Natural Frequencies of Rotating Bladed Disks Using Clamped-Free Blade Modes

Abstract

The problem of calculating the natural frequencies of a practical rotating bladed disk assembly is solved by use of a new dynamic substructuring method employing the free modes of the disk and the clamped-free modes of the blade. The bladed disk may have lacing-wires at any radius. The lacing-wire, or any other general elastic connection element, is assumed to extend around the whole circumference. Hence, the assembly fulfills the requirements for a circumferentially periodic structure. Centrifugal effects are included. The free modes of the disk are used to describe the dynamics of the disk by a 4 × 4 receptance matrix. The row of blades is described by a dynamic stiffness matrix of order 4 + 10l, where l is the number of lacing-wires. The dynamic stiffness matrix of the blading is formed directly from the modes of one single clamped-free blade without any lacing-wire. The lacing-wires are treated as elastic and massless. The zeroes of the resulting transcendental frequency determinant of order 4 + 10l are solved by the sign-count method. The calculation procedure has proved to be very efficient. Further, it enjoys the precious property of being automatic and infallible in the sense that there is no risk of missing any frequency whatever the spacing of natural frequencies. Experimentally found frequencies are compared to calculated ones.