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FRACTAL-BASED ANALYSIS OF THE INFLUENCE OF CUTTING DEPTH ON COMPLEX STRUCTURE OF CUTTING FORCES IN ROUGH END MILLING

Department of Mechanical Engineering School of Engineering, Monash University, Selangor, Malaysia

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Department of Mechanical, Materials and Manufacturing Engineering, University of Nottingham Malaysia Campus, 43500 Semenyih, Malaysia

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CHANG TECK SENG

Faculty of Engineering and Technology, Multimedia University, Jalan Ayer Keroh Lama, 75450 Melaka, Malaysia

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https://doi.org/10.1142/S0218348X18500688Cited by:25 (Source: Crossref)

Abstract

Analysis of the cutting forces during machining operations is an important issue. The rough end mill with the serrated profile is broadly used for reduction of cutting forces during milling operation. Since cutting force changes in random behavior during end milling, in this paper we employ fractal theory to analyze the complex structure of cutting force signal. For this purpose, we investigated the influence of variations of cutting depth on variations of fractal structure of cutting forces in wet and dry machining conditions. The results of our analysis showed the variations of fractal structure of cutting forces between different cutting depths, in wet and dry conditions. The employed methodology in this research is not limited to rough end milling and can potentially be applied to other types of machining operations, where the variations of cutting forces is an important issue.

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References

1. W. Baohai, Y. Xue, L. Ming and G. Ge, Cutting force prediction for circular end milling process, Chin. J. Aeronaut. 26(4) (2013) 1057–1063. Crossref, Web of Science, Google Scholar
2. W. H. Lai, Modeling of cutting forces in end milling operations, Tamkang J. Sci. Eng. 3(1) (2000) 15–22. Google Scholar
3. L. Shi, E. F. Liu, Y. Zhang, P. Chen and Z. B. Li, The simulation of cutting force of free-form surface machining with ball-end milling cutter, in 2009 IEEE Int. Conf. Industrial Engineering and Engineering Management, Hong Kong, pp. 2314–2318, 2009. https://doi.org/10.1109/IEEM.2009.5373028 Google Scholar
4. A. V. M. Subramanian, M. D. G. Nachimuthu and V. Cinnasamy, Assessment of cutting force and surface roughness in LM6/SiCp using response surface methodology, J. Appl. Res. Technol. 15(30) (2017) 283–296. Crossref, Google Scholar
5. A. Akhavan Farid, S. Sharif and H. Namazi, Effect of machining parameters and cutting edge geometry on surface integrity when drilling and hole making in Inconel 718, SAE Int. J. Mater. Manuf. (2009). https://doi.org/10.4271/2009-01-1412 Crossref, Google Scholar
6. N. H. Razak, Z. W. Chen and T. Pasang, Effects of increasing feed rate on tool deterioration and cutting force during end milling of 718plus superalloy using cemented tungsten carbide tool, Metals 7(10) (2017) 441. https://doi.org/10.3390/met7100441 Crossref, Web of Science, Google Scholar
7. J. F. Nie and A. Morton, The effect of grain size on cutting force in end milling of Inconel 718C, Mater. Sci. Forum (2010) 484–487. https://doi.org/10.4028/www.scientific.net/MSF.654-656.484 Google Scholar
8. S. Shajari, M. H. Sadeghi and H. Hassanpour, The influence of tool path strategies on cutting force and surface texture during ball end milling of low curvature convex surfaces, Sci. World J. (2014). https://doi.org/10.1155/2014/374526 Crossref, Web of Science, Google Scholar
9. J. Hou, W. Zhou, H. Duan, G. Yang, H. Xu and N. Zhao, Influence of cutting speed on cutting force, flank temperature, and tool wear in end milling of Ti-6Al-4V alloy, Int. J. Adv. Manuf. Technol. 70(9–12) (2014) 1835–1845. Crossref, Web of Science, Google Scholar
10. D. Huo, W. Chen, X. Teng, C. Lin and K. Yang, Modeling the influence of tool deflection on cutting force and surface generation in micro-milling, Micromachines 8(6) (2017) 188. https://doi.org/10.3390/mi8060188 Crossref, Web of Science, Google Scholar
11. H. Yangui et al., Influence of cutting and geometrical parameters on the cutting force in milling, Engineering 2 (2010) 751–761. Crossref, Google Scholar
12. H. Namazi, Can we mathematically correlate brain memory and complexity? ARC J. Neurosci. 3(2) (2018) 1–3. https://doi.org/10.20431/2456-057X.0302003 Google Scholar
13. V. V. Kulish, Partial Differential Equations (Pearson, 2010). Google Scholar
14. H. Namazi et al., The analysis of the influence of fractal structure of stimuli on fractal dynamics in fixational eye movements and EEG signal, Sci. Rep. 6 (2016) 26639. https://doi.org/10.1038/srep26639 Crossref, Web of Science, Google Scholar
15. H. Namazi et al., A signal processing based analysis and prediction of seizure onset in patients with epilepsy, Oncotarget 7(1) (2016) 342–350. https://doi.org/10.18632/oncotarget.6341 Crossref, Web of Science, Google Scholar
16. H. Namazi, V. V. Kulish, F. Delaviz and A. Delaviz, Diagnosis of skin cancer by correlation and complexity analyses of damaged DNA, Oncotarget 6(40) (2015) 42623–42631. https://doi.org/10.18632/oncotarget.6003 Crossref, Google Scholar
17. H. Namazi et al., The fractal based analysis of human face and DNA variations during aging, Biosci. Trends. 10 (2016). https://doi.org/10.5582/bst.2016.01182 Crossref, Web of Science, Google Scholar
18. H. R. Namazi, Fractal-based analysis of the influence of music on human respiration, Fractals 25 (2017). https://doi.org/10.1142/s0218348x17500591 Web of Science, Google Scholar
19. M. Mozaffarilegha, H. R. Namazi, M. Ahadi and S. Jafari, Complexity based analysis of the difference in speech-evoked Auditory Brainstem Responses (s-ABR) between binaural and monaural listening conditions, Fractals (2018). https://doi.org/10.1142/S0218348X18500524 Link, Web of Science, Google Scholar
20. H. Namazi and S. Jafari, Age-based variations of fractal structure of EEG signal in patients with epilepsy, Fractals (2018). https://doi.org/10.1142/S0218348X18500512 Link, Web of Science, Google Scholar
21. H. Namazi, A. Daneshi, H. Azarnoush, S. Jafari and F. Towhidkhah, Fractal based analysis of the influence of auditory stimuli on eye movements, Fractals, doi:10.1142/S0218348X18500408. Google Scholar
22. H. Namazi and V. V. Kulish, Fractional diffusion based modelling and prediction of human brain response to external stimuli, Comput. Math. Methods Med. 2015 (2015) 148534. https://doi.org/10.1155/2015/148534 Crossref, Web of Science, Google Scholar
23. H. Namazi et al., Analysis of the influence of memory content of auditory stimuli on the memory content of EEG signal, Oncotarget 7 (2016) 56120–56128. https://doi.org/10.18632/oncotarget.11234 Crossref, Web of Science, Google Scholar
24. H. Namazi, Can we study the correlation between human brain signal and other biological signals? ARC J. Neurosci. 2(2) (2017) 7–9. https://doi.org/10.20431/2456-057X.0202003 Google Scholar
25. H. Namazi, Can we explain the memory transfer between generations by mathematical analysis of DNA Walk? ARC J. Neurosci. 2(2) (2017) 1–3. https://doi.org/10.20431/2456-057X.0202001 Google Scholar
26. H. Namazi, Can we correlate the spider’s brain activity to it spinning web activity? ARC J. Neurosci. 2(1) (2017) 17–18. https://doi.org/10.20431/2456-057X.0201005 Google Scholar
27. R. H. Namazi, The complexity based analysis of the correlation between spider’s brain signal and web, ARC J. Neurosci. 2(4) (2017) 38–44. https://doi.org/10.20431/2456-057X.0203006 Google Scholar
28. H. R. Namazi, Fractal based analysis of movement behavior in animal foraging, ARC J. Neurosci. 2(3) (2017) 1–3. https://doi.org/10.20431/2456-057X.0203001 Google Scholar
29. H. Namazi, A. Akrami and V. V. Kulish, The analysis of the influence of odorant’s complexity on fractal dynamics of human respiration, Sci. Rep. 6 (2016) 1–8. Crossref, Web of Science, Google Scholar
30. H. Namazi and V. V. Kulish, Fractal based analysis of the influence of odorants on heart activity, Sci. Rep. 6 (2016) 38555. https://doi.org/10.1038/srep38555 Crossref, Web of Science, Google Scholar
31. H. Namazi, V. V. Kulish and A. Wong, Mathematical modelling and prediction of the effect of chemotherapy on cancer cells, Sci. Rep. 5 (2015) 13583. https://doi.org/10.1038/srep13583 Crossref, Web of Science, Google Scholar
32. H. Namazi, A. Akrami, R. Haghighi, A. Delaviz and V. V. Kulish, Analysis of the influence of element's entropy on the bulk metallic glass (BMG) entropy, Complex. Strength. Metall. Mater. Trans. A, doi:10.1007/s11661-016-3870-3. Google Scholar
33. R. Yuan, Q. Zhou, Q. Zhang and Y. Xie, Fractal theory and contact dynamics modeling vibration characteristics of damping blade, Adv. Math. Phys. (2014) 549430. https://doi.org/10.1155/2014/549430 Web of Science, Google Scholar
34. S. Davies and P. Hall, Fractal analysis of surface roughness by using spatial data, Ser. B Stat. Methodol., doi:10.1111/1467-9868.00160. Google Scholar
35. J. Li, Y. Cao, Y. Ying and S. Li, A rolling element bearing fault diagnosis approach based on multifractal theory and gray relation theory, PLoS One 11(12) (2016) e0167587. https://doi.org/10.1371/journal.pone.0167587 Crossref, Web of Science, Google Scholar
36. G. Zheng, J. Zhao, Z. Li, X. Cheng and L. Li, Fractal characterization of the friction forces of a graded ceramic tool material, Int. J. Adv. Manuf. 74(5–8) (2014) 707–714. Crossref, Web of Science, Google Scholar
37. W. Wang, Y. Su, B. Yuan, K. Wang and X. Cao, Numerical simulation of fluid flow through fractal-based discrete fractured network, Energies 11(286) (2018). https://doi.org/10.3390/en11020286 Google Scholar
38. Z. Deng, X. Liu, Y. Huang, C. Zhang and Y. Chen, Heat conduction in porous media characterized by fractal geometry, Energies 10 (2017) 1230. https://doi.org/10.3390/en10081230 Crossref, Web of Science, Google Scholar
39. M. R. Schroeder, Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise (Dover Publications, 1991). Google Scholar
40. H. Namazi and M. Kiminezhadmalaie, Diagnosis of lung cancer by fractal analysis of damaged DNA, Comput. Math. Methods Med. 2015 (2015) 1–13. Web of Science, Google Scholar
41. W. Chen, J. Zhuang, W. Yu and Z. Wang, Measuring complexity using FuzzyEn, ApEn, and SampEn, Med. Eng. Phys. 31 (2009) 61–68. Crossref, Web of Science, Google Scholar
42. K. Seetharaman, H. Namazi and V. V. Kulsih, Phase lagging model of brain response to external stimuli—modeling of single action potential, Comput. Biol. Med. 42 (2012) 857–862. Crossref, Web of Science, Google Scholar
43. H. Namazi, V. V. Kulish, A. Wong and S. Nazeri, Mathematical based calculation of drug penetration depth in solid tumors, Biomed. Res. Int. 2016 (2016) 8437247. https://doi.org/10.1155/2016/8437247 Crossref, Web of Science, Google Scholar
44. H. Namazi and V. V. Kulish, A mathematical based calculation of a myelinated segment in axons, Comput. Biol. Med. 43(6) (2013) 693–698. https://doi.org/10.1016/j.compbiomed.2013.03.005 Crossref, Web of Science, Google Scholar
45. H. Namazi and V. V. Kulish, Mathematical modeling of human brain neuronal activity in the absence of external stimuli, J. Med. Imag. Health Inform. 2(4) (2012) 400–407. Crossref, Web of Science, Google Scholar
46. S. Gohari, S. Sharifi and Z. Vrcelj, A novel explicit solution for twisting control of smart laminated cantilever composite plates/beams using inclined piezoelectric actuators, Compos. Struct. 161 (2016) 477–504. Crossref, Web of Science, Google Scholar
47. S. Gohari, S. Sharifi and Z. Vrcelj, New explicit solution for static shape control of smart laminated cantilever piezo-composite-hybrid plates/beams under thermo-electro-mechanical loads using piezoelectric actuators, Compos. Struct. 145 (2016) 89–112. Crossref, Web of Science, Google Scholar
48. S. Gohari, S. Sharifi, G. Sharifishourabi, Z. Vrcelj and R. Abadi, Effect of temperature on crack initiation in gas formed structures, J. Mech. Sci. Technol. 27(12) (2013) 3745–3754. Crossref, Web of Science, Google Scholar