## 2 Proposed Method
### Requirements for Active Damping System  
In order to effectively contrast chatter, both frequency and direction of the unstable vibration must be considered. Indeed, the first aspect defines the frequency range of vibrations that must be damped (crucial for sensors and actuators choice), while the second one is related to actuation directions (crucial for actuators optimal placing). Chatter frequency can be estimated by means of chatter prediction models or experimentally measured and it is related to system dynamics. Actuators and sensors resonance frequency should be at least five times greater than chatter frequency in order to guarantee sufficiently low inertia and an effective response time of the active system. The direction along which the chatter arises depends both on chatter type and on boring bar dynamic behavior. In particular, in case of primary chatter, unstable vibrations occur in the cutting velocity direction (Figure 2a), while in case of regenerative chatter, instability is related to vibrations along radial depth of the cut direction (Figure 2b).  
Figure 1: Active boring bar scheme.  
Figure 2: (**a**) Primary chatter; (**b**) regenerative chatter; (**c**) boring bar most flexible directions (red lines).  
Therefore, in the first case, optimal actuation direction is along cutting velocity, while in the second case, it is necessary to actuate in the radial depth of cut direction. As observed by [PERSON] and [PERSON] [PERSON] and [PERSON] (1998), chatter passes from primary to regenerative varying radial depth of cut, due to the presence of tool nose, which determines cutting force direction. In deep boring process, tools, due to the high aspect ratio, are highly flexible in both these direction (Figure 2c). Then, in order to ensure a damping effect independently of depth of cut, active boring bar must be able to reduce vibrations both along cutting velocity and feed direction.  
In addition to these requirements, since DVF control logic acts only on frequency range close to the system natural frequency, the active boring bar design should consider static behavior as a constraint: standard and active boring should share the same static behavior and adding the actuation system should not worsen the static and dynamic response of the structure with the control off.  
Lastly, technological limits must be considered. In particular, since tool overhang is selected based on the maximum hole depth that can be manufactured, while radial size is constrained by the minimum hole radius, the final solution cannot imply a significant overhang reduction or radial size increase.  
Summarizing, five requirements were identified:  
1. The damping system should be capable of generating counteracting forces in the frequency range of the unwanted vibrations to be mitigated.
2. The active boring bar should be capable of damping vibrations along two directions.
3. The dynamic and static behavior of the active boring bar, with control off, should be as close as possible to the ones of the standard system.
4. The housing of the actuators should not reduce the actual exploiting overhang of the standard boring bar.
5. The housing of the actuators should not exceed a given radial dimension.