# Mathematical model of micro turning process

• Iwona Piotrowska
• Christina Brandt
• Hamid Reza Karimi
• Peter Maass
ORIGINAL ARTICLE

## Abstract

In recent years, significant advances in turning process have been achieved greatly due to the emergent technologies for precision machining. Turning operations are common in the automotive and aerospace industries where large metal workpieces are reduced to a fraction of their original weight when creating complex thin structures. The analysis of forces plays an important role in characterizing the cutting process, as the tool wear and surface texture, depending on the forces. In this paper, the objective is to show how our understanding of the micro turning process can be utilized to predict turning behavior such as the real feed rate and the real cutting depth, as well as the cutting and feed forces. The machine cutting processes are studied with a different model compared to that recently introduced for grinding process by Malkin and Guo (2006). The developed two-degrees-of-freedom model includes the effects of the process kinematics and tool edge serration. In this model, the input feed is changing because of current forces during the turning process, and the feed rate will be reduced by elastic deflection of the work tool in the opposite direction to the feed. Besides this, using the forces and material removal during turning, we calculate the effective cross-sectional area of cut to model material removal. With this model, it is possible for a machine operator, using the aforementioned turning process parameters, to obtain a cutting model at very small depths of cut. Finally, the simulated and experimental results prove that the developed mathematical model predicts the real position of the tool tip and the cutting and feed forces of the micro turning process accurately enough for design and implementation of a cutting strategy for a real task.

## Keywords

Turning process Model analysis Simulation

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## References

1. 1.
Cheng K, Luo X, Ward R (2005) The effects of machining process variables and tooling characterisation on the surface generation. Int J Manuf Sci Technol 25:1089–1097
2. 2.
Cheng K, Luo XC, Luo XK, Liu XW (2005) A simulated investigatin on the machining instability and dynamic surface generation. Int J Manuf Sci Technol 26:718–725
3. 3.
Dassanayake AV, Suh CS (2008) On nonlinear cutting response and tool chatter in turning operation. Commun Nonlinear Sci Numer Simul 13:979–1001
4. 4.
Kopac J, Sali S (2001) Tool wear monitoring during the turning process. J Mater Process Technol 112:312–316
5. 5.
Olgac N, Zhao G (1987) A relative stability study on the dynamics of the turning mechanism. Trans ASME 109:164–170
6. 6.
Ozlu E, Budak E (2006) Analytical stability models for turning and boring operations - part I: model development. ASME J Manuf Sci Eng 129(4):726–732
7. 7.
Ozlu E, Budak E (2007) Comparison of one-dimensional and multi-dimensional models in stability analysis of turning operations. Int J Mach Tools Manuf 47:1875–1883
8. 8.
Rao BC, Shin YC (1999) A comprehensive dynamic cutting force model for chatter prediction in turning. Int J Mach Tools Manuf 39:1631–1654
9. 9.
Ravindra HV, Srinivasa YG, Krishnamurthy R (1993) Modeling of tool wear based on cutting forces in turning. Wear 169(1):25–32
10. 10.
Wang J (2001) Development of a chip flow for turning operations. Int J Mach Tools Manuf 41:1265–1274
11. 11.
Wang J, Mathew P (1995) Development of a general tool model for turning operations based on a variable flow stress theory. Int J Mach Tools Manuf 35:71–90
12. 12.
Weller EJ, Schrier HM, Weichbrodt B (1969) What sound can be expected from a worn tool? J Eng Ind 91:525–534Google Scholar
13. 13.
Altintas Y (2000) Manufacturing automation: metal cutting mechanics. Machine tool vibrations and CNC design. Cambridge University Press, CambridgeGoogle Scholar
14. 14.
Malkin S (1989) Grinding technology: theory and application of machining with abrasives. Ellis Horwod and Wiley, Chichester (1996) (Reprinted by SME)Google Scholar
15. 15.
Riemer O (2001) Trennmechanismen und Oberflächenfeingestalt bei der Mirozerspannung kristallier und amorpher Werkstoffe. Aachen, ShakerGoogle Scholar
16. 16.
Malkin S, Guo C (2006) Model based simulation of grinding processes. http://www.abrasivesmagazine.com/mtext/product/Model%20Based%20Simulation.pdf

© Springer-Verlag London Limited 2009

## Authors and Affiliations

• Iwona Piotrowska
• 1
• Christina Brandt
• 2
• Hamid Reza Karimi
• 2
• Peter Maass
• 2
1. 1.Center of Industrial MathematicsUniversity of BremenBremenGermany
2. 2.University of BremenBremenGermany