A new nonlinear rotor model supported by the rolling bearing is established under the consideration of the bearing with waviness fault, the unbalanced excitation, the nonlinear Hertz contact force, the varying compliance vibration, and, especially, the physical nonlinear stiffness of the shaft material. The expression with cubic nonlinear terms is adopted to characterize the physical nonlinear stiffness of the shaft material, and the sinusoidal wave is applied to describe the shape characteristics of the waviness fault. The dynamic equations of motion for the new model are developed, and the calculation example of the rotor system supported by the bearing JIS6306 is solved by the variable step-size Runge–Kutta methods to study the effect of the waviness, the clearance, the mass eccentricity on the dynamic behavior. The research results show that growth of the amplitude for the waviness changes the energy distribution of the vibration process; the enlargement of bearing clearance will reduce the stability of the system; the increase in the number of the waviness will make the order of the frequency components changed; for the nonlinear stiffness bearing-rotor system with waviness fault, the augment of mass eccentricity will enhance the impact of the nonlinear stiffness on the system.

Rolling element bearing is a key component in the rotating machinery, especially in the rotor-bearing system which often shows a complex nonlinear dynamic characteristic due to the presence of the internal clearance between the rolling elements and the races. A nonlinear model of the rotor-bearing is developed and the nonlinear dynamic analysis is carried out in this article. The dynamic equations are derived based on the Hertzian contact theory, considering whether there existed an internal clearance between a rolling element and the races at a moment and how much the contact force of the rolling element is during the interface. With the help of the bifurcation diagrams, Poincare maps and the orbit of center for the axis, the effect of the rotating speed, the clearance, and the stiffness on the dynamic response are investigated. The bearing system exhibits the complicated dynamic behaviors such as the periodic motion, the quasi-periodic motion, the chaos, and the jump phenomenon; the rolling element system is sensitive to the variation of the rotating speed, the clearance, and the stiffness in some ranges. The results are meaningful to the practical prediction of the vibrational response; the work is significant in theoretical understanding of the nonlinear dynamic mechanism. This research offers an analytical method to check the parameters to prevent the bearings from the dangerous working conditions.

Based on the macroslip friction model, a new dynamic model of the shrouded blades for rotating machinery is developed to study the impact vibration between the adjacent blades. Unlike the traditional analytical method of the shrouded blade based on the simple Coulomb friction model, a new approach is developed that the macroslip friction model is used to represent a more accurate rubbing behavior (more closer to reality) between the shrouds. By means of the harmonic balance method, the friction force and the normal pressure are translated into the equivalent stiffness and the equivalent damping. The Galerkin method is adopted to reduce the dimension of the equation to obtain the 1-DOF equation of motion, and the dynamic response of the shrouded blade is solved by Runge–Kutta numerical method. The effects of parameters such as the gap of shrouds, the mass of the tip, the contact angle, and the normal stiffness between the shrouded blades on the damping characteristics are discussed. The results show that the gap of tips has a significant effect on the vibration amplitude of the blade. Within a certain range, with the decrease of the gap, the amplitude of the blade tip is getting smaller while the resonant speed is increasing. The mass of the shroud has little effect on the damping characteristics, while the contact angle has a great influence on the equivalent stiffness and damping. Increasing the contact angle to a certain extent can effectively reduce the vibration amplitude of the blade, and the normal contact stiffness also has an important influence in reducing the vibration. The research results based on the new method in this paper are compared with the published articles and agree well. The research work is important to the accurate calculations and design and control of the shrouded blades for rotating machinery.

When the dual rotor system of the aircraft engine is operating, the mass eccentricity of the power turbine rotor and the misalignment of the shaft coupling or the bearing will cause too large vibration of the rotor; this vibration leads to the rub-impact between the rotor and the casing. The power turbine rotor from the dual rotor system is taken as the research object in this paper. Considering the misalignment, the resulting rub-impact faults, the imbalance of rotor and the disk offset, the equation of motion for the system is developed according to the Lagrangian Equation, and then the Range-Kutta Method is adopted to solve the equation. The influence of the key parameters such as the rotating speed, the misalignment angle and the rub-impact clearance on the dynamics of the system is studied; the finite element analysis was carried out to validate the correctness of the theoretical modeling method. The results show that the rub-impact increases the stiffness of the system; the Hopf bifurcation occurs in the misalignment and rub-impact coupling system; the vibrational stability near the half of the switching speed slumps with the increase of the misalignment angle; with increasing of the stiffness, the number of the chaotic zone increases, and the range of the chaos is widening; enlarging the rub-impact clearance is beneficial to reduce the degree of the rub-impact system and enhance the stability of the system.

It is easy for the rotor system to produce the plastic deformation at the support after a long-term operation, this change will cause looseness of the bolt. Due to the particularity of the material and the structure for the bearing base and foundation, the elastic force of the support is nonlinear. Larger vibration of the loosening rotor under the nonlinear support will occur, resulting in the impact-rub between the rotor and stator. In order to study the dynamic behaviors of the loosening-rubbing coupling rotor system under the nonlinear support, the model is established to analyze the influencing mechanism of the key parameters such as the eccentricity, the disk offset, the looseness gap, the rubbing gap, and the nonlinear parameters on the vibrational responses of the system. The piecewise cubic nonlinear expression is applied to describe the nonlinear support with the loosing bolt; Coulomb friction is employed to characterize the rubbing of the impact-rub. The research results show that the nonlinear support will stimulate and amplify the nonlinear dynamic behaviors of the rotor system; there exists a threshold for the effect of the loosening gap on the vibrational characteristics of the system; increasing nonlinear parameters to a certain degree will cause the increase of the proportion of quasi-period and chaos. The research focus and conclusions are certain innovative in this paper. The work is of great value for fault diagnosis and structural design.