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

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.

Get full access to this article

View all access options for this article.

References

Arnold

R. N.

1946 Proc. Instn mech. Engrs, Lond., vol. 154, p. 261, ‘Mechanism of tool vibration in the cutting of steel’.

Doi

Kato

1956 Trans. Amer. Soc. mech. Engrs, vol. 78, No. 5, p. 1127, ‘Chatter vibration of lathe tools’.

Tobias

S. A.

Fishwick

1956 Proc. Instn mech. Engrs, Lond., vol. 170, p. 232, ‘Vibrations of radial-drilling machines under test and working conditions’.

Tobias

S. A.

1959 Proc. Instn mech. Engrs, Lond., vol. 173, p. 474, ‘Vibrations of vertical milling machines under test and working conditions’.

Tlusty

1955 Schwerindustrie der Tschechoslovakei, vol. 1, No. 1, p. 8, ‘Berechnung des Rahmens der Werkzeugmaschine’.

Kuchma

L. K.

1956 Vestnik Maschinostroyeniya, No. 9, p. 35, ‘Vibration-proof Boring Bars’ (Résumé published in Engineers' Digest, 1957, vol. 18, No. 2, p. 68).

Duncan

W. J.

1947 Aero. Research Council, R. and M. 2000, ‘Mechanical admittances and their applications to oscillation problems’.

Bishop

R. E. D.

1954 J. R. aero. Soc., p. 703, ‘Analysis and synthesis of vibrating systems’.

Gurney

J. P.

Tobias

S. A.

1962 Trans. Amer. Soc. mech. Engrs, J. Engng for Industry, February, ‘A graphical analysis of regenerative machine tool instability’.

10.

Duncan

W. J.

1945 Phil. Mag., vol. 36, p. 715, ‘Principal directions of loading and the principal directions of force oscillation at a point of an elastic body or system’.