## 3 Numerical Simulations and Discussion
### Effect of Sensor Resolution
#### 3.4.1 Results
From 1 to 97 Hz, the coefficients of #7 bearing cannot be identified. From 1 to 107 Hz, the coefficients of #8 bearing cannot be identified. Similar results can be obtained from simulations of g1.1 and g1.4 whose results are shown in Figures 9 and 10 in Appendix B. According to Figure 9, the following can be obtained. 1. 0.1 nm resolution. Some identification errors of the main stiffness coefficients are smaller than 10%. While for the main damping coefficients, most of the identification errors are smaller than 10%. In the x direction, the amounts of LEFPs of k1.xx, k2.xx,..., k8.xx are 190, 173, 106, 267, 183, 323, 142 and 166, respectively. While for c1.xx, c2.xx,..., c8.xx, the amounts are 900, 659, 477, 880, 954, 749, 790 and 959, respectively. In the y direction, there are 114, 73, 49, 87, 113, 250, 115 and 25 LEFPs of k1.yy, k2.yy,..., k8.yy, respectively. While for c1.yy, c2.yy,..., c8.yy, the numbers are 869, 703, 480, 925, 974, 777, 805 and 942, respectively. As for the cross-coupled stiffness coefficients in the x direction, there are a few LEFPs of k1.xy, k2.xy,..., k8.xy whose numbers are 7, 58,144, 106, 73, 106, 291 and 143, respectively, whereas the amounts of LEFPs of c1.xy, c2.xy,..., c8.xy are 356, 689, 447, 913, 971, 594, 754 and 781, respectively. In the y direction, the numbers of LEFPs of k1.yx, k2.yx,..., k8.yx are 109, 127, 61, 213, 118, 184, 93 and 32, respectively. However, there are more LEFPs of c1.yx, c2.yx,..., c8.yx, whose numbers are 545, 751, 457, 972, 980, 678, 665 and 678, respectively. 1 um resolution. Few identification errors of the main stiffness coefficients are smaller than 10%. While for the main damping coefficients, several identification errors are smaller than 10%. In the x direction, the amounts of LEFPs of k1.xx, k2.xx,..., k8.xx are only 0, 6, 3, 1, 2, 4, 1 and 0, respectively. While for c1.xx, c2.xx,..., c8.xx, the amounts are 1, 46, 40, 61, 46, 60, 92 and 1, respectively. In the y direction, there are only 0, 3, 2, 0, 1, 2, 1 and 0 LEFPs of k1.yy, k2.yy,..., k8.yy, respectively. While for c1.yy, c2.yy,..., c8.yy, the numbers are 16, 41, 58, 60, 47, 109, 113 and 50, respectively. As for the cross-coupled stiffness coefficients in the x direction, there are very few LEFPs of k1.xy, k2.xyz,..., k8.xy whose numbers are 0, 0, 7, 0, 0, 2, 11 and 0, respectively, whereas the amounts of LEFPs of c1.xy, c2.xy,..., c8.xy are 356, 689, 447, 913, 971, 594, 754 and 781, respectively. In the y direction, the numbers of LEFPs of k1.yx, k2.yx,..., k8.yx are 0, 1, 4, 0, 1, 2, 0 and 0, respectively. However, there are several LEFPs of c1.yx, c2.yx,..., c8.yx, whose numbers are 0, 44, 60, 69, 52, 112, 56 and 2, respectively. Other simulation results that the bearing coefficients cannot be identified in some frequency intervals are obtained as follows. 1. At 1 Hz, k5.xx, k6.xx and k8.xx, c5.xx, c6.xx and c8.xx, k1.yy, k4.yy and k5.yy, c1.yy, c4.yy and c5.yy, k5.xy, k6.xy and k8.xy, c5.xy, c6.xy and c8.xy, k1.yx, k4.yx and k5.yx, c1.yx, c4.yx and c5.yx cannot be identified when the resolution is 0.1 nm. 2. When 1 um resolution is used, k1.xx and c1.xx, k1.xy and c1.xy cannot be identified from 1 to 481 Hz and 515 to 1123 Hz. From 1 to 115 Hz, k2.xx and c2.xx, k2.xy and c2.xy cannot be identified. From 1 to 105 Hz, k3.xx and c3.xx, k3.xy and c3.xy cannot be identified. From 1 to 467 Hz, k4.xx and c4.xx, k4.xy and c4.xy cannot be identified. From 1 to 307 Hz, k5.xx and c5.xx, k5.xy and c5.xy cannot be identified. From 1 to 335 Hz, k6.xx and c6.xx and c6.xy cannot be identified. From 1 to 109 Hz and 121 to 249 Hz, at 859 Hz, from 863 to 865 Hz, k7.xx and c7.xx, k7.xy and c7.xy cannot be identified. From 1 to 797 Hz and 865 to 1289 Hz, k8.xx and c8.xx, k8.xy and c8.xy cannot be identified. As for the coefficients in the y direction, k1.yy and c1.yy, k1.yx and c1.yx cannot be identified from 1 to 477 Hz and 511 to 1117 Hz. From 1 to 109 Hz, k2.yy and c2.yy, k2.yx and c2.yx cannot be identified. From 1 to 101 Hz, k3.yy and c3.yy cannot be identified.