## 4 Results
### Unbalanced Disc in Off-Center Position (Rotor025 un)
The plot reveals multiple concentric rings of varying probabilities, representing a complex, layered structure in the shaft's orbital behavior. For the cross-sectional analysis of the Rotor025 un configuration, we applied the same logic as in Figure 9. Four areas were identified (I, II, III, IV), corresponding to the left and right sides of the horizontal cross-section (A-A), and the lower and upper parts of the vertical cross-section (B-B). These areas are evaluated separately to provide a detailed understanding of the shaft's orbital behavior in different quadrants. Figure 19 represents the horizontal (A-A) cross-section analysis of the Rotor025 un shaft orbital, where the disk is mounted off-center at 1/4 of the shaft length. It shows Position I (a) and Position II (b) of the orbit. Both positions display roughly normal distributions of horizontal positions. Position I spans from about \(-2.6\) [mm] to \(-2.1\) [mm], and Position II ranges from 0.65 [mm] to 1.15 [mm]. The vertical spread is similar for both positions. Figure 18: Contour plot of shaft orbital position probability for the Rotor025 un configuration at critical speed. Figure 20 presents a side-by-side comparison of the probability distributions for the left (blue) and right (orange) sides of the horizontal cross-section in the Rotor025 un configuration. Both distributions show a roughly normal shape, but with a higher spike around \(0.85\,\mathrm{[mm]}\) and the sign of bimodal distribution of the second (right) position. The right-side distribution appears slightly more skewed compared to the left (to the axis of rotation). Figure 21 shows the vertical (B-B) cross-section analysis for the lower (Position III) and upper (Position IV) parts of the Rotor025 un shaft orbital. Position III ranges from about \(-2.65\,\mathrm{[mm]}\) to \(-2.15\,\mathrm{[mm]}\), while Position IV spans from \(0.6\,\mathrm{[mm]}\) to \(1.1\,\mathrm{[mm]}\). Both exhibit roughly normal distributions with asymmetry. The horizontal distribution remains similar. Figure 19: Horizontal (A–A) cross-section of the Rotor025 un shaft orbital: (**a**) Position I; (**b**) Position II. Figure 20: Horizontal axis cross-section A–A distribution for Rotor025 un configuration. Figure 22 represents a side-by-side comparison of the vertical position distributions for the lower (yellow) and upper (purple) parts of the orbit. Both distributions have an approximate shape of normal distribution and are noticeably skewed towards the central axis of rotation. The characteristic orbital patterns identified for different configurations can aid in fault diagnosis. Unusual orbital behaviors can be more accurately linked to specific issues based on our probabilistic findings. The boxplots (Figures 23 and 24) reveal a wider orbital pattern for Rotor05 un across both horizontal and vertical planes. The median positions are farther from the rotational axis, indicating a larger overall orbital diameter. The data also show a higher degree of symmetry in orbital behavior. Additionally, there is a greater presence of outliers compared to Rotor025 un. These characteristics suggest a more dynamic orbital motion for Rotor05 un. Figure 21: Vertical (B–B) cross-section of the Rotor025 un shaft orbital: (**a**) Position III; (**b**) Position IV. Figure 22: Vertical axis cross-section B–B of Rotor025 un. In contrast, Rotor025 un demonstrates a narrower orbital pattern, particularly in positions I and III. The median positions are closer to the rotational axis, implying a smaller orbital diameter. The data suggest a slight asymmetry in orbital behavior, likely influenced by the off-center disk placement. Outliers are less prominent compared to Rotor05 un. Overall, Rotor025 un exhibits a more constrained and less variable orbital motion. Table 1 presents a detailed quantitative comparison of shaft orbital positions for the Rotor05 un and Rotor025 un configurations across horizontal (A-A) and vertical (B-B) cross-sections.