Effect of thermal-expansion-induced dynamic air gap displacement on vibration characteristics in high-speed motorized spindle rotors

The heat generated by the built-in motor was the primary thermal source during the operation of high-speed motorized spindles. It caused thermal expansion of the motor rotor, leading to an air gap displacement between the stator and rotor, which intensified the influence of unbalanced magnetic pull on the vibration of the rotor system. A nonlinear dynamic equation for the rotor system of the high-speed motorized spindle was established, incorporating motor rotor thermal expansion, stator-rotor air gap displacement, and unbalanced magnetic pull. Bifurcation diagrams, phase trajectories, and orbit diagrams were used to analyze the effects of rotational speed and the initial design air gap length on the vibration response of the rotor system. Research results indicate that the growth characteristics of thermal expansion in the built-in motor rotor of high-speed motorized spindles lead to nonlinear contraction of the air gap length, which alters the harmonic components of the unbalanced magnetic pull. The synergistic interaction between these phenomena triggers a parametric resonance effect, causing the system response to bifurcate from multi-periodic to quasi-periodic motion and ultimately destabilizing the system. Furthermore, by optimizing the initial design of air gap length and establishing a stable operating interval, the vibration effects induced by air gap displacement due to rotor thermal expansion can be effectively suppressed, reducing resonance risks caused by period-doubling bifurcations. These findings could contribute to improving the design and operational stability of high-speed motorized spindles, with potential applications in fields such as precision machining, aerospace, and high-speed tool manufacturing, where maintaining system accuracy and minimizing vibration are significant for improving overall performance and reliability.