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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.

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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.

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