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Research Papers

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

[+] Author and Article Information
Xingwu Zhang

State Key Laboratory for Manufacturing System Engineering,
Xi’an Jiaotong University,
Xi’an, Shaanxi 710049, China;
School of Mechanical Engineering,
Xi’an Jiaotong University,
Xi’an, Shaanxi 710049, China
e-mail: xwzhang@mail.xjtu.edu.cn

Ziyu Yin

State Key Laboratory for Manufacturing System Engineering,
Xi’an Jiaotong University,
Xi’an, Shaanxi 710049, China;
School of Mechanical Engineering,
Xi’an Jiaotong University,
Xi’an, Shaanxi 710049, China
e-mail: 2606443498@qq.com

Jiawei Gao

China National Aeronautical Radio Electronics Research Institute,
Shanghai 200241, China
e-mail: bodie926@126.com

Jinxin Liu

State Key Laboratory for Manufacturing System Engineering,
Xi’an Jiaotong University,
Xi’an, Shaanxi 710049, China;
School of Mechanical Engineering,
Xi’an Jiaotong University,
Xi’an, Shaanxi 710049, China
e-mail: jinxin.liu@xjtu.edu.cn

Robert X. Gao

Department of Mechanical and Aerospace Engineering,
Case Western Reserve University,
Cleveland, OH 44106
e-mail: robert.gao@case.edu

Hongrui Cao

State Key Laboratory for Manufacturing System Engineering,
Xi’an Jiaotong University,
Xi’an, Shaanxi 710049, China;
School of Mechanical Engineering,
Xi’an Jiaotong University,
Xi’an, Shaanxi 710049, China
e-mail: chr@mail.xjtu.edu.cn

Xuefeng Chen

State Key Laboratory for Manufacturing System Engineering,
Xi’an Jiaotong University,
Xi’an, Shaanxi 710049, China;
School of Mechanical Engineering,
Xi’an Jiaotong University,
Xi’an, Shaanxi 710049, China
e-mail: chenxf@mail.xjtu.edu.cn

1Corresponding author.

Manuscript received January 17, 2018; final manuscript received February 18, 2019; published online March 22, 2019. Assoc. Editor: Satish Bukkapatnam.

J. Manuf. Sci. Eng 141(5), 051003 (Mar 22, 2019) (13 pages) Paper No: MANU-18-1037; doi: 10.1115/1.4043020 History: Received January 17, 2018; Accepted February 19, 2019

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.

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Figures

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Fig. 2

The comparison of the SLD before and after averaging

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Fig. 1

(a) Dynamic model of the milling process and (b) a spindle with active chatter control

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Fig. 9

Control module of the spindle test system

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Fig. 5

(a) OLSLD and CLSLD with weighting matrix Q1 and Q2; (b) open-loop time response of milling system (point (b = 1 mm and Ω = 20,000 rpm)) with U = 0

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Fig. 6

(a) A closed-loop time response of milling system with weighting matrix Q1; (b) active control force with weighting matrix Q1; (c) a closed-loop time response of milling system with weighting matrix Q2; and (d) active control force with weighting matrix Q2. The design of feedback control gain is based on b = 1 mm and Ω = 20,000 rpm

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Fig. 7

(a) CLSLD of the axial depth of cut (1 mm) and spindle speeds (10,000 rpm, 15,000 rpm, and 20,000 rpm); (b) active control force (x direction) at three different spindle speeds; (c) CLSLD of the spindle speed (20,000 rpm) and the axial depth of cut (1 mm, 2 mm, and 3 mm); (d) active control force (x direction) for three different axial depths of cut

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Fig. 8

Intelligent spindle module with associated sensors and actuators

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Fig. 10

The closed-loop data flow of active chatter control

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Fig. 3

The principle chart of the discrete time-delay optimal control method

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Fig. 4

The control flow chart during active chatter suppression

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Fig. 12

OLSLD and CLSLD in the experiment

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Fig. 13

Surface finish of two workpieces used in the milling experiment, with the control off and on

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Fig. 11

(a) Acceleration signals in the time domain between control off and control on and (b) acceleration signals in the frequency domain between control off and control on

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