## 1 Introduction  
The use of interference fits (press fits and shrink fits) constitutes a widely spread method for assembling mechanical components such as shafts and the components generally called hubs, including gears, bearings, pulleys, wheels, etc. [1; 2; 3]. Thus, both movement and torque can be transmitted between the assembled components: the shaft and the hub [1; 2; 3]. An interference fit is generated when the radial dimension of one component of the interference fit (shaft and hub) is lower than the other. As result, pressure occurs at the contact between the shaft and hub due to the so-called radial interference. Interference fits can be manufactured by two techniques: (i) axial insertion of the shaft into the hub, resulting in the so-called press fit [1; 4; 5], and (ii) by increasing the size of the hub by raising the temperature through dilatation and then placing the shaft inside the hub [1; 3; 6; 7; 8]. Later, the hub is cooled down to room temperature, recovering the initial dimensions and pressuring the shaft. Obviously, the contact pressure is dependent on the magnitude of the radial interference [9; 10; 11]. The ISO standard for fits and tolerances [12] recommends certain interference fits for a given application. The theoretical expressions used for designing interference fits are derived from the theory of elasticity; more concretely, this is the theory of thick-walled pressure cylinders [10; 11]. According to these equations, a uniform distribution of stress at the shaft-hub interface is predicted. However, it is well known that a high stress concentration is locatedat the edges of the hub [11; 13; 14] and, hence, the design equations lead to an underestimation of the real stress state. As result, the mechanical performance of the assembled components can be reduced under in-service conditions [15; 16; 17; 18]. Thus, taking into account the in-service conditions the high stress concentration at the shaft-hub interface can produce plastic strains that lead to undesirable effects such as vibrations or fretting fatigue failure [18; 19; 20]. Thus, a realistic estimation of such stress concentrations is a key issue in the design process of interference fits. Therefore, designs leading to relieve such stress concentrations and, therefore, obtain a uniformly distributed contact pressure similar to the one predicted by theory are welcomed. In this sense, many studies have focused on reducing stress concentrations by modifying hub geometry [21; 22; 23; 24]. The most common modifications are the use of round grooves [22], contact rings [25], and chamfer hubs [26; 27]. Thus, [PERSON] et al. [21] proposed a method of reducing the maximum contact pressure at the press-fitted contact edge by optimizing the location and size of a stress relief groove in the hub face, reducing the stress by about 30%. In [22], numerical FEM simulations were carried out for obtaining design equations that provide the optimal dimensions (groove diameter and distance from interface) of the round groove. The influence of diverse geometric parameters, shaft/hub length ratio, shaft/hub diameter ratio, and the relative size of the notched hub were analyzed by FEM simulations in [23]. A general qualitative description of the diverse methods used for reducing stress concentrations was included in [24]. An analysis of the reductions of the stress concentrations at the hub edge by FEM simulations considering contact rings was carried out in [25], revealing the optimum contact ring thickness and the influence of the elastic material properties in such stress reductions. A preliminary analysis of the reductions of the stress concentrations by using chamfer hubs was developed in [26]. [PERSON] discussed diverse optimized designs that improve the contact pressure distribution considering chamfer hubs and elliptical grooves and a combined chamfer and elliptical cut [27].