## 3 Methodology  
In our previous study [19], we investigated the dynamic behavior of two rotor configurations: a centrally mounted unbalanced disk (Rotor05 un) and an off-center unbalanced disk (Rotor025 un). We employed a Jeffcott rotor system model, with each rotor simplified as an identical shaft-disc with an eccentric mass. This model comprised a flexible steel shaft with uniform circular cross-section, a rigid disk with a mass imbalance, SKF 61805 deep groove ball bearings, and aluminum shaft shackles. The bearings incorporated stiffness, non-linearity, and realistic contact behavior. The aluminum shaft shackles acted as a shaft adapter between the bearings and the shaft. The study develops a method to estimate critical velocity for flexible rotors with uncertain parameters. It highlights the impact of mass distribution on rotor behavior and demonstrates the value of probabilistic analysis in understanding rotor dynamics. While the method is effective, it is computationally intensive and relies on accurate model assumptions. Building upon the previously validated numerical model, this study focuses on shaft orbital analysis incorporating uncertainty. Experimental validation was conducted for a rotational speed of 377 [rad/s] (60 [Hz]) with a 6.1 [g] unbalance mass. Comparison of experimental and simulated orbital trajectories (Figure 3) revealed good agreement, indicating that the numerical model captures the essential characteristics of the rotor's motion reasonably well. The Monte Carlo simulation process used in this study builds upon the method described in our previous work [19]. This analysis was conducted using Adams Insight, a component of MSC Adams/View software (version 2023.4), which implements the Monte Carlo method for design optimization and uncertainty analysis. This method randomly sets values of the specified design factors for each run of the simulation. The investigation aims to evaluate the impact of real-world variations on the design's performance. By conducting over 400 trials, statistical predictions regarding the design's response can be established. The method's foundation lies in representing parameters using a Probability Density Function (PDF). The investigation strategy chosen was the Monte Carlo method, and the design type was Full Factorial, which is a comprehensive method. It incorporates every potential combination of levels (number of possible values that can be taken by a design factor) for each design factor. The number of runs required follows a mathematical formula: m'n, where \"m\" is the number of levels and \"n\" represents the number of factors. However, it is good to note that, as the values of \"m\" and \"n\" escalate,  
Figure 3: Comparison of numerical and experimental shaft orbital [19]. Full Factorial becomes more appropriate for experiments involving a limited number of factors as the number of runs increases exponentially. Based on the specified design type, Adams Insight produces a design matrix. In this study, we identified key design factors affecting dynamics of the analyzed rotor configurations, such as bearing damping, bearing clearance, and mass imbalance. For each parameter, we defined a suitable PDF based on expected real-world variations and manufacturing tolerances. For each run, we recorded key outputs such as critical speeds and orbital characteristics. Overall methodology can be summarized in these five points:  
1. Input variables (key design factors) were specified;
2. For each input variable, an interval of permissible values was defined;
3. Assuming a normal distribution on this interval, a set of values was randomly generated in Adams Insight, which were then put into the computational model;
4. A calculation was performed for this set of input variables. The Newmark solver (Adams) was used here because stability of the solution and low computation time were also required with random selection of input variables and repeated computations;
5.