Delay Equations with Fluctuating Delay: Application to Variable Speed Machining

Abstract

AbstractThe suppression of regenerative chatter by spindle speed variation is attracting increasing attention. In this paper, we study nonlinear delay differential equations with periodic delays which model the machine tool chatter with continuously modulated spindle speed. We make use of the center manifold reduction and the method of normal forms to determine the periodic solutions and analyze the tool motion. Analytical results are very close to those obtained experimentally.Key wordsDelay equationsmachine tool chattercenter manifoldnormal forms