Abstract
The governing equations for a simple, singly regenerative system are solved in closed form. A metal cutting system is chosen as the model for the theory. The exponential growth index α is expressed in terms of various machine and operating parameters. When α > 0, chatter grows exponentially with time. When α < 0, the system is stable. Plots of α versus speed indicate that at higher spindle speeds αmax is greater, but there is a greater range of stable speeds between unstable zones. Plots of α versus chatter frequency, cutting stability index, lobe precession, and a newly defined variable (the ratio of apparent to actual cutting compliance) indicate that the lobe precession effect is the best sensor for a stability detector. In the special case, α = 0 the general theory reduces to the stability boundary theory developed previously.
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