ABSTRACT
The load-induced stress field in the inner ring under the ball can be calculated [1]. It can be represented by O'iL, with i = x, y, or z, where the x, y, and z axes are defined such that x is parallel with the circumferential direction, y is parallel with the axial direction, and z is directed opposite to the surface normal direction; x = 0, y = 0, and z = ° correspond with the bottom location of the groove in the inner ring in the ball/ring contact. It follows for x = ° and y = 0, for the inner ring in contact with the highest loaded ball in a 6309 type
[2] deep-groove ball bearing, in case of a radial bearing load of 28 kN, which causes a o"H(max) of 3.8 GPa, that 0" xL, 0" land 0" z L are all compressive, as shown in Fig. 3a, such that 10" z L 1 is larger than 100xLI and 100yLI (for a circular Hertzian contact area it holds that O"xL = O"l)·
The state of applied stress below the contact surface thus is triaxial with gradients of stress in all three directions. These subsurface stresses decrease with increasing distance to the contact surface. To indicate the most severely loaded region in a multi axial stress field, several criteria have been proposed in the past. Here the one due to von Mises is applied. Yielding is expected to occur preferably at locations where the von Mises equivalent stress O"E L, calculated according to the maximum-shear-energy criterion, exceeds a critical value [3]; O"EL is given by:
where O"xL, O"l, and O"zL are the principal load-induced stress components.
