# Failure Life Prediction of Hub Bearing in Composite Tooling
## 4 Experimental Evaluation of the Life of the Hub Bearing  
### Determination of Accelerated Life Test Conditions  
Although the target life of the composite working implement is B\({}_{10}\) 800 h, the target life of the hub bearing was determined as B\({}_{10}\) 1200 h because the hub bearing should have higher reliability than the composite working implement. The zero-failure test time to ensure the target life can be calculated with equation (3). The primary failure mechanism of the bearing is fatigue failure, and the shape parameter was 2.0 when the life distribution was assumed to follow the Weibull distribution [18]. Figure 13: Contact footprint between balls and raceways. (**a**) Inner/Outer raceway of row 1 (**b**) Inner/Outer raceway of row 2. When calculated with the confidence level of 0.9 (90%), the number of test samples of 1, and the reliability of 0.9 (90%), the zero-failure test time was shown to be 5610 h.  
\[T_{ZFT}=B_{p}\bigg{[}\frac{\ln(1-CL)}{n\ln(R)}\bigg{]}^{\frac{1}{\beta}} \tag{3}\]  
where,  
\(T_{ZFT}\): Zero-failure test time  
\(B_{p}\): Target life of the hub bearing  
\(CL\): Confidence level  
\(n\): Number of test samples  
\(R\): Reliability  
\(\beta\): Shape parameter  
As for the zero-failure test time, one sample of the hub bearing should be tested under the equivalent load condition for 5610 h, and no failure should occur during the test. However, since it is challenging to conduct the test for 5610 h, conditions for the accelerated life test were selected. The load and rotation speeds for the accelerated life test of the hub bearing were determined using the inverse-power model, which is mainly used as an accelerated life test model of bearings [13,18]. The equivalent speed of the hub bearing was 132.6 rpm, and 200 rpm was selected as the rotation speed for the acceleration test considering the temperature of the hub bearing, etc. The equivalent load imposed on the actual hub bearing is 1.98 kN, but a static load of 6 kN was applied as the accelerated test load in consideration of the measured load during the field test of the composite working implement. The acceleration index was set to 3 because the hub bearing is a ball bearing. The acceleration factor (\(AF\)) and the zero-failure accelerated life test time (\(T_{ZFAULT}\)) for the calculation of the accelerated life test time of the hub bearing were calculated using Equations (4) and (5). \[AF=\bigg{(}\frac{P_{test}}{P_{eq}}\bigg{)}^{\frac{1}{\beta}}\bigg{(}\frac{N_{ test}}{N_{eq}}\bigg{)} \tag{4}\]  
\[T_{ZFAULT}=\frac{T_{ZFT}}{AF} \tag{5}\]  
where,  
\(AF\): Acceleration factor  
\(P_{test}\): Accelerated test load  
\(P_{eq}\): Equivalent load  
\(x\): Slope of the Wohler curve  
(Acceleration index)  
\(N_{test}\): Accelerated test rotation speed  
\(N_{eq}\): Equivalent rotation speed  
\(T_{ZFAULT}\): Accelerated life test time  
The resultant total \(AF\) is 42.23, and the accelerated life test time is 133 h.  
The static safety factor and fatigue life of the hub bearing, the loads acting on the inner and outer raceways of the hub bearing, the contact stress, and whether there were any contact stress and truncation were analytically checked under the conditions of the rotation speed of 200 rpm and the static load of 6 kN. The operating condition was changed so that the outer raceway of the hub bearing would be fixed, and the inner raceway of the hub bearing would rotate to better consider the boundary conditions of the actual accelerated life test. The static safety factor of the hub bearing was shown to be 6.03, which was greater than 3 recommended in ISO 76, and the fatigue life was shown to be 149.8 h with a 95.4% decrease compared to the life when the preload was 0 \(\mu m\) as shown in Section 3.2[17].