Implementation of the Contensou–Erismann Model of Friction in Frame of the Hertz Contact Problem on Modelica

Abstract

An approximate model to compute resulting wrench of the dry friction tangent forces in frame of the Hertz contact problem is built up. An approach under consideration develops in a natural way the contact model constructed earlier. Generally an analytic computation of the integrals in the Contensou-Erismann model leads to the cumbersome calculation, decades of terms, including rational functions depending in turn on complete elliptic integrals. To implement the elastic bodies contact interaction computer model fast enough one builds up an approximate model in the way initially proposed by Contensou. To verify the model built results obtained by several authors were applied. First the Tippe-Top dynamic model is used as an example under testing. It turned out the top revolution process is identical to one simulated with use of the set-valued functions approach. In addition, the ball bearing dynamic model was also used to verify different approaches to the tangent forces computational implementation in details. A model objects corresponding to contacts between balls and raceways were replaced by ones of a new class developed here. Then the friction model of the approximate Contensou type embedded into the whole bearing dynamic model was thoroughly tested.

Revised and Improved Implementation of the Spur Involute Gear Dynamical Model

“…Base template for contact model Note that according to the approach previously im-plemented in[8] contact objects have a class being a template which has four class parameters responsible for implementation of: (a) geometry of surfaces at contact; (b) model of normal elastic contact forces; (c) model of normal viscous forces; (d) model of tangent (ususally friction) forces. Visual representation of base template with empty sockets for the above four parameters see inFigure 8.…”

Application and experimental validation of new computational models of friction forces and rolling resistance

“…The piece-wise linear approximation of integral friction model for elliptic contact area and the Hertz stress distribution was presented in paper [15]. Kireenkov [15] constructed the coupled model of friction forces and rolling resistance for circular contact area with Coulomb friction law and fully developed sliding. He used the second-order Padé approximants, which are more accurate and suitable for qualitative analysis.…”

“…The same group of authors proposed for this contact an ellipse as an alternative efficient approximation of the relation between the magnitude of friction force and moment [27]. The piece-wise linear approximation of integral friction model for elliptic contact area and the Hertz stress distribution was presented in paper [15]. Kireenkov [15] constructed the coupled model of friction forces and rolling resistance for circular contact area with Coulomb friction law and fully developed sliding.…”