# Noise Identification for an Automotive Wheel Bearing
## 5 Simulation for Structural Defect
To quantitatively represent the radial deformations of the outer ring of the inboard/outboard row and compare these values, the roundness of the outer ring raceways of the inboard/outboard rows was investigated. The analysis location for roundness in the outer ring raceway of the inboard/outboard row is shown in Figure 13. The roundness shapes of the outer ring raceways of the inboard/outboard rows are shown in Figure 14. These roundness shapes were drawn by extracting the radial deformation data for nodes on the same lines in the circumferential direction shown in Figure 13. The roundness in Figure 13(a) is observed as a shape that deforms inward near the flanges and deforms outward between the flanges, whereas the roundness in Figure 13(b) is observed as a shape that deforms outward near the flanges and deforms inward between the flanges. Consequently, the roundness shapes in Figure 13(a),b show the same tendency as the analysis results for the radial deformations in Figure 13(a),b, respectively. The roundness value was calculated as the sum of the maximum deformation values in the inward and outward radial directions. The roundness of the inboard row in Figure 13(a) has values of 4.23, 5.48, and 6.66  in the order of locations 1, 2, and 3, respectively, and the roundness of the outboard row in Figure 13(b) has values of 4.41, 6.81, and 9.01 in the order of locations 1, 2, and 3, respectively. When comparing the roundness values corresponding to the same location in the inboard/outboard row, the roundness value of the outboard row is greater than that of the inboard row. Furthermore, as the analysis location moved outward, the change in roundness value in the outboard row was larger than the change in roundness value in the inboard row. This implies that the radial deformation in the outboard row was higher than the radial deformation in the inboard row when the bolt was fastened. Figure 9:0 Analysis for the radial deformation of the assembled wheel bearing. Figure 9:1 Radial deformation in the outer ring raceway: (**a**) inboard row and (**b**) outboard row. Finally, the relationship between the deformation of the outer ring and vibration of the wheel bearing was investigated. For analysis, the roundness and vibration of the outer ring were obtained with respect to the variation in the bolt tightening torques of 60, 100, and 140 Nm. The roundness of the outer ring is analytically computed using simulation as in the previous analysis, and the analysis location corresponds to location 3 of the outboard row as shown in Figure 9:2 The vibration of the outer ring was experimentally measured when the wheel bearing rotated at 200 RPM, and the peak vibration magnitudes in the outboard row were analyzed at the characteristic frequency, \(f_{\text{BPFO}}\) (22.73 Hz at 200 RPM). Figure 15 shows the values of vibration magnitude and roundness for bolt tightening torques of 60, 100, and 140 Nm. As shown in Figure 15, when the bolt tightening torques are 60, 100, and 140 Nm, the roundness of the outer ring in the outboard row is 0.005, 0.009, and 0.013 mm, respectively. Meanwhile, the vibration magnitudes were 0.053, 0.078, and 0.105 m/s\({}^{2}\), respectively, with respect to the bolt tightening torque. Consequently, when the bolt-tightening torque increases, not only the value of roundness but also the vibration magnitude increases. Therefore, it can be concluded that the deterioration of the roundness in the outer ring by bolt fastening leads to vibration in the assembled wheel bearing. Figure 9:3 Roundness of the outer ring raceway according to the location: (**a**) inboard row and (**b**) outboard row. Figure 9:4 Analysis locations for the roundness of the outer ring raceway in inboard/outboard row.