Basics for a Single-Degree-of-Freedom Rotor

Abstract

This chapter specifies the definitions, calculation and measurement of basic vibration properties: natural frequency, modal damping, resonance and Q-value ( Q-factor) .

Basic properties featuring in a vibrating system, which are obtained from the free vibration waveform, are:

• Natural frequency f _n [Hz], or natural angular (or, circular) frequency ω _n =2π f _n [rad/s]

• Damping ratio ζ [–], or logarithmic decrement δ = 2π ζ [–]

Using these parameters, the resonance caused by forced excitation can be predicted with

• Resonance frequency (critical speed in unbalanced vibration) = natural frequency f _n [Hz]

• Resonance sensitivity Q = 1/(2ζ ) [–]

Since separation of resonance or reduction of the Q-value are fundamental requirements in the vibration design of rotating machinery, the placements of a natural frequency and the damping ratio are very important design indices.