Roundness errors in BTA drilling and a model of waviness and lobing caused by resonant forced vibrations of its long drill shaft

The original purpose of this work was to propose an equation system to describe the kind of drilling in which the tools are with pronounced shaft length. The equation system turned out to disclose the low frequency mechanism of hole lobes. The proposed system is composed of Euler-Bernoulli beam equation representing tool shaft, and an excitation force in form of Fourier series. An empirical cutting force was established and related cutting force components were calculated. And the accumulated contribution of modes and harmonics was evaluated. The solution for the proposed equation system allowed a prediction of hole roundness which was consistent with experimental results for different conditions. The solution also allowed an investigation into the waviness and lobes. The results suggested that the bizarre phenomenon of lobes on hole is in reality waviness described by Tlusty for milling. The rigorous mathematical nature of the proposed equation built solid foundation for former empirical observation of waviness and lobes on work pieces. [DOI: 10.111511.1765142]