# A Corrected Adaptive Balancing Approach of Motorized Spindle Considering Air Gap Unbalance
## 2 Unbalance and Force of Motorized Spindle
### Electromagnetic Unbalance and Force
#### 2.2.5 Main Component of UMP Affecting the Balancing Capacity  
The ZYS-170 MD12Y16 motorized spindle used in this paper is a four-pole three-phase asynchronous frequency conversion motor; thus, its rotation speed is calculated by  
\[n=\frac{60f_{1}}{p}=30f_{1}, \tag{18}\]  
where \(f_{1}\) is the frequency of the motor power supply.  
Then, the rotating frequency of spindle is obtained by  
\[f_{r}=\frac{n}{60}=0.5f_{1}. \tag{19}\]  
According to Equations (13) and (17), the order and frequency of the electromagnetic forces were calculated, as listed in Table 1; since the high-order forces cause a low-level vibration, the electromagnetic forces over the fourth order were ignored.  
It can be seen from Table 1 that the first-order 1\(\times\) rotation frequency electromagnetic forces (EFs) were caused by dynamic air gap eccentricity, which consists of three parts including the EF caused by interaction of the main and \(p\pm 1\)-order harmonic field, the EF caused by interaction of the rotor tooth harmonic and \(\mu\pm 1\)-order harmonic field, and the EF caused by interaction of the stator tooth harmonic and \(v\pm 1\)-order harmonic field. Furthermore, the components of the first-order 1\(\times\) rotation frequency electromagnetic forces are listed in Table 2, which represent the main components of the UMP affecting the frequency-domain balancing capacity; MFD is shorthand for magnetic flux density.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Electromagnetic Force (EF)**} & \multicolumn{2}{c}{**No Eccentricity**} & \multicolumn{2}{c}{**Dynamic Eccentricity**} \\ \cline{2-5}  & **Order** & **Frequency** & **Order** & **Frequency** \\ \hline EF caused by main magnetic field & 4 & 2\(f_{1}\) & 4 & 2\(f_{1}\) \\ \hline EF caused by interaction of the tooth harmonic magnetic fields of the stator and rotor & 0 & 12\(f_{1}\) & 0 & 12\(f_{1}\) \\ \cline{2-5}  & 4 & \(\dfrac{14f_{1}}{26f_{1}}\) & 4 & 14\(f_{1}\) \\ \hline EF caused by interaction of the main and \(p\pm 1\)-order harmonic magnetic field & None & 1 & 0.5\(f_{1}\) \\ \hline EF caused by interaction of the stator tooth harmonic and \(\mu\pm 1\)-order harmonic magnetic field & None & 3 & 1.5\(f_{1}\) \\ \hline EF caused by interaction of the rotor tooth harmonic and \(\mu\pm 1\)-order harmonic magnetic field & None & 1 & 0.5\(f_{1}\) \\ \hline EF caused by interaction of the rotor tooth harmonic and \(v\pm 1\)-order harmonic magnetic field & None & 1 & 11.5\(f_{1}\) \\ \hline EF caused by interaction of the stator tooth harmonic and \(v\pm 1\)-order harmonic magnetic field & None & 1 & 12.5\(f_{1}\) \\ \hline EF caused by interaction of the rotor tooth harmonic and \(v\pm 1\)-order harmonic magnetic field & None & 3 & 13.5\(f_{1}\) \\ \hline EF caused by interaction of the stator tooth harmonic and \(v\pm 1\)-order harmonic magnetic field & None & 1 & 0.5\(f_{1}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Electromagnetic forces of ZYS-170 MD12Y16 motorized spindle under no eccentricity and dynamic air gap eccentricity.