Rolling bearings for machine tool spindles are desired to have high-rigidity and high-speed performance to meet complex machining operations and to utilize production capacity to the full. For this reason high speed and high load spindle bearing systems are demanded. Among the rolling bearings, angular contact ball bearings are most widely used for high speed spindles due to their relatively low temperature rise at high rotational speeds. Although, in high-loaded and high-speed operating conditions, it is important to predict the friction torques which can be increased rapidly due to ball inertia forces in high speed condition.
The purpose of this study is to develop the equations of motion for balls and to analyze characteristics of the friction torques for angular contact ball bearings under various thrust loads. The sliding velocity profiles between the ball and the raceways were obtained by the 3-D quasi-dynamic equations of motion including both centrifugal force and gyroscopic moment derived by vector matrix algebra. The frictions at the contact areas were obtained by the Bair-Winer's non-Newtonian rheological model and the Hamrock-Dowson's central film thickness in EHL analysis. The nonlinear equations were solved by the Newton-Raphson method and the underrelaxation iterative method. The friction torque and ball behaviors with various loads, ball materials, and contact angles were predicted by this model. It was shown that the friction torque was sensitive to the thrust load and the contact angle, and that the friction torque and the pitch angle of the bearing with ceramic balls were smaller than those of the bearing with steel balls.
Experiments were conducted to verify the validity of the theoretical model. Friction torques and temperatures on high speed angular contact ball bearings for the machine tool spindles were measured using a new type of test rig. The test bearings ran with oil-air lubrication under the thrust loads from 320 N to 1920 N at the rotational speed of up to 12000 rpm. The experimental results with the sufficient feed of the lubricant showed that the friction torques were sensitive to the thrust loads and the rotational speeds, and that the friction torques were higher than those with insufficient lubrication. The measured torques were compared with theoretical results which were obtained by both the conventional formula and the present model, and it was found that the torques obtained by the conventional formula showed remarkable discrepancy from the test results and that friction torques obtained by this theoretical model considering rolling frictions and sliding frictions gave good agreements with experimental results.
In case of the bearings with steel balls, electrical contact resistances were measured in order to evaluate the lubricant film formation in the contact areas. With insufficient lubrication and high thrust loads, the collapse of the lubricant film was detected even at a high rotational speed. It was concluded that in order for these high speed bearings to run in the condition of fluid lubrication, it was required to monitor not only the temperature increase but also the lubricant film formation in contact areas, resulting from the change of the applied load and the lubricant amount.
The present theoretical model of friction torque can be used for the prediction of the power loss for high speed angular contact ball bearings, and the measured results can be used as information for designing spindles or determining the operating condition.
