## 3 Numerical Simulations and Discussion
### Effect of Sensor Resolution
#### 3.4.2 Discussion  
For Algorithm I, the following can be obtained when considering sensor resolutions. 1. The numbers of LEFPs of the main stiffness coefficients are bigger than those of the main damping coefficients. It is indicated that the main stiffness coefficients of rolling bearings can be better identified than the main damping coefficients. 2. The amounts of LEFPs decrease when the sensor resolution is reduced. Only several stiffness coefficients' relative errors are bigger than 10% when the sensor resolution is 0.1 nm. However, when the sensor resolution is 1 um, nearly half of the frequency points at which the stiffness coefficients' relative errors are bigger than 10% in the simulation of g4.4. When the sensor resolution is 0.1 nm, there are only dozens of, even zero LEFPs of the main stiffness coefficients in the simulation of g4.4. It is indicated that the stiffness bearing can be well identified by Algorithm I when the sensor resolution is 0.1 nm. While for the main damping coefficients, the number of LEFPs is much less than those of the main stiffness coefficients, which indicates that the stiffness coefficients cannot be well-identified. However, the damping coefficients of rolling bearings are far less than the stiffness coefficients. Hence, the damping coefficients of rolling bearings can be considered as zero. Therefore, Algorithm I can be used for rolling bearing in a multi-span and multi-disc rolling bearing-rotor system when the resolution is 0.1 nm. As for Algorithm II used for rolling bearings, the following can be obtained. 1. The numbers of LEFPs of the main stiffness coefficients are far greater than those of the main damping coefficients and the cross-coupled stiffness and damping coefficients. Hence, the main stiffness coefficients of rolling bearings can be better identified than the other coefficients. The reason is also that there is a very big difference between the main stiffness coefficients and the other coefficients of rolling bearings. 2. The amounts of LEFPs decrease when the sensor resolution is reduced. In the computational example g4.4, when the sensor resolution is 0.1 nm, there is less than half of the LEFPs of the main stiffness coefficients of #3, #5 and #6 bearing. There are about seven hundred LEFPs of the main stiffness coefficients of #2, #4 and #8 bearing. There are about nine hundred LEFPs of the main stiffness coefficients of #1 and #7 bearing. When the resolution is 1 um, the number of LEFPs decreases to less than 100. While for oil journal bearings, the following can be obtained for Algorithm II. 1. The numbers of LEFPs of the damping coefficients of journal bearings are bigger than those of the stiffness coefficients, which indicates that the damping coefficients of journal bearings can be better identified than the stiffness coefficients. 2. The amount of LEFPs decrease when the sensor resolution is reduced. In the computational example h4.4, when the sensor resolution is 0.1 nm, most relative errors of the damping coefficients are lower than 10%. When the sensor resolution is 1 um, the LEFPs decrease to less than 100. As for the stiffness coefficients, the number of LEFPs is much less than that of the damping coefficients. There are only several, even zero LEFPs of the stiffness coefficients in the simulation of h4.4. For journal bearings, it is necessary to identify the four stiffness coefficients and the four damping coefficients. Therefore, the sensor resolution plays a key role when using the two algorithms. The sensor resolution affects the measured errors of the unbalance responses. Low resolution causes big measured errors. Hence, high sensor resolution is very important for improving identification accuracy. Moreover, the sensors' resolution has a considerable influence on unbalance responses at low rotating speed (frequency). This causes big measured errors of unbalance responses. Therefore, at low frequencies, the identification errors are big, and the coefficients cannot even be estimated when the resolution is low.