2.1 Subsurface shear stress
Most of the rolling contact fatigue failure originates from subsurface, so it is important to analyze the subsurface stress field during rolling contact. Note that the traditional Hertz contact theory is no longer applicable to subsurface stress analysis. Johnson26calculated the principal stress at any depth under contact surface theoretically, and then used the Mohr circle to calculate shear stress. The subsurface shear stress reaches its maximum and minimum values at a certain depth, and changes alternately along the direction paralleling to bearing raceway. In this work, a two-dimensional (2D) finite element model was established to simulate the contact between ball and raceway. Due to the normal stress on subsurface is compressive, and compressive stress will hinder crack growth, the alternating shear stress is the key factor to result in damage accumulation and microcrack propagation.27 Therefore, only shear stress is used in the following research. Fig. 2 shows the distribution of shear stress in the contact area between ball and raceway. Ball has a diameter of 5.5 mm and inner race has a radius of 9.63 mm in the 2D contact model (shown in Fig. 2a). Contact analysis implemented in ABAQUS was used. Fig. 2b shows the nephogram of shear stress distribution in the contact area. It shows that the distribution of shear stress along the raceway has maximum and minimum values. Note that we are only interested in the stress distribution and ignore the specific stress value. Fig. 2c shows the maximum shear stress and the maximum orthogonal shear stress on the subsurface under contact load. The x -axis represents the direction along raceway, and \(\tau_{\max}\) represents the maximum orthogonal shear stress which will change alternately as bearing runs.\(\tau_{y\max}\) stands for the maximum shear stress along they -axis.