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

Abstract

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.

Effect of asymmetric shroud gap and shroud friction coefficient on vibration response of shrouded blades

“…And based on the bilinear hysteresis friction model and Coulomb friction model, the nonlinear characteristics and vibration reduction characteristics of the shrouded blade are compared and analyzed. Nan et al 12,13 studied the combined effect of impact friction between the shrouded blades by performing a nonlinear dynamic analysis of the shrouded turbine blades. Based on the macroscopic slip friction model, the dynamics model of rotating machinery with shrouded blades is established.…”

Self-shrouded torsional blade model equivalence and blade vibration response analysis

“…And the finite element method is adopted to verify the validity of the model. Some scholars use the Timoshenko beam model, [7][8][9][10][11]13 and others use the Euler-Bernoulli beam model without considering the shear effect. 14,15,17,18 These models are replaced with real blades for finite element simulation analysis.…”

“…The effect of shrouded blade gap on the amplitude is illustrated. Guofang Nan 10 simplified the shrouded blade as a cantilever beam blade model with concentrated mass. Based on the macroscopic sliding friction model, a dynamic model of rotating machines with shrouded blades was established to study the impact vibration problem between adjacent blades.…”

Forced Response Vibration Analysis of the Turbine Blade with Coupling between the Normal and Tangential Direction

“…In this method, excitation, nonlinear force, and the system's response are represented by Fourier series approximation. is method is so common in the calculation of forced response analysis of frictionally damped bladed disks [22][23][24][25]. Using the Harmonic balance method and the alternative frequency-domain method (HB-AFT method) Creates a robust method that other general analytical methods such as multiple-scale failed to give analytical method can use to calculate analytical solution [26].…”