Theory and Methodology of Optimally Measuring Vibratory Strains in Closely Spaced Modes

Abstract

Stress ratios are traditionally used to infer maximum stresses in blades from strain measurements. This method may not be applicable to all the modes of modern low aspect ratio (LAR) blades since LAR blades often have high frequency “tip” modes that are so closely spaced that slight changes in structural properties can cause significant mode shape changes. In this paper, it is first shown that the actual tip modes of a LAR blade can be well approximated as linear combinations of the “nominal” modes. The stress field of the blade can then be estimated by calculating the modal content from multiple strain measurements. However, since placement and gage inaccuracies can introduce significant errors in the calculation, it is necessary to find the optimal gage placement that minimizes the error in estimated stresses. An error estimate using “norms” and an efficient optimization method are developed for this purpose.