An analytical model of chatter vibration in metal cutting

Abstract A new analytical model of chatter vibration in metal cutting is presented. The basic cutting mechanics adopted in the model is derived from a predictive machining theory based on a shear zone model of chip formation. A feature of this model is that variations of the undeformed chip thickness and rake angle due to the machine tool vibration are taken into account in determining the cutting forces and the forces are then coupled with the equations of motion to solve for the vibrational amplitudes with iterative techniques. Non-linearities in dynamic cutting processes caused by the effects of tool disengagement from the cut and cutting process damping are also included in the model. It is shown that the proposed model can be applied to make predictions for the suppression of chatter vibration by a change of tool geometries.

[1]  W. F. Hastings,et al.  A machining theory for predicting chip geometry, cutting forces etc. from work material properties and cutting conditions , 1980, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[2]  W. F. Hastings,et al.  Predicting the strain rate in the zone of intense shear in which the chip is formed in machining from the dynamic flow stress properties of the work material and the cutting conditions , 1977, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[3]  Etsuo Marui,et al.  Chatter Vibration of Lathe Tools. Part 1: General Characteristics of Chatter Vibration , 1983 .

[4]  Krzysztof Jemielniak,et al.  Suppression of self-excited vibration by the spindle speed variation method , 1984 .

[5]  Krzysztof Jemielniak,et al.  Numerical simulation of non-linear chatter vibration in turning , 1989 .

[6]  G. Boothroyd.  Temperatures in Orthogonal Metal Cutting , 1963 .

[7]  T. M. Liu,et al.  Automated Chatter Suppression by Tool Geometry Control , 1985 .

[8]  S. A. Tobias,et al.  Theory of finite amplitude machine tool instability , 1984 .

[9]  M. C. Shaw,et al.  Mechanics of Machining: An Analytical Approach to Assessing Machinability , 1989 .

[10]  P. Oxley,et al.  An Experimental Investigation of the Influence of Speed and Scale on the Strain-Rate in a Zone of Intense Plastic Deformation , 1969 .

[11]  Chun Liu,et al.  An Analytical Model of Cutting Dynamics. Part 1: Model Building , 1985 .

[12]  W. A. Knight,et al.  Chatter in turning: Some effects of tool geometry and cutting conditions , 1972 .

[13]  W. F. Hastings,et al.  Minimum work as a possible criterion for determining the frictional conditions at the tool/chip interface in machining , 1976, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[14]  J. S. Lin,et al.  A nonlinear dynamic model of cutting , 1990 .