## 5 Analysis and Calculation of Power Loss and Efficiency of a Two-State Logic Transmission  
The power loss of planetary transmission is currently mainly analyzed and calculated using the meshing power method, mainly calculating the meshing power during the planetary gear transmission process. This is because the planetary transmission mechanism usually adopts the method of conversion mechanism when calculating its speed or transmission ratio. By attaching a virtual rotation speed opposite to the rotation speed of the planetary array system, the planetary array system can be viewed as a \"fixed axis gear\" system with zero rotation speed of the planetary array. However, the relative speed and friction condition of the planetary carrier between the gears in the original planetary gear system have not changed, and the meshing power between the converted \"fixed shaft gear\" and the gears in the original planetary gear train remains unchanged. Since the input power \(p_{i}\) is equal to the sum of the output power \(p_{o}\) and the loss power \(p_{i}\), the efficiency of the gear transmission is the ratio of the output power \(p_{o}\) to the input power \(p_{i}\)  
\[\eta=\frac{P_{o}}{P_{i}}=\frac{P_{i}-P_{i}}{P_{i}} \tag{10}\]  
It is assumed that the tooth ring in the planetary row or the sun wheel has a fixed value, there is no fixed component \(j\), the speed is \(\omega_{j}\), the torque acting on the above is \(M_{j}\) and the rotational torque of the frame is \(\omega_{h}\) and \(M_{h}\), respectively. So, the meshing power of component \(j\) is \(P_{mesh}=M_{j}\big{(}\omega_{j}-\omega_{h}\big{)}=M_{j}\omega_{j}\big{(}1- \frac{\omega_{h}}{\omega_{j}}\big{)}\). The speed ratio \(\frac{\omega_{h}}{\omega_{j}}\) between frame \(h\) and component \(j\) is sometimes greater than 1 and sometimes less than 1 in different types of planetary arrays. There are two situations where the converted meshing power \(P_{mesh}\) and the transmitted power \(P_{j}=M_{j}\omega_{j}\) of the original gear train have the same or different directions, which brings complex direction judgments to power flow calculations. The [PERSON] efficiency calculation formula effectively solves this complex situation and provides a shortcut for calculating power loss and efficiency. The following uses the [PERSON] efficiency calculation formula to calculate the efficiency of the above gear (limited to space), respectively, through the kinematic transmission ratio and the dynamic transmission ratio. For the first gear, the formula is as follows:  
\[i=k_{21}k_{22}k_{41}k_{42}(1+k_{51}k_{52})=k_{2}k_{4}(1+k_{5}) \tag{11}\] \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Array of Planets** & **Gear** & & & & & \\ \cline{3-7}  & Sun & 1 & k\({}_{11}\)k\({}_{12}\) & 1 & k\({}_{11}\)k\({}_{12}\) & 1 \\  & Planet & 1 & k\({}_{12}\) & 1 & k\({}_{12}\) & 1 \\  & Ring & 1 & 1 & 1 & 1 & 1 \\  & Carrier & 1 & 0 & 1 & 0 & 0 \\ \hline  & Sun & 1 & k\({}_{11}\)k\({}_{12}\) & 1 & k\({}_{11}\)k\({}_{12}\) & 1 \\  & Planet & 1/k\({}_{21}\) & k\({}_{11}\)k\({}_{12}\)/k\({}_{21}\) & 1 & k\({}_{11}\)k\({}_{12}\) & 1/k\({}_{21}\) \\  & Ring & 1/k\({}_{21}\)k\({}_{22}\) & k\({}_{11}\)k\({}_{12}\)/k\({}_{21}\)k\({}_{22}\) & 1 & k\({}_{11}\)k\({}_{12}\) & 1/k\({}_{21}\)k\({}_{22}\) \\  & Carrier & 0 & 0 & 1 & k\({}_{11}\)k\({}_{12}\) & k\({}_{11}\)k\({}_{12}\) \\ \hline  & Sun & 1/k\({}_{21}\)k\({}_{22}\) & k\({}_{11}\)k\({}_{12}\)/k\({}_{21}\)k\({}_{22}\) & 1 & k\({}_{11}\)k\({}_{12}\) & K\({}_{31}\)k\({}_{32}\)/k\({}_{21}\)k\({}_{22}\) \\  & Planet & 1/k\({}_{21}\)k\({}_{22}\) & k\({}_{11}\)k\({}_{12}\)/k\({}_{21}\)k\({}_{22}\) & 1 & k\({}_{11}\)k\({}_{12}\) & k\({}_{32}\)/k\({}_{21}\)k\({}_{22}\) \\  & Ring & 1/k\({}_{21}\)k\({}_{22}\) & k\({}_{11}\)k\({}_{12}\)/k\({}_{21}\)k\({}_{22}\) & 1 & k\({}_{11}\)k\({}_{12}\) & 1/k\({}_{21}\)k\({}_{22}\) \\  & Carrier & 1/k\({}_{21}\)k\({}_{22}\) & k\({}_{11}\)k\({}_{12}\)/k\({}_{21}\)k\({}_{22}\) & 1 & k\({}_{11}\)k\({}_{12}\) & 0 \\ \hline \hline \end{tabular}
\end{table}