Equilibrium and stability in spinning disk systems with application to computer hard disk drives, CD -ROMs, zip disks, and industrial circular saws - Warner, Grant Miller (ProQuest Dissertations & Theses, 2003)
In this dissertation we address problems related to equilibrium and stability in spinning disk systems. The problems considered here are optimal profiles for spinning disks with respect to critical speed, multiple equilibria in hydrodynamically coupled disks rotating in an enclosure, and the dynamic stability of thin, warped rotating disks. Chapter 2 presents thickness profiles for rotating disks that maximize critical speed. The disk thickness is permitted to vary between fixed lower and upper bounds, the lower bound corresponding to the minimum thickness saw capable of supporting the in-plane stresses associated with cutting forces and rotation, the upper bound corresponding to the thickness of the saw teeth. The optimal thickness profile consists of two annuli, the inner one with thickness equal to the upper bound, the outer one with thickness equal to the lower bound. With the optimal thickness profile, the critical speed can be raised up to 24%, depending on the clamping ratio of the disk and the lower bound. Optimal thickness profiles and increases in critical speeds are described and compared to existing saw designs. In Chapter 3 experimental results are reported and a simple model proposed to explain a phenomenon in which the equilibrium deflection of a flexible disk rotating inside a narrow housing undergoes an abrupt jump when the rotation speed is varied slightly. Discontinuous jumps are observed in a small fraction (25%) of Zip disks rotating between 3000 rpm and 4500 rpm. For those disks exhibiting jumps, the jumps are repeatable for both increases and decreases in rotation speed during a test; no hysteresis is observed. A disk that initially exhibits the jump phenomenon may fail to exhibit jumps several days or weeks later and vice versa. Numerical results for a rotating membrane hydrodynamically coupled to the surrounding flow show that the number of possible equilibria is a sensitive function of the radial flows above and below the disk. In particular, a small change in radial flow from a radially inward flow to a radially outward flow can abruptly change the number of possible equilibria from two to one. The characteristics of this transition are compatible with the experimental observations. In Chapter 4 non-linear, asymmetric equilibria of a thin rotating disk uniformly loaded by gravity and their stability are computed using the spectral collocation method. Stability boundaries as a function of rotation speed and loading magnitude are computed for uniform disks, eccentrically loaded disks, and for disks with an initial pre-warp. Experimental results aimed at corroborating these findings are presented but are inconclusive due to aerodynamically induced vibration of the disk. The experiments do indicate the presence of a backward traveling wave traveling at 1/4 of the disk rotation speed. The results presented provide quantitative guidelines for the influence of transverse loading on the stability of thin rotating disks.