# Enhancing Chatter Stability for Milling Thin-Walled Blades by Designing Non-Uniform Allowance
## 1 Introduction
proposes an active control technique to decrease milling vibration by utilizing a voice coil motor and a laser displacement detector as actuator and sensor, whose results demonstrate the feasibility and superiority of the proposed technique as well as the closed-loop system [23]. Moreover, [PERSON] et al. proposes an active control method using piezoelectric patch actuators to enhance the stability of the milling process [24]. These scholars approach chatter suppression from the perspective of active control, who design the actuator installed in the spindle system based on the working conditions. Though somehow cumbersome, this implementation is more effective in reducing tool chatter. However, the suppression effect is still limited to thin-walled parts. Furthermore, to enhance cutting stability, one can alter the milling cutter's structural parameters by adjusting its helix angle and tooth pitch distribution. For instance, [PERSON] et al. examines the impact of variable pitch on end milling cutters for surface quality and flatness. The findings demonstrate that an irregular pitch end milling cutter can decrease chatter when milling thin-walled parts and simultaneously increase cutting speed [25]. [PERSON] et al. conducted an analysis and comparison of the standard, variable-pitch and wave cutters for suppressing chatter in thin-walled milling, whose experiment results demonstrated that the wave cutter has a certain degree of advantage in chatter suppression for thin-walled machining and this cutter can effectively reduce chatter in thin-walled machining [26]. [PERSON] et al. creates a cutting force model for variable-pitch end mills and confirms the link between material removal and vibration response using the optimal inter-tooth angle [27]. [PERSON] et al. devises a non-uniform helical tool dynamics equation and suggests cutting stability limitations. The dependability of the forecast model was authenticated through experiments [28]. [PERSON] et al. establishes a model for demonstrating the dynamic and stability aspects of variable pitch/helix angle milling that takes into account tool runout. He proposes an updated cross-axis and cross-point modal testing method to obtain dynamic parameters that can effectively circumvent vibration issues [29]. The researchers mentioned above focus primarily on the non-uniform side milling of flat-bottomed milling cutters; however, there are limited studies on the milling of thin-walled parts with ball-ended cutters. [PERSON] et al. proposed an optimization method of machining process with non-uniform allowance of integral impeller to accurately improve and predict chatter stability region of machining process [30]. [PERSON] et al. determined and optimized the allowance distribution state of simple thin-walled workpiece in semi-finishing machining based on eigenvalue sensitivity analysis method [31]. However, for complex thin-walled blade structures, the improvement of machining stability through non-uniform margin design still deserves further in-depth research. There are also methods available for the milling process system to absorb and damp vibrations by modifying the system damping mode. For instance, [PERSON] et al. devises a kinetic model for MRF clamping grounded on fuel-solid coupling kinetic theory and puts forth an MRF composite fixture to diminish milling vibration [32]. [PERSON] et al. suggests a method for suppressing forced vibration in thin-walled workpieces, where STF can effectively suppress the forced vibration effect during the milling process [33]. [PERSON] et al. proposes a theoretical methodology to analyze the dynamic behavior of the thin-walled workpiece milling process filled with a viscous fluid to suppress chattering. Optimal process parameters have been achieved through a dynamic model of the spindle-tool system and a thin-walled workpiece immersed in a viscous fluid [34]. [PERSON] et al. developed a novel technique to attenuate chattering vibration of a thin-walled workpiece by immersing the milling system in a viscous fluid.