Research Papers

Suppression of Regenerative Chatter in a Plunge-Grinding Process by Spindle Speed

[+] Author and Article Information
Yao Yan

e-mail: yanyao19860624@gmail.com

Jian Xu

e-mail: xujian@tongji.edu.cn
School of Aerospace Engineering
and Applied Mechanics,
Tongji University,
Shanghai 200092, China

1Corresponding author.

Contributed by the Manufacturing Engineering Division of ASME for publication in the Journal of Manufacturing Science and Engineering. Manuscript received November 11, 2012; final manuscript received January 21, 2013; published online July 17, 2013. Assoc. Editor: Tony Schmitz.

J. Manuf. Sci. Eng 135(4), 041019 (Jul 17, 2013) (9 pages) Paper No: MANU-12-1332; doi: 10.1115/1.4023724 History: Received November 11, 2012; Revised January 21, 2013

This paper utilizes an effective control strategy to suppress the regenerative chatter in a plunge-grinding process. To begin with, the dynamical interaction between the workpiece and the grinding wheel is considered as a major factor influencing the grinding stability. Mathematically, the grinding stability is studied through numerical eigenvalue analysis. Consequently, critical chatter boundaries are obtained to distinguish the chatter-free and the chatter regions. As known, the grinding is unstable and the chatter happens in the chatter region. To observe the chatter vibrations, an analytical method and numerical simulations are employed. As a result, chatter vibrations both with and without losing contact between the workpiece and the wheel are obtained. Meanwhile, the coexistence of the chatter and the stable grinding is also found in the chatter-free region. Finally, a control strategy involving spindle speed variation (SSV) is introduced to suppress the chatter. Then, its effectiveness is analytically investigated in terms of the method of multiple scales (MMS).

Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.


Kong, F. S., Liu, P., and Zhao, X. G., 2011, “Simulation and Experimental Research on Chatter Suppression Using Chaotic Spindle Speed Variation,” ASME J. Manuf. Sci. Eng., 133(1), p. 014502. [CrossRef]
Brecher, C., Esser, M., and Witt, S., 2009, “Interaction of Manufacturing Process and Machine Tool,” CIRP Ann., 58(2), pp. 588–607. [CrossRef]
Inasaki, I., Karpuschewski, B., and Lee, H. S., 2001, “Grinding Chatter-Origin and Suppression,” CIRP Ann., 50(2), pp. 515–534. [CrossRef]
Altintas, Y., and Weck, M., 2004, “Chatter Stability of Metal Cutting and Grinding,” CIRP Ann., 53(2), pp. 619–642. [CrossRef]
Jayaram, S., Kapoor, S. G., and DeVor, R. E., 2000, “Analytical Stability Analysis of Variable Spindle Speed Machining,” ASME J. Manuf. Sci. Eng., 122(3), pp. 391–397. [CrossRef]
Long, X. H., and Balachandran, B., 2007, “Stability Analysis for Milling Process,” Nonlinear Dyn., 49(3), pp. 349–359. [CrossRef]
Bayly, P. V., Lamar, M. T., and Calvert, S. G., 2002, “Low-Frequency Regenerative Vibration and the Formation of Lobed Holes in Drilling,” ASME J. Manuf. Sci. Eng., 124(2), pp. 275–285. [CrossRef]
Li, H. Q., and Shin, Y. C., 2007, “A Time Domain Dynamic Simulation Model for Stability Prediction of Infeed Centerless Grinding Processes,” ASME J. Manuf. Sci. Eng., 129(3), pp. 539–550. [CrossRef]
Arnold, R. N., 1946, “The Mechanism of Tool Vibration in the Cutting of Steel,” Proc. Inst. Mech. Eng., 154, pp. 261–284. [CrossRef]
Hahn, R. S., 1954, “On the Theory of Regenerative Chatter in Precision-Grinding Operations,” ASME Paper No. 53-A-159.
Rowe, W. B., 2009, Principles of Modern Grinding Technology, Elsevier, New York.
Li, H. Q., and Shin, Y. C., 2006, “Wheel Regenerative Chatter of Surface Grinding,” ASME J. Manuf. Sci. Eng., 128(2), pp. 393–403. [CrossRef]
Snoeys, R., 1969, “Dominating Parameters in Grinding Wheel and Workpiece Regenerative Chatter,” Proceeding of the 10th International Conference on Machine Tool Design and Research, pp. 325–348.
Miyashita, M., Hashimoto, F., Kanai, A., and Okamura, K., 1982, “Diagram for Selecting Chatter Free Conditions of Centerless Grinding,” CIRP Ann., 31(1), pp. 221–223. [CrossRef]
Thompson, R. A., 1986, “On the Doubly Regenerative Stability of a Grinder: The Mathematical Analysis of Chatter Growth,” ASME J. Eng. Ind., 108(2), pp. 83–92. [CrossRef]
Thompson, R. A., 1986, “On the Doubly Regenerative Stability of a Grinder: The Theory of Chatter Growth,” ASME J. Eng. Ind., 108(2), pp. 75–82. [CrossRef]
Li, H. Q., and Shin, Y. C., 2006, “A Time-Domain Dynamic Model for Chatter Prediction of Cylindrical Plunge Grinding Processes,” ASME J. Manuf. Sci. Eng., 128(2), pp. 404–415. [CrossRef]
Yuan, L., Keskinen, E., and Jarvenpaa, V. M., 2005, “Stability Analysis of Roll Grinding System With Double Time Delay Effects,” Proceedings of IUTAM Symposium on Vibration Control of Nonlinear Mechanisms and Structures, H.Ulbrich, and W.Gunthner, eds., Springer, New York, Vol. 130, pp. 375–387.
Liu, Z. H., and Payre, G., 2007, “Stability Analysis of Doubly Regenerative Cylindrical Grinding Process,” J. Sound Vib., 301(2), pp. 950–962. [CrossRef]
Werner, G., 1978, “Influence of Work Material on Grinding Forces,” CIRP Ann., 27(1), pp. 243–248.
Chung, K.-W., and Liu, Z., 2011, “Nonlinear Analysis of Chatter Vibration in a Cylindrical Transverse Grinding Process With Two Time Delays Using a Nonlinear Time Transformation Method,” Nonlinear Dyn., 66, pp. 441–456. [CrossRef]
Xu, J., Chung, K. W., and Chan, C. L., 2007, “An Efficient Method for Studying Weak Resonant Double HOPF Bifurcation in Nonlinear Systems With Delayed Feedbacks,” SIAM J. Appl. Dyn. Syst., 6(1), pp. 29–60. [CrossRef]
Al-Regib, E., Ni, J., and Lee, S. H., 2003, “Programming Spindle Speed Variation for Machine Tool Chatter Suppression,” Int. J. Mach. Tools Manuf., 43(12), pp. 1229–1240. [CrossRef]
Namachchivaya, N. S., and Roessel, H. J. V., 2003, “A Centre-Manifold Analysis of Variable Speed Machining,” Dyn. Syst., 18(3), pp. 245–270. [CrossRef]
Otto, A., Kehl, G., Mayer, M., and Radons, G., 2011, “Stability Analysis of Machining With Spindle Speed Variation,” Adv. Mater. Res., 223, pp. 600–609. [CrossRef]
Long, X. H., Balachandran, B., and Mann, B., 2007, “Dynamics of Milling Processes With Variable Time Delays,” Nonlinear Dyn., 47(1), pp. 49–63. [CrossRef]
Zatarain, M., Bediaga, I., Munoa, J., and Lizarralde, R., 2008, “Stability of Milling Processes With Continuous Spindle Speed Variation: Analysis in the Frequency and Time Domains, and Experimental Correlation,” CIRP Ann., 57(1), pp. 379–384. [CrossRef]
Bediaga, I., Zatarain, M., Munoa, J., and Lizarralde, R., 2011, “Application of Continuous Spindle Speed Variation for Chatter Avoidance in Roughing Milling,” Proc. Inst. Mech. Eng., Part B, 225(5), pp. 631–640. [CrossRef]
Inasaki, I., Cheng, C., and Yonetsu, S., 1976, “Suppression of Chatter in Grinding,” Bull. Jpn. Soc. Precis. Eng., 9(1), pp. 133–138.
Knapp, B. R., 1999, “Benefits of Grinding With Variable Workspeed,” M.S. thesis, College of Engineering, The Pennsylvania State University, Philadelphia, PA.
Alvarez, J., Barrenetxea, D., Marquinez, J. I., Bediaga, I., and Gallego, I., 2011, “Effectiveness of Continuous Workpiece Speed Variation (CWSV) for Chatter Avoidance in Throughfeed Centerless Grinding,” Int. J. Mach. Tools Manuf., 51(12), pp. 911–917. [CrossRef]
Barrenetxea, D., Marquinez, J. I., Bediaga, I., Uriarte, L., and Bueno, R., 2009, “Continuous Workpiece Speed Variation (CWSV): Model Based Practical Application to Avoid Chatter in Grinding,” CIRP Ann., 58(1), pp. 319–322. [CrossRef]
Nayfeh, A. H., Chin, C.-M., and Pratt, J., 1997, “Perturbation Methods in Nonlinear Dynamics—Applications to Machining Dynamics,” ASME J. Manuf. Sci. Eng., 119(4A), pp. 485–493. [CrossRef]
Nayfeh, A. H., and Pai, P. F., 2004, Linear and Nonlinear Structural Mechanics, Wiley, Hoboken, NJ.
Nayfeh, A. H., 2008, “Order Reduction of Retarded Nonlinear Systems—The Method of Multiple Scales Versus Center-Manifold Reduction,” Nonlinear Dyn., 51, pp. 483–500. [CrossRef]
Nayfeh, A. H., and Mook, D. T., 1979, Nonlinear Oscillations, Wiley Interscience, New York.
Yan, Y., Xu, J., and Wang, W., 2012, “Nonlinear Chatter With Large Amplitude in a Cylindrical Plunge Grinding Process,” Nonlinear Dyn., 69(4), pp. 1781–1793. [CrossRef]
Zhang, S., and Xu, J., 2011, “Oscillation Control for N-Dimensional Congestion Control Model via Time-Varying Delay,” Sci. China Ser. E: Technol. Sci., 54(8), pp. 2044–2053. [CrossRef]
Zhang, S., and Xu, J., 2011, “Time-Varying Delayed Feedback Control for an Internet Congestion Control Model,” Discrete Contin. Dyn. Syst., Ser. B, 16(2), pp. 653–668. [CrossRef]
Engelborghs, K., Luzyanina, T., and Roose, D., 2002, “Numerical Bifurcation Analysis of Delay Differential Equations Using DDE-BIFTOOL,” ACM Trans. Math. Softw., 28(1), pp. 1–21. [CrossRef]
Hashimoto, F., Kanai, A., Miyashita, M., and Okamura, K., 1984, “Growing Mechanism of Chatter Vibrations in Grinding Processes and Chatter Stabilization Index of Grinding Wheel,” CIRP Ann., 33(1), pp. 259–263. [CrossRef]
Thompson, R. A., 1974, “On the Doubly Regenerative Stability of a Grinder,” ASME J. Eng. Ind., 96(1), pp. 275–280. [CrossRef]
Fu, J. C., Troy, C. A., and Morit, K., 1996, “Chatter Classification by Entropy Functions and Morphological Processing in Cylindrical Traverse Grinding,” Precis. Eng., 18, pp. 110–117. [CrossRef]


Grahic Jump Location
Fig. 2

Dynamical penetrations

Grahic Jump Location
Fig. 1

Schematic of the cylindrical plunge-grinding process

Grahic Jump Location
Fig. 3

Equivalent model of the cylindrical plunge-grinding process

Grahic Jump Location
Fig. 4

Linear chatter boundaries with respect to different values of τ1: (a) τ1 = 11, (b) τ1 = 12, (c) τ1 = 13, (d) τ1 = 14

Grahic Jump Location
Fig. 6

Distributions of the maximum and the minimum values of the dimensionless depth of cut δ*(t) = 1 + δd(t) with respect to τ2. When no chatter vibrations occur, one has δd(t)= y2(t) - y1(t) + y1(t - τ1) - y2(t - τ2) = 0 and δ*(t) = 1. On the contrary, when chatter vibrations happen (δd(t)≠0), the recorded values of δ*(t) turn up on both sides of δ*(t) = 1.

Grahic Jump Location
Fig. 7

The time series of the dimensionless depth of cut δ*(t) with respect to different values of τ2: (a) the chatter vibration without losing contact for τ2 = 17.928, (b) the chatter vibration with losing contact for τ2 = 17.926, (c) the chatter vibration with large amplitude in the chatter-free region for τ2 = 18.98, (d) the stable grinding process for τ2 = 18.98

Grahic Jump Location
Fig. 8

The surface of g = 0

Grahic Jump Location
Fig. 9

Parameter plane of the SSV amplitudes when ɛτ2ɛ =-0.4

Grahic Jump Location
Fig. 5

The magnified region marked by the dashed frame in Fig. 4

Grahic Jump Location
Fig. 11

The effect of SSV control with ɛΔ1 = ɛΔ2 = 0.02

Grahic Jump Location
Fig. 10

The time series of the dimensionless depth of cut δ*(t) with respect to different situations marked in Fig. 9: (a) the time series of δ*(t) without SSV control (ɛΔ1 = ɛΔ2 = 0 at point I), (b) the time series of δ*(t) with weak SSV control (ɛΔ1 = ɛΔ2 = 0.015 at point II), (c) the time series of δ*(t) with strong SSV control (ɛΔ1 = ɛΔ2 = 0.02 at point III)



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In