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.

Rotary kiln installation forms a very complex system, as it consists of various components which affect cement production. However, some problems with particle settling are encountered during operation of tertiary air installation. This paper reports on the results of a study into gas-particle flow in a tertiary air duct installation. This flow was calculated using Euler method for air motion and Lagrange method for particle motion. The results in this paper demonstrate that study focus on the tertiary air installation is a practical measure without the analysis of other processes in the rotary kiln. A solution to this problem offers several alternatives of modifying the inlet to the tertiary air duct. As a result of numerical calculations, we demonstrate the influence of geometry of a rotary kiln modification on the number of large particles transported in the tertiary air duct. The results indicate that in order to reduce large particles, rotary kiln head geometry needs to be modified, and a particle settler should be installed at its outlet.