Prediction of cutting force in turning of UD-GFRP using mathematical model and simulated annealing

Abstract

Glass fiber reinforced plastics (GFRPs) composite is considered to be an alternative to heavy exortic materials. According to the need for accurate machining of composites has increased enormously. During machining, the obtaining cutting force is an important aspect. The present investigation deals with the study and development of a cutting force prediction model for the machining of unidirectional glass fiber reinforced plastics (UD-GFRP) composite using regression modeling and optimization by simulated annealing. The process parameters considered include cutting speed, feed rate and depth of cut. The predicted values radial cutting force model is compared with the experimental values. The results of prediction are quite close with the experimental values. The influences of different parameters in machining of UD-GFRP composite have been analyzed.

Key words： UD-GFRP; ANOVA; radial cutting force; PCD tool; Taguchi method; regression analysis; simulated annealing; multi objective techniques

Acknowledgements

The authors were indebted to Maharashtra Engineering Industry, Satara Maharashtra (P) Ltd. for supplying the UD-GFRP rods used in this work.

Notations

b0, b1, b2, b3 a, b, c X0, X1, X2, X 3 Fr A B C K T0 SA η y ϵ Ŷ

Estimates of parameters Exponentially determined constant Logarithmic transformations of machining parameters Radial force/kg Cutting speed/rpm Feed rate/(mm·rev-1) Depth of cut/mm Constant Temperature Simulated annealing Cutting force response Measured cutting force Experimental error Estimated response based on first order model/kg

References

1 Strategic Engineering (P) Ltd. Chennai, Piping Manual, 2002.

2 Ramkumar J, Aravindan S, Malhotra S K, Krishnamurthy R. An enhancement of the machining performance of GFRP by oscillatory assisted drilling. International Journal of Advanced Manufacturing Technology, 2004, 23(3-4): 240–244

3 Caprino G, Nele L.Cutting forces in orthogonal cutting of unidirectional GFRP composites. Journal of Engineering Materials and Technology, 1996, 118(3), 419–425

4 Koplev A, Lystrup A, Vorm T. The cutting process, chips and cutting forces in machining CFRP. Composites, 1983, 14(4), 371–376

5 Yang W H, Tarng Y S. Design optimization of cutting parameters for turning operations based on the Taguchi method. Journal of Materials Processing Technology, 1998, 84(1-3): 122–129

6 Zuperl U, Cus F, Mursec B, Ploj T. A hybrid analytical-neural network approach to the determination of optimal cutting conditions. Journal of Materials Processing Technology, 2004, 157-158 (20): 82–90

7 Wang X M, Zhang L C. Machining damage in unidirectional fibre-reinforced plastics. In: Proceedings of the Third International Conference on Abrasive Technology, Brisbane, Australia, 1999

8 Wang X M, Zhang L C. An experimental investigation into the orthogonal cutting of unidirectional fibre-reinforced plastics. International Journal of Machine Tools & Manufacture, 2003, 43(10): 1015–1022

9 Mahdi M, Zhang L C. A finite element model for the orthogonal cutting of fibre-reinforced composite materials. Journal of Materials Processing Technology, 2001, 113(1-3): 373–377

10 Mahdi M, Zhang L C. An adaptive three-dimensional finite element algorithm for the orthogonal cutting of composite materials. Journal of Materials Processing Technology, 2001, 113(1-3): 368–372

11 Sun F H, Wu Z Y, Zhong J W, Chen M. High speed milling of SiC particle reinforced aluminum-based MMC with coated carbide inserts. Key Engineering Materials, 2004, 274-276: 457–462

12 Davim J P, Mata F. Influence of cutting parameters on surface roughness in turning glass-fiber-reinforced-plastics using statistical analysis. Industrial Lubrication and Tribology, 2004, 56(5): 270–274

13 Davim J P, Mata F. Optimisation of surface roughness on turning fiber reinforced plastics (FRPs) with diamond cutting tools. International Journal of Advanced Manufacturing Technology, 2005, 26(4): 319–323

14 Sreejith P S, Krishnamurthy R, Malhotra S K, Narayanasamy K. Evaluation of PCD tool performance during machining of carbon/phenolic ablative composites. Journal of Materials Processing Technology, 2000, 104(1-2): 53–58

15 Isik B, Kentli A. Multicriteria optimization of cutting parameters in turning of UD-GFRP materials considering sensitivity. International Journal of Advanced Manufacturing Technology, 2009, 44(11,12): 1144–1153

16 Hussain S A, Pandurangadu V, kumar K P. Machinability of glass fiber reinforced plastic (GFRP) composite materials. International Journal of Engineering, Science and Technology, 2011, 3 (4): 103–118

17 Batalha M O. Introduction to Production Engineering. Rio de Janeiro: Elsevier Publisher, 2008

18 Chaves A A, Biajoli F L, Mine O M, Souza M J F. Exact and heuristic modeling for solving a generalization of the travelling salesman problem. In: Brazilian Symposium of Operational Research, Sobrapo, 2004, 1364–1378

19 Duran O, Barrientos R, Cosalter L A. Application of genetic algorithm and Taylor expanded equation in obtaining maximum efficiency range. In: Proceedings of IV Brazilian Congress on Manufacturing Engineering, Cobef, 2007

20 Dhavamani C, Alwarsamy T. Optimization of cutting parameters of composite materials using genetic algorithm. European Journal of Scientific Research, 2011, 63(2): 279–285

21 Palanikumar K, Latha B, Senthilkumar V S, Karthikeyan R. Multiple performance optimizations in machining of GFRP composites by a PCD tool using non-dominated sorting genetic algorithm (NSGA-II). Metals and Materials International, 2009, 15(2): 249–258

22 Rajasekaran T, Palanikumar K, Vinayagam B K. Application of fuzzy logic for modeling surface roughness in turning CFRP composites using CBN tool. Production Engineering, 2011, 5(2): 191–199

23 Jain R K, Jain V K. Optimum selection of machining conditions in abrasive flow using neural networks. Journal of Materials Processing Technology, 2000, 108(1): 62–67

24 Ingber L. Simulated annealing: Practice versus theory. Mathematical and Computer Modelling, 1993, 18(11): 29–57

25 Goffe W L, Ferrier G D, Rogers J. Global optimization of statistical functions with simulated annealing. Journal of Econometrics, 1993, 60: 65–99.

26 Saravanan R, Asokan P, Sachithanandam M. Comparative analysis of conventional and non-conventional optimizations techniques for CNC turning process. International Journal of Advanced Manufacturing Technology, 2001, 17(7): 471–476

27 Sarker R, Yao X. Simulated annealing and joint manufacturing batch-sizing. Yugoslav Journal of Operations Research, 2003, 13(2): 245–259

28 Kolahan F, Abachizadeh M. Optimizing turning parameters for cylindrical parts using simulated annealing method. World Academy of Science, Engineering and Technology, 2008, 46: 436–439

29 Yang S, Srinivas J, Mohan S, Lee D, Balaji S. Optimization of electric discharge machining using simulated annealing. Journal of Materials Processing Technology, 2009, 209(9): 4471–4475

30 Coppini N L, Librantz A F H, Rosa A F C, Carvalho A A M. Simulated annealing applied to minimize the idleness and maximize the contribution margin for generics flexibles machining cells. In: Proceedings of 2nd International Conference on Engineering Optimization, Lisbon, Portugal, 2010

31 Farhad K A, Hamid K, A statistical approach for predicting and optimizing depth of cut in AWJ machining for 6063-T6 Al alloy. International Journal of Aerospace and Mechanical Engineering, 2011, 2(5): 143–146

32 Harvey K, Ansell M P. Improved timber connections using bonded-in GFRP rods. http://timber.ce.wsu.edu/Resources/papers/p4.pdf

33 Ross P J. Taguchi Techniques for Quality Engineering. New York: McGraw-Hills Book Company, 1988

34 Kirkpatrick S, Gelatt C D Jr, Vecchi M P. Optimization by simulated annealing. Science, 1983, 220: 671–680

PMID

35 Metropolis N, Rosenbluth A, Telland Teller E. Equation of state calculations by fast computing machines. Journal of Chemical Physics, 1953, 21(6): 1087

36 Balram S. Study of simulated annealing based algorithms for multiobjective optimization of a constrained problem. Computers & Chemical Engineering, 2004, 28(9): 1849–1871

37 Eglese R W. A tool for operational research. European Journal of Operational Research, 1990, 46(3): 271–281

38 Venkataraman P. Applied Optimization with MATLAB Programming, New York, Wiely, 2002, 360-385