Research Papers

Backlash Identification in Two-Mass Systems by Delayed Relay Feedback

[+] Author and Article Information
Michael Ruderman

Department of Engineering Sciences,
University of Agder,
Grimstad 4879, Norway
e-mail: michael.ruderman@uia.no

Shota Yamada

Department of Advanced Energy,
The University of Tokyo,
Chiba 277-8561, Japan
e-mail: yamada.shota13@ae.k.u-tokyo.ac.jp

Hiroshi Fujimoto

Department of Advanced Energy,
The University of Tokyo,
Chiba 277-8561, Japan
e-mail: fujimoto@k.u-tokyo.ac.jp

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received February 26, 2018; final manuscript received January 22, 2019; published online February 21, 2019. Assoc. Editor: Soo Jeon.

J. Dyn. Sys., Meas., Control 141(6), 061007 (Feb 21, 2019) (10 pages) Paper No: DS-18-1096; doi: 10.1115/1.4042672 History: Received February 26, 2018; Revised January 22, 2019

Backlash, also known as mechanical play, is a piecewise differentiable nonlinearity which exists in several actuated systems, comprising, e.g., rack-and-pinion drives, shaft couplings, toothed gears, and other machine elements. Generally, the backlash is nested between the moving parts of a complex dynamic system, which handicaps its proper detection and identification. A classical example is the two-mass system which can approximate numerous mechanisms connected by a shaft (or link) with relatively high stiffness and backlash in series. Information about the presence and extent of the backlash is seldom exactly known and is rather conditional upon factors such as wear, fatigue, and incipient failures in the components. This paper proposes a novel backlash identification method using one-side sensing of a two-mass system. The method is based on the delayed relay operator in feedback that allows stable and controllable limit cycles to be induced and operated within the (unknown) backlash gap. The system model, with structural transformations required for the one-side backlash measurements, is given, along with the analysis of the delayed relay in velocity feedback. Experimental evaluations are shown for a two-inertia motor bench that has coupling with backlash gap of about 1 deg.

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Fig. 1

Two-mass system with backlash

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Fig. 2

Block diagram of two-mass system with backlash in the link

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Fig. 3

Equivalent block diagram for modeling the two-mass system with backlash described by the play-type hysteresis operator

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Fig. 4

Relay feedback system with motor dynamics in the loop

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Fig. 5

Symmetric unimodal limit cycle

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Fig. 6

Drifting limit cycle of amplitude-asymmetric relay (α > α+)

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Fig. 7

Relative displacement of the load after the backlash impact as a function of the relay parameter e according to Eq.(22); qualitative example

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Fig. 8

Motor and load displacement during the gap and engagement modes

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Fig. 9

Experimental setup with a gear coupling

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Fig. 10

Frequency characteristics measurements of the setup from the motor torque to the motor-side angle versus the fitted two-mass system model

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Fig. 11

Friction-velocity identification measurements

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Fig. 12

Nominal backlash identified using both encoders

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Fig. 13

Measured xL-xm map in case 1

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Fig. 14

Measured xL-xm map in case 2

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Fig. 15

Steady limit cycle caused by delayed relay feedback

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Fig. 16

Backlash identification using the proposed method, case 1

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Fig. 17

Backlash identification using the proposed method, case 2

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Fig. 18

Backlash identification using the reference method, case 3

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Fig. 19

Backlash identification using the reference method, case 4



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