Dynamic analysis of a rotating beam subjected to repeating axial and transverse forces for simulating a lathing process

The dynamics of the workpiece of a lathe is simulated in the presented paper. A rotating Rayleigh beam is chosen as a simple model of the workpiece. The beam or the workpiece is subjected to forces from the cutting tool of the lathe. The external forces, in transverse and axial directions, are traveling in a repeating or periodic motion. The force in the axial direction is a large cutting force resulting in coupled bending deformation while forces in the transverse directions are the contacting forces. In this paper, the governing equations of the rotating Rayleigh beam are derived by Hamilton's principle. The external, periodic forces resulted from the tool are expressed in Fourier series. Galerkin's method is then chosen for disceretizing the partial differential equations. The instability regions of the responses are determined by using the method of multiple scales and the Floquet theory. Fast Fourier transform gives the frequency domain responses for examining the dynamic characteristics. The numerical results are discussed. Parametric studies are also performed.