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  • Fokker-Planck equation  (1)
  • Impacts with friction  (1)
  • 1
    Electronic Resource
    Electronic Resource
    Rattling models from deterministic to stochastic processes (1990)
    Springer
    Nonlinear dynamics 1 (1990), S. 63-74 
    Details
    ISSN: 1573-269X
    Keywords: backlash ; impacts ; discrete mappings ; Fokker-Planck equation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Rattling in gears is a consequence of backlashes. It can be generated in those gear-wheels of a car transmission system, which are not under load. Models of rattling are established in three stages. from a straightforward patching method we proceed to a discrete mapping description and to a stochastic model applying the well-known Fokker-Planck equation. All three model stages are consistent and, moreover, they represent a good picture of the real world, which has been proven by tests.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01857585
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  • 2
    Electronic Resource
    Electronic Resource
    Multiple impacts with friction in rigid multibody systems (1995)
    Springer
    Nonlinear dynamics 7 (1995), S. 471-497 
    Details
    ISSN: 1573-269X
    Keywords: Impacts with friction ; multibody systems ; unilateral constraints ; complementarity problems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract An impact model for two-dimensional contact situations is developed which contains the main physical effects of a compliance element in the normal direction and a series of a compliance and Coulomb friction elements in the tangential direction. For systems with multiple impacts a unilateral formulation based on Poisson's hypothesis is used to describe the impulses which are transferred in the normal direction. The event of an impact is divided into two phases. The phase of compression ends with vanishing approaching velocity if normal impulses are transferred and is equivalent to a completely inelastic collision. The phase of expansion allows the bodies to separate under the action of the normal impulses whenever they are large enough. The absolute values of the tangential impulses are bounded by the magnitudes of the normal impulses, due to the Coulomb friction relationship on the impulse level. One part of the transferred tangential impulse during compression is assumed to be partly reversible which may be regarded as an application of Poisson's law. The remaining part is completely irreversible and considered friction. This formulation contains the special case of completely elastic tangential impacts as well as the situation when only Coulomb friction acts. It is proven that the presented impact model is always dissipative or energy preserving. The evaluation of the problem is done by solving one set of complementarity conditions during compression and a nearly identical set of equations during expansion. The theory is applied to some basic examples which demonstrate the difference between Newton's and Poisson's hypotheses.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00121109
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