# Self-Tuning Algorithm for Tuneable Clamping Table for Chatter Suppression in Blade Recontouring
## 1 Introduction  
The manufacturing and repair of fan, compressor and turbine blades constitute very high added-value industrial processes with a high relevance in the aerospace manufacturing industry. Due to the continuous increase in raw material and manufacturing costs, the specific weight of maintenance, repair and overhaul (MRO [1, 2]) processes of engine parts has been increasing in recent years, which in some applications can result in savings of up to 70% of the total costs compared to disposal and replacement with a remanufactured component [3]. Among the four main stages of the blade repair process (pre-inspection, welding, machining and post-inspection [4]), the machining or recontouring stage is of particular interest due to the specific problems that arise during these operations. The aim of the recontouring stage is to remove, by machining operations, the excess material added in the welding stage (see Figure 1a,b) using additive manufacturing technologies such as laser cladding [5] or laser metal deposition [6] and achieve the final blade geometry. Although these operations have traditionally been performed through manual belt grinding, the need to automate the process to the extent possible has encouraged the engine part maintenance industry to move towards milling-based recontouring (see Figure 1c), performed on 5-axis machines or hybrid cells in which welding and machining operations are performed in the same clamping [7, 8]. In any case, milling operations on thin-walled blades are always a complicated task due to static deflections and, especially, the occurrence of regenerative chatter. The inherently low stiffness and damping properties of the thin-walled blades result in a large dynamic flexibility at the points to be recontoured and largely promote the onset of chatter. Chatter is a type of self-excited vibration caused by the regenerative effect, whereby each cutting edge cuts the wavy pattern left by the vibration in the previous pass [9; 10]. Under certain cutting parameters, this closed-loop relationship can become unstable and result in deep surface marks that can lead to rejection of the machined blade, accelerated tool wear and damage to machine tool components. Chatter suppression can be tackled in different ways [11], such as spindle speed tuning based on a stability lobe diagram (SLD), optimized tool geometries [12] or continuous spindle speed variation [13]. However, the difficult-to-cut titanium, nickel and cobalt alloys commonly used for the blades and the uneven and varying dynamics of blades greatly restrict the applicability of process parameter tuning techniques. The optimization of tool or process parameters may not be effective when the dynamics of the part are altered, or a severe decrease in tool life may occur if the spindle speed is outside the narrow recommended cutting speed range. Increasing the dynamic stiffness of the blade by means of stiffening devices or dampers provides a different approach to reduce the tendency to regenerative chatter without actually changing the process parameters. The application of stiffening devices based on the clamping of the blade near the tip (see Figure 1d) is the most widespread technique at industrial level to prevent chatter in blade MRO processes. To cope with different blade geometries and dimensions, a wide set of fixtures is required, which must also have a certain level of flexibility to cope with the shape deviation of the damaged blade and not to cause an excessive static deflection. In this regard, the use of low melting point alloys as pinpoint has also been investigated as a more flexible stiffening alternative [14]. On the other hand, active and passive dampers can also be implemented to increase the dynamic stiffness of the blades. Active dampers can improve the dynamic stiffness of the part by counteracting the measured vibration by means of an actuator. This idea has recently been implemented to successfully damp flexible parts during heavy duty milling operations on thin walls [15].