On the operational similarities of bladed rotor vibrations with casing contacts

Abstract

Rotor-to-stator rubbing in rotating machinery, resulting from tight clearances, introduces complex dynamics that can potentially leading to high vibrations and machine failure. Initially, the emphasis was placed on models addressing cylinder-to-cylinder rubbing; however, recent attention has shifted towards examining blade-tip contact in turbines, that exerts a substantial influence on the systems dynamics and efficiency. This study investigates the impact of blade number variation on bladed rotor systems, emphasizing on the types of motion that occur as function of the operational speed. A bladed rotor model is proposed, incorporating a Jeffcott rotor with blades represented as damped elastic pendulums. The equations of motion are derived and numerical simulations are performed to explore the system's behaviour with varying blade numbers (3, 5, 7, and 10) and to analyse bifurcation diagrams and contact forces. Results reveal distinct regions: periodic motion (I and III) and chaotic motion (II and IV), with chaotic regions occurring at specific fractions of the natural frequency and the number of blades. The study concludes that chaotic motions are associated with larger displacements and higher contact forces, and the vibrational behaviour becomes less hazardous as the number of blades increases. The findings provide insights for turbine design modifications to enhance system reliability and prevent unexpected failures.