An Enhanced Beam Modeling for the Vibration Analysis of Rotating Blades

Abstract

The design process of turbine blades begins with the preliminary design phase in which various design variables related to mechanical durability and aerodynamic performance are determined, leading to the detailed design phase in which full-scale performance and durability are analyzed through commercial finite element codes. In this study, an enhanced blade vibration model, which is suitable for use in the preliminary design stage of the blade, is presented. The proposed model is a beam model that can express the nonlinear three-dimensional behavior of blades in linearized equations of motion as the three motion of tension, bending, and torsion are coupled together. Unlike conventional beam models that employ nonlinear strain energy to represent nonlinear deformation of the blade, the proposed model employs linear form of strain energy. The employment of linear strain energy results in the mode functions of the cantilever beam being comparison functions that satisfy the boundary conditions of the system. Thus, global approximation methods such as the assumed mode method can be used to obtain rapid and accurate converged numerical results. The proposed model is a computationally very lightweight model since the discretization of the continuous system by global approximation can minimize the degree of freedom of the system required for analysis. Therefore, when the proposed model is used for the preliminary design of the blade, it is possible to quickly present the vibration analysis results according to the design change through parameterization of various blade design factors and cross-sectional shapes. Using this proposed model, the results of vibration analysis of a rotating blade according to various vibration parameters are presented in this study. The effects of vibration parameters related to blade shape such as eccentricity and pretwist angle of the cross-section on the natural frequencies and mode shapes are investigated. Functionally graded material properties are also considered. In addition, variations of vibration characteristics caused by temperature effects on the outside and inside of blades, when operating at high temperature environment are also investigated. The derived results were compared with the results obtained through a commercial finite element analysis program to verify the accuracy.