## 3 Numerical Simulations and Discussion
### Effect of Sensor Resolution
#### 3.4.1 Results
In the x direction, the amounts of LEFPs of k1.xx, k2.xx,..., k8.xx are 982, 786, 444, 719, 422, 446, 729 and 997, respectively. While for c1.xx, c2.xx,..., c8.xx, the amounts are only 23, 6, 2, 10, 5, 7, 3 and 25, respectively. In the y direction, there are 988, 755, 466, 694, 422, 441, 754 and 996 LEFPs of k1.yy, k2.yy,..., k8.yy, respectively. While for c1.yy, c2.yy,..., c8.yy, the amounts are only 18, 7, 3, 5, 0, 6, 3 and 32, respectively. As for the cross-coupled stiffness coefficients in the x direction, there is no one LEFP of k1.xy, k2.xy,..., k8.xy, whereas there are a few LEFPs of c1.xy, c2.xy,..., c8.xy. The amounts are 177, 13, 10, 12, 6, 12, 16 and 290, respectively. In the y direction, the amounts of LEFPs of k1.yx, k2.yx,..., k8.yx are all zero. However, there are some LEFPs of c1.yx, c2.yx,..., c8.yx, whose numbers are 194, 14, 13, 11, 4, 9, 9 and 293, respectively. 1. 1 nm resolution. For the main stiffness coefficients, there are many identification errors smaller than 10%. While for the main damping coefficients, only several identification errors are smaller than 10%. In the x direction, the amounts of LEFPs of k1.xx, k2.xx,..., k8.xx are 978, 749, 375, 590, 281, 327, 618 and 983, respectively. While for c1.xx, c2.xx,..., c8.xx, the amounts are only 27, 6, 4, 11, 2, 8, 3 and 27, respectively. In the y direction, there are 985, 698, 396, 563, 257, 317, 634 and 987 LEFPs of k1.yy, k2.yy,..., k8.yy, respectively. While for c1.yy, c2.yy,..., c8.yy, the amounts are only 19, 5, 3, 5, 3, 4, 2 and 28, respectively. As for the cross-coupled stiffness coefficients in the x direction, there is no one LEFP of k1.xy, k2.xy,..., k8.xy, whereas there are a few low error frequency points of c1.xy, c2.xy,..., c8.xy. The amounts are 160, 14, 11, 17, 4, 16, 15 and 239, respectively. In the y direction, the numbers of LEFPs of k1.yx, k2.yx,..., k8.yx are all zero. However, there are some LEFPs of c1.yx, c2.yx,..., c8.yx, whose numbers are 165, 15, 10, 9, 6, 8, 13 and 224, respectively. 1 um resolution. There are only some identification errors of the main stiffness coefficients smaller than 10% and several identification errors of the main damping coefficients are bigger than 10%. In the x direction, the amounts of LEFPs of k1.xx, k2.xx,..., k8.xx are 195, 36, 25, 16, 17, 14, 11 and 79 and 983, respectively. While for c1.xx, c2.xx,..., c8.xx, the amounts are only 24, 5, 2, 2, 2, 1, 0 and 10, respectively. In the y direction, there are 213, 40, 24, 24, 12, 17, 13 and 85 LEFPs of k1.yy, k2.yy,..., k8.yy, respectively. While for c1.yy, c2.yy,..., c8.yy, the numbers are only 12, 6, 0, 1, 1, 2, 2 and 9, respectively. As for the cross-coupled stiffness coefficients in the x direction, the LEFPs of k1.xy, k2.xy,..., k8.xy are 0, 0, 0, 0, 0, 0 and 1, respectively, whereas there are a few LEFPs of c1.xy, c2.xy,..., c8.xy. The amounts are 15, 5, 4, 2, 3, 3, 1 and 5, respectively. In the y direction, the numbers of LEFPs of k1.yx, k2.yx,..., k8.yx are 0, 0, 0, 0, 1, 0 and 0, respectively. However, there are some LEFPs of c1.yx, c2.yx,..., c8.yx, whose numbers are only 15, 4, 3, 2, 1, 3, 1 and 4, respectively. Other simulations results in which the bearing coefficients cannot be identified in some frequency intervals are obtained as follows. 1. When the resolution is 1 nm, the coefficients of #1-3 bearing cannot be identified at 1 Hz. From 1 to 3 Hz, the coefficients of #4 and #6-8 bearing cannot be identified. From 1 to 5 Hz, the coefficients of #5 bearing cannot be identified. 2. When the resolution is 1 um, the coefficients of #1 bearing cannot be identified from 1 to 65 Hz. From 1 to 57 Hz, the coefficients of #2 bearing cannot be identified. From 1 to 83 Hz, the coefficients of #3 bearing cannot be identified. From 1 to 99 Hz, the coefficients of #4 bearing cannot be identified. From 1 to 163 Hz, the coefficients of #5 bearing cannot be identified. From 1 to 133 Hz, the coefficients of #6 bearing cannot be identified. From 1 to 97 Hz, the coefficients of #7 bearing cannot be identified.