## 1 Introduction  
Tilting pad journal bearings (TPJB) are widely used in turbomachines. Their benefit is an improved rotor stability at higher speeds with respect to fixed-pad journal bearings, due to very low stiffness and damping cross-coupled coefficients. In Figure 1, some common pivot types are depicted: rocker back that is cylinder on cylindrical seat (hereafter referred as RB), ball and socket that is sphere on spherical seat (B&S), and flexural. The RB pivot has a theoretical line contact and typically undergoes a rolling motion with negligible sliding [1, 2]. The B&S pivot has a theoretical point contact and may involve some sliding motion [3]. The main advantage of a B&S pivot is that it can allow some degree of axial shaft misalignment and comply with rotor sag. In a flexural pivot bearing, the pad and the bearing housing do not form a contact pair but are a single piece and their connection allows for elastic deformation and pad tilting [4]. The major advantages of flexural pivots are no contact wear at pad-housing interface and robustness to pad fluttering. Geometrical parameters, materials, and surface treatments must be optimized in pivot design since they have a great influence on stress and wear due to the reduced and highly loaded contact areas. In addition, the characteristics of pivots can greatly influence the bearing rotor dynamic behavior with their stiffness and damping characteristics. Some researchers have studied numerically the effect of pivot radial stiffness on the bearing characteristics [5; 6] and on the journal nonlinear dynamics [7]. The radial stiffness of an RB or B&S pivot can be evaluated through classical [PERSON] theory if the contact is non-conformal [8]. However, [PERSON]'s formulas are not reliable for quasi-conformal contacts, as observed experimentally in [9], and whenever [PERSON]'s hypotheses are not satisfied and contact stiffness assessment is important, the latter should be evaluated more accurately [10]. Recently, [PERSON] et al. proposed a theory for the estimation of radial stiffness of quasi-conformal B&S contact [11]. When the pivot radial stiffness is considered, the bearing direct stiffness coefficients are lower with respect to the rigid pivot models. [PERSON] et al. [12] numerically and experimentally studied the influence of pivot radial stiffness on the bearing characteristics and rotor stability in a vertical-rotor-bearing system. Experimental works compared the behavior of RB and B&S TPJB showing the negligibility of cross-coupled stiffness terms in the former [1; 2] along with lower power loss and pad temperature [13]. They attributed the results to friction in the B&S pivot. Therefore, while friction is usually neglected in numerical simulation of RB TPJB, quite a few papers can be found on modeling of B&S TPJB, including friction. [PERSON] et al. [14] proposed a mathematical model for the B&S pad-pivot friction explaining its influence on the bearing characteristics. [PERSON] et al. [15] showed that varying bearing loads, the pivot friction could result in non-synchronous pad tilting and journal vibrations. [PERSON] et al. [16; 17] focused on the pad-pivot friction-induced nonlinear rotor dynamic phenomena and bifurcations. The Stribeck curve model was applied for friction. [PERSON] et al. [18] proposed a detailed B&S model to predict TPJB dynamics, employing the Bengisu-Akay and Lu-Gre models to describe static and dynamic friction. Hence, dynamic friction and sliding have been addressed by some papers but, to the authors' knowledge, little attention has been given to the effect of static friction in RB pivots and to the consequent pad rolling motion. It is a common practice for bearing calculation software to assume a fixed theoretical pivot point [19]. However, the pad rolling motion changes the circumferential coordinate of the theoretical contact point. The purpose of this paper is to provide a way to implement the effect of RB pad rolling in a commercial bearing calculation software.