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Spatial Discretization of Serpentine Belt Drive Dynamics Using Constrained Basis Functions

[+] Author Affiliations
Robert G. Parker, Shrenik Shah, Lingyuan Kong

Ohio State University, Columbus, OH

Paper No. IMECE2002-32368, pp. 177-189; 13 pages
doi:10.1115/IMECE2002-32368
From:
  • ASME 2002 International Mechanical Engineering Congress and Exposition
  • Design Engineering
  • New Orleans, Louisiana, USA, November 17–22, 2002
  • Conference Sponsors: Design Engineering Division
  • ISBN: 0-7918-3628-2 | eISBN: 0-7918-1691-5, 0-7918-1692-3, 0-7918-1693-1
  • Copyright © 2002 by ASME

abstract

An efficient method for calculating the eigensolutions and dynamic response of a serpentine belt drive is presented. The model is a hybrid discrete-continuous one where the motions consist of rotations of the pulleys, rotation of the tensioner arm, and transverse vibrations of the continuum belt spans adjacent to the tensioner. The speed of solution results from discretization of the belt spans where the unusual feature is the use of Lagrange multipliers to enforce the geometric boundary conditions at the belt-tensioner interface. The method reduces the computational effort by several orders of magnitude compared to published methods using the same model. Also, it is not susceptible to numerical problems that binder the published methods. The sensitivities of the belt drive natural frequencies to system parameters are also studied. The model parameters under consideration include belt longitudinal stiffness, tensioner spring stiffiness, span tensions, belt transport speed, belt density, and pulley moments of inertia. Exact solutions for the eigensensitivities to these parameters are obtained using perturbation methods. The exact formulae are reduced to simple expressions related to the modal strain and kinetic energies. The eigensensitivities are readily determined, quantitatively and qualitatively, by inspection of the modal energy distributions. An example is presented to demonstrate the capabilities of the methods.

Copyright © 2002 by ASME

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