The nonlinear friction function was defined based on the velocity and forces to yield accurate solutions. They found that the stick-slip vibrations only happened when the velocity was low. [PERSON] et al. [7] provide a review of the complex phenomena of stick-slip motions in dynamic systems. The existence of solutions, damping properties, friction impacts, chaotic motions, etc., are discussed. [PERSON] [8] made the effort to explore complete stable solutions of a nonlinear, flexible rotor system with friction and stick-slip impacts. Three or four stable solutions were obtained when the oscillation amplitude exceeded the rotor/stator boundaries. In terms of large rotor/stator clearance, stick motions govern the vibration, and damage is caused where the vibration with a large backward whirling frequency and large amplitude happen when the clearance is large. [PERSON] et al. [9] focused on the torsional vibration of a rotor/stator system subjected to dry frictions. They found that torsional vibrations could be caused by the stick-slip conditions when forward or backward whirling occurred. The forward whirling triggered torsional vibration when the rotor/stator was in contact, while the backward whirling led to torsional vibration when the rotor/stator was in impact conditions. [PERSON] and [PERSON] [10] studied the vibration reduction in the friction-involved, nonlinear system. Suitable damping was defined to limit and remove the vibration caused by the sliding motions. The optimal design of the static/kinetic friction ratios was performed to eliminate the friction-induced vibrations of the nonlinear system. [PERSON] and [PERSON] [11; 12] studied the conditions to trigger the backward whirling in a discontinuous, self-excited, nonlinear system subjected to dry frictions. The critical coefficients of the dry frictions during contact were obtained where the angular velocity of the rotor/stator system was smaller than the critical angular velocity. One focused on finding the intrinsic factors, which caused the occurrence of the backward whirling motions in the dynamic system with dry frictions. The occurrence conditions and damages of rotor/stator-contact dynamic systems were systematically studied [13; 14]. The determination criteria of the occurrence of sliding motions are provided by [PERSON] and [PERSON] [15]. They define the function of the friction as exponential and polynomial forms with variables of velocities. [PERSON] et al. [16] investigated the sliding motions of a discontinuous, self-excited, nonlinear rotor system with rotor/stator contact. A new approach is proposed in the research, which solves the occurrence conditions of the backward whirling caused by the dry frictions analytically. Various sliding regimes and switching domains have been obtained [17]. [PERSON] et al. [18] studied a nonlinear rotor system subjected to gas foil forces. The vibration patterns and stability conditions were studied. A new model with LuGre friction was developed to obtain the sliding motions when the system is in contact. [PERSON] et al. [19] investigated the nonlinear vibration patterns of a bearing-rotor system with sliding motions. They established experiments for data to develop theoretical models with rubbing effects. They found that the bearing could be unstable when rubbing happened. [PERSON] et al. [20] designed a novel piezoelectric actuation device based on sliding motions. A new driving algorithm was developed to increase the stick-slip motion and reduce slipping motions. For the detection of the rotor/stator contact, [PERSON] et al. [21] adopted a clipped sinewave model for the spectral analysis of the vibration state of the rotor/stator interaction. Analytical relationships of the amplitudes for the spectral composition's components of a signal on the dimensionless radial gap of the rotor/stator system were established. Based on their model, the rotor/stator contact could be diagnosed.