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RESEARCH PAPERS

Dynamics of Multibody Systems With Spherical Clearance Joints

[+] Author and Article Information
P. Flores1

Departamento de Engenharia Mecânica, Universidade do Minho, Campus de Azurém, 4800-058 Guimarães Portugalpflores@dem.uminho.pt

J. Ambrósio

 Instituto de Engenharia Mecânica (IDMEC), Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisboa Portugaljorge@dem.ist.utl.pt

J. C. Claro

Departamento de Engenharia Mecânica, Universidade do Minho, Campus de Azurém, 4800-058 Guimarães Portugaljcpclaro@dem.uminho.pt

H. M. Lankarani

Department of Mechanical Engineering, Wichita State University, Wichita, KS 67260hamid.lankarani@wichita.edu

1

Corresponding author.

J. Comput. Nonlinear Dynam 1(3), 240-247 (Mar 03, 2006) (8 pages) doi:10.1115/1.2198877 History: Received January 04, 2006; Revised March 03, 2006

This work deals with a methodology to assess the influence of the spherical clearance joints in spatial multibody systems. The methodology is based on the Cartesian coordinates, with the dynamics of the joint elements modeled as impacting bodies and controlled by contact forces. The impacts and contacts are described by a continuous contact force model that accounts for geometric and mechanical characteristics of the contacting surfaces. The contact force is evaluated as function of the elastic pseudo-penetration between the impacting bodies, coupled with a nonlinear viscous-elastic factor representing the energy dissipation during the impact process. A spatial four-bar mechanism is used as an illustrative example and some numerical results are presented, with the efficiency of the developed methodology discussed in the process of their presentation. The results obtained show that the inclusion of clearance joints in the modelization of spatial multibody systems significantly influences the prediction of components’ position and drastically increases the peaks in acceleration and reaction moments at the joints. Moreover, the system’s response clearly tends to be nonperiodic when a clearance joint is included in the simulation.

Copyright © 2006 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Spherical joint with clearance in a multibody system

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Figure 2

Penetration between the socket and the ball

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Figure 3

Contact forces defined at the points of contact between socket and ball

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Figure 4

Modes of the ball motion inside the socket

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Figure 5

Force versus penetration

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Figure 6

Rigid body in Cartesian coordinates

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Figure 7

Spatial four bar mechanism which includes a spherical clearance joint between the coupler and rocker

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Figure 8

Normal contact force at the clearance joint and corresponding reaction force in the ground-rocker revolute joint for the first impact

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Figure 9

Hysteresis loop of the first three impacts at the clearance joint. The contact force decreases from impact to impact because no energy is feed to the system.

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Figure 10

Z-coordinate of rocker center of mass

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Figure 11

Z-velocity of rocker center of mass

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Figure 12

Z-acceleration of rocker center of mass

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Figure 13

Y-component of the reaction moment at the ground-rocker revolute joint

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Figure 14

Module of the eccentricity vector

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Figure 15

First simulation’s instants in which free flight motion and impacts followed by rebounds are visible

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Figure 16

Ball center trajectory inside the socket. Permanent or continuous contact, i.e., the ball follows the socket wall.

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Figure 17

Poincaré map: ideal joint

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Figure 18

Poincaré map: spherical clearance joint

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