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

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.