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Coupled models of rolling, sliding and whirling friction.

It is proposed the essentially new combined models of friction of rubbed rigid solids under conditions of combined kinematics when besides the sliding and whirling there is a motion of rolling. A correlation between friction of rolling and sliding is modelling on the base experimental investigations from the tyre and railway industry. In correspondence with these results, the main influence of the rolling on the force state in the area of contact consists in the asymmetry of the diagram of the distribution of the normal contact stresses. This asymmetry is well described by the linear function with one coefficient that depends on the direction of motion and velocity of rolling and it leads to appearance of nonzero lateral component of the friction force. Under the proposed model of friction are understudied the interrelations between friction force components, torques and velocities. The model involves the replacement of exact integral expressions for the net vector and torque of the dry friction forces, formed with the assumption that Coulomb's friction law is valid at each point of the contact area, by appropriate Pade approximations. This approach substantially simplifies the combined dry friction modeling, making the calculation of double integrals over the contact area unnecessary. Unlike available models, the model based on the Pade approximations enables one to account adequately for the relationship between force and kinematical characteristics over the entire range of angular and linear velocities. The approximate model preserves all properties of the model based on the exact integral expressions and correctly describes the behaviour of the net vector and torque of the friction forces and their first derivatives at zero and infinity. Moreover, one does not have even to calculate the integrals to determine the coefficients of the Pade approximation. The corresponded coefficients can be identified from experiments. Consequently, the models based on Pade approximations may be considered as reological models of combined dry friction.