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Research Papers

A Study on the Dynamics of Spatial Mechanisms With Frictional Spherical Clearance Joints

[+] Author and Article Information
Filipe Marques

Departamento de Engenharia Mecânica,
Universidade do Minho, Campus de Azurém,
Guimarães 4804-533, Portugal
e-mail: fmarques@dem.uminho.pt

Fernando Isaac

Departamento de Engenharia Mecânica,
Universidade do Minho, Campus de Azurém,
Guimarães 4804-533, Portugal
e-mail: efinhoisaac@hotmail.com

Nuno Dourado

Departamento de Engenharia Mecânica,
Universidade do Minho,
Campus de Azurém,
Guimarães 4804-533, Portugal
e-mail: nunodourado@dem.uminho.pt

António Pedro Souto

2C2T/Departamento de Engenharia Têxtil,
Universidade do Minho,
Campus de Azurém,
Guimarães 4804-533, Portugal
e-mail: souto@det.uminho.pt

Paulo Flores

Departamento de Engenharia Mecânica,
Universidade do Minho,
Campus de Azurém,
Guimarães 4804-533, Portugal
e-mail: pflores@dem.uminho.pt

Hamid M. Lankarani

Department of Mechanical Engineering,
Wichita State University,
Wichita, KS 67260-133
e-mail: hamid.lankarani@wichita.edu

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received September 1, 2016; final manuscript received March 17, 2017; published online May 4, 2017. Assoc. Editor: Jozsef Kovecses.

J. Comput. Nonlinear Dynam 12(5), 051013 (May 04, 2017) (10 pages) Paper No: CND-16-1414; doi: 10.1115/1.4036480 History: Received September 01, 2016; Revised March 17, 2017

An investigation on the dynamic modeling and analysis of spatial mechanisms with spherical clearance joints including friction is presented. For this purpose, the ball and the socket, which compose a spherical joint, are modeled as two individual colliding components. The normal contact-impact forces that develop at the spherical clearance joint are determined by using a continuous force model. A continuous analysis approach is used here with a Hertzian-based contact force model, which includes a dissipative term representing the energy dissipation during the contact process. The pseudopenetration that occurs between the potential contact points of the ball and the socket surface, as well as the indentation rate play a crucial role in the evaluation of the normal contact forces. In addition, several different friction force models based on the Coulomb's law are revisited in this work. The friction models utilized here can accommodate the various friction regimens and phenomena that take place at the contact interface between the ball and the socket. Both the normal and tangential contact forces are evaluated and included into the systems' dynamics equation of motion, developed under the framework of multibody systems formulations. A spatial four-bar mechanism, which includes a spherical joint with clearance, is used as an application example to examine and quantify the effects of various friction force models, clearance sizes, and the friction coefficients.

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Figures

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Fig. 1

General representation of a typical spherical joint with clearance in spatial mechanisms

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Fig. 2

Relative indentation between the ball and socket

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Fig. 3

Behavior of the friction force models: (a) Coulomb, (b) Ambrósio, (c) Threlfall, (d) Stribeck, (e) piecewise-linear, and (f) Bengisu and Akay

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Fig. 4

Schematic representation of the spatial four-bar mechanism with a spherical clearance joint

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Fig. 5

(a) Z-position of the rocker, (b) Z-velocity of the rocker, (c) Z-acceleration of the rocker, and (d) mechanical energy variation

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Fig. 6

Eccentricity ratio evolution with time: (a) frictionless clearance joint and (b) clearance joint with friction

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Fig. 7

Portrait phases of rocker Z-position versus Z-velocity and rocker Z-velocity versus Z-acceleration: (a) and (b) ideal joint; (c) and (d) frictionless clearance joint, and (e) and (f) clearance joint with friction

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Fig. 8

Influence of the friction force model on the four-bar mechanism's response

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Fig. 9

Influence of the clearance size on the four-bar mechanism's response

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Fig. 10

Influence of the coefficient of friction on the four-bar mechanism's response

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Fig. 11

Effect of the joint model, friction force model, clearance size, and friction coefficient on the computational efficiency

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