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An automatic tensioner used in an engine front end accessory drive system (EFEADS) is taken as a study example in this paper. The working torque of the tensioner, which consists of the spring torque caused by a torsional spring and the frictional torques caused by the contact pairs, is analyzed by a mathematic analysis method and a finite element method. And the calculation and simulation are validated by a torque measurement versus angular displacement of a tensioner arm. The working torques of the tensioner under a loading and an unloading process are described by a bilinear hysteretic model, and are written as a function with a damping ratio. The rule of the action for the damping devices is investigated based on the simulation and a durability test of the tensioner. A finite element method for the tensioner without damping device is established. Then the radial deformation for the torsional spring under an unconstrained state is obtained.