16 Nonlinear Modeling for Adaptive Suppression of Axial Drilling Vibration 199 0.076 m 0.381 m 0.305 m 0.025 m 0.279 m 0.686 m 0.483 m 0.254 m 0.254 m 0.279 m One Tri-axial Accelerometer Drill Chuck/Spindle Drill Bit Drill Press Speed Selection Belts Motor Column Table Clamp Table Fig. 16.4 Drill press modal analysis experimental setup Fig. 16.5 Aluminum plate modal analysis experimental setup process, which is a form of curve fitting, has been implemented in the past 40 years to characterize the linear dynamic properties of structures [7–9]. The Rational Fraction Polynomial (RFP) method, developed by Richardson and Formenti, is a technique to estimate parameters directly from the FRF. The RFP method solves a set of linear equations for the unknown numerator and denominator polynomial coefficients of a given frequency data set. The curve fitting models can be described as either Eq. (16.3) or Eq. (16.4) also known as Rational Fraction Form or Partial Fraction Form, respectively (where rk and pk are the k th residue and pole ( ¢k Cj¨k) respectively, ¢k is the k th rate of decay, ¨k is the k th oscillation frequency, and j D p 1) (Richardson and Formenti 1982).
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