# Parametric Selection of Optimized Epicyclic Gearbox Layouts for Wind Power Plant Applications
## 3 Methods
### 2-SPEED Software Program  
The 2-SPEED software program was purposefully developed by the author [PERSON] to identify viable gearbox solutions under application constraints, and it is equipped with both multiplier and reducer gear calculation subsystems. The software was used to identify the optimal solutions discussed in this paper, and its principle of operation must be explained. The program identifies and synthesizes the schemes and layout variants of two-carrier epicyclic gear trains and their parameters that satisfy the user-imposed parameters of power rating, overall transmission ratio, input torque, and input shaft rotational speed. The user is also able to impose additional design constraints, e.g., component gearest parameters, material limitations, etc. Within these limits, the program searches for valid gear train configurations which are listed in user-determined priority, according to the criteria of maximum efficiency, minimum weight, or minimal size. The program also contains a weighted coefficient method-based multi-criteria optimization routine for the selection of gear train schemes and layouts, as every two-carrier gear train may be built using several schemes and layout variants; however, each solution may be the best one according to a different optimization criterion. The program is capable of calculations on single- and two-carrier gear trains, and it can calculate two-carrier gear trains with three and four external shafts. Trains with three or more carriers are considered combinations of single- and two-carrier gear trains and dealt with accordingly. The user is required to provide input data through a text file containing the following information:  
* Interval of the required transmission ratio(s) (\(i_{\text{min}}\ldots i_{\text{max}}\)), stated from the lowest to the highest, including the required tolerance;
* Minimal durability requirement of the planet bearings, \(L\), h;
* Planet bearing type (rolling or sliding);
* Input torque \(T_{\text{A}}\), Nm;
* Input shaft speed, \(n_{\text{A}}\), min\({}^{-1}\);* Target intervals of planetary gear set torque ratios (\(t_{\rm{Imin}}\dots t_{\rm{Imax}}\)) and (\(t_{\rm{IImin}}\dots t_{\rm{IImax}}\));
* Tooth number of the first and second gegaret sun gears \(z_{\rm{II}}\) and \(z_{\rm{II}}\);
* Data for calculation of the relative losses \(\psi_{0}\);
* Gearset module(s) according to ISO 54 [53] or DIN 780 [54];
* Data for sizing based on tooth flank stress;
* Data for sizing based on tooth root stress. The program contains separate subroutines (Figure 7) depending on the case, whether reducer gear trains (\(\left\lvert i\right\rvert>1\)) or multiplier gear trains (\(0<\left\lvert i\right\rvert<1\)) are calculated, but all subroutines sift through all of the valid combinations of ideal torque ratios of the component gear trains \(t_{\rm{I}}\) and \(t_{\rm{II}}\), keeping only those that provide an overall transmission ratio within the user-determined limits, with a user-selectable option to operate with a fixed number of planet gears \(p\), or for the software to vary that number within acceptable limits (\(p=3\dots 6\)) [33]. The ideal torque ratios \(t\) are calculated using the tooth numbers of the sun \(z_{1}\) and ring gears \(z_{3}\) for component gear train I (Equation (12)) and for component gear train II (Equation (13)):  
\[t_{\rm{I}}=\frac{\left\lvert z_{\rm{3I}}\right\rvert}{z_{\rm{II}}}, \tag{12}\]  
\[t_{\rm{II}}=\frac{\left\lvert z_{\rm{3 II}}\right\rvert}{z_{\rm{III}}} \tag{13}\]  
The tooth numbers of the sun gear \(z_{1}\) and planet gear \(z_{2}\) are compared and adjusted accordingly to prevent undercutting. The tooth numbers of the ring gears \(z_{\rm{3I}}\) and \(z_{\rm{3 II}}\) are then set to obtain \(t_{\rm{I}}=t_{\rm{II}}=1.5\) or derived from any user-selected value, if the user input satisfies the condition of \(1.5\leq t_{\rm{I}}\), \(t_{\rm{II}}\leq 11.7\). The first ring gear is then enlarged by one tooth and checked for assembly conditions [55].