It is well known that the presence of entrained air bubbles in hydraulic oil can significantly reduce the effective bulk modulus of hydraulic oil. The effective bulk modulus of a mixture of oil and air as pressure changes is considerably different than when the oil and air are not mixed. Theoretical models have been proposed in the literature to simulate the pressure sensitivity of the effective bulk modulus of this mixture. However, limited amounts of experimental data are available to prove the validity of the models under various operating conditions. The major factors that affect pressure sensitivity of the effective bulk modulus of the mixture are the amount of air bubbles, their size and the distribution, and rate of compression of the mixture. An experimental apparatus was designed to investigate the effect of these variables on the effective bulk modulus of the mixture. The experimental results were compared with existing theoretical models, and it was found that the theoretical models only matched the experimental data under specific conditions. The purpose of this paper is to specify the conditions in which the current theoretical models can be used to represent the real behavior of the pressure sensitivity of the effective bulk modulus of the mixture. Additionally, a new theoretical model is proposed for situations where the current models fail to truly represent the experimental data.

A pressure-compensated valve (PC valve) is a type of flow control device that is a combination of a control orifice and a compensator (often called a hydrostat). The compensator orifice modulates its opening to maintain a constant pressure drop across the control orifice. In other words, the PC valve is so designed that the flow rate through the valve is governed only by the opening of the control orifice and is independent of the total pressure drop across the valve. Because of the high nonlinearities associated with this type of valve, it is impossible, in practice, to design such a valve where the flow rate is completely unaffected by the pressure drop across the valve. In this paper, the effect of the nonlinearities on the performance of the PC valve is investigated. First, a generic nonlinear model of a PC valve is developed. Using this model, all possible operating conditions can be determined. Then a linearized model is developed and used to analyze the dynamic behavior of the PC valve. The model can then be used to evaluate and improve the design and operation of the valve for specific applications.

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In digital valves, stepper motors are often used as the electro-to-mechanical interface. To sustain both high speed of response and good quantitative accuracy, a special algorithm has been designed to control the stepper motor to produce a continuous displacement. Unlike conventional proportional magnets or torque motors, the input current to the stepper motor is cyclic (stage control) which has been shown to reduce magnetic saturation and hysteresis. In this paper a special mathematical formulation is developed to simulate magnetic saturation and hysteresis which can be applied to a generic situation. The mathematical formulation derived is one in which hysteresis and saturation parameters are established; an error rate of both saturation and hysteresis is defined from this. Since the error rates are easily determined experimentally or through manufacturers’ specifications, the parameters can be found from these mathematical formulations. The parameters can then be used to predict the hysteresis and saturation characteristics. Special experiments are designed to obtain the input-output characteristics of a stepper motor/valve system under single and multi-stage control. The model follows the experimental results reasonably well and can be used with confidence to model any system with hysteresis and saturation. The model also predicts very well the effects of using stage control in reducing hysteresis and saturation in a practical valve.

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