## 2 Proposed Method
### Actuators Housing Strategy and Preload Estimation  
To protect the actuators against lateral forces, spherical end-tips are adopted (Figure 5a). The main advantage of this configuration are: (i) since the joint between actuator and slot can be schematized by a hinge, shear stress are not transferred to the actuators (Figure 5b) (ii) thanks to the spherical shape of the components, the contact between actuators and boring bar is guaranteed even in case of tool deflection (Figure 5c) and (iii) the correct alignment of actuators, after tool deflection, is guaranteed. Figure 4: Evaluated solutions of (**a**) one actuator (**b**) two parallels actuators, (**c**) two side actuators, (**d**) four actuators along x and y direction and (**e**) selected configuration. In order to protect piezo electric actuators from tensile stress, actuators must be preloaded [20]. Manufacturers suggest a value for a basic preload that is the minimum preload in case of no additional forces act on the actuator. In our case, due to tool deflection, the preload required is the sum of basic preload and an additional preload able to compensate the distancing of the hemispherical slots, in which actuators are installed. The most critical condition is identified by chatter, where cutting forces, as well as distancing of the two sections, are maximum. Cutting forces in chatter condition may be measured or estimated, while relative displacement between interface sections can be computed using a Finite Element (FE) approach: exploiting the condition of dynamic equivalence between original and modified boring bar (requirement 3. in Section 2.1), the model of the original boring bar can be used to estimate the maximum distancing of the section in correspondence of the contact surface with actuators. An impulsive force with the same amplitude and direction of the maximum cutting force in chatter condition should be applied at the tool tip (i.e., where cutting forces are exchanged) in order to estimate frequency spectra of displacement in correspondence of the interfaces between tool and actuator. Then, minimum additional preload should be calculated as the force able to compensate maximum displacement. In the case when the boring bar section is not symmetric within the x and y axis, global preload must be adjusted in order to obtain a null resultant moment on the section. Once preload is estimated, the most effective and easy to apply preload system was detected. The most adopted solution in literature is a mechanical mechanism composed by flexure, moving platform and screw [20] (Figure 6a). This solution ensures the adjustment of the preload, but the presence of different moving components affects the effectiveness of the actuator, since part of the motion of the actuator is reduced by the flexibility of the additional components. Considering the importance of the effectiveness in the defined application, a different mechanism that exploits mechanical interference is proposed. In the proposed design, the actuator is forced inside the housing with a defined interference that preloads the actuator inside the slot. This solution allows to reduce the number of components required, hence increasing the actuator effectiveness. In the proposed design, preload is applied using a threaded insert with a spherical housing, as presented in Figure 6b. The advantages of this solution are that it is easy to assemble, and the required preload can be easily obtained by a proper design of the insert. However, interference must be accurately identified, since preload cannot be adjusted or changed. The correct interference must compensate the deformations, due to preload, of actuators and slots also considering local deformations in the contact area between actuators and slots. In the  
Figure 5: (**a**) Housing strategy; (**b**) schematized configuration; (**c**) contact between actuators and boring bar in case of tool deflection. Figure 6: Preload mechanism: (**a**) mechanical [20]; (**b**) by interference (selected solution).