Dynamic Balancing Of Rotating Shaft

Dynamic Balancing Of Rotating Shaft

Introduction

The first important work in the field of nonlinear dynamics of shafts is due to Bolotin. He analyzed the vibration of a rotating shaft considering geometric stiffening effect. Yamamoto et al. considered the combination resonances in a symmetrical rotating shaft system with nonlinear spring characteristics. The theoretical results were validated with experiments. In another paper, they investigated the subharmonic oscillations of order 1/2 and some types of combination resonances in a nonlinear rotating shaft. Ishida et al. considered the internal resonances in a symmetrical nonlinear rotating shaft system. They investigated the coincidence of critical speeds of 1/2-order subharmonic oscillation and a synchronous backward precession. They showed the region of subharmonic oscillation occurrence was separated into two parts. Ertas and Anlas modeled a nonlinear rotating machine with a two-degree-of-freedom system. They investigated the primary and internal resonances of the system. They extracted critical values of mass and spring ratios for the presence of an internal resonance. Ishida et al. discussed nonlinear forced oscillations in a rotating shaft with quartic nonlinearity in the restoring force. To justify the theoretical analysis, experiments were carried out and results were compared. Shaw and Shaw examined the forced vibration of a rotating shaft with internal damping. They used the center manifold approach and showed that the resonance is an example of a periodically perturbed Hopf bifurcation. Ishida et al. examined the nonstationary vibration of a rotating shaft, which accelerated through a critical speed of a 1/3-order subharmonic forward precession. Nonstationary vibration characteristics for primary, combination and subharmonic resonances were compared. Ishida and Yamamoto investigated subharmonic oscillations of order 1/2 in a nonlinear rotating shaft with internal damping. Nonlinearity was due to an angular clearance of the bearing and internal damping was due to the friction in the bearing. They showed a self-excited oscillation occurred in a wide range above the major critical speed. Dynamics and instability of a non-linear rotating shaft-disk with large transverse displacement were analyzed by Chang and Cheng.

In this research, the combination resonances of a simply supported rotating shaft with nonlinearities in curvature and inertia will be investigated. Rotary inertia and gyroscopic effects will be included, but shear deformation is neglected. The equations of motion are derived with the in-extensionality assumption and then transformed to the complex form. To analyze the combination resonances, the method of harmonic balance will be applied to the complex form of the equations of motion. The frequency-response curves are plotted for the first two modes. The effects of diametrical mass moment of inertia, eccentricity and external damping coefficient are investigated on the steady state response of the rotating shaft. The loci of saddle node bifurcation points will be plotted as functions of damping coefficient and eccentricity. To validate the results of harmonic balance method, numerical simulations are carried out.

Aim of the study

The aim of this study is to analyze the dynamic balancing of rotating shaft.

Literature Review

Ishida reviewed the researches on the nonlinear vibration and chaos in rotordynamics ...