## 4 Results
### Unbalanced Disc in Off-Center Position (Rotor025 un)  
Figure 15 shows the configuration of a rotor with an unbalanced disk positioned off-center, at a distance of 4 of the bearing span. As the shaft deflects, the disk tilts relative to the axis of rotation, which may exhibit a stronger influence of the gyroscopic effect. This can potentially change the system's stiffness and \"shift\" the critical speed to higher values [17; 20; 22]. The gyroscopic effect arises due to the misalignment between the disk's axis of rotation and the shaft's axis of rotation. The scatter plot in Figure 16 shows the critical speed calculated independently for numerous individual simulations (\"trials\"). The horizontal axis of the scatter plot represents the number of individual simulation runs. The critical speed ranges from 1100 to 1200 [rad/s], with an average value of 1146.1 [rad/s], which can be seen in the attached histogram (Figure 16). The dispersion of critical speed is approximately 8.3%, or \(\pm\)4.15% relative to the average value of 1146.1 [rad/s]. The corresponding rotational frequency, which is approximately 182 [Hz], is shown on the secondary y-axis. Compared to the previous configuration with a centrally located unbalanced disk (Figure 5), this configuration shows greater sensitivity to the unbalanced additional mass by approximately 2% within the range of critical speed values. The histogram exhibits (for the evaluated number of  
Figure 14: Normal probability plots of shaft orbital positions for Rotor05 un configuration: (**a**) horizontal cross-section (A–A); (**b**) vertical cross-section (B–B). Figure 15: Schematic display of Rotor025 un configuration. simulation runs) two peaks of critical speed, one around 1140 [rad/s] and the other in the region of 1160 [rad/s], suggesting a bimodal probability distribution (Figure 16). Figure 17 illustrates the probability distribution of the shaft's orbital positions for the Rotor025 un configuration. The 3D projection (Figure 17a) provides a volumetric visualization of the probability density, with height and color representing probability. The top view (Figure 17b) reveals a ring-like pattern of probabilities, where the axes represent horizontal and vertical displacements in millimeters. The color scale in both figures indicates probability density. Figure 16: Critical speed analysis for Rotor025 un configuration. Left: scatterplot of critical speeds across multiple simulation trials. Right: histogram showing the probability distribution of critical speeds. Figure 17: Probability of shaft orbital position for Rotor025 un configuration: (**a**) 3D view of the shaft orbital probability distribution; (**b**) top view of the probability distribution. This visualization confirms the circular orbit observed in a previous analysis of Rotor05 un (Figure 7) and suggests a stable oscillation amplitude throughout the rotation. The highest probability concentrates in the central circle of the ring, indicating a well-defined orbital path with limited dispersion. In comparison with the Rotor05 un configuration, this figure shows a smaller orbital diameter. The probability is more evenly distributed around the ring, likely due to the wider range of calculated critical speeds. This more uniform distribution suggests a more consistent orbital behavior despite the off-center disk placement, highlighting the complex dynamics introduced by the disk's position. A contour plot (Figure 18) illustrates the probability distribution of the shaft's orbital positions for the Rotor025 un configuration, where the unbalanced disk is mounted off-center at a distance of \(\lambda\)4 of the bearing span. The overall circular shape indicates that the shaft's orbit remains predominantly circular, despite the asymmetric disk placement. Interestingly, the distribution appears largely symmetrical, suggesting a balanced behavior that counters intuitive expectations for an off-center configuration.