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Dry friction distributed over a contact patch between a rigid body and a visco-elastic plane

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Abstract

We consider the dynamics of an absolutely rigid body moving along a rough horizontal plane. We assume that the plane deforms during the motion so that the contact patch is non-planar and has non-zero, but comparatively small area. In the contact patch, the vertical reactions are proportional to the vertical deformations and their rates, that is, we consider Kelvin–Voigt model. The tangent forces are assumed to be classic Coulomb dry friction in sliding regime (no stiction in contact patch). Due to the viscous part of Kelvin–Voigt law, the contact patch, the plane’s normal reaction, friction force and torque depend on the position, orientation, velocity of the center of mass and the angular velocity of the body. The model does not involve any additional dynamic parameter and gives the friction force and torque directly for any given state of the body. To show the advances of the model, we recall the analytical solution of Cauchy’s initial problem with general initial conditions of ODE governing the dynamics of the homogeneous sphere on a horizontal plane (results of Zobova and Treschev in Proc. Steklov Inst. Math. 281:91–118, 2013). Here we generalize the model for arbitrary convex bodies and study its main properties. The model is compared to the continuous velocity-base friction model for pure sliding (Brown and McPhee in ASME J. Comput. Nonlinear Dyn. 11(5):054502, 2016) and to the combined dry friction (Awrejcewicz and Kudra in Multibody Syst. Dyn., 2018, https://doi.org/10.1007/s11044-018-9624-9) in case of sliding with spinning. We illustrate the model considering the results of numerical integration of the Cauchy problem for a controlled differential-drive vehicle on a horizontal plane.

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Notes

  1. Wheels with tires are more suitable for the vehicles. However, here we give an example of a particular MBS modeling with the proposed contact model. As a prospect, we notice that the model can be generalized for a contact of deformable body and rigid plane that can be more suitable for the modeling of wheels with tires.

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Acknowledgement

The work is supported by Russian Foundation for Basic Research (project 16-01-00338).

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  1. Lomonosov Moscow State University, Leninskie gory, 1, 119234, Moscow, Russia

    Alexandra A. Zobova

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  1. Alexandra A. Zobova
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Correspondence to Alexandra A. Zobova.

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Zobova, A.A. Dry friction distributed over a contact patch between a rigid body and a visco-elastic plane. Multibody Syst Dyn 45, 203–222 (2019). https://doi.org/10.1007/s11044-018-09637-1

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