## 1 Introduction  
Nowadays, interference fits are widely used in multiple applications within the mechanical engineering field due to their high efficiency and simple manufacturing process. The aim is to transmit torque between the shaft and the hub, a generic name used for representing diverse mechanical components such as gears, bearings, pulleys, etc. An interference fit can be assembled by two different methods: (i) axial, by inserting the shaft into the hub applying an axial force (press fit) [1, 2], or radial, by a thermal cycle either heating the hub or cooling the shaft (shrink fit) [3, 4, 5].  
Traditional methods for designing interference fits are based on Lame equations obtained from the theory of elasticity. These equations estimate a uniform distribution of stress at the interface shaft/hub [6, 7]. However, stress concentrations appear at the edges of the hub when the parts joined do not have the same length, as was observed by photoelasticity techniques [8]. This case is very common in mechanical engineering, with the shaft length longer than the hub length. Accordingly, the values obtained using the theoretical equations are not realistic for estimating the contact pressure and the stress that both parts undergo [3, 6, 9]. This is an issue of major concern since those stress concentrations can limit the service life in adequate conditions of the joint, leading to failure [10, 11, 12, 13]. Under certain conditions, the stress field at the interface during the assembly process can overcome the material yield strength leading to yielding. This way, in the study of [PERSON] and [PERSON] [14], the influence of the reduction in the yield strength at high temperatures in contact pressure of a shrink fit was demonstrated. In a similar way, [PERSON] and [PERSON] [15] have analyzed the stress distribution for thermally assembled shaft/hubs focusing on the plastic strain zone that appears due to the manufacturing process. To reduce or even eliminate these undesirable stress concentrations, diverse methods were proposed in the past [16; 17; 18; 19], and this way, the service life of the components of a shrink fit is enlarged. One of the aforesaid methods consists of inserting a contact ring of a material with a lower stiffness between the shaft and the hub in the way, shown in Figure 1.  
Diverse studies have used finite element method (FEM) simulations with the aim of reaching a complete characterization of the mechanical behavior of the assembled parts [11; 20; 21; 22; 23; 24; 25], in particular of the stress concentration of an interference fit.  
The aim of this study consists of revealing the influence on the stress distribution at the interface, on one hand of the width of the contact ring, and on the other hand, of the elastic mechanical properties (Young modulus and Poisson coefficient) of the contact ring. This way, the reduction in the stress concentration factors (SCFs) can be quantified, and the optimal conditions to be used in the design of interference fits with contact rings can be estimated. To achieve these goals, diverse numerical simulations by FEM were carried out using a commercial FEM code (MSC.MARC) considering commonly used interference fits recommended by the ISO standard for fits and tolerances [26].