117   Table 3 shows key setup parameters for the system that were fixed during the study. Table 4 shows the  various run cases  studied along with the resulting mounted preload condition from all three codes. As  shown, ORBIS correlates much closer with BRGS14 than BRGS10. Average difference between ORBIS  and BRGS14, for all cases considered, is within 5.3%. It is believed that the earlier version of Leveille’s  code (BRGS10) does not contain an account for ring clamping, which would explain wh y it predicts lower  mounted preloads.  It is not known how  Leveille modeled the bearing ring stiffness, particularly the derivation  of the equivalent diameter for  the grooved side of the races.  A common rule of thumb for ring influences is  to take approximately 80% of the interference as internal clearance loss in the bearing. This method is not recommended as it assumes a fixed ratio of the stiffness between the boundary and bearing ring.  

Table 3.  Setup p arameters for mounted preload study   Parameter  Value  Parameter  Value   Pitch Dia ., mm (in)  171.45 ( 6.750 ) Housing O.D. , mm (in)  202.18 ( 7.960 )  Ball Dia ., mm (in)  9.525 ( 0.375)  Modulus of Elasticity, Rings & Balls , GPa  (psi) 200 ( 2.90E+07)   No. Balls  42 Poisson's Ratio, Rings & Balls  0.28  Shoulder Height (h/d)  0.206  Coefficient of Thermal Expansion, Rings &  Balls , 1/°C  1.02E -05  Dam Height (h/d)  0.011  Modulus of Elasticity, Shaft & Housing,  GPa (psi)  112 ( 1.62E+07)   Row Width , mm (in)  19.05 ( 0.750 ) Poisson's  Ratio , Shaft & Housing  0.31  Row Straddle, mm (in)  19.05 ( 0.750)  Coefficient of Thermal Expansion, Shaft &  Housing , 1/°C  8.82E-06  Shaft I.D. , mm (in)  134.62 ( 5.300 )  

Table 4.  Mounted preload s tudy  results   Initial Conditions  (Free)  Mounted Preload (N )  Contact  Angle  (deg)  I.R. & O.R.  Curvature  Shaft /  Housing  Temp (°C)  I.D.  Clearance  (mm ) O.D.  Clearance  (mm ) Clamping  Force (N ) Ground   Preload (N ) BRGS10  BRGS14  ORBIS  V2.4.1   22.5 54.5 76/76   0.01397  0.01905   53378  5115  5538  6112  5858   -10/-10 5373  5133  5084   66/76  3327  3861  3643   4226  2300  2931  2718   20.0 2447  3051  2851   22.5 55.0 2331  2954  2749   25.0 54.0 2108  2785  2540   0.02286  0.03048  2189  2264  2246   0.00508  0.00762  2838  3318  3087  

Case Studies   This first example is taken from the proceedings of the 22nd AMS [3]. Here, we focus on Loewenthal’s first  case  study . The described design consists of a large thin section (12” (30.5- cm) O.D., 11” (27.9- cm) I.D.  and 0.250”  (6.35- mm) diameter balls)  duplex pair  of angular contact bearings, oriented face- to-face that is  hard preloaded in beryllium structure. The bearing system must operate with fairly  large radial thermal  gradients.  Loewenthal mentions  that he found it more expedient to construct a special purpose bearing  code to solve this class of problem.  In his  study , Loewenthal constructed a design plot to show maximum  contact stresses versus the radial thermal gradient.  Using the Sensitivity Utility within ORBIS and holding  the outer race temperature fixed while varying the shaft temperature the maximum contact stresses were solved. These data were then exported from ORBIS for post processing and, as shown in Figure 7,