This paper presents our characterization of dynamics underlying the cylindrical grinding of shafts using accelerometer signals gathered from a set of designed experiments. The results of our characterizations show that the dynamics, under steady state, evolves into a finite-dimensional, perhaps chaotic, attractor contaminated by noise, with fractal dimension values hovering between 3.1 and 3.8. The major implication of this finding is in the development of tractable models to control this industrially important shaft grinding process.
Issue Section:
Technical Papers
1.
Xiao
, G.
, and Malkin
, S.
, 1996
, “On-Line Optimization of Internal Cylindrical Grinding Cycles
,” CIRP Ann.
, 45
(1
), pp. 287
–292
.2.
Thompson
, R. A.
, 1986
, “On the Doubly Regenerative Stability of a Grinder: The Theory of Chatter Growth
,” ASME J. Eng. Ind.
, 108
, pp. 75
–82
.3.
Thompson
, R. A.
, 1986
, “On the Doubly Regenerative Stability of a Grinder: The Mathematical Analysis of Chatter Growth
,” ASME J. Eng. Ind.
, 108
, pp. 83
–92
.4.
Davies, M. A., 1998, “Dynamic Problems in Hard Turning, Milling, and Grinding,” Dynamics and Chaos in Manufacturing Processes, F. C. Moon, ed., Wiley, New York, NY, pp. 57–91.
5.
Abarbanel, H. D. I., 1995, Analysis of Observed Chaotic Data, Springer, New York, NY.
6.
Berger
, B. S.
, Minis
, I.
, Chen
, Y. H.
, Chavali
, A.
, and Rokni
, M.
, 1995
, “Attractor Embedding in Metal Cutting
,” J. Sound Vib.
, 18
, pp. 936:942
936:942
.7.
Bukkapatnam
, S. T. S.
, Lakhtakia
, A.
, and Kumara
, S. R. T.
, 1995
, “Analysis of Sensor Signals Shows That Turning Process on a Lathe Exhibits Low-Dimensional Chaos
,” Phys. Rev. E
, 52
, pp. 2375
–2387
.8.
Bukkapatnam
, S. T. S.
, Kumara
, S. R. T.
, and Lakhtakia
, A.
, 2000
, “Fractal Estimation of Flank Wear in Machining
,” ASME J. Dyn. Syst., Meas., Control
, 122
, pp. 89
–94
.9.
Moon, F. C., and Johnson, M. A., 1998, “Nonlinear Dynamics and Chaos in Manufacturing Processes,” Dynamics and Chaos in Manufacturing Processes, F. C. Moon, ed., Wiley, New York, NY, pp. 3–32.
10.
Montgomery, D. C., 1976, Design and Analysis of Experiments, Wiley, New York.
11.
Eckmann
, J.-P.
, and Ruelle
, D.
, 1985
, “Ergodic Theory of Chaos and Strange Attractors
,” Rev. Mod. Phys.
, 57
, pp. 617
–656
.12.
Ruelle, D., 1989, Chaotic Evolution and Strange Attractors, Cambridge University Press, Cambridge, UK.
13.
Seydel, R., 1994, Practical Bifurcation and Stability Analysis. From Equilibrium to Chaos, Springer, New York, NY.
14.
Nayfeh, A., and Balachandran, B., 1995, Applied Nonlinear Dynamics: Analytical, Computational and Experimental Methods, Wiley, New York, NY.
15.
Bukkapatnam
, S. T. S.
, Kumara
, S. R. T.
, and Lakhtakia
, A.
, 1999
, “Analysis of Acoustic Emission in Machining
,” ASME J. Manuf. Sci. Eng.
, 121
, pp. 568
–573
.16.
Johnson
, M. A.
, and Moon
, F. C.
, 2001
, “Nonlinear Techniques to Characterize Prechatter and Chatter Vibrations in the Machining of Metals
,” Int. J. Bifurcation Chaos Appl. Sci. Eng.
, 11
(2
), pp. 449
–467
.17.
Palanna
, R.
, and Bukkapatnam
, S. T. S.
, 2002
, “The Concept of Model-Based Tampering for Improving Process Performance: An Illustrative Application to Turning Process
,” International Journal of Machining Sciences and Technology
, 6
(2
), pp. 263
–282
.18.
Palanna, R., 2002, “Model-Based Tampering for Improving Process Performance: Application to Grinding of Shafts,” Ph.D. Thesis, Epstein Department of Industrial and Systems Engineering, University of Southern California, Los Angeles, CA.
19.
Davies
, M. A.
, and Balachandran
, B.
, 2001
, “Impact Dynamics in Milling of Thin-Walled Structures
,” Nonlinear Dyn.
, 4
, pp. 375
–392
.20.
Pratt
, J. R.
, and Nayfeh
, A. H.
, 2001
, “Chatter Control and Stability of a Cantilever Boring Bar Under Regenerative Chatter Conditions
,” Philos. Trans. R. Soc. London
, 359
, pp. 759
–792
.21.
Moon
, F. C.
, and Kalmar-Nagy
, T.
, 2001
, “Nonlinear Models for Complex Dynamics in Cutting Materials
,” Philos. Trans. R. Soc. London
, 359
, pp. 695
–711
.Copyright © 2004
by ASME
You do not currently have access to this content.