# Adaptive Control of Active Magnetic Bearing against Milling Dynamics
## 1 Introduction  
### Active Magnetic Bearing (AMB)  
Active magnetic bearing (AMB) is a magnetic actuator. In the past two decades, AMB has been gradually adopted as a non-contact, lubrication-free, and levitation-efficient device in various industrial applications. Owing to its merits, such as the capability to regulate spindle dynamics, AMB has become a potential element for high-speed rotating machinery, e.g., milling machines [1; 2; 3], gas turbines [4; 5], turbo-molecular pumps [6], and so on.  
There are two common configurations of AMB, _i.e._, radial design and modified radial design, as shown in Figure 1[7]. Radial design is also called the planar type because all of the EM (electromagnetic) poles are placed on the same cross-plane. Although the axial length of the radial design is relatively short, the coil turns wound on individual EM poles are very limited. Since the magnetic force is induced by the coils, the force intensity of the radial design AMB is, therefore, restrained. To enhance the magnetic force, the modified radial design was proposed [8]. The EM poles of each magnetic flux loop in radial design (see the dotted line in Figure 1a) are re-arranged to make all the magnetic flux passing along the axial direction (see the dotted line in Figure 1b). Since the number of EM poles in each cross-plane of the modified radial design is merely a half of that of the planar design, the interior space between adjacent poles is significantly increased so that more coil turns can be wound on each yoke to increase the intensity of the magnetic force.  
AMB is a promising technology for machining on account of low wear and friction, low maintenance cost, and long operating life. [PERSON] _et al._[9] reported the design, analysis, and experimental results of a miniature spindle using magnetic bearings for very high-speed micromachining. The spindle is controlled with a DSP-based controller to evaluate the ability of tool orbit control under a spindle speed of 200,000 RPM. The control currents applied to AMBs allow them to not only stabilize the supported spindle but also to actively suppress chatter in the milling process. [PERSON] _et al._[10] proposed a dynamical model of an active magnetic bearing spindle (AMBS) to identify the machining stability of high speed milling (HSM). The AMB and the servo, the flexible mode of rotor, the regenerative effect, and the nonlinearity when the tool leaves the cut under large vibrations are all taken into consideration in this model for the prediction of HSM stability. A sensitivity study of controller performance has been accomplished in this research as well. Another issue regarding the stability of the rotor-AMB system during acceleration/deceleration has been investigated by [PERSON] _et al._[11]. Since the rotational speed variation or acceleration/deceleration may destroy the stability of rotor-AMB system, an adaptive control strategy is designed to stabilize the system and to suppress chatter simultaneously. In addition to eliminating machining vibration, AMBs are also superior in the regulation of spindle position. A study of tool position control with the aid of AMBs during HSM was introduced by [PERSON] _et al._[12]. An improvement in the determination of surface micro-topography characteristics has been reported by [PERSON] _et al._[13]. The electromagnetic actuator (EMA) is employed to compensate for the spindle run-out error and the thermal displacement. An advanced EMA-spindle system has then been proposed for the purpose of generating a micro-pattern on a fixed work surface [14]. A proportional-integral-derivative (PID) controller and adaptive feed-forward cancellation are both adopted to stabilize the system and to compensate for the shaft run-out, respectively. Similar research of spindle control or chatter suppression with the aid of AMBs have also been published in the past five years [15; 16; 17].