## 4 Results
### Unbalanced Disc in the Rotor Central Position (Rotor05 un)
The top histogram displays the probability distribution of positions along A-A, providing insight into the likelihood of the shaft being at specific horizontal locations. The right-side histogram shows the distribution of vertical deviations from A-A, indicating the spread of points around the cross-section line. To better see the difference between the positions I, and II, Figure 11 illustrates the probability distribution of the shaft's horizontal positions along the A-A cross-section plane, distinguishing between the left (position I, blue) and right (position II, orange) sides of the orbital. Each side of the distribution roughly follows a normal (Gaussian) pattern, though not perfectly symmetrically. Distributions are asymmetrical. The right side (orange) shows a slightly higher peak probability and a narrower spread compared to the left side (blue). Figure 9: Cross-sectional analysis locations for Rotor05 un configuration. Figure 12 illustrates the distribution of shaft positions along the vertical cross-section B-B, for the lower and upper semicircles of the orbital, respectively. The central scatterplot in each figure represents individual points from multiple shaft orbitals. Here, the horizontal axis shows deviation from B-B, while the vertical axis represents the position along B-B. The top histogram displays the probability distribution of horizontal deviations from B-B, showing the lateral spread of the shaft's position. The right-side histogram shows the distribution of positions along B-B, indicating the likelihood of the shaft being at specific vertical locations. Figure 11: Horizontal axis cross-section A–A. Figure 10: Horizontal (A–A) cross-section of the Rotor05 un shaft orbital: (**a**) Position I; (**b**) Position II. The histogram in Figure 13 shows the probability distribution of the shaft's vertical positions along the B-B cross-section plane. The upper and lower distributions show notable asymmetry. The lower distribution (yellow) exhibits a broader, more uniform spread, while the upper distribution (purple) is more concentrated with a higher peak probability. The asymmetry and non-uniform spread suggest the presence of anisotropic forces or structural asymmetries in the rotor system. The more uniform spread in the lower semicircle might indicate greater variability in shaft position, possibly due to gravitational effects or system-specific factors. The probability distributions (Figures 11 and 13) are not perfectly symmetric or identical, which could indicate slight imbalances or asymmetries in the rotor system The similarity between horizontal and vertical distributions suggests a nearly circular orbit. The clear separation between peaks in both directions indicates a well-defined orbital path with minimal deviation. Figure 12: Vertical (B–B) cross-section of the Rotor05 un shaft orbital: (**a**) Position III. ; (**b**) Position IV. Figure 13: Vertical axis cross-section B–B of Rotor05 un. The plots in Figure 14 assess the normality of the shaft's position distribution in both horizontal (A-A) and vertical (B-B) cross-sections. This figure presents four normal probability plots, each corresponding to a different quadrant of the shaft's orbital motion at critical speed. All four plots in Figure 14 show a generally linear trend, indicating that the shaft's horizontal and vertical positions approximately follow a normal distribution. Plots also display some deviation from perfect linearity, particularly at the extremes, which is common in real-world data. These deviations might indicate the presence of outliers or suggest that the underlying distributions have slightly heavier tails than a perfect normal distribution.