# Self-Tuning Algorithm for Tuneable Clamping Table for Chatter Suppression in Blade Recontouring
## 1 Introduction
Besides, passive damping solutions in the form of tuned mass dampers (TMDs) [16] or Lanchester dampers [17], have lately been applied for chatter avoidance in blade and similar thin-walled part milling. Nevertheless, the application of the technologies developed so far to blade recontouring may not be feasible, as they require direct attachment of the device close to the machining point, which may interfere with the machining trajectory or pose a major difficulty when dealing with blades with complex geometries. Figure 1: Blade repairing process. (**a**) Laser metal deposition for blade tip repair [6]. (**b**) Excess of material to be removed [6]. (**c**) Recontouring by means of 5-axis milling. (**d**) Clamping fixture for blade recontouring operations. As opposed to the in-parallel architecture of regular TMDs, the tuneable clamping table (TCT [18]) is an application case of mode tuning with an in-series architecture, which can increase the damping of the critical mode by tuning a highly damped and controlled mode close to the targeted mode in the frequency band. Its in-series architecture provides the capability to achieve the tuning between the controlled mode and the critical mode of the blade with a universal clamping system and without any direct intervention in the cutting zone. Nevertheless, in mode tuning devices fine tuning is essential to achieve a maximum increase in dynamic stiffness. To this effect, the algebraic expressions for optimal \(H_{\infty}\) tuning for a TCT have already been developed [18], which are the equivalent--but different--to classical TMD amplitude tuning methodologies [19; 20]. When the aim is to maximize milling stability, the aforementioned strategies are no longer optimal [21], and specific tuning procedures based on the optimization of the real part of the receptance function have to be applied [22; 23]. In any case, whatever the objective function, the aim of these strategies is to achieve a wide-bandwidth tuning, considering that neither the part dynamics nor the frequency of the external excitation are subject to change during normal operation. In an industrial environment where a wide variety of parts--and therefore, dynamics--exists and therefore a high degree flexibility and automation is sought, the TCT provides a blade clamping solution to mitigate chatter vibrations with a universal clamping system and minimal interference with the cutting process. This paper presents a self-tuning algorithm for the tuneable clamping table for efficient blade manufacturing and repair. Benefiting from the possibility of externally tuning the frequency and damping of its active mode, its iterative nature allows the device's chatter suppressing capability to be exploited to the maximum extent and also provides the capacity to adapt to blades with uneven dynamics. The analytical expressions for iterative tuning are introduced, which are implemented in an algorithm running in real-time during the milling process. The algorithm is then validated through semidiscretization and initial value time-domain simulations, showing a superior performance compared to regular wide-bandwidth tuning methods.