Vibration analysis of ball bearing considering waviness under high speed and an axial load

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 2 f_s-30 kHz (f_s: 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.