Reliability assessment of critical speed in spinning disks under uncertainty

Ensuring the structural integrity of spinning disks under uncertain operating conditions is essential for high-speed engineering systems. This study presents a reliability-based assessment of out-of-plane vibrations by incorporating uncertainty in key design parameters. An exact analytical solution from the literature is adopted to compute the first critical speed with high precision. Sensitivity analysis shows that variations in radius, thickness, and elastic modulus significantly affect the onset of dynamic instability. These parameters, together with angular velocity, are treated as independent random variables. A limit state function is defined based on the first critical speed, and the reliability index is evaluated using Monte Carlo simulation. Results indicate a steep decline in the reliability index as angular velocity approaches the critical threshold, emphasizing the importance of accounting for parameter variability in design. This approach provides valuable insight into the probabilistic behavior of spinning disks and supports safer and more efficient designs in demanding applications such as turbines, brake and clutch systems, cutting disks, and data storage devices.