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ALARM LAB

ALARM LAB. OPTIMUM CONDITIONS FOR VARIABLE PITCH MILLING. Hassan Fazelinia • Nejat Olgac Department of Mechanical Engineering University of Connecticut. ALARM LAB. Outline. The Problem and Motivation Process Dynamics Review of CTCR Paradigm

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ALARM LAB

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  1. ALARM LAB OPTIMUM CONDITIONS FOR VARIABLE PITCH MILLING Hassan Fazelinia • Nejat Olgac Department of Mechanical Engineering University of Connecticut

  2. ALARM LAB Outline • The Problem and Motivation • Process Dynamics • Review of CTCR Paradigm (A unique process for Multiple Time Delayed Systems) • Measure of Chatter Rejection • Optimization problem

  3. 1= 70 2= 110 1= 90 2= 90 Variable Pitch end mill Uniform Pitch end mill Variable vs. Uniform Pitch Cutter Notable earlier work: [1] Slavicek, J., 1965, “The Effect of Irregular Tooth Pitch on Stability of Milling.” 6th MTDR Conference, London, Pergamon Press. [2] Minis, I. and Yanushevsky, R. , 1993, "A New Theoretical Approach for the Prediction of Machine Tool Chatter in Milling." ASME Journal of Engineering for Industry 115(1), 1-8. [3] Altintas, Y. and Budak, E., 1995, "Analytical Prediction of Stability Lobes in Milling." Annals of the CIRP 44(1), 357-362.

  4. + Feed Cutter force formation chip loads (process / material specific) Cutter dynamics ID (setup specific) Process Dynamics • Olgac, N. and Sipahi, R., “A Unique Methodology for Chatter Stability Mapping in Simultaneous Machining”. ASME, Journal of Manufacturing Science and Engineering, 2005. 127(4). • Sipahi, R. and Olgac, N. ,Stability in Variable-Pitch Milling Regarding Regenerative Chatter, IMECE 2006

  5. System Characteristic Equation • four-flute-two-pitch cutter :

  6. Stability outlook for 4 mm axial depth-of-cut (stable zones: shaded) CTCR reveals the stability regions * * [R. Sipahi: PhD Thesis 2005]

  7. a a Comparison of CTCR result (red) and, [Y. Altintas, 1999] (black) Comparison of CTCR results

  8. E2 E5 E3 E4 E1 Measure of chatter rejection:

  9. Finding the real part of rightmost characteristic roots (still an open problem in mathematics) • Status-quo: Numerical approximations: Infinitesimal Generator Approx. [D. Breda 2005] DDE-BIFTOOL [K. Engelborghs 2000] …..

  10. Optimization Problem • Objective: Maximizing the metal removal rate while avoiding the onset of chatter • The pitch angle selection on the tool. • Optimum depth of cut and the spindle speed?

  11. Objective function: • Measure of chatter rejection: • Spindle speed: • Axial depth of cut:

  12. J J Preliminary results:

  13. Optimum points for different depth of cut

  14. On going studies: Experimental validation Optimization for different number of flutes Acknowledgment: NSF, DoE, Pratt & Whitney Conclusion

  15. Thank You! Questions?

  16. Dynamic Depth of Cut Cutting Forces Tool Displacement Feed + + TF 1 TF 2 - + Regenerative Effect / Delays Cutter force formation chip loads (process / material specific) Cutter dynamics ID (setup specific) and is 2D transfer function between is the nominal cutting force under rigid tool assumption. : cutting force constants when tooth i is in the cut when tooth i is out of the cut rotation matrix transforming to , periodic in : axial depth of cut : the number of teeth : the tooth passing period between the i th and i + 1st teeth : delay operator [4] Olgac, N. and Sipahi, R., “A Unique Methodology for Chatter Stability Mapping in Simultaneous Machining”. ASME, Journal of Manufacturing Science and Engineering, 2005. 127(4).

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