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A major challenge in predicting driveline torsionals is the modeling of major energy dissipation mechanisms in the driveline. Primary candidates for such mechanisms are viscous dampers and dry friction (hysteresis) dampers which are specifically included by the designers to disperse the energy of torsional vibrations. The inherent structural and other internal damping in the components of the driveline is small as compared to those of viscous and dry friction dampers. Past attempts to model clutch hysteresis have repeatedly resorted to the classical approach of modeling that has been reported many years ago. However, such an approach is oversimplified and assumes, for instance, that the hysteretic effects are independent of the frequency. In addition, the motion of the damper is assumed to be purely harmonic. Also, such studies rely solely upon the static hysteresis characterization of the elements, particularly within the clutch.

A detailed methodology is presented in this paper for a complete assessment of various forces, torques, and kinematic effects due to universal joint angularities and shaft yoke phasing. A modular approach has been adopted wherein constitutive equations represent each of the key elements of a driveline namely the driveshaft, coupling shaft, universal joint, and the transmission/axle shafts. Concentrated loads are used wherever loads are being transferred between the elements of a driveline. Local matrices are developed for the equilibrium of the respective driveline members. The local matrices are then assembled into a global matrix and solved for the kinematic state of the complete driveline. A 6x15 matrix has been developed to represent a general shaft in the system and a 6x10 matrix has been developed for a universal joint cross. This gives us a complete picture of all the loads on all driveline members.