Modeling and dynamic analysis of a pilot-operated pressure-regulating solenoid valve used in automatic transmission with bond graphs

The pilot-operated pressure-regulating solenoid valve (PPRSV) is a key component of the automatic transmission (AT) in automobiles, and its performance significantly affects the efficiency and service lift of the AT and even road safety. However, few studies are devoted to the mathematical model of the PPRSV, and there is especially a lack of test equipment to verify its pressure control performance. Thus, the goal of this study is to find an effective and convenient modeling method and to verify the correctness of the model through simulations and experimentation. The bond graphs method, which is widely utilized to study hydraulic dynamics because it can easily identify the parameter process and consider the interactions in a hydraulic system, is selected here to help develop the numerical model of the PPRSV. The effective bulk modulus of hydraulic fluid was dynamically analyzed by considering the effect of the temperature, pressure and entrapped air. To consider the time delays of the electrical actuation and spool motion, the time delay element and Kirchhoff’s and Ohm’s laws are emphatically discussed to show the nonlinearity of forces. In addition, the Dahl model was used to more clearly express the static friction force to examine the hysteresis of the valve pressure. The comparative simulated and experimental studies confirm that the developed model can be used to study the control performance of the PPRSV, and the modeling method developed in this paper is feasible and handy.