Research Papers

Integration of Geometry and Analysis for Vehicle System Applications: Continuum-Based Leaf Spring and Tire Assembly

[+] Author and Article Information
Zuqing Yu

Department of Mechanic
and Electronic Engineering,
Harbin Institute of Technology,
Harbin, Heilongjiang 150001, China

Yiguan Liu

College of Engineering,
Nanjing Agricultural University,
Nanjing, Jiangsu 210031, China;
College of Auto Engineering,
Nanjing Communications Institute
of Technology,
Nanjing, Jiangsu 211188, China

Brian Tinsley, Ahmed A. Shabana

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

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received April 9, 2015; final manuscript received July 18, 2015; published online October 23, 2015. Assoc. Editor: Ahmet S. Yigit.

J. Comput. Nonlinear Dynam 11(3), 031011 (Oct 23, 2015) (11 pages) Paper No: CND-15-1093; doi: 10.1115/1.4031151 History: Received April 09, 2015; Revised July 18, 2015

The development of new and complex vehicle models using the absolute nodal coordinate formulation (ANCF) and multibody systems (MBS) algorithms is discussed in this paper. It is shown how a continuum-based finite element (FE) leaf spring and tire assembly can be developed at a preprocessing stage and integrated with MBS algorithms, allowing for the elimination of dependent variables before the start of the dynamic simulations. Leaf springs, which are important elements in the suspension system of large vehicles, are discretized using ANCF FEs and are integrated with ANCF tire meshes to develop new models with significant details. To this end, the concept of the ANCF reference node (ANCF-RN) is used in order to systematically assemble the vehicle model using linear algebraic constraint equations that can be applied at a preprocessing stage. These algebraic constraint equations define new FE connectivity conditions that include the leaf spring shackle/chassis assembly, tire flexible tread/rigid rim assembly, tire/axle assembly, and revolute joints between different vehicle components. The approach presented in this paper allows for using both gradient deficient and fully parameterized ANCF FEs to develop the new models. In order to develop accurate leaf spring models, the prestress of the leaves and the contact forces between leaves are taken into consideration in the ANCF models developed in this investigation. Numerical results are presented in order to demonstrate the use of the computational framework described in this paper to build continuum-based leaf spring/tire assembly that can be integrated with complex vehicle models. The results of this paper also demonstrate the feasibility of developing a CAD (computer-aided design)/analysis system in which the geometry and analysis mesh of a complete vehicle can be developed in one step, thereby avoiding the incompatibility and costly process of using different codes in the flexible MBS analysis.

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Fig. 5

Combined curvature of clamped blades [24]. (a) Leaves before assembling and (b) assembled spring.

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Fig. 6

Typical leaf spring structure

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Fig. 4

Leaf spring classification according to their structure. (a) Fully elliptic, (b) three-quarter-elliptic, (c) half- or semi-elliptic, (d) quarter-elliptic, (e) transverse-mounted semi-elliptic, and (f) cantilever-mounted semi-elliptic.

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Fig. 3

Leaf spring classification according to the number of leaves. (a) Multileaf spring, (b) single-leaf spring, and (c) tapered-leaf spring.

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Fig. 2

Entire vehicle model using one FE mesh

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Fig. 1

Early simple leaf spring models. (a) Traditional leaf spring, (b) simple equivalent spring model, (c) SAE three-link model, and (d) lumped mass/beam elements.

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Fig. 10

Leaf spring model with shackle and chassis

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Fig. 7

Geometry description of the initially curved structure

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Fig. 8

Prestress of the leaf spring

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Fig. 13

Vertical displacement of the chassis in the single-leaf spring model ( prestress free and prestressed)

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Fig. 14

Distribution of stress components. (a) Distribution of σxx and (b) distribution of σzz.

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Fig. 18

z component of the rx vector of the front axle

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Fig. 12

Distribution of stress components. (a) Distribution of σxx and (b) distribution of σzz.

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Fig. 15

Vehicle configuration during running

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Fig. 16

Longitudinal displacement of the vehicle body

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Fig. 17

Longitudinal velocity of the vehicle body



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