195 approximately 0.2 between the TBA rollers and race ring [5]. Nominally, a coefficient of friction of 0.2  ensures that the SARJ system maintains dynamic stability, which allows the race ring to react loads distributed along the full contact patch of the trundle bearing rollers . However, an instability arises when  the ratio of thrust load to normal load  rises above a critical value of 0.4 . At this level of friction, an  overturning moment caused by small misalignments in the roller, and subsequent thrust forces, cause the  trundle bearing roller to tilt about its camber axis . The roller tilt causes a decrease in the roller race  contact and an associated increase in stress at the contact. Test data determined that friction levels in excess of 0.4 are expected if no lubricant exists in the bearing contact , provided that sufficient roller  misalignments are present  [5].   Bearing Material Properties and Susceptibility to Spallation The anomaly team postulated that increased friction between the roller/race interface could cause a  stress field with the maximum shear stresses at the nitride case/15-5PH core interface . The team also  determined that the solid film gold lubricant was not properly adhered to the rollers [6]. Without the gold  lubricant in place, the system becomes susceptible to  increased shear and normal stresses . The high shear  stresses at the case/core interface could lead to subsurface initiated spalling of the case material .  Multiple tests were performed over several months in an attempt to reproduce this failure mechanism. Tests performed at the  LMSSC facilities in Sunnyvale on a  Trundle Roller Rig were successful in recreating the  spalling effect observed on-orbit [7] . The test rig  loaded a 440C roller against a nitrided 15-5PH  coupon . The roller was then rolled in a reciprocating  motion along the coupon’s surface . Figure 8 above shows a test coupon from the rig . The inset in the  figure shows an example of a “fingernail” type spall . Spalls of this type were also noted in on-orbit  inspection photos .    Applied Loading The Trundle Test Rig confirmed that subsurface spalling could be induced in the SARJ bearing materials given sufficiently high stress conditions. Additional work was required to validate that the TBA roller kinematics were capable of generating the high stresses required given the expected loading conditions .    A dynamic simulation was developed to perform analysis of the SARJ trundle bearings. The purpose of this simulation was to quantify the loads between each of the trundle bearing rollers and the race ring. The simulation included the race ring deformation caused by the thermal environment, the stiffness of the trundle bearing itself, and the stiffness of the inboard and outboard trusses of the ISS. It also included the structural flexibility of the ISS trusses. The simulations were used to perform parametric studies in support of the closure of the SARJ Fault Tree events. The simulation used traction data obtained from NASA GRC testing for the contact between the race ring and the TBA rollers both with and without gold coating .  The simulation was used to estimate the loads at the roller to race ring interface and to illustrate the kinematic behavior of the TBA rollers . The development and results of this simulation are discussed  below    Analysis of Roller Edge Loading

The effect of small angular misalignments on rolling traction forces has been studied by a number of investigators, as summarized by K.L. Johnson in [8] . Solutions to the governing equations of rolling have  been developed in closed form for a few geometries, and powerful numerical methods have been developed to address the problem for more general application . These methods are important for the  present investigation because the angular misalignment of the trundle bearing rollers can lead to dramatic changes in the loads and stresses on the race ring surfaces.  Figure 8. Trundle Test Rig Coupon   Showing Fingernail Type Spalling [7]   NASA/CP-2010-216272