Abstract

Reaming is a very common machine tool operation, which is performed to enlarge previously drilled holes to a precise size. If a reamer with evenly spaced teeth oscillates transversely as it cuts, the resulting hole is not round. Typically the hole profile exhibits N-1 or N+1 “lobes”, where N is the number of cutting flutes on the tool. This type of profile is caused by periodic motion, or “whirl”, of the tool at N cycles/revolution (the tooth passing frequency). From kinematics, it is clear that the direction and frequency of whirl determines the number of lobes on the hole profile. However, the mechanism that causes the oscillation has remained unclear, especially when the tooth passing frequency is well below the natural frequency of the tool. In this paper, a simplified model of the reamer is proposed which includes cutting forces and forces on the sides and clearance faces of the flutes. The cutting forces include a time-delayed component due to the effect of the previous tooth’s passage. In order to study efficiently the response of the tool at low speeds, a quasi-static numerical method is used. A Newton-Raphson method is used to solve the nonlinear equations of static equilibrium at every point in the simulation. The model remains dynamic because of the regenerative effect of the time delay, and successfully predicts the qualitative behavior of the reamer under several different cutting conditions.

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