## 1 Introduction  
The study of the motion of the rotational machine, i.e., rotor dynamics, is one of the most important areas in the engineering practice. The research of rotor dynamics finds its use in a broad spectrum of applications, from the big machines for energy production to those small ones found in the medical equipment. The mathematical models of a rotor and simulating the response to the activity of disturbing forces means a big aid in the developmental process of new structures and removal of problem related to already existing structures. The characteristics of a bearing where rotors are supported have a big influence on the rotor dynamic. The rolling bearings are the most used elements for the support of rotational machines. One of the most important problems related to rotational machines is the reduction of vibration and the increase of the accuracy of the spin of rotors supported on the rolling bearings, especially for the rotors operating with high rotational speeds. The rotation precision is often conditioned with the characteristics of vibration that are generated in the rolling bearings. Because of that, the problems related to the generation of vibrations in the rolling bearings should be treated with particular attention. The main causes for vibration generation in rolling bearings are as follows [1]:  
* The specific construction and the specific way of functioning of rolling bearing (varying compliance (VC) vibrations-structural vibrations),
* Micro and macro geometry errors of bearing elements (vibrations with technological origin),
* Damage of bearing elements (vibrations due to damage of bearings elements). The construction of bearing affects the vibration generation in all the three mentioned cases. However, only in the (VC) vibrations, the construction of the bearing is the main cause of vibrations. Some hold the opinion that the VC vibrations in bearings cannot be avoided, even in ideally made rolling bearings and even in the absence of an external load [2; 3]. In the other two cases, the vibrations occur because of various imperfections or damage which emerge during the fabrication or exploitation of bearings. With the correct production methods, maintenance, and exploitation, these vibrations can be reduced, and can even be avoided. The first systematic researches varying compliance (VC) vibrations were done by [PERSON] [4]. [PERSON] studied the model of bearing considering the Hertzian contact and the clearance nonlinearities. The contact interaction between rolling elements and races is simplified as non-linear springs. [PERSON] concluded that VC vibrations occur on the ball passage frequency (BPF) and its harmonics. [PERSON] and [PERSON] [5] later showed that even in the presence of elastohydrodynamic lubricating film between balls and races, a peak at the BPF appears in the spectrum. The model proposed by [PERSON] is a 2 DOF model for bearing-rotor systems to study the varying compliance. This model and its modifications were later widely used in research by a large number of authors [5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15]. Mostly these are 2 DOF models, however, 4 DOF and 5 DOF models were also used lately. So, for example, [PERSON] et al. [6] developed a two-dimensional model of the dynamic behavior of a rigid rotor in rolling bearings by observing the balance equation of bearing assembly as a system of elastically connected masses. Using this model, they have studied the problem of shaft rotation accuracy of highly precise machine tools at high rotation speeds. They also concluded that vibrations at BPF were dominant in the vibration spectrum. This observation was also confirmed by the experiment. [PERSON], [PERSON], and [PERSON] in [7] use the 2 DOF model to study the effect of radial internal clearance on the dynamics behavior of a rigid rotor. They concluded that internal clearance is the biggest cause of unstable behavior of a rigid rotor and that subharmonic and chaotic behavior is strongly dependent on the size of the radial clearance.