Time-delay feedback control of lathe cutting tools

Abstract

For some machining operations, tool vibrations decay with time, the trivial solution is a stable equilibrium solution, and hence the machined surface is smooth. For other operating conditions, the trivial solution is unstable and the tool undergoes large oscillations called chatter, which might be periodic, quasiperiodic, or chaotic, and hence the surface finish will not be smooth. Therefore, chatter must be avoided or mitigated to maintain machining tolerances, preserve surface finish, and prevent tool breakage. Therefore, extensive research has been devoted to the understanding of the mechanisms of, modeling of, and methods of controlling machine–tool chatter. In this paper, we show that the region of linearly stable trivial solution can be widened considerably using time-delay acceleration feedback.

Stability and perturbation analysis of a one-degree-of-freedom doubly clamped microresonator with delayed velocity feedback control

“…Rezaie and Jahed Motlagh (2011) addressed a new adaptive delayed displacement feedback controller to stabilize a class of chaotic time-delayed systems with a variable parameter. Nayfeh and Nayfeh (2012) proposed a delayed acceleration feedback control strategy to mitigate regenerative chatter in turning on lathes. Recently, by the application of the finite difference technique combined with Floquet theory, Masri et al.…”

Non-linear analysis and quench control of chatter in plunge grinding

“…After the signals are transferred to a computer, the control force κðy 3 ðτÞÀy 4 ðτÞÞ 3 is calculated. Then this force is applied on the wheel holder by an actuator, such as a piezoelectric stack, a magnetostrictive, or an electrostrictive actuator [40].…”

“…As seen in Eq. (23), the bifurcation control can be realized by a close loop control strategy [1,40]. Specifically, the wheel and workpiece velocities (y 3 ðτÞ and y 4 ðτÞ) at the contact point are recorded by a laser velocimeter.…”

Stability analysis in machining process by using adaptive closed-loop feedback control system in turning process

“…They concluded that the damping ratio of the cutting tool increased about four times. Researchers (Al-Regib et al, 2003;Ding et al, 2020;Fallah and Moetakef-Imani, 2019;Insperger and Stepan, 2004;Kovacic, 1998;Khasawneh and Munch, 2016;Liu et al, 2016;Long and Balachandran, 2017;Moradi et al, 2009;Nayfeh and Nayfeh, 2011;Siddhpura et al, 2017) studied the control strategy for chatter suppression in cutting process. In view of this, they were successful in deriving an effective control law that suppresses chatter and finally helps in providing stability in the machining process by adjusting the amplitude and frequency of spindle speed variation.…”