Stochastic Processes to Model Impact Events in a Vibratory Cavitation Erosion Apparatus
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Cavitation erosion is caused by bubble collapse causing micro jets and shockwave that impact the surfaces of materials: these impacts occur randomly over time. As such, Stochastic processes, specifically the Poisson process, can be used to model impacts as random events occurring over time. Peaks in pressure amplitude measurements made in time with a high-speed PVDF transducer in a vibratory cavitation erosion apparatus based on the ASTM G32 standard were defined as impact events. Using cumulative impact as a function of time, the rate parameter of the Poisson process was observed to vary periodically, which indicates that the process may be a non-homogeneous Poisson process (NHPP). Using a nonparametric estimation method, the NHPP’s cumulative rate function was estimated, and then was fitted to a sinusoidal function with a frequency effectively equal to the vibratory apparatus’ vibration and an average impact rate of 1.04×105 impacts per second.