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Research Papers: Friction and Wear

Dynamic Analysis of 4-SPS/CU Parallel Mechanism Considering Three-Dimensional Wear of Spherical Joint With Clearance

[+] Author and Article Information
Gengxiang Wang

Faculty of Mechanical and Precision
Instrument Engineering,
Xi'an University of Technology,
P.O. Box 373,
Xi'an, Shaanxi 710048, China
e-mail: wanggengxiang27@163.com

Hongzhao Liu

Faculty of Mechanical and Precision
Instrument Engineering,
Xi'an University of Technology,
P.O. Box 373,
Xi'an, Shaanxi 710048, China
e-mail: liu-hongzhao@163.com

Peisheng Deng

Faculty of Mechanical and Precision
Instrument Engineering,
Xi'an University of Technology,
P.O. Box 373,
Xi'an, Shaanxi 710048, China
e-mail: dengpeisheng2009@163.com

Kaiming Yin

Faculty of Mechanical and Precision
Instrument Engineering,
Xi'an University of Technology,
P.O. Box 373,
Xi'an, Shaanxi 710048, China
e-mail: jackberlin@126.com

Guanggang Zhang

Faculty of Mechanical and Precision
Instrument Engineering,
Xi'an University of Technology,
P.O. Box 373,
Xi'an, Shaanxi 710048, China
e-mail: zhggsdut@163.com

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received February 28, 2016; final manuscript received July 20, 2016; published online January 25, 2017. Assoc. Editor: Sinan Muftu.

J. Tribol 139(2), 021608 (Jan 25, 2017) (11 pages) Paper No: TRIB-16-1066; doi: 10.1115/1.4034763 History: Received February 28, 2016; Revised July 20, 2016

The dynamic performance of 4-SPS/CU (spherical joint, prismatic joint, cylindrical joint, and universal joint) parallel mechanism considering spherical joint with clearance is developed, and the three-dimensional (3D) wear property of the socket is based on the Archard's wear model. First, the kinematics model of spherical joint with clearance is established, and the updated procedure pertaining to the contact mechanics and wear state is explained via a flowchart. An improved contact force model was proposed by Flores et al. contact force model through a revised contact stiffness coefficient. The normal and tangential contact forces between ball and socket are calculated using the improved contact force model and a modified Coulomb friction model. Second, the dynamic model of the parallel mechanism considering spherical joint with clearance is formulated based on the multibody equations of motion. In order to obtain the 3D wear property of spherical joint with clearance, the contact force is decomposed into three components in the global coordinate system. The three components of sliding distance are computed based on the 3D revolute property of the parallel mechanism. Finally, the contact pressures in three different directions are calculated by the corresponding contact force and approximate contact area components for the sake of predicting the 3D wear depth of socket based on the Archard's wear model. The simulation results show that the wear depth in different directions along the socket surface is nonuniform, which affects the performance of 4-SPS/CU parallel mechanism.

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Figures

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Fig. 1

Contact kinematic of spherical joint with clearance

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Fig. 2

Relationship between contact and wear

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Fig. 3

Evolution of the hysteresis damping factor as a function of the coefficient of restitution

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Fig. 4

Contact stiffness coefficient, clearance size, and contact deformation

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Fig. 5

Contact stiffness coefficient, impact velocity, and coefficient of restitution

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Fig. 6

Contact stiffness coefficient versus coefficient of restitution

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Fig. 7

Modified Coulomb friction model

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Fig. 8

A 4-SPS/CU parallel mechanism with a spherical clearance

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Fig. 9

Transfer of the contact force

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Fig. 10

Three-dimensional wear simulation process of parallel mechanism with spherical clearance joint

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Fig. 11

Reaction force of spherical joint located at A1 with clearance

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Fig. 12

Acceleration of moving platform

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Fig. 13

Angle displacement of moving platform

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Fig. 14

Angle velocity of moving platform

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Fig. 15

Socket surface accumulated wear depth at x0-axis orientation

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Fig. 16

Wear profile on the socket at x0-axis orientation (subtracted to a circle of 1 μm)

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Fig. 17

Socket surface accumulated wear depth at y0-axis orientation

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Fig. 18

Wear profile on the socket at y0-axis orientation (subtracted to a circle of 1 μm)

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Fig. 19

Three-dimensional wear surface of the socket

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