beari ngs, the data are in the same order of magnitude of each other,  for the same size bearing . However,  since the all -steel bearing tends to have a higher LQF than the hybrid bearing, this indicates that the torque  output of an all -steel bearing will be slightly higher than the hybrid if all other conditions are equal.  

Figure 12. Normalized LQF vs. average temperature for 178 N ( 40 lb) load and constant temperature  gradient of 12°C for 305- size all -Steel and Hybrid Bearing  

Dependence of LQF on DT  For both test bearings, the data generally show that LQF increases in direct proportion with the temperature  differential ( DT) across the bearing (Figures 4,5,9,  and 10) . We surmise that this is not due to an increase  in the actual quantity of oil, but more likely due to imperfections in the model since  it fails to account for  the  circumstances created by the large differential across the bearing. For example, the model may  underestimate the actual viscosity, and correct for this by overestimating the quantity . The viscosity used  in the calculations of LQF shown here was chosen to be the viscosity  at the temperature midway between  the outer and inner race temperatures . However, because the dependence of viscosity on temperature is  not linear, the actual average viscosity will be lower than the viscosity at average te mperature. The deviation  (from the average viscosity) of the low temperature outer race contact will be larger than the deviation of the warmer inner race contact, resulting in an underestimate of the viscosity if the average viscosity is used in the model . To account for a given amount of measured torque, an underestimate of the viscosity would  result in an overestimate of the LQF  (Equation 6) . This error will increase with increasing DT, resulting in a  gradual increase in LQF with DT . Since the actual temperature of the oil at each interface (inner and outer  raceway) is not known, the magnitude of this error could not be calculated to determine if it can account for the entire effect observed here.    We note, however,  that the magnitude of the temperature differentials studied here is larger than one would  likely encounter in a typical application. This large DT  was imposed to aid in the measurement of thermal  conductance. Therefore, the results are important for the purposes of thermal analysis of test articles but  are not expected to have significant impact on typical applications.  

Dependence of LQF on Load   Figures 6 and 11 show a moderate dependence of LQF on load for both the all -steel and hybrid bearings .  The LQF generally increases in direct proportion to the load, although deviation from this trend was observed at the highest load with the hybrid bearing. The cause of this dependence has not been  determined. As the load is increased, the dimensions of the conformal contact between the balls  and races  will change. This change in the contact geometry could possibly result  in an increase of the volume of oil in  the contact meniscus  due to having a larger interfacial surface area in close proximity . This would  hypothetically be an actual increase in the lubricant quantity .    The load dependence may also be partly due to changes in the width of the Hertzian contact ellipse . Since  our model for viscous drag torque (Equation 6) is independent of load, it does not account for any increased  viscous drag due to expansion of the contact ellipse. The Palmgren- Snare model [ 8] neglects any such  NASA/CP—2018-219887 555