Receptance coupling model for variable dynamics in fixed-free thin rib machining

An analytical approach for predicting thin rib, fixed-free beam dynamics with varying geometries is presented. The proposed method uses receptance coupling substructure analysis (RCSA) to predict the stepped thickness beam receptances (or frequency response functions) at the fixed-free beam's free end and at the change in thickness. The assembly receptances are calculated by rigidly connecting receptances that describe the individual stepped beam sections, where the section receptances are computed using the Timoshenko beam model. Comparisons with finite element calculations are completed to verify the technique. It is observed that the RCSA predictions agree closely with finite element results. Experiments are also performed, where the stepped beam thickness is changed by multiple machining passes, and receptance measurements are carried out between passes. The RCSA predictions are compared to experimental results for natural frequency and stiffness. Agreement in natural frequency to within two percent is reported.