Delay equations with fluctuating delay related to the regenerative chatter II: analysis of reduced bifurcation equation

Abstract

In this article, we study the reduced bifurcation equations of the nonlinear delay differential equations with periodic delays, which models the machine tool chatter with continuously modulated spindle speed to determine the periodic solutions and analyze the tool motion. Analytical results show both modest increase of stability and existence of periodic solutions close to the new stability boundary.

Keywords:

• Bifurcation equation
• Periodic solutions
• Stability boundaries
• AMS Subject Classifications: 34C35
• 34K15
• 34K20