## 1 Introduction  
One of the most important tasks of rolling bearings is to transfer load from the rotary elements to the supports. This takes place through a certain number of rolling elements, from the rotating ring to the stationary one. The load that rolling elements transfer, i.e., the internal load distribution, is an essential feature of rolling bearing, in particular for the determination of static and dynamic load rating, service life, the characteristics of stiffness, the accuracy of rotation, vibration characteristics, the losses due to friction, heat calculation, etc. It is known that the calculation of the load distribution on the rolling elements is very complicated. It is nonlinear and a statically indeterminate problem, which requires that in addition to the static equilibrium equation, additional conditions have to be introduced, based on the connection between the contact stress and deformation, according to [PERSON]'s contact theory [1]. Furthermore, in the case of rolling bearings, the internal load distribution is a time-varying value, which is dependent on the position of the rolling elements on the raceways. Time variability, static indeterminacy, and nonlinearity have meant that the calculation of the internal load distribution can only be solved numerically, through many iterations, using [PERSON]'s iteration or a similar method. However, because of its significant importance, especially for engineering practice, a large number of authors are dealing with methods to simplify the calculation of the internal load distribution of rolling bearings, and are trying to develop as simple but sufficiently accurate methods as possible. The first papers that dealt with these problems are related to the study by [PERSON] [2]. [PERSON] used the Hertzian contact theory and derived an equation for calculation of the load of the most loaded rolling element for the radial ball bearing with zero clearance. The resulting solution for rolling bearing (ball or roller) with nominal clearances was later expanded by [PERSON] [3]. [PERSON]'s expressions are still in use for the calculation of the static load rating of rolling bearing [4, 5]. However, the [PERSON]'s expressions have one serious drawback. They do not consider the size of the internal radial clearance, but only its presence, which is described through the so-called Stribeck's number. That number is 4.37 for the ball bearing without radial clearance, and 4.08 for a roller bearing. For bearings with clearance greater than 0, [PERSON]'s number is 5. Later in the calculation process, [PERSON] introduced the so-called [PERSON]'s integral [6]. The first comprehensive mathematical model for determining the load distribution for rolling bearing was developed by [PERSON] [7]. He observed an ideal rolling bearing with an internal radial clearance and proposed a mathematical model to determine the load distribution as a nonlinear equation system. The model of [PERSON] was later developed by [PERSON] and [PERSON] [8], as well as [PERSON] [1]. [PERSON] [1], using [PERSON]'s integrals, describes the size of the contact zone through a load distribution factor (\(\epsilon\)) and solves the load distribution problem by the method of trial and error. Based on the assumed distribution factor, the deflection of the bearing is determined. In the next step, equilibrium equations are solved, and the process is repeated until the given accuracy is satisfied. [PERSON]'s model was later used for different purposes and has been further developed by a large number of authors, such as [PERSON] [9; 10] [PERSON] [11], [PERSON] [12] [PERSON] [13], [PERSON] and [PERSON] [14; 15], [PERSON] et al. [16], [PERSON] et al. [17], etc. However, the mathematical calculation using the [PERSON] model implies many iterations of computers, which often causes complications in concrete applications in practice. The great practical significance comes from a paper by a research group gathered around Professor [PERSON] [18; 19; 20; 21].