Solenoid valve is a very important hydraulic actuator for an automatic transmission\nin terms of shift quality. The same form of pressure for the clutch and the input\ncurrent are required for an ideal control. However, the gap between a pressure and a\ncurrent can occur which brings a delay in a transmission and a decrease in quality.\nThis problem is caused by hysteresis phenomenon. As the ascending or descending\nmagnetic field is applied to the solenoid, different thrust forces are generated. This\npaper suggests the calculation method of the thrust force considering the hysteresis\nphenomenon and consequently the accurate force can be obtained. Such hysteresis\noccurs in ferromagnetic materials, however the hysteresis phenomenon includes a\nminor hysteresis loop which begins with an initial magnetization curve and is generated\nby DC biased field density. As the core of the solenoid is ferromagnetic material, an\naccurate thrust force is obtained by applying the minor hysteresis loop compared to\nthe force calculated by considering only the initial magnetization curve. An analytical\nbackground and the detailed explanation of measuring the minor hysteresis loop are\npresented. Furthermore experimental results and finite element analysis results are\ncompared for the verification.
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