Nonlinear models of chatter in drilling processes

We develop a nonlinear model of chatter in drilling that incorporates friction of the material on the cutting tool and its interaction with the axial-torsional mode of vibration seen in twist drills. Stability criteria are determined for both regenerative and non-regenerative chatter, and the effect of tool parameters and the friction law itself on the results is analysed. Our analysis shows that the exact form of the friction law is not critical in the stability calculation, only the size of the friction coefficient for steady cutting, and the slope of the friction law at the steady cutting state. However, its interaction with the geometry of the vibration is crucial. In the laboratory, drilling vibrational instabilities can occur at frequencies less than the natural frequency of the excited mode of the drill, and we find this result depends critically on the shape of the vibration mode projected onto the cutting edge of the drill.

[1]  R. Sridhar,et al.  A General Formulation of the Milling Process Equation: Contribution to Machine Tool Chatter Research—5 , 1968 .

[2]  John S. Agapiou,et al.  Calculation of main cutting edge forces and torque for drills with arbitrary point geometries , 1992 .

[3]  D. W. Wu,et al.  An Analytical Model of Cutting Dynamics. Part 2: Verification , 1985 .

[4]  I. E. Minis,et al.  A New Theoretical Approach for the Prediction of Machine Tool Chatter in Milling , 1993 .

[5]  Brian F. Feeny,et al.  Bifurcation sequences of a Coulomb friction oscillator , 1993, Nonlinear Dynamics.

[6]  F. Moon,et al.  Chaos in a Forced Dry-Friction Oscillator: Experiments and Numerical Modelling , 1994 .

[7]  Keith A. Young,et al.  Theory of Torsional Chatter in Twist Drills: Model, Stability Analysis and Composition to Test , 2001 .

[8]  S. M. Wu,et al.  Computer Models for the Mechanics of Three-Dimensional Cutting Processes—Part II: Results for Oblique End Turning and Drilling , 1988 .

[9]  Brian F. Feeny.  THE NONLINEAR DYNAMICS OF OSCILLATORS WITH STICK-SLIP FRICTION , 1996 .

[10]  Francis C. Moon,et al.  Dynamics and chaos in manufacturing processes , 1998 .

[11]  Y. S. Tarng,et al.  Detection and suppression of drilling chatter , 1994 .

[12]  P. J. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[13]  M. E. Merchant.  Mechanics of the Metal Cutting Process. I. Orthogonal Cutting and a Type 2 Chip , 1945 .

[14]  Matthew A. Davies,et al.  NONLINEAR DYNAMICS MODEL FOR CHIP SEGMENTATION IN MACHINING , 1997 .

[15]  I. Grabec.  Chaotic dynamics of the cutting process , 1988 .

[16]  S. A. Tobias,et al.  A Theory of Nonlinear Regenerative Chatter , 1974 .

[17]  Ioannis Minis,et al.  The nonlinear dynamics of metal cutting , 1992 .

[18]  R. Sridhar,et al.  A Stability Algorithm for the General Milling Process: Contribution to Machine Tool Chatter Research—7 , 1968 .

[19]  Igor Grabec,et al.  Chaos generated by the cutting process , 1986 .

[20]  R. A. Williams.  A Study of the Drilling Process , 1974 .

[21]  Keith A. Young,et al.  Analysis of Tool Oscillation and Hole Roundness Error in a Quasi-Static Model of Reaming , 2001 .

[22]  Marian Wiercigroch,et al.  Material removal rate prediction for ultrasonic drilling of hard materials using an impact oscillator approach , 1999 .

[23]  Lakhtakia,et al.  Analysis of sensor signals shows turning on a lathe exhibits low-dimensional chaos. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[24]  Jon R. Pratt,et al.  Design and Modeling for Chatter Control , 1999 .

[25]  A. G. Ulsoy,et al.  COMPLEX GEOMETRY, ROTARY INERTIA AND GYROSCOPIC MOMENT EFFECTS ON DRILL VIBRATIONS , 1995 .

[26]  C. Y. Cheng,et al.  A study of the drilling process , 1970 .

[27]  Alain Molinari,et al.  Analysis of nonlinear vibrations in metal cutting , 1998 .

[28]  Yusuf Altintas,et al.  Analytical Prediction of Stability Lobes in Milling , 1995 .

[29]  Sean G. Calvert,et al.  Low-Frequency Regenerative Vibration and the Formation of Lobed Holes in Drilling , 2002 .

[30]  G. Stépán.  Retarded dynamical systems : stability and characteristic functions , 1989 .

[31]  J. Tlusty,et al.  Dynamics of High-Speed Milling , 1986 .

[32]  Sue Ann Campbell,et al.  Complex dynamics and multistability in a damped harmonic oscillator with delayed negative feedback. , 1995, Chaos.

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

[34]  P. Bayly,et al.  Stability Analysis of Interrupted Cutting With Finite Time in the Cut , 2000, Manufacturing Engineering.

[35]  Etsuo Marui,et al.  Suppression of Chatter Vibration in Drilling , 1998 .

[36]  M. Ortiz,et al.  Modelling and simulation of high-speed machining , 1995 .

[37]  Ali H. Nayfeh,et al.  Perturbation Methods in Nonlinear Dynamics—Applications to Machining Dynamics , 1997 .

[38]  A. Galip Ulsoy,et al.  Effects of Drill Vibrations on Cutting Forces and Torque , 1994 .

[39]  Ozan Tekinalp,et al.  Modeling and Finite Element Analysis of Drill Bit Vibrations , 1989 .

[40]  Y. S. Tarng,et al.  Adaptive pattern recognition of drilling chatter , 1995 .