There has been a lot of research in the development of a hybrid hydraulic actuator driven by various smart materials. The basic operation of these actuators involves high frequency bidirectional operation of the active material which is converted to unidirectional motion by a set of valves. The response of the actuator also shows resonant peaks similar to that of SDOF mechanical systems and indicates a region of maximum output. At these high driving frequencies, the inertial effects of the fluid mass dominate over the viscous effects and the problem becomes unsteady in nature. Geometrical parameters of the flow path are also important. Due to the high pressures existing inside the actuator and the presence of entrained air, compressibility of the hydraulic oil also has to be taken into account. Hybrid actuators using the magnetostrictive material Terfenol-D and the electrostrictive material PMN have been developed in our laboratory, with hydraulic oil as the working fluid. Several key design parameters, which include output cylinder size, diaphragm thickness, reed valve thickness and tubing diameter, along with operational conditions, like input current and bias pressure within the fluid, have been varied to identify a set of optimum driving conditions. Tests at no-load and with load have been carried out for unidirectional motion of the output piston. To characterize the input driving circuitry and magnetic flux path, we have also carried out dynamic tests with the Terfenol-D rod and analyzed its magnetic circuit (flux density vs. frequency) response. In this paper, we develop a mathematical model of the hydraulic hybrid actuator to show the basic operational principle under no-load and loaded conditions and to describe the resonance phenomenon affecting the system performance. The dynamics of the input driving circuit have been included in the model. The fluid passages have been represented using the transmission line model, giving rise to strongly coupled ordinary differential equations which are solved using a lumped parameter approach. This model is then used to calculate the no-load velocity of the actuator and also its blocked force. Finally, we use the model to find optimal pumping frequency to get highest performance with different active materials and also to predict the pump sizing for desired output velocity and load lifting capability.

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