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The planetary gear transmissions are widely used in industrial applications for motion and power transmission such as automotive, aerospace, robotics, machinery etc., because of their significant advantages including the compact structure, selfcentering capability, high power density, high transmission ratios, high degree of efficiency, durability in operation, low level of noise and vibrations. Design of planetary gear transmissions depends on a large number of parameters, some of those are: material, module, addendum, profile shift, tooth thickness, dedendum, cutter tip radius, pressure angle, gear width etc. The analysis and optimization of one simple planetary gearbox marked as Aha b was performed in this paper. The letters in the mark Aha b mean: A-the single-sided satellite, b-the fixed gear (internal toothed gear), a-the central gear (driving gear), h-the satellite carrier (connected to the output shaft) [1], [2]. Planetary gearbox of this type is shown in Figure 1, and next to already mentioned gears and satellite carrier, it consists of three satellites (g), as well. The optimization of a simple planetary gear train was performed by authors of [3], they were observing the results obtained by changing the number of gear teeth, module, number of satellites and gear width. For development of a mathematical model for multi objective optimization they used the Puerto and ELECTRE methods and noticed that the correlations between used methods are obvious. This kind of approach shows that the other planetary gear transmission types can be subjects of the multi objective optimization. The multi objective approach in optimization is much faster with the use of the Taguchi-Grey method. For optimization of the plastic gear production authors in [4] applied the hybrid integration of Taguchi parametric design, the Grey relational analysis and the principal component analysis. For demonstration of efficiency and validity of the proposed hybrid optimization methods, in controlling all the influential injection molding processing parameters during the plastic gear manufacturing, a plastic gear was used. The optimal combination of different process parameters is determined in order to minimize the shrinkage behavior in tooth thickness, addendum circle and dedendum circle of the molded gear. They concluded that the proposed optimization method can produce a plastic-molded gear with minimum shrinkage behavior of 1.8% in tooth thickness, 1.53% in addendum circle and 2.42% in dedendum circle and it should be noted that these values are less than the values in the main experiment. Therefore, defects related to shrinkage that lead to severe failure in plastic gears can be effectively minimized while satisfying the demand of the global plastic gear industry [5]. The Taguchi method is a well-known optimization method, which is used in a variety of applications [5], [6]. Application of this method ensures savings in labor and time costs, with simultaneously examining several parameters in several experimental conditions, providing the quantitative information, [7], [8]. Limitation of the Taguchi method is that it can only be applied to solve individual objective problems and cannot be used for problems with multiple objectives optimization, especially when there are different performance characteristics needed. However, this problem has been overcome and the optimization of multiple objectives can be performed by combining the Taguchi method and the Grey relational analysis to optimize the multiple characteristics [9]. Combination of the Taguchi method and the Grey relational analysis was used for optimization of the EDM process (Electrical Discharge Machining) in [10]. Parameters of machining (workpiece polarity, pulse on time, duty factor, open discharge voltage, discharge current and dielectric fluid) were optimized considering the multiple performance characteristics including material removal rate, surface roughness and electrode wear ratio. The Taguchi-Grey method was really Slavica Miladinovic Sandra Velickovic Blaza Stojanovic Ruzica Nikolic*

Optimization of Parameters of a Planetary Gearbox Using the Taguchi-Grey Relational Analysis