Abstract
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.
Highlights
The systems with finitely many degrees of freedom and piecewise linear elastic characteristics describe a broad class of engineering objects [1, pp. 59–74]
In [21, 9], it was shown that the approximation of piecewise linear characteristics by polynomial curves may lead to incorrect results in the study of stability of solutions and to significant errors in the numerical analysis of periodic motions of systems with strong nonlinearities
We propose a new approach to the determination of the Shaw–Pierre nonlinear normal modes of forced vibrations in strongly nonlinear systems with piecewise linear elastic characteristic
Summary
The systems with finitely many degrees of freedom and piecewise linear elastic characteristics describe a broad class of engineering objects [1, pp. 59–74]. The analytic investigation of free oscillations in systems with piecewise linear elastic characteristic was carried out in [10, 18, 20]. The chaotic oscillations in piecewise linear systems with two and three degrees of freedom were studied in [6, 7]. The possibility of combination of the method of nonlinear normal modes with the Rauscher technique for the analysis of the Kauderer–Rosenberg nonlinear normal modes under the conditions of forced vibrations was studied in the book [19, pp. In the present work, forced vibrations in strongly nonlinear piecewise linear systems with any number of degrees of freedom are studied by the Shaw–Pierre method of nonlinear normal modes and the Rauscher technique. As a result of application of this approach, the nonautonomous dynamical systems are reduced to equivalent autonomous systems, which are used to compute the Shaw–Pierre nonlinear normal modes
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