Bearings serve as vital components in mechanical rotary systems, with their stiffness and temperature directly impacting operational efficiency. To enhance rotational precision, increase assembly rigidity, and minimise shaft vibration during machine operation, preloaded rolling bearings are frequently employed—such as those in machine tool spindles.

How do preload and rotational speed affect bearing stiffness?

The stiffness of machine tool spindle bearings constitutes a critical performance metric. Stiffness relates not only to load and rotational speed but also to frictional heat and preloading methods. Stiffness calculations form the foundation for analysing the dynamic characteristics of spindle units.

I. Effects of Preload Method and Rotational Speed

Under constant pressure preload, radial stiffness increases slightly with rising rotational speed, while axial and angular stiffness decrease rapidly. Under locating preload, radial, axial, and angular stiffness all increase rapidly with rotational speed, though the increase in axial and angular stiffness is relatively gradual. The stiffness variation patterns of ceramic ball bearings resemble those of all-steel bearings, though the changes are more gradual. Under locating preload, centrifugal forces on the inner ring and balls, coupled with friction heat, increase the contact load between inner and outer rings. Concurrently, the outer ring contact angle decreases while the inner ring contact angle increases, thereby enhancing contact stiffness. However, the reduction in outer ring contact angle moderates the increase in axial and angular stiffness.

1. Influence of Preload

As preload increases, the radial, axial, and angular stiffness of the bearing increase slightly, though the effect is minimal. Compared to locating preload, this influence is more pronounced for positioning preload. This occurs because increased preload enlarges the contact angles between inner and outer rings while simultaneously raising the contact load, thereby enhancing radial, axial, and angular stiffness. Nevertheless, the changes in contact load and contact angle induced by preload are relatively minor compared to those caused by rotational speed and component displacement, thus limiting their impact on bearing stiffness. This also explains why changes under locating preload are smaller than those under locating preload.

2. Influence of raceway curvature radius

As the curvature radius of the inner and outer raceways increases, radial, axial, and angular stiffness decrease. However, this effect is negligible, with only positional preload exhibiting slightly more pronounced stiffness changes. This occurs because increased curvature radius enhances contact deformation. Consequently, the influence on stiffness is generally negligible when selecting raceway curvature radius.

3. Influence of Ball Count

Under locating preload, increasing the number of balls slightly enhances radial, axial, and angular stiffness. While more balls increase stiffness, the same preload results in reduced contact load. Their combined effect does increase bearing stiffness, albeit modestly.

Under constant pressure preload, increasing the number of balls markedly enhances radial stiffness. However, when rotational speed reaches a certain threshold, axial and angular stiffness conversely decrease, albeit to a negligible extent. This occurs because, under constant pressure preload, although increased ball count reduces the inner ring contact load, it simultaneously decreases the inner ring contact angle. Their combined effect markedly increases radial stiffness while slightly reducing axial and angular stiffness.

Therefore, when increasing ball count, the preload must be correspondingly raised. Only when the contact load remains constant can increased ball count enhance bearing stiffness.

4. Influence of Ball Diameter

Under locating preload, increasing ball diameter slightly enhances radial, axial, and angular stiffness. Larger balls generate greater centrifugal forces, reducing the outer ring contact angle while increasing the inner ring contact angle. Concurrently, this increases contact loads on both rings, collectively boosting bearing stiffness. Under locating preload, the impact of centrifugal force variations on contact load is minimal, thus the effect of ball diameter changes on stiffness is negligible.

Under locating preload, increasing ball diameter enhances radial stiffness while reducing axial and angular stiffness, though the latter effects are minor. This occurs because the enlarged ball diameter increases centrifugal force, reducing the contact angles of both rings. Consequently, the outer ring contact load increases while the inner ring contact load remains largely unchanged. Thus, radial stiffness increases, while axial and angular stiffness decrease slightly. Therefore, reducing ball diameter not only improves speed performance but also does not compromise stiffness characteristics. This theoretically substantiates that reducing ball diameter represents one of the current development trends for spindle bearings.

What effects do preload and rotational speed exert upon bearing temperature?

Under preload, contact deformation within spindle bearings induces axial displacement of both inner and outer rings while altering the contact angle. Figure 3 illustrates the displacement of spindle bearing inner and outer rings under combined radial, axial, and torque loading.