Vibration of circular saws containing slots

The natural modes of transverse vibration of circular saws containing radial slots are analyzed in this paper. Incision of equally-spaced asymmetry, equally sized, radial slots at the rim of a saw creates in some, but surprisingly not all, of the vibration modes of the circular saw. It causes the repeated natural frequencies in these asymmetric modes to split into two distinct values. These vibration modes are called the split modes. The vibration modes associated with the repeated natural frequencies, typical of the axisymmetric saw plate, are called the repeated modes. A relationship predicting which vibration modes are split and which are repeated for any configuration of slots on the saw is presented in this paper. Further, it is shown that parametric, transverse vibration instability can be excited in the split modes of the slotted saw by the saw guides and the workpiece. These parametric vibrations can not be excited in the repeated modes. The theoretical predictions of split and repeated vibration modes and the excitation of parametric instability are confirmed by experiments.