Improving the correlation of structural FEA models by the application of automated high density robotized laser Doppler vibrometry

Abstract

Sound has had an intricate relation with the wellbeing of humans since time immemorial. It has the ability to enhance the quality of life immensely when present as music; at the same time, it can degrade its quality when manifested as noise. Hence, understanding its sources and the processes by which it is produced gains acute significance. Although various theories exist with respect to evolution of bells, it is indisputable that they carry millennia of cultural significance, and at least a few centuries of perfection with respect to design, casting and tuning. Despite the science behind its design, the nuances pertaining to founding and tuning have largely been empirical, and conveyed from one generation to the next. Post-production assessment for bells remains largely person-centric and traditional. However, progressive bell manufacturers have started adopting methods such as finite element analysis (FEA) for informing and optimising their future model designs. To establish confidence in the FEA process it is necessary to correlate the virtual model against a physical example. This is achieved by performing an experimental modal analysis (EMA) and comparing the results with those from FEA. Typically to collect the data for an EMA, the vibratory response of the structure is measured with the application of accelerometers. This technique has limitations; principally these are the observer effect and limited geometric resolution. In this paper, 3-dimensional laser Doppler vibrometry (LDV) has been used to measure the vibratory response with no observer effect due to the non-contact nature of the technique; resulting in higher accuracy measurements as the input to the correlation process. The laser heads were mounted on an industrial robot that enables large objects to be measured and extensive data sets to be captured quickly through an automated process. This approach gives previously unobtainable geometric resolution resulting in a higher confidence EMA. This is used to correlate with FEA up to significantly higher frequencies. Automated, robotized measurements made it possible to easily capture 4000 geometric points per bell. Measurements were made for two carillon bells manufactured by John Taylor & Co., weighing about 100 and 150 kilos. The bells were mounted as freely as possible to allow them to resonate without constraint. They were excited with an electrodynamic shaker attached to an area of the bell where the clapper would normally strike. The frequency response functions (FRF) were collected for each geometry location, and solved to calculate the mode shape for each harmonic. Proprietary system software (Robovib and PSV from Polytec GmbH) was used to measure and capture data. The EMA was solved using industry standard tools from the Siemens PLM suite (LMS Test.Lab Polymax). The deviation for partials/harmonics (in cents) was found to be less than 1.6% from that predicted by the design rules. The mode shapes obtained from model based FEA analysis also correlated well with those from measurements.