# Parametric Selection of Optimized Epicyclic Gearbox Layouts for Wind Power Plant Applications
## 2 The Structure of Epicyclic Gear Trains  
To understand the structure of a multi-carrier epicyclic gear train, it is necessary to start from its basic building block, the simple epicyclic gear train. This basic gear train is classified as 1 AI according to the German classification system, 2k-h, type A according to [PERSON], or \(\overline{\text{AI}}\) according to [PERSON] and [PERSON], and it is required for the assembly of any complex planetary gear train (PGT) [31]. The schematic representation of this simple train is provided in Figure 1.  
Its basic parts are the sun, or central gear 1, annulus or ring gear 3, three or more planet gears 2, and the planet carrier H. The specific torques acting on its shafts have been added to the Wolf\(-\)Arnaudov symbol [49]. The different lines of the Wolf\(-\)Arnaudov symbol correspond to gearset shafts, notably the thin line to the sun gear shaft, the thick line to the ring gear shaft, and finally the double line to the planet carrier shaft. The thickness of the lines also corresponds to the intensity of the torques acting on the gear train shafts; \(T_{1}\) and \(T_{3}\) are equidirectional external torques of different size, while \(T_{\text{H}}\) is the largest torque, equal to the absolute value of the sum of the other two torques and, therefore, marked with a double line. The ideal torque ratio \(t\) of the gear train numerically equals the negative value of the internal transmission ratio \(i_{0}\), and it corresponds to the ratio of the number of ring gear teeth \(z_{3}\) to the number of sun gear teeth \(z_{1}\) (Equation (1)). \[t=\frac{T_{3}}{T_{1}}=\frac{|z_{3}|}{z_{1}}=-i_{0}>+1, \tag{1}\]  
The calculation of the shaft torque ratio is provided by Equation (2) as the relation of the torque on the sun gear shaft \(T_{1}\) to the torque on the ring gear shaft \(T_{3}\) and the torque on the planet carrier shaft \(T_{\text{H}}\). \[T_{1}:T_{3}:T_{\text{H}}=+1:+t:-(1+t), \tag{2}\]  
A multi-carrier gear train is created by connecting the shafts of its basic gear trains. This paper deals with two- and three-carrier gear trains, one-speed, two-carrier trains with three external shafts composed of two basic component trains will be considered, while three-carrier gear trains will be created by series connecting a two-carrier train with a simple component train. As the two-carrier trains do not need to have shifting capabilities, two-carrier trains with three external shafts will be used, having two single and one connecting shaft, the fourth connecting shaft being internal, as schematically shown in Figure 2. The external shaft torques (\(T_{\text{W}}\), \(T_{\text{N}}\), and \(T_{\text{E}}\)) have been labelled following the cardinal directions (W, N, and E). The respective ideal torque ratios (\(t_{\text{I}}\) and \(t_{\text{II}}\)) and efficiencies (\(\eta_{\text{OI}}\) and \(\eta_{\text{OII}}\)) of the respective component gear trains have been marked. Each component gear train may be arranged in six different ways (Figure 3), enabling the creation of 36 different epicyclic gear train layouts [50], showing that the basic component trains may be combined to create 36 different gear train schemes. However, some schemes are kinematically isomorphous, reducing this number to 21 in practice [51], Figure 4.  
Figure 1: Simple planetary gear train (**left**); Wolf\(-\)Arnaudov symbol (**right**). Every gear train scheme is capable of six different operating modes or layout arrangements, as any external shaft may be used as the reaction element, while the other two external shafts may be used as either input or output, resulting in a total of 126 different transmission variants (21 schemes \(\times\) 6 operating modes = 126) [50]. The power input and output are noted by cardinal directions, while the cardinal direction of the reactive stationary element is placed in parentheses.