Material fixed to bearing steel (E*=115.4 GPa, nu=0.3). Contact angle a=0 (deep-groove ball bearing); race conformity (groove curvature) is not modelled. Moving the load slider re-pressurizes the animation toward the new target load.
Left = the ball pressed onto the raceway and flattening / the red semi-ellipse = contact pressure p(x) / the contours below the ball = subsurface shear stress (peaking at depth ≈0.48a below the surface). Raising the load grows the contact patch 2a and the pressure.
In a radially loaded ball bearing the total load is not shared equally among the balls. Stribeck's analysis shows that the stress is concentrated on the single most heavily loaded ball.
Maximum load per ball (alpha is the contact angle, alpha = 0 for a deep-groove bearing):
$$F_\text{max} = \frac{5\,F_\text{radial}}{Z\,\cos\alpha}$$Equivalent radius of curvature for the concave inner-race contact and the convex outer-race contact:
$$\frac{1}{R_{eq,i}} = \frac{1}{r_b} - \frac{1}{R_i},\qquad \frac{1}{R_{eq,o}} = \frac{1}{r_b} + \frac{1}{R_o}$$Contact radius and peak Hertz pressure (sphere-on-plane, E* is the equivalent modulus):
$$a = \left(\frac{3\,F\,R_{eq}}{4\,E^*}\right)^{1/3},\qquad p_\text{max} = \frac{3F}{2\pi a^2} = \frac{1}{\pi}\left(\frac{6\,F\,E^{*2}}{R_{eq}^{\,2}}\right)^{1/3}$$Elastic approach δ and the (semi-ellipsoidal) pressure distribution:
$$\delta = \frac{a^2}{R_{eq}},\qquad p(r) = p_\text{max}\sqrt{1-\left(\tfrac{r}{a}\right)^2}$$The maximum shear stress occurs below the surface, not at it:
$$\tau_\text{max} \approx 0.31\,p_\text{max}\quad(\text{at depth } z \approx 0.48\,a)$$The outer race has the smaller equivalent radius of curvature, so its contact patch is smaller and its peak contact pressure is higher than the inner race. Fatigue cracks initiate at this subsurface τ_max location.