Vibrations of balanced fault-free ball bearings

This paper investigates the vibrations of balanced fault-free ball bearings. A lumped mass-damper-spring model is adopted including the use of the Hertzian contact theory to represent the stiffness of the bearing rolling elements. We found that the equilibrium point of the bearing undergoes a supercritical pitchfork bifurcation as the bearing internal clearance increases. We developed closed-form expressions for the frequency-response functions of the horizontal and vertical motions of bearings with small internal clearance (below the bifurcation point). We also developed a chaos map to describe the locations and intensity of chaos in the internal clearance–shaft speed parameter space for bearings with larger internal clearance (beyond the bifurcation point).