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It is well known that the entrained air in oil causes appreciable reduction in the stiffness of hydraulic systems. It makes the response delays of the systems and sometimes destroys the stability. Because the hydraulic systems used in most of automatic transmissions are operated in relatively low pressure and high temperature, it is very important to analyze the effects of the air included in automatic transmission fluid. However, it is hard to derive the generalized model to describe the effective bulk modulus theoretically or measure it in actual operating conditions of automatic transmissions. This paper reviews the previous studies of the air effects in hydraulic systems and the measurement techniques of the effective bulk modulus in operating conditions. Based on this work, the theoretical model with moderate complexity and the measurement technique of the effective bulk modulus considering entrained air effect at real operating conditions are suggested.

Generally, the widely used hydraulic control system in automatic transmissions is pulse width modulation (PWM) type. It consists in a PWM solenoid valve and a reducing type second stage valve, so called pressure control valve (PCV), to amplify pressure or flow rate. In this study, the mathematical models of the PWM solenoid valve and the PCV with moderate complexity are proposed. Then, their behavior is analyzed from the steady state characteristics. Finally, we find that there are good matches between the dynamic simulation results and the experimental data.