Modular approximate discrete modeling for blisk system with triple closed-loop equivalence method

Abstract

At present, the lumped-parametric model is often used in the preliminary design of bladed disks. However, the lack of systematic modeling methods leads to high errors. In order to develop the systematic modeling method and improve the equivalence accuracy, this paper considers the comprehensive equivalence from the aspects of natural characteristics, transient forced responses, and steady-state forced responses under aerodynamic excitations. This paper includes two novelties. First, based on the modular equation of blisk system, an approximate discrete model is derived for computational efficiency. Second, a triple closed-loop equivalence method with modal weight optimization is developed innovatively for optimal equivalence parameters. The method can significantly improve the accuracy of element parameters in the lumped-parametric model and achieve the comprehensive equivalence to actual blisk. Compared with the existing equivalence method, the average errors of natural frequencies in the whole mode interval and in the high-density mode interval are reduced by 41.75 % and 36.76 %, respectively. The maximum and average displacement errors of the transient response are reduced by 51.76 % and 58.98 %, respectively. Furthermore, vibration characteristics of the mass and stiffness mistuned blisks are analyzed under traveling wake excitation during acceleration and deceleration processes by approximate discrete model and determined parameters.