13.16 Your FBD should have resulted in Fleft = -1000N and 
Fright =  2000N, both radial.  The roller bearing life comes out 
to a stupendous  71,540 million cycles. The deep-groove ball 
bearing equivalent radial  load coefficients are X=1 and Y=0, 
because Pa/Pr = 0.25 < 0.27 which  is  e from the table.  
The result, life is 343 million revs.

13.17 The cylindrical roller bearing life goes down to 
7100 million.   Pa/Pr is now 0.5 for the ball, and effective load 
P = 1360N.  This  gives a ball bearing life of 1091 million revs.  
This arrangement  gives  a longer life, better balanced between
the two bearings.

13.18 Your FBDs should result in Fa = -1125N, Fb = 4375N, 
and  Faxial = 1165N.  The life of the roller at A is 3061 million 
revs.   Using X = 0.56 and Y = 1.8 gives an effective load of 4547N, 
and a  ball  life of 1556 million revs.  So the ball will fail first.

8.5 The race radii are -8.84mm and -44.52mm,  The curvature sum, R, 
is 10.03mm.  AlphaR is 21.036.  The eliptic integrals are script 
E = 1.027 and script F = 3.307.  The equivalent modulus is 227.5GPa.  
Dx is 9.42mm; Dy is 1.355mm.  Max deflection is 73.7 microns.