Natural Frequencies of Conical Boring Bars

摘要

In the process of boring, the proper selection for the section shape of a boring bar can improve the quality and efficiency of mechanical processing by suppressing its vibration. The boring bar can be simplified as a cantilever beam with variable cross-section. By employing a shape function of the cross-section, the first and second natural frequencies of cantilever beams with different cross-section shapes are investigated via assumed modes method. The influence of the taper and the convexity of the cross section on natural frequency is also analyzed. By solving the principal stiffness and mass of each mode, the influence of the cross-section shape on principal stiffness and mass is studied. By numerical calculating, the influence of the change rate of the corresponding principal stiffness and mass on natural frequency is analyzed. Finally, the design principles of variable cross-section cantilever beam are　given.