## 1 Introduction  
A boring bar is a tool used for installing cutters and transferring power during boring operation. Cutting holes with satisfactory depths is a difficult problem in boring work. When cutting deep holes, as the boring bar is slender and with a weak dynamic stiffness, chatter occurs easily. When chatter occurs, the surface finish of the cut will be poor, the cutting efficiency will be lowered, and the cutter may be destroyed. To overcome the problem of chatter and to effectively improve the chatter stability during boring, researchers have conducted many studies [1; 2; 3; 4; 5; 6; 7; 8; 9; 10]. Based on the different methods of vibration reduction and control of a boring bar, these studies can be divided into the following three categories. The first category is the design of dynamic vibration absorbers (DVAs). Many researchers have designed DVAs to reduce vibrations and improve the stability of boring bars. For example, [PERSON] et al. [11] designed a new type of damping boring bar with a DVA. The test results showed that it could effectively reduce vibrations and render good cutting performances. [PERSON] et al. [12] designed and analyzed a three-dimensional model of a damped boring bar using the ANSYS software. The results showed that the proposed damping boring bar exhibited good damping performance. [PERSON] et al. [13] focused on the optimal selection of the parameters of a passive DVA attached to a boring bar. The results showed that their method yielded good improvements of the stability performance. [PERSON] et al. [14] designed a device to reduce vibrations by adding a DVA to the boring bar. By changing the axial pressure, their method could change the stiffness of the DVA and effectively suppress the vibrations of the boring bar. [PERSON] et al. [15] designed a variable-stiffness dynamic vibration absorber (VSDVA), and the proposed dynamic model could produce the best vibration reduction by adjusting the stiffness of the VSDVA. [PERSON] et al. [16] proposed a composite DVA with a particle damper (PD) to reduce the additional mass of the DVA and improve the vibration control performance. The results indicated that the vibration reduction performance of the composite DVA significantly outperformed a traditional DVA and single PD. The previous work showed that to design an ideal DVA, it is necessary to accurately understand the dynamic cutting parameters and cutting environment of the boring bar. The second category is the design of active vibration reduction controllers. Many active vibration reduction controllers are designed to achieve active vibration reduction of the boring bar and achieve stable cutting. For example, [PERSON] et al. [17] studied the effect of piezoelectric shunt damping on the chatter vibrations in a boring process. Theoretical and experimental analysis showed that the application of piezoelectric shunt damping could achieve a significant increase in the absolute stability limit in boring operations. [PERSON] et al. [18] presented a noncontact magnetic actuator fit with fiber optic displacement sensors. By mounting the actuator on a computer numerical control (CNC) lathe, they conducted experiments. The experimental results showed that the bending mode of the boring bar was actively damped, and the dynamic stiffness of the system increased significantly. To increase the damping and static stiffness of the boring bar during cutting, [PERSON] et al. [19; 20] designed a 3-degree freedom linear magnetic actuator. Cutting tests showed that the cutting rate could be improved using this method. However, these approaches have the following disadvantages: (1) additional auxiliary equipment and complex control are needed, (2) the application scope is limited, and (3) these systems involve high energy consumption and high costs. The third category is to improve the dynamic stiffness of the boring bar.