Abstract
The theoretical analysis of vibration of hollow-cone valves is developed using conformal mapping to find the potential function with and without circulation. Hydrodynamic forces are obtained by integrating the unsteady Bernoulli equation. The equations of motion with two degrees-of-freedom are considered and are based on the assumption that the displacements of the vane and valve are small. Vibrational frequency, amplitude, acceleration, and pressure distribution on the vanes are calculated and compared with field experiments. A safety parameter is introduced to ensure that valves can operate in a satisfactory condition without undue vibration.
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