Modeling and Calibration for Crack Detection in Circular Shafts Supported on Bearings Using Lateral and Torsional Vibration Measurements

In this paper the requisite foundational numerical and experimental investigations that are carried out, to model the “uncracked and cracked” shaft and to identify its bending and torsional vibration responses, are reported. The cylindrical shaft used in this experimental study is continuous over two spans (with a cantilever span carrying a propeller) with ball-bearing supports. During modal tests the backward end of shaft (away from the propeller end and connecting it to an electric motor, required for online monitoring) is fixed to one of the test frame supports; later on this backward end will be connected to an electric motor to carry out online modal monitoring for crack identification. In the numerical study, beam elements are used for modeling the bending and torsional vibrations of the rotating shaft. The paper describes in detail the numerical “linear spring” models developed for representing the effects of “ball bearings and the (experimental test) frame supports” on the vibration frequencies. Shaft response parameters are obtained using modal analysis software, LMS Test Lab, for bending vibrations monitored using accelerometers, and three “sets” of shear strain gages fixed at three different shaft locations measure the torsional vibrations. Effects of different crack depths on bending and torsional frequencies and mode shapes are investigated experimentally and numerically, and the results interpreted to give better comprehension of its vibratory behavior