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Research Papers

Theoretical and Experimental Identification of Clearance Nonlinearities for a Continuum Structure

[+] Author and Article Information
Jie Liu

State Key Laboratory for Manufacturing
Systems Engineering,
Xi'an Jiaotong University,
Xi'an 710049, China
e-mail: jieliu2013@stu.xjtu.edu.cn

Bing Li

Professor
State Key Laboratory for Manufacturing
Systems Engineering,
Xi'an Jiaotong University,
Xi'an 710049, China
e-mail: bli@mail.xjtu.edu.cn

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received December 20, 2015; final manuscript received February 21, 2016; published online May 12, 2016. Assoc. Editor: Arend L. Schwab.

J. Comput. Nonlinear Dynam 11(4), 041019 (May 12, 2016) (18 pages) Paper No: CND-15-1443; doi: 10.1115/1.4033005 History: Received December 20, 2015; Revised February 21, 2016

Clearance is unavoidable in many engineering structures due to the manufacturing and installation errors. These clearances can cause intense impact and wear of the contacting pairs, which may change the dynamic response and eventually reduce the movement precision and the service life of the transmission system. Parameters identification of the clearance would provide better understanding of dynamic behaviors of the clearance and contribute significantly for the control of the induced disturbance and deviation. In this paper, based on dynamic characteristics of the clearance nonlinearity, the piecewise fitting method is first proposed to identify the clearance value of the continuum structure. During the proposed method, first, the rough scope of the clearance value extracted from the displacement response is divided into subintervals. And then, the nonlinear force is fitted by the piecewise linear function in the subintervals. Once the equivalent stiffness is obtained, the clearance value can be calculated by the sorting nonlinear force–displacement curve. The feasibility of the piecewise fitting method was verified by a cantilever beam system with clearances in simulation. Besides, some influence factors of this identification method, including the clearance value, exciting force level and measurement noise, are fully discussed to illustrate the robustness of this method. Moreover, an experiment system of a cantilever beam with adjustable clearances was designed to experimentally validate the effectiveness of the proposed method, and the results show that the piecewise fitting method can precisely identify the clearance value of continuous systems.

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Figures

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Fig. 1

Mechanical model of the cantilever with single clearance

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Fig. 2

Mechanical model of the cantilever with two clearances

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Fig. 3

Characteristic curve of the clearance nonlinearity

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Fig. 4

Second derivative plot of the PDF

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Fig. 5

Overlapping phenomenon of the nonlinear force–displacement curve. (a) Original curve and (b) sorting curve.

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Fig. 6

Flowchart of the piecewise fitting algorithm

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Fig. 7

Displacement response at clearance location

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Fig. 8

Contrast diagram of FRFs between the underlying linear system and nonlinear system

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Fig. 9

Second derivative plot of PDF at the clearance location

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Fig. 10

Sorting nonlinear fitting force–displacement curve

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Fig. 11

FRFs of the underlying system between the displacement signals at clearance and the input force

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Fig. 12

Contrast diagram of FRFs between the underlying linear system and nonlinear system. (a) Between clearance 1 and the input force location and (b) between clearance 2 location and the input force location.

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Fig. 13

Second derivative plots of PDF at the clearance location. (a) Clearance 1 and (b) clearance 2.

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Fig. 14

Sorting nonlinear fitting force–displacement curve. (a) Clearance 1 and (b) clearance 2.

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Fig. 15

FRFs of the underlying system. (a) Between clearance 1 and the input force location and (b) between clearance 2 and the input force location.

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Fig. 16

Displacement response of the 0.30 mm case at the clearance location

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Fig. 17

Clearance test-bed

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Fig. 18

Enlarged drawing of the clearance-adjustment setup

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Fig. 19

Experimental facility of the complete test system

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Fig. 20

Schematic diagram of the experimental scheme. (a) Single clearance case and (b) two clearances case.

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Fig. 21

Measurement method of the clearance value. (a) Schematic diagram and (b) measurement curve.

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Fig. 22

Measurement result of small clearance. (a) Displacement response of small cantilever and (b) displacement response of cantilever.

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Fig. 23

Measurement result of big clearance. (a) Displacement response of small cantilever and (b) displacement response of cantilever.

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Fig. 24

Contrast diagram of FRFs between the underlying linear system and nonlinear system

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Fig. 25

Displacement response at clearance location

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Fig. 26

Second derivative plot of PDF at the clearance location

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Fig. 27

Sorting nonlinear fitting force–displacement curve

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Fig. 28

FRFs of the underlying system between the displacement signals at clearance and the input force

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Fig. 29

Second derivative plots of PDF at the clearance location. (a) Clearance 1 and (b) clearance 2.

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Fig. 30

Sorting nonlinear fitting force–displacement curves. (a) Clearance 1 and (b) clearance 2.

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Fig. 31

FRFs of the underlying system. (a) Between clearance 1 and the input force location and (b) between clearance 2 and the input force location.

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