There are two ways to apply axial preload to bearings : one is constant pressure preload, and the other is positioning preload. Under constant pressure preload, the radial stiffness of the bearing increases slightly with the increase of speed, while the axial and angular stiffness decreases rapidly. Under positioning preload, the radial, axial and angular stiffness of the bearing increase rapidly with the increase of speed, but the increase of axial and angular stiffness is relatively gentle.
1. Influence of preload
As the preload increases, the radial, axial and angular stiffness of the bearing increases slightly, but the effect is small. Compared with the positioning preload, this effect is more significant for the constant pressure preload. This is because the increase in the preload increases the contact angle of the inner and outer rings, and also increases the contact load, thereby increasing the radial, axial and angular stiffness. However, the changes in contact load and contact angle caused by the preload are smaller than those caused by speed and part displacement, so the impact on the bearing stiffness is limited. This is also the reason why the change under positioning preload is smaller than that under constant pressure preload.
2. Influence of channel curvature radius
As the radius of curvature of the inner and outer ring raceways increases, the radial, axial and angular stiffness decreases, but this effect is small. Only the change in stiffness under positioning preload is slightly more obvious. This is because the increase in the radius of curvature of the raceway increases the contact deformation. Therefore, when selecting the radius of curvature of the raceway, its effect on stiffness can be ignored.
3. The influence of the number of balls
Under positioning preload, the increase in the number of balls slightly increases the radial, axial and angular stiffness. The increase in the number of balls increases the stiffness, but under the same preload, the increase in the number of balls will reduce the contact load. The result of their combined effect can increase the stiffness of the bearing, but it is less.
Under constant pressure preload, the increase in the number of balls significantly increases the radial stiffness, while when the speed increases to a certain value, the axial and angular stiffness decreases, but the change is very small. This is because under constant pressure preload, although the increase in the number of balls reduces the inner ring contact load, it also reduces the inner ring contact angle. Their combined effect significantly increases the radial stiffness of the bearing, while slightly reducing the axial and angular stiffness.
Therefore, the preload should be increased accordingly when the number of balls increases. Only when the contact load is the same can the bearing stiffness be increased by increasing the number of balls.
4. The influence of ball diameter
Under positioning preload, the ball diameter increases, and the radial, axial and angular stiffness increase slightly. The increase in ball diameter increases the centrifugal force of the ball, reduces the outer ring contact angle, and increases the inner ring contact angle, but at the same time increases the contact load of the inner and outer rings. The combined effect of these increases the bearing stiffness. Because the centrifugal force change has little effect on the contact load under positioning preload, the change in ball diameter has little effect on stiffness.
Under constant pressure preload, the radial stiffness increases with the increase of ball diameter, while the axial and angular stiffness decreases, but the effect is small. This is because the increase of ball diameter increases the centrifugal force of the ball, reduces the contact angle of the inner and outer rings, increases the contact load of the outer ring, and the contact load of the inner ring remains basically unchanged, so the radial stiffness increases, while the axial and angular stiffness decreases slightly. Therefore, reducing the ball diameter not only improves the speed performance, but also does not reduce the stiffness performance. This also proves theoretically that reducing the diameter of the ball is one of the current development trends of spindle bearings.
5. Effect of initial contact angle
Under positioning preload, the increase of initial contact angle significantly reduces radial stiffness and significantly increases axial and angular stiffness. This is because the increase of initial contact angle reduces the radial component of contact stiffness and increases the axial component. At the same time, the contact load decreases under the same preload.
Under constant pressure preload, the increase of initial contact angle significantly reduces radial stiffness; at low speed, axial and angular stiffness increase, and at high speed, there is basically no change. This is because under constant pressure preload, the inner and outer rings allow axial displacement. In order to maintain the balance of force, the contact angle of the outer ring is almost close to 0, and the size of the initial contact angle has little effect on the contact angle of the outer ring. Similarly, the initial contact angle increases, and the contact load decreases under the same preload.
Therefore, increasing the initial contact angle of the bearing under positioning preload can improve the axial and angular stiffness, while increasing the initial contact angle under constant pressure preload not only fails to improve the axial and angular stiffness, but reduces the radial stiffness.
