## 3 Measurement of Placement Error of Non-Contact Encoder Sensor  
Each non-contact encoder sensor arranged on the sensor base acquires position information by sharing one encoder scale attached to the center of the rotor. However, the mechanical placement error and the scale placement error of the non-contact encoder may cause X and Y axis eccentricity, respectively, during rotation control as shown in Figure 8.  
In Figure 8, the X-Y axis placement error of the non-contact encoder occurs and the scale is located at the center without any placement error. In the case of Figure 8, there is no error in the placement of the non-contact encoder, but it represents the occurrence of placement error of the encoder scale. In these two cases, a difference occurs in obtaining information about the rotational position of the same rotor in each stator. Due to the difference in positional information, each stator applies a different current of the rotation command and an eccentricity occurs.  
The error distance can be measured by using the error angle that occurs when two non-contact encoders rotate 180\({}^{\circ}\), as shown in Figure 9.  
If the error distance of the Y axis is measured as shown in Figure 9, the encoder scale is sensed by rotating the rotor from the initial positions of non-contact encoders A and B. If there is an arrangement error as shown in Figure 9, the difference in the rotational  
Figure 8: Problems caused by attachment error of non-contact encoder: (**a**) non-contact encoder’s X-Y axis placement error (accurate encoder scale placement); (**b**) encoder scale X-Y axis placement error (accurate non-contact encoder placement).  
Figure 9: Non-contact encoder placement and placement error measurement: (**a**) non-contact encoder scale and Y-axis encoder arrangement; (**b**) measurement of distance C caused by placement error of encoder scale and non-contact encoder.  
position angle of the non-contact encoder B occurs by \(\theta\) at the sensing position of 180\({}^{\circ}\) of the non-contact encoder A.  
Figure 10 is an enlarged picture of the error distance and error angle in Figure 9b. If the difference between the position information of the non-contact encoder A and B is \(\theta_{error}\) and the radius of the encoder scale is \(R_{scale}\), the arrangement error distance \(C_{error}\) of the two encoders can be calculated and measured through Equation (2). By additionally measuring the placement error value of the X-axis in this way, all of the placement error values of the X-Y axis can be measured. \(S\) is the arc length when the error range \(\theta_{error}\)  
\[C_{error}=2R_{scale}\sin\frac{\theta_{error}}{2} \tag{2}\]  
As shown in Figure 8b, the placement error of the encoder scale can also be measured through Equation (2) in the same way. If you acquire position information by setting the error value as a real-time offset value during the initial setup, you can acquire stable rotation position information.  
It is assumed that there is no error in the arrangement of the non-contact encoder and encoder scale. If the rotor of the rotary magnetic levitation system is moved by centrifugal force as shown in Figure 11, the same phenomenon as Figure 8b can occur. At this time, the X-Y axis position error value \(C_{translation}\) is the same as the moving distance of the X-Y axis rotor. Therefore, through this method, it is possible to measure the eccentricity of the magnetic levitation system through the method of measuring the arrangement error of the non-contact encoder.  
Figure 11: Measurement of travel distance by centrifugal force of magnetic levitation system.  
Figure 10: Error distance measurement using the difference in position value of two non-contact encoders.