## 5 Parametric Analysis of the Amplitude of VC Vibration in Rolling Bearings
### Loaded Rolling Bearing the Influence of the Total Number of Rolling Elements and External Load  
The diagrams in Figures 10-13. show the influence of the external radial load and the total number of rolling elements on the basic parameters that define the VC vibrations of the rolling bearing (bearing deflection (\(w_{o}\)) and (\(w_{e}\)), \(pp\)-amplitude due to contact deformations (\(\Delta_{2}\)) and total \(pp\)-amplitude (\(\Delta\))). In order to exclude the influence of the internal bearing construction, the analysis was made with respect to the ratio of the external radial load and the effective bearing stiffness coefficient (\(Q\)/\(K\)). The analysis was made for bearings with an internal radial clearance of \(e=15~{}\upmu\)m.  
It is clear that the increase of the external radial load causes an increase of the contact deformations in bearing and, consequently, an increase in the bearing deflection. However, for bearings with a larger number of rolling elements, this increase is much milder. The diagrams in Figures 10 and 11 confirm that an increase in the total number of rolling elements in the bearing significantly influences the reduction of bearing deflection. In Figure 12, the change in \(pp\)-amplitude due to contact deformations (\(\Delta_{2}\)) is shown. In relation to the total number of rolling elements in the bearing, the diagram in the figure can be divided into two characteristic areas. The first area refers to bearings with a small total number of rolling elements (\(z\leq 6\)). In this area, with increasing external radial load, the level of \(pp\)-amplitude (\(\Delta_{2}\)) increases significantly. For these bearings, the maximum number of roller bearings that can be found in the load zone is \(z_{s}=3\), that is, the external load is transferred according to _the support system 2-3_. In Section 5.3, it is shown that in _the support system 2-3_, very high values of the \(pp\)-amplitude (\(\Delta_{2}\)) occur and the total VC vibrations are more influenced by the contact deformations. In the second area, due to the larger number of rolling elements in the bearing, the contact deformations are smaller and the level of \(pp\)-amplitude \(\Delta_{2}\) decreases. Figure 11: Three-dimensional dependence of bearing deflection (\(w_{e}\)) on the total number of rolling elements (\(z\)) and level of external load (\(Q\)), for the BSE position of rolling bearing. Figure 10: Three-dimensional dependence of bearing deflection (\(w_{o}\)) on the total number of rolling elements (\(z\)) and level of external load (\(Q\)), for the BSO position of rolling bearing. In Figure 13, the change of the total \(pp\)-amplitude of VC vibrations (\(\Delta\)) is shown. Three characteristic areas can be distinguished in this diagram. The first two areas are characterized by quite high values of the total \(pp\)-amplitude. In the first area, the \(pp\)-amplitude takes values up to \(-15~{}\upmu\)m and in the second area up to \(8~{}\upmu\)m. The first area refers to bearings with a total number of rolling elements \(z\leq 6\). Due to the small number of rolling elements the contact deformations are large in this area. Therefore, in the first region, the influence of contact deformations on VC vibrations is predominant, and the  
Figure 12: Three-dimensional dependence of vibration amplitude due to contact deformations (\(\Delta_{2}\)) on the total number of rolling elements (\(z\)) and level of external load (\(Q\)). Figure 13: Three-dimensional dependence of the total amplitude of VC vibration (\(\Delta\)) on the total number of rolling elements (\(z\)) and the level of external load (\(Q\)). total \(pp\)-amplitude (\(\Delta\)) is negative. The second area refers to bearings with a total number of rolling elements from 7 to 9. Due to the larger number of rolling elements, a significant decrease in amplitude (\(\Delta_{2}\)) occurs in this region, so high values of total \(pp\)-amplitude are a consequence of high values of amplitude \(\Delta_{1}\). The values of total \(pp\)-amplitude in this region are positive.