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Sliding mode control with a disturbance observer (SMC-DO) is proposed for suppressing the sprung mass vibration in a quarter-car with double-wishbone active suspension system (ASS), which contains the geometry structure of the upper and lower control arms. The governing equations of double-wishbone ASS are obtained by the balance-force analysis of the sprung mass in ASS. Considering uncertainties in damping, stiffness, and external disturbance acting on the sprung mass, we design a disturbance observer based on a sliding mode control (SMC) to estimate these uncertainties under the unknown road excitation. By the Lyapunov minimax approach, the uniform boundedness and the uniform ultimate boundedness of ASS with the proposed control are rigorously proved. Through co-simulation of ADAMS software and MATLAB/Simulink software, the sprung mass acceleration of ASS can be obtained with and without the proposed control.

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.