The end play of the bearing shown in Figure 1A (P E1) is related to the ball diameter ( d1) by the following  relationship:  PE1 = 2B 1d1 sin/g69/g20           Eq (1)  Where B 1 is the total curvature for the bearing in Figure 1A, given by:  B1 = 1 1 1/g16/g14dr dri o              Eq (2)  Where ro is the inner ring radius and ri is the inner ring radius.  Similar relationships may be written for the bearing shown in Figure 1B, with the subscript 2 substituted  for 1. For each experimental data poi nt, the change in end play ( /g39PE =P E1-PE2) is measured with the  techniques described below. The full-speed contact angle /g692 is measured by observing the ratio of the  shaft rotational frequency to the ball group rotational frequency. The total film thickness, the sum of the  inner and outer ring EHD films, is given by d2 – d1. Solving from equation 3, the total film thickness is  given by:  d2 – d1 = 1 2 21 11 sin2sin 2dd/g16/g37/g39/g53/g16 /g37/g40 /g69/g69              Eq (3)  Although this technique provides a quantitative measure of the sum of the inner and outer film  thicknesses, it gives no information that allows one to discern how much of that sum is due to each  interface. An approximate ratio can be obtained through the application of conventional EHD film  thickness analytical methods [7]. This approach was used here to demonstrate that the film thickness at  the inner ring is approximately 40% of the total, and the film thickness at the outer ring is the remaining 60%. Therefore, in our final analysis will treat the inne r ring film thickness as being approximately 40% of  the total film thickness.  Experimental Method  A pair of 304 sized bearings is mounted in a face-to-face (DF) configuration inside a steel housing, as  shown in Figure 2. A single pair of hybrid bearings, with CRU20 rings, Si3N4 balls and a phenolic cage,  was used for all experiments shown here. The preload force is both applied and measured using a  compliant, ring-shaped load cell compressed between the lower bearing and the cartridge. A spacer separates the outer ring of the lower bearing from the load cell. To simplify alignment, the load cell bears  on the housing through a ball-in-cone arrangement. Preload is set by screwing the upper and lower  housing halves together. The upper end of the shaft is attached to a high-speed precision spindle that rotates the inner rings. The entire assembly hangs from the motor spindle by a connection to the shaft.  The housing and outer rings are prevented from rotating by a lever arm (not shown) that bears on a  second load cell to measure  bearing drag torque.   In this arrangement, the outer ring of the upper bearing is stationary with respect to the housing, while the  outer ring of the lower bearing tr anslates axially through a di stance equal to the sum of the two bearing  displacements. Since the motion of each outer ring is equal to half of the change in end play, the total  measured axial translation of the outer ring of the lower bearing (the sum of both bearings) is equal to the  total change in end play of each bearing, /g39P E. The bearing test cartridge is instrumented  with sensors to  detect displacement of the outer ring and changes in the operating preload. These sensors provide the  change in end play that is used to determine film thickness with the “load change method” and the “air  gap displacement method” described below.  109