DYNAMICS OF AN UNBALANCED SHAFT INTERACTING WITH A LIMITED POWER-SUPPLY

Rotation of an elastically mounted unbalanced shaft may be in general affected by its lateral vibration, due to a ''vibrational torque''. Th is interaction is nonlinear, and can be neglected only in case of an u nlimited power supply. Whenever the available power of the drive is co mparable with power consumption due to vibration, various nonlinear ph enomena may be observed, the most well-known of these being the so cal led Sommerfeld effect - slowing down or complete capture of the shaft at resonance. The corresponding steady-state motions and their stabili ty can be studied by asymptotic methods, as applied to the governing n onlinear set of two second-order equations. However, study of transien t motions in general requires numerical solution. This numerical solut ion is obtained here, and extensive parametric studies are performed o f the Sommerfeld effect. In particular, the influence is evaluated of damping ratio and slope of the torque-speed curve of the drive on a pa ssage/capture threshold. The results of numerical simulation, as well as experiments with a physical model, also demonstrate the effect of s mooth passage through resonance with a limited power supply, based on using a ''switch'' of suspension stiffness from a certain artificially increased value to the design one. A brief description is presented a lso of time-variant components of the resonant amplitude and rotationa l frequency responses in the case of capture, as observed both in nume rical simulation studies and in experiments. Whilst these components a re small compared with the corresponding constant ones, i.e. steady-st ate vibration amplitude and rotational frequency, the above observatio ns indicate the possibility for periodic or chaotic nonstationarity in the system's response.