Análise das vibrações no processo de fresamento de topo esférico de superfícies planas inclinadas de aço ferramenta endurecido AISI D6

Abstract

Ball-end milling is widely employed in the finishing of molds and dies, a process characterized by intermittent cutting and by the complex dynamics between the hemispherical tool geometry and the machined surface. Tools with high length-to-diameter ratios, often required for deep cavities, intensify vibratory phenomena that compromise surface integrity and tool life. Although several studies have investigated the effect of cutting path orientation on surface quality, few have simultaneously integrated vibration measurements, cutting forces, and topography in ball-end milling. Addressing this gap, the present work investigated the influence of cutting path orientations (OTCs) and tooth passing frequency on the surface quality of inclined flat surfaces of hardened AISI D6 steel (55-56 HRC), machined with a 10 mm diameter TiSiN-coated solid carbide (WC-10 % Co) ball-end mill and 110 mm overhang (L/D = 11). The dynamic behavior of the tool-holder system was characterized through Frequency Response Function, identifying the dominant mode at 663.8 Hz. In the first stage, eight OTCs were applied at three surface inclination angles (15°, 45°, and 75°) at 3840 rpm, with three repetitions per condition, totaling 72 tests. In the second stage, spindle speed was varied from 1225 to 10,000 rpm across 40 levels, to map the influence of tooth passing frequency on dynamic response and surface finish. In the third stage, the OTCs were reassessed under a more stable condition (7075 rpm). The instrumentation simultaneously integrated inductive displacement sensors, a piezoelectric dynamometer, and an open-field microphone. 3D surface roughness was characterized by optical interferometric profilometry, with Sa and Sz parameters analyzed with and without a roughness filter. Signals were analyzed in the time domain, through frequency spectra via Fast Fourier Transform, and using the Symmetric Dot Pattern (SDP) technique as a complementary tool for instability identification. The results revealed a strong dependence of surface topography on the proximity between tooth passing frequency and the system’s natural modes, confirming the predominance of forced vibrations. The excitation of non-harmonic components proved to be the most relevant indicator of process instability, with a direct impact on surface integrity. RMS displacement values showed no direct relationship with roughness, while spectral content proved decisive for topographic quality. At the 15° inclination, the HDC orientation (horizontal downward concordant) yielded the best surface finish, demonstrating that the down milling cutting mechanism was the determining factor under this condition. At 45°, the horizontal downward orientations (HDC and HDD) achieved the lowest roughness values, whereas at 75° this trend reversed, with horizontal upward orientations (HAC and HAD) delivering the best performance. Among vertical orientations, VDD consistently produced the best finish at 45° and 75°. Under the higher stability condition (7075 rpm), a marked roughness reduction was observed for most OTCs, with the most pronounced effect at 75°, where horizontal upward orientations achieved equivalent finishes regardless of down milling or discordant cutting. Inverse OTC pairs with similar dynamic responses were identified at 45° and 75°, enabling a conceptual reclassification based on tilt (tool inclination perpendicular to the feed direction) and lead (inclination along the feed direction) angles that extends the geometric interpretation of three-axis milling strategies to the multi-axis machining context.