Implementation of the Contensou–Erismann tangent forces model 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 constructed earlier. The dry friction force and torque are integrated over the contact elliptic area. Generally, an analytic computation of the integrals mentioned leads to the cumbersome calculation, tens 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.