On the operational similarities of bladed rotor vibrations with casing contacts

Rotor-to-stator rubbing in rotating machinery, resulting from tight clearances, introduces complex dynamics that can potentially lead to high vibrations and machine failure. Historically, the rubbing models were addressed using cylinder-to-cylinder contacts; however, recent attention has shifted towards examining blade-tip contact in turbines, which affects the systems dynamics and efficiency. This study investigates the impact of the variations in blade number on bladed rotor systems, emphasizing on the types of motion that occur as function of the operational speed in the sub-critical range. A simplified bladed rotor model has been developed, using 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) in order to analyse displacements, contact forces and bifurcation diagrams as function of the rotating speed. Results reveal distinct regions: periodic motion (I and III) and chaotic motion (II and IV) appear alternatively in the bifurcation diagram, with the 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. In addition, the appearance of periodic and chaotic motions occur in the same regions by scaling the rotating speed with the number of blades and natural frequency of the system. From an operational perspective, this dynamic investigation offers valuable insights into the severity of blade rubbing in industrial systems. It can guide the implementation of mitigation solutions to prevent worst-case failure scenarios and help to perform adjustments to either operational or design parameters.