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Research Papers

Ideal Compliant Joints and Integration of Computer Aided Design and Analysis

[+] Author and Article Information
Ashraf M. Hamed, Antonio M. Recuero, Ahmed A. Shabana

Department of Mechanical
and Industrial Engineering,
University of Illinois at Chicago,
842 West Taylor Street,
Chicago, IL 60607

Paramsothy Jayakumar, Michael D. Letherwood, David J. Gorsich

U.S. Army RDECOM-TARDEC,
6501 E. 11 Mile Road,
Warren, MI 48397-5000

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received December 5, 2013; final manuscript received June 26, 2014; published online January 12, 2015. Assoc. Editor: Dan Negrut.

This material is declared a work of the US Government and is not subject to copyright protection in the United States. Approved for public release; distribution is unlimited.

J. Comput. Nonlinear Dynam 10(2), 021015 (Mar 01, 2015) (14 pages) Paper No: CND-13-1316; doi: 10.1115/1.4027999 History: Received December 05, 2013; Revised June 26, 2014; Online January 12, 2015

This paper discusses fundamental issues related to the integration of computer aided design and analysis (I-CAD-A) by introducing a new class of ideal compliant joints that account for the distributed inertia and elasticity. The absolute nodal coordinate formulation (ANCF) degrees of freedom are used in order to capture modes of deformation that cannot be captured using existing formulations. The ideal compliant joints developed can be formulated, for the most part, using linear algebraic equations, allowing for the elimination of the dependent variables at a preprocessing stage, thereby significantly reducing the problem dimension and array storage needed. Furthermore, the constraint equations are automatically satisfied at the position, velocity, and acceleration levels. When using the proposed approach to model large scale chain systems, differences in computational efficiency between the augmented formulation and the recursive methods are eliminated, and the central processing unit (CPU) times resulting from the use of the two formulations become similar regardless of the complexity of the system. The elimination of the joint constraint equations and the associated dependent variables also contribute to the solution of a fundamental singularity problem encountered in the analysis of closed loop chains and mechanisms by eliminating the need to repeatedly change the chain or mechanism independent coordinates. It is shown that the concept of the knot multiplicity used in computational geometry methods, such as B-spline and NURBS (nonuniform rational B-spline), to control the degree of continuity at the breakpoints is not suited for the formulation of many ideal compliant joints. As explained in this paper, this issue is closely related to the inability of B-spline and NURBS to model structural discontinuities. Another contribution of this paper is demonstrating that large deformation ANCF finite elements can be effective, in some multibody systems (MBS) applications, in solving small deformation problems. This is demonstrated using a heavily constrained tracked vehicle with flexible-link chains. Without using the proposed approach, modeling such a complex system with flexible links can be very challenging. The analysis presented in this paper also demonstrates that adding significant model details does not necessarily imply increasing the complexity of the MBS algorithm.

Copyright © 2015 by ASME
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References

Figures

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Fig. 6

Algorithm flow chart: (a) nonlinear constraints and (b) new linear constraints

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Fig. 4

Intermediate coordinate system

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Fig. 3

Structure with slope discontinuity

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Fig. 2

Structure without slope discontinuity

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Fig. 1

Euler–Bernoulli beam element

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Fig. 8

Deformation modes: (a) stretch mode, (b) bending mode, and (c) cross section deformation

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Fig. 9

Tracked vehicle model

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Fig. 10

Sprocket rotational velocity

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Fig. 11

Chassis forward velocity (-·-·-·-·- rigid model, ----- closed loop flexible model, - - - - - - open loop flexible model)

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Fig. 12

Forward displacement of the chassis (-·-·-·-·- rigid model, ----- closed loop flexible model, - - - - - - open loop flexible model)

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Fig. 13

Vertical displacement of the chassis (-·-·-·-·- rigid model, ----- closed loop flexible model, - - - - - - open loop flexible model)

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Fig. 14

Node-32 forward position (----- rigid model, - - - - - - flexible models)

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Fig. 15

Motion trajectory of a flexible track link point

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Fig. 16

First joint longitudinal forces (----- rigid model, - - - - - - flexible models)

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Fig. 17

First joint vertical forces (----- rigid model, - - - - - - flexible models)

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Fig. 18

Axial deformation of first link of the right chain at t = 5s magnified by a factor of 105 (- - - - - - initial configuration, ----- deformed configuration)

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Fig. 19

Transverse deformation of first link of the right chain at t = 5s magnified by a factor of 105 (- - - - - - initial configuration, ----- deformed configuration)

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Fig. 20

Right chain axial stress at t = 5s

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Fig. 21

Right chain axial force distribution at t = 5s

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