State Dependent Regenerative Delay Model for High-Speed Milling Processes

A 2 DOF dynamic model of regenerative chatter model with state-dependent time delay is developed in milling proceSses.Regenerative effects,"ploughing"or"rubbing"effects between the flank of the cutting edge and the machined surface,and feed effects are considered.It is shown that the regenerative delay is detemined bv the combination of the cutter rotation and the tool vibrations resulting in a state-dependent time delay.The governing equation is a delay-differential equation with state-dependent delay(SD-DDE),as opposed to the standard models with constant time delay.Based on Frechet derivative theory,the linearization of periodic state-dePendent delay differential equation is also investigated.For a system with practical milling parameters.the incorporation of the state.dependent delay into the model does not essentially affect the linear stability properties of the system.