General Analysis of Two-Degree-of-Freedom Instability in Machine Tools

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Abstract
This paper utilizes the concept of receptances to investigate the stability of machine tools under orthogonal cutting conditions when regeneration does not take place, i.e. on the first pass, or when there is no overlapping of successive cuts. A criterion of stability is derived involving the receptances of the machine for displacements between the tool and the workpiece. The stability criterion is not derived in terms of a lumped parameter model with a limited number of modes, so that the stability of any machine can be realistically analysed. The effect of changes in the direction of the cutting force on the stability of a horizontal milling machine is theoretically examined. Mohr's circle for receptance, analogous to Mohr's circle for stress, is introduced and used to apply the stability criterion to cases in which the normal to the cut surface changes in direction.
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