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Two electric wheel motors are used to propel the rear-driven three-wheeled (3W) electric welfare vehicle independently. Due to the lack of the traditional mechanical differential, the right/left rear tractive forces and the corresponding rotational speeds cannot coordinate with each other automatically while cornering, which might increase the required steering angle and torque. An electric differential system is proposed in this paper to solve this problem. The proposed system controls the rotational speeds of both wheel motors according to different vehicle speeds and steering angles. A 12-degree-of-freedom 3W vehicle model, which is established in AutoSim and verified using the experimental data of the prototype vehicle, is used for the driver-in-the-loop verification in Matlab/Simulink. The preliminary result shows that the proposed system can effectively reduce the steering torques and roll angles during cornering.