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A typical wind turbine powertrain consists of a bladed rotor followed by a gearbox and finally a generator. The gearbox connects the rotor low-speed shaft to the generator high-speed shaft, increasing the rotational speed to the values more suitable for electricity production. In literature, analytical models proposed for this system are, predominantly, based on multibody approach, where torsion is the only degree of freedom considered in vibratory analyses. Nevertheless, the internal components of the gearbox couple movements in all directions, producing combined axial, torsional and bending loads, which results in complex dynamic effects that are still underexplored by scientific literature. The purpose of the present work is to study the vibratory behavior of a variable speed, horizontal axis type, 1 MW class wind turbine powertrain. In this study, a finite element model was used. The elements have 5 degrees of freedom per node; the axial movements were not considered. In this model the variable stiffness effects of the helical gear meshing were included resulting in a linear time-varying system, even with the rotor operating under constant rotational speed. The bearings were considered to be linear. The modal parameters of the equivalent time-invariant system are presented. Simulations with the wind turbine operating in constant and variable rotation speed conditions were made and the results were analyzed using stationary and not stationary signal processing tools. These results showed the presence of dynamic forces inside the gearbox containing frequency components equal to the gear meshing frequencies and its multiples. Depending on the operation machine speed and the gear pair characteristics, it is demonstrated that these forces may excite the natural frequencies of the system, and in turn, this can lead to premature wear of the wind turbine components. It is also verified the occurrence of second-order resonances and linear time-varying systems characteristics.