An earlier work by the authors presented a solution for the added ultrahigh-speed stability lobe that has been shown to exist for intermittent and other periodically time varying machining processes. That earlier first-order solution was not clearly extendible to a higher order. A more general analytical technique presented here does permit higher-order results. The solution is developed first for the case of zero damping for which a final closed-form symbolic result can be realized up to second order. More important than improved accuracy, the higher-order nature of the result confirms that there exist multiple added lobes and permits a mathematical description of their locations along the spindle-speed axis. A solution is then derived for the structurally damped case, where the first-order case permits a final closed-form symbolic result while the second-order case requires computational evaluation. The first-order result matches perfectly the previously published one, as expected. The second-order result improves accuracy, measured relative to numerical simulation results, and, more important, permits a second added lobe to be predicted. The second added lobe tends to cut into the region of the high-speed stability peak that is predicted under traditional zero-frequency (time-averaged) analyses. The damped solutions also indicate that structural damping of the dominant mode becomes virtually unimportant at ultrahigh speeds.

This content is only available via PDF.
You do not currently have access to this content.