Control of circular-disk stability with membrane stresses

Membrane stresses alter the dynamic behavior and stability of circular-disk elements, such as circular saws and grinding wheels, by shifting the disk's natural frequency spectrum. Such shifts are directly related to variation in the critical rotation speed at which standing-wave-resonance instability occurs. Negative critical-speed variations reduce the disk stability, and positive critical-speed variations increase stability. The present paper theoretically and experimentally investigates the relationship between the state of disk-membrane stress, critical rotation speed, and the frequency spectrum in radially symmetric disk problems. The observed critical-speed variations are theoretically predictable and well understood. The approach of a shifting critical-speed instability can be predicted by monitoring the disk-frequency spectrum.