## 1 Introduction  
Journal bearings are among the most widespread mechanical components. Their function is to support shafts carrying radial loads and to reduce friction. The load-carrying capacity is strongly related to the pressure distribution in the convergent/divergent clearance between journal and ring. During operation, in fact, the axes of the journal and the ring are not coaxial. Therefore, the convergent clearance is significantly pressurized while after the smallest clear opening size the pressure decreases instantaneously. The minimum pressure achievable (\(p_{o}\)) is physically limited by the vaporization. Once this value is reached, the liquid phase evaporates impeding a further pressure decrement. The vaporization pressure is a physical property of the lubricant. The cavitation leads to an unbalance in the pressure distribution that is, in turn, responsible for the supporting effect. One of the the first works on journal bearings was published by [PERSON] [1] more than 100 years ago. The [PERSON]'s equations were solved for a bearing having an infinite length. Subsequent studies by [PERSON] [2] improved the approach. The Sommerfeld solution can be applied to bearings for which the ratio between the axial length and the diameter L/D is significantly greater than one [3]. With this assumption, the pressure gradient in the axial direction can be neglected. Moreover, the equations can be solved only assuming that the convergent/divergent is fully lubricated. Cavitation effects and the consequent limitation of the pressure due to vaporization are also neglected. The full-Sommerfeld solution therefore predicts a symmetric distribution of the pressures with negative values in the divergent. Consequently, the equilibrium position of the journal is estimated to be just below the ring center, without any lateral shift. This result has been proven to be wrong [4] and never observed experimentally. The full-Sommerfeld theory was extended by [PERSON] [5] in 1914. He proposed to substitute the negative values with the vaporization pressure. Figure 1 shows an example of results achievable with the full- and the half-Sommerfeld models in terms of pressure distribution along the journal. A similar approach was presented by [PERSON] [6]. Another important work was presented by [PERSON] and [PERSON] [7; 8; 9]. In the last years, thanks to the increasing computational power, more and more numerical methods were presented by several authors among which [PERSON] et al. [11] and [PERSON] et al. [12] who used computational fluid dynamics (CFD) to overcome the infinite length approximation. These models do still not include vaporization, and the artificial substitution of negative values with the vaporization pressure is required. A similar model was developed by [PERSON] et al. [3]. [PERSON] et al. [13] validated their CFD approach using the experimental measurements by [PERSON] et al. [14]. The work of [PERSON] [15] is based on the hypothesis of keeping the pressure constant in the caviting region. Other numerical analyses where presented by several authors. Among them [PERSON] et al. [16] and [PERSON] et al. [17] compared the numerical results with the measured data by [PERSON] et al. [4] and [PERSON] et al. [18], respectively. [PERSON] et al. [19] developed a Newton-Raphson based approach including a simple vapor cavitation model for the study of big-end bearings. The author has already experience with bearings [20]. He presented a full 3D numerical approach that includes the vaporization effects. The model was developed in the OpenFOAM(r) [21] environment. Different cavitation models--e.g., [PERSON] [22], [PERSON] [23], and [PERSON] [24; 25; 26]--were compared. For sake of completeness, in the recent years new cavitation models capable to ensure the mass conservation are available but were not included in the present study. The CFD results in terms of pressure distributions were validated by comparison with the data by [PERSON] et al. and by [PERSON] [27].