Chaos and fatigue in mechanical systems
The work reported in this thesis investigates the effect of chaos and other types of non-linear motion on the fatigue life prediction of mechanical components in a number of physical systems. Three different dynamic systems were investigated. A rotor system with a radial clearance, a boiler-tube type system and a vibration absorber type system with a small Two-Mass System. Mathematical models are presented for each system and experimental test rigs are constructed. Numerical simulations of the rotor system are presented and show good correlation between theoretical and experimental results. Displacement data from the experimental test rigs was scaled to represent stresses within the mechanical components of the test rigs in two different ways. Firstly, the data was scaled uniformly across each range of tests for each system. A second method was utilised to scale the data so that each set of data had the same RMS response amplitude, to reduce the effect that relative magnitude of motion has on fatigue life predictions. Both types of scaled data were then processed using commercially available fatigue analysis software to provide fatigue lives for specific test runs. The Rainflow cycle counting method with the Goodman mean stress hypothesis and the Haibach fatigue damage criterion was used for the fatigue life calculations throughout this work. Relative comparisons between the fatigue lives at different operating conditions were made for all three systems, and conclusions were drawn using the most relevant data. These conclusions show that motion containing side bands in the frequency domain, indicating a modulating effect in the time domain, have a significantly more damaging effect on the fatigue life than simple harmonic motion. High order super-harmonic content in the response also ahs a more damaging effect. Conclusions regarding the effects of chaotic motion are less clear. Both more damaging and less damaging situations were found. No conclusive evidence was found that chaos is generally good or generally bad for the fatigue life of dynamic system components, however evidence that side bands, sub-harmonic and super-harmonic motion is generally damaging is presented. The use of one-dimensional mappings was also investigated to provide a theoretical source of chaotic motion in a response that is similar to that of simple dynamic systems. Again, no strong conclusive evidence was found to conclude that chaos was ‘good’ or ‘bad’ for the fatigue life of dynamic system components.