# Ball Bearings Theory

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In the literature, several models for ball bearings have been proposed to explain the gyroscopic effect and the centrifugal forces. Kurvinen et al. [5] improved the model provide by Sopanen and Mikkola [6, p. 201-211], [7, p. 213-223] and added the centrifugal forces and gyroscopic moment and contemplated the defect in the ball bearings. Kärkkäinen et al. [1, p. 606, 608] considered rotational inertia of the ball and inner ring and aerodynamic torque. In a recent pepper of the Halminen et al. [2, p. 692-705] the model for the cageless bearing is developed based on the available model for the bearing with the cage.

The friction between the rotor and inner race will affect the whirling motion of the rotor [1, p. 613], [8, p. 79-89]. As a result
267-269]. The accuracy of the results for both analytical and numerical method for calculating contact stress highly depends on the calculation of the loads exerted on the contact surface faces. Calculation of this load requires prior knowledge in the rotor dynamic and bearing model. Rolling contact stress is also imperative part of the analysis of the railroad industry and several studied has been done to model the contact stress and fatigue in rail road industry [16]. In addition, Ekberg et. all, [17, p. 899-909] considered effect of surface, subsurface stress, rolling contact and effect of defect in the contact surfaces to predict the rolling contact …show more content…
It is challenging to obtain the stress that is a consequent of the contact in an infinitesimal area. Although, the Hertzain stress model is an analytical method developed based on the theory of elasticity and can be applied to obtain the contact stress in the ball bearing. In this method the normal contact force should be known. Calculation of the normal force as a result of the contact of the ball on races is one the important step in investigating the maximum contact stress. In addition to the static force due to the weight of the rotor, the relative position of the rotor with respect to the bearing and penetration of the ball on races are essential for obtaining the normal force. In order to achieve above information, the detail model for ball bearing, simulation of the rotor during the dropdown should be taken into account. The calculation of the deformation of the race as a result of contact is critical data for determining the contact

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