Abstract
It is presented a new approach for dry friction modeling under conditions of combined kinematics. The main distinguish feature of this approach is building of friction models which are suitable for using in differential equations of motion. Under the proposed models of friction are understudied the interrelations between friction force components, torques and velocities which are represented be the analytical functions. The procedure of the models constructing consists of the two parts. In the first part, the exact integral expressions for the net vector and torque are formed with the assumption that Coulomb's friction law in classical forms is valid at each point of the contact area. To describe influence of sliding on the force state inside of contact spot, it is proposed the simple asymptotic representations for the contact stresses distributions based on their general properties known from the theoretical results of the theory of elasticity. In the second part the exact integral models are replaced by appropriate Pade expansions. These replacements substantially simplify 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 expansions enables one to account adequately for the relationship between force and kinematical characteristics over the entire range of angular and linear velocities. The approximate models preserve all properties of the models based on the exact integral expressions and correctly describe 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 approximations. The corresponded coefficients can be identified from experiments. Consequently, the models based on Pade expansions may be considered as phenomelogical models of combined dry friction. One of the main advantages of proposed models is obviating a necessity to solve the problem of the theory of elasticity and exactly define the boundaries of area of contact. Introduced models enable correctly describe such classical mechanical effects as the deviation from the straight line the mass center trajectories of the heavy disk which is sliding with rotation on rough plane.
