Shafts mounted on bearings are subjected to vibrations due to many known and unknown causes. In many cases the causes of vibrations of a shaft may be initiated from the bearing parts and their manufacturing qualities. The mechanical vibration of a shaft mounted on bearings can be interpreted as chaotic oscillation of the shaft axis during its rotation and faster translation of mass in a chaotic manner and in unaccountably multiple directions. If we can determine these micro translations of mass-load including their velocity, it is possible to assess the energy created by the process of chaotic oscillations of the shaft-mass. In this article mathematical and physical modelling of scattered energy of vibrations emanated from individual causes of vibrations and the model of total scattered energy of vibrations are presented. The models correlating the total scattered energy of vibrations with the manufacturing and exploitation qualities of bearings can be used for vibration assessment of any rotating unit.