A New Approach for Solving Rub-Impact Dynamic Characteristics of Shrouded Blades Based on Macroslip Friction Model

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.