The complex service environment of railway vehicles leads to changes in the wheel–rail adhesion coefficient, and the decrease in critical speed may lead to hunting instability. This paper aims to reveal the diversity of periodic hunting motion patterns and the internal correlation relationship with wheel–rail impact velocities after the hunting instability of a bogie system. A nonlinear, non-smooth lateral dynamic model of a bogie system with 7 degrees of freedom is constructed. The wheel–rail contact relations and the piecewise smooth flange forces are the main nonlinear, non-smooth factors in the system. Based on Poincaré mapping and the two-parameter co-simulation theory, hunting motion modes and existence regions are obtained in the parameter plane consisting of running speed v and the wheel–rail adhesion coefficient μ. Three-dimensional cloud maps of the maximum lateral wheel–rail impact velocity are obtained, and the correlation with the hunting motion pattern is analyzed. The coexistence of periodic hunting motions is further revealed based on combined bifurcation diagrams and multi-initial value phase diagrams. The results show that grazing bifurcation causes the number of wheel–rail impacts to increase at a low-speed range. Periodic hunting motion with period number n = 1 has smaller lateral wheel–rail impact velocities, whereas chaotic motion induces more severe wheel–rail impacts. Subharmonic periodic hunting motion windows within the speed range of chaotic motion, pitchfork bifurcation, and jump bifurcation are the primary forms that induce the coexistence of periodic motion.

The misalignment of the coupling device is one of the most common typical faults in rotating machinery. It is noted that the misalignment of the coupling is the origin of the nonlinear vibration of the rotor system,which is further exacerbated by the combined effects of misalignment and rub-impact. This paper aims to reveal the nonlinear dynamic behavior of the misalignment-rub-impact combined rotor(MRCR) system. The equilibrium equation of MRCR system is derived by Newton’s second law, and the 4th-order Runge-Kutta method is used to solve the nonlinear equation. Moreover, the vibration mode and distribution region of the system presented in the (u,v)-two-parameter plane are obtained, which directly reflects the correlation between the vibration response of the system and the continuous change of important parameters. Furthermore, the maximum rub-impact force and duty cycle 3D cloud maps are employed to characterize the system impact’s intensity and duration ratio. The response characteristics of the system and the evolution process of the bifurcation are analyzed in detail by using two kinds of one-parameter bifurcation diagram, axis orbits, time-domain waveform, FFT spectrum diagram, Poincaré maps section and flow chart. The results indicate that the MRCR system presents complex nonlinear characteristics.In space,the rotor and stator can be in three positions: no contact, intermittent contact and full contact.The grazing bifurcation cause the number of rotor and staor impacts to increase.The misalignment fault has small effect on the dynamic behavior of the rotor system at low rotation speed. The magnitude of the misalignment change the frequency component of the system at medium and high ration speeds, significantly influencing the nonlinear dynamic behavior of the rotor system. This research will be beneficial to the fault diagnosis and design of the system in engineering.

Sliding bearings–rotor systems are widely present in rotating machinery structures. The dynamic behavior triggered by friction and rub-impact faults is a key factor restricting the safe and stable operation of a rotor system. Existing studies mainly focus on analyzing dynamic characteristics but rarely explore the degree of friction and rub-impact in the system. This paper takes the sliding bearing–double-disk rotor system with friction and rub-impact as the research model, and defines the concept of the rubbing ratio. It analyzes the influence of relevant structural parameters on the system. The results reveal that the system exhibits rich nonlinear dynamics. Specifically, increasing either the rotor–stator clearance or the lubricant viscosity can drive the system into a broader regime of chaotic motion, while simultaneously reducing the extent of the rub-impact contact region. As the stator stiffness increases from 10⁷ N/m to 9 × 10⁷ N/m, the number of chaotic windows in the bifurcation diagram increases from one to three, while the maximum rubbing force rises by approximately 58% and the rubbing ratio increases from 50% to 56%. The phenomenon of coexisting attractors in the system is also revealed and analyzed. The above research results help to reveal the motion laws of this type of rotor system and have certain guiding significance for parameter matching and optimization design of the system dynamics.