UBC Theses and Dissertations
Crack identification in slow rotating machinery using on-line vibration measurements and 3D finite element analysis Keiner, Henning
Vibration monitoring and with it the possibility of on-line machine fault detection and diagnostics have been the focus of maintenance engineering in recent years. In particular, the on-line identification of rotor cracks in turbines, pumps or other rotating machinery holds the potential of great economic benefit due to reduced down-time and loss in production. This work investigates aspects in the development of a crack identification system based on inverse analysis using on-line vibration measurements and 3D Finite Element modeling. A 3D Finite Element modeling approach, the nodal crack force approach, was developed to model the non-linear crack breathing behaviour of rotor cracks. The approach linearizes the equations of motion around the point of static deflection and solves them in a rotating frame of reference, significantly reducing the computational requirements. Results show good agreement with results from analytical methods and 3D Finite Element transient analysis. The nodal crack force approach was also shown to yield a better model of the crack face opening behaviour for larger cracks than the traditional node de-coupling method. A scaled-down experimental setup of a pressure washer drum was developed to experimentally investigate the vibrations of a cracked rotor. The experimental setup was used to compare measured vibration signatures from three different crack implementation methods: the bolt removal method, the gap insertion method and the placement of a grown fatigue crack. Results show that the two experimental crack simulation methods yield a comparable vibration response to a grown fatigue crack at significantly lower cost. The bolt removal method was chosen to conduct an experimental parameter study of the influence of crack size and location on the vibration behaviour of the drum. Measured vibration response curves for different crack sizes were clearly distinguishable from one another, and they were matched closely by the Finite Element results, making the identification of crack size and location using an inverse analysis approach feasible. The inverse analysis problem was solved as a non-linear constraint parameter optimization problem where the objective function consists of a weighted least squares difference between measured and modeled system response. Crack identification for a known crack location yielded results within 10 % of the true crack size. It was also shown that the identified crack size was mostly independent of the chosen weighting function and that simple, global optimization algorithms yield better results than gradient-based methods. Identification of crack size and location was performed using a multi-variable approach and by de-coupling of the optimization parameters making use of the discrete nature of the crack location parameter. While both methods yield satisfactory results, decoupling led to improved stability and lower computational requirements for a limited number of discrete crack locations. Instead of identifying one final solution point, a confidence measure was introduced, supplying information about the objective function around the global minimum. This led to an improved solution for practical purposes.
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