A deep groove steel ball bearing contains ten balls of diameter 12.7 mm. In this case, the material of both surfaces is steel with the following properties: Young's Modulus E = 213 GPa, Poisson's Ratio = 0.29. The outer ring has a groove radius of 6.6mm and the diameter of the contact track is 77.8 mm. If the bearing carries a maximum radial load of 1200N determine the maximum contact pressure, po. in the ball outer race contact. < Discuss what is likely to occur if initial yield occurs at po > 385MPa. Assume contact will yield in a fully plastic manner if pm > 0.4H where Hardness of the steel can be taken as 2.0 GPa. If a diamond coating where available with E = 1150 GPa and v= 0.07, Hardness 80GPa, what thickness would be required? < what component(s) need coating? < what adhesive shear strength with the substrate would stop coating delamination? E* 1 Rx HR a v1-v + E E || = || - 1 + Rx Ry Hertz gives semi-minor and semi-major axes of the contact ellipse: < 3k EWR TE" 3EWR k* = = 1 1 + Rx R2x b = 1 + R Rzy 1 -) Where k is the ellipticity parameter (k = a/b), and E is an elliptic integral of the second kind. These can be derived from 'Approximate solutions which can be taken as k = 0.6360 1.0339 (22) The pressure distribution is: a/be z/a Tmax/Po = E = 1.0003 + Mean pressure = Pm (2po/3) = (W/nab) < W = 5F/n < Where n = number of rolling elements. F is the maximum radial load. < 0.785 0.3 p(x, y) = Po 1 0.5968Rx Ry {1-2-2 y) /2 H Table: shear stress depth and maximum values as a function of a/b ratios 0.2 < 0.745 0.322 0.4 0.665 0.325 0.6 0.59 0.323 0.8 0.53 0.317 1.0 0.48 0.31