# Quasi-Static Load Sharing Characteristics of a Planetary Fear Set with Planet Journal Bearings
## 4 Results and Discussion
### Influence Parameters  
The bearing support stiffness of a planetary gear set has a great effect on the load sharing factor [31; 32]. The journal bearing stiffness and the load sharing factor are analyzed with different influential parameters. The following figures show the influence of each parameter on the stiffness and the load sharing factor. The structure characteristics of the planetary gear set applied in the computation remain constant. Table 1 gives the structure parameters of the planetary gear set. Table 2 gives the reference parameters in Equations (19)-(27) for estimating the cumulative meshing error. Figure 9 presents significant variations of the load sharing factor and the journal bearing stiffness with different lengths and diameter ratios of the journal bearings. Both the stiffness and the load sharing factor changed significantly when the lengths and diameter ratio was smaller than 0.75. Under the same rotation speed and load, smaller lengths and diameter ratio increases the eccentricity ratio. When the lengths and diameter ratio becomes larger, the eccentricity ratio also decreases. It seems that the influence of the lengths and diameter ratios is similar to that of the rotation speed. The results also indicate that the load sharing factor is relatively low when the ratio is around 0.7. It is important to choose a suitable ratio to get a proper load sharing factor. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Sun** & **Planet** & **Ring** \\ \hline Number of planets & - & 4 & - \\ Number of teeth & 48 & 30 & 108 \\ Normal module & 1 & 1 & 1 \\ Pressure angle (\({}^{\circ}\)) & 20 & 20 & 20 \\ Helix angle (\({}^{\circ}\)) & 20 & 20 & 20 \\ Center distance (mm) & \multicolumn{2}{c}{39} & 39 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of the planetary gear set. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Component** & **Parameter** & **Value** \\ \hline sun & \(\beta_{s}\) & \(3^{\circ}\) \\ planet & \(\beta_{pi}\) & \(2^{\circ}/1^{\circ}/1.5^{\circ}/1.5^{\circ}\) \\ carrier & \(\beta_{c}\) & \(9^{\circ}\) \\ ring & \(\beta_{r}\) & \(1.8^{\circ}\) \\ sun & \(\gamma_{s}\) & \(6^{\circ}\) \\ ring & \(\gamma_{r}\) & \(3.6^{\circ}\) \\ gear & \(\alpha_{w}\) & \(20^{\circ}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Reference parameters for meshing errors calculation. Figure 9: Load sharing factor vs. lengths and diameter ratios. Figure 10 illustrates the trends of the load sharing factor and the journal bearing stiffness of the planetary gear with the relative clearance \(\psi\), which is calculated by _c/r_. As the relative clearance increased, the stiffness and the load sharing factor both decreased to be stable. When the relative clearance is small, the oil film is thin and the stiffness is large under the same load and rotation speed. As the relative clearance becomes larger, the minimum film thickness will be smaller so as to achieve sufficient load capacity. Thus, the relative clearance should not be too large. Figure 11 shows the load sharing factor and the journal bearing stiffness with different viscosity values. The rotation speed was lower in Figure 11a and was higher in Figure 11b. As the viscosity increased, the bearing stiffness and the load sharing factor increased under the same speed and load. It seems that the load sharing factor reached a minimum value with a small viscosity at the lower rotation speed. As the rotation speed increased, the stiffness and the load sharing factor also became larger. However, the load sharing factor change rate slowed down with a larger viscosity. Figure 11: _Cont._  
Figure 10: Load sharing factor vs. relative clearance. The variations of the load sharing factor and the bearing stiffness of the load are illustrated in Figure 12. It can be found that the load sharing factor is not only determined by the bearing stiffness. As the load increased, the bearing stiffness increased. However, the load sharing factor decreased to a stable value at last.