## 5 Case Analysis of Load-Sharing Performance  
### Case Analysis of Load-Sharing Performance on Efficiency  
Based on the basic parameters of the herringbone tooth star gear train in a GTF (as shown in Table 1), the load sharing and efficiency of the gear train were simulated and analyzed in Romax. The variation curve of load distribution with time for a five way split star gear train under standard installation is shown in Figure 7. The following conclusions can be drawn from the figure: (1) under the standard installation, the load of the five-way split herringbone gear train is also uneven. (2) The load distribution of input torque is determined by the two-stage meshing transmission, which is mainly reflected in the fact that the first- and second-stage transmissions have the same load distribution coefficient. (3) The load distribution curve changes periodically with the meshing position of the herringbone tooth meshing pair. Figure 6: Equivalent engagement error of the sun gear. The variation curve of the load-sharing coefficient of the herringbone tooth star gear train with input power under a five-way shunt is shown in Figure 8. It can be seen from the figure that the load-sharing coefficient of the gear train decreases with the increase in power, and the load-sharing coefficient is about 1.16 at the rated power. The load coefficient of the gear train with installation error was analyzed, and the conclusion is consistent with that of the theoretical analysis. The details are as follows: (1) In the five-way meteor gear train, the center distance between the sun gear and the \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Sun Gear** & **Star Gear** & **Annular Gear** \\ \hline Tooth number & 43 & 42 & 127 \\ Tooth width (mm) & \(60\times 2\) & \(59\times 2\) & \(57\times 2\) \\ Rotation speed (r/min) & 7463 & \(-7640.69\) & \(-2526.84\) \\ Power (KW) & & 20,000 & \\ Normal module (mm) & & 3.5 & \\ Normal pressure angle (\({}^{\circ}\)) & & 22.5 & \\ Spiral angle (\({}^{\circ}\)) & & 26.969 & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Basic parameters of herringbone tooth star gear train in a GTF. Figure 8: The load-sharing coefficient varying with the input power of herringbone star gear system. Figure 7: Load coefficient of the herringbone gear train under standard installation: (**a**) internal contact, (**b**) external contact. inner gear ring under the standard installation is zero. (2) Under non-standard installation, regardless of whether the sun gear or the inner gear ring has installation error, the center distance between the inner gear ring and the sun gear appears. (3) The absolute value and direction angle of the center distance between the inner gear ring and the sun gear due to the installation error have different effects on the load of each shunt branch of the gear train, but they affect the load distribution coefficient of the gear train as a whole. (4) When the size and azimuth of the center distance between the inner gear ring and the sun gear are the same, regardless of whether the center distance comes from the sun gear or the inner gear ring, the influence on the load-sharing coefficient of the whole gear train is basically the same, as shown in Table 2. (5) The center distance error mainly affects the branch load coefficient on the direction angle of the center distance. In engineering application, this point may be used to reduce the load coefficient of the gear train by setting an appropriate value for the center distance error. Considering the load coefficient, the efficiency of the star gear train was analyzed. The efficiency curve varying with torque is shown in Figure 9. From the efficiency curve, the uneven distribution of five shunt loads will reduce the efficiency of the gear train, and the greater the load-sharing coefficient, the lower the efficiency. Without load-sharing measures, the load coefficient of the star gear train with a five-way power split is about 1.12, which is slightly lower than the efficiency of theoretical load sharing.