Modeling of Dynamic Instability Via Segmented Cutting Coefficients and Chatter Onset Detection in High-Speed Micromilling of Ti6Al4V

Abstract

Miniature components with complex shape can be created by micromilling with excellent form and finish. However, for difficult-to-machine materials, such as Ti-alloys, failure of low-flexural stiffness microtools is a big limitation. High spindle speeds (20,000–100,000 rpm) can be used to reduce the undeformed chip thickness and the cutting forces to reduce the catastrophic failure of the tool. This reduced uncut chip thicknesses, in some cases lower than the cutting edge radius, can result in intermittent chip formation which can lead to dynamic variation in cutting forces. In addition, the run-out and the misalignment effects are amplified at higher rotational speeds which can induce dynamic force variation. These dynamic force variations coupled with low-flexural rigidity of micro end mill can render the process unstable. Consequently, accurate prediction of forces and stability is essential in high-speed micromilling. Most of the previous studies reported in the literature use constant cutting coefficients in the mechanistic cutting force model which does not yield accurate results. Recent work has shown significant improvement in the prediction of cutting forces with velocity–chip load dependent coefficients but a single-function velocity–chip model fails to predict the forces accurately at very high speeds (>80,000 rpm). This inaccurate force prediction affects the predicted stability boundary at those speeds. Hence, this paper presents a segmented approach, wherein a function is fit for a given range of speeds to determine the chip load dependent cutting coefficients. The segmented velocity–chip load dependent cutting coefficient improves the cutting force prediction at high speeds, which yields much accurate stability boundary. This paper employs two degrees-of-freedom (2DOF) model with forcing functions based on segmented velocity–chip load dependent cutting coefficients. Stability lobe diagram based on 2DOF model has been created for different speed ranges using Nyquist stability criterion. Chatter onset has been identified experimentally via accelerometer data and the power spectral density (PSD) analysis of the machined surface topography. Critical spatial chatter frequencies and magnitudes of PSD corresponding to onset of instability have also been determined for different conditions.