抄録
Rotor systems possessing a number of rotor blades are characterized by a set of linear differential equations with periodically time-varying parameters. For such rotor systems, the multi-blade coordinate (MBC) transformation can be applied to transform all coordinates of the individual rotor blades into the multi-blade coordinates, which describe overall motion of the rotor blade group in the inertial reference frame. Especially, in the case where all the rotor blades are identical both structurally and aerodynamically, periodically time-varying parameters in the equation-of-motion are eliminated in the process of the coordinate transformation and it allows the ordinary eigen-value analysis for linear time-invariant systems to be applied. In the field of wind turbines, therefore, the MBC transformation technique has been commonly adopted to obtain eigen-solutions of a wind turbine system, under the assumption that all the rotor blades are identical both structurally and aerodynamically. The MBC transformation, however, often leads to erroneous eigen-solutions, unless the degree of asymmetry on the row of rotor blades is negligibly small. In the present paper, a coordinate transformation approach that employs the Hill's method of infinite order determinants is proposed to carry out the stability analysis for the periodically time-varying linear system, regardless of the group symmetry condition of the rotor blades. A numerical example is treated to demonstrate the effectiveness of the proposed approach in yielding precise eigen-solutions against the conventional MBC transformation technique.
