In the current research of the magnetic circuit model of the servo valve torque motor, the magnetic flux leaking from working air-gaps is regarded as constant. However, the working air-gaps leakage flux varies with the armature rotation angle, which affects the accuracy of the existing mathematical model of the torque motor. To solve this problem, a new mathematical model of the torque motor with two working air-gaps is built. First, different from the previous model, the variation of the working air-gaps leakage flux is considered in the magnetic circuit model. A more detailed mathematical model of the torque motor is established based on the magnetic circuit model. Second, the finite element method is used to reveal that there is a linear relationship between working air-gaps leakage flux and armature rotation angle in a certain range of rotation angles. Then, the new model is validated by numerical calculation, which indicates that the theoretical results calculated by this new model show better agreement with the simulation results compared to the previous model when the armature rotation angle increases. Further, the theoretical results of the electromagnetic torque constant and magnetic spring stiffness acquired by the new model and the previous model are compared. The comparison shows that the variation of the working air-gaps leakage flux has the greatest influence on the magnetic spring stiffness. Finally, the experiments on the torque motor are conducted to verify the accuracy of the new model. The theoretical results obtained by this new model are better consistent with the experimental results than that obtained by the previous model. This study shows that considering the variation of working air-gaps leakage flux is valuable to improve the accuracy of the magnetic circuit model of the torque motor, which provides an effective guidance for the structural optimization and performance prediction of the torque motor.

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