Effects of Thermal Damping on the Dynamic Response of a Hydraulic Motor-Accumulator System

A hydraulic accumulator is often modeled as a gas spring following a polytropic process, but this fails to properly account for the dissipative effects of heat transfer which produce damping and phase shift in the dynamic behavior. A thermal time constant can properly characterize the heat transfer between the charge gas and the accumulator walls, and it is shown that for the linearized case the accumulator becomes equivalent to the Anelastic Model. The transfer function for the accumulator is derived, and the mathematical solution is presented for a hydraulic accumulator coupled to the inlet of a hydraulic motor where the load force is subject to a small, sinusoidal variation with time. Experimental data are presented to show that the accumulator can be accurately modeled using a thermal time constant, and the Anelastic Model would adequately describe the accumulator for the case of small perturbations.