Dynamic stability of shaft interconnected through joint: A review

Parametric instability is an important machine design consideration because it may cause failures such as fatigueand breakage in machine components. The problem of parametricinstability in drive system is reviewed in this paperfocusing on shafts that are interconnected through joint. The review covers aspects of modelling of the shafts, methods ofsolving parametric equation (Mathieu or Mathieu-Hill equation)in the drive system and sources of parametric instability inrotating shafts. Lumped-mass model has been used in modeling the drive shaft system during the early work. In order toobtain a realistic condition, continuous model has been established that considers the mass of the shaft. However thesestudies lacked in considering more degrees of freedom thatcan give better representation of the problem. The methods ofsolving Mathieu or Mathieu-Hill type equation in drive system are reviewed, analytical and numerical. Parametricinstability in a rotating shaft system is due to asymmetric shaft, anisotropic bearing, cracked and the applied periodic axialcompressive loading. In the case of the rotating shafts interconnected with joint, parametric instability may be a result ofperiodic variation of velocity ratio and the angular misalignment.

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