Vibrations indicate bearing damage: General Industry Coverage

Many machine tool spindles are supported in the housing by rolling-element bearings. Cutting forces, spindle unbalance and spindle preload impose cyclic loads on the bearing’s balls and races. For example, a point on the inner surface of a race experiences a high-compression load as a ball rolls past, and that load is released after the ball passes.

Over time, the cyclic loading produces fatigue failure, damaging the surfaces of races and balls. This kind of damage causes vibration and noise, limits bearing life and eventually requires bearing replacement.

Courtesy of S. Smith

Figure 1. Cross section of angular contact ball bearing kinematics.

The occurrence and progression of damage can be detected by measuring vibrations on the spindle housing. Every time a ball passes a damaged spot on a race, it produces a “click,” and the frequency of the clicks can identify where the damage has occurred. As the damage increases, the clicks become stronger.

The frequency of the clicks can be determined from the bearing kinematics (Figure 1). At low spindle speeds, the inertia of the rolling element does not matter, and the ball makes contact with the inner and outer races at points A and B, respectively. The inner race rotates with the spindle shaft, and the outer race is fixed in the housing. If the rotational frequency of the shaft is ω, the velocity of point A is:

The velocity of point B is 0 because it is attached to the fixed housing. If the pitch diameter, measured across the spindle to the center of the balls, is E, the ball diameter is d, and the contact angle is φ, then:

The velocity of the ball center is the average of the velocities of the two contact points:

Combining those three equations gives the velocity of the ball center as:

The rotational frequency of the ball set and the separator is: