Estimating bolt tightness from measured vibrations: Influence of nonlinear boundary stiffness and damping

In this work we present a technique to assess the level of bolt tightness and to quantify the tension based on measured natural frequencies and damping ratios of the bolt. This technique is investigated experimentally and theoretically. A simple model for the bolt that consists of a pre-stressed one-dimensional beam linear equation with linear and nonlinear stiffness and damping at its boundaries is investigated to explain experimental results.

Figure 1a shows the squared first bending natural frequency for a bolt as function of bolt tension. At low tension the squared natural frequency rapidly increases with tension. As the bolt is gradually tightened the squared frequency starts changing approximately linearly with tension [1]. Figure 1b shows the first mode damping ratio of the bolt as function of the bolt tension.

At low tension the damping ratio decreases rapidly with tension and then starts slowly decreasing for higher tension. A mathematical beam model with linear/nonlinear stiffness and damping at its boundaries is used to explain the experimental results.