Closed-form solutions for surface location error in milling

This paper provides two new analytical solutions for the computation of surface location errors, or part geometry errors that arise due to forced vibrations of the cutting tool, during stable milling. Prior studies of surface location error have applied numerical simulation and semi-analytical methods (e.g., temporal finite element analysis) to this problem. This work provides new results that show analytical solutions for the problem of surface location error are possible. The analytical approaches are based on frequency domain and harmonic balance analyses. Comparisons between the analytical results, time domain simulation, and experiment are included.