Discrete Time-Delay Optimal Control Method for Experimental Active Chatter Suppression and Its Closed-Loop Stability Analysis

Abstract

Chatter is a self-excited and unstable vibration phenomenon during machining operations, which affects the workpiece surface quality and the production efficiency. Active chatter control has been intensively studied to mitigate chatter and expand the boundary of machining stability. This paper presents a discrete time-delay optimal control method for chatter suppression. A dynamical model incorporating the time-periodic and time-delayed characteristic of active chatter suppression during the milling process is first formulated. Next, the milling system is represented as a discrete linear time-invariant (LTI) system with state-space description through averaging and discretization. An optimal control strategy is then formulated to stabilize unstable cutting states, where the balanced realization method is applied to determine the weighting matrix without trial and error. Finally, a closed-loop stability lobe diagram (CLSLD) is proposed to evaluate the performance of the designed controller based on the proposed method. The CLSLD can provide the stability lobe diagram with control and evaluate the performance and robustness of the controller cross the tested spindle speeds. Through many numerical simulations and experimental studies, it demonstrates that the proposed control method can make the unstable cutting parameters stable with control on, reduce the control force to 21% of traditional weighting matrix selection method by trial and error in simulation, and reduce the amplitude of chatter frequency up to 78.6% in experiment. Hence, the designed controller reduces the performance requirements of actuators during active chatter suppression.

Development of a vibration free machine structure for high-speed micro-milling center

“…Semm et al [21] incorporated substructure coupling approach considering local and global damping to improve the accuracy of FEM simulation in order to determine damping performance of a machine tool. Zhang et al [22] proposed a discrete time-delay chatter control method with closed loop chatter stability model for milling process. It stabilized the machining parameters and reduced the amplitude of chatter vibration by 78.6%.…”

Experimental oscillation-assisted cylindrical plunge grinding

“…This kinematics of the plunge grinding process reduces chatter by interfering with one of its causes, namely workpiece regeneration. The active methods of chatter counteract were also considered for the other machining processes [12][13][14]. The authors of publications [15][16][17][18][19][20][21] analyzed similar issues for grinding.…”

Implementation of an Add-on Device that Monitors the Sound of a Machine Tool and Automatically Suppresses Chatter

“…Many researchers have been studying chatter recognition and suppression techniques, and developed various methods to actively or passively modify the system behavior to solve the chatter problem. (2)(3)(4)(5)(6)(7)(8)(9) Faassen et al (10) showed that the milling model of a machine is dependent on the spindle speed; they used the D-partitioning method to find the critical depth of cut for specific spindle speeds. Grossi et al (11) proposed the spindle speed rampup test to obtain a stability lobe diagram without requiring knowledge of the process.…”