Implementation of the Contensou–Erismann model for tangent forces in the Hertz contact problem

In frame of the Hertz contact problem an approximate model to compute resulting wrench of the dry friction tangent forces is built up. The wrench consists of the total friction force and the drilling friction torque. An approach under consideration develops in a natural way the contact model built up earlier. The dry friction forces and torque are integrated over the contact elliptic spot. Generally an analytic computation of the integrals mentioned 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 the approximate model in the direction as it was proposed by Contensou. The model under construction is one derived from the Contensou simplified model in the following directions: (a) the model is anisotropic: the total friction forces along ellipse axes are different; (b) for the translatory and almost translatory relative motions one uses the Coulomb friction law regularization; (c) the approximate model for the drilling torque also has been constructed. To verify the model built the results obtained by several authors were used. The Tippe-Top dynamic model is used as a an example under testing. It turned out the top revolution process is identical to one simulated using the set-valued functions approach. The ball bearing dynamic model is used to verify different approaches to the tangent forces computational implementation in details. The model objects corresponding to contacts between the balls and raceways were replaced by ones of new class developed here. Then the old friction model of the regularized Coulomb type and the new one, approximate Contensou, each embedded into the whole bearing dynamic model were thoroughly tested and compared. It turned out the simplified Contensou approach provides the computer model even faster in compare with the case of the point contact.