Based on the rolling bearing vibration measurement principle in ISO standard, a nonlinear dynamic model of ball bearing is built and motion equations of the inner ring, outer ring, and rolling elements are derived by using Lagrange’s equation. The ball bearing model includes the influence of waviness, rotational speed, external load, arbor supporting stiffness and arbor eccentricity. Ball bearing high-speed vibration tests are performed and used to verify the theoretical results. Simulated results showed that specific waviness orders produced the principal frequencies that were proportional to rotational speed. Rotational speed mainly affected the value of the natural frequency of the bearing system, and RMS (Root Mean Square) of the full band had a great fluctuation with the increase of rotational speed. In the experiment, spectrum and RMS of 2fs-30 kHz (fs: the rotational frequency of inner ring/arbor) under high speed could include not only the influence of rotational speed but also principal frequencies produced by waviness, which could cover the part of requirements of the standard bearing vibration measurement.

Bearings of three-bearing shafts are usually treated as ideally-rigid articulated supports. In literature, the reactions of supports and bending moments of multibearing shafts are calculated taking into consideration only shaft elasticity. In fact, also deformation is present in these bearings, and it changes the shaft bending line. The deformation thus influences distribution of bending moment and reaction of supports. It is the most important difference when comparing two-bearing with three-bearing shafts.

Moreover, in most types of bearings, a reactive bending moment is the response of bearing to unparallel position of inner bearing rings in relation to outer rings, that is to the tilt angle. As a result, real loads of rolling elements differ from theoretical ones.

The aim of the paper is to develop a method of calculating generalized loads in rolling bearings of a three-bearing shaft taking into consideration shaft deformation, deformations in bearings and reactive moments of bearings caused by tilt angle.

Commonly used computations of basic rating life of a bearing system are based on the ISO 281:1990 standard. These computations include dynamic load capacity of a given bearing, its effective load and average rotational speed, whereas they omit distribution of external load acting upon particular rolling parts depending, among other things, on: - displacement in bearing (displacements in three directions and declination in two planes), - slackness in bearings. The aim of the presented theoretical research is to solve a problem of fatigue life of a ball bearing taking into consideration displacement in bearing resulting from elasticity of a three-bearing shaft, elasticity of bearings and their internal slackness.