# Quasi-Static Load Sharing Characteristics of a Planetary Fear Set with Planet Journal Bearings
## 1 Introduction  
In planetary gear sets, multiple planet gears are used to form power split and planetary gears provide higher power density than parallel axis gears [1]. The planetary gear set has been widely applied in wind turbines [2] and automatic transmissions [3; 4]. It uses three or more spaced planet gears. In the ideal situation, each planet gear equally shares the load. However, planet gear loads are not always equally distributed in practice. With unequal loads, planet-bearing forces increase, leading to reduced bearing life and failures [5; 6]. Further, the planet-bearing often operates at a high rotation speed to satisfy a higher power density requirement [7; 8]. This also affects the planet-bearing reliability. Due to better performance at a high rotation speed [9], the journal bearing becomes an appropriate planet-bearing choice, as shown in Figure 1.  
Load sharing in planetary gear sets has been investigated extensively. [PERSON] [10] indicated that floating central members could lead to perfect load sharing in a three-planet gear set. In 1986, [PERSON] [11] showed that load sharing characteristics are improved with the increasing input torque by an experimental study. The shear strain of planet pins was measured to investigate the load sharing characteristics. The studies mainly focused on the three-planet system. In 1994, [PERSON] [12] established a nonlinear time-varying dynamic model and quantitatively investigated the influences of the main design parameters, manufacturing, and assembly errors on load sharing conditions. The load sharing characteristics of the four-planet system were investigated. A reasonable agreement between the mathematical model and the test results was achieved [13]. [PERSON] also establisheda dynamic planetary transmission model [14], by which the design parameters could be given to an arbitrary number of planets. The four-planet system research was also expanded by adding a flexible ring gear [15]. [PERSON] and [PERSON] [16] investigated the influence of manufacturing errors using an improved contact model. [PERSON] [17] and [PERSON] [18] indicated that the stiffness of the needle bearings has a major influence on gear contact pattern, and the double pinion planetary arrangement is more likely to result in off-centered loading. [PERSON] [19] also physically explained the basic mechanism of unequal load sharing and obtained the analytical expressions to estimate unequal load sharing caused by position errors. On this basis, [PERSON] [20] proposed the concept of a load sharing map to describe the load sharing characteristics of planetary gears with arbitrary position errors and load levels. [PERSON] [21] designed a new low spring constant planet pin that was shown to have significantly superior load sharing characteristics. Considering the instantaneous geometric shapes influenced by tooth deformations and errors, [PERSON] and [PERSON] [22] illustrated the influence of planet position errors on the load sharing characteristics.  
Most of the investigations focused on the load sharing characteristics of planetary gear sets with planet rolling bearings. The bearing stiffness can be considered as a constant. However, for the planetary gear set using journal bearings, the bearing stiffness becomes variable. It leads to more complicated load sharing characteristics. The paper studies the load sharing characteristics of planetary gear sets using planet journal bearings. A load sharing analysis model considering the hydrodynamic effect of the journal bearing is established. The influences of bearing parameters on load sharing characteristics are analyzed. It is aimed to provide an effective method for the design of the high-speed planetary gear set using planet journal bearings.