Effects of Elevated Temperatures on Rocking Vibration of Rotating Disk and Spindle Systems

This paper studies how temperature variations affect natural frequencies of rocking vibration of a rotating disk and spindle system through mathematical modeling and experimental measurements. Existing literature has shown that both radial bearing stiffness $krr$ and natural frequency $ω01B$ of one-nodal-diameter disk modes could substantially affect natural frequencies $ω01U$ of rocking vibration. In this paper, a preliminary experiment first identifies that relaxation of bearing stiffness $krr$ is the dominating factor to shift the natural frequency $ω01U$ at elevated temperatures. In addition, the bearing relaxation primarily results from thermal mismatch between the bearing raceways and the rotating hub. Guided by the experimental results, a mathematical model is developed to determine how temperature variations affect bearing contact angles, bearing preloads, and subsequently the radial bearing stiffness $krr.$ Based on the bearing stiffness $krr$ and disk frequency $ω01B$ at elevated temperatures, one can predict natural frequency $ω01U$ of rocking vibration through the mathematical model by Shen and Ku (1997). Finally, $ω01U$ of a rotating disk and spindle system are measured in a thermal chamber to validate the theoretical predictions.