ArticleDamping: It's Role in Rotor Stability Rotor Isolation
by Frederick C. Nelson
The paper discusses linear damping, (viscous and hysteretic) and nonlinear damping, in the first section of the paper the focus is on linear models of the damping within the material of a monolithic structure or system. In the second section, the effects of viscous and hysteretic damping on the stability of a flexible rotor are discussed and equations provided. In the third section, the effects of viscous and hysteretic damping on the isolation of an unbalanced rigid rotor with equations are discussed.
Damping is different. When faced with a set of design drawings, engineers have little difficulty in computing the mass and close estimates of the stiffness of the depicted structure; errors in the stiffness are usually due to the uncertainties of the contact stiffness between mating parts. However, there is no general analytical procedure for computing the damping of the structure. Instead, engineers rely on their experience with similar structures or make an educated guess, which is later verified or corrected by prototype testing. This difference in capability rests on the fact that mass and stiffness are macroscopic properties while damping is a microscopic property. The development of a link between the macroscopic description of damping needed by engineers and microscopic theories of the material scientist is one of the major open problems of structural dynamics.
The inability to make close estimates of damping at the design stage can be a distinct disadvantage. In this review, two mechanical systems are discussed for which an accurate knowledge of damping, either by type or by value, is essential to obtaining accurate predictions of performance. The first case is the stability of a flexible rotor with internal damping; the second is the isolation of an unbalanced, rigid rotor from its foundation.
LINEAR DAMPING MODELS
From a computational point of view, linear damping models are much preferred. But are they realistic? The answer is yes, provided the stresses are low, i.e. well below the fatigue strength of the material. However, the lure of linearity is great, and it is often imposed regardless of stress level. Since there is ample evidence that damping becomes strongly nonlinear at high stress levels, it is not surprising that in those cases linear models lead to poor predictions.
The two common linear damping models are viscous and hysteretic. The notable features of Eq. (3) are that D has a linear dependence on is and a quadratic dependence on x̂ In the 1920’s and 30’s, experiments by several investigators, most notably Kimball and Lovell, confirmed the quadratic dependence on x̂ but showed little evidence of a linear dependence on ω. Thus it has long been known that the linear viscous damper is a poor Model for material damping. Strangely, this has had little effect on its prominent use in teaching students about structural vibrations.”
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