Mistuning for Minimum Maximum Bladed Disk Forced Response

Abstract

A theory is presented for minimizing the maximum forced response amplitude of any blade in any mode for an isolated fami ly of turbine engine bladed disk modes. An infinitely long linear mistuning pattern, defined by a constant inter -blade stiffness increment, is shown to minimize amplitude magnification. This infinite linear mistuning pattern can be truncated to provide a n approximate mini -max solution for bladed disks with finite N. The linear mistuning method is demonstrated numerically and experimentally . I. Introduction LADED disks, such as those in fans, compressors, and turbines, rotate through circumferential pressu re disturbances caused by struts, vanes, stators, or other obstructions in the gas path of turbine engines. These disturbances cause engine order excitation, where the engine order refers to the number of equally spaced disturbances either upstream or dow nstream of the bladed disk. The resulting blade vibration can lead to high cycle fatigue (HCF) failures as cycles quickly accumulate due to the high rotational rates of turbine engines. HCF has historically led to the premature failure of major aircraft engine components and in some instances has resulted in the loss of the total engine and aircraft. Estimates put the cost of HCF at over $400 m illion per year 1 . HCF is exacerbated by mistuning, a breakdown in the cyclic symmetry of bladed disks. A tuned bladed disk is defined as one in which all sectors have identical properties. Differences in the geometries, material properties, or interface boundary conditions of blades inevitably result in a mistuned bladed disk. The maximum blade response amplitude to engine order excitation, or maximum response for short, is almost always greater for a mistuned bladed disk than for a tuned bladed disk. Therefore, mistuning tends to shorten component life and negative ly impact the durability and reliability of engi nes. Because of the importance of mistuning to turbine engine durability, a large amount of research has been publis hed on the subject. Srinivasan 2 has surveyed much of the literature. The effect of mistuning on turbine bladed disk forced vibration is of ten described using the term amplitude magnification, which is the maximum mistuned blade response across a range of excitation frequencies divided by the maximum t uned blade response. Whitehead