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Research Papers

Active Control of an Active Magnetic Bearings Supported Spindle for Chatter Suppression in Milling Process

[+] Author and Article Information
Tao Huang

State Key Laboratory of Digital Manufacturing
Equipment and Technology,
School of Mechanical Science and Engineering,
Huazhong University of Science and Technology,
Wuhan 430074, China;
School of Electrical Engineering and
Computer Science,
University of Newcastle,
Callaghan, New South Wales 2308, Australia

Zhiyong Chen

School of Electrical Engineering and
Computer Science,
University of Newcastle,
Callaghan, New South Wales 2308, Australia
e-mail: zhiyong.chen@newcastle.edu.au

Hai-Tao Zhang

School of Automation, Key Laboratory of
Image Processing and Intelligent Control,
State Key Laboratory of Digital Manufacturing Equipments and Technology,
Huazhong University of Science and Technology,
Wuhan 430074, China

Han Ding

State Key Laboratory of Digital Manufacturing Equipment and Technology,
School of Mechanical Science and Engineering,
Huazhong University of Science and Technology,
Wuhan 430074, China

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received November 3, 2014; final manuscript received June 1, 2015; published online August 3, 2015. Assoc. Editor: Jingang Yi.

J. Dyn. Sys., Meas., Control 137(11), 111003 (Aug 03, 2015) (11 pages) Paper No: DS-14-1452; doi: 10.1115/1.4030841 History: Received November 03, 2014

In machining process, chatter is an unstable dynamic phenomenon which causes overcut and quick tool wear, etc. To avoid chatter, traditional methods aim to optimize machining parameters. But they have inherent disadvantage in gaining highly efficient machining. Active magnetic bearing (AMB) is a promising technology for machining on account of low wear and friction, low maintenance cost, and long operating life. The control currents applied to AMBs allow not only to stabilize the supported spindle but also to actively suppress chatter in milling process. This paper, for the first time, studies an integrated control scheme for stability of milling process with a spindle supported by AMBs. First, to eliminate the vibration of an unloaded spindle rotor during acceleration/deceleration, we present an optimal controller with proper compensation for speed variation. Next, the controller is further enhanced by adding an adaptive algorithm based on Fourier series analysis to actively suppress chatter in milling process. Finally, numerical simulations show that the stability lobe diagram (SLD) boundary can be significantly expanded. Also, a practical issue of constraints on controller output is discussed.

Copyright © 2015 by ASME
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References

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Figures

Grahic Jump Location
Fig. 1

Illustration of the simplified model and frames and the assembly drawing of a spindle supported by AMBs

Grahic Jump Location
Fig. 2

The y-axis represents the maximum real part of the eigenvalues of the system's state matrix. The stability of the system with u1 designed at the nominal speed might be lost when the spindle speed changes. For example, (a) u1 is designed at r0 = 0 rpm and the system becomes unstable for r > 6000 rpm (noting the maximum real part of the eigenvalues is positive); and (b) u1 is designed at r0 = 3000 rpm and the system is unstable at r = 0. In both cases, we set the angular acceleration r· = 0 rs-2 (revolution per second squared).

Grahic Jump Location
Fig. 3

The y-axis represents the maximum real part of the eigenvalues of the system's state matrix. The stability of the system with u1 designed at the nominal speed might be lost when the spindle accelerates. For example, (a) u1 is designed at r0 = 0 rpm and the system becomes unstable when the angular acceleration is less than 0 rs-2 for r = 6000 rpm and (b) u1 is designed at r0 = 3000 rpm and the system becomes unstable when the angular acceleration is greater than 25 rs-2 for r = 10 rpm.

Grahic Jump Location
Fig. 4

The unloaded system accelerates from still to 2000 rpm with a fixed acceleration 10 rs−2 (a) under u1 without compensation and (b) under u1 with compensation for rotational speed variation

Grahic Jump Location
Fig. 5

SLDs for the system without u2(u2 = 0): (a) for the system with the controller u2 in Eq. (28) with the Fourier series order n = 1 and (b) for the system with the controller u2 in Eq. (28) with n = 2

Grahic Jump Location
Fig. 6

The perturbation system is unstable for ap = 0.5 mm and Ω = 6000 rpm

Grahic Jump Location
Fig. 7

The perturbation system is stable for ap = 0.5 mm and Ω = 6000 rpm under the controller u2 in Eq. (28) for n = 1, 2

Grahic Jump Location
Fig. 8

The displacements of the tool with feed per teeth 0.1 mm for ap = 0.5 mm and Ω = 6000 rpm under the controller u2 in Eq. (28) for n = 1, 2

Grahic Jump Location
Fig. 9

Controller outputs of u1, u2, and u1+u2 for n = 1 with ap = 0.5 mm and Ω = 6000 rpm

Grahic Jump Location
Fig. 10

Controller outputs of u1, u2, and u1+u2 for n = 2 with ap = 0.5 mm and Ω = 6000 rpm

Grahic Jump Location
Fig. 11

Supporting forces provided by AMBs in (a) the x2 direction and (b) the y2 direction, for n = 1

Grahic Jump Location
Fig. 12

Supporting forces provided by AMBs in (a) the x2 direction and (b) the y2 direction, for n = 2

Grahic Jump Location
Fig. 13

Maximum absolute values of u1 in the x2 and y2 directions with ap = 0.5 mm

Grahic Jump Location
Fig. 14

SLDs with considering the control current limit ulim = 20 mA

Grahic Jump Location
Fig. 15

The system is stable for ulim = 10 mA, ap = 0.5 mm, and Ω = 6000 rpm under the controller (28) for n = 2

Grahic Jump Location
Fig. 16

The system is unstable for ulim = 8 mA, ap = 0.5 mm, and Ω = 6000 rpm under the controller (28) for n = 2

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