Probabilistic Analysis of Orbital Characteristics of Rotary Systems with Centrally and Off-Center Mounted Unbalanced Disks

Abstract

Rotor dynamics plays a crucial role in the performance and safety of rotating machinery, with disk position and unbalance significantly impacting system behavior. This study investigates the dynamic characteristics of two rotor configurations: a centrally mounted unbalanced disk (Rotor05un) and an off-center unbalanced disk (Rotor025un). Using numerical simulations and Monte Carlo analysis, we examined critical speeds and orbital patterns for both configurations. Probability distributions of shaft orbital positions revealed distinct patterns for each configuration. Quantile analysis revealed approximate linear trends for Rotor025un, suggesting higher system stiffness and more predictable behavior near critical speeds. Cross-sectional analyses of the orbits provided insights into the complex interactions between disk position, gyroscopic effects, and system natural frequencies. These findings provide valuable insights for rotor system design, particularly for applications with non-ideal mass distributions. The study goes beyond traditional critical speed analysis to examine orbital patterns and point on orbit occurrence from a probabilistic perspective. Based on the simulation of the orbits, an orbital is determined that allows the probability of the shaft occurring at the analyzed distance from the origin to be determined. The paper also offers insights into the complex interaction behavior of chosen rotor configurations and highlights the importance of considering disk position in predicting and optimizing rotor dynamic behavior, contributing to the development of more robust and efficient rotating machinery.

Keywords

• rotordynamics
• unbalanced mass
• uncertainty
• Monte Carlo analysis
• Laval rotor
• orbital analysis