# Failure Life Prediction of Hub Bearing in Composite Tooling
## 3 Prediction of the Life of the Hub Bearing
### Analysis of the Life and Characteristics of the Hub Bearing according to Changes in the Preload  
The hub bearing is located between the disk narrow and the disk narrow arm. The disk narrow is bolted to the outer raceway cover of the hub bearing, and the threaded part of the shaft protruding from the inner raceway of the hub bearing is inserted into a hole located in the disk narrow arm and fastened with a nut. The fastening torque determines the preload of the hub bearing used when the disk narrow arm is attached to the inner raceway of the hub bearing, and the fatigue life of the hub bearing varies according to changes in the preload. Therefore, changes in the fatigue life according to the preload of the hub bearing were analyzed. Utilizing the finite element model of the disk narrow assembly, the fatigue life of the hub bearing was predicted using the ISO 281 standard while increasing the preload of the hub bearing by 5 \(\mu m\). from 0 to 50 \(\mu m\). [12; 16]. The bearing life was the longest as B\({}_{10}\) 3600 h when the preload of the hub bearing was in a range of 20-30 \(\mu m\). The bearing life sharply decreased when the preload exceeded 40 \(\mu m\). The bearing life was B\({}_{10}\) 3245 h when the preload amount was 0 \(\mu m\) and B\({}_{10}\) 3154 h when the preload was 40 \(\mu m\). Therefore, when assembling the disk narrow, the fastening torque should be determined so that the preload of the hub bearing is within a range of 0 to 40 \(\mu m\), as shown in Figure 10.  
Changes in the loads applied to the inner/outer raceways of the two rows of bearings according to the preload of the hub bearing, the maximum contact stress, and truncation, and the static safety factor of the bearings according to ISO 76 were identified [17]. The maximum contact stress of ball bearings should not exceed 4200 MPa, and the safety factor should not be smaller than 3 [17]. The loads applied to the inner/outer raceways of the two rows of bearings decreased and increased with the preload of the hub bearing, as seen in Figure 11[12]. When the preload was 0 \(\upmu\)m, the maximum load was shown to be 0.98 kN in row 1 and 1.41 kN in row 2. Figure 12 showed contact stress levels of the inner/outer raceways of the bearing when the preload was 0 \(\mu m\) and when the preload was 25 \(\mu m\), at which the maximum life was shown. The maximum contact stress levels were shown to be 2230 MPa and 2171 MPa at the inner raceway of the bearing, and it was identified that the number of balls that meet raceways increased. The contact stress of the inner raceway of the bearing tended to be higher than that of the outer raceway, stemming from the difference between the radius of curvature of the inner raceway and that of the outer raceway. The position where the maximum contact stress acts  
Figure 9: FE model of disk narrow assembly. (**a**) Disk narrow arm (**b**) Disk narrow. in row 1 of the bearing is different by 180\({}^{\circ}\) from that in row 2 of the bearing. This difference is because the contact occurs at the 90\({}^{\circ}\) position in row 1 while occurring at the 270\({}^{\circ}\) position in row 2 because of the deformation of the shaft located in the inner raceway of the bearing and bearing misalignment. The static safety factor of the bearing was shown to be 20.57. Figure 13 is the graph that shows the contact pattern to check the presence of truncation in the inner/outer raceways of the bearing. The thick solid lines placed vertically on the \(x\)-axis at equidistant intervals show the positions where actual contact occurred when a load was applied, and the balls met the inner/outer raceways. When a load acts in the y-direction from the outer raceway to the balls, 0\({}^{\circ}\) is the center of the cross-section of the width of the inner/outer raceways. The positions along the \(y\)-axis mean that contacts occur on the left or right of the center. The reason that the contacts occur on the left or the right is the occurrence of axial loads.