【正文】 actuator to the load. The power, however, is the work per unit time. The power can be increased by increasing the frequency.This system utilizes a stack actuator to drive a piston in a hydraulic pump. In order to pensate for the small displacements of the stack, system development has focused on high frequency potential. By implementing an inlet and outlet check valve in the pump, the fluid flow is rectified to generate linear motion of a hydraulic actuator. In addition, in order to achieve an inlet stroke in the pump, the stack is kept under pression by mechanical loading and hydraulic pressure. In the current system, an actuator with (3/8) bore achieved 280 N (62 Ibs.) of blocking force and had free translation rate of cm/sec ( in/s).PIEZOHYDRAULIC WORK CYCLE Previous work developed by Mauk, Menchaca, and Lynch [2] illustrated the efficiency for the piezohydraulic pump design. The efficiency of the piezohydraulic pump will be summarized using a full thermodynamic work cycle.Theoretically, the power output of the piezoelectric in the hydraulic pump application is double that of an impedance matched spring loaded piezoelectric. In classical impedance matching, a spring element represents the load to be displaced by direct actuation of the PZT. Work is the product of the force applied and the distance through which it acts, as shown in Figure 1. The blocking force is the maximum load the piezoelectric can achieve (). The free displacement correlates to the maximum strain at zero load (). Real loads will exist somewhere between these two extremes.In the piezohydraulic application, implementing a fluid can double the amount of work per cycle, see Figure 2. First a voltage is applied to the stack actuator which drives a piston forward increasing the pressure in the pump. At the impedance matched load, this force is half the blocking force. Next the check valve opens, allowing fluid flow at constant force. At point A the electric field begins to decrease. The fluid pressure begins to decrease returning the system to equilibrium. The inlet check valve then opens supplying fluid to the pump for another cycle starting again at point O.The work cycle from Figure 2 can be used to develop equations for the efficiency as defined by the ratio of mechanical output to electrical input of the stack actuator. The constitutive laws of the piezoelectric material along with the thermodynamic cycle must be incorporated to determine efficiency.The constitutive laws are given by Equations (14): (1) (2) (3) (4)where are strain ponents, are stress ponents, are electric field ponents, are electric displacement ponents, are pliance ponents at fixed electric field, are piezoelectric ponents, are dielectric permittivity ponents at fixed stress, are stiffness ponents at fixed electric field, are piezoelectric ponents, and are dielectric permittivity ponents at fixed strain.The electric field/electric displacement diagram is used along with the stress/strain diagram to determine the theoretical efficiency according to the constitutive laws. The stress/strain diagram is analogous to the force/displacement work cycle in Figure 2, see Figure 3. The efficiency is based on a plete reversible thermodynamic cycle. The electric field/electric displacment curve is shown in Figure 4.The electrical work done is the area within the parallelogram on the electric field/electric displacement diagram. Mauck, Menchaca, and Lynch [2,3] illustrated that the efficiency is theoretically 100% by using the constitutive laws along with the stress/strain and electric field/electric displacement diagrams. This assumes a path independent reversible thermodynamic cycle.PIFZOHYDRAULIC PUMP DESIGNThe hydraulic system consist of a PZT stack actuator, high frequency check valves, a fourway valve, and linear actuator. Figures 5 and 6 illustrate the schematic of the PZT Pump system.Hydraulic ActuatorNote that actuation force and blocking force represent different performance parameters. Actuation force is the amount of force the actuator maintains during actuation. Blocking force is the amount of force the actuator produces in the stopped position. Blocking force is always higher than actuation force.TESTING AND RESULTSThe system was evaluated for flow rate and pressure response. Standard hydraulic oil was pared to a low viscosity silicon oil. The accumulator of the PZT Pump system was charged to MPa(350 psi). A 1000V/2A/350Hz power supply and sine wave from a function generator were used for input. At 800V, maximum flow rate was achieved at 60 Hz. Flow rates in excess of 300 ccm and pressures of MPa (570 psi) were attained.A (3/8) bore linear hydraulic actuator was installed in the PZT Pump system. The actuator maintained an estimated 280 N (62 Ibs.) of blocking force and a no load speed of cm/sec ( in/s). The blocking force was directly calculated from the measured MPa (570 psi) as pared to the bore diameter. Figure 7 shows the pressure response of the pump at different voltage inputs. Note that the system responds well until 30 Hz.Figure 8 illustrates the flow rate data of the PZT Pump system. The optimal operating frequency was approximately 60 Hz. Note that the maximum flow rate at 800V is 310 ccm.Standard hydraulic oil with viscosity of 100 cSt was pared to a low viscosity silicon oil. The viscosity of the silicon oil is cSt. The flow rate performance is pared at 800 V, see Figure 9. The maximum flow rate increased from 120 ccm to 310 ccm.A mm (9/16) bore linear actuator was installed in the PZT Pump for evaluating flow rate response with respect to actuator loads. The actuator was loaded up to 142 N (32 Ibs). Reasonable actuation rates were achieved at 800 V, see Figure 10.CONCLUSIONThe improvements made in the PZT Pump were designed to increase actuator speed and evaluate robustness to actuator loads. A switching po