Movement of a Solid Body across a Horizontal Plane with a Circular Area of the Bearing and Uniform Load Distribution under Asymmetric Orthotropic Friction

Motion of a thin elliptic plate under symmetric and asymmetric orthotropic friction forces

“…For both the symmetric and asymmetric cases, the sliding and spinning end simultaneously. This important outcome was also achieved for nonuniform pres sure distributions: for a circular plate with respect to the isotropic friction force and axisymmetric normal pressure in [33], under linear pressure distribution in [34], and for an elliptic plate under linear pressure distribution and symmetric orthotropic friction in [20]. However, figure 3 shows a significant difference in the behavior of β(t), ϑ(t) curves with respect to the asymmetry of the friction force.…”

“…If the initial values of the angular and linear (sliding) velocities are nonzero, it is difficult to reach any analytic simplifications. In our paper [20], the system of equations ( 6) was solved in the (ξ, η) coordinate system, but with this approach the accuracy of results was not satisfied enough. Furthermore, at most final points the method tends to oscillate significantly, because near β = β * , a situation with a singularity may appear.…”

“…Area 1, velocities oriented to the IV quadrant. 1,4,17,20 all velocities are directed to the same quadrant.…”

“…During the search limit values of ϑ * , β * with equations ( 17) and (20), it may occur that there are no roots. Thus, we should solve equations (22) and ( 24) to find ϑ * , δ * .…”

“…We attempt to finalize the work we have done during the last few years. We investigated a circular area with symmetric 2 O Silantyeva and N Dmitriev orthotropic friction and uniform pressure distribution in [18], an elliptic area with symmetric orthotropic friction and uniform pressure distribution in [19], linear pressure distribution in [20], a mass point with asymmetric friction in [21], a mass point and elliptic plate with asymmetric friction in [22] and a ring with asymmetric friction in [23]. In these works, we considered different analytic approaches to find out the friction force and friction moment and finally came to the idea that the method presented in the current paper was most suitable for studying the asymmetry of friction.…”