# Enhancing Chatter Stability for Milling Thin-Walled Blades by Designing Non-Uniform Allowance
## 2 Description of the Methodology
### Results and Discussion  
(1) Vibration acceleration spectrum analysis  
The acceleration spectra of the blade basin and suction tip parts are collected as shown in Figure 9, and it can be seen from the vibration acceleration spectra at the milled tip parts that when using the processing strategy of non-uniform stiffness enhancement proposed herein, both the value of the peak acceleration and the density of the acceleration spectra along the distribution of the vibration frequency are much smaller than those with uniform allowance milling process. (2) Machining surface topography analysis  
The surface morphology after machining of the two process strategies is shown in Figure 10, and the vibration pattern on the surface of the blade basin e.g., Figure 9(a)--A surface and blade suction e.g., Figure 9(a)--B surface is very significant when using the traditional process strategy of uniform allowance milling. However, the non-uniform allowance milling using the process strategy proposed herein significantly reduces the vibration pattern regardless of the blade basin e.g., Figure 9(b)--A surface and blade suction e.g., Figure 9(b)--B surface. The results are consistent when testing the roughness of both process schemes. Specim A adopts the traditional uniform allowance program for the surface geometric accuracy testing blade basin and suction, the geometric cross-section part of the super poor, the surface of the existence of obvious vibration pattern, and the tip part of the blade is particularly significant. The root part of the blade vibration marks will be shallow. The measurement of the sampling part of the roughness of the suction Ra is about 2.77 \(\upmu\)m and the basin Ra 2.68 \(\upmu\)m. Specim B adopts the non-uniform process strategy for the surface geometric accuracy testing of the blade basin and suction. The strategy can ensure the size as well as the smooth cross-section of the blade body profile transition. It  
Figure 8: Blade milling machining test site. also guarantees obvious vibration pattern, with the sampling part roughness the suction Ra measured about 1.85 \(\upmu\)m and the basin Ra 1.73 \(\upmu\)m.  
In fact, some scholars have already done a lot of basic work on improving the rigidity of the workpiece itself through non-uniform allowance. Reference [36] facing complex thin-walled blade parts, based on the theory of regenerative vibration analysis, established a comparison chart of the stability lobe of uniform allowance and non-uniform allowance. Theoretically, it shows that non-uniform allowance is beneficial to improve the milling stability of the blade and reduce the cutting vibration of the blade during the cutting process. However, in the design of the allowance, a rough gradient layout based on experience is adopted, which limits the accuracy of the allowance distribution. Reference [39] proposed a non-uniform allowance allocation method based interim state stiffness of thin-walled parts finishing machining features. The stiffness index is simplified as proportional to the  
Figure 10: Comparison of surface morphology between two milling process. Figure 9: Comparison of acceleration spectra for milling process options. area and thickness of the machined surface. By evaluating the interim state stiffness of each machining feature and allocating non-uniform allowances, the stiffness in finishing machining of thin-walled parts is ensured. This method, similar to the former, is also an empirical allowance non-uniform design, which can be well approximated for thin-walled frame parts with geometric structural rules. However, this method is not suitable for complex composite features like blades. Reference [36] proposes a non-uniform allowance planning method for thin-walled parts based on static deformation constraints of the workpiece.