## 1 Introduction
### Literature Review  
To analyze gear meshing losses, [PERSON] et al. [13] proposed a dynamic lumped mass model of a four-degree-of-freedom (4-DOF) gear system, and two separate formulas for friction coefficient were used to calculate friction power losses for gears of different geometries under various working conditions. However, the influence of different lubrication conditions on gear transmission efficiency was not been considered in the study. [PERSON] et al. [14] studied the influence factor of friction factor on the efficiency of spur gears with tip reliefs, calculated them using the average friction factor along the mesh cycle, and then compared with values obtained using an enhanced friction factor formula based on the fundamentals of elastohydrodynamic lubrication, but the study does not consider the effect of temperature on the elastohydrodynamic lubrication.  
[PERSON] et al. [15] used experimental data to derive the average friction factor of meshing gear pairs, and discussed the relationship between friction coefficient and the type of lubricating oil. [PERSON] et al. [16] designed a machine for testing power losses and then experimentally determined the variation in gear frictional losses during each individual tooth engagement period. [PERSON] et al. [17] calculated the frictional power loss on the tooth surface and meshing efficiency of a planetary gear train by considering elastic deformation of the flexible ring gear and dynamic friction in the contact region, but did not consider the influence of different lubrication conditions on gear transmission efficiency. [PERSON] et al. [18] proposed a method for calculating gear meshing efficiency using data from a gear testing machine.  
Recently, graph-based methods have become a major research focus [19]. Graph-based methods can be used to calculate the transmission efficiency of epicyclic gear trains, and effectively remove the need to manually determine the power flow direction, which can be cumbersome and error-prone. [PERSON] et al. [20] proposed a method for designing automatic transmission configuration schemes based on the lever analogy. In addition, they established a process for synthesizing multi-row multi-speed automatic transmissions; whereas a three-row mixed connection was the preferred connection, both two-row and three-row connections were demonstrated.  
[PERSON] et al. [21] presented a hypergraph-based approach for the kinematic analysis of complex gear trains. The hypergraphs were used to aid in the understanding of the inter-relation between the various branches of the mechanism and to develop the kinematic equations. [PERSON] et al. [22] proposed a method for calculating the efficiency of complex gear trains using graph and screw theory and established a one-to-one mapping relation between friction and efficiency, but the efficiency calculation considers the tooth surface friction power loss, ignoring other power losses.  
[PERSON] et al. [23] used graph theory to model a 2-DOF planetary gear transmission and a constraint analysis and the virtual power ratio were used to predict the efficiency of the system. Similarly, [PERSON] et al. [24] performed motion, torque, and power balances of a single-stage planetary gear transmission, plotted the power flow diagram of a 2K-H planetary gear transmission, and derived a power distribution law for the closed planetary gear transmission system. Finally, [PERSON] et al. [25] proposed a power flow analysis method based on matrix operations to determine power flow and transmission efficiencies of multi-stage planetary gear transmission systems.