Vibration suppression and surface roughness control in flexible blade polishing: modeling, simulation and optimization

In the flexible polishing process for blisk, tool vibration represents a critical factor governing surface integrity and machining stability. However, comprehensive modeling of the dynamic behavior of flexible polishing tools and its quantitative correlation with the final surface quality remains underdeveloped. This study proposes an integrated force-vibration-roughness coupled simulation and multi-objective optimization framework aimed at suppressing tool vibration and regulating polished surface roughness. Initially, the flexible polishing tool and its connecting rod were modeled as a cantilever beam system, and a vibration differential equation incorporating normal and axial force excitations was formulated. Through polishing force measurements and coordinate transformations, time-domain expressions for normal and axial forces were derived via Fourier series fitting and subsequently applied as boundary conditions within a finite element model to determine the tool-tip vibration response. Simulation results indicated that normal vibration displacement was the dominant component, on the order of 10 -1 mm. Based on these findings, single-abrasive trajectory equations and surface topography generation algorithms were developed, revealing that normal vibration significantly impairs surface quality. Subsequently, a second-order polynomial regression model relating surface roughness and normal vibration RMS was constructed via central composite design (CCD) to minimize both objectives. The Pareto frontier was identified using a genetic algorithm, enabling the determination of an optimal process parameter window: spindle speed n∈[7663,8000] r/min, compression depth a p ∈[1.487, 1.6] mm, feed rate v w ∈[173.8, 279.2] mm/min, and abrasive grit size of abrasive grain M∈[583,734]. Experimental results demonstrate a significant 34% decrease in surface roughness (S a ), which dropped from an average of 0.54 μm to 0.35 μm within the optimized parameter range. All measured values were below 0.4 μm. Additionally, the root mean square (RMS) of normal vibration was maintained within 0.75 mm, ensuring stable vibration levels during processing and maintaining stable surface quality. These results meet the engineering requirements for precision polishing of aircraft blades.