Research studies have shown that several centrifugal pump shafts failure are due to the inability to model the optimal stress on the shaft during operation. Most recent studies revealed that the parameters that impacts backpressure have not been properly model for optimal performance during operation. The parameters that impacts backpressure such as stress varying on the shaft are random and therefore the tool of random mechanics can be used to model and simulate the optimal forces during backpressure. In this project the major stresses that impacts backpressure are simulated to determine the optimal stress distribution that a pump shaft can withstand during operation. An auto 360 diffusion desk was used in the modeling and simulation process and the varying stresses on the shaft during backpressure were used to determine the optimal load the shaft can withstand during backpressure. The following results were theoretically derived and validated during modeling and simulation process. It was shown that an increased backpressure during pump operation increases the stress propagation on the shaft spindle and as the backpressure continuous to increased, the key slot stresses increases which leads to an increase in straining that impact shaft performance. The simulated data revealed failure mode after the optimal load on the shaft was exceeded during operation. The obtained simulated results revealed that at extremely high backpressure beyond the optimal stress on the shaft, failure possibility are revealed on the pump shaft and the failure are normally originate slot keyway and propagation of the stress distribution increases during operation

Keywords: optimization, simulation, stress distribution, failure, and backpressure