Non-linear dynamics of a one-way clutch in belt-pulley systems

One-way clutches are frequently used in the serpentine belt accessory drives of automobiles and heavy vehicles. The clutch plays a role similar to a vibration absorber in order to reduce belt/pulley vibration and noise and increase belt life. This paper analyzes a two-pulley system where the driven pulley has a one-way clutch between the pulley and accessory shaft that engages only for positive relative displacement between these components. The belt is modelled with linear springs that transmit torque from the driving pulley to the accessory pulley. The one-way clutch is modelled as a piecewise linear spring with discontinuous stiffness that separates the driven pulley into two degrees of freedom. The harmonic balance method combined with arclength continuation is employed to illustrate the non-linear dynamic behavior of the one-way clutch and determine the stable and unstable periodic solutions for given parameters. The results are confirmed by numerical integration and the bifurcation software AUTO. At the first primary resonance, most of the responses are aperiodic, including quasiperiodic and chaotic solutions. At the second primary resonance, the peak bends to the left with classical softening non-linearity because clutch disengagement decouples the pulley and the accessory over portions of the response period. The dependence on clutch stiffness, excitation amplitude, and inertia ratio between the pulley and accessory is studied to characterize the non-linear dynamics across a range of conditions.