Managing heat in spindle bearings

Unconstrained, rigid physical objects have six degrees of freedom, or six independent directions of possible motion. There is translation in each of three perpendicular linear directions (X, Y and Z) and rotation about each of those directions. In an airplane, that would correspond to pitch, yaw and roll.

A machine tool spindle is relatively rigid and supported in a fixed housing by spindle bearings. The bearings are intended to constrain five of the six degrees of freedom, allowing rotation of the spindle around its long axis (the Z-axis by convention). Figure 1 shows a schematic cross-section of one side of an angular-contact ball bearing supporting a spindle.

All images courtesy S. Smith

Figure 1. An angular-contact ball bearing without spindle rotation and the contact forces shown as arrows.

In this case, the inner race of the bearing sits against a solid shoulder on the spindle, and a preload is applied as indicated by the green arrow. If the bearing components were absolutely rigid, each of the balls would make contact with the outer race on one point and the inner race on one point. But because the balls and the races are not absolutely rigid, each contact point is spread over a small area.

The preload keeps the balls in contact with both races and stiffens the support by compressing the balls, which act as springs that become stiffer as they are squeezed. In some spindles, the preload is applied by tightening a nut (fixed preload), and, in others, it is applied by a spring or pneumatic pressure (constant preload). Constant preload designs keep the preload more constant even if the spindle expands due to temperature increases.

When the spindle is not rotating or rotating at a slow speed (Figure 1), the preload force is the horizontal component of the contact forces shown by the blue and purple arrows.

The contact forces are larger than the preload force because the races act like wedges. The contact forces on the inner and outer races are equal in size and point in opposite directions, as shown in the small diagram to the left in Figure 1. In this case, the ball rolls on both races and spins about an axis perpendicular to the contact forces.

As the spindle begins to rotate (Figure 2), other forces appear, including the centrifugal force indicated by the red arrow. The balls have mass, and, as they rotate around the spindle axis, a force (F) appears that is equal to the mass of the ball (m) times the distance from the spindle axis (r) times the rotational speed of the ball around the spindle axis (ω) squared.