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Research Papers

Dynamic Modeling and Response Analysis of a Planar Rigid-Body Mechanism With Clearance

[+] Author and Article Information
Chen Xiulong

College of Mechanical and
Electronic Engineering,
Shandong University of Science and Technology,
Qingdao 266590, China
e-mail: cxldy99@163.com

Jiang Shuai

College of Mechanical and
Electronic Engineering,
Shandong University of Science and Technology,
Qingdao 266590, China
e-mail: 605897943@qq.com

Deng Yu

College of Mechanical and
Electronic Engineering,
Shandong University of Science and Technology,
Qingdao 266590, China
e-mail: dengyuwork@126.com

Wang Qing

Institute of NanoEngineering,
Shandong University of Science and Technology,
Qingdao 266590, China
e-mail: profqwang@163.com

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received March 22, 2018; final manuscript received September 22, 2018; published online March 14, 2019. Assoc. Editor: Corina Sandu.

J. Comput. Nonlinear Dynam 14(5), 051004 (Mar 14, 2019) (15 pages) Paper No: CND-18-1117; doi: 10.1115/1.4042602 History: Received March 22, 2018; Revised September 22, 2018

In order to understand dynamic responses of planar rigid-body mechanism with clearance, the dynamic model of the mechanism with revolute clearance is proposed and the dynamic analysis is realized. First, the kinematic model of the revolute clearance is built; the amount of penetration depth and relative velocity between the elements of the revolute clearance joint is obtained. Second, Lankarani-Nikravesh (L-N) and the novel nonlinear contact force model are both used to describe the normal contact force of the revolute clearance, and the tangential contact force of the revolute clearance is built by modified Coulomb friction model. Third, the dynamic model of a two degrees-of-freedom (2DOFs) nine bars rigid-body mechanism with a revolute clearance is built by the Lagrange equation. The fourth-order Runge–Kutta method has been utilized to solve the dynamic model. And the effects of different driving speeds of cranks, different clearance values, and different friction coefficients on dynamic response are analyzed. Finally, in order to prove the validity of numerical calculation result, the virtual prototype model of 2DOFs nine bars mechanism with clearance is modeled and its dynamic responses are analyzed by adams software. This research could supply theoretical basis for dynamic modeling, dynamic behaviors analysis, and clearance compensation control of planar rigid-body mechanism with clearance.

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References

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Figures

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Fig. 1

Structure diagram of nine bars mechanism without clearance

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Fig. 2

Structure diagram of nine bars mechanism with clearance

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Fig. 3

Model of revolute clearance: (a) free flight mode, (b) contact mode, and (c) impact mode

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Fig. 4

Coordinate system of mechanism with clearance

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Fig. 5

The response curves of the mechanism: (a) displacement of slider, (b) velocity of slider, (c) acceleration of slider, (d) contact force, (e) driving torque of crank 1, (f) driving torque of crank 4, and (g) shaft center trajectory

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Fig. 6

The response curves of mechanism: (a) displacement of slider, (b) displacement error of slider, (c) velocity of slider, (d) velocity error of slider, (e) acceleration of slider, (f) contact force, (g) driving torque of crank 1, and (h) driving torque of crank 4

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Fig. 7

Shaft center trajectory and penetration depth: (a) clearance = 0.3 mm, (b) clearance = 0.5 mm, (c) clearance = 1 mm, and (d) penetration depth

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Fig. 8

Displacement of slider: (a) ω1=−π(rad/s),ω4=π(rad/s) and (b) ω1=−5π(rad/s),ω4=5π(rad/s)

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Fig. 9

Velocity of slider: (a) ω1=−π(rad/s),ω4=π(rad/s) and (b) ω1=−5π(rad/s),ω4=5π(rad/s)

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Fig. 10

Acceleration of slider: (a) ω1=−π(rad/s),ω4=π(rad/s) and (b) ω1=−5π(rad/s),ω4=5π(rad/s)

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Fig. 11

Displacement error of slider: (a) ω1=−π(rad/s),ω4=π(rad/s) and (b) ω1=−5π(rad/s),ω4=5π(rad/s)

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Fig. 12

Velocity error of slider: (a) ω1=−π(rad/s),ω4=π(rad/s) and (b) ω1=−5π(rad/s),ω4=5π(rad/s)

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Fig. 13

Contact force: (a) ω1=−π(rad/s),ω4=π(rad/s) and (b) ω1=−5π(rad/s),ω4=5π(rad/s)

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Fig. 14

Driving torque of crank 1: (a) ω1=−π(rad/s),ω4=π(rad/s) and (b) ω1=−5π(rad/s),ω4=5π(rad/s)

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Fig. 15

Driving torque of crank 4: (a) ω1=−π(rad/s),ω4=π(rad/s) and (b) ω1=−5π(rad/s),ω4=5π(rad/s)

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Fig. 16

Penetration depth: (a) ω1=−π(rad/s),ω4=π(rad/s) and (b) ω1=−5π(rad/s),ω4=5π(rad/s)

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Fig. 17

Shaft center trajectory: (a) ω1=−π(rad/s),ω4=π(rad/s) and (b) ω1=−5π(rad/s),ω4=5π(rad/s)

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Fig. 18

Acceleration of slider

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Fig. 20

Driving torque of crank 1

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Fig. 21

Driving torque of crank 4

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Fig. 22

The trajectory of shaft center

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Fig. 23

Displacement of slider

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Fig. 24

Velocity of slider

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Fig. 25

Acceleration of slider

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Fig. 27

Driving torque of crank 1

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Fig. 28

Driving torque of crank 4

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