Stability of an ID sawblade cutting a crystal ingot

This paper is a theoretical study on the stability of ID (inner-diameter) sawblade cutting a crystal ingot. Both the reaction from the ingot and the negative air pressure between the blade and the ingot are considered and their effects are represented by a series of parallel translational springs. The solution is obtained by the method of multi-modal expansion, further by applying the Galerkin method to the governing equations of system. Numerical results are obtained for a blade cutting a 12-inch crystal ingot. Results obtained show that the lateral reaction from ingot can cause the flutter instability for the ID sawblade, while the in-plane reaction force from ingot and the negative air pressure make little effect on the dynamics of working sawblade. Further it is shown that there are no flutter or divergence instability regions in the neighborhood of the practical operation speed of ID sawblade cuting a 12-inch crystal ingot, which also leads to a conclusion that the instability of blade vibration does not affect the surface finish of the produced wafer.