Modeling and Dynamics Analysis of a Dual-Mass Flywheel with the Conformal Contact Action of Friction Damping Ring and Pressure Plate

To study the nonlinear dynamic characteristics of the dual-mass flywheel (DMF) under the conformal contact action between the friction damping ring and primary flywheel pressure plate, the contact action model is established and analyzed based on Winkler model. Through analysis and calculation, the contact deformation, contact pressure at different contact positions, and equivalent torsional contact stiffness are obtained. The nonlinear dynamic analysis model of three-degree-of-freedom (3DOF) which takes the conformal contact into account and two-degree-of-freedom (2DOF) without considering conformal contact is established. The approximate analytical solution of the nonlinear frequency characteristics of the system at steady state is derived. By comparing with the results obtained from numerical method, the theoretical analysis process is proved to be valid. And it is found that the overall amplitude and angular displacement transmissibility of the 3DOF model are smaller than the 2DOF model, especially at resonance frequency. The effects of the friction damping ring moment inertia, stiffness of DMF, and axial friction torque on the frequency characteristics of system and angular displacement transmissibility are analyzed. The forced vibration response analysis of the 3DOF model is conducted, through which the torsional angle variations of the primary flywheel, friction damping ring, and secondary flywheel with time are obtained. The results show that the amplitude of the secondary flywheel is much smaller than that of the primary flywheel, indicating that the DMF has prominent damping performance.

Analysis of the non-periodic oscillations of a self-excited friction-damped system with closely spaced modes

It is widely known that dry friction damping can bound the self-excited vibrations induced by negative damping. The vibrations typically take the form of (periodic) limit cycle oscillations. However, when the intensity of the self-excitation reaches a condition of maximum friction damping, the limit cycle loses stability via a fold bifurcation. The behavior may become even more complicated in the presence of any internal resonance conditions. In this work, we consider a two-degree-of-freedom system with an elastic dry friction element (Jenkins element) having closely spaced natural frequencies. The symmetric in-phase motion is subjected to self-excitation by negative (viscous) damping, while the symmetric out-of-phase motion is positively damped. In a previous work, we showed that the limit cycle loses stability via a secondary Hopf bifurcation, giving rise to quasi-periodic oscillations. A further increase in the self-excitation intensity may lead to chaos and finally divergence, long before reaching the fold bifurcation point of the limit cycle. In this work, we use the method of complexification-averaging to obtain the slow flow in the neighborhood of the limit cycle. This way, we show that chaos is reached via a cascade of period-doubling bifurcations on invariant tori. Using perturbation calculus, we establish analytical conditions for the emergence of the secondary Hopf bifurcation and approximate analytically its location. In particular, we show that non-periodic oscillations are the typical case for prominent nonlinearity, mild coupling (controlling the proximity of the modes), and sufficiently light damping. The range of validity of the analytical results presented herein is thoroughly assessed numerically. To the authors’ knowledge, this is the first work that shows how the challenging Jenkins element can be treated formally within a consistent perturbation approach in order to derive closed-form analytical results for limit cycles and their bifurcations.

Optimization on hysteresis dynamic model of metal rubber material based on dry friction damping term

As one kind of porous elastic metal material, metal rubber is used in vibration isolation widely due to its better damping characteristic. During loading and unloading, the elastoplastic deformation and damping characteristics of this material are usually described by constructing its dynamic model. Although traditional models can describe the hysteresis performance, the accurate parameter identification of material structure under different preparation conductions is limited due to its complex expression or equivalent math form. In this paper, a dynamic hysteresis model is optimized through adding a dry friction damping term based on the micro-element analysis theory and analysis method of material mesoscopic structure. The relation among the manufacture technic, size of metal wire and vibration parameters were established, which accurately describes hysteresis characteristic of metal rubber by dry friction when the metal wires are in the state of slipping contact. The result is verified by the harmonic vibration experiment that the model has good adaptability and convenience, especially can improve the accuracy and convenience of parameter identification on the forming materials of metal rubber.

Analysis of the non-periodic oscillations of a self-excited friction-damped system with closely-spaced modes

It is widely known that dry friction damping can bound the self-excited vibrations induced by negative damping. The vibrations typically take the form of (periodic) limit cycle oscillations. However, when the intensity of the self-excitation reaches a condition of maximum friction damping, the limit cycle loses stability via a fold bifurcation. The behavior may become even more complicated in the presence of any internal resonance conditions. In this work, we consider a two-degree-of-freedom system with an elastic dry friction element (Jenkins element) having closely spaced natural frequencies. The symmetric in-phase motion is subjected to self-excitation by negative (viscous) damping, while the symmetric out-of-phase motion is positively damped. In a previous work, we showed that the limit cycle loses stability via a secondary Hopf bifurcation, giving rise to quasi-periodic oscillations. A further increase of the self-excitation intensity may lead to chaos and finally divergence, long before reaching the fold bifurcation point of the limit cycle. In this work, we use the method of Complexification-Averaging to obtain the slow flow in the neighborhood of the limit cycle. This way, we show that chaos is reached via a cascade of period doubling bifurcations on invariant tori. Using perturbation calculus, we establish analytical conditions for the emergence of the secondary Hopf bifurcation and approximate analytically its location. In particular, we show that non-periodic oscillations are the typical case for prominent nonlinearity, mild coupling (controlling the proximity of the modes) and sufficiently light damping. The range of validity of the analytical results presented herein is thoroughly assessed numerically. To the authors' knowledge, this is the first work that shows how the challenging Jenkins element can be treated formally within a consistent perturbation approach in order to derive closed-form analytical results for limit cycles and their bifurcations.