature lubricant degradation. With future integration into the Lubrication Pentagon Theory in mind, this study investigated lubricant-temperature prediction using a thermal network method, which is suitable for iterative calculations and can represent the temperature distribution inside a bearing²⁾.

In this study, the thermal network method was applied to a bearing test rig using grease-lubricated bearings. A schematic of the test rig is shown in Fig.2. Two test bearings were subjected to an axial load and rotated during the test.

Type 6305 bearings were used in the test. The ambient temperature was 25 °C, and the axial load was 1,000 N. Urea grease was used as the lubricant, with a fill quantity of 3.4 g. The rotational speed was increased stepwise through 12 speed levels: 500, 630, 870, 1,185, 1,665, 2,190, 2,970, 4,020, 5,400, 7,350, 9,900, and 13,000 min⁻¹.

During the test, bearing torque, rotational speed, and outer-ring temperature were measured. Oil film thickness and the oil film breakdown ratio were also measured by the electrical impedance method³⁾. Bearing torque and rotational speed were used as inputs to the thermal network model, while the outer-ring temperature and oil-film thickness were used to validate the calculated results.

The electrical impedance method is used to evaluate the lubrication condition inside a bearing and to determine the thickness of the oil film formed in the contact region and the oil-film breakdown ratio.

In the thermal network model, the bearing and test rig were divided into multiple regions, each represented by a node. A thermal capacitance was assigned to each node, and the nodes were connected by thermal resistances. In a rotating bearing, the mechanical power dissipated by friction is converted mainly into heat. The rate of heat generation in the bearing can therefore be estimated from the bearing torque and rotational speed. At the present stage, to verify the validity of the lubricant-temperature prediction model, the heat generation rate was calculated from the measured bearing torque and rotational speed and used as an input to the thermal network model. In the future, the model is intended to be combined with the bearing-torque prediction formula in the Lubrication Pentagon Theory so that lubricant temperature can be predicted directly from operating conditions.

The outer-ring temperature predicted by the thermal network method was compared with the measured outer-ring temperature. In addition, the theoretical oil-film thickness was calculated from the estimated lubricant temperature and compared with the oil-film thickness measured by the electrical impedance method.

Fig.3 shows the time histories of torque M, the temperatures at the respective locations T, the oil-film breakdown ratio α, and oil-film thickness h. The outer-ring temperature calculated by the thermal network method, T_outer, was in good agreement with the measured outer-ring temperature, T_{outer_test}. This indicates that the developed thermal network model approximately reproduces the thermal behavior of the bearing test rig. The calculated lubricant temperature, T_grease, tended to be higher than the outer-ring temperature. The difference between the lubricant and outer-ring temperatures became particularly large in the high-speed range.

Next, the theoretical oil-film thickness h_{outer_test} was calculated using the measured outer-ring temperature, and h_grease was calculated using the estimated lubricant temperature. These values were compared with the oil-film thickness h_EIM measured by the electrical impedance method. The theoretical oil-film thickness calculated using the outer-ring temperature deviated substantially from the measured oil-film thickness. By contrast, when the lubricant temperature predicted by the thermal network method was used, the calculated oil-film thickness was in good agreement with the measured value in the low- to medium-speed range of 500 to 1,185 min⁻¹. This result demonstrates that, when evaluating oil-film thickness in the low- to medium-speed range, it is important to account for the temperature of the lubricant that actually performs the lubrication rather than the more readily measurable outer-ring temperature.

In the high-speed range, however, the theoretical oil-film thickness calculated using the lubricant temperature also deviated from the measured value. The oil-film breakdown ratio α increased in this range. A tendency for torque to decrease despite increasing rotational speed was also observed. These results suggest the onset of lubricant starvation, in which an insufficient amount of lubricant is supplied to the contact. Starvation can reduce oil-film thickness through mechanisms that cannot be explained solely by the decrease in viscosity caused by a temperature rise, and may therefore have contributed to the discrepancy between the theoretical and measured values in the high-speed range.