# Dynamic Simulation of a 5 Degrees of Freedom Rotor Dropping on a Protective Bearing
## 3 Characteristic Analysis of Dynamic Simulation Model of 5-Dof Rotor-Protective Bearing System  
### Simulation Study on Load Distribution of Protective Bearing  
After completing the geometric parameter calculation of the protective bearing and rotor and the rotor-protective bearing system modeling in ADAMS, the protective bearing model needs to be verified in order to verify the accuracy of the model and parameter setting due to the complex internal structure of the protective bearing. According to the research on bearing load in the literature [8], when the inner ring of the protective bearing is subjected to radial load, the bearing area is general to its circumference, and each rolling body bears different loads, and its reasonable and radial loads are consistent. Assuming that the load on the inner ring of the protection bearing is known, the load on the maximum  
Figure 1: Schematic diagram of the 5-DOF rotor–protective bearing drop system modeling.  
bearing ball A is known, and the angle between the balls is known, then the force on each part of the bearing is known. The protective bearing model is shown in Figure 2.  
The load bearing of the bearing inner ring is borne by multiple balls, and the force balance can be obtained as follows [28]:  
\[F_{r}=Q_{A}+2Q_{B}\cos\gamma+2Q_{C}\cos 2\gamma+\dots \tag{8}\]  
Satisfaction relationship between balls [29]:  
\[\frac{Q_{B}}{Q_{A}}=\cos^{2/3}\gamma,\;\frac{Q_{C}}{Q_{A}}=\cos^{2/3}2\gamma, \tag{9}\]  
The relationship between the maximum load of the ball, the load on the inner ring, and the number of rolling elements \(Z\) can be simplified as follows [30]:  
\[Q_{A}=\frac{4.36}{Z}F_{r} \tag{10}\]  
Since the general rolling element inside the bearing has clearance, the actual bearing area is less than half of the bearing circumference, which is equivalent to fewer bearing balls under the same load, so the load borne by the maximum bearing ball in the actual situation is greater, and it is desirable to obtain:  
\[Q_{A}=\frac{5}{Z}F_{r} \tag{11}\]  
Figure 2: Schematic diagram of protective bearing modeling.  
The dynamic verification of the established angular contact bearing is carried out in ADAMS. Firstly, a constant speed is set for the inner ring of the bearing, and a radial load is set in the direction of the \(Y\)-axis of the inner ring of the bearing. Because the rotor falls on the protection bearing at the speed of 6000 r/min in the working condition, and it is a five-degree of freedom system, the load on a single protection bearing is 5000 N. The simulation time is 0.1 s. The inner ring load is shown in Figure 3.  
Taking Z = 29, it can be concluded that the maximum bearing capacity of the ball is 946 N, and it can be seen that the ball load in the simulation results is basically about 1000 N, which verifies the correctness of the simulation model. The reason for the error may be due to the choice of a 10 \(\upmu\)m clearance in the bearing modeling, and to the theoretical deduction of the calculation of the maximum bearing capacity of the ball; there are only two types: no clearance and clearance. The error may be caused by the difference in the clearance value.