## 5 Parametric Analysis of the Amplitude of VC Vibration in Rolling Bearings
### Loaded Rolling Bearing the Influence of Internal Radial Clearance and External Load  
Figures 6-9 present the three-dimensional diagrams of the bearing deflection (\(w_{o}\)) and (\(w_{e}\)) in BSO and BSE positions, as well as the sizes of the vibration amplitude due to the contact deformations (\(\Delta_{2}\)) and the total amplitudes of VC vibrations (\(\Delta\)), depending on the size of the internal radial clearance and external radial load, for the 6206 ball bearing. The value of the internal radial clearance was varied in the range from 0 to 60 \(\upmu\)m on the diagrams. That is nearly equal to the maximal recommended value of internal radial clearance for the 6206 ball bearing [30]. The value of the external radial load was varied up to a static load rating of the bearing 6206, which is \(Q=11200\) N.  
The diagrams of the dependence of relative displacement of bearing rings (\(w_{o}\)) and (\(w_{e}\)) due to the contact deformations are given in Figures 6 and 7. The contact deformations of bearing elements increase together with the increase of the level of external radial load, but also with the increase of internal radial clearance size. However, the increase of the contact deformations is fairly more pronounced for the increase of the external radial load. The fact that the zones of various colors are almost parallel with the axis of internal radial clearance clearly indicates this. Also, it can be observed that there is a somewhat higher level of bearing deflection, at support on an odd (\(w_{o}\)) in relation to the support on an even (\(w_{e}\)) number of rolling elements. As the amplitude of the vibrations due to contact deformation (\(\Delta_{2}\)) is equal to the difference of the bearing deflection in the BSO and BSE positions (Equation (17)), the level of this amplitude has a positive value for all the combination of the external radial load and internal radial clearance of bearing. This is also shown in the diagram shown in Figure 8.  
Figure 6: Three-dimensional dependence of bearing deflection (\(w_{o}\)) on the size of internal radial clearance (\(e\)) and level of external load (\(Q\)), for the BSO position of 6206-single-row ball bearing. Figure 8: Three-dimensional dependence of vibration amplitude due to contact deformations (\(\Delta_{2}\)) on the size of internal radial clearance (\(e\)) and level of external load (\(Q\)) for the 6206-single-row ball bearing. Figure 7: Three-dimensional dependence of bearing deflection (\(w_{e}\)) on the size of internal radial clearance (\(e\)) and level of external load (\(Q\)), for the BSE position of 6206-single-row ball bearing. In Figure 8 the change of the \(pp\)-amplitude due to the contact deformations (\(\Delta_{2}\)) has been presented. In relation to the level of external radial load, we can discern two characteristic areas in this diagram. The first area is characterized by a high gradient of vibration amplitude due to the contact deformations (\(\Delta_{2}\)). In this area, the support of the inner ring is carried out by _support systems 1-2_, or possibly by _support systems 2-3_ (see Section 4.2). Because of the low intensity, the external radial load is not enough for the entering of a bigger number of rolling elements into contact with the bearing rings. The smaller number of rolling elements that transfer the external load, results in a less convenient load distribution into the bearing and in a sharper gradient of contact deformations. Hence, the steeper shape of the diagram of \(pp\)- amplitude \(\Delta_{2}\) in the direction of the external radial load in this area. On the other side, and increasing the clearance will also cause an increase in the level of the amplitude \(\Delta_{2}\) in this area, except for _support system 1-2_. In _support systems 1-2_, the size of the clearance does not affect the vibration amplitude \(\Delta_{2}\). The vibration amplitude due to the contact deformation stays constant, regardless of the increase of internal radial clearance in _support systems 1-2_.