322    Figure 9. Ball bearing contact stress maps for enveloping random vibration load case (3 sigma and 1  sigma)   This condition was deemed acceptable in light of guidance per NASA -STD-5017A [4] which states:   Bearings should be preloaded with a load calculated to withstand the operational environments with no   unloaded balls, known as “gapping.” Gapping under operational conditions is undesirable but may be  tolerable in certain cases. However, increased component testing that verifies performance in this condition  becomes necessary because it is difficult to pr edict the effects of gapping analytically. Testing should  demonstrate lubricant lifetime, bearing component lifetime, specified functional performance and shaft  stiffness. Under non- operational environments, it may be permissible to have some balls unloaded .  Because the analysis failed to predict the torque anomaly encountered in test, a sensitivity analysis was  performed to investigate the effect of varying bearing dimensional parameters and other analysis inputs.  The list of cases considered and the resul ting effect on maximum mean Hertzian contact stress is presented  in Table 4.   The highest stress (283  kpsi/1950 MPa) was predicted for Case 11a in which bearing internal preload is  lost. This could occur if the flexible clamp holding the bearings together is defeated by excessive axial  loads. The clamp was designed taking into account only the axial component of the launch loads.  Accordingly, the pre- set bearing internal preload was selected to be 306 lb (1.36 kN) [ 5], corresponding to  the axial load Fx without the 1.3 FoS. The clamp was sized to produce 3X this force (918 lb/4.08 kN ) to  press the inner races of the bearings together  [6]. A higher clamp force would have required increasing the  size of the clamp and the fasteners securing it, which would have exceeded the volumetric constraints on  the mechanism design. The bearing spacers were precision ground to ensure the same internal preload in  the assembly that the manufacturer ground into the bearings.   The clamp design failed to consider  the axial resultant of the moment loading on the bearing assembly  during launch, which is significant. When this is included for Case 1, the clamp must resist a total axial force  of 1056 lb (4.70 kN)  (neglecting friction at the mount interfaces, which would tend to reduce the required  force). For Case 2, the total axial force to be resisted is 532  lb (2.37 kN) . This force could cause the bearings  to separate and result in additional unloaded balls and more concentrated loads in the bearing. Comparing  Case 1 and Case 11a, this is what the analysis predicts. However, a load margin of ~0.6 is still predicted  against the non- operating contact  stress allowable (335 ksi /2310 MPa) for 440C bearing steel in high  precision, low torque ripple applications found in NASA -STD-5017A Table 2.   Under these conditions, it is difficult to predict exactly what would happen in test using conventional analysis  tools. It is al so difficult to diagnose from the test data whether the bearing races moved during vibration or 0.010.020.030.040.050.060.012 345 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 262728 293031 3233343536373839404142434445464748495051525354555657 58Bearing Loads per Ball (lbf), Row1 & Row2, 3 Sigma Case Thrust Load (X), R1 Radial Load, R1 Thrust Load (X), R2 Radial Load, R2 0.05.010.015.020.025.012 345 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 262728 293031 3233343536373839404142434445464748495051525354555657 58Bearing Loads per Ball (lbf), Row1 & Row2, 1 Sigma Case Thrust Load (X), R1 Radial Load, R1 Thrust Load (X), R2 Radial Load, R2