The variable displacement axial piston pump has been the subject of much research, having been studied from the controls, noise reduction, and design perspectives. The resulting body of research is large and very diverse in content. A review of the available publications was conducted for this paper in order to identify those works that would be most helpful in developing a complete and accurate mathematical model of an axial piston pump.

Most of the available publications can be classified into one of two general groups; those describing a small group of components to understand specific phenomena or those describing the entire pump for control or design purposes. The significant mathematical developments in various publications regarding specific phenomena, particularly those works involving nonlinear friction or pressure transients, were identified by the authors in this paper. When the mathematical developments of the phenomena specific effects are combined with the widely accepted kinematics equations for the pump, an accurate numerical model can be developed.

Works on linearized lumped parameter models and parameter sensitivity were examined for this paper and the limitations of these types of models were addressed. While linearized models offer mathematical simplicity, they suffer from poor accuracy over a wide range of operating conditions and do not reflect instantaneous swashplate dynamics.

This paper offers insight into the required complexity of a mathematical model that is necessary to achieve a desired accuracy as well as providing the appropriate references to develop that model.

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