Methods to estimate subpixel level small motion from video of vibrating cutting tools

Abstract

Cutting tools can vibrate with frequencies of up to a few kHz with amplitudes ranging from a few µm to hundreds of µm. To characterize these vibrations using vision-based modal analysis methods, video of vibrating tools must be acquired at high speed and resolution. High speed acquisition will ensure modes are temporally resolved without aliasing, whereas high resolution acquisition ensures that the pixel size is small enough to resolve small motion. However, since most digital cameras trade speed for resolution, estimating small motion of high frequency modes becomes difficult. To address this issue, this paper presents new methods to estimate small motion from video of vibrating cutting tools. Two methods are illustrated on a video of a slender end mill. One is hardware-based, and the other is software-based. In the hardware-based method, we use combinations of extension tubes and a reverse ring fitted with a standard lens to achieve a pixel size of as less as 1.3 µm. In the software-based method, we leverage the capability of intensity- and phase-based motion registration methods to detect small subpixel level motion, even when the pixel size is 83 µm. In both methods we use the object’s own features to detect and register motion, thus overcoming the limitation of digital image correlation schemes that need markers for target tracking. Modal parameters evaluated from motion estimated with both methods are found to agree with those extracted from twice integrated accelerations. Since methods proposed herein proffer new ways to register small oscillatory motion, we believe that our findings will further help leverage the adoption of vision-based modal analysis methods in machine tool systems as an alternative to the more traditional experimental modal analysis procedures.