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Research Papers

Translational Joints With Clearance in Rigid Multibody Systems

[+] 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, Avenida 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 67260-133hamid.lankarani@wichita.edu

1

Corresponding author.

J. Comput. Nonlinear Dynam 3(1), 011007 (Nov 26, 2007) (10 pages) doi:10.1115/1.2802113 History: Received October 12, 2006; Revised May 21, 2007; Published November 26, 2007

A computational methodology for dynamic description of rigid multibody systems with translational clearance joints is presented and discussed in this work. Over the past years, extensive work has been done to study the dynamic effect of the revolute joints with clearance in multibody systems, in contrast with the little work devoted to model translational joints with clearance. In a joint with translation clearance, there are many possible ways to set the physical configuration between the slider and guide, namely: (i) no contact between the two elements, (ii) one corner of the slider in contact with the guide surface, (iii) two adjacent slider corners in contact with the guide surface, and (iv) two opposite slider corners in contact with the guide surfaces. The proposed methodology takes into account these four different situations. The conditions for switching from one case to another depend on the system dynamics configuration. The existence of a clearance in a translational joint removes two kinematic constraints from a planar system and introduces two extra degrees of freedom in the system. Thus, a translational clearance joint does not constrain any degree of freedom of the mechanical system but it imposes some restrictions on the slider motion inside the guide limits. When the slider reaches the guide surfaces, an impact occurs and the dynamic response of the joint is modeled by contact-impact forces. These forces are evaluated here with continuous contact force law together with a dissipative friction force model. The contact-impact forces are introduced into the system’s equations of motion as external generalized forces. The proposed methodology is applied to a planar multibody mechanical system with a translational clearance joint in order to demonstrate its features.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

Standard procedure to solve the differential-algebraic equations of motion of a multibody system

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Figure 2

Planar translational joint with clearance constituted by a slider and its guide

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Figure 3

Different scenarios for the slider motion inside the guide: (a) no contact, (b) one corner in contact with the guide, (c) two adjacent corners in contact with guide, and (d) two opposite corners in contact with guide

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Figure 4

Generic translational clearance joint in a multibody system

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Figure 5

(a) Noncontact situation and (b) penetration between the slider corner A and guide surface

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Figure 6

(a) Contact between two plane surfaces and (b) contact between a spherical surface and a plane

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Figure 7

Contact forces defined at the points of contact between the slider and guide

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Figure 8

Slider-crank mechanism with a translational clearance joint

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Figure 9

(a) Slider velocity, (b) slider acceleration, (c) crank moment, and (d) dimensionless slider trajectories inside the guide

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Figure 10

Driving crank moment for different clearance sizes in the translational clearance joint

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Figure 11

Dimensionless slider path for different clearance sizes in the translational clearance joint

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Figure 12

Poincaré maps for different clearance sizes in the translational clearance joint

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Figure 13

Contact force between the slider and guide surface: (a) Lankarani and Nikravesh model given by Eq. 20 and (b) linear contact model for two plane surfaces expressed by Eq. 18

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Figure 14

Driving crank moment: (a) Lankarani and Nikravesh model given by Eq. 20 and (b) linear contact model for two plane surfaces expressed by Eq. 18

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