Figure $9\mathrm{.}26$ shows the cross$-$frequency response $($receptance$)$ locus for a lathe between the cutting$-$force direction and the normal to the cut surface. It is assumed that variations in cutting force occur only because of variations in the undeformed chip thickness.

a$.$ Prepare a sketch of the stability chart for fully regenerative cutting conditions in terms of the critical values of the chip$-$thickness coefficient, indicating some of the cutting speeds for the minima on the chart and also the frequency range in which instability will occur.

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Fundamentals of Machining and Machine Tools

FIGURE $9\mathrm{.}26$ Operative frequency response locus for a milling machine tool structure.

b$.$ What will be the form of the stability chart for machining under conditions in which no overlapping of successive cuts occurs?

c$.$ If$,$ instead of a turning operation, the process were a slab$-$milling operation with a cutter having $20$ teeth with an average of three engaged with the workpiece at any time, what difference would this make to the stability chart?