## 1 Introduction
The study of the effect of clearance on a bearing's dynamic performance, quality, and operating life has gained a lot of attention lately because of the development of high-speed rotors [8]. Clearance non-linearity is different from most of the other non-linearities because it cannot be approximated by a mathematical series [7]. [PERSON] et al. [9] and [PERSON] et al. [10] also used a modified 2 DOF model to study the nonlinear phenomena and chaotic behavior of a rigid rotor in a roller bearing. The first model with 5 DOF was developed by [PERSON] et al. [11] and they applied it to the machine tool spindles. They have represented the bearings by nonlinear springs included elastohydrodynamic effects. This investigation was later refined by [PERSON] et al. [12], proposing a general dynamic model of the ball bearing-rotor system. They used the finite element method to model the contact stiffness. A little later, [PERSON] et al. [13] propose their 5 DOF dynamic model of the rotor system supported by angular contact ball bearings. Five-degree-of-freedom models are used by many researchers to study the influence of various factors on the vibration generation of bearings. Thus, for example, [PERSON] et al. [14] study the effect of preload and varying contact angle on bearing vibration. [PERSON] and [PERSON] [15] study the influence of rings misalignment on the dynamic characteristics of cylindrical roller bearings, and [PERSON] et al. [16] influence of different ball number and rotor eccentricity on VC vibrations. However, most of the above studies mainly merely verify the influence of the different factors on vibrations in the rotor-bearing system. Many studies only state that VC vibrations exist in the rotor-bearing system and that they occur on the BPF and that certain factors have an influence on the VC vibrations amplitude. Parametric analysis is very rarely performed. The reason for this lies primarily in the great complexity of these models. All of these models are distinguished by their expressive non-linearity. Most of the mentioned models are encompass systems of differential equations, which describe the complex movement of the rigid rotor in rolling bearing, including the problem of nonlinear elastohydrodynamic contact between rolling elements and races. For solving systems of differential equations, most authors use the Newton-Raphson method, while for obtaining a vibration spectrum the fast Fourier's transformation (FFT) is commonly used. These models are extremely difficult for solving and they require a large number of complicated mathematical operations. Because of that, any parametric analysis would take a very long time. In this connection, the model of [PERSON] and [PERSON] is particularly interesting because of its simplicity. [PERSON] [17] investigated the VC vibrations of a rigid rotor in an ideal rolling bearing with an internal radial clearance and found that these vibrations can be represented by the equation of the absolute sinusoid. The frequency of these vibrations is equal to the ball passage frequency (BPF). [PERSON] [18] further developed the research of [PERSON]. Using the research of [PERSON], in this paper, a new mathematical model for vibration response prediction of a rigid rotor in rolling bearing has been presented. The simple mathematical record makes the developed model very convenient for practical usage. The model is based on a new approach in the analysis of rolling bearing which is presented in the papers [19; 20; 21; 22]. For the time being, the model considers only the VC vibrations of rolling bearing and it refers to an ideally made bearing with the radial contact and internal radial clearance. Based on the presented model a parametric analysis of mutual influence between internal radial clearance and external radial load on the VC vibrations of rolling bearing is conducted. These two parameters are the most influential factors for generating VC vibrations for a given type of rolling bearing [23].