This paper presents a mathematical model of a radial ball piston pump/motor. The specific application of the pump is for direct integration with a high speed electric motor for use in off highway vehicles. The pump/motor must operate across all four quadrants with high flow rates at a low pressure differential. The model captures the major mechanical and volumetric losses within the hydraulic machine with specific attention given to the ball-cylinder interface and the pintle-rotor interface. The leakage and shear at the ball piston interface are dependent on the position of the ball piston in the cylinder; therefore, the dynamics of the ball piston are calculated. The pintle-rotor model includes the port geometry, which influences the flow rates into and out of the pump/motor. Leakage and shear at the interface are dependent on the gap height between the two surfaces; consequently, the model calculates the radial forces acting on the rotor and uses journal bearing theory to predict the eccentricity. This eccentricity balances the other forces and is necessary to determine the interface losses. Lastly, the importance of these dynamics is evaluated to determine which are needed in a future optimization framework. It is shown that considering the dynamics of both interfaces captures significantly more losses and results in a more accurate model than an earlier simplified one.

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