Due to the dry friction effect, there is a lot of non-smooth behavior in rotor/stator rubbing systems. Based on the investigation of the global response characteristics of a piecewise smooth rotor/stator rubbing system, non-smooth characteristics including stick-slip oscillations and sliding bifurcations have been revealed in dry friction backward whirl with Coulomb friction. To get a deeper insight into the non-smooth characteristics of rotor/stator rubbing systems, it is essential and necessary to study the more complicate friction model, such as Stribeck friction model, which takes into account the viscous damping and the static friction. On the one hand, it has been found that the viscous damping has an effect on the global response characteristics. It is found in this work that as the viscous damping increases gradually from small to a threshold, the region of partial rubs gradually expanded, the region of synchronous full annular rub gradually shrank, and the region of no rub and dry friction backward whirl is almost unchanged. When the viscous damping continues to increase to exceed the threshold value, the region of partial rubs becomes the region of dry friction backward whirl. As the viscous damping continues to further increase, the region of synchronous full annular rub and no rub all becomes the region of dry friction backward whirl. On the other hand, it is also found that the static friction affects the characteristics of stick-slip oscillations rather than the global response characteristics. As the maximum static friction coefficient increases, it changes from behavior of grazing-sliding to continuous pure rolling and then to behavior of switching-sliding.