# Parametric Selection of Optimized Epicyclic Gearbox Layouts for Wind Power Plant Applications
## 3 Methods
### 2-SPEED Software Program
The corresponding ideal torque ratio is recorded or discarded, depending on whether the assembly conditions have been met or not, and the procedure is repeated until the maximum allowable ideal torque ratio for that component gear train, or the geometrical upper limit for planetary gear trains of 11.7, is reached [49]. The same procedure is repeated on the second basic component gear for every valid torque ratio of the first gearset, creating a set of possible transmission ratios. When a valid solution is found, a full calculation is performed and the parameters of that solution are stored (basic component gear train geometry, component efficiency, transmission ratio, overall efficiency, etc.) as a function of the ideal torque ratios of the component gear trains \(t_{\rm{I}}\) and \(t_{\rm{II}}\). The best gearbox scheme and layout variant are extracted from the dataset by means of single- or multi-criteria optimization. The following information will be written to the output text file for all valid solutions:  
* Alphanumeric scheme and layout variant;
* Corresponding component gearest ideal torque ratios \(t_{\rm{I}}\) and \(t_{\rm{II}}\);
* Kinematic transmission ratio(s) \(i\);
* Tooth numbers of all the gears \(z_{\rm{II}}\), \(z_{\rm{2I}}\), \(z_{\rm{3I}}\), \(z_{\rm{1 II}}\), \(z_{\rm{2 II}}\), and \(z_{\rm{3 II}}\) and number of planet gears \(p_{\rm{I}}\) and \(p_{\rm{II}}\);
* Modules \(m_{\rm{n}}\) of both gearsets;
* Ratios of the ring gear reference diameters \(d_{\rm{3I}}/d_{\rm{3 II}}\);
* Approximate masses of individual component gear trains;
* Approximate total mass of the whole gear train;
* Reference diameter of the larger ring gear \(d_{\rm{3 max}}\);
* Ratio of the larger and smaller ring gear reference diameter, \(d_{\rm{3 max}}/d_{\rm{3 min}}\). The approximate masses of the gear trains are calculated by assuming the external gears to be solid steel cylinders with reference diameters \(d_{1}\) and \(d_{2}\) while the ring gear is assumed to be a hollow cylinder with the internal diameter equal to \(d_{3}\), and the external diameter equal to \(1.22\)\(d_{3}\)[51; 56]. The density of steel defaults to 7850 kg/m\({}^{3}\) unless otherwise specified. The gear width-to-diameter ratio \(\psi_{\rm{b}}\) defaults to 0.8 without user input. The software is also capable of calculating the component gear train internal efficiencies \(\eta_{\text{QI}}\) and \(\eta_{\text{QII}}\) based on the number of teeth of the respective sun gear \(z_{1}\), the ideal torque ratio of the component gear train \(t\), and the coefficients of churning losses \(k_{\text{c}}\), planet bearing losses \(k_{\text{b}}\), and seal frictional losses \(k_{\text{s}}\), by application of the expressions from [51]. Additional subroutines, omitted from the block diagram, enable tooth root and tooth flank stress calculations and selection of gear modules according to input or output torque demands. The executable has been coded as a Win32 console application using Visual Fortran 95. A full calculation cycle required to prepare data ready for kinematic validation takes about 3 to 5 min on a contemporary PC. The program running time depends on whether sun gear tooth number and/or planet gear number variations have been requested. Most of the running time is divided between sifting through ideal torque ratio combinations and the sorting of valid ideal torque ratio pairs according to the user-imposed selection criteria. Figure 7: Simplified 2-SPEED block diagram. Finally, all valid layout variants must pass a kinematic validation. During this procedure, a kinematic scheme (Figure 8) of the layout variant is created, and the scheme is checked to verify whether it is physically possible to connect the internal components and the input/output shafts in the intended manner, and whether the gear train satisfies other application-imposed design and technological criteria. This will enable the optimal variant to be selected, as in some cases the best solution may fail the kinematic validation, and the third- or second-best solution will then be used.