Statistical Modeling, Optimization and Sensitivity Analysis of Tool’s Geometrical Parameters on Process Force in Automatic Cortical Bone Drilling Process

Document Type : Original Article

Authors

Department of Mechanical Engineering, Arak University of Technology, Arak, Iran

Abstract

One of the most prevalent machining processes in medical treatments is bone drilling process. During bone drilling, excessive process force can cause breakage, crack initiation and severe damage to bone tissue. In this paper, a systematic study with simultaneous use of response surface method, sensitivity analysis based on Sobol method and regression analysis is performed for investigation the effect of helix angle and point angle of the tool as the most important geometrical parameters on imposed force to the bone during drilling process. Initially, using design of experiments and response surface method, imposed force to the bone is modeled and the governing second order linear regression equation is derived and verified. Then, using Sobol sensitivity analysis, with ability to quantify the sensitivity, it is attempted to investigate the effect of input parameters on drilling force. Finally, optimization of the process inputs is followed to find the best combination which yields the desired drilling force. The minimum drilling force, within the range of input parameters, coincides with point angle of 90 and helix angle of 18. This minimal force is lower than the force in surgery and standard tools. The results showed that an increasing in point angle leads to an increase in drilling force. Also, it is concluded that there is an optimum value for using the helix angle in bone drilling process with minimum imposed force.

Keywords


1.     Singh, R. P., Pandey, P. M., Behera, Ch., Mridha, A. R. "Effects of rotary ultrasonic bone drilling on cutting force and temperature in the human bones.", Proceedings of the IMechE, Part H: Journal of Engineering in Medicine, (2020). DOI: 10.1177/0954411920925254
2.     Ying, Zh., Shu, L., Sugita, N. "Experimental and Finite Element Analysis of Force and Temperature in Ultrasonic Vibration Assisted Bone Cutting.", Annals of Biomedical Engineering, Vol. 48, (2020), 1281–1290. DOI: 10.1007/s10439-020-02452-w
4.     Zhang, A., Bian, C., Zhang, X., Zhang, J., Liu, Z., Zhang, S. "Effect of feed condition on thrust force and torque during continuous and step-by-step drilling of cortical bone.", Procedia CIRP, Vol. 89, (2020), 201-206. DOI: 10.1016/j.procir.2020.05.143
5.     Gupta, V., Singh, R. P., Pandey, P. M., Gupta, R. "In vitro comparison of conventional surgical and rotary ultrasonic bone drilling techniques.", Proceedings of the IMechE, Part H: Journal of Engineering in Medicine, (2020). DOI: 10.1177/0954411919898301
 6.    Sui, J., Sugita, N. "Experimental Study of Thrust Force and Torque for Drilling Cortical Bone.", Annals of Biomedical Engineering, Vol. 47, (2019), 802-812. DOI: 10.1007/s10439-018-02196-8
7.     Sarparast, M., Ghoreishi, M., Jahangirpoor, T., Tahmasbi, V. "Modelling and optimisation of temperature and force behaviour in high-speed bone drilling.", Biotechnology & Biotechnological Equipment, Vol. 33, No. 1, (2019), 1616-1625. DOI: 10.1080/13102818.2019.1684841
8.     Alam, K., Piya, S., Al-Ghaithi, A., Silberschmidth, V. "Experimental investigation on the effect of drill quality on the performance of bone drilling.", Biomedical Engineering, Vol. 65, No. 1, (2019), 113-120. DOI: 10.1515/bmt-2018-0184 
9.     Zolfaghari, M., Ghoreishi, M., Tahmasbi, V. "Temperature in bone drilling process: Mathematical modeling and Optimization of effective parameters.", International Journal of Engineering, Transactions A: Basics, Vol. 29, No. 7, (2016), 946-953. DOI: 10.5829/idosi.ije.2016.29.07a.09
10.   Singh, G., Jain, V., Gupta, D., Sharma, A. "Parametric effect of vibrational drilling on osteonecrosis and comparative histopathology study with conventional drilling of cortical bone.", Proceedings of the IMechE, Part H: Journal of Engineering in Medicine, Vol. 232, No. 10, (2018), 975-986. DOI: 10.1177/0954411918794983
11.   Augustin, G.,  Zigman, T., Davila, S., Udilljak, T., Staroveski, T., Brezak, D., Babic, S. "Cortical bone drilling and thermal osteonecrosis.", Clinical Biomechanics (Bristol, Avon), Vol. 27, No. 4, (2011), 313-325. DOI: 10.1016/j.clinbiomech.2011.10.010
12.   Pandey, R. K., Panda, S. S. "Evaluation of delamination in drilling of bone.", Medical Engineering and Physics, Vol. 37, No. 7, (2015), 657-664. DOI: 10.1016/j.medengphy.2015.04.008
13.   Tuijthof, G., Frühwirt, C., Kment, C. "Influence of tool geometry on drilling performance of cortical and trabecular bone.", Medical Engineering and Physics, Vol. 35, No. 8, (2013), 1165-1172.
14.   Singh, G., Jain, V., Gupta, D., Ghai, A. "Optimization of process parameters for drilled hole quality characteristics during cortical bone drilling using Taguchi method.", Journal of the Mechanical Behavior of Biomedical Materials, Vol. 62, (2016), 355-365. DOI: 10.1016/j.jmbbm.2016.05.015
15.   Green, S. A., Dahl, M. T., Intramedullary Limb Lengthening. Gewerbestrasse: Springer International Publishing, 2017.
16.   Höller, C., Technical and Economic Analysis of the Process of Surgical Bone Drilling and Improvement Potentials. Master's Theses, Graz University of Technology, 2015.
17.   Tahmasbi, V., Ghoreshi, M., Zolfaghari, M. "Temperature in bone drilling process: Mathematical modeling and Optimization of effective parameters.", International Journal of Engineering, Transactions A: Basics, Vol. 29, No. 7, (2016), 946-953. DOI: 10.5829/idosi.ije.2016.29.07a.09
18.   Sui, J., Sugita, N. "Experimental Study of Thrust Force and Torque for Drilling Cortical Bone.",Annals of BiomedicalEngineering, Vol. 47, No. 3, (2019), 802-812. DOI: 10.1007/s10439-018-02196-8
19.   Ghoreishi, M., Tahmasbi, V. "Optimization of material removal rate in dry electro-discharge machining process.", Modares Mechanical Engineering, Vol. 14, No. 12, (2015), 113-121.
20.   Montgomery, D. C., Design and Analysis of Experiments: Second Edittion. New York: John Wiley & Sons, 2008.
21.   Hou, T. H., Su, C. H., Liu, W. L. "Parameters optimization of a nano-particle wet milling process using the Taguchi method, response surface method and genetic algorithm.", Powder Technology, Vol. 173, No. 3, (2007), 153-162. DOI: 10.1016/j.powtec.2006.11.019
22.   Sobol, I. M. "Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates.", Mathematics and Computers in Simulation, Vol. 55, No. 1-3, (2001), 271-280. DOI: 10.1016/S0378-4754(00)00270-6
23.   Korayem, M. H., Rastegar, Z., Taheri, M. "Sensitivity analysis of nano-contact mechanics models in manipulation of biological cell.", Nanoscience and Nanotechnology, Vol. 2, No. 3, (2012), 49-56. DOI: 10.5923/j.nn.20120203.02
24.   Wang, W., Shi, Y., Yang, N., Yuan, X. "Experimental analysis of drilling process in cortical bone.", Medical Engineering and Physics, Vol. 36, No. 2, (2014), 261-266. DOI: 10.1016/j.medengphy.2013.08.006
25.   Alam, K., Ghodsi, M., Al-Shabibi, A., Silberschmidt, V. "Experimental Study on the Effect of Point Angle on Force and Temperature in Ultrasonically Assisted Bone Drilling.", Journal of Medical and Biological Engineering, Vol. 38, No. 2, (2018), 236-243. DOI: 10.1007/s40846-017-0291-8
26.   Knight, W. A., Boothroyd, G., Fundamentals of metal machining and machine tools. Florida: CRC Press, 2005.
27.   Altintas, Y., Manufacturing automation: metal cutting mechanics, machine tool vibrations, and CNC design. Cambridge: Cambridge university press, 2012.
28.   Natali, C.,  Ingle, P., Dowell, J. "Orthopaedic bone drills–can they be improved? Temperature changes near the drilling face.", The Journal of Bone and Joint Surgery. British volume, Vol. 78-B, No. 3, (1996) 357-362. DOI: 10.1302/0301-620X.78B3.0780357
29.   Farnworth, G., Burton, J., "Optimization of drill geometry for orthopaedic surgery.", in Proceedings of the Fifteenth International Machine Tool Design and Research Conference 1975. Springer, 10.1007/978-1-349-01986-1_27